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 1   Table of Content
 3   Executive Summary ................................................................................................................................... 6
 5   7.1       Introduction, conceptual framework, and advances since AR5.................................................. 11
 7   BOX 7.1: The energy budget framework – forcing and response .......................................................... 12
 9   7.2       Earth’s energy budget and its changes through time .................................................................. 14
10      7.2.1         Present-day energy budget ...................................................................................................... 15
11      7.2.2         Changes in Earth’s energy budget ........................................................................................... 16
12       Changes in Earth’s TOA energy budget .................................................................................. 16
13       Changes in the global energy inventory................................................................................... 17
14       Changes in Earth’s surface energy budget ............................................................................... 19
16   BOX 7.2: The Global Energy Budget ...................................................................................................... 21
18   7.3       Effective radiative forcing ............................................................................................................ 22
19      7.3.1         Methodologies and representation in models; overview of adjustments ................................... 23
20      7.3.2         Greenhouse Gases .................................................................................................................. 27
21       Carbon Dioxide ...................................................................................................................... 27
22       Methane ................................................................................................................................. 29
23       Nitrous oxide .......................................................................................................................... 30
24       Halogenated species................................................................................................................ 30
25       Ozone ..................................................................................................................................... 30
26       Stratospheric water vapour ...................................................................................................... 31
27       Synthesis ................................................................................................................................ 32
28      7.3.3         Aerosols ................................................................................................................................. 33
29       Aerosol-radiation interactions ................................................................................................. 34
30        Observation-based lines of evidence ................................................................................... 34
31        Model-based lines of evidence ............................................................................................ 34
32        Overall assessment of IRFari and ERFari ............................................................................ 35
33       Aerosol-cloud interactions ...................................................................................................... 36
34        Observation-based evidence ................................................................................................ 37
35        Model-based evidence ........................................................................................................ 40
36        Overall assessment of ERFaci ............................................................................................. 41
37       Energy budget constraints on the total aerosol ERF ................................................................. 41
38       Overall assessment of total aerosol ERF.................................................................................. 42
39      7.3.4         Other agents ........................................................................................................................... 44
40       Land use ................................................................................................................................. 44
41       Contrails and aviation-induced cirrus ...................................................................................... 45
42       Light absorbing particles on snow and ice ............................................................................... 45
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 1      Solar ....................................................................................................................................... 46
 2      Galactic Cosmic Rays ............................................................................................................. 47
 3      Volcanic aerosols.................................................................................................................... 47
 4      7.3.5        Synthesis of Global Mean Radiative Forcing, Past and Future ................................................. 48
 5      Major changes in forcing since IPCC AR5 .............................................................................. 48
 6      Summary ERF assessment ...................................................................................................... 49
 7      Temperature Contribution of forcing agents ............................................................................ 51
 9   Cross-Chapter Box 7.1: Physical emulation of Earth System Models for scenario classification and
10   knowledge integration in AR6 ................................................................................................................. 53
12   7.4      Climate feedbacks ........................................................................................................................ 59
13      7.4.1        Methodology of the feedback assessment ................................................................................ 59
14      7.4.2        Assessing climate feedbacks ................................................................................................... 60
15      Planck response ...................................................................................................................... 61
16      Water vapour and temperature lapse rate feedbacks................................................................. 61
17      Surface albedo feedback ......................................................................................................... 63
18      Cloud feedbacks ..................................................................................................................... 64
19       Decomposition of clouds into regimes ................................................................................. 64
20       Assessment for individual cloud regimes ............................................................................. 66
21       Synthesis for the net cloud feedback ................................................................................... 69
22      Biogeophysical and non-CO2 biogeochemical feedbacks ......................................................... 70
23       Non-CO2 biogeochemical feedbacks ................................................................................... 71
24       Biogeophysical feedbacks ................................................................................................... 71
25       Synthesis of biogeophysical and non-CO2 biogeochemical feedbacks .................................. 72
26      Long term radiative feedbacks associated with ice sheets ........................................................ 72
27      Synthesis ................................................................................................................................ 73
28      Climate feedbacks in ESMs .................................................................................................... 75
29      7.4.3        Dependence of feedbacks on climate mean state ..................................................................... 76
30      State-dependence of feedbacks in models ................................................................................ 76
31      State-dependence of feedbacks in the paleoclimate proxy record ............................................. 77
32      Synthesis of state-dependence of feedbacks from modelling and paleoclimate records ............ 78
33      7.4.4        Relationship between feedbacks and temperature patterns ....................................................... 79
34      Polar amplification ................................................................................................................. 79
35       Critical processes driving polar amplification ...................................................................... 80
36       Polar amplification from proxies and models during past climates associated with CO2 change
37                      ........................................................................................................................................... 82
38       Overall assessment of polar amplification ........................................................................... 84
39      Tropical Pacific sea-surface temperature gradients .................................................................. 85
40       Critical processes determining changes in tropical Pacific sea-surface temperature gradients 85
41       Tropical Pacific temperature gradients in past high-CO2 climates ........................................ 86
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 1       Overall assessment of tropical Pacific sea-surface temperature gradients under CO2 forcing 87
 2      Dependence of feedbacks on temperature patterns................................................................... 87
 4   7.5       Estimates of ECS and TCR .......................................................................................................... 91
 5      7.5.1        Estimates of ECS and TCR based on process understanding.................................................... 92
 6      ECS estimated using process-based assessments of the forcing and feedbacks ......................... 92
 7      Emulating process-based ECS to TCR .................................................................................... 93
 8      7.5.2        Estimates of ECS and TCR based on the instrumental record .................................................. 95
 9      Estimates of ECS and TCR based on the global energy budget ................................................ 95
10      Estimates of ECS and TCR based on climate model emulators ................................................ 98
11      Estimates of ECS based on variability in Earth’s top-of-atmosphere radiation budget .............. 99
12      Estimates of ECS based on the climate response to volcanic eruptions .................................. 100
13      Assessment of ECS and TCR based on the instrumental record ............................................. 100
14      7.5.3        Estimates of ECS based on paleoclimate data ........................................................................ 101
15      Estimates of ECS from the Last Glacial Maximum ............................................................... 101
16      Estimates of ECS from glacial-interglacial cycles ................................................................. 102
17      Estimates of ECS from warm periods of the pre-Quaternary.................................................. 102
18      Synthesis of ECS based on paleo radiative forcing and temperature ...................................... 103
19      7.5.4        Estimates of ECS and TCR based on emergent constraints .................................................... 106
20      Emergent constraints using global or near-global surface temperature change ....................... 107
21      Emergent constraints focused on cloud feedbacks and present-day climate ............................ 108
22      Assessed ECS and TCR based on emergent constraints ......................................................... 109
23      7.5.5        Combined assessment of ECS and TCR ................................................................................ 110
24      7.5.6        Considerations on the ECS and TCR in global climate models and their role in the assessment ...
25                   ............................................................................................................................................. 113
26      7.5.7        Processes underlying uncertainty in the global temperature response to forcing ..................... 115
28   7.6       Metrics to evaluate emissions ..................................................................................................... 118
29      7.6.1        Physical description of metrics.............................................................................................. 118
30      Radiative properties and lifetimes. ........................................................................................ 118
31      Physical indicators ................................................................................................................ 119
32      Carbon cycle responses and other indirect contributions ........................................................ 120
33      Comparing long-lived with short-lived greenhouse gases ...................................................... 122
34      Emission metrics by compounds ........................................................................................... 124
36   BOX 7.3: Physical considerations in emission-metric choice................................................................ 125
38      7.6.2        Applications of emission metrics .......................................................................................... 126
40   Frequently Asked Questions .................................................................................................................. 128
41      FAQ 7.1:        What is the Earth’s energy budget, and what does it tell us about climate change? ............. 128

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1      FAQ 7.2:          Clouds – What is the role in a warming climate? ............................................................... 130
2      FAQ 7.3:          What is equilibrium climate sensitivity and how does it relate to future warming? ............. 132
4   References .............................................................................................................................................. 134
6   Figures.................................................................................................................................................... 175

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 1   Executive Summary
 3   This chapter assesses the present state of knowledge of Earth’s energy budget, that is, the main flows of
 4   energy into and out of the Earth system, and how these energy flows govern the climate response to a
 5   radiative forcing. Changes in atmospheric composition and land use, like those caused by anthropogenic
 6   greenhouse gas emissions and emissions of aerosols and their precursors, affect climate through
 7   perturbations to Earth’s top-of-atmosphere energy budget. The effective radiative forcings (ERFs) quantify
 8   these perturbations, including any consequent adjustment to the climate system (but excluding surface
 9   temperature response). How the climate system responds to a given forcing is determined by climate
10   feedbacks associated with physical, biogeophysical and biogeochemical processes. These feedback processes
11   are assessed, as are useful measures of global climate response, namely equilibrium climate sensitivity (ECS)
12   and the transient climate response (TCR). This chapter also assesses emission metrics, which are used to
13   quantify how the climate response due to the emission of different greenhouse gases compares to the
14   response to the emission of carbon dioxide (CO2). This chapter builds on the assessment of carbon cycle and
15   aerosol processes from Chapters 5 and 6, respectively, to quantify non-CO2 biogeochemical feedbacks and
16   the ERF for aerosols. Chapters 3, 4, 5, 6 and 9 use the assessment of ERF, ECS and TCR from this chapter to
17   help understand historical and future temperature changes, the response to cumulative emissions, the
18   remaining carbon budget and sea level rise respectively. This chapter builds on findings from the IPCC Fifth
19   Assessment Report (AR5), the Special Report on Global Warming of 1.5°C (SR1.5), the Special Report on
20   Ocean and Cryosphere in a Changing Climate (SROCC) and the Special Report on Climate Change and
21   Land (SRCCL). Very likely ranges are presented unless otherwise indicated.
23   Earth’s Energy Budget
25   Since AR5, the accumulation of energy in the Earth system, quantified by changes in the global energy
26   inventory for all components of the climate system, has become established as a robust measure of the
27   rate of global climate change on interannual-to-decadal timescales. Compared to changes in global
28   surface air temperature (GSAT), the global energy inventory exhibits less variability, which can mask
29   underlying climate trends. Compared to AR5, there is increased confidence in the quantification of changes
30   in the global energy inventory due to improved observational records and closure of the sea level budget.
31   Energy will continue to accumulate in the Earth system until at least the end of the 21st century, even under
32   strong mitigation scenarios, and will primarily be manifest through ocean warming and associated with
33   continued sea level rise through thermal expansion. (high confidence) {7.2.2, Box 7.2, Table 7.1, Chapter 9
34   Cross-Chapter Box 9.1, Table 9.5, 9.2.2, 9.6.3}
36   The global energy inventory increased by 435 [325 to 545] Zettajoules (ZJ) for the period 1971–2018
37   and 153 [101 to 206] ZJ for the period 2006–2018. This corresponds to an Earth energy imbalance of 0.57
38   [0.43 to 0.72] W m-2 for the period 1971–2018, increasing to 0.79 [0.52 to 1.06] W m-2 for the period 2006–
39   2018, expressed per unit area of Earth’s surface. Ocean heat uptake is by far the largest contribution and
40   accounts for 91% of the total energy change. Compared to AR5, the contribution from land heating has been
41   revised upwards from about 3% to about 5%. Melting of ice and warming of the atmosphere account for
42   about 3% and 1% of the total change respectively. More comprehensive analysis of inventory components
43   and cross-validation of satellite and in situ-based global heating rates lead to a more confident assessment
44   relative to AR5. (high confidence) {Box 7.2, 7.2.2, Table 7.1,}
46   Improved quantification of effective radiative forcing, the climate system radiative response, and the
47   observed energy increase in the Earth system for the period 1971–2018 demonstrate improved closure
48   of the global energy budget compared to AR5. Combining the likely range of ERF with the central
49   estimate of radiative response gives an expected energy gain of 340 [47 to 662] ZJ. Combining the likely
50   range of climate response with the central estimate of ERF gives an expected energy gain of 340 [147 to
51   527] ZJ. Both estimates are consistent with an independent observation-based assessment of the global
52   energy increase of 284 [96 to 471] ZJ, (very likely range) expressed relative to the estimated 1850-1900
53   Earth energy imbalance. (high confidence) {7.2.2, Box 7.2, 7.3.5, 7.5.2}
55   Since AR5, additional evidence for a widespread decline (or dimming) in solar radiation reaching the
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 1   surface is found in the observational records between the 1950s and 1980s, with a partial recovery
 2   (brightening) at many observational sites thereafter (high confidence). These trends are neither a local
 3   phenomenon nor a measurement artefact (high confidence). Multi-decadal variation in anthropogenic aerosol
 4   emissions are thought to be a major contributor (medium confidence), but multi-decadal variability in
 5   cloudiness may also have played a role. The downward and upward thermal radiation at the surface has
 6   increased in recent decades, in line with increased greenhouse gas concentrations and associated surface and
 7   atmospheric warming and moistening (medium confidence). {7.2.2}
 9   Effective Radiative Forcing
11   For carbon dioxide, methane, nitrous oxide and chlorofluorocarbons, there is now evidence to
12   quantify the effect on ERF of tropospheric adjustments (e.g., from changes in atmospheric
13   temperatures, clouds and water vapour). The assessed ERF for a doubling of carbon dioxide
14   compared to 1750 levels (3.93 ± 0.47 W m-2) is larger than in AR5. Effective radiative forcings (ERF),
15   introduced in AR5, have been estimated for a larger number of agents and shown to be more closely related
16   to the temperature response than the stratospheric-temperature adjusted radiative forcing. For carbon dioxide,
17   the adjustments include the physiological effects on vegetation. (high confidence) {7.3.2}
19   The total anthropogenic ERF over the industrial era (1750–2019) was 2.72 [1.96 to 3.48] W m-2. This
20   estimate has increased by 0.43 W m-2 compared to AR5 estimates for 1750–2011. This increase includes
21   a +0.34 W m-2 from increases in atmospheric concentrations of well-mixed greenhouse gases (including
22   halogenated species) since 2011, a +0.15 W m-2 from upwards revisions of their radiative efficiencies and a
23   +0.10 W m-2 from re-evaluation of the ozone and stratospheric water vapour ERF. The 0.59 W m-2 increase
24   in ERF from greenhouse gases is partly offset by a better-constrained assessment of total aerosol ERF that is
25   more strongly negative than in AR5, based on multiple lines of evidence (high confidence). Changes in
26   surface reflectance from land-use change, deposition of light-absorbing particles on ice and snow, and
27   contrails and aviation-induced cirrus have also contributed to the total anthropogenic ERF over the industrial
28   era, with –0.20 [–0.30 to –0.10] W m–2 (medium confidence), +0.08 [0 to 0.18] W m–2 (low confidence) and
29   +0.06 [0.02 to 0.10] W m-2 (low confidence), respectively. {7.3.2, 7.3.4, 7.3.5}
31   Anthropogenic emissions of greenhouse gases (GHGs) and their precursors contribute an ERF of 3.84
32   [3.46 to 4.22] W m-2 over the industrial era (1750–2019). Most of this total ERF, 3.32 [3.03 to 3.61] W
33   m-2, comes from the well-mixed greenhouse gases, with changes in ozone and stratospheric water
34   vapour (from methane oxidation) contributing the remainder. The ERF of GHGs is composed of 2.16
35   [1.90 to 2.41] W m-2 from carbon dioxide, 0.54 [0.43 to 0.65] W m-2 from methane, 0.41 [0.33 to 0.49] W m-2
36   from halogenated species, and 0.21 [0.18 to 0.24] W m-2 from nitrous oxide. The ERF for ozone is 0.47 [0.24
37   to 0.71] W m-2. The estimate of ERF for ozone has increased since AR5 due to revised estimates of precursor
38   emissions and better accounting for effects of tropospheric ozone precursors in the stratosphere. The
39   estimated ERF for methane has slightly increased due to a combination of increases from improved
40   spectroscopic treatments being somewhat offset by accounting for adjustments. (high confidence) {7.3.2,
41   7.3.5}
43   Aerosols contribute an ERF of –1.3 [–2.0 to –0.6] W m-2 over the industrial era (1750–2014) (medium
44   confidence). The ERF due to aerosol–cloud interactions (ERFaci) contributes most to the magnitude of
45   the total aerosol ERF (high confidence) and is assessed to be –1.0 [–1.7 to –0.3] W m-2 (medium
46   confidence), with the remainder due to aerosol–radiation interactions (ERFari), assessed to be –0.3 [–
47   0.6 to 0.0] W m-2 (medium confidence). There has been an increase in the estimated magnitude but a
48   reduction in the uncertainty of the total aerosol ERF relative to AR5, supported by a combination of
49   increased process-understanding and progress in modelling and observational analyses. ERF estimates from
50   these separate lines of evidence are now consistent with each other, in contrast to AR5, and support the
51   assessment that it is virtually certain that the total aerosol ERF is negative. Compared to AR5, the assessed
52   magnitude of ERFaci has increased, while the magnitude of ERFari has decreased. The total aerosol ERF
53   over the period 1750–2019 is less certain than the headline statement assessment. It is also assessed to be
54   smaller in magnitude at –1.1 [–1.7 to –0.4] W m-2, primarily due to recent emission changes (medium
55   confidence). {7.3.3, 7.3.5, 2.2.6}
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 2   Climate Feedbacks and Sensitivity
 4   The net effect of changes in clouds in response to global warming is to amplify human-induced
 5   warming, that is, the net cloud feedback is positive (high confidence). Compared to AR5, major
 6   advances in the understanding of cloud processes have increased the level of confidence and decreased
 7   the uncertainty range in the cloud feedback by about 50%. An assessment of the low-altitude cloud
 8   feedback over the subtropical oceans, which was previously the major source of uncertainty in the net cloud
 9   feedback, is improved owing to a combined use of climate model simulations, satellite observations, and
10   explicit simulations of clouds, altogether leading to strong evidence that this type of cloud amplifies global
11   warming. The net cloud feedback, obtained by summing the cloud feedbacks assessed for individual
12   regimes, is 0.42 [–0.10 to 0.94] W m-2 °C–1. A net negative cloud feedback is very unlikely. (high
13   confidence) {7.4.2, Figure 7.10, Table 7.10}
15   The combined effect of all known radiative feedbacks (physical, biogeophysical, and non-CO2
16   biogeochemical) is to amplify the base climate response, also known as the Planck temperature
17   response (virtually certain). Combining these feedbacks with the base climate response, the net feedback
18   parameter based on process understanding is assessed to be –1.16 [–1.81 to –0.51] W m-2 °C–1, which is
19   slightly less negative than that inferred from the overall ECS assessment. The combined water vapour and
20   lapse rate feedback makes the largest single contribution to global warming, whereas the cloud feedback
21   remains the largest contribution to overall uncertainty. Due to the state-dependence of feedbacks, as
22   evidenced from paleoclimate observations and from models, the net feedback parameter will increase
23   (become less negative) as global temperature increases. Furthermore, on long time scales the ice sheet
24   feedback parameter is very likely positive, promoting additional warming on millennial time scales as ice
25   sheets come into equilibrium with the forcing. (high confidence) {7.4.2, 7.4.3, 7.5.7}
27   Radiative feedbacks, particularly from clouds, are expected to become less negative (more amplifying)
28   on multi-decadal timescales as the spatial pattern of surface warming evolves, leading to an ECS that is
29   higher than was inferred in AR5 based on warming over the instrumental record. This new
30   understanding, along with updated estimates of historical temperature change, ERF, and Earth’s
31   energy imbalance, reconciles previously disparate ECS estimates (high confidence). However, there is
32   currently insufficient evidence to quantify a likely range of the magnitude of future changes to current
33   climate feedbacks. Warming over the instrumental record provides robust constraints on the lower end of the
34   ECS range (high confidence), but owing to the possibility of future feedback changes it does not, on its own,
35   constrain the upper end of the range, in contrast to what was reported in AR5. {7.4.4, 7.5.2, 7.5.3}
37   Based on multiple lines of evidence the best estimate of ECS is 3°C, the likely range is 2.5°C to 4°C,
38   and the very likely range is 2°C to 5°C. It is virtually certain that ECS is larger than 1.5°C. Substantial
39   advances since AR5 have been made in quantifying ECS based on feedback process understanding, the
40   instrumental record, paleoclimates and emergent constraints. There is a high level of agreement among the
41   different lines of evidence. All lines of evidence help rule out ECS values below 1.5°C, but currently it is not
42   possible to rule out ECS values above 5 °C. Therefore, the 5°C upper end of the very likely range is assessed
43   to have medium confidence and the other bounds have high confidence. {7.5.5}
45   Based on process understanding, warming over the instrumental record, and emergent constraints,
46   the best estimate of TCR is 1.8°C, the likely range is 1.4°C to 2.2°C and the very likely range is 1.2°C to
47   2.4°C (high confidence). {7.5.5}
49   On average, CMIP6 models have higher mean ECS and TCR values than the CMIP5 generation of
50   models. They also have higher mean values and wider spreads than the assessed best estimates and
51   very likely ranges within this Report. These higher ECS and TCR values can, in some models, be traced to
52   changes in extra-tropical cloud feedbacks that have emerged from efforts to reduce biases in these clouds
53   compared to satellite observations (medium confidence). The broader ECS and TCR ranges from CMIP6 also
54   lead the models to project a range of future warming that is wider than the assessed warming range, which is
55   based on multiple lines of evidence. However, some of the high-sensitivity CMIP6 models are less consistent
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 1   with observed recent changes in global warming and with paleoclimate proxy data than models with ECS
 2   within the very likely range. Similarly, some of the low-sensitivity models are less consistent with the
 3   paleoclimate data. The CMIP models with the highest ECS and TCR values provide insights into high-risk,
 4   low-likelihood futures, which cannot be excluded based on currently-available evidence. (high confidence)
 5   {4.3.1, 4.3.4, 7.4.2, 7.5.6}
 7   Climate Response
 9   The total human-forced GSAT change from 1750–2019 is calculated to be 1.29 [0.99 to 1.65] °C. This
10   calculation is an emulator-based estimate, constrained by the historic GSAT and ocean heat content
11   changes from Chapter 2 and the ERF, ECS and TCR from this chapter. The calculated GSAT change is
12   composed of a well-mixed greenhouse gas warming of 1.58 [1.17 to 2.17] °C (high confidence), a warming
13   from ozone changes of 0.23 [0.11 to 0.39] °C (high confidence), a cooling of –0.50 [–0.22 to –0.96] °C from
14   aerosol effects (medium confidence), and a –0.06 [–0.15 to +0.01] °C contribution from surface reflectance
15   changes from land-use change and light absorbing particles on ice and snow (medium confidence). Changes
16   in solar and volcanic activity are assessed to have together contributed a small change of –0.02 [–0.06 to
17   +0.02] °C since 1750 (medium confidence). {7.3.5}
19   Uncertainties regarding the true value of ECS and TCR are the dominant source of uncertainty in
20   global temperature projections over the 21st century under moderate to high GHG emission scenarios.
21   For scenarios that reach net zero carbon dioxide emissions, the uncertainty in the ERF values of
22   aerosol and other short-lived forcings contribute substantial uncertainty in projected temperature.
23   Global ocean heat uptake is a smaller source of uncertainty in centennial-time-scale surface warming. (high
24   confidence) {7.5.7}
26   The assessed historical and future ranges of GSAT change in this Report are shown to be internally
27   consistent with the Report’s assessment of key physical-climate indicators: greenhouse gas ERFs, ECS
28   and TCR. When calibrated to match the assessed ranges within the assessment, physically based emulators
29   can reproduce the best estimate of GSAT change over 1850–1900 to 1995–2014 to within 5% and the very
30   likely range of this GSAT change to within 10%. Two physically based emulators match at least two-thirds
31   of the Chapter 4-assessed projected GSAT changes to within these levels of precision. When used for multi-
32   scenario experiments, calibrated physically based emulators can adequately reflect assessments regarding
33   future GSAT from Earth system models and/or other lines of evidence. (high confidence) {Cross-Chapter
34   Box 7.1}
36   It is now well understood that the Arctic warms more quickly than the Antarctic due to differences in
37   radiative feedbacks and ocean heat uptake between the poles, but that surface warming will eventually
38   be amplified in both poles (high confidence). The causes of this polar amplification are well understood,
39   and the evidence is stronger than at the time of AR5, supported by better agreement between modelled and
40   observed polar amplification during warm paleo time periods (high confidence). The Antarctic warms more
41   slowly than the Arctic owing primarily to upwelling in the Southern Ocean, and even at equilibrium is
42   expected to warm less than the Arctic. The rate of Arctic surface warming will continue to exceed the global
43   average over this century (high confidence). There is also high confidence that Antarctic amplification will
44   emerge as the Southern Ocean surface warms on centennial time scales, although only low confidence
45   regarding whether the feature will emerge during the 21st century. {7.4.4}
47   The assessed global warming potentials (GWP) and global temperature-change potentials (GTP) for
48   methane and nitrous oxide are slightly lower than in AR5 due to revised estimates of their lifetimes
49   and updated estimates of their indirect chemical effects (medium confidence). The assessed metrics now
50   also include the carbon-cycle response for non-CO2 gases. The carbon cycle estimate is lower than in AR5,
51   but there is high confidence in the need for its inclusion and in the quantification methodology. Metrics for
52   methane from fossil fuel sources account for the extra fossil CO2 that these emissions contribute to the
53   atmosphere and so have slightly higher emission metric values than those from biogenic sources (high
54   confidence). {7.6.1}
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 1   New emission metric approaches such as GWP* and the combined-GTP (CGTP) are designed to relate
 2   emission rates of short-lived gases to cumulative emissions of CO2. These metric approaches are well
 3   suited to estimate the GSAT response from aggregated emissions of a range of gases over time, which
 4   can be done by scaling the cumulative CO2 equivalent emissions calculated with these metrics by the
 5   transient climate response to cumulative emissions of carbon dioxide. For a given multi-gas emission
 6   pathway, the estimated contribution of emissions to surface warming is improved by either using these new
 7   metric approaches or by treating short- and long-lived GHG emission pathways separately, as compared to
 8   approaches that aggregate emissions of GHGs using standard GWP or GTP emission metrics. By contrast, if
 9   emissions are weighted by their 100-year GWP or GTP values, different multi-gas emission pathways with
10   the same aggregated CO2 equivalent emissions rarely lead to the same estimated temperature outcome. (high
11   confidence) {7.6.1, Box 7.3}
13   The choice of emission metric affects the quantification of net zero GHG emissions and therefore the
14   resulting temperature outcome after net zero emissions are achieved. In general, achieving net zero CO2
15   emissions and declining non-CO2 radiative forcing would be sufficient to prevent additional human-caused
16   warming. Reaching net zero GHG emissions as quantified by GWP-100 typically results in global
17   temperatures that peak and then decline after net zero GHGs emissions are achieved, though this outcome
18   depends on the relative sequencing of mitigation of short-lived and long-lived species. In contrast, reaching
19   net zero GHG emissions when quantified using new emission metrics such as CGTP or GWP* would lead to
20   approximate temperature stabilization (high confidence) {7.6.2}

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 1   7.1    Introduction, conceptual framework, and advances since AR5
 3   This chapter assesses the major physical processes that affect the evolution of Earth’s energy budget and the
 4   associated changes in surface temperature and the broader climate system, integrating elements that were
 5   dealt with separately in previous reports.
 7   The top-of-atmosphere (TOA) energy budget determines the net amount of energy entering or leaving the
 8   climate system. Its time variations can be monitored in three ways, using: (i) satellite observations of the
 9   radiative fluxes at the TOA; (ii) observations of the accumulation of energy in the climate system; and (iii)
10   observations of surface energy fluxes. When the TOA energy budget is changed by a human or natural cause
11   (a radiative forcing), the climate system responds by warming or cooling (i.e., the system gains or loses
12   energy). Understanding of changes in the Earth’s energy flows helps understanding of the main physical
13   processes driving climate change. It also provides a fundamental test of climate models and their projections.
15   This chapter principally builds on AR5 (Boucher, 2012; Church et al., 2013; Collins et al., 2013a; Flato et
16   al., 2013; Hartmann et al., 2013; Myhre et al., 2013b; Rhein et al., 2013). It also builds on the subsequent
17   SR1.5 (IPCC, 2018), SROCC (IPCC, 2019a) and SRCCL (IPCC, 2019b), as well as community-led
18   assessments (e.g., Bellouin et al. (2019) covering aerosol radiative forcing and Sherwood et al. (2020)
19   covering equilibrium climate sensitivity).
21   Throughout this chapter, global surface air temperature (GSAT) is used to quantify surface temperature
22   change (see Cross-Chapter Box 2.3, Chapter 4 Section 4.3.4). The total energy accumulation in the Earth
23   system represents a metric of global change that is complementary to GSAT but shows considerably less
24   variability on interannual-to-decadal timescales (Section 7.2.2). Research and new observations since AR5
25   have improved scientific confidence in the quantification of changes in the global energy inventory and
26   corresponding estimates of Earth’s energy imbalance (Section 7.2). Improved understanding of adjustments
27   to radiative forcing and of aerosol-cloud interactions have led to revisions of forcing estimates (Section 7.3).
28   New approaches to the quantification and treatment of feedbacks (Section 7.4) have improved the
29   understanding of their nature and time-evolution, leading to a better understanding of how these feedbacks
30   relate to Equilibrium Climate Sensitivity (ECS). This has helped to reconcile disparate estimates of ECS
31   from different lines of evidence (Section 7.5). Innovations in the use of emission metrics have clarified the
32   relationships between metric choice and temperature policy goals (Section 7.6), linking this chapter to WGIII
33   which provides further information on metrics, their use, and policy goals beyond temperature. Very likely
34   (5% to 95%) ranges are presented unless otherwise indicated. In particular, the addition of (one standard
35   deviation) indicates that the range represents one standard deviation.
37   In Box 7.1 an energy budget framework is introduced, which forms the basis for the discussions and
38   scientific assessment in the remainder of this chapter and across the report. The framework reflects advances
39   in the understanding of the Earth system response to climate forcing since the publication of AR5. A
40   schematic of this framework and the key changes relative to the science reported in AR5 are provided in
41   Figure 7.1.
46   Figure 7.1: A visual abstract of the chapter, illustrating why the Earth’s energy budget matters and how it relates to
47               the underlying chapter assessment. The methods used to assess processes and key new findings relative to
48               AR5 are highlighted.
50   [END FIGURE 7.1 HERE]
53   A simple way to characterise the behaviour of multiple aspects of the climate system at once is to summarise
54   them using global-scale metrics. This report distinguishes between “climate metrics” (e.g., ECS, TCR) and
55   “emission metrics” (such as the global warming potential; GWP, or global temperature potential; GTP), but
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 1   this distinction is not definitive. Climate metrics are generally used to summarise aspects of the surface
 2   temperature response (Box 7.1). Emission metrics are generally used to summarise the relative effects of
 3   emissions of different forcing agents, usually greenhouse gases (see Section 7.6). The climate metrics used in
 4   this report typically evaluate how the Earth system response varies with atmospheric gas concentration or
 5   change in radiative forcing. Emission metrics evaluate how radiative forcing or a key climate variable (such
 6   as GSAT) is affected by the emissions of a certain amount of gas. Emission-related metrics are sometimes
 7   used in mitigation policy decisions such as trading greenhouse gas reduction measures and life cycle
 8   analysis. Climate metrics are useful to gauge the range of future climate impacts for adaptation decisions
 9   under a given emission pathway. Metrics such as the transient climate response to cumulative emissions of
10   carbon dioxide (TCRE) are used in both adaptation and mitigation contexts: for gauging future global
11   surface temperature change under specific emission scenarios, and to estimate remaining carbon budgets that
12   are used to inform mitigation policies (see Chapter 5, Section 5.5).
14   Given that TCR and ECS are metrics of GSAT response to a theoretical doubling of atmospheric CO2 (Box
15   7.1), they do not directly correspond to the warming that would occur under realistic forcing scenarios that
16   include time-varying CO2 concentrations and non-CO2 forcing agents (such as aerosols and land-use
17   changes). It has been argued that TCR, as a metric of transient warming, is more policy-relevant than ECS
18   (Frame et al., 2006; Schwartz, 2018). However, as detailed in Chapter 4, both established and recent results
19   (Forster et al., 2013; Gregory et al., 2015; Marotzke and Forster, 2015; Grose et al., 2018; Marotzke, 2019)
20   indicate that TCR and ECS help explain variation across climate models both over the historical period and
21   across a range of concentration-driven future scenarios. In emission-driven scenarios the carbon cycle
22   response is also important (Smith et al., 2019). The proportion of variation explained by ECS and TCR
23   varies with scenario and the time period considered, but both past and future surface warming depend on
24   these metrics (Section 7.5.7).
26   Regional changes in temperature, rainfall, and climate extremes have been found to correlate well with the
27   forced changes in GSAT within Earth System Models (ESMs) (Giorgetta et al., 2013; Tebaldi and Arblaster,
28   2014; Seneviratne et al., 2016; Chapter 4, Section 4.6.1). While this so-called ‘pattern scaling’ has important
29   limitations arising from, for instance, localized forcings, land-use changes, or internal climate variability
30   (Deser et al., 2012; Luyssaert et al., 2014), changes in GSAT nonetheless explain a substantial fraction of
31   inter-model differences in projections of regional climate changes over the 21st century (Tebaldi and Knutti,
32   2018). This Chapter’s assessments of TCR and ECS thus provide constraints on future global and regional
33   climate change (Chapter 4 and Chapter 11).
36   [START BOX 7.1 HERE]
38   BOX 7.1: The energy budget framework – forcing and response
39   The forcing and response energy budget framework provides a methodology to assess the effect of individual
40   drivers of global mean surface temperature response, and to facilitate the understanding of the key
41   phenomena that set the magnitude of this temperature response. The framework used here is developed from
42   that adopted in previous IPCC reports (see Ramaswamy et al., 2019 for a discussion). Effective Radiative
43   Forcing (ERF), introduced in AR5 (Boucher et al., 2013; Myhre et al., 2013b) is more explicitly defined in
44   this report and is employed as the central definition of radiative forcing (Sherwood et al. 2015, Box 7.1,
45   Figure 1a). The framework has also been extended to allow variations in feedbacks over different timescales
46   and with changing climate state (Section 7.4.4; Section 7.4.3).
48   The GSAT response to perturbations that give rise to an energy imbalance is traditionally approximated by
49   the following linear energy budget equation, in which ΔN represents the change in the top-of-atmosphere
50   (TOA) net energy flux, ΔF is an effective radiative forcing perturbation to the TOA net energy flux, α is the
51   net feedback parameter and ΔT is the change in GSAT:
53                                   ΔN = ΔF + α ΔT          Box 7.1, Equation (7.1)
55   ERF is the TOA energy budget change resulting from the perturbation, excluding any radiative response
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 1   related to a change in GSAT (i.e., ΔT =0). Climate feedbacks (α) represent those processes that change the
 2   TOA energy budget in response to a given ΔT.
 7   Box 7.1, Figure 1: Schematics of the forcing-feedback framework adopted within the assessment, following
 8                      Equation 7.1. Illustrated is how the Earth’s TOA net energy flux might evolve for a hypothetical
 9                      doubling of atmospheric CO2 concentration above preindustrial levels, where an initial positive
10                      energy imbalance (energy entering the Earth system, shown on the y-axis) is gradually restored
11                      towards equilibrium as the surface temperature warms (shown on the x-axis). a) illustrates the
12                      definitions of ERF for the special case of a doubling of atmospheric CO2 concentration, the
13                      feedback parameter and the ECS. b) illustrates how approximate estimates of these metrics are made
14                      within the chapter and how these approximations might relate to the exact definitions adopted in
15                      panel a).
17   [END BOX 7.1, FIGURE 1 HERE]
20   The effective radiative forcing, ERF (ΔF; units: W m-2) quantifies the change in the net TOA energy flux of
21   the Earth system due to an imposed perturbation (e.g., changes in greenhouse gas or aerosol concentrations,
22   in incoming solar radiation, or land-use change). ERF is expressed as a change in net downward radiative
23   flux at the TOA following adjustments in both tropospheric and stratospheric temperatures, water vapour,
24   clouds, and some surface properties, such as surface albedo from vegetation changes, that are uncoupled to
25   any GSAT change (Smith et al., 2018b). These adjustments affect the TOA energy balance and hence the
26   ERF. They are generally assumed to be linear and additive (Section 7.3.1). Accounting for such processes
27   gives an estimate of ERF that is more representative of the climate change response associated with forcing
28   agents than stratospheric-temperature-adjusted radiative forcing (SARF) or the instantaneous radiative
29   forcing (IRF) (Section 7.3.1). Adjustments are processes that are independent of GSAT change, whereas
30   feedbacks refer to processes caused by GSAT change. Although adjustments generally occur on timescales
31   of hours to several months, and feedbacks respond to ocean surface temperature changes on timescales of a
32   year or more, timescale is not used to separate the definitions. ERF has often been approximated as the TOA
33   energy balance change due to an imposed perturbation in climate model simulations with sea-surface
34   temperature and sea-ice concentrations set to their pre-industrial climatological values (e.g., Forster et al.,
35   2016). However, to match the adopted forcing-feedback framework, the small effects of any GSAT change
36   from changes in land surface temperatures need to be removed from the TOA energy balance in such
37   simulations to give an approximate measure of ERF (Box 7.1, Figure 1b and Section 7.3.1).
39   The feedback parameter, α , (units: W m-2 °C-1) quantifies the change in net energy flux at the TOA for a
40   given change in GSAT. Many climate variables affect the TOA energy budget, and the feedback parameter
                                                                      𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑
41   can be decomposed, to first order, into a sum of terms 𝛼𝛼 = ∑𝑥𝑥 𝜕𝜕𝜕𝜕 𝑑𝑑T], where x represents a variable of the
42   Earth system that has a direct effect on the energy budget at the TOA. The sum of the feedback terms (i.e., 𝛼𝛼
43   in Equation 7.1) governs Earth’s equilibrium GSAT response to an imposed ERF. In previous assessments, α
44   and the related ECS have been associated with a distinct set of physical processes (Planck response and
45   changes in water vapour, lapse rate, surface albedo, and clouds) (Charney et al., 1979). In this assessment, a
46   more general definition of α and ECS is adopted such that they include additional Earth system processes
47   that act across many timescales (e.g., changes in natural aerosol emissions or vegetation). Because, in our
48   assessment, these additional processes sum to a near-zero value, including these additional processes does
49   not change the assessed central value of ECS but does affect its assessed uncertainty range (Section 7.4.2).
50   Note that there is no standardised notation or sign convention for the feedback parameter in the literature.
51   Here the convention is used that the sum of all feedback terms (the net feedback parameter, 𝛼𝛼) is negative for
52   a stable climate that radiates additional energy to space with a GSAT increase, with a more negative value of
53   𝛼𝛼 corresponding to a stronger radiative response and thus a smaller GSAT change required to balance a
54   change in ERF (Equation 7.1). A change in process x amplifies the temperature response to a forcing when
55   the associated feedback parameter 𝛼𝛼𝑥𝑥 is positive (positive feedback) and dampens the temperature response
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 1   when 𝛼𝛼𝑥𝑥 is negative (negative feedback). New research since AR5 emphasises how feedbacks can vary over
 2   different timescales (Section 7.4.4) and with climate state (Section 7.4.3), giving rise to the concept of an
 3   effective feedback parameter that may be different from the equilibrium value of the feedback parameter
 4   governing ECS (Section 7.4.3).
 6   The equilibrium climate sensitivity, ECS (units: °C), is defined as the equilibrium value of ΔT in response to
 7   a sustained doubling of atmospheric CO2 concentration from a pre-industrial reference state. The value of
 8   ERF for this scenario is denoted by ∆F2𝑥𝑥𝑥𝑥𝑥𝑥2 , giving ECS = −∆F2𝑥𝑥𝑥𝑥𝑥𝑥2 /𝛼𝛼 from Equation (7.1) applied at
 9   equilibrium (see Box 7.1, Figure 1a and Section 7.5). Equilibrium refers to a steady state where ΔN averages
10   to zero over a multi-century period. ECS is representative of the multi-century to millennial ΔT response to
11   ∆F2𝑥𝑥𝑥𝑥𝑥𝑥2 , and is based on a CO2 concentration change so any feedbacks that affect the atmospheric
12   concentration of CO2 do not influence its value. As employed here, ECS also excludes the long-term
13   response of the ice sheets (Section which may take multiple millennia to reach equilibrium, but
14   includes all other feedbacks. Due to a number of factors, studies rarely estimate ECS or α at equilibrium or
15   under CO2 forcing alone. Rather, they give an effective feedback parameter (Section 7.4.1 and Box 7.1,
16   Figure 1b) or an effective ECS (Section 7.5.1 and Box 7.1, Figure 1b), which represent approximations to the
17   true values of α or ECS. The effective ECS represents the equilibrium value of ΔT in response to a sustained
18   doubling of atmospheric CO2 concentration that would occur assuming the effective feedback parameter
19   applied at that equilibrium state. For example, a feedback parameter can be estimated from the linear slope
20   of ΔN against ΔT over a set number of years within ESM simulations of an abrupt doubling or quadrupling of
21   atmospheric CO2 (2×CO2 or 4×CO2, respectively), and the ECS can be estimated from the intersect of this
22   regression line with ΔN = 0 (see Box 7.1, Figure 1b). To infer ECS from a given estimate of effective ECS
23   necessitates that assumptions are made for how ERF varies with CO2 concentration (Section 7.3.2) and how
24   the slope of ΔN against ΔT relates to the slope of the straight line from ERF to ECS (see Section 7.5 and Box
25   7.1, Figure 1b). Care has to be taken when comparing results across different lines of evidence to translate
26   their estimates of the effective ECS into the ECS definition used here (Section 7.5.5).
28   The transient climate response, TCR (units: °C), is defined as the ΔT for the hypothetical scenario in which
29   CO2 increases at 1% yr-1 from a pre-industrial reference state to the time of a doubling of atmospheric CO2
30   concentration (year 70) (Section 7.5). TCR is based on a CO2 concentration change, so any feedbacks that
31   affect the atmospheric concentration of CO2 do not influence its value. It is a measure of transient warming
32   accounting for the strength of climate feedbacks and ocean heat uptake. The transient climate response to
33   cumulative emissions of carbon dioxide (TCRE) is defined as the transient ΔT per 1000 Gt C of cumulative
34   CO2 emission increase since preindustrial. TCRE combines information on the airborne fraction of
35   cumulative CO2 emissions (the fraction of the total CO2 emitted that remains in the atmosphere at the time of
36   doubling, which is determined by carbon cycle processes) with information on the TCR. TCR is assessed in
37   this chapter, whereas TCRE is assessed in Chapter 5, Section 5.5.
39   [END BOX 7.1 HERE]
42   7.2   Earth’s energy budget and its changes through time
44   Earth’s energy budget encompasses the major energy flows of relevance for the climate system (Figure 7.2).
45   Virtually all the energy that enters or leaves the climate system does so in the form of radiation at the TOA.
46   The TOA energy budget is determined by the amount of incoming solar (shortwave) radiation and the
47   outgoing radiation that is composed of reflected solar radiation and outgoing thermal (longwave) radiation
48   emitted by the climate system. In a steady state climate, the outgoing and incoming radiative components are
49   essentially in balance in the long-term global mean, although there are still fluctuations around this balanced
50   state that arise through internal climate variability (Brown et al., 2014; Palmer and McNeall, 2014).
51   However, anthropogenic forcing has given rise to a persistent imbalance in the global mean TOA radiation
52   budget that is often referred to as Earth’s energy imbalance (e.g., Trenberth et al., 2014; von Schuckmann et
53   al., 2016) and is a key element in energy budget framework (N, Box 7.1, Equation 7.1) and an important
54   metric of the rate of global climate change (Hansen et al., 2005a; von Schuckmann et al., 2020). In addition
55   to the TOA energy fluxes, Earth’s energy budget also includes the internal flows of energy within the climate
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 1   system, which characterize the climate state. The surface energy budget consists of the net solar and thermal
 2   radiation as well as the non-radiative components such as sensible, latent and ground heat fluxes (Figure 7.2
 3   upper panel). It is a key driver of the global water cycle, atmosphere and ocean dynamics, as well as a
 4   variety of surface processes.
 7   7.2.1    Present-day energy budget
 9   Figure 7.2 (upper panel) shows a schematic representation of Earth’s energy budget for the early 21st
10   century, including globally-averaged estimates of the individual components (Wild et al., 2015). Clouds are
11   important modulators of the global energy fluxes. Thus, any perturbations in the cloud fields, such as forced
12   by aerosol-cloud interactions (Section 7.3) or through cloud feedbacks (Section 7.4) can have a strong
13   influence on the energy distribution in the climate system. To illustrate the overall effects that clouds exert
14   on the energy fluxes, Figure 7.2 (lower panel) also shows the energy budget in the absence of clouds, with
15   otherwise identical atmospheric and surface radiative properties. It has been derived by taking into account
16   information contained in both in-situ and satellite radiation measurements taken under cloud-free conditions
17   (Wild et al., 2019). A comparison of the upper and lower panels in Figure 7.2 shows that without clouds, 47
18   W m-2 less solar radiation is reflected back to space globally (53 ± 2 W m-2 instead of 100 ± 2 W m-2), while
19   28 W m-2 more thermal radiation is emitted to space (267 ± 3 W m-2 instead of 239± 3 W m-2). As a result,
20   there is a 20 W m-2 radiative imbalance at the TOA in the clear-sky energy budget (Figure 7.2 lower panel),
21   suggesting that the Earth would warm substantially if there were no clouds.
26   Figure 7.2: Schematic representation of the global mean energy budget of the Earth (upper panel), and its
27               equivalent without considerations of cloud effects (lower panel). Numbers indicate best estimates for
28               the magnitudes of the globally averaged energy balance components in W m–2 together with their
29               uncertainty ranges in parentheses (5–95 % confidence range), representing climate conditions at the
30               beginning of the 21st century. Note that the cloud-free energy budget shown in the lower panel is not the
31               one that Earth would achieve in equilibrium when no clouds could form. It rather represents the global
32               mean fluxes as determined solely by removing the clouds but otherwise retaining the entire atmospheric
33               structure. This enables the quantification of the effects of clouds on the Earth energy budget and
34               corresponds to the way clear-sky fluxes are calculated in climate models. Thus, the cloud-free energy
35               budget is not closed and therefore the sensible and latent heat fluxes are not quantified in the lower panel.
36               Adapted from Wild et al. (2015, 2019).
38   [END FIGURE 7.2 HERE]
41   AR5 (Church et al., 2013; Hartmann et al., 2013; Myhre et al., 2013b) highlighted the progress in
42   quantifying the TOA radiation budget following new satellite observations that became available in the early
43   21st Century (Clouds and the Earth’s Radiant Energy System, CERES; Solar Radiation and Climate
44   Experiment, SORCE). Progress in the quantification of changes in incoming solar radiation at the TOA is
45   discussed in Chapter 2, Section 2.2. Since AR5, the CERES Energy Balance EBAF Ed4.0 product was
46   released, which includes algorithm improvements and consistent input datasets throughout the record (Loeb
47   et al., 2018a). However, the overall precision of these fluxes (uncertainty in global mean TOA flux 1.7%
48   (1.7 W m-2) for reflected solar and 1.3% (3.0 W m-2) for outgoing thermal radiation at the 90% confidence
49   level) is not sufficient to quantify the Earth’s energy imbalance in absolute terms. Therefore, adjustments
50   within the uncertainty ranges of the CERES reflected solar and emitted thermal TOA fluxes were applied to
51   the entire EBAF record to ensure that the net TOA flux for July 2005–June 2015 was consistent with the
52   estimated Earth’s energy imbalance for the same period based on ocean heat content (OHC) measurements
53   and energy uptake estimates for the land, cryosphere and atmosphere (Johnson et al., 2016; Riser et al., 2016;
54   Section ESMs typically show good agreement with global mean TOA fluxes from CERES-EBAF.
55   However, as some ESMs are known to calibrate their TOA fluxes to CERES or similar data (Hourdin et al.,
56   2017), this is not necessarily an indication of model accuracy, especially as ESMs show significant
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 1   discrepancies on regional scales, often related to their representation of clouds (Trenberth and Fasullo, 2010;
 2   Donohoe and Battisti, 2012; Hwang and Frierson, 2013; Li et al., 2013b; Dolinar et al., 2015; Wild et al.,
 3   2015).
 5   The radiation components of the surface energy budget are associated with substantially larger uncertainties
 6   than at the TOA, since they are less directly measured by passive satellite sensors from space and require
 7   retrieval algorithms and ancillary data for their estimation (Raschke et al., 2016; Kato et al., 2018; Huang et
 8   al., 2019). Confidence in the quantification of the global mean surface radiation components has increased
 9   recently, as independent estimates now converge to within a few W m-2 (Wild, 2017). Current best estimates
10   for downward solar and thermal radiation at Earth’s surface are near 185 W m-2 and 342 W m-2, respectively
11   (Figure 7.2). These estimates are based on complementary approaches that make use of satellite products
12   from active and passive sensors (L’Ecuyer et al., 2015; Kato et al., 2018) and information from surface
13   observations and Earth System Models (ESMs) (Wild et al., 2015). Inconsistencies in the quantification of
14   the global mean energy and water budgets discussed in AR5 (Hartmann et al., 2013) have been reconciled
15   within the (considerable) uncertainty ranges of their individual components (Wild et al., 2013, 2015;
16   L’Ecuyer et al., 2015). However, on regional scales, the closure of the surface energy budgets remains a
17   challenge with satellite-derived datasets (Loeb et al., 2014; L’Ecuyer et al., 2015; Kato et al., 2016).
18   Nevertheless, attempts have been made to derive surface energy budgets over land and ocean (Wild et al.,
19   2015), over the Arctic (Christensen et al., 2016a) and over individual continents and ocean basins (L’Ecuyer
20   et al., 2015; Thomas et al., 2020). Since AR5, the quantification of the uncertainties in surface energy flux
21   datasets has improved. Uncertainties in global monthly mean downward solar and thermal fluxes in the
22   CERES-EBAF surface dataset are, respectively, 10 W m-2 and 8 W m-2 (converted to 5% to 95% ranges)
23   (Kato et al., 2018). The uncertainty in the surface fluxes for polar regions is larger than in other regions
24   (Kato et al., 2018) due to the limited number of surface sites and larger uncertainty in surface observations
25   (Previdi et al., 2015). The uncertainties in ocean mean latent and sensible heat fluxes are approximately 11
26   W m-2 and 5 W m-2 (converted to 5% to 95% ranges), respectively (L’Ecuyer et al., 2015). A recent review
27   of the latent and sensible heat flux accuracies over the period 2000 to 2007 highlights significant differences
28   between several gridded products over ocean, where root mean squared differences between the multi-
29   product ensemble and data at more than 200 moorings reached up to 25 W m-2 for latent heat and 5 W m-2 for
30   sensible heat (Bentamy et al., 2017). This uncertainty stems from the retrieval of flux-relevant
31   meteorological variables, as well as from differences in the flux parameterizations (Yu, 2019). Estimating
32   the uncertainty in sensible and latent heat fluxes over land is difficult because of the large temporal and
33   spatial variability. The flux values over land computed with three global datasets vary by 10% to 20%
34   (L’Ecuyer et al., 2015).
36   ESMs also show larger discrepancies in their surface energy fluxes than at the TOA due to weaker
37   observational constraints, with a spread of typically 10-20 W m-2 in the global average, and an even greater
38   spread at regional scales (Li et al., 2013b; Wild et al., 2013; Boeke and Taylor, 2016; Wild, 2017; Zhang et
39   al., 2018a; Wild, 2020). Differences in the land-averaged downward thermal and solar radiation in CMIP5
40   ESMs amount to more than 30 and 40 W m-2, respectively (Wild et al., 2015). However, in the global multi-
41   model mean, the magnitudes of the energy budget components of the CMIP6 ESMs generally show better
42   agreement with reference estimates than previous model generations (Wild, 2020).
44   In summary, since AR5, the magnitudes of the global mean energy budget components have been quantified
45   more accurately, not only at the TOA, but also at the Earth’s surface, where independent estimates of the
46   radiative components have converged (high confidence). Considerable uncertainties remain in regional
47   surface energy budget estimates as well as their representation in climate models.
50   7.2.2     Changes in Earth’s energy budget
52    Changes in Earth’s TOA energy budget
54   Since 2000, changes in the TOA energy fluxes can be tracked from space using CERES satellite
55   observations (Figure 7.3). The variations in TOA energy fluxes reflect the influence of internal climate
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 1   variability, particularly that of ENSO, in addition to radiative forcing of the climate system and climate
 2   feedbacks (Allan et al., 2014; Loeb et al., 2018a). For example, globally, the reduction in both outgoing
 3   thermal and reflected solar radiation during La Niña conditions in 2008/2009 led to an energy gain for the
 4   climate system, whereas enhanced outgoing thermal and reflected solar radiation caused an energy loss
 5   during the El Niños of 2002/2003 and 2009/2010 (Figure 7.3; Loeb et al., 2018a). An ensemble of CMIP6
 6   models is able to track the variability in the global mean TOA fluxes observed by CERES, when driven with
 7   prescribed sea-surface temperatures (SSTs) and sea-ice concentrations (Figure 7.3; Loeb et al., 2020). Under
 8   cloud-free conditions, the CERES record shows a near zero trend in outgoing thermal radiation (Loeb et al.,
 9   2018a), which combined with an increasing surface upwelling thermal flux implies an increasing clear-sky
10   greenhouse effect (Raghuraman et al., 2019). Conversely, clear-sky solar reflected TOA radiation in the
11   CERES record covering March 2000 to September 2017 shows a decrease due to reductions in aerosol
12   optical depth in the Northern Hemisphere and sea-ice fraction (Loeb et al., 2018b; Paulot et al., 2018).
14   An effort to reconstruct variations in the net TOA fluxes back to 1985, based on a combination of satellite
15   data, atmospheric reanalysis and high-resolution climate model simulations (Allan et al., 2014; Liu et al.,
16   2020), exhibits strong interannual variability associated with the volcanic eruption of Mt Pinatubo in 1991
17   and the ENSO events before 2000. The same reconstruction suggests that Earth’s energy imbalance
18   increased by several tenths of a W m-2 between the periods 1985–1999 and 2000–2016, in agreement with
19   the assessment of changes in the global energy inventory (Section, Box 7.2, Figure 1). Comparisons
20   of year-to-year variations in Earth’s energy imbalance estimated from CERES and independent estimates
21   based on ocean heat content change are significantly correlated with similar phase and magnitude (Johnson
22   et al., 2016; Meyssignac et al., 2019), promoting confidence in both satellite and in situ-based estimates
23   (Section
25   In summary, variations in the energy exchange between Earth and space can be accurately tracked since the
26   advent of improved observations since the year 2000 (high confidence), while reconstructions indicate that
27   the Earth’s energy imbalance was larger in the 2000s than in the 1985–1999 period (high confidence).
32   Figure 7.3: Anomalies in global mean all-sky TOA fluxes from EBAF Ed4.0 (solid black lines) and various
33               CMIP6 climate models (coloured lines) in terms of (a) reflected solar, (b) emitted thermal and (c)
34               net TOA fluxes. The multi-model means are additionally depicted as dotted black lines. Model fluxes
35               stem from simulations driven with prescribed SSTs and all known anthropogenic and natural forcings.
36               Shown are anomalies of 12-month running means. All flux anomalies are defined as positive downwards,
37               consistent with the sign convention used throughout this chapter. The correlations between the multi-
38               model means (dotted black lines) and the CERES records (solid black lines) for 12-month running means
39               are 0.85, 0.73 and 0.81 for the global mean reflected solar, outgoing thermal and net TOA radiation,
40               respectively. Adapted from Loeb et al. (2020). Further details on data sources and processing are
41               available in the chapter data table (Table 7.SM.14).
43   [END FIGURE 7.3 HERE]
46   Changes in the global energy inventory
48   The global energy inventory quantifies the integrated energy gain of the climate system associated with
49   global ocean heat uptake, warming of the atmosphere, warming of the land, and melting of ice. Due to
50   energy conservation, the rate of accumulation of energy in the Earth system (Section 7.1) is equivalent to the
51   Earth energy imbalance (N in Box 7.1, Equation 7.1). On annual and longer timescales, changes in the global
52   energy inventory are dominated by changes in global OHC (Rhein et al., 2013; Palmer and McNeall, 2014;
53   Johnson et al., 2016). Thus, observational estimates and climate model simulations of OHC change are
54   critical to the understanding of both past and future climate change (Chapter 2, Section, Chapter 3,
55   Section, Chapter 4, Section, Chapter 9, Section
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 1   Since AR5, both modelling and observational-based studies have established Earth’s energy imbalance
 2   (characterised by OHC change) as a more robust metric of the rate of global climate change than GSAT on
 3   interannual-to-decadal timescales (Palmer and McNeall, 2014; von Schuckmann et al., 2016; Wijffels et al.,
 4   2016; Cheng et al., 2018; Allison et al., 2020a). This is because GSAT is influenced by large unforced
 5   variations, for example linked to ENSO and Pacific decadal variability (Roberts et al., 2015; Yan et al.,
 6   2016; Cheng et al., 2018). Measuring OHC change more comprehensively over the full ocean depth results
 7   in a higher signal-to-noise ratio and a timeseries that increases steadily over time (Box7.2, Figure 1; Allison
 8   et al., 2020). In addition, understanding of the potential effects of historical ocean sampling on estimated
 9   global ocean heating rates has improved (Durack et al., 2014; Good, 2017; Allison et al., 2019) and there are
10   now more estimates of OHC change available that aim to mitigate the effect of limited observational
11   sampling in the Southern Hemisphere (Lyman and Johnson, 2008; Cheng et al., 2017; Ishii et al., 2017).
13   The assessment of changes in the global energy inventory for the periods 1971-2018, 1993-2018 and 2006–
14   2018 draws upon the latest observational timeseries and the assessments presented in other chapters of this
15   report. The estimates of OHC change come directly from the assessment presented in Chapter 2, Section
16 The assessment of land and atmospheric heating comes from von Schuckmann et al. (2020), based
17   on the estimates of Cuesta-Valero et al. (2021) and Steiner et al. (2020), respectively. Heating of inland
18   waters, including lakes, reservoirs and rivers, is estimated to account for < 0.1 % of the total energy change,
19   and is therefore neglected from this assessment (Vanderkelen et al., 2020). The cryosphere contribution from
20   melting of grounded ice is based on the mass loss assessments presented in Chapter 9, Sections 9.4.1
21   (Greenland ice sheet), 9.4.2 (Antarctic ice sheet) and 9.5.1 (glaciers). Following AR5, the estimate of heating
22   associated with loss of Arctic sea ice is based on a reanalysis (Schweiger et al., 2011), following the methods
23   described by Slater et al. (2021). Chapter 9, Section 9.3.2 finds no significant trend in Antarctic sea ice area
24   over the observational record, a zero contribution is assumed. Ice melt associated with the calving and
25   thinning of floating ice shelves are based on the decadal rates presented in Slater et al. (2021). For all
26   cryospheric components, mass loss is converted to heat input using a latent heat of fusion of 3.34 × 105 J Kg-
     1 -1
27     C with the second-order contributions from variations associated with ice type and warming of ice from
28   sub-freezing temperatures neglected, as in AR5. The net change in energy, quantified in Zetta Joules (1 ZJ =
29   1021 Joules), is computed for each component as the difference between the first and last year of each period
30   (Table 7.1). The uncertainties in the depth-interval contributions to OHC are summed to get the uncertainty
31   in global OHC change. All other uncertainties are assumed to be independent and added in quadrature.
36   Table 7.1:    Contributions of the different components of the global energy inventory for the periods 1971 to 2018,
37                 1993 to 2018 and 2006 to 2018 (Box 7.2, Cross-chapter box 9.1). Energy changes are computed as the
38                 difference between annual mean values or year mid-points. The total heating rates correspond to Earth’s
39                 energy imbalance and are expressed per unit area of Earth’s surface.
      Component              1971 to 2018                     1993 to 2018                      2006 to 2018
                       Energy Gain (ZJ)         %       Energy Gain (ZJ)         %        Energy Gain (ZJ)         %
      Ocean          396.0 [285.7 to 506.2]    91.0   263.0 [194.1 to 331.9]    90.9     138.8 [86.4 to 191.3]    90.7

      0-700 m        241.6 [162.7 to 320.5]    55.6   151.5 [114.1 to 188.9]    52.4      75.4 [48.7 to 102.0]    49.3
      700-2000 m      123.3 [96.0 to 150.5]    28.3    82.8 [59.9 to 105.6]     28.6      49.7 [29.0 to 70.4]     32.4
      > 2000 m         31.0 [15.7 to 46.4]      7.1    28.7 [14.5 to 43.0]      9.9        13.8 [7.0 to 20.6]     9.0

      Land             21.8 [18.6 to 25.0]     5.0      13.7 [12.4 to 14.9]      4.7        7.2 [6.6 to 7.8]       4.7

      Cryosphere       11.5 [9.0 to 14.0]      2.7        8.8 [7.0 to 10.6]      3.0        5.4 [3.9 to 6.8]       3.5

      Atmosphere         5.6 [4.6 to 6.7]      1.3        3.8 [3.2 to 4.3]       1.3        1.6 [1.2 to 2.1]       1.1

      TOTAL            434.9 [324.5 to 545.5] ZJ         289.2 [220.3 to 358.2] ZJ        153.1 [100.6 to 205.5] ZJ

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         Heating            0.57 [0.43 to 0.72] W m-2            0.72 [0.55 to 0.89] W m-2   0.79 [0.52 to 1.06] W m-2

 2   [END TABLE 7.1 HERE]
 5   For the period 1971–2010, AR5 (Rhein et al., 2013) found an increase in the global energy inventory of 274
 6   [196 to 351] ZJ with a 93% contribution from total OHC change, about 3% for both ice melt and land
 7   heating, and about 1% for warming of the atmosphere. For the same period, this Report finds an upwards
 8   revision of OHC change for the upper (< 700 m depth) and deep (> 700 m depth) ocean of about 8% and
 9   20% compared to AR5 and a modest increase in the estimated uncertainties associated with the ensemble
10   approach of Palmer et al. (2021). The other substantive change compared to AR5 is the updated assessment
11   of land heating, with values approximately double those assessed previously, based on a more
12   comprehensive analysis of the available observations (von Schuckmann et al., 2020; Cuesta-Valero et al.,
13   2021). The result of these changes is an assessed energy gain of 329 [224 to 434] ZJ for the period 1971–
14   2010, which is consistent with AR5 within the estimated uncertainties, despite the systematic increase.
16   The assessed changes in the global energy inventory (Box 7.2, Figure 1a; Table 7.1) yields an average value
17   for Earth’s energy imbalance (N, Box 7.1, Equation 7.1) of 0.57 [0.43 to 0.72] W m-2 for the period 1971 to
18   2018, expressed relative to Earth’s surface area (high confidence). The estimates for the periods 1993 to
19   2018 and 2006 to 2018 yield substantially larger values of 0.72 [0.55 to 0.89] W m-2 and 0.79 ± [0.52 to
20   1.06] W m-2, respectively, consistent with the increased radiative forcing from greenhouse gases (high
21   confidence). To put these numbers in context, the 2006–2018 average Earth system heating is equivalent to
22   approximately 20 times the rate of global energy consumption in 2018 1.
24   Consistent with AR5 (Rhein et al., 2013), ocean warming dominates the changes in total Earth system
25   heating (high confidence), accounting for 91% of the observed change for all periods considered (Table 7.1).
26   The contributions from the other components across all periods are approximately 5% from land heating, 3%
27   for cryosphere heating and 1% associated with warming of the atmosphere (high confidence). The assessed
28   percentage contributions are similar to the recent study by von Schuckmann et al. (2020) and the total
29   heating rates are consistent within the assessed uncertainties. Cross-validation of heating rates based on
30   satellite and in situ observations (Section and closure of the global sea-level budget using consistent
31   datasets (Cross-Chapter Box 9.1; Chapter 9, Table 9.5) strengthen scientific confidence in the assessed
32   changes in the global energy inventory relative to AR5.
35       Changes in Earth’s surface energy budget
37   AR5 (Hartmann et al., 2013) reported pronounced changes in multi-decadal records of in situ observations of
38   surface solar radiation, including a widespread decline between the 1950s and 1980s, known as “global
39   dimming”, and a partial recovery thereafter, termed “brightening” (see also Chapter 12, Section 12.4). Over
40   the past decades, these changes have interacted with closely-related elements of climate change, such as
41   global and regional warming rates (Li et al., 2016b; Wild, 2016; Du et al., 2017; Zhou et al., 2018a), glacier
42   melt (Ohmura et al., 2007; Huss et al., 2009), the intensity of the global water cycle (Wild, 2012) and
43   terrestrial carbon uptake (Mercado et al., 2009). These observed changes have also been used as emergent
44   constraints to quantify aerosol effective radiative forcing (see Section
46   Since AR5, additional evidence for dimming and/or subsequent brightening up to several percent per decade,
47   based on direct surface observations, has been documented in previously less studied areas of the globe, such
48   as in Iran, Bahrain, Tenerife, Hawaii, the Taklaman desert and the Tibetan Plateau (Elagib and Alvi, 2013;
49   You et al., 2013; Garcia et al., 2014; Longman et al., 2014; Rahimzadeh et al., 2015). Strong decadal trends
50   in surface solar radiation remain evident after careful data quality assessment and homogenization of long-

     1, accessed 13 April 2021
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 1   term records (Sanchez-Lorenzo et al., 2013; Manara et al., 2015; Sanchez-Lorenzo et al., 2015; Wang et al.,
 2   2015; Li et al., 2016b; Manara et al., 2016; Wang and Wild, 2016; He et al., 2018b; Yang et al., 2018).
 3   Since AR5, new studies on the potential effects of urbanization on solar radiation trends indicate that these
 4   effects are generally small, with the exception of some specific sites in Russia and China (Wang et al., 2014;
 5   Imamovic et al., 2016; Tanaka et al., 2016). Also, surface-based solar radiation observations have been
 6   shown to be representative over large spatial domains of up to several degrees latitude/longitude on monthly
 7   and longer timescales (Hakuba et al., 2014; Schwarz et al., 2018). Thus, there is high confidence that the
 8   observed dimming between the 1950s and 1980s and subsequent brightening are robust and do not arise from
 9   measurement artefacts or localised phenomena.
11   As noted in AR5 (Hartmann et al., 2013) and supported by recent studies, the trends in surface solar
12   radiation are less spatially coherent since the beginning of the 21st century, with evidence for continued
13   brightening in parts of Europe and the USA, some stabilization in China and India, and dimming in other
14   areas (Augustine and Dutton, 2013; Sanchez-Lorenzo et al., 2015; Manara et al., 2016; Soni et al., 2016;
15   Wang and Wild, 2016; Jahani et al., 2018; Pfeifroth et al., 2018; Yang et al., 2018; Schwarz et al., 2020).
16   The CERES-EBAF satellite-derived dataset of surface solar radiation (Kato et al., 2018) does not indicate a
17   globally significant trend over the short period 2001–2012 (Zhang et al., 2015), whereas a statistically
18   significant increase in surface solar radiation of +3.4 W m−2 per decade over the period 1996–2010 has been
19   found in the Satellite Application Facility on Climate Monitoring (CM SAF) record of the geostationary
20   satellite Meteosat, which views Europe, Africa and adjacent ocean (Posselt et al., 2014).
22   Since AR5 there is additional evidence that strong decadal changes in surface solar radiation have occurred
23   also under cloud-free conditions, as shown for long term observational records in Europe, USA, China, India
24   and Japan (Xu et al., 2011; Gan et al., 2014; Manara et al., 2016; Soni et al., 2016; Tanaka et al., 2016;
25   Kazadzis et al., 2018; Li et al., 2018a; Yang et al., 2019; Wild et al., 2021). This suggests that changes in the
26   composition of the cloud-free atmosphere, primarily in aerosols, contributed to these variations, particularly
27   since the second half of the 20th century (Wild, 2016). Water vapour and other radiatively active gases seem
28   to have played a minor role (Wild, 2009; Mateos et al., 2013; Posselt et al., 2014; Yang et al., 2019). For
29   Europe and East Asia, modelling studies also point to aerosols as an important factor for dimming and
30   brightening by comparing simulations that include/exclude variations in anthropogenic aerosol and aerosol-
31   precursor emissions (Golaz et al., 2013; Nabat et al., 2014; Persad et al., 2014; Folini and Wild, 2015;
32   Turnock et al., 2015; Moseid et al., 2020). Moreover, decadal changes in surface solar radiation have often
33   occurred in line with changes in anthropogenic aerosol emissions and associated aerosol optical depth
34   (Streets et al., 2006; Wang and Yang, 2014; Storelvmo et al., 2016; Wild, 2016; Kinne, 2019). However,
35   further evidence for the influence of changes in cloudiness on dimming and brightening is emphasized in
36   some studies (Augustine and Dutton, 2013; Parding et al., 2014; Stanhill et al., 2014; Pfeifroth et al., 2018;
37   Antuña-Marrero et al., 2019). Thus, the contribution of aerosol and clouds to dimming and brightening is
38   still debated. The relative influence of cloud-mediated aerosol effects versus direct aerosol radiative effects
39   on dimming and brightening in a specific region may depend on the prevailing pollution levels (Wild, 2016;
40   Section 7.3.3).
42   ESMs and reanalyses often do not reproduce the full extent of observed dimming and brightening (Wild and
43   Schmucki, 2011; Allen et al., 2013; Zhou et al., 2017a; Storelvmo et al., 2018; Moseid et al., 2020; Wohland
44   et al., 2020), potentially pointing to inadequacies in the representation of aerosol mediated effects or related
45   emission data. The inclusion of assimilated aerosol optical depth inferred from satellite retrievals in the
46   MERRA2 reanalysis (Buchard et al., 2017; Randles et al., 2017) helps to improve the accuracy of the
47   simulated surface solar radiation changes in China (Feng and Wang, 2019). However, non-aerosol related
48   deficiencies in model representations of clouds and circulation, and/or an underestimation of natural
49   variability, could further contribute to the lack of dimming and brightening in ESMs (Wild, 2016; Storelvmo
50   et al., 2018).
52   AR5 reported evidence for an increase in surface downward thermal radiation based on different studies
53   covering in total 1964–2008, in line with expectation from an increased radiative forcing from greenhouse
54   gases and the warming and moistening of the atmosphere. Updates of the longest observational records from
55   the Baseline Surface Radiation Network continue to show an increase at the majority of the sites, in line with
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 1   an overall increase predicted by ESMs on the order of 2 W m-2 decade-1 (Wild, 2016). Upward longwave
 2   radiation at the surface is rarely measured but expected to have increased over the same period due to rising
 3   surface temperatures.
 5   Turbulent fluxes of latent and sensible heat are also an important part of the surface energy budget (Figure
 6   7.2). Large uncertainties in measurements of surface turbulent fluxes continue to prevent the determination
 7   of their decadal changes. Nevertheless, over the ocean, reanalysis-based estimates of linear trends from 1948
 8   to 2008 indicate high spatial variability and seasonality. Increases in magnitudes of 4 to 7 W m-2 decade-1 for
 9   latent heat and 2 to 3 W m-2 decade-1 for sensible heat in the western boundary current regions are mostly
10   balanced by decreasing trends in other regions (Gulev and Belyaev, 2012). Over land, the terrestrial latent
11   heat flux is estimated to have increased in magnitude by 0.09 W m-2 decade-1 from 1989 to 1997, and
12   subsequently decreased by 0.13 W m-2 decade-1 from 1998 to 2005 due to soil moisture limitation mainly in
13   the Southern Hemisphere (derived from Mueller et al. (2013)). These trends are small in comparison to the
14   uncertainty associated with satellite-derived and in-situ observations, as well as from land surface models
15   forced by observations and atmospheric reanalyses. Ongoing advances in remote sensing of
16   evapotranspiration from space (Mallick et al., 2016; Fisher et al., 2017; McCabe et al., 2017b, 2017a), as
17   well as terrestrial water storage (Rodell et al., 2018) may contribute to future constraints on changes in latent
18   heat flux.
20   In summary, since AR5, multidecadal trends in surface solar radiation up to several percent per decade have
21   been detected at many more locations also in remote areas. There is high confidence that these trends are
22   widespread, and not localised phenomena or measurement artefacts. The origin of these trends is not fully
23   understood, although there is evidence that anthropogenic aerosols have made a substantial contribution
24   (medium confidence). There is medium confidence that downward and upward thermal radiation has
25   increased since the 1970s, while there remains low confidence in the trends in surface sensible and latent
26   heat.
29   [START BOX 7.2 HERE]
31   BOX 7.2:     The Global Energy Budget
33   This box assesses the present knowledge of the global energy budget for the period 1971–2018, i.e. the
34   balance between radiative forcing, the total climate feedback and observations of the changes in the global
35   energy inventory (Box 7.2, Figure 1a, d).
37   The net ERF of the Earth system since 1971 has been positive (Box 7.2, Figure 1b, e; Section 7.3), mainly as
38   a result of increases in atmospheric greenhouse gas concentrations (Chapter 2, Section 2.2.8 and Section
39   7.3.2). The ERF of these positive forcing agents have been partly offset by that of negative forcing agents,
40   primarily due to anthropogenic aerosols (Section 7.3.3), which dominate the overall uncertainty. The net
41   energy inflow to the Earth system from ERF since 1971 is estimated to be 937 ZJ (1 ZJ = 1021 J) with a likely
42   range of 644 to 1259 ZJ (Box 7.2, Figure 1b).
44   The ERF-induced heating of the climate system results in increased thermal radiation to space via the Planck
45   response, but the picture is complicated by a variety of climate feedbacks (Box 7.1; Section 7.4.2) that also
46   influence Earth’s radiative response (Box 7.2, Figure 1c). The total radiative response is estimated by
47   multiplying the assessed net feedback parameter, α, from process-based evidence (Section 7.4.2, Table 7.10)
48   with the observed GSAT change for the period (Chapter 2, Cross Chapter Box 2.3) and time-integrating
49   (Box 7.2, Figure 1c). The net energy outflow from the Earth system associated with the integrated radiative
50   response 1971 is estimated to be 621 ZJ with a likely range of 419 to 823 ZJ. Assuming a pattern effect
51   (Section 7.4.4) on α of -0.5 W m-2 C-1 would lead to a systematically larger energy outflow by about 250 ZJ.
53   Combining the likely range of integrated radiative forcing (Box 7.2, Figure 1b) with the central estimate of
54   integrated radiative response (Box 7.2, Figure 1c) gives a central estimate and likely range of 340 [47 to 662]
55   ZJ (Box 7.2, Figure 1f). Combining the likely range of integrated radiative response with the central estimate
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 1   of integrated radiative forcing gives a likely range of 340 [147 to 527] ZJ (Box 7.2, Figure 1f). Both
 2   calculations yield an implied energy gain in the climate system that is consistent with an independent
 3   observation-based assessment of the increase in the global energy inventory expressed relative to the
 4   estimated 1850-1900 Earth energy imbalance (Box 7.2, Figure 1a; Section 7.5.2) with a central estimate and
 5   very likely range of 284 [96 to 471] ZJ (high confidence) (Box 7.2, Figure 1d; Table 7.1). Estimating the total
 6   uncertainty associated with radiative forcing and radiative response remains a scientific challenge and
 7   depends on the degree of correlation among the two (Box 7.2, Figure 1f). However, the central estimate of
 8   observed energy change falls well with the estimated likely range assuming either correlated or uncorrelated
 9   uncertainties. Furthermore, the energy budget assessment would accommodate a substantial pattern effect
10   (Section during 1971–2018 associated with systematically larger values of radiative response (Box
11   7.2, Figure 1c), and potentially improved closure of the global energy budget. For the period 1970-2011,
12   AR5 reported that the global energy budget was closed within uncertainties (high confidence) and consistent
13   with the likely range of assessed climate sensitivity (Church et al., 2013). This report provides a more robust
14   quantitative assessment based on additional evidence and improved scientific understanding.
15   In addition to new and extended observations (Section 7.2.2), confidence in the observed accumulation of
16   energy in the Earth system is strengthened by cross-validation of heating rates based on satellite and in situ
17   observations (Section and closure of the global sea-level budget using consistent datasets (Cross-
18   Chapter Box 9.1; Chapter 9, Table 9.5). Overall, there is high confidence that the global energy budget is
19   closed for 1971–2018 with improved consistency compared to AR5
24   Box 7.2, Figure 1:   Estimates of the net cumulative energy change (ZJ = 1021 Joules) for the period 1971–2018
25                        associated with: (a) observations of changes in the Global Energy Inventory (b) Integrated
26                        Radiative Forcing; (c) Integrated Radiative Response. Black dotted lines indicate the central
27                        estimate with likely and very likely ranges as indicated in the legend. The grey dotted lines
28                        indicate the energy change associated with an estimated pre-industrial Earth energy imbalance of
29                        0.2 W m-2 (panel a) and an illustration of an assumed pattern effect of –0.5 W m–2 °C–1 (panel c).
30                        Background grey lines indicate equivalent heating rates in W m–2 per unit area of Earth’s
31                        surface. Panels (d) and (e) show the breakdown of components, as indicated in the legend, for
32                        the Global Energy Inventory and Integrated Radiative Forcing, respectively. Panel (f) shows the
33                        Global Energy Budget assessed for the period 1971–2018, i.e. the consistency between the
34                        change in the Global Energy Inventory relative to pre-industrial and the implied energy change
35                        from Integrated Radiative Forcing plus Integrated Radiative Response under a number of
36                        different assumptions, as indicated in the figure legend, including assumptions of correlated and
37                        uncorrelated uncertainties in Forcing plus Response. Shading represents the very likely range for
38                        observed energy change relative to pre-industrial and likely range for all other quantities. Forcing
39                        and Response timeseries are expressed relative to a baseline period of 1850–1900. Further
40                        details on data sources and processing are available in the chapter data table (Table 7.SM.14).
42   [END BOX 7.2, FIGURE 1 HERE]
45   [END BOX 7.2 HERE]
48   7.3   Effective radiative forcing
50   Effective radiative forcing (ERF) quantifies the energy gained or lost by the Earth system following an
51   imposed perturbation (for instance in greenhouse gases, aerosols or solar irradiance). As such it is a
52   fundamental driver of changes in the Earth’s TOA energy budget. ERF is determined by the change in the
53   net downward radiative flux at the TOA (see Box 7.1) after the system has adjusted to the perturbation but
54   excluding the radiative response to changes in surface temperature. This section outlines the methodology
55   for ERF calculations in Section 7.3.1 and then assesses the ERF due to greenhouse gases in Section 7.3.2,
56   aerosols in Section 7.3.3 and other natural and anthropogenic forcing agents in Section 7.3.4. These are
57   brought together in Section 7.3.5 for an overall assessment of the present-day ERF and its evolution over the
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 1   historical time period since 1750 until 2019. The same section also evaluates the surface temperature
 2   response to individual ERFs.
 5   7.3.1   Methodologies and representation in models; overview of adjustments
 7   As introduced in Box 7.1, AR5 (Boucher et al., 2013; Myhre et al., 2013b) recommended ERF as a more
 8   useful measure of the climate effects of a physical driver than the stratospheric-temperature-adjusted
 9   radiative forcing (SARF) adopted in earlier assessments. AR5 assessed that the ratios of surface temperature
10   change to forcing resulting from perturbations of different forcing agents were more similar between species
11   using ERF than SARF. ERF extended the SARF concept to account for not only adjustments to stratospheric
12   temperatures, but also responses in the troposphere and effects on clouds and atmospheric circulation,
13   referred to as “adjustments”. For more details see Box 7.1. Since circulation can be affected, these responses
14   are not confined to the locality of the initial perturbation (unlike the traditional stratospheric-temperature
15   adjustment).
17   This chapter defines “adjustments” as those changes caused by the forcing agent that are independent of
18   changes in surface temperature, rather than defining a specific timescale. AR5 used the terminology “rapid
19   adjustment”, but in this assessment the definition is based on the independence from surface temperature
20   rather than the rapidity. The definition of ERF in Box 7.1 aims to have a clean separation between forcing
21   (energy budget changes that are not mediated by surface temperature) and feedbacks (energy budget changes
22   that are mediated by surface temperature). This means that changes in land or ocean surface temperature
23   patterns (for instance as identified by Rugenstein et al. (2016b)) are not included as adjustments. As in
24   previous assessments (Forster et al., 2007; Myhre et al., 2013b) ERFs can be attributed simply to changes in
25   the forcing agent itself or attributed to components of emitted gases (see Chapter 6, Figure 6.12). Because
26   ERFs can include chemical and biospheric responses to emitted gases, they can be attributed to precursor
27   gases even if those gases do not have a direct radiative effect themselves. Similar chemical and biospheric
28   responses to forcing agents can also be included in the ERF in addition to their direct effects.
30   Instantaneous Radiative Forcing (IRF) is defined here as the change in the net TOA radiative flux following
31   a perturbation, excluding any adjustments. SARF is defined here as the change in the net radiative flux at
32   TOA following a perturbation including the response to stratospheric temperature adjustments. These differ
33   from AR5 where these quantities were defined at the tropopause (Myhre et al., 2013b). The net IRF values
34   will be different using the TOA definition. The net SARF values will be the same as with the tropopause
35   definition, but will have a different partitioning between the longwave and shortwave. Defining all quantities
36   at the TOA enables consistency in breaking down the ERF into its component parts.
38   The assessment of ERFs in AR5 was preliminary because ERFs were only available for a few forcing agents,
39   so for many forcing agents the report made the assumption that ERF and SARF were equivalent. A body of
40   work published since AR5 is discussed in this section that has computed ERFs across many more forcing
41   agents and models, closely examined the methods of computation, quantified the processes involved in
42   causing adjustments and examined how well ERFs predict the ultimate temperature response. This work is
43   assessed to have led to a much-improved understanding and increased confidence in the quantification of
44   radiative forcing across the Report. These same techniques allow for an evaluation of radiative forcing
45   within Earth System Models (ESMs) as a key test of their ability to represent both historical and future
46   temperature changes (Chapter 3, Section 3.3.1 and Chapter 4, Section 4.3.4).
48   The ERF for a particular forcing agent is the sum of the IRF and the contribution from the adjustments, so in
49   principle this could be constructed bottom-up by calculating the IRF and adding in the adjustment
50   contributions one-by-one or together. However, there is no simple way to derive the global tropospheric
51   adjustment terms or adjustments related to circulation changes without using a comprehensive climate model
52   (e.g., CMIP5/6). There have been two main modelling approaches used to approximate the ERF definition in
53   Box 7.1. The first approach is to use the assumed linearity (Equation 7.1) to regress the net change in the
54   TOA radiation budget (ΔN) against change in global mean surface temperature (ΔT) following a step change
55   in the forcing agent (Gregory et al., 2004; Box 7.1, Figure 1). The ERF (ΔF) is then derived from ΔN when
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 1   ΔT=0. Regression-based estimates of ERF depend on the temporal resolution of the data used (Modak et al.,
 2   2016, 2018). For the first few months of a simulation both surface temperature change and stratospheric
 3   temperature adjustment occur at the same time, leading to misattribution of the stratospheric temperature
 4   adjustment to the surface temperature feedback. Patterns of sea-surface temperature change also affect
 5   estimates of the forcing obtained by regression methods (Andrews et al., 2015). At multidecadal timescales
 6   the curvature of the relationship between net TOA radiation and surface temperature can also lead to biases
 7   in the ERF estimated from the regression method (Armour et al., 2013; Andrews et al., 2015; Knutti et al.,
 8   2017; Section 7.4). The second modelling approach to estimate ERF is to set the ΔT term in Box 7.1
 9   (Equation 7.1) to zero. It is technically difficult to constrain land surface temperatures in ESMs (Shine et al.,
10   2003; Ackerley and Dommenget, 2016; Andrews et al., 2021), so most studies reduce the ΔT term by
11   prescribing the SSTs and sea-ice concentrations in a pair of “fixed-SST” (fSST) simulations with and
12   without the change in forcing agent (Hansen et al., 2005b). An approximation to ERF (ΔFfsst) is then given
13   by the difference in ΔNfsst between the simulations. The fSST method has less noise due to internal
14   variability than the regression method. Nevertheless a 30-year fSST integration or 10 × 20-year regression
15   ensemble needs to be conducted in order to reduce the 5–95% confidence range to 0.1 W m-2 (Forster et al.,
16   2016), thus neither method is practical for quantifying the ERF of agents with forcing magnitudes of order
17   0.1 W m-2 or smaller. The internal variability in the fSST method can be further constrained by nudging
18   winds towards a prescribed climatology (Kooperman et al., 2012). This allows the determination of the ERF
19   of forcing agents with smaller magnitudes but excludes adjustments associated with circulation responses
20   (Schmidt et al., 2018). There are insufficient studies to assess whether these circulation adjustments are
21   significant.
23   Since the near-surface temperature change over land, ΔTland, is not constrained in the fSST method, this
24   response needs to be removed for consistency with the Section 7.1 definition. These changes in the near-
25   surface temperature will also induce further responses in the tropospheric temperature and water vapour that
26   should also be removed to conform with the physical definition of ERF. The radiative response to ΔTland can
27   be estimated through radiative transfer modelling in which a kernel, k, representing the change in net TOA
28   radiative flux per change in unit near-surface temperature change over land (or an approximation using land
29   surface temperature), is precomputed (Smith et al., 2018b; Richardson et al., 2019; Tang et al., 2019; Smith
30   et al., 2020a). Thus ERF ≈ ΔFfsst - k ΔTland. Since k is negative this means that ΔFfsst underestimates the ERF.
31   For 2×CO2 this term is around 0.2 W m-2 (Smith et al., 2018b, 2020a). There have been estimates of the
32   corrections due to tropospheric temperature and water vapour (Tang et al., 2019; Smith et al., 2020a)
33   showing additional radiative responses of comparable magnitude to those directly from ΔTland. An alternative
34   to computing the response terms directly is to use the feedback parameter, α, (Hansen et al., 2005b;
35   Sherwood et al., 2015; Tang et al., 2019). This gives approximately double the correction compared to the
36   kernel approach (Tang et al., 2019). The response to land surface temperature change varies with location
37   and even for GSAT change k is not expected to be the same as α (Section 7.4). One study where land-surface
38   temperatures are constrained in a model (Andrews et al., 2021) finds this constraint adds +1.0 W m-2 to ΔFfsst
39   for 4×CO2, thus confirming the need for a correction in calculations where this constraint is not applied. For
40   this assessment the correction is conservatively based only on the direct radiative response kernel to ΔTland as
41   this has a strong theoretical basis to support it. While there is currently insufficient corroborating evidence to
42   recommend including tropospheric temperature and water vapour corrections in this assessment, it is noted
43   that the science is progressing rapidly on this topic.
45   TOA radiative flux changes due to the individual adjustments can be calculated by perturbing the
46   meteorological fields in a climate model’s radiative transfer scheme (partial radiative perturbation approach)
47   (Colman, 2015; Mülmenstädt et al., 2019) or by using precomputed radiative kernels of sensitivities of the
48   TOA radiation fluxes to changes in these fields (as done for near-surface temperature change above) (Vial et
49   al., 2013; Zelinka et al., 2014; Zhang and Huang, 2014; Smith et al., 2018b, 2020a). The radiative kernel
50   approach is easier to implement through post-processing of output from multiple ESMs, whereas it is
51   recognized that the partial radiation perturbation approach gives a more accurate estimate of the adjustments
52   within the setup of a single model and its own radiative transfer code. There is little difference between using
53   a radiative kernel from the same or a different model when calculating the adjustment terms, except for
54   stratospheric temperature adjustments where it is important to have sufficient vertical resolution in the
55   stratosphere in the model used to derive the kernel (Smith et al., 2018b, 2020b).
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 2   For comparison with offline radiative transfer calculations the SARFs can be approximated by removing the
 3   adjustment terms (apart from stratospheric temperature) from the ERFs using radiative kernels to quantify
 4   the adjustment for each meteorological variable. Kernel analysis by Chung and Soden (2015) suggested a
 5   large spread in CO2 SARF across climate models, but their analysis was based on regressing variables in a
 6   coupled-ocean experiment rather than using a fSST approach which leads to a large spread due to natural
 7   variability (Forster et al., 2016). Adjustments computed from radiative kernels are shown for seven different
 8   climate drivers (using a fSST approach) in Figure 7.4. Table 7.2 shows the estimates of SARF, ΔFfsst and
 9   ERF (corrected for land surface temperature change) for 2×CO2 from the nine climate models analysed in
10   Smith et al. (2018b). The SARF shows a smaller spread over previous studies (Pincus et al., 2016; Soden et
11   al., 2018) and most estimates are within 10% of the multi-model mean and the assessment of 2×CO2 SARF
12   in Section 7.3.2 (3.75 W m-2). It is not possible from these studies to determine how much of this reduction
13   in spread is due to convergence in the model radiation schemes or the meteorological conditions of the
14   model base states; nevertheless the level of agreement in this and earlier intercomparisons gives medium
15   confidence in ESM’s ability to represent radiative forcing from CO2. The 4×CO2 CMIP6 fSST experiments
16   (Smith et al., 2020a) in Table 7.2 include ESMs with varying levels of complexity in aerosols and reactive
17   gas chemistry. The CMIP6 experimental setup allows for further climate effects of CO2 (including on
18   aerosols and ozone) depending on model complexity. The chemical effects are adjustments to CO2 but are
19   not separable from the SARF in the diagnosis in Table 7.2. In these particular models, this leads to higher
20   SARF than when only CO2 varies, however there are insufficient studies to make a formal assessment of
21   composition adjustments to CO2.
26   Table 7.2:   SARF, ΔFfsst, and ERF diagnosed from ESMs for fSST CO2 experiments. 2×CO2 data taken from fixed
27                atmospheric composition experiments (Smith et al., 2018b). 4×CO2 data taken from CMIP6 experiments
28                with interactive aerosols (and interactive gas phase chemistry in some) (Smith et al., 2020a). The
29                radiative forcings from the 4×CO2 experiments are scaled by 0.476 for comparison with 2×CO2
30                (Meinshausen et al., 2020). SARF is approximated by removing the (non-stratospheric temperature)
31                adjustment terms from the ERF. In Smith et al. (2018b) separation of temperature adjustments into
32                tropospheric and stratospheric contributions is approximate based on a fixed tropopause of 100 hPa at the
33                equator, varying linearly in latitude to 300 hPa at the poles. In Smith et al. (2020b) this separation is
34                based on the model-diagnosed tropopause. ERF is approximated by removing the response to land surface
35                temperature change from ΔFfsst. The confidence range is based on the inter-model standard deviation.
36   .
                  2 × CO2 (W m-2)                   SARF                     ΔFfsst           ERF
                  (Smith et al., 2018b)
                  HadGEM2-ES                        3.45                     3.37             3.58
                  NorESM1                           3.67                     3.50             3.70
                  GISS-E2-R                         3.98                     4.06             4.27
                  CanESM2                           3.68                     3.57             3.77
                  MIROC-SPRINTARS                   3.89                     3.62             3.82
                  NCAR-CESM1-CAM5                   3.89                     4.08             4.39
                  HadGEM3                           3.48                     3.64             3.90
                  IPSL-CM5A                         3.50                     3.39             3.61
                  MPI-ESM                           4.27                     4.14             4.38
                  NCAR-CESM1-CAM4                   3.50                     3.62             3.86
                  Multi-model Mean and              3.73 ± 0.44              3.70 ± 0.44      3.93 ± 0.48
                  5-95% confidence range
                  0.476 × 4×CO2 (W m-2)
                  (Smith et al., 2020a)
                  ACCESS-CM2                        3.56                     3.78             3.98
                  CanESM5                           3.67                     3.62             3.82
                  CESM2                             3.56                     4.24             4.48
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                  CNRM-CM6-1                        3.99                    3.81              4.01
                  CNRM-ESM2-1                       3.99                    3.77              3.94
                  EC-Earth3                                                 3.85              4.04
                  GFDL-CM4                          3.65                    3.92              4.10
                  GFDL-ESM4                         3.27                    3.68              3.85
                  GISS-E2-1-G                       3.78                    3.50              3.69
                  HadGEM3-GC31-LL                   3.61                    3.85              4.07
                  IPSL-CM6A-LR                      3.84                    3.81              4.05
                  MIROC6                            3.63                    3.48              3.69
                  MPI-ESM1-2-LR                     3.74                    3.97              4.20
                  MRI-ESM2-0                        3.76                    3.64              3.80
                  NorESM2-LM                        3.58                    3.88              4.10
                  NorESM2-MM                        3.62                    3.99              4.22
                  UKESM1-0-LL                       3.49                    3.78              4.01
                  Multi-model Mean and              3.67 ± 0.29             3.80 ± 0.30       4.00 ± 0.32
                  5-95% confidence range
 2   [END TABLE 7.2 HERE]
 7   Figure 7.4: Radiative adjustments at top of atmosphere for seven different climate drivers as a proportion of
 8               forcing. Tropospheric temperature (orange), stratospheric temperature (yellow), water vapour
 9               (blue), surface albedo (green), clouds (grey) and the total adjustment (black) is shown. For the
10               greenhouse gases (carbon dioxide, methane, nitrous oxide, CFC-12) the adjustments are expressed as a
11               percentage of SARF, whereas for aerosol, solar and volcanic forcing they are expressed as a percentage of
12               IRF. Land surface temperature response (outline red bar) is shown, but included in the definition of
13               forcing. Data from Smith et al. (2018b) for carbon dioxide and methane, Smith et al. (2018b) and Gray et
14               al. (2009) for solar, Hodnebrog et al. (2020b) for nitrous oxide and CFC-12, Smith et al. (2020a) for
15               aerosol, and Marshall et al. (2020) for volcanic. Further details on data sources and processing are
16               available in the chapter data table (Table 7.SM.14).
18   [END FIGURE 7.4 HERE]
21   ERFs have been found to yield more consistent values of GSAT change per unit forcing than SARF, i.e. 𝛼𝛼
22   shows less variation across different forcing agents (Rotstayn and Penner, 2001; Shine et al., 2003; Hansen
23   et al., 2005b; Marvel et al., 2016; Richardson et al., 2019). Having a consistent relationship between forcing
24   and response is advantageous when making climate projections using simple models (Cross-Chapter Box
25   7.1) or emission-metrics (Section 7.6). The definition of ERF used in this assessment, which excludes the
26   radiative response to land surface temperature changes, brings the α values into closer agreement than when
27   SARF is used (Richardson et al., 2019), although for individual models there are still variations particularly
28   for more geographically localised forcing agents. However, even for ERF, studies find that 𝛼𝛼 is not identical
29   across all forcing agents (Shindell, 2014; Shindell et al., 2015; Modak et al., 2018; Modak and Bala, 2019;
30   Richardson et al., 2019). Section 7.4.4 discusses the effect of different SST response patterns on 𝛼𝛼. Analysis
31   of the climate feedbacks (Kang and Xie, 2014; Gregory et al., 2016, 2020; Marvel et al., 2016; Duan et al.,
32   2018; Persad and Caldeira, 2018; Stuecker et al., 2018; Krishnamohan et al., 2019) suggests a weaker
33   feedback (i.e., less-negative 𝛼𝛼) and hence larger sensitivity for forcing of the higher latitudes (particularly the
34   Northern Hemisphere). Nonetheless, as none of these variations are robust across models, the ratio of 1/𝛼𝛼
35   from non-CO2 forcing agents (with approximately global distributions) to that from doubling CO2 is within
36   10% of unity.
38   In summary, this Report adopts an estimate of ERF based on the change in TOA radiative fluxes in the
39   absence of GSAT changes. This allows for a theoretically cleaner separation between forcing and feedbacks
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 1   in terms of factors respectively unrelated and related to GSAT change (Box 7.1). ERF can be computed from
 2   prescribed SST and sea-ice experiments after removing the TOA energy budget change associated with the
 3   land surface temperature response. In this assessment this is removed using a kernel accounting only for the
 4   direct radiative effect of the land surface temperature response. To compare these results with sophisticated
 5   high spectral resolution radiative transfer models the individual tropospheric adjustment terms can be
 6   removed to leave the SARF. SARFs for 2×CO2 calculated by ESMs from this method agree within 10% with
 7   the more sophisticated models. The new studies highlighted above suggest that physical feedback parameters
 8   computed within this framework have less variation across forcing agents. There is high confidence that an
 9   𝛼𝛼 based on ERF as defined here varies by less (less than variation 10% across a range of forcing agents with
10   global distributions), than 𝛼𝛼 based on SARF. For geographically localised forcing agents there are fewer
11   studies and less agreement between them, resulting in low confidence that ERF is a suitable estimator of the
12   resulting global mean near-surface temperature response.
15   7.3.2     Greenhouse Gases
17   High spectral resolution radiative transfer models provide the most accurate calculations of radiative
18   perturbations due to greenhouse gases (GHGs) with errors in the IRF of less than 1% (Mlynczak et al., 2016;
19   Pincus et al., 2020). They can calculate IRFs with no adjustments, or SARFs by accounting for the
20   adjustment of stratospheric temperatures using a fixed dynamical heating. It is not possible with offline
21   radiation models to account for other adjustments. The high resolution model calculations of SARF for
22   carbon dioxide, methane and nitrous oxide have been updated since AR5, which were based on Myhre et al.
23   (1998). The new calculations include the shortwave forcing from methane and updates to the water vapour
24   continuum (increasing the total SARF of methane by 25%) and account for the absorption band overlaps
25   between carbon dioxide and nitrous oxide (Etminan et al., 2016). The associated simplified expressions,
26   from a re-fitting of the Etminan et al. (2016) results by Meinshausen et al. (2020), are given in
27   Supplementary Table 7.SM.1. The shortwave contribution to the IRF of methane has been confirmed
28   independently (Collins et al., 2018). Since they incorporate known missing effects we assess the new
29   calculations as being a more appropriate representation than Myhre et al. (1998).
31   As described in Section 7.3.1, ERFs can be estimated using ESMs, however the radiation schemes in climate
32   models are approximations to high spectral resolution radiative transfer models with variations and biases in
33   results between the schemes (Pincus et al., 2015). Hence ESMs alone are not sufficient to establish ERF best
34   estimates for the well-mixed GHGs (WMGHGs). This assessment therefore estimates ERFs from a
35   combined approach that uses the SARF from radiative transfer models and adds the tropospheric adjustments
36   derived from EMSs.
38   In AR5, the main information used to assess components of ERFs beyond SARF was from Vial et al. (2013)
39   who found a near-zero non-stratospheric adjustment (without correcting for near-surface temperature
40   changes over land) in 4×CO2 CMIP5 model experiments, with an uncertainty of ±10% of the total CO2 ERF.
41   No calculations were available for other WMGHGs, so ERF was therefore assessed to be approximately
42   equal to SARF (within 10%) for all WMGHGs.
44   The effect of WMGHGs in ESMs can extend beyond their direct radiative effects to include effects on ozone
45   and aerosol chemistry and natural emissions of ozone and aerosol precursors, and in the case of CO2 to
46   vegetation cover through physiological effects. In some cases these can have significant effects on the
47   overall radiative budget changes from perturbing WMGHGs within ESMs (Myhre et al., 2013b; Zarakas et
48   al., 2020; O’Connor et al., 2021; Thornhill et al., 2021a). These composition adjustments are further
49   discussed in Chapter 6 (Section 6.4.2).
52    Carbon Dioxide
54   The SARF for CO2 has been slightly revised due to updates to spectroscopic data and inclusion of the
55   absorption band overlaps between N2O and CO2 (Etminan et al., 2016). The formulae fitting to the Etminan
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 1   et al. (2016) results in Meinshausen et al. (2020) are used. This increases the SARF due to doubling CO2
 2   slightly from 3.71 W m-2 in AR5 to 3.75 W m-2. Tropospheric responses to CO2 in fSST experiments have
 3   been found to lead to an approximate balance in their radiative effects between an increased radiative forcing
 4   due to water vapour, cloud and surface albedo adjustments and a decrease due to increased tropospheric
 5   temperature and land surface temperature response (Vial et al., 2013; Zhang and Huang, 2014; Smith et al.,
 6   2018b, 2020a; Table 7.3). The ΔFfsst includes any effects represented within the ESMs on tropospheric
 7   adjustments due to changes in evapotranspiration or leaf area (mainly affecting surface and boundary layer
 8   temperature, low cloud amount and albedo) from the CO2-physiological effects (Doutriaux-Boucher et al.,
 9   2009; Cao et al., 2010; Richardson et al., 2018b). The effect on surface temperature (negative longwave
10   response) is consistent with the expected physiological responses and needs to be removed for consistency
11   with the ERF definition. The split between surface and tropospheric temperature responses was not reported
12   in Vial et al. (2013) or Zhang and Huang (2014) but the total of surface and tropospheric temperature
13   response agrees with Smith et al. (2018b, 2020b) giving medium confidence in this decomposition.
14   Doutriaux-Boucher et al. (2009) and Andrews et al. (2021) (using the same land surface model) find a 13%
15   and 10% increase respectively in ERF due to the physiological responses to CO2. The physiological
16   adjustments are therefore assessed to make a substantial contribution to the overall tropospheric adjustment
17   for CO2 (high confidence), but there is insufficient evidence to provide a quantification of the split between
18   physiological and thermodynamic adjustments. These forcing adjustments due to the effects of CO2 on plant
19   physiology differ from the biogeophysical feedbacks due to the effects of temperature changes on vegetation
20   discussed in Section The adjustment is assumed to scale with the SARF in the absence of evidence
21   for non-linearity. The tropospheric adjustment is assessed from Table 7.3 to be +5% of the SARF with an
22   uncertainty of 5%, which is added to the Meinshausen et al. (2020) formula for SARF. Due to the agreement
23   between the studies and the understanding of the physical mechanisms there is medium confidence in the
24   mechanisms underpinning the tropospheric adjustment, but low confidence in its magnitude.
29   Table 7.3:      Adjustments to the TOA CO2 forcing due to changes in stratospheric temperature, surface and
30                   tropospheric temperatures, water vapour, clouds and surface albedo, as a fraction of the SARF. ERF is
31                   defined in this report as excluding the surface temperature response.
      Percentage        Surfac Trop.         Strat.    Surface      Water     Clouds    Troposphere       Troposphere
      of SARF           e temp temp          temp      albedo       vapour              (inc. surface)    (excl. surface)
      Vial et al.            –20%                         2%          6%       11%           –1%
      Zhang and               –23%            26%                       6%     16%           –1%
      Smith et al.       –6%       –16%       30%         3%            6%     12%           –1%               +5%
      Smith et al.       –6%       –15%       35%         3%            6%     15%           +3%               +9%
34   [END TABLE 7.3 HERE]
37   The ERF from doubling CO2 (2×CO2) from the 1750 level (278 ppm Chapter 2, Section is assessed
38   to be 3.93 ± 0.47 W m-2 (high confidence). Its assessed components are given in Table 7.4. The combined
39   spectroscopic and radiative transfer modelling uncertainties give an uncertainty in the CO2 SARF of around
40   10% or less (Etminan et al., 2016; Mlynczak et al., 2016). The overall uncertainty in CO2 ERF is assessed as
41   ±12%, as the more uncertain adjustments only account for a small fraction of the ERF (Table 7.3). The
42   2×CO2 ERF estimate is 0.2 W m-2 larger than using the AR5 formula (Myhre et al., 2013b) due to the
43   combined effects of tropospheric adjustments which were assumed to be zero in AR5. CO2 concentrations
44   have increased from 278 ppm in 1750 to 410 ppm in 2019 (Chapter 2, Section The historical ERF
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 1   estimate from CO2 is revised upwards from the AR5 value of 1.82 ± 0.38 W m-2 (1750 to 2011) to 2.16
 2   ±0.26 W m-2 (1750 to 2019) in this assessment, from a combination of the revisions described above (0.06 W
 3   m-2) and the 19 ppm rise in atmospheric concentrations between 2011 and 2019 (0.27 W m-2). The ESM
 4   estimates of 2×CO2 ERF (Table 7.2) lie within ±12% of the assessed value (apart from CESM2). The
 5   definition of ERF can also include further physiological effects for instance on dust, natural fires and
 6   biogenic emissions from the land and ocean, but these are not typically included in the modelling set up for
 7   2×CO2 ERF.
12   Table 7.4:       Assessed ERF, SARF and tropospheric adjustments to 2×CO2 change since preindustrial times compared
13                    to the AR5 assessed range (Myhre et al., 2013b). Adjustments are due to changes in tropospheric
14                    temperatures, water vapour, clouds and surface albedo and land cover and are taken from Smith et al.
15                    (2018b) and assessed as a percentage of SARF (Table 7.3). Uncertainties are based on multi-model
16                    spread in Smith et al. (2018b). Note some of the uncertainties are anticorrelated, which means that they
17                    do not sum linearly.
      2×CO2             AR5        SARF       Tropospheric   Water         Cloud         Surface       Total          ERF
      forcing           SARF/      (W m-2)    temperature    vapour        adjustment    albedo and    tropospheric   (W m-2)
                        ERF                   adjustment     adjustment    (W m-2)       land cover    adjustment
                                              (W m-2)        (W m-2)                     adjustment    (W m-2)
                                                                                         (W m-2)
      2×CO2 ERF           3.71       3.75        –0.60           0.22          0.45          0.11          0.18        3.93
      5%–95%               10%      <10%          ±6%           ±4%            ±7%           ±2%           ±7%         ±12%
      uncertainty        (SARF)
      ranges as            20%
      percentage of       (ERF)
21   [END TABLE 7.4 HERE]
24      Methane
26   The SARF for methane (CH4) has been substantially increased due to updates to spectroscopic data and
27   inclusion of the shortwave absorption (Etminan et al., 2016). Adjustments have been calculated in nine
28   climate models by Smith et al. (2018b). Since CH4 is found to absorb in the shortwave near infrared, only
29   adjustments from those models including this absorption are taken into account. For these models the
30   adjustments act to reduce the ERF because the shortwave absorption leads to tropospheric heating and
31   reductions in upper tropospheric cloud amounts. The adjustment is –14% ± 15% which counteracts much of
32   the increase in SARF identified by Etminan et al. (2016). Modak et al. (2018) also found negative forcing
33   adjustments from a methane perturbation including shortwave absorption in the NCAR CAM5 model, in
34   agreement with the above assessment. The uncertainty in the shortwave component leads to a higher
35   radiative modelling uncertainty (14%) than for CO2 (Etminan et al., 2016). When combined with the
36   uncertainty in the adjustment, this gives an overall uncertainty of ± 20%. There is high confidence in the
37   spectroscopic revision but only medium confidence in the adjustment modification. CH4 concentrations have
38   increased from 729 ppb in 1750 to 1866 ppb in 2019 (Chapter 2, Section The historical ERF
39   estimate from AR5 of 0.48 ± 0.10 W m-2 (1750 to 2011) is revised to 0.54 ± 0.11 W m-2 (1750 to 2019) in
40   this assessment from a combination of spectroscopic radiative efficiency revisions (+0.12 W m-2),
41   adjustments (–0.08 W m-2) and the 63 ppb rise in atmospheric CH4 concentrations between 2011 and 2019
42   (+0.03 W m-2). As the adjustments are assessed to be small, there is high confidence in the overall
43   assessment of ERF from methane. Increased methane leads to tropospheric ozone production and increased
44   stratospheric water vapour, so that an attribution of forcing to methane emissions gives a larger effect than
45   that directly from the methane concentration itself. This is discussed in detail in Chapter 6, Section 6.4.2 and
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 1   shown in Figure 6.12.
 4   Nitrous oxide
 6   The tropospheric adjustments to nitrous oxide (N2O) have been calculated from 5 ESMs as 7% ± 13% of the
 7   SARF (Hodnebrog et al., 2020b). This value is therefore taken as the assessed adjustment, but with low
 8   confidence. The radiative modelling uncertainty is ± 10% (Etminan et al., 2016), giving an overall
 9   uncertainty of ± 16%. Nitrous oxide concentrations have increased from 270 ppb in 1750 to 332 ppb in 2019
10   (Chapter 2, Section The historical ERF estimate from N2O is revised upwards from 0.17 ± 0.06 W
11   m-2 (1750 to 2011) in AR5 to 0.21 ± 0.03 W m-2 (1750 to 2019) in this assessment, of which 0.02 W m-2 is
12   due to the 7 ppb increase in concentrations, and 0.02 W m-2 to the tropospheric adjustment. As the
13   adjustments are assessed to be small there remains high confidence in the overall assessment.
15   Increased nitrous oxide leads to ozone depletion in the upper stratosphere which will make a positive
16   contribution to the direct ERF here (Chapter 6, Section 6.4.2, Figure 6.12) when considering emission-based
17   estimates of ERF.
20   Halogenated species
22   The stratospheric-temperature adjusted radiative efficiencies (SARF per ppb increase in concentration) for
23   halogenated compounds are reviewed extensively in Hodnebrog et al. (2020a), an update to those used in
24   AR5. Many halogenated compounds have lifetimes short enough that they can be considered short-lived
25   climate forcers (Table 6.1). As such, they are not completely “well-mixed” and their vertical distributions are
26   taken into account when determining their radiative efficiencies. The WMO (World Meteorological
27   Organization, 2018) updated the lifetimes of many halogenated compounds and these were used in
28   Hodnebrog et al. (2020a).
30   The tropospheric adjustments to chlorofluorocarbons (CFCs), specifically CFC-11 and CFC-12, have been
31   quantified as 13% ± 10% and 12% ± 14% of the SARF respectively (Hodnebrog et al., 2020b). The assessed
32   adjustment to CFCs is therefore 12 % ± 13% with low confidence due to the lack of corroborating studies.
33   There have been no calculations for other halogenated species so for these the tropospheric adjustments are
34   therefore assumed to be 0 ± 13% with low confidence. The radiative modelling uncertainties are 14% and
35   24% for compounds with lifetimes greater than and less than 5 years respectively (Hodnebrog et al., 2020a).
36   The overall uncertainty in the ERFs of halogenated compounds is therefore assessed to be 19% and 26%
37   depending on the lifetime. The ERF from CFCs is slowly decreasing, but this is compensated for by the
38   increased forcing from the replacement species (HCFCs and HFCs). The ERF from HFCs has increased by
39   0.028 ± 0.05 W m-2. Thus, the concentration changes mean that the total ERF from halogenated compounds
40   has increased since AR5 from 0.360 ± 0.036 W m-2 to 0.408 ± 0.078 W m-2 (Table 7.5). Of this 0.034 W m-2
41   is due to increased radiative efficiencies and tropospheric adjustments, and 0.014 W m-2 due to increases in
42   concentrations. As the adjustments are assessed to be small there remains high confidence in the overall
43   assessment.
45   Halogenated compounds containing chlorine and bromine lead to ozone depletion in the stratosphere which
46   will reduce the associated ERF (Morgenstern et al., 2020). Chapter 6, Section 6.4 and Figure 6.12 assess the
47   ERF contributions due to the chemical effects of reactive gases.
50   Ozone
52   Estimates of the pre-industrial to present-day tropospheric ozone radiative forcing are based entirely on
53   models. The lack of pre-industrial ozone measurements prevents an observational determination. There have
54   been limited studies of ozone ERFs (MacIntosh et al., 2016; Xie et al., 2016; Skeie et al., 2020). Skeie et al.
55   (2020) found little net contribution to the ERF from tropospheric adjustment terms for 1850-2000 change in
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 1   ozone (tropospheric and stratospheric ozone combined), although MacIntosh et al. (2016) suggested that
 2   increases in stratospheric or upper tropospheric ozone reduces high cloud and increases low cloud, whereas
 3   an increase in lower tropospheric ozone reduces low cloud. Further studies suggest that changes in
 4   circulation due to decreases in stratospheric ozone affect Southern Hemisphere clouds and the atmospheric
 5   levels of sea salt aerosol that would contribute additional adjustments, possibly of comparable magnitude to
 6   the SARF from stratospheric ozone depletion (Grise et al., 2013, 2014, Xia et al., 2016, 2020). ESM
 7   responses to changes in ozone depleting substances (ODS) in CMIP6 show a much more negative ERF than
 8   would be expected from offline calculations of SARF (Morgenstern et al., 2020; Thornhill et al., 2021b)
 9   again suggesting a negative contribution from adjustments. However there is insufficient evidence available
10   to quantify this effect.
12   Without sufficient information to assess whether the ERFs differ from SARF, this assessment relies on
13   offline radiative transfer calculations of SARF for both tropospheric and stratospheric ozone. Checa-Garcia
14   et al. (2018) found SARF of 0.30 W m-2 for changes in ozone (1850–1860 to 2009–2014). These were based
15   on precursor emissions and ODS concentrations from the Coupled Chemistry Model Initiative (CCMI)
16   project (Morgenstern et al., 2017). Skeie et al. (2020) calculated an ozone SARF of 0.41 ± 0.12 W m-2 (1850
17   to 2010) (from five climate models and one chemistry transport model) using CMIP6 precursor emissions
18   and ODS concentrations (excluding models without fully interactive ozone chemistry and one model with
19   excessive ozone depletion). The ozone precursor emissions are higher in CMIP6 than in CCMI which
20   explains much of the increase compared to Checa-Garcia et al. (2018).
22   Previous assessments have split the ozone forcing into tropospheric and stratospheric components. This does
23   not correspond to the division between ozone production and ozone depletion and is sensitive to the choice
24   of tropopause (Myhre et al., 2013b) (high confidence). The contributions to total SARF in CMIP6 (Skeie et
25   al., 2020) are 0.39 ± 0.07 and 0.02 ± 0.07 W m-2 for troposphere and stratosphere respectively (using a 150
26   ppb ozone tropopause definition). This small positive (but with uncertainty encompassing negative values)
27   stratospheric ozone SARF is due to contributions from ozone precursors to lower stratospheric ozone and
28   some of the CMIP6 models showing ozone depletion in the upper stratosphere, where depletion contributes a
29   positive radiative forcing (medium confidence).
31   As there is insufficient evidence to quantify adjustments, for total ozone the assessed central estimate for
32   ERF is assumed to be equal to SARF (low confidence) and follows Skeie et al. (2020) since that study uses
33   the most recent emission data. The dataset is extended over the entire historical period following Skeie et al.
34   (2020) with a SARF for 1750 to 1850 of 0.03 W m-2 and for 2010 to 2018 of 0.03 W m-2, to give 0.47 [0.24
35   to 0.70] W m-2 for 1750 to 2019. This maintains the 50% uncertainty (5%–95% range) from AR5 which is
36   largely due to the uncertainty in pre-industrial emissions (Rowlinson et al., 2020). There also high
37   confidence that this range includes uncertainty due to the adjustments. The CMIP6 SARF is more positive
38   than the AR5 value of 0.31 W m-2 for the period 1850 to 2011 (Myhre et al., 2013b) which was based on the
39   Atmospheric Chemistry and Climate Intercomparison Project (ACCMIP) (Shindell et al., 2013). The
40   assessment is sensitive to the assumptions on precursor emissions used to drive the models, which are larger
41   in CMIP6 than ACCMIP.
43   In summary, although there is insufficient evidence to quantify adjustments, there is high confidence in the
44   assessed range of ERF for ozone changes over the 1750 to 2019 period, giving an assessed ERF of 0.47
45   [0.24 to 0.70] W m-2.
48   Stratospheric water vapour
50   This section considers direct anthropogenic effects on stratospheric water vapour by oxidation of methane.
51   Since AR5 the SARF from methane-induced stratospheric water vapour changes has been calculated in two
52   models (Winterstein et al., 2019; O’Connor et al., 2021), both corresponding to 0.09 W m-2 (1850 to 2014,
53   by scaling the Winterstein et al., 2019 study). This is marginally larger than the AR5 assessed value of
54   0.07±0.05 W m-2 (Myhre et al., 2013b). However, O’Connor et al. (2021) found the ERF to be
55   approximately zero due to a negative cloud adjustment. Wang and Huang (2020) quantified the adjustment
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 1   terms to a stratospheric water vapour change equivalent to that from a 2×CO2 warming (which has different
 2   vertical profile, though also largest in the lower stratosphere). They found that the ERF was less than 50% of
 3   the SARF due to high cloud decrease and upper tropospheric warming. The assessed ERF is therefore
 4   0.05±0.05 W m-2 with a lower limit reduced to zero and the central value and upper limit reduced to allow
 5   for adjustment terms. This still encompasses the two recent SARF studies. There is medium confidence in the
 6   SARF from agreement with the recent studies and AR5. There is low confidence in the adjustment terms.
 8   Stratospheric water vapour may also change as an adjustment to species that warm or cool the upper
 9   troposphere-lower stratosphere region (Forster and Joshi, 2005; Stuber et al., 2005), in which case it should
10   be included as part of the ERF for that compound. Changes in GSAT are also associated with changes in
11   stratospheric water vapour as part of the water vapour climate feedback (Section
14      Synthesis
16   The GHGs (excluding ozone and stratospheric water vapour) ERF over 1750 to 2019 is assessed to be 3.32 ±
17   0.29 W m-2. It has increased by 0.49 W m-2 compared to AR5 (reference year 2011) (high confidence). Most
18   of this has been due to an increase in CO2 concentration since 2011 [0.27 ± 0.03 W m-2], with concentration
19   increases in CH4, N2O and halogenated compounds adding 0.02, 0.02 and 0.01 W m-2 respectively (Table
20   7.5). Changes in the radiative efficiencies (including adjustments) of CO2, CH4, N2O and halogenated
21   compounds have increased the ERF by an additional 0.15 W m-2 compared to the AR5 values (high
22   confidence). Note that the ERFs in this section do not include chemical effects of GHGs on production or
23   destruction of ozone or aerosol formation (see Chapter 6, Section 6.2.2). The ERF for ozone is considerably
24   increased compared to AR5 due to an increase in the assumed ozone precursor emissions in CMIP6
25   compared to CMIP5, and better accounting for the effects of both ozone precursors and ODSs in the
26   stratosphere. The ERF for stratospheric water vapour is slightly reduced. The combined ERF from ozone and
27   stratospheric water vapour has increased since AR5 by 0.10 ± 0.50 W m-2 (high confidence), although the
28   uncertainty ranges still include the AR5 values.
33   Table 7.5:     Present-day mole fractions in ppt (pmol mol–1) (except where specified) and ERF (in W m–2) for the
34                  WMGHGs. Data taken from Chapter 2, Section 2.2.3. The data for 2011 (the time of the AR5 estimates)
35                  are also shown. Some of the concentrations vary slightly from those reported in AR5 owing to averaging
36                  different data sources. Individual species are reported where 1750-2019 ERF is at least 0.001 W m-2.
37                  Radiative efficiencies for the minor gases are given in Supplementary Table 7.SM.7. Uncertainties in the
38                  ERF for all gases are dominated by the uncertainties in the radiative efficiencies. Tabulated global mixing
39                  ratios of all well mixed GHGs and ERFs from 1750-2019 are provided in Annex III.
                                                                         ERF with respect to         ERF with respect to
                                                                         1850                        1750
                              2019      2011       1850       1750       2019           2011         2019          2011
      CO2 (ppm)               409.9     390.5      285.5      278.3      2.012±0.241    1.738        2.156±0.259 1.882
      CH4 (ppb)               1866.3    1803.3     807.6      729.2      0.496±0.099    0.473        0.544±0.109 0.521
      N2O (ppb)               332.1     324.4      272.1      270.1      0.201±0.030    0.177        0.208±0.031 0.184
      HFC-134a                107.6     62.7       0.         0.         0.018          0.010        0.018         0.010
      HFC-23                  32.4      24.1       0.         0.         0.006          0.005        0.006         0.005
      HFC-32                  20.0      4.7        0.         0.         0.002          0.001        0.002         0.001
      HFC-125                 29.4      10.3       0.         0.         0.007          0.002        0.007         0.002
      HFC-143a                24.0      12.0       0.         0.         0.004          0.002        0.004         0.002
      SF6                     10.0      7.3        0.         0.         0.006          0.004        0.006         0.004
      CF4                     85.5      79.0       34.0       34.0       0.005          0.004        0.005         0.004
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      C2F6                 4.8          4.2     0.      0.          0.001          0.001    0.001           0.001
      CFC-11               226.2        237.3   0.      0.          0.066          0.070    0.066           0.070
      CFC-12               503.1        528.6   0.      0.          0.180          0.189    0.180           0.189
      CFC-113              69.8         74.6    0.      0.          0.021          0.022    0.021           0.022
      CFC-114              16.0         16.3    0.      0.          0.005          0.005    0.005           0.005
      CFC-115              8.7          8.4     0.      0.          0.002          0.002    0.002           0.002
      HCFC-22              246.8        213.2   0.      0.          0.053          0.046    0.053           0.046
      HCFC-141b            24.4         21.4    0.      0.          0.004          0.003    0.004           0.003
      HCFC-142b            22.3         21.2    0.      0.          0.004          0.004    0.004           0.004
      CCl4                 77.9         86.1    0.      0.          0.013          0.014    0.013           0.014
      Sum of CFCs                                                   0.276          0.289    0.276           0.289
      Sum of HCFCs                                                  0.061          0.053    0.061           0.053
      Sum of HFCs                                                   0.040          0.022    0.040           0.022
      Sum of                                                        0.408±0.078    0.394    0.408±0.078     0.394
         Total                                                      3.118±0.258    2.782    3.317±0.278     2.981
 3   [END TABLE 7.5 HERE]
 6   7.3.3   Aerosols
 8   Anthropogenic activity, and particularly burning of biomass and fossil fuels, has led to a substantial increase
 9   in emissions of aerosols and their precursors, and thus to increased atmospheric aerosol concentrations since
10   pre-industrial times (Chapter 2, Section 2.2.6 and Figure 2.9; Chapter 6, Section 6.3.5). This is particularly
11   true for sulphate and carbonaceous aerosols (Chapter 6, Section 6.3.5). This has in turn led to changes in the
12   scattering and absorption of incoming solar radiation, and also affected cloud micro- and macro-physics and
13   thus cloud radiative properties. Aerosol changes are heterogeneous in both space and time and have impacted
14   not just Earth’s radiative energy budget but also air quality (Chapter 6, Section 6.1.1 and 6.6.2). Here, the
15   assessment is focused exclusively on the global mean effects of aerosols on Earth’s energy budget, while
16   regional changes and changes associated with individual aerosol compounds are assessed in Chapter 6,
17   Sections 6.4.1 and 6.4.2.
19   Consistent with the terminology introduced in Box 7.1, the ERF due to changes from direct aerosol-radiation
20   interactions (ERFari) is equal to the sum of the instantaneous TOA radiation change (IRFari) and the
21   subsequent adjustments. Likewise, the ERF following interactions between anthropogenic aerosols and
22   clouds (ERFaci, referred to as “indirect aerosol effects” in previous assessment reports) can be divided into
23   an instantaneous forcing component (IRFaci) due to changes in cloud droplet (and indirectly also ice crystal)
24   number concentrations and sizes, and the subsequent adjustments of cloud water content or extent. While
25   these changes are thought to be induced primarily by changes in the abundance of cloud condensation nuclei
26   (CCN), a change in the number of ice nucleating particles (INPs) in the atmosphere may also have occurred,
27   and thereby contributed to ERFaci by affecting properties of mixed-phase and cirrus (ice) clouds. In the
28   following, an assessment of IRFari and ERFari (Section focusing on observation-based (Section
29 as well as model-based (Section evidence is presented. The same lines of evidence are
30   presented for IRFaci and ERFaci in Section These lines of evidence are then compared with TOA
31   energy budget constraints on the total aerosol ERF (Section before an overall assessment of the total
32   aerosol ERF is given in Section For the model-based evidence, all estimates are generally valid for
33   2014 relative to 1750 (the time period spanned by CMIP6 historical simulations), while for observation-
34   based evidence the assessed studies use slightly different end points, but they all generally fall within a
35   decade (2010-2020).
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 2   Aerosol-radiation interactions
 4   Since AR5, deeper understanding of the processes that govern aerosol radiative properties, and thus IRFari,
 5   has emerged. Combined with new insights into adjustments to aerosol forcing, this progress has informed
 6   new observation- and model-based estimates of ERFari and associated uncertainties.
 9 Observation-based lines of evidence
10   Estimating IRFari requires an estimate of industrial-era changes in Aerosol Optical Depth (AOD) and
11   absorption AOD, which are often taken from global aerosol model simulations. Since AR5, updates to
12   methods of estimating IRFari based on aerosol remote sensing or data-assimilated reanalyses of atmospheric
13   composition have been published. Ma et al. (2014) applied the method of Quaas et al. (2008) to updated
14   broadband radiative flux measurements from CERES, MODIS-retrieved AODs, and modelled anthropogenic
15   aerosol fractions to find a clear-sky IRFari of −0.6 W m−2. This would translate into an all-sky estimate of
16   about −0.3 W m−2 based on the clear-to-all-sky ratio implied by Kinne (2019). Rémy et al. (2018) applied the
17   methods of Bellouin et al. (2013b) to the reanalysis by the Copernicus Atmosphere Monitoring Service,
18   which assimilates MODIS total AOD. Their estimate of IRFari varies between −0.5 W m-2 and −0.6
19   W m−2 over the period 2003–2018, and they attribute those relatively small variations to variability in
20   biomass-burning activity. Kinne (2019) provided updated monthly total AOD and absorption AOD
21   climatologies, obtained by blending multi-model averages with ground-based sun-photometer retrievals, to
22   find a best estimate of IRFari of −0.4 W m−2. The updated IRFari estimates above are all scattered around the
23   midpoint of the IRFari range of −0.35 ± 0.5 W m−2 assessed by AR5 (Boucher et al., 2013).
25   The more negative estimate of Rémy et al. (2018) is due to neglecting a small positive contribution from
26   absorbing aerosols above clouds and obtaining a larger anthropogenic fraction than Kinne (2019). Rémy et
27   al. (2018) also did not update their assumptions on black carbon anthropogenic fraction and its contribution
28   to absorption to reflect recent downward revisions (Section Kinne (2019) made those revisions, so
29   more weight is given to that study to assess the central estimate of satellite-based IRFari to be only slightly
30   stronger than reported in AR5 at –0.4 W m-2. While uncertainties in the anthropogenic fraction of total AOD
31   remain, improved knowledge of anthropogenic absorption results in a slightly narrower very likely range
32   here than in AR5. The assessed best estimate and very likely IRFari range from observation-based evidence
33   is therefore –0.4 ± 0.4 W m-2 , but with medium confidence due to the limited number of studies available.
36 Model-based lines of evidence
37   While observation-based evidence can be used to estimate IRFari, global climate models are needed to
38   calculate the associated adjustments and the resulting ERFari, using the methods described in Section 7.3.1.
39   A range of developments since AR5 affect model-based estimates of IRFari. Global emissions of most major
40   aerosol compounds and their precursors are found to be higher in the current inventories, and with increasing
41   trends. Emissions of the sulphate precursor SO2 are a notable exception; they are similar to those used in
42   AR5 and approximately time-constant in recent decades (Hoesly et al., 2018). Myhre et al. (2017) showed, in
43   a multi-model experiment, that the net result of these revised emissions is an IRFari trend that is relatively
44   flat in recent years (post-2000), a finding confirmed by a single-model study by Paulot et al. (2018).
46   In AR5, the assessment of the black carbon (BC) contribution to IRFari was markedly strengthened in
47   confidence by the review by Bond et al. (2013), where a key finding was a perceived model underestimate of
48   atmospheric absorption when compared to Aeronet observations (Boucher et al., 2013). This assessment has
49   since been revised considering new knowledge on the effect of the temporal resolution of emission
50   inventories (Wang et al., 2016), the representativeness of Aeronet sites (Wang et al., 2018), issues with
51   comparing absorption retrieval to models (Andrews et al., 2017a), and the ageing (Peng et al., 2016), lifetime
52   (Lund et al., 2018b) and average optical parameters (Zanatta et al., 2016) of BC. Consistent with these
53   updates, Lund et al. (2018a) estimated the net IRFari in 2014 (relative to 1750) to be –0.17 W m-2, using
54   CEDS emissions (Hoesly et al., 2018) as input to a chemical transport model. They attributed the weaker
55   estimate relative to AR5 (–0.35 ± 0.5 W m-2; Myhre et al., 2013a) to stronger absorption by organic aerosol,
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 1   updated parameterization of BC absorption, and slightly reduced sulphate cooling. Broadly consistent with
 2   Lund et al. (2018a), another single-model study by Petersik et al. (2018) estimated an IRFari of –0.19 W m-2.
 3   Another single-model study by Lurton et al. (2020) reported a more negative estimate at –0.38 W m-2, but is
 4   given less weight here because the model lacked interactive aerosols and instead used prescribed
 5   climatological aerosol concentrations.
 7   The above estimates support a less negative central estimate and a slightly narrower range compared to those
 8   reported for IRFari from ESMs in AR5 of –0.35 [–0.6 to –0.13] W m-2. The assessed central estimate and
 9   very likely IRFari range from model-based evidence alone is therefore –0.2 ± 0.2 W m-2 for 2014 relative to
10   1750, with medium confidence due to the limited number of studies available. Revisions due to stronger
11   organic aerosol absorption, further developed BC parameterizations and somewhat reduced sulphate
12   emissions in recent years.
14   Since AR5 considerable progress has been made in the understanding of adjustments in response to a wide
15   range of climate forcings, as discussed in Section 7.3.1. The adjustments in ERFari are principally caused by
16   cloud changes, but also by lapse rate and atmospheric water vapour changes, all mainly associated with
17   absorbing aerosols like BC. Stjern et al. (2017) found that for BC, about 30% of the (positive) IRFari is
18   offset by adjustments of clouds (specifically, an increase in low clouds and decrease in high clouds) and
19   lapse rate, by analysing simulations by five Precipitation Driver Response Model Intercomparison Project
20   (PDRMIP) models. Smith et al. (2018b) considered more models participating in PDRMIP and suggested
21   that about half the IRFari was offset by adjustments for BC, a finding generally supported by single-model
22   studies (Takemura and Suzuki, 2019; Zhao and Suzuki, 2019). Thornhill et al. (2021b) also reported a
23   negative adjustment for BC based on AerChemMIP (Collins et al., 2017) but found it to be somewhat
24   smaller in magnitude than those reported in Smith et al. (2018b) and Stjern et al. (2017). In contrast, Allen et
25   al. (2019) found a positive adjustment for BC and suggested that most models simulate negative adjustment
26   for BC because of a misrepresentation of aerosol atmospheric heating profiles.
28   Zelinka et al. (2014) used the Approximate Partial Radiation Perturbation technique to quantify the ERFari
29   in 2000 relative to 1860 in nine CMIP5 models; they estimated the ERFari (accounting for a small
30   contribution from longwave radiation) to be –0.27 ± 0.35 W m-2. However, it should be noted that in Zelinka
31   et al. (2014) adjustments of clouds caused by absorbing aerosols through changes in the thermal structure of
32   the atmosphere (termed the semidirect effect of aerosols in AR5) are not included in ERFari but in ERFaci.
33   The corresponding estimate emerging from the Radiative Forcing Model Intercomparison Project (RFMIP,
34   Pincus et al., 2016) is –0.25 ± 0.40 W m-2 (Smith et al., 2020a), which is generally supported by single-
35   model studies published post-AR5 (Zhang et al., 2016; Fiedler et al., 2017; Nazarenko et al., 2017; Zhou et
36   al., 2017c; Grandey et al., 2018; Zhou et al., 2018b). A 5% inflation is applied to the CMIP5 and CMIP6
37   fixed-SST derived estimates of ERFari from Zelinka et al. (2014) and (Smith et al., 2020a) to account for
38   land surface cooling (Table 7.6). Based on the above, ERFari from model-based evidence is assessed to be –
39   0.25 ± 0.25 W m-2.
42 Overall assessment of IRFari and ERFari
43   The observation-based assessment of IRFari of –0.4 ± 0.4 W m-2 and the corresponding model-based
44   assessment of –0.2 ± 0.2 W m-2 can be compared to the range of –0.45 W m-2 to –0.05 W m-2 that emerged
45   from a comprehensive review in which an observation-based estimate of anthropogenic AOD was combined
46   with model-derived ranges for all relevant aerosol radiative properties (Bellouin et al., 2019). Based on the
47   above, IRFari is assessed to be –0.25 ± 0.2 W m-2 (medium confidence).
49   ERFari from model-based evidence is –0.25 ± 0.25 W m-2, which suggests a small negative adjustment
50   relative to the model-based IRFari estimate, consistent with the literature discussed in Adding this
51   small adjustment to our assessed IRFari estimate of –0.25 W m-2, and accounting for additional uncertainty
52   in the adjustments, ERFari is assessed to –0.3 ± 0.3 (medium confidence). This assessment is consistent with
53   the 5% to 95 % confidence range for ERFari in Bellouin et al. (2019) of –0.71 to –0.14 W m-2, and notably
54   implies that it is very likely that ERFari is negative. Differences relative to Bellouin et al. (2019) reflect the
55   range of estimates in Table 7.6 and the fact that a more negative ERFari than -0.6 W m-2 would require
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 1   adjustments that considerably augment the assessed IRFari, which is not supported by the assessed literature.
 6   Table 7.6:     Present-day ERF due to changes in aerosol-radiation interactions (ERFari) and changes in aerosol-cloud
 7                  interactions (ERFaci), and total aerosol ERF (ERFari+aci) from GCM CMIP6 (2014 relative to 1850)
 8                  (Smith et al., 2020a and later model results) and CMIP5 (year 2000 relative to 1860) (Zelinka et al.,
 9                  2014). CMIP6 results are simulated as part of RFMIP (Pincus et al., 2016). An additional 5% is applied to
10                  the CMIP5 and CMIP6 model results to account for land-surface cooling (Smith et al., 2020b; Figure
11                  7.4).
      Models                                          ERFari                   ERFaci                 ERFari+aci
                                                      (W m-2)                  (W m-2)                (W m-2)
      ACCESS-CM2                                      –0.24                    –0.93                  –1.17
      ACCESS-ESM1-5                                   –0.07                    –1.19                  –1.25
      BCC-ESM1                                        –0.79                    –0.69                  –1.48
      CanESM5                                         –0.02                    –1.09                  –1.11
      CESM2                                           +0.15                    –1.65                  –1.50
      CNRM-CM6-1                                      –0.28                    –0.86                  –1.14
      CNRM-ESM2-1                                     –0.15                    –0.64                  –0.79
      EC-Earth3                                       –0.39                    –0.50                  –0.89
      GFDL-CM4                                        –0.12                    –0.72                  –0.84
      GFDL-ESM4                                       –0.06                    –0.84                  –0.90
      GISS-E2-1-G (physics_version=1)                 –0.55                    –0.81                  –1.36
      GISS-E2-1-G (physics_version=3)                 –0.64                    –0.39                  –1.02
      HadGEM3-GC31-LL                                 –0.29                    –0.87                  –1.17
      IPSL-CM6A-LR                                    –0.39                    –0.29                  –0.68
      IPSL-CM6A-LR-INCA                               –0.45                    –0.35                  –0.80
      MIROC6                                          –0.22                    –0.77                  –0.99
      MPI-ESM-1-2-HAM                                 +0.10                    –1.40                  –1.31
      MRI-ESM2-0                                      –0.48                    –0.74                  –1.22
      NorESM2-LM                                      –0.15                    –1.08                  –1.23
      NorESM2-MM                                      –0.03                    –1.26                  –1.29
      UKESM1-0-LL                                     –0.20                    –0.99                  –1.19
      CMIP6 average and 5 to 95%                      –0.25 ± 0.40             –0.86 ± 0.57           –1.11 ± 0.38
      confidence range (2014–1850)
      CMIP5 average and 5 to 96%                      –0.27 ± 0.35             –0.96 ± 0.55           –1.23 ± 0.48
      confidence range (2000–1860)

14   [END TABLE 7.6 HERE]
17      Aerosol-cloud interactions
19   Anthropogenic aerosol particles primarily affect water clouds by serving as additional cloud condensation
20   nuclei (CCN) and thus increasing cloud drop number concentration (Nd) (Twomey, 1959). Increasing Nd
21   while holding liquid water content constant reduces cloud drop effective radius (re), increases the cloud
22   albedo, and induces an instantaneous negative radiative forcing (IRFaci). The clouds are thought to
23   subsequently adjust by a slowing of the drop coalescence rate, thereby delaying or suppressing rainfall. Rain
24   generally reduces cloud lifetime and thereby liquid water path (LWP, i.e., the vertically integrated cloud
25   water) and/or cloud fractional coverage (Cf) (Albrecht, 1989), thus any aerosol-induced rain delay or
26   suppression would be expected to increase LWP and/or Cf. Such adjustments could potentially lead to an
27   ERFaci considerably larger in magnitude than the IRFaci alone. However, adding aerosols to non-
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 1   precipitating clouds has been observed to have the opposite effect (i.e., a reduction in LWP and/or Cf)
 2   (Lebsock et al., 2008; Christensen and Stephens, 2011). These findings have been explained by enhanced
 3   evaporation of the smaller droplets in the aerosol-enriched environments, and resultant enhanced mixing
 4   with ambient air, leading to cloud dispersal.
 6   A small subset of aerosols can also serve as ice nucleating particles (INPs) that initiate the ice phase in
 7   supercooled water clouds, and thereby alter cloud radiative properties and/or lifetimes. However, the ability
 8   of anthropogenic aerosols (specifically BC) to serve as INPs in mixed-phase clouds has been found to be
 9   negligible in recent laboratory studies (e.g., Vergara-Temprado et al. (2018)). No assessment of the
10   contribution to ERFaci from cloud phase changes induced by anthropogenic INPs will therefore be
11   presented.
13   In ice (cirrus) clouds (cloud temperatures less than –40° C), INPs can initiate ice crystal formation at relative
14   humidity much lower than that required for droplets to freeze spontaneously. Anthropogenic INPs can
15   thereby influence ice crystal numbers and thus cirrus cloud radiative properties. At cirrus temperatures,
16   certain types of BC have in fact been demonstrated to act as INPs in laboratory studies (Ullrich et al., 2017;
17   Mahrt et al., 2018), suggesting a non-negligible anthropogenic contribution to INPs in cirrus clouds.
18   Furthermore, anthropogenic changes to drop number also alter the number of droplets available for
19   spontaneous freezing, thus representing a second pathway through which anthropogenic emissions could
20   affect cirrus clouds.
23 Observation-based evidence
24   Since AR5, the analysis of observations to investigate aerosol-cloud interactions has progressed along
25   several axes: (i) The framework of forcing and adjustments introduced rigorously in AR5 has helped better
26   categorize studies; (ii) the literature assessing statistical relationships between aerosol- and cloud in satellite
27   retrievals has grown, and retrieval uncertainties are better characterized; (iii) advances have been made to
28   infer causality in aerosol-cloud relationships.
33   Table 7.7:   Studies quantifying aspects of the global ERFaci that are mainly based on satellite retrievals and were
34                published since AR5. All forcings/adjustments as global annual mean values in W m-2. Most studies split
35                the ERFaci into IRFaci and adjustments in LWP and cloud fraction separately. All published studies only
36                considered liquid clouds. Some studies assessed the IRFaci and the LWP adjustment together and called
37                this “intrinsic forcing”(Christensen et al., 2017) and the cloud fraction adjustment “extrinsic forcing”.
38                Published uncertainty ranges are converted to 5%–95 % confidence intervals, and “n/a” indicates that the
39                study did not provide an estimate for the relevant IRF/ERF.
               IRFaci          LWP adjustment           Cloud fraction adjustment                      Reference
              –0.6±0.6              n/a                            n/a                  Bellouin et al. (2013a)
         –0.4 [–0.2 to –1.0]        n/a                            n/a                  Gryspeerdt et al. (2017)
              –1.0±0.4              n/a                            n/a                  McCoy et al. (2017a)
                 n/a                n/a                    –0.5 [–0.1 to –0.6]          Gryspeerdt et al. (2016)
                 n/a             +0.3 to 0                         n/a                  Gryspeerdt et al. (2019)
              –0.8±0.7              n/a                            n/a                  Rémy et al. (2018)
                –0.53             +0.15                            n/a                  Toll et al. (2019)
        –1.14 [–1.72 to –0.84]      n/a                            n/a                  Hasekamp et al. (2019)
             –1.2 to -0.6           n/a                            n/a                  McCoy et al. (2020)
        –0.69 [–0.99 to –0.44]      n/a                            n/a                  Diamond et al. (2020)

                   “intrinsic forcing”
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                       –0.5 ± 0.5                              –0.5 ± 0.5            Chen et al. (2014)
                       –0.4 ± 0.3                                 n/a                Christensen et al. (2016b)
                       –0.3 ± 0.4                              –0.4 ± 0.5            Christensen et al. (2017)
 2   [END TABLE 7.7 HERE]
 5   In AR5 the statistical relationship between cloud microphysical properties and aerosol index (AI; AOD
 6   multiplied by Ångström exponent) was used to make inferences about IRFaci were assessed alongside other
 7   studies which related cloud quantities to AOD. However, it is now well-documented that the latter approach
 8   leads to low estimates of IRFaci since AOD is a poor proxy for cloud-base CCN (Penner et al., 2011; Stier,
 9   2016). Gryspeerdt et al. (2017) demonstrated that the statistical relationship between droplet concentration
10   and AOD leads to an inferred IRFaci that is underestimated by at least 30%, while the use of AI leads to
11   estimates of IRFaci to within ±20%, if the anthropogenic perturbation of AI is known.
13   Further, studies assessed in AR5 mostly investigated linear relationships between cloud droplet
14   concentration and aerosol (Boucher et al., 2013). Since in most cases the relationships are not linear, this
15   leads to a bias (Gryspeerdt et al., 2016). Several studies did not relate cloud droplet concentration, but cloud
16   droplet effective radius to the aerosol (Brenguier et al., 2000). This is problematic since then, in order to
17   infer IRFaci, stratification by cloud LWP is required (McComiskey and Feingold, 2012). Where LWP
18   positively co-varies with aerosol retrievals (which is often the case), IRFaci inferred from such relationships
19   is biased towards low values. Also, it is increasingly evident that different cloud regimes show different
20   sensitivities to aerosols (Stevens and Feingold, 2009). Averaging statistics over regimes thus bias the
21   inferred IRFaci (Gryspeerdt et al., 2014b). AR5 concluded that IRFaci estimates tied to satellite studies
22   generally show weak IRFaci (Boucher et al., 2013), but when correcting for the biases discussed above, this
23   is no longer the case.
25   Since AR5, several studies assessed the global IRFaci from satellite observations using different methods
26   (Table 7.7). All studies relied on statistical relationships between aerosol- and cloud quantities to infer
27   sensitivities. Four studies inferred IRFaci by estimating the anthropogenic perturbation of Nd. For this,
28   Bellouin et al. (2013a) and Rémy et al. (2018) made use of regional-seasonal regressions between satellite-
29   derived Nd and AOD following Quaas et al. (2008), while Gryspeerdt et al. (2017) used AI instead of AOD
30   in the regression to infer IRFaci. McCoy et al. (2017a) instead used the sulphate specific mass derived in the
31   MERRA aerosol reanalysis that assimilated MODIS AOD (Rienecker et al., 2011). All approaches have in
32   common the need to identify the anthropogenic perturbation of the aerosol to assess IRFaci. Gryspeerdt et al.
33   (2017) and Rémy et al. (2018) used the same approach as Bellouin et al. (2013a), while McCoy et al. (2017a)
34   used an anthropogenic fraction from the AEROCOM multi-model ensemble (Schulz et al., 2006). Chen et al.
35   (2014), Christensen et al. (2016b) and Christensen et al. (2017) derived the combination of IRFaci and the
36   LWP adjustment to IRFaci (“intrinsic forcing” in their terminology). They relate AI and cloud albedo
37   statistically and use the anthropogenic aerosol fraction from Bellouin et al. (2013a). This was further refined
38   by Hasekamp et al. (2019) who used additional polarimetric satellite information over ocean to obtain a
39   better proxy for CCN. They derived an IRFaci of –1.14 [–1.72 to –0.84] W m-2. The variant by Christensen
40   et al. (2017) is an update compared to the Chen et al. (2014) and Christensen et al. (2016b) studies in that it
41   better accounts for ancillary influences on the aerosol retrievals such as aerosol swelling and 3D radiative
42   effects. McCoy et al. (2020) used the satellite-observed hemispheric difference in Nd as an emergent
43   constraint on IRFaci as simulated by GCMs to obtain a range of –1.2 to –0.6 W m-2 (95% confidence
44   interval). Diamond et al. (2020) analysed the difference in clouds affected by ship emissions with
45   unperturbed clouds and based on this inferred a global IRFaci of –0.69 [–0.99 to –0.44] W m-2.
47   Summarising the above findings related to statistical relationships and causal aerosol effects on cloud
48   properties, there is high confidence that anthropogenic aerosols lead to an increase in cloud droplet
49   concentrations. Taking the average across the studies providing IRFaci estimates discussed above and
50   considering the general agreement among estimates (Table 7.7), IRFaci is assessed to be –0.7 ± 0.5 W m-2
51   (medium confidence).

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 2   Multiple studies have found a positive relationship between cloud fraction and/or cloud LWP and aerosols
 3   (e.g., Nakajima et al., 2001; Kaufman and Koren, 2006; Quaas et al., 2009). Since AR5, however, it has been
 4   documented that factors independent of causal aerosol-cloud interactions heavily influence such statistical
 5   relationships. These include the swelling of aerosols in the high relative humidity in the vicinity of clouds
 6   (Grandey et al., 2013) and the contamination of aerosol retrievals next to clouds by cloud remnants and
 7   cloud-side scattering (Várnai and Marshak, 2015; Christensen et al., 2017). Stratifying relationships by
 8   possible influencing factors such as relative humidity (Koren et al., 2010) does not yield satisfying results
 9   since observations of the relevant quantities are not available at the resolution and quality required. Another
10   approach to tackle this problem was to assess the relationship of cloud fraction with droplet concentration
11   (Gryspeerdt et al., 2016; Michibata et al., 2016; Sato et al., 2018). The relationship between satellite-
12   retrieved cloud fraction and Nd was found to be positive (Christensen et al., 2016b, 2017; Gryspeerdt et al.,
13   2016), implying an overall adjustment that leads to a more negative ERFaci. However, since retrieved Nd is
14   biased low for broken clouds this result has been called into question (Grosvenor et al., 2018). Zhu et al.
15   (2018) proposed to circumvent this problem by considering Nd of only continuous thick cloud covers, on the
16   basis of which Rosenfeld et al. (2019) still obtained a positive cloud fraction – Nd relationship.
18   The relationship between LWP and cloud droplet number is debated. Most recent studies (primarily based on
19   MODIS data) find negative statistical relationships (Michibata et al., 2016; Toll et al., 2017; Sato et al.,
20   2018; Gryspeerdt et al., 2019), while Rosenfeld et al. (2019) obtained a modest positive relationship. To
21   increase confidence that observed relationships between aerosol emissions and cloud adjustments are causal,
22   known emissions of aerosols and aerosol precursor gases into otherwise pristine conditions have been
23   exploited. Ship exhaust is one such source. Goren and Rosenfeld (2014) suggested that both LWP and Cf
24   increase in response to ship emissions, contributing approximately 75% to the total ERFaci in mid-latitude
25   stratocumulus. Christensen and Stephens (2011) found that such strong adjustments occur for open-cell
26   stratocumulus regimes, while adjustments are comparatively small in closed-cell regimes. Volcanic
27   emissions have been identified as another important source of information (Gassó, 2008). From satellite
28   observations, Yuan et al. (2011) documented substantially larger Cf, higher cloud tops, reduced precipitation
29   likelihood, and increased albedo in cumulus clouds in the plume of the Kilauea volcano. Ebmeier et al.
30   (2014) confirmed the increased LWP and albedo for other volcanoes. In contrast, for the large Holuhraun
31   eruption, Malavelle et al. (2017) did not find any large-scale change in LWP in satellite observations.
32   However, when accounting for meteorological conditions, McCoy et al. (2018) concluded that for cyclonic
33   conditions, the extra Holuhraun aerosol did enhance LWP. Toll et al. (2017) examined a large sample of
34   volcanoes and found a distinct albedo effect, but only modest LWP changes on average. Gryspeerdt et al.
35   (2019) demonstrated that the negative LWP – Nd relationship becomes very small when conditioned on a
36   volcanic eruption, and therefore concluded that LWP adjustments are small in most regions. Similarly, Toll
37   et al. (2019) studied clouds downwind of various anthropogenic aerosol sources using satellite observations
38   and inferred an IRFaci of –0.52 W m-2 that was partly offset by 29% due to aerosol-induced LWP decreases.
40   Apart from adjustments involving LWP and Cf, several studies have also documented a negative relationship
41   between cloud-top temperature and AOD/AI in satellite observations (e.g., Koren et al., 2005). Wilcox et al.
42   (2016) proposed that this could be explained by BC absorption reducing boundary layer turbulence, which in
43   turn could lead to taller clouds. However, it has been demonstrated that the satellite-derived relationships are
44   affected by spurious co-variation (Gryspeerdt et al., 2014a), and it therefore remains unclear whether a
45   systematic causal effect exists.
47   Identifying relationships between INP concentrations and cloud properties from satellites is intractable
48   because the INPs generally represent a very small subset of the overall aerosol population at any given time
49   or location. For ice clouds, only few satellite studies have investigated responses to aerosol perturbations so
50   far. Gryspeerdt et al. (2018) find a positive relationship between aerosol and ice crystal number for cold
51   cirrus under strong dynamical forcing, which could be explained by an overall larger number of solution
52   droplets available for homogeneous freezing in polluted regions. Zhao et al. (2018) conclude that the sign of
53   the ice crystal size – aerosol relationship depends on humidity. While these studies support modelling results
54   finding that ice clouds do respond to anthropogenic aerosols (Section, no quantitative conclusions
55   about IRFaci or ERFaci for ice clouds can be drawn based on satellite observations.
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 2   Only a handful of studies have estimated the LWP and Cf adjustments that are needed for satellite-based
 3   estimates of ERFaci. Chen et al. (2014) and Christensen et al. (2017) used the relationship between cloud
 4   fraction and AI to infer the cloud fraction adjustment. Gryspeerdt et al. (2017) used a similar approach but
 5   tried to account for non-causal aerosol – cloud fraction correlations by using Nd as a mediating factor. These
 6   three studies together suggest a global Cf adjustment that augments ERFaci relative to IRFaci by –0.5 ± 0.4
 7   W m–2 (medium confidence). For global estimates of the LWP adjustment, evidence is even scarcer.
 8   Gryspeerdt et al. (2019) derived an estimate of the LWP adjustment using a method similar to Gryspeerdt et
 9   al. (2016). They estimated that the LWP adjustment offsets 0 to 60% of the (negative) IRFaci (0 to +0.3 W
10   m-2). Supporting an offsetting LWP adjustment, Toll et al. (2019) estimated a moderate LWP adjustment of
11   29% (+0.15 W m-2). The adjustment due to LWP is assessed to be small, with a central estimate and very
12   likely range of 0.2 ± 0.2 W m–2 , but with low confidence due to the limited number of studies available.
14   Combining IRFaci and the associated adjustments in Cf and LWP (adding uncertainties in quadrature),
15   considering only liquid-water clouds and evidence from satellite observations alone, the central estimate and
16   very likely range for ERFaci is assessed to be –1.0 ± 0.7 W m–2 (medium confidence). The confidence level
17   and wider range for ERFaci compared to IRFaci reflect the relatively large uncertainties that remain in the
18   adjustment contribution to ERFaci.
21 Model-based evidence
22   As in AR5, the representation of aerosol-cloud interactions in ESMs remains a challenge, due to the limited
23   representation of important sub-gridscale processes, from the emissions of aerosols and their precursors to
24   precipitation formation. ESMs that simulate ERFaci typically include aerosol-cloud interactions in liquid
25   stratiform clouds only, while very few include aerosol interactions with mixed-phase-, convective-, and ice
26   clouds. Adding to the spread in model-derived estimates of ERFaci is the fact that model configurations and
27   assumptions vary across studies, for example when it comes to the treatment of oxidants, which influence
28   aerosol formation, and their changes through time (Karset et al., 2018).
30   In AR5, ERFaci was assessed as the residual of the total aerosol ERF and ERFari, as the total aerosol ERF
31   was easier to calculate based on available model simulations (Boucher et al., 2013). The central estimates of
32   total aerosol ERF and ERFari in AR5 were –0.9 W m-2 and –0.45 W m-2, respectively, yielding an ERFaci
33   estimate of –0.45 W m-2. This value is much less negative than the bottom-up estimate of ERFaci from
34   ESMs presented in AR5 (–1.4 W m-2) and efforts have been made since to reconcile this difference. Zelinka
35   et al. (2014) estimated ERFaci to be –0.96 ± 0.55 W m-2 (including semi-direct effects, and with land-surface
36   cooling effect applied) based on nine CMIP5 models (Table 7.6). The corresponding ERFaci estimate based
37   on 17 RFMIP models from CMIP6 is slightly less negative at –0.86 ± 0.57 W m-2 (Table 7.6). Other post-
38   AR5 estimates of ERFaci based on single model studies are either in agreement with or slightly larger in
39   magnitude than the CMIP6 estimate (Gordon et al., 2016; Fiedler et al., 2017; Neubauer et al., 2017; Karset
40   et al., 2018; Regayre et al., 2018; Zhou et al., 2018b; Fiedler et al., 2019; Golaz et al., 2019a; Diamond et al.,
41   2020).
43   The adjustment contribution to the CMIP6 ensemble mean ERFaci is –0.20 W m-2, though with considerable
44   differences between the models (Smith et al., 2020a). Generally, this adjustment in ESMs arises mainly from
45   LWP changes (e.g., Ghan et al., 2016), while satellite observations suggest that cloud cover adjustments
46   dominate and that aerosol effects on LWP are over-estimated in ESMs (Bender et al., 2019). Large-eddy-
47   simulations also tend to suggest an over-estimated aerosol effect on cloud lifetime in ESMs, but some report
48   an aerosol-induced decrease in cloud cover that is at odds with satellite observations (Seifert et al., 2015).
49   Despite this potential disagreement when it comes to the dominant adjustment mechanism, a substantial
50   negative contribution to ERFaci from adjustments is supported both by observational and modelling studies.
52   Contributions to ERFaci from anthropogenic aerosols acting as INPs are generally not included in CMIP6
53   models. Two global modelling studies incorporating parameterizations based on recent laboratory studies
54   both found a negative contribution to ERFaci (Penner et al., 2018; McGraw et al., 2020), with central
55   estimates of –0.3 and –0.13 W m-2, respectively. However, previous studies have produced model estimates
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 1   of opposing signs (Storelvmo, 2017). There is thus limited evidence and medium agreement for a small
 2   negative contribution to ERFaci from anthropogenic INP-induced cirrus modifications (low confidence).
 4   Similarly, aerosol effects on deep convective clouds are typically not incorporated in ESMs. However,
 5   cloud-resolving modelling studies support non-negligible aerosol effects on the radiative properties of
 6   convective clouds and associated detrained cloud anvils (Tao et al., 2012). While global ERF estimates are
 7   currently not available for these effects, the fact that they are missing in most ESMs adds to the uncertainty
 8   range for the model-based ERFaci.
10   From model-based evidence, ERFaci is assessed to –1.0 ± 0.8 W m-2 (medium confidence). This assessment
11   uses the mean ERFaci in Table 7.6 as a starting point, but further allows for a small negative ERF
12   contribution from cirrus clouds. The uncertainty range is based on those reported in Table 7.6, but widened
13   to account for uncertain but likely non-negligible processes currently unaccounted for in ESMs.
16 Overall assessment of ERFaci
17   The assessment of ERFaci based on observational evidence alone (–1.0 ± 0.7 W m-2) is very similar to the
18   one based on model-evidence alone (–1.0 ± 0.8 W m-2), in strong contrast to what was reported in AR5. This
19   reconciliation of observation-based and model-based estimates is the result of considerable scientific
20   progress and reflects comparable revisions of both model-based and observation-based estimates. The strong
21   agreement between the two largely independent lines of evidence increases confidence in the overall
22   assessment of the central estimate and very likely range for ERFaci of –1.0 ± 0.7 W m-2 (medium
23   confidence). The assessed range is consistent with but narrower than that reported by the review of Bellouin
24   et al. (2019) of –2.65 to –0.07 W m-2. The difference is primarily due to a wider range in the adjustment
25   contribution to ERFaci in Bellouin et al. (2019), however adjustments reported relative to IRFaci ranging
26   from 40% to 150% in that study are fully consistent with the ERFaci assessment presented here.
29   Energy budget constraints on the total aerosol ERF
31   Energy balance models of reduced complexity have in recent years increasingly been combined with Monte
32   Carlo approaches to provide valuable “top-down” (also called inverse) observational constraints on the total
33   aerosol ERF. These top-down approaches report ranges of aerosol ERF that are found to be consistent with
34   the global mean temperature record and, in some cases, also observed ocean heat uptake. However, the total
35   aerosol ERF is also used together with the historical temperature record in Section 7.5 to constrain ECS and
36   TCR. Using top-down estimates as a separate line of evidence also for the total aerosol ERF would therefore
37   be circular. Nevertheless, it is useful to examine the development of these estimates since AR5 and the
38   degree to which these estimates are consistent with the upper and lower bounds of the assessments of total
39   aerosol ERF (ERFari+ERFaci).
41   When the first top-down estimates emerged (e.g., Knutti et al., 2002), it became clear that some of the early
42   (“bottom-up”) ESM estimates of total aerosol ERF were inconsistent with the plausible top-down range.
43   However, as more inverse estimates have been published, it has increasingly become clear that they too are
44   model-dependent and span a wide range of ERF estimates, with confidence intervals that in some cases do
45   not overlap (Forest, 2018). It has also become evident that these methods are sensitive to revised estimates of
46   other forcings and/or updates to observational data sets. A recent review of 19 such estimates reported a
47   mean of –0.77 W m-2 for the total aerosol ERF, and a 95% confidence interval of –1.15 W m-2 to
48   –0.31 W m-2 (Forest, 2018). Adding to that review, a more recent study using the same approach reported an
49   estimate of total aerosol ERF of –0.89 [–1.82 to –0.01] W m-2 (Skeie et al., 2018). However, in the same
50   study, an alternative way of incorporating ocean heat content in the analysis produced a total aerosol ERF
51   estimate of –1.34 [–2.20 to –0.46] W m-2, illustrating the sensitivity to the manner in which observations are
52   included. A new approach to inverse estimates took advantage of independent climate radiative response
53   estimates from eight prescribed SST and sea-ice concentration simulations over the historical period to
54   estimate the total anthropogenic ERF. From this a total aerosol ERF of –0.8 [–1.6 to +0.1] W m-2 was
55   derived (valid for near-present relative to the late 1800s). This range was found to be more invariant to
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 1   parameter choices than earlier inverse approaches (Andrews and Forster, 2020).
 3   Beyond the inverse estimates described above, other efforts have been made since AR5 to constrain the total
 4   aerosol ERF. For example, Stevens (2015) used a simple (1-dimensional) model to simulate the historical
 5   total aerosol ERF evolution consistent with the observed temperature record. Given the lack of temporally
 6   extensive cooling trends in the 20th century record and the fact that the historical evolution of greenhouse gas
 7   forcing is relatively well constrained, the study concluded that a more negative total aerosol ERF than –1.0
 8   W m-2 was incompatible with the historical temperature record. This was countered by Kretzschmar et al.
 9   (2017), who argued that the model employed in Stevens (2015) was too simplistic to account for the effect of
10   geographical redistributions of aerosol emissions over time. Following the logic of Stevens (2015), but
11   basing their estimates on a subset of CMIP5 models as opposed to a simplified modelling framework, they
12   argued that a total aerosol ERF as negative as –1.6 W m-2 was consistent with the observed temperature
13   record. Similar arguments were put forward by Booth et al. (2018), who emphasized that the degree of non-
14   linearity of the total aerosol ERF with aerosol emission is a central assumption in Stevens (2015).
16   The historical temperature record was also the key observational constraint applied in two additional studies
17   (Rotstayn et al., 2015; Shindell et al., 2015) based on a subset of CMIP5 models. Rotstayn et al. (2015)
18   found a strong temporal correlation (> 0.9) between the total aerosol ERF and the global surface temperature.
19   They used this relationship to produce a best estimate for the total aerosol ERF of –0.97 W m-2, but with
20   considerable unquantified uncertainty, in part due to uncertainties in the TCR. Shindell et al. (2015) came to
21   a similar best estimate for the total aerosol ERF of –1.0 W m-2 and a 95% confidence interval of –1.4 to –0.6
22   W m-2 but based this on spatial temperature and ERF patterns in the models in comparison with observed
23   spatial temperature patterns.
25   A separate observational constraint on the total ERF was proposed by Cherian et al. (2014), who compared
26   trends in downward fluxes of solar radiation observed at surface stations across Europe (described in Section
27 to those simulated by a subset of CMIP5 models. Based on the relationship between solar radiation
28   trends and the total aerosol ERF in the models, they inferred a total aerosol ERF of –1.3 W m-2 and a
29   standard deviation of ± 0.4 W m-2.
31   Based solely on energy balance considerations or other observational constraints, it is extremely likely that
32   the total aerosol ERF is negative (high confidence), but extremely unlikely that the total aerosol ERF is more
33   negative than –2.0 W m-2 (high confidence).
36   Overall assessment of total aerosol ERF
38   In AR5 (Boucher et al., 2013), the overall assessment of total aerosol ERF (ERFari+aci) used the median of
39   all ESM estimates published prior to AR5 of –1.5 [–2.4 to –0.6] W m-2 as a starting point, but placed more
40   confidence in a subset of models that were deemed more complete in their representation of aerosol-cloud
41   interactions. These models, which included aerosol effects on mixed-phase, ice and/or convective clouds,
42   produced a smaller estimate of –1.38 W m-2. Likewise, studies that constrained models with satellite
43   observations (five in total), which produced a median estimate of –0.85 W m-2, were given extra weight.
44   Furthermore, a longwave ERFaci of 0.2 W m-2 was added to studies that only reported shortwave ERFaci
45   values. Finally, based on higher resolution models, doubt was raised regarding the ability of ESMs to
46   represent the cloud adjustment component of ERFaci with fidelity. The expert judgement was therefore that
47   aerosol effects on cloud lifetime were too strong in the ESMs, further reducing the overall ERF estimate. The
48   above lines of argument resulted in a total aerosol assessment of –0.9 [–1.9 to –0.1] W m-2 in AR5.
50   Here, the best estimate and range is revised relative to AR5 (Boucher et al., 2013), partly based on updates to
51   the above lines of argument. Firstly, the studies that included aerosol effects on mixed-phase clouds in AR5
52   relied on the assumption that anthropogenic black carbon (BC) could act as INPs in these clouds, which has
53   since been challenged by laboratory experiments (Kanji et al., 2017; Vergara-Temprado et al., 2018). There
54   is no observational evidence of appreciable ERFs associated with aerosol effects on mixed-phase and ice
55   clouds (Section, and modelling studies disagree when it comes to both their magnitude and sign
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 1   (Section Likewise, very few ESMs incorporate aerosol effects on deep convective clouds, and
 2   cloud-resolving modelling studies report different effects on cloud radiative properties depending on
 3   environmental conditions (Tao et al., 2012). Thus, it is not clear whether omitting such effects in ESMs
 4   would lead to any appreciable ERF biases, or if so, what the sign of such biases would be. As a result, all
 5   ESMs are given equal weight in this assessment. Furthermore, there is now a considerably expanded body of
 6   literature which suggests that early modelling studies that incorporated satellite observations may have
 7   resulted in overly conservative estimates of the magnitude of ERFaci (Section Finally, based on
 8   an assessment of the longwave ERFaci in the CMIP5 models, the offset of +0.2 W m-2 applied in AR5
 9   appears to be too large (Heyn et al., 2017). As in AR5, there is still reason to question the ability of ESMs to
10   simulate adjustments in LWP and cloud cover in response to aerosol perturbation, but it is not clear that this
11   will result in biases that exclusively increase the magnitude of the total aerosol ERF (Section
13   The assessment of total aerosol ERF here uses the following lines of evidence: satellite-based evidence for
14   IRFari, model-based evidence for IRFari and ERFari, satellite-based evidence of IRF/ERFaci, and finally
15   model-based evidence for ERFaci. Based on this, ERFari and ERFaci for 2014 relative to 1750 are assessed
16   to –0.3 ± 0.3 W m-2 and –1.0 ± 0.7 W m-2, respectively. There is thus strong evidence for a substantive
17   negative total aerosol ERF, which is supported by the broad agreement between observation-based and
18   model-based lines of evidence for both ERFari and ERFaci that has emerged since AR5 (Gryspeerdt et al.,
19   2020). However, considerable uncertainty remains, particularly with regards to the adjustment contribution
20   to ERFaci, as well as missing processes in current ESMs, notably aerosol effects on mixed-phase, ice and
21   convective clouds. This leads to a medium confidence in the estimate of ERFari+aci and a slight narrowing
22   of the uncertainty range. Because the estimates informing the different lines of evidence are generally valid
23   for approximately 2014 conditions, the total aerosol ERF assessment is considered valid for 2014 relative to
24   1750.
26   Combining the lines of evidence and adding uncertainties in quadrature, the ERFari+aci estimated for 2014
27   relative to 1750 is assessed to be –1.3 [–2.0 to –0.6] W m-2 (medium confidence). The corresponding range
28   from Bellouin et al. (2019) is –3.15 to –0.35 W m-2, thus there is agreement for the upper bound while the
29   lower bound assessed here is less negative. A lower bound more negative than -2.0 W m-2 is not supported by
30   any of the assessed lines of evidence. There is high confidence that ERFaci contributes most (75–80%) to the
31   total aerosol effect (ERFari+aci). In contrast to AR5 (Boucher et al., 2013), it is now virtually certain that the
32   total aerosol ERF is negative. Figure 7.5 depicts the aerosol ERFs from the different lines of evidence along
33   with the overall assessments.
35   As most modelling and observational estimates of aerosol ERF have end points in 2014 or earlier, there is
36   limited evidence available for the assessment of how aerosol ERF has changed from 2014 to 2019. However,
37   based on a general reduction in global mean AOD over this period (Chapter 2, Section 2.2.6, Figure 2.9),
38   combined with a reduction in emissions of aerosols and their precursors in updated emission inventories
39   (Hoesly et al., 2018), the aerosol ERF is assessed to have decreased in magnitude from about 2014 to 2019
40   (medium confidence). Consistent with Chapter 2, Figure 2.10, the change in aerosol ERF from about 2014 to
41   2019 is assessed to be +0.2 W m-2, but with low confidence due to limited evidence. Aerosols are therefore
42   assessed to have contributed an ERF of –1.1 [–1.7 to –0.4] W m–2 over 1750–2019 (medium confidence).
47   Figure 7.5: Net aerosol effective radiative forcing from different lines of evidence. The headline AR6 assessment
48               of –1.3 [–2.0 to –0.6] W m–2 is highlighted in purple for 1750–2014 and compared to the AR5 assessment
49               of –0.9 [–1.9 to –0.1] W m–2 for 1750–2011. The evidence comprising the AR6 assessment is shown
50               below this: energy balance constraints (–2 to 0 W m–2 with no best estimate), observational evidence from
51               satellite retrievals of –1.4 [–2.2 to –0.6] W m–2, and climate model-based evidence of –1.25 [–2.1 to –0.4]
52               W m–2. Estimates from individual CMIP5 (Zelinka et al., 2014) and CMIP6 (Smith et al., 2020a and
53               Table 7.6) models are depicted by blue and red crosses respectively. For each line of evidence the
54               assessed best-estimate contributions from ERFari and ERFaci are shown with darker and paler shading
55               respectively. The observational assessment for ERFari is taken from the IRFari. Uncertainty ranges are
56               given in black bars for the total aerosol ERF and depict very likely ranges. Further details on data sources
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 1                 and processing are available in the chapter data table (Table 7.SM.14).
 3   [END FIGURE 7.5 HERE]
 6   7.3.4     Other agents
 8   In addition to the large anthropogenic ERFs associated with WMGHGs and atmospheric aerosols assessed in
 9   Sections 7.3.2 and 7.3.3, land use change, contrails and aviation-induced cirrus and light absorbing particles
10   deposited on snow and ice have also contributed to the overall anthropogenic ERF and are assessed in
11   Sections, and Changes in solar irradiance, galactic cosmic rays and volcanic eruptions
12   since pre-industrial times combined represent the natural contribution to the total (anthropogenic + natural)
13   ERF and are discussed in Sections, and
16    Land use
18   Land use forcing is defined as those changes in land surface properties directly caused by human activity
19   rather than by climate processes (see also Chapter 2, Section 2.2.7). Land use change affects the surface
20   albedo. For example, deforestation typically replaces darker forested areas with brighter cropland, and thus
21   imposes a negative radiative forcing on climate, while afforestation and reforestation can have the opposite
22   effect. Precise changes depend on the nature of the forest, crops and underlying soil. Land use change also
23   affects the amount of water transpired by vegetation (Devaraju et al., 2015). Irrigation of land directly affects
24   the evaporation (Sherwood et al., 2018) causing a global increase of 32 500 m3 s−1 due to human activity.
25   Changes in evaporation and transpiration affect the latent heat budget, but do not directly affect the top-of-
26   atmosphere radiative fluxes. The lifetime of water vapour is so short that the effect of changes in evaporation
27   on the greenhouse contribution of water vapour are negligible (Sherwood et al., 2018). However, evaporation
28   can affect the ERF through adjustments, particularly through changes in low cloud amounts. Land
29   management affects the emissions or removal of greenhouse gases from the atmosphere (such as CO2, CH4,
30   N2O). These emission changes have the greatest effect on climate (Ward et al., 2014), however they are
31   already included in greenhouse gas inventories. Land use change also affects the emissions of dust and
32   biogenic volatile organic compounds (BVOCs), which form aerosols and affect the atmospheric
33   concentrations of ozone and methane (Chapter 6, Section 6.2.2). The effects of land use on surface
34   temperature and hydrology were recently assessed in SRCCL (Jia et al., 2019).
36   Using the definition of ERF from Section 7.1, the adjustment in land surface temperature is excluded from
37   the definition of ERF, but changes in vegetation and snow cover (resulting from land use change) are
38   included (Boisier et al., 2013). Land use change in the mid-latitudes induces a substantial amplifying
39   adjustment in snow cover. Few climate model studies have attempted to quantify the ERF of land use
40   change. Andrews et al. (2017b) calculated a very large surface albedo ERF (–0.47 W m–2) from 1860 to 2005
41   in the HadGEM2-ES model although they did not separate out the surface albedo change from snow cover
42   change. HadGEM2-ES is known to overestimate the amount of boreal trees and shrubs in the unperturbed
43   state (Collins et al., 2011) so will tend to overestimate the ERF associated with land use change. The
44   increases in dust in HadGEM2-ES contributed an extra –0.25 W m–2, whereas cloud cover changes added a
45   small positive adjustment (0.15 W m–2) consistent with a reduction in transpiration. A multi-model
46   quantification of land use forcing in CMIP6 models (excluding one outlier) (Smith et al., 2020a) found an
47   IRF of –0.15 ± 0.12 W m–2 (1850 to 2014), and an ERF (correcting for land surface temperature change) of -
48   0.11 ± 0.09 W m–2. This shows a small positive adjustment term (mainly from a reduction in cloud cover.
49   CMIP5 models show an IRF of –0.11 [–0.16 to –0.04] W m-2 (1850 to 2000) after excluding unrealistic
50   models (Lejeune et al., 2020).
52   The contribution of land use change to albedo changes has recently been investigated using MODIS and
53   AVHRR to attribute surface albedo to geographically-specific land cover types (Ghimire et al., 2014). When
54   combined with a historical land use map (Hurtt et al., 2011) this gives a 1700 to 2005 SARF of
55   –0.15 ± 0.01 W m-2 (of which –0.12 W m–2 is from 1850). This study accounted for correlations between
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 1   vegetation type and snow cover, but not the adjustment in snow cover identified in (Andrews et al., 2017b).
 3   The indirect contributions of land use change through biogenic emissions is very uncertain. Decreases in
 4   biogenic volatile organic compounds (BVOCs) reduce ozone and methane (Unger, 2014), but also reduce the
 5   formation of organic aerosols and their effects of clouds Scott et al. (2017). Adjustments through changes in
 6   aerosols and chemistry are model dependent (Zhu et al., 2019a; Zhu and Penner, 2020), and it is not yet
 7   possible to make an assessment based on a limited number of studies.
 9   The contribution of irrigation (mainly to low cloud amount) is assessed as –0.05 [–0.1 to 0.05] W m-2 for the
10   historical period (Sherwood et al., 2018).
12   Since the CMIP5 and CMIP6 modelling studies are in agreement with Ghimire et al. (2014), that study is
13   used as the assessed albedo ERF. Adding the irrigation effect to this gives an overall assessment of the ERF
14   from land use change of –0.20 ± 0.10 W m-2 (medium confidence). Changes in ERF since 2014 are assumed
15   to be small compared to the uncertainty, so this ERF applies to the period 1750 to 2019. The uncertainty
16   range includes uncertainties in the adjustments.
19   Contrails and aviation-induced cirrus
21   ERF from contrails and aviation-induced cirrus is taken from the assessment of Lee et al. (2020), at 0.057
22   [0.019 to 0.098] W m–2 in 2018 (see Chapter 6, Section 6.6.2 for an assessment of the total effects of
23   aviation). This is rounded up to address its low confidence and the extra year of air traffic to give an assessed
24   ERF over 1750–2019 of 0.06 [0.02 to 0.10]. This assessment is given low confidence due to the potential for
25   missing processes to affect the magnitude of contrails and aviation-induced cirrus ERF.
28   Light absorbing particles on snow and ice
30   In AR5, it was assessed that the effects of light absorbing particles (LAPs) did probably not significantly
31   contribute to recent reductions in Arctic ice and snow (Vaughan et al., 2013). The SARF from LAPs on
32   snow and ice was assessed to +0.04 [+0.02 to +0.09] W m-2 (Boucher et al., 2013), a range appreciably lower
33   than the estimates given in AR4 (Forster et al., 2007). This effect was assessed to be low confidence (medium
34   evidence, low agreement) (Table 8.5 in Myhre et al., 2013b).
36   Since AR5 there has been progress in the understanding of the physical state and processes in snow that
37   governs the albedo reduction by black carbon (BC). The SROCC (IPCC, 2019a) assessed that there is high
38   confidence that darkening of snow by deposition of BC and other light absorbing aerosol species increases
39   the rate of snow melt (Section 2.2 in Hock et al., 2019; Section 3.4 in Meredith et al., 2019). He et al.
40   (2018a) found that taking into account the non-spherical shape of snow grains and internal mixing of BC in
41   snow both significantly altered the effects of BC on snow albedo. The reductions of snow albedo by dust and
42   black carbon have been measured and characterised in the Arctic, the Tibetan Plateau, and mid latitude
43   regions subject to seasonal snowfall including North America and Northern and Eastern Asia (Qian et al.,
44   2015).
46   Since AR5, two further studies of global IRF from black carbon on snow deposition are available, with best
47   estimates of 0.01 W m-2 and 0.04 W m–2 (Lin et al., 2014; Namazi et al., 2015). Organic carbon deposition
48   on snow and ice has been estimated to contribute a small positive IRF of 0.001 to 0.003 W m–2 (Lin et al.,
49   2014). No comprehensive global assessments of mineral dust deposition on snow are available, although the
50   effects are potentially large in relation to the total LAPs on snow and ice forcing (Yasunari et al., 2015).
52   Most radiative forcing estimates have a regional emphasis. The regional focus makes estimating a global
53   mean radiative forcing from aggregating different studies challenging, and the relative importance of each
54   region is expected to change if the global pattern of emission sources changes (Bauer et al., 2013). The lower
55   bound of the assessed range of black carbon on snow and ice is extended to zero to encompass Lin et al.
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 1   (2014), with the best estimate unchanged resulting in 0.04 [0.00 to 0.09] W m–2. The efficacy of black carbon
 2   on snow forcing was estimated to be 2 to 4 times as large as for an equivalent CO2 forcing as the effects are
 3   concentrated at high latitudes in the cryosphere (Bond et al., 2013). However, it is unclear how much of this
 4   effect is due to radiative adjustments leading to a higher ERF, and how much comes from a less negative
 5   feedback α due the high latitude nature of the forcing. To estimate the overall ERF, the IRF is doubled
 6   assuming that part of the increased efficacy is due to adjustments. This gives an overall assessed ERF of
 7   +0.08 [0.00 to 0.18] W m–2, with low confidence.
10   Solar
12   Variations in the total solar irradiance (TSI) represent a natural external forcing agent. The dominant cycle is
13   the solar 11-year activity cycle, which is superimposed on longer cycles (Chapter 2, Section 2.2). Over the
14   last three 11-year cycles, the peak-to-trough amplitude in TSI has differed by about 1 W m–2 between solar
15   maxima and minima (Chapter 2, Figure 2.2).
17   The fractional variability in the solar irradiance, over the solar cycle and between solar cycles, is much
18   greater at short wavelengths in the 200–400 nm band than for the broad visible/IR band that dominates TSI
19   (Krivova et al., 2006). The IRF can be derived simply by ΔTSI × (1 – albedo)/4 irrespective of wavelength,
20   where the best estimate of the planetary albedo is usually taken to be 0.29 and ΔTSI represents the change in
21   total solar irradiance (Stephens et al., 2015). (The factor 4 arises because TSI is per unit area of Earth cross
22   section presented to the Sun and IRF is per unit area of Earth’s surface). The adjustments are expected to be
23   wavelength dependent. Gray et al. (2009) determined a stratospheric temperature adjustment of –22% to
24   spectrally resolved changes in the solar radiance over one solar cycle. This negative adjustment is due to
25   stratospheric heating from increased absorption by ozone at the short wavelengths, increasing the outgoing
26   longwave radiation to space. A multi-model comparison (Smith et al., 2018b) calculated adjustments of –4%
27   due to stratospheric temperatures and –6% due to tropospheric processes (mostly clouds), for a change in
28   TSI across the spectrum (Figure 7.4). The smaller magnitude of the stratospheric temperature adjustment is
29   consistent with the broad spectral change rather than the shorter wavelengths characteristic of solar variation.
30   A single model study also found an adjustment that acts to reduce the forcing (Modak et al., 2016). While
31   there has not yet been a calculation based on the appropriate spectral change, the –6% tropospheric
32   adjustment from Smith et al. (2018b) is adopted along with the Gray et al. (2009) stratospheric temperature
33   adjustment. The ERF due to solar variability over the historical period is therefore represented by 0.72 ×
34   ΔTSI × (1 – albedo)/4 using the TSI timeseries from Chapter 2, Section 2.2.1.
36   AR5 (Myhre et al., 2013b) assessed solar SARF from around 1750 to 2011 to be 0.05 [0.00 to 0.10] W m–2
37   which was computed from the seven-year mean around the solar minima in 1745 (being closest to 1750) and
38   2008 (being the most recent solar minimum). The inclusion of tropospheric adjustments that reduce ERF
39   (compared to SARF in AR5) has a negligible effect on the overall forcing. Prior to the satellite era, proxy
40   records are used to reconstruct historical solar activity. In AR5, historical records were constructed using
41   observations of solar magnetic features. In this assessment historical time series are constructed from
42   radiogenic compounds in the biosphere and in ice cores that are formed from cosmic rays (Steinhilber et al.,
43   2012).
45   In this assessment the TSI from the Paleoclimate Model Intercomparison Project Phase 4 (PMIP4)
46   reconstruction is used (Jungclaus et al., 2017; Chapter 2, Section 2.2.1). Proxies constructed from the 14C and
47      Be radiogenic records for the SATIRE-M model (Vieira et al., 2011) and 14C record for the PMOD model
48   (Shapiro et al., 2011) for the 1745 solar minimum provide 1745 to 2008 ERFs of –0.01, –0.02 and
49   0.00 W m-2 respectively. An independent dataset from the National Oceanic and Atmospheric
50   Administration’s Climate Data Record (Coddington et al., 2016; Lean, 2018) provides a 1745 to 2008 ERF
51   of +0.03 W m-2. One substantially higher ERF estimate of +0.35 W m-2 derived from TSI reconstructions is
52   provided by Egorova et al. (2018). However, the estimate from Egorova et al. (2018) hinges on assumptions
53   about long-term changes in the quiet Sun for which there is no observed evidence. Lockwood and Ball
54   (2020) analysed the relationship of observed changes in cosmic ray fluxes and recent, more accurate, TSI
55   data and derived ERF between −0.01 and +0.02 W m-2 and Yeo et al. (2020) modelling showed the
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 1   maximum possible ERF to be 0.26 ± 0.09 W m-2. Hence the Egorova et al. (2018) estimate is not explicitly
 2   taken into account in the assessment presented in this section.
 4   In contrast to AR5, the solar ERF in this assessment uses full solar cycles rather than solar minima. The pre-
 5   industrial TSI is defined as the mean from all complete solar cycles from the start of the 14C SATIRE-M
 6   proxy record in 6755 BCE to 1744 CE. The mean TSI from solar cycle 24 (2009–2019) is adopted as the
 7   assessment period for 2019. The best estimate solar ERF is assessed to be 0.01 W m-2, using the 14C
 8   reconstruction from SATIRE-M, with a likely range of –0.06 to +0.08 W m-2 (medium confidence). The
 9   uncertainty range is adopted from the evaluation of Lockwood and Ball (2020) using a Monte Carlo analysis
10   of solar activity from the Maunder Minimum to 2019 from several datasets, leading to an ERF of –0.12 to
11   +0.15 W m-2. The Lockwood and Ball (2020) full uncertainty range is halved as the period of reduced solar
12   activity in the Maunder Minimum had ended by 1750 (medium confidence).
15   Galactic Cosmic Rays
17   Variations in the flux of galactic cosmic rays (GCR) reaching the atmosphere are modulated by solar activity
18   and affect new particle formation in the atmosphere through their link to ionization of the troposphere (Lee
19   et al., 2019). It has been suggested that periods of high GCR flux correlate with increased aerosol and CCN
20   concentrations and therefore also with cloud properties (e.g., Dickinson, 1975; Kirkby, 2007).
22   Since AR5, the link between GCR and new particle formation has been more thoroughly studied, particularly
23   by experiments in the CERN CLOUD chamber (Cosmics Leaving OUtdoor Droplets) (Dunne et al., 2016;
24   Kirkby et al., 2016; Pierce, 2017). By linking the GCR-induced new particle formation from CLOUD
25   experiments to CCN, Gordon et al. (2017) found the CCN concentration for low clouds to differ by 0.2% to
26   0.3% between solar maximum and solar minimum of the solar cycle. Combined with relatively small
27   variations in the atmospheric ion concentration over centennial time scales (Usoskin et al., 2015), it is
28   therefore unlikely that cosmic ray intensity affects present day climate via nucleation (Yu and Luo, 2014;
29   Dunne et al., 2016; Pierce, 2017; Lee et al., 2019).
31   Studies continue to seek a relationship between GCR and properties of the climate system based on
32   correlations and theory. Svensmark et al. (2017) proposed a new mechanism for ion-induced increase in
33   aerosol growth rate and subsequent influence on the CCN concentration. The study does not include an
34   estimate of the resulting effect on atmospheric CCN concentration and cloud radiative properties.
35   Furthermore, Svensmark et al. (2009, 2016) find correlations between GCRs and aerosol and cloud
36   properties in satellite and ground based data. Multiple studies investigating this link have challenged such
37   correlations (Kristjánsson et al., 2008; Calogovic et al., 2010; Laken, 2016).
39   AR5 concluded that the GCR effect on CCN is too weak to have any detectable effect on climate and no
40   robust association was found between GCR and cloudiness (Boucher et al., 2013). Published literature since
41   then robustly support these conclusions with key laboratory, theoretical and observational evidence. There is
42   high confidence that GCRs contribute a negligible ERF over the period 1750 to 2019.
45   Volcanic aerosols
47   There is large episodic negative radiative forcing associated with SO2 being ejected into the stratosphere
48   from explosive volcanic eruptions, accompanied by more frequent smaller eruptions (Chapter 2, Figure 2.2;
49   Cross-Chapter Box 4.1). From SO2 gas, reflective sulphate aerosol is formed in the stratosphere where it may
50   persist for months, reducing the incoming solar radiation. The volcanic SARF in AR5 (Myhre et al., 2013b)
51   was derived by scaling the stratospheric aerosol optical depth (SAOD) by a factor of –25 W m–2 per unit
52   SAOD from Hansen et al. (2005b). Quantification of the adjustments to SAOD perturbations from climate
53   model simulations have determined a significant positive adjustment driven by a reduction in cloud amount
54   (Marshall et al., 2020; Figure 7.4). Analysis of CMIP5 models provide a mean ERF of –20 W m-2 per unit
55   SAOD (Larson and Portmann, 2016). Single model studies with successive generations of Hadley Centre
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 1   climate models produce estimates between –17 and –19 W m-2 per unit SAOD (Gregory et al., 2016;
 2   Marshall et al., 2020), with some evidence that ERF may be non-linear with SAOD for large eruptions
 3   (Marshall et al., 2020). Analysis of the volcanically active periods of 1982-1985 and 1990-1994 using the
 4   CESM1(WACCM) aerosol-climate model provided an SAOD to ERF relationship of –21.5 (± 1.1) W m–2
 5   per unit SAOD (Schmidt et al., 2018). Volcanic SO2 emissions may contribute a positive forcing through
 6   effects on upper tropospheric ice clouds, due to additional ice nucleation on volcanic sulphate particles
 7   (Friberg et al., 2015; Schmidt et al., 2018), although one observational study found no significant effect
 8   (Meyer et al., 2015). Due to limited agreement, the contribution to volcanic ERF due to sulphate aerosol
 9   effects on ice clouds is not included in the overall assessment.
11   Non-explosive volcanic eruptions generally yield negligible global ERFs due to the short atmospheric
12   lifetimes (a few weeks) of volcanic aerosols in the troposphere. However, as discussed in Section, the
13   massive fissure eruption in Holuhraun, Iceland persisted for months in 2014 and 2015 and did in fact result
14   in a marked and persistent reduction in cloud droplet radii and a corresponding increase in cloud albedo
15   regionally (Malavelle et al., 2017). This shows that non-explosive fissure eruptions can lead to strong
16   regional and even global ERFs, but because the Holuhraun eruption occurred in NH winter, solar insolation
17   was weak and the observed albedo changes therefore did not result in an appreciable global ERF (Gettelman
18   et al., 2015).
20   The ERF for volcanic stratospheric aerosols is assessed to be –20 ± 5 W m–2 per unit SAOD (medium
21   confidence) based on the CMIP5 multi-model mean from the Larson and Portmann (2016) SAOD forcing
22   efficiency calculations combined with the single-model results of Gregory et al. (2016), Schmidt et al. (2018)
23   and Marshall et al. (2020). This is applied to the SAOD timeseries from Chapter 2, Section 2.2.2 to generate
24   a timeseries of ERF and temperature response shown in Chapter 2, Figure 2.2 and Figure 7.8 respectively.
25   The period from 500 BC to 1749, spanning back to the start of the record of Toohey and Sigl (2017), is
26   defined as the pre-industrial baseline and the volcanic ERF is calculated using an SAOD anomaly from this
27   long-term mean. As in AR5, a pre-industrial to present-day ERF assessment is not provided due to the
28   episodic nature of volcanic eruptions.
31   7.3.5     Synthesis of Global Mean Radiative Forcing, Past and Future
33    Major changes in forcing since IPCC AR5
35   AR5 introduced the concept of ERF and radiative adjustments, and made a preliminary assessment that the
36   tropospheric adjustments were zero for all species other than the effects of aerosol-cloud interaction and
37   black carbon. Since AR5, new studies have allowed for a tentative assessment of values for tropospheric
38   adjustments to CO2, CH4, N2O, some CFCs, solar forcing, and stratospheric aerosols, and to place a tighter
39   constraint on adjustments from aerosol-cloud interaction (Sections 7.3.2, 7.3.3, 7.3.4). In AR6, the definition
40   of ERF explicitly removes the land-surface temperature change as part of the forcing, in contrast to AR5
41   where only sea-surface temperatures were fixed. The ERF is assessed to be a better predictor of modelled
42   equilibrium temperature change (i.e. less variation in feedback parameter) than SARF (Section 7.3.1).
44   As discussed in Section 7.3.2, the radiative efficiencies for CO2, CH4 and N2O have been updated since AR5
45   (Etminan et al., 2016). There has been a small (1%) increase in the stratospheric-temperature adjusted CO2
46   radiative efficiency, and a +5% tropospheric adjustment has been added. The stratospheric-temperature
47   adjusted radiative efficiency for CH4 is increased by 25% (high confidence). The tropospheric adjustment is
48   tentatively assessed to be –14% (low confidence). A +7% tropospheric adjustment has been added to the
49   radiative efficiency for N2O and +12% to CFC-11 and CFC-12 (low confidence).
51   For aerosols there has been a convergence of model and observational estimates of aerosol forcing, and the
52   partitioning of the total aerosol ERF has changed. Compared to AR5 a greater fraction of the ERF is assessed
53   to come from ERFaci compared to the ERFari. It is now assessed as virtually certain that the total aerosol
54   ERF (ERFari+aci) is negative.
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 2      Summary ERF assessment
 4   Figure 7.6 shows the industrial-era ERF estimates for 1750 to 2019 for the concentration change in different
 5   forcing agents. The assessed uncertainty distributions for each individual component are combined with a
 6   100,000-member Monte Carlo simulation that samples the different distributions, assuming they are
 7   independent, to obtain the overall assessment of total present-day ERF (Supplementary Material 7.SM.1).
 8   The corresponding emissions based ERF figure is shown in Chapter 6, Figure 6.12.
13   Figure 7.6: Change in effective radiative forcing from 1750 to 2019 by contributing forcing agents (carbon
14               dioxide, other well-mixed greenhouse gases (WMGHGs), ozone, stratospheric water vapour,
15               surface albedo, contrails and aviation-induced cirrus, aerosols, anthropogenic total, and solar).
16               Solid bars represent best estimates, and very likely (5–95%) ranges are given by error bars. Non-CO2
17               WMGHGs are further broken down into contributions from methane (CH4), nitrous oxide (N2O) and
18               halogenated compounds. Surface albedo is broken down into land use changes and light absorbing
19               particles on snow and ice. Aerosols are broken down into contributions from aerosol-cloud interactions
20               (ERFaci) and aerosol-radiation interactions (ERFari). For aerosols and solar, the 2019 single-year values
21               are given (Table 7.8) that differ from the headline assessments in both cases. Volcanic forcing is not
22               shown due to the episodic nature of volcanic eruptions. Further details on data sources and processing are
23               available in the chapter data table (Table 7.SM.14).
25   [END FIGURE 7.6 HERE]
30   Table 7.8:     Summary table of ERF estimates for AR6 and comparison with the four previous IPCC assessment
31                  reports. Prior to AR5 values are SARF. For AR5 ari and aci are ERF, all other values assume ERF equals
32                  SARF. 5% to 95% ranges are shown. Volcanic ERF is not added to the table due to the episodic nature of
33                  volcanic eruptions which makes it difficult to compare to the other forcing mechanisms. Solar ERF is
34                  based on TSI and not spectral variation.

                        Global Mean Effective Radiative Forcing (W m–2)
     Driver             SAR           TAR        AR4        AR5         AR6                      Comment
                        (1750–1993) (1750–       (1750–     (1750–      (1750–2019)
                                      1998)      2005)      2011)
     CO2                1.56 [1.33    1.46 [1.31 1.66 [1.49 1.82 (1.63 2.16 [1.90                Increases in
                        to 1.79]      to 1.61]   to 1.83]   to 2.01)    to 2.41]                 concentrations.
     CH4                0.47 [0.40    0.48 [0.41 0.48 [0.43 0.48 [0.43 0.54 [0.43                Changes to radiative
                        to 0.54       to 0.55]   to 0.53]   to 0.53]    to 0.65]                 efficiencies.
                                                                                                 Inclusion of
     N2O                0.14 [0.12    0.15 [0.14 0.16 [0.14 0.17 [0.14 0.21 [0.18
                        to 0.16]      to 0.16]   to 0.18]   to 0.20]    to 0.24]
     Halogenated        0.26 [0.22    0.36 [0.31 0.33 [0.30 0.36 [0.32 0.41 [0.33
     species            to 0.30]      to 0.41]   to 0.36]   to 0.40]    to 0.49]
     Tropospheric       0.4 [0.2      0.35 [0.20 0.35 [0.25 0.40 [0.20 0.47 [0.24                Revised precursor
     ozone              to 0.6]       to 0.50]   to 0.65]   to 0.60]    to 0.71]                 emissions. No
     Stratospheric      –0.1 [–0.2 to –0.15      –0.05      –0.05 [–                             tropospheric
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     ozone            –0.05]         [–0.25      [–0.15            0.15                        adjustment assessed.
                                     to –0.05]   to 0.05]          to 0.05]                    No trop-strat

     Stratospheric    Not estimated [0.01 to     0.07 [0.02        0.07 [0.02   0.05 [0.00     Downward revision
     water vapour                    0.03]       to 0.1])          to 0.12]     to 0.10]       due to adjustments.
     Aerosol–         –0.5 [–0.25 to Not         –0.50 [–          –0.45 [–     –0.22 [–0.47   ERFari magnitude
     radiation        –1.0]          estimated   0.90              0.95         to 0.04]       reduced by about 50%
     interactions                                to –0.10]         to 0.05]                    compared to AR5,
                                                                                               based on agreement
                                                                                               between observation-
                                                                                               based and modelling-
                                                                                               based evidence
     Aerosol–cloud [–1.5 to 0.0] [–2.0 to        –0.7 [–1.8 –0.45 [–1.2 –0.84 [–1.45           ERFaci magnitude
     interactions  (sulphate     0.0]            to –0.3]   to 0.0]     to –0.25]              increased by about
                   only)         (all            (all                                          85% compared to AR5,
                                 aerosols)       aerosols)                                     based on agreement
                                                                                               between observation-
                                                                                               based and modelling-
                                                                                               based lines of evidence
      Land use        Not estimated –0.2 [–0.4 –0.2 [–0.4          –0.15 [–     –0.20 [–0.30   Includes irrigation.
                                    to 0.0]    to 0.0]             0.25 to –    to –0.10]
     Surface albedo Not estimated Not            0.10 [0.00        0.04 [0.02   0.08 [0.00     Increased since AR5 to
     (black+organic               estimated      to 0.20]          to 0.09]     to 0.18]       better account for
     carbon aerosol                                                                            temperature effects
     on snow and
     Combined       Not estimated [0.00 to       Not               0.05 [0.02   0.06 [0.02     Narrower range since
     contrails and                0.04]          estimated         to 0.15]     to 0.10]       AR5
     induced cirrus

     Total         Not estimated Not             1.6 [0.6 to 2.3 [1.1 to 2.72 [1.96 to         Increase due to
     anthropogenic               estimated       2.4]        3.3]        3.48]                 greenhouse gases,
                                                                                               compensated slightly
                                                                                               by aerosol ERFaci
     Solar            0.3 [0.1       0.3 [0.1 to 0.12 [0.06        0.05 [0.0    0.01 [–0.06    Revised historical TSI
     irradiance       to 0.5]        0.5]        to 0.30]          to 0.10]     to 0.08]       estimates and
 2   [END TABLE 7.8 HERE]
 5   The total anthropogenic ERF over the industrial era (1750–2019) is estimated as 2.72 [1.96 to 3.48] W m–2
 6   (Table 7.8; Annex III) (high confidence). This represents a 0.43 W m–2 increase over the assessment made in
 7   AR5 (Myhre et al., 2013b) for the period 1750–2011. This increase is a result of compensating effects.
 8   Atmospheric concentration increases of greenhouse gases since 2011 and upwards revisions of their forcing
 9   estimates have led to a 0.59 W m–2 increase in their ERF. Whereas, the total aerosol ERF is assessed to be
10   more negative compared to AR5, due to revised estimates rather than trends (high confidence).
12   Greenhouse gases, including ozone and stratospheric water vapour from methane oxidation, are estimated to

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 1   contribute an ERF of 3.84 [3.46 to 4.22] W m–2 over 1750–2019. Carbon dioxide continues to contribute the
 2   largest part (56 ± 16 %) of this GHG ERF (high confidence).
 4   As discussed in Section 7.3.3, aerosols have in total contributed an ERF of –1.1 [–1.7 to –0.4] W m–2 over
 5   1750-2019 (medium confidence). Aerosol-cloud interactions contribute approximately 75–80% to this ERF
 6   with the remainder due to aerosol-radiation interactions (Table 7.8).
 8   For the purpose of comparing forcing changes with historical temperature change (Section 7.5.2), longer
 9   averaging periods are useful. The change in ERF from the second half of the 19th century (1850–1900)
10   compared with a recent period (2006–2019) is 2.20 [1.53 to 2.91] W m–2, of which 1.71 [1.51 to 1.92] W m–2
11   is due to CO2.
14   Temperature Contribution of forcing agents
16   The estimated contribution of forcing agents to the 2019 global surface air temperature (GSAT) change
17   relative to 1750 is shown in Figure 7.7. These estimates were produced using concentration-derived ERF
18   timeseries presented in Chapter 2, Figure 2.10 and described in Supplementary Material 7.SM.1.3. The
19   resulting GSAT changes over time are shown in Figure 7.8. The historical timeseries of ERFs for the
20   WMGHGs can be derived by applying the ERF calculations of Section 7.3.2 to the observed timeseries of
21   WMGHG concentrations in Chapter 2, Section 2.2.
23   These ERF timeseries are combined with a two-layer emulator (Cross-Chapter Box 7.1, Supplementary
24   Material 7.SM.2) using a 2,237-member constrained Monte Carlo sample of both forcing uncertainty (by
25   sampling ERF ranges) and climate response (by sampling ECS, TCR and ocean heat capacity ranges). The
26   net model warming over the historical period is matched to the assessment of historical GSAT warming from
27   1850–1900 to 1995–2014 of 0.85 [0.67 to 0.98]°C (Chapter 2, Cross-Chapter Box 2.3) and ocean heat
28   content change from 1971 to 2018 (Section, therefore the model gives the breakdown of the GSAT
29   trend associated with different forcing mechanisms that are consistent with the overall GSAT change. The
30   model assumes that there is no variation in feedback parameter across forcing mechanism (see Section 7.3.1)
31   and variations in the effective feedback parameter over the historical record (Section 7.4.4). The distribution
32   of ECS was informed by Section 7.5.5 and chosen to approximately maintain the best estimate and
33   likely/very likely ranges assessed in that section (see also Supplementary Material 7.SM.2). The TCR has an
34   ensemble median value of 1.81°C, in good agreement with Section 7.5.5. Two error bars are shown in Figure
35   7.7. The dashed error bar shows the contribution of ERF uncertainty (as assessed in the Section 7.3
36   subsections) employing the best estimate of climate response with an ECS of 3.0 °C. The solid bar is the
37   total response uncertainty using the Section 7.5.5 assessment of ECS. The uncertainty in the historic
38   temperature contributions for the different forcing agents are mostly due to uncertainties in ERF, yet for the
39   WMGHG the uncertainty is dominated by the climate response as its ERF is relatively well known (Figure
40   7.7). From the assessment of emulator responses in Cross-Chapter Box 7.1, there is high confidence that
41   calibrated emulators such as the one employed here can represent the historical GSAT change from 1850-
42   1900 to 1995–2014 to within 5% for the best estimate and 10% for the very likely range (Supplementary
43   Table 7.SM.4). This gives high confidence in the overall assessment of GSAT change for the response to
44   ERFs over 1750–2019 derived from the emulator.
46   The total human forced GSAT change from 1750–2019 is calculated to be 1.29 [1.00 to 1.65] °C (high
47   confidence). Although the total emulated GSAT change has high confidence, the confidence of the individual
48   contributions matches those given for the ERF assessment in Section 7.3 subsections. The calculated GSAT
49   change is comprised of a well-mixed greenhouse gas warming of 1.58 [1.17 to 2.17] °C (high confidence), a
50   warming from ozone changes of 0.23 [0.11 to 0.39] °C (high confidence), a cooling of –0.50 [–0.22 to –0.96]
51   °C from aerosol effects (medium confidence). The aerosol cooling has considerable regional time
52   dependence (Chapter 6, Section 6.4.3) but has weakened slightly over the last 20 years in the global mean
53   (Figure 7.8 and Chapter 2, Figure 2.10). There is also a –0.06 [–0.15 to +0.01] °C contribution from surface
54   reflectance changes which dominated by land-use change (medium confidence). Changes in solar and
55   volcanic activity are assessed to have together contributed a small change of –0.02 [–0.06 to +0.02] °C since
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 1   1750 (medium confidence).
 3   The total (anthropogenic plus natural) emulated GSAT between 1850–1900 and 2010–2019 is 1.14 [0.89 to
 4   1.45]°C, compared to the assessed GSAT of 1.06 [0.88 to 1.21] °C (Section 2.3.1; Cross Chapter Box 2.3).
 5   The emulated response is slightly warmer than the observations and has a larger uncertainty range. As the
 6   emulated response attempts to constrain to multiple lines of evidence (Supplementary Material 7.SM.2), only
 7   one of which is GSAT, they should not necessarily be expected to exactly agree. The larger uncertainty
 8   range in the emulated GSAT compared to the observations is reflective of the uncertainties in ECS, TCR and
 9   ERF (particularly the aerosol ERF) which drive the emulator response.
11   The emulator gives a range of GSAT response for the 1750 to the 1850–1900 period of 0.09 [0.04 to 0.14 ]
12   °C from a anthropogenic ERFs. These results are used as a line of evidence for the assessment of this change
13   in Chapter 1 (Cross-Chapter Box 1.2), which gives an overall assessment of 0.1 °C [likely range -0.1 to 0.3]
14   °C.
19   Figure 7.7: The contribution of forcing agents to 2019 temperature change relative to 1750 produced using the
20               two-layer emulator (Supplementary Material 7.SM.2), constrained to assessed ranges for key
21               climate metrics described in Cross-Chapter Box 7.1. The results are from a 2,237-member ensemble.
22               Temperature contributions are expressed for carbon dioxide, other well-mixed greenhouse gases
23               (WMGHGs), ozone, stratospheric water vapour, surface albedo, contrails and aviation-induced cirrus,
24               aerosols, solar, volcanic, and total. Solid bars represent best estimates, and very likely (5–95%) ranges are
25               given by error bars. Dashed error bars show the contribution of forcing uncertainty alone, using best
26               estimates of ECS (3.0°C), TCR (1.8°C) and two-layer model parameters representing the CMIP6 multi-
27               model mean. Solid error bars show the combined effects of forcing and climate response uncertainty
28               using the distribution of ECS and TCR from Tables 7.13 and 7.14, and the distribution of calibrated
29               model parameters from 44 CMIP6 models. Non-CO2 WMGHGs are further broken down into
30               contributions from methane (CH4), nitrous oxide (N2O) and halogenated compounds. Surface albedo is
31               broken down into land use changes and light absorbing particles on snow and ice. Aerosols are broken
32               down into contributions from aerosol-cloud interactions (ERFaci) and aerosol-radiation interactions
33               (ERFari). Further details on data sources and processing are available in the chapter data table (Table
34               7.SM.14).
36   [END FIGURE 7.7 HERE]
39   Figure 7.8 presents the GSAT timeseries using ERF timeseries for individual forcing agents rather than their
40   aggregation. It shows that for most of the historical period the long timescale total GSAT trend estimate from
41   the emulator closely follows the CO2 contribution. The GSAT estimate from non-CO2 greenhouse gas
42   forcing (from other WMGHGs and ozone) has been approximately cancelled out in the global average by a
43   cooling GSAT trend from aerosol. However, since 1980 the aerosol cooling trend has stabilised and may
44   have started to reverse so over the last few decades the long-term warming has been occurring at a faster rate
45   than that expected by CO2 alone (high confidence, see also Chapter 2, Section 2.2.6 and 2.2.8). Throughout
46   the record, but especially prior to 1930, periods of volcanic cooling dominate decadal variability. These
47   estimates of the forced response are compared with model simulations and attributable warming estimates in
48   Chapter 3, Section 3.3.1.
53   Figure 7.8: Attributed global surface air temperature change (GSAT) from 1750 to 2019 produced using the
54               two-layer emulator (Supplementary Material 7.SM.2), forced with ERF derived in this chapter
55               (displayed in Chapter 2, Figure 2.10) and climate response constrained to assessed ranges for key
56               climate metrics described in Cross-Chapter Box 7.1. The results shown are the medians from a 2,237-
57               member ensemble that encompasses uncertainty in forcing and climate response (year-2019 best
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 1                estimates and uncertainties are shown in Figure 7.7 for several components). Temperature contributions
 2                are expressed for carbon dioxide, methane, nitrous oxide, other well-mixed greenhouse gases
 3                (WMGHGs), ozone, aerosols, other anthropogenic forcings, total anthropogenic, solar, volcanic, and
 4                total. Shaded uncertainty bands show very likely ranges. Further details on data sources and processing
 5                are available in the chapter data table (Table 7.SM.14).
 7   [END FIGURE 7.8 HERE]
12   Cross-Chapter Box 7.1:          Physical emulation of Earth System Models for scenario classification and
13                                   knowledge integration in AR6
15   Contributors: Zebedee Nicholls (Australia), Malte Meinshausen (Australia/Germany), Piers Forster
16   (UK), Kyle Armour (USA), Terje Berntsen (Norway), William Collins (UK), Christopher Jones (UK), Jared
17   Lewis (Australia/New Zealand), Jochem Marotzke (Germany), Sebastian Milinski (Germany), Joeri Rogelj
18   (Austria/Belgium), Chris Smith (UK)
20   Climate model emulators are simple physically-based models that are used to approximate large-scale
21   climate responses of complex Earth System Models (ESMs). Due to their low computational cost they can
22   populate or span wide uncertainty ranges that ESMs cannot. They need to be calibrated to do this and, once
23   calibrated, they can aid inter-ESM comparisons and act as ESM extrapolation tools to reflect and combine
24   knowledge from ESMs and many other lines of evidence (Geoffroy et al., 2013a; Good et al., 2013; Smith et
25   al., 2018a). In AR6, the term 'climate model emulator' (or simply emulator) is preferred over 'simple’ or
26   ‘reduced-complexity climate model' to reinforce their use as specifically calibrated tools (Cross-Chapter Box
27   7.1, Figure 1). Nonetheless, simple physically-based climate models have a long history of use in previous
28   IPCC reports (Chapter 1, Section Climate model emulators can include carbon and other gas cycles
29   and can combine uncertainties along the cause-effect chain from emissions to temperature response.
30   AR5(Collins et al., 2013a) used the MAGICC6 emulator (Meinshausen et al., 2011a) in a probabilistic setup
31   (Meinshausen et al., 2009) to explore the uncertainty in future projections. A simple impulse response
32   emulator (Good et al., 2011) was also used to ensure a consistent set of ESM projections could be shown
33   across a range of scenarios. AR5 WGI Chapter 8 (Myhre et al., 2013b) employed a two-layer emulator for
34   quantifying Global Temperature Potentials (GTP). In AR5 WGIII (Clarke et al., 2014), MAGICC6 was also
35   used for the classification of scenarios, and in AR5 Synthesis Report (IPCC, 2014) this information was used
36   to estimate carbon budgets. In SR1.5, two emulators were used to provide temperature projections of
37   scenarios: the MAGICC6 model, which was used for the scenario classification, and the FaIR1.3 model
38   (Millar et al., 2017; Smith et al., 2018a).
40   SR1.5 found that the physically-based emulators produced different projected non-CO2 forcing and
41   identified the largely unexplained differences between the two emulators used as a key knowledge gap
42   (Forster et al., 2018). This led to a renewed effort to test the skill of various emulators. The Reduced
43   Complexity Model Intercomparison Project (RCMIP; Nicholls et al. (2020)) found that the latest generation
44   of the emulators can reproduce key characteristics of the observed changes in global surface air temperature
45   (GSAT) together with other key responses of ESMs (Cross-Chapter Box 7.1, Figure 1a). In particular,
46   despite their reduced structural complexity, some emulators are able to replicate the non-linear aspects of
47   ESM GSAT response over a range of scenarios. GSAT emulation has been more thoroughly explored in the
48   literature than other types of emulation. Structural differences between emulation approaches lead to
49   different outcomes and there are problems with emulating particular ESMs. In conclusion, there is medium
50   confidence that emulators calibrated to single ESM runs can reproduce ESM projections of the forced GSAT
51   response to other similar emissions scenarios to within natural variability (Meinshausen et al., 2011b;
52   Geoffroy et al., 2013a; Dorheim et al., 2020; Nicholls et al., 2020; Tsutsui, 2020), although larger differences
53   can remain for scenarios with very different forcing characteristics. For variables other than GSAT there has
54   not yet been a comprehensive effort to evaluate the performance of emulators.

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 1   Application of emulators in AR6 WGI
 2   Cross-Chapter Box 7.1 Table 1 shows the use of emulators within the WGI Report. The main use of
 3   emulation in the Report is to estimate GSAT change from Effective Radiative Forcing (ERF) or
 4   concentration changes, where various versions of a two layer energy budget emulator are used. The two-
 5   layer emulator is equivalent to a two-timescale impulse response model (Geoffroy et al., 2013b,
 6   Supplementary Material 7.SM.2). Both a single configuration version and probabilistic forms are used. The
 7   emulator is an extension of the energy budget equation (Equation 7.1) and allows for heat exchange between
 8   the upper- and deeper-ocean layers, mimicking the ocean heat uptake that reduces the rate of surface
 9   warming under radiative forcing (Gregory, 2000; Held et al., 2010; Winton et al., 2010; Armour, 2017;
10   Mauritsen and Pincus, 2017; Rohrschneider et al., 2019). Although the same energy budget emulator
11   approach is used, different calibrations are employed in various sections, to serve different purposes and
12   keep lines of evidence as independent as possible. Chapter 9 additionally employs projections of ocean heat
13   content from the Chapter 7 two-layer emulator to estimate the thermostatic component to future sea-level
14   rise (see Chapter 9, Section 9.6.3 and Supplementary Material 7.SM.2).
16   Emission-driven emulators, as opposed to ERF- or concentration-driven emulators are also used in the
17   Report. In Chapter 4 (Section 4.6) MAGICC7 is used to emulate GSAT beyond 2100 since its long-term
18   response has been assessed to be fit-for-purpose to represent the behaviour of ESMs. In Chapter 5 (Section
19   5.5) MAGICC7 is used to explore the non-CO2 GSAT contribution in emissions scenarios. In Chapter 6 and
20   Chapter 7 (Section 7.6), two-layer model configurations were tuned to match the probabilistic GSAT
21   responses of FaIRv1.6.2 and MAGICC7 emission-driven emulators. For Chapter 6 the two median values
22   from FaIRv1.6.2 and MAGICC7 emulators are averaged and then matched to the best-estimate ECS of 3°C
23   and TCR of 1.8 °C (Table 7.13 and Table 7.14) under the best-estimate ERF due to a doubling of CO2 of
24   3.93 W m-2 (Table 7.4). For Section 7.6 a distribution of responses are used from the two emulators to
25   estimate uncertainties in Global Temperature-change Potentials.
30   Cross-Chapter Box 7.1, Table 1: Use of emulation within the WGI report
          Chapter (Ch) and           Application and emulator type                                 Emulated
          Section                                                                                  Variables

          Ch1, Cross Chapter-        Estimate anthropogenic temperature change pre-1850,           GSAT
          Box 1.2                    based on radiative forcing time series from Chapter 7.
                                     Uses the Chapter 7 calibrated 2-layer emulator: a two-
                                     layer energy budget emulator, probabilistically calibrated
                                     to AR6 ECS, TCR, historical warming and ocean heat
                                     uptake ranges, driven by the Chapter 7 concentration
                                     based ERFs.

          Ch 3, Section 3.3          Investigation of the historical temperature response to       GSAT
                                     individual forcing mechanisms to compliment detection
          Ch 7, Section 7.3          and attribution results. Uses the Chapter 7 calibrated two-
                                     layer emulator.

          Ch 4, Box 4.1              Understanding the spread in global surface air         GSAT
                                     temperature increase of CMIP6 models and comparison to
                                     other assessments; assessment of contributions to
                                     projected temperature uncertainty. Uses a two-layer
                                     emulator calibrated to the Chapter 7 ECS and TCR

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                                assessment driven by Chapter 7 best-estimate ERFs.

     Ch 4, Section 4.6          Emulators used to assess differences in radiative forcing    ERF, GSAT
                                and GSAT response between RCP and SSP scenarios.
                                Uses the Chapter 7 ERF timeseries and the MAGICC7
                                probabilistic emission-driven emulator for GSAT
                                calibrated to the WGI assessment.

     Ch 4, Section 4.7          Emulator used for long-term GSAT projections (post-          GSAT
                                2100) to complement the small number of ESMs with
                                data beyond 2100. Uses the MAGICC7 probabilistic
                                emission-driven emulator calibrated to the WGI

     Ch 5, Section 5.5          Estimated non-CO2 warming contributions of mitigation        GSAT
                                scenarios at the time of their net zero CO2 emissions for
                                integration in the assessment of remaining carbon
                                budgets. Uses the MAGICC7 probabilistic emission-
                                driven emulator calibrated to the WGI assessment.

     Ch 6, Section 6.6          Estimated contributions to future warming from SLCFs         GSAT
                                across SSP scenarios based on ERF timeseries. Uses a
     Ch 6, Section 6.7          single two-layer emulator configuration derived from the
                                medians of MAGICC7 and FaIRv1.6.2 AR6 WG1 GSAT
                                probabilistic responses and the best-estimate of ECS and

     Ch.7, Section 7.5          Estimating a process based TCR from a process based          TCR
                                ECS. Uses a two-layer emulator in probabilistic form
                                calibrated to process based estimates from Chapter 7; a
                                different calibration compared to the main Chapter 7

     Ch 7, Section 7.6          Deriving emission metrics. Uses two-layer emulator           Global
                                configurations derived from MAGICC7 and FaIRv1.6.2           Temperature-
                                AR6 WG1 probabilistic GSAT responses.                        change
                                                                                             Potentials and

     Ch 9, Section 9.6          Deriving global mean sea level projections. Uses the         Sea level and
                                Chapter 7 calibrated two-layer emulator for GSAT and         ice loss
                                ocean heat content, where GSAT drives regional
                                statistical emulators of ice sheets and glaciers.

     Ch 11, Section 11.2        Regional patterns of response are compared to global         Various
     and Cross-Chapter          mean trends. Assessed literature includes projections with   regional

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          Box 11.1                   a regional pattern scaling and variability emulator.             information

 5   Emission-driven emulators for scenario classification in AR6 WGIII
 7   As in AR5 and SR1.5, emission-driven emulators are used to communicate outcomes of the physical climate
 8   science assessment and uncertainties to quantify the temperature outcome associated with different emission
 9   scenarios. In particular, the computational efficiency of these emulators allows the analysis of a large
10   number of multi-gas emissions scenarios in terms of multiple characteristics, e.g., year of peak temperature
11   or the 2030 emission levels in line with keeping global warming to below 1.5°C or 2.0 oC.
13   Four emission-driven emulators have been considered as tools for WGIII to explore the range of GSAT
14   response to multiple scenarios beyond those assessed in WGI. The four emulators are CICERO-SCM (Skeie
15   et al., 2017, 2021), FaIRv1.6.2 (Millar et al., 2017; Smith et al., 2018a), MAGICC7 (Meinshausen et al.,
16   2009) and OSCARv3.1.1 (Gasser et al., 2017a, 2020). Each emulator's probabilistic distribution has been
17   calibrated to capture the relationship between emissions and GSAT change. The calibration is informed by
18   the WGI assessed ranges of ECS, TCR, historical GSAT change, ERF, carbon cycle metrics and future
19   warming projections under the (concentration-driven) SSP scenarios. The emulators are then provided as a
20   tool for WGIII to perform a GSAT-based classification of mitigation scenarios consistent with the physical
21   understanding assessed in WGI.. The calibration step reduced the emulator differences identified in SR1.5.
22   Note that evaluation of both central and range estimates of each emulator’s probabilistic projections is
23   important to assess the fitness-for-purpose for the classification of scenarios in WGIII based on information
24   beyond the central estimate of GSAT warming.
29   Cross-Chapter Box 7.1, Figure 1: A comparison between the global-mean surface air temperature response of
30                                   various calibrated simple climate models, assessed ranges and Earth System
31                                   Models. The top panels compare the assessed historical GSAT time series (Chapter
32                                   2, Cross Chapter Box 2.3) with four multi-gas emulators calibrated to replicate
33                                   numerous assessed ranges (Cross-Chapter Box 7.1, Table 2 below) (panel a) and
34                                   also compares idealized CO2-only concentration scenario response for one ESM
35                                   (IPSL CM6A-LR) and multiple emulators which participated in RCMIP Phase 1
36                                   (Nicholls et al., 2020) calibrated to that single ESM (panel b). The bottom panels
37                                   compare this Report’s assessed ranges for GSAT warming (Chapter 4, Box 4.1)
38                                   under the multi-gas scenario SSP1-2.6 with the same calibrated emulators as in
39                                   panel a (panel c and d). For context, a range of CMIP6 ESM results are also shown
40                                   (thin lines in bottom-left panel c and open circles in bottom-right panel d). Panel b)
41                                   adapted from Nicholls et al. (2020). Further details on data sources and processing
42                                   are available in the chapter data table (Table 7.SM.14).
47   MAGICC7 and FaIRv1.6.2 emission based emulators are able to represent the WGI assessment to within
48   small differences (defined here as within typical rounding precisions of ±5% for central estimates and ±10%
49   for ranges) across more than 80% of metric ranges (Cross-Chapter Box 7.1, Table 2 below). Both calibrated
50   emulators are consistent with assessed ranges of ECS, historical GSAT, historical ocean heat uptake, total
51   greenhouse gas ERF, methane ERF and the majority of the assessed SSP warming ranges. FaIRv1.6.2 also
52   matches the assessed central value of TCRE and airborne fraction. Whereas, MAGICC7 matches the
53   assessed TCR ranges as well as providing a closer fit to the SSP warming ranges for the lower emission
54   scenarios. In the evaluation framework considered here, CICERO-SCM represents historical warming to
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 1   within 2% of the assessed ranges and also represents future temperatures ranges across the majority of the
 2   assessment although it lacks the representation of the carbon cycle. In this framework, OSCARv3.1.1 is less
 3   able to represent the assessed projected GSAT ranges although it matches the range of airborne fraction
 4   estimates closely and the assessed historical GSAT likely range to within 0.5%. Despite these identified
 5   limitations, both CICERO-SCM and OSCARv3.1.1 provide additional information for evaluating the
 6   sensitivity of scenario classification to model choice.
 8   How emulators match the assessed ranges used for the evaluation framework is summarised here and in
 9   Table 2. The first is too low projections in 2081–2100 under SSP1-1.9 (8% or 15% too low for the central
10   estimate and 15% or 25% too low for the lower end in the case of MAGICC7 or FaIRv1.6.2, respectively).
11   The second is the representation of the aerosol effective radiative forcing (both MAGICC7 and FaIRv1.6.2
12   are greater than 8% less negative than the central assessed range and greater than 10% less negative for the
13   lower assessed range), as energy balance models struggle to reproduce an aerosol ERF with a magnitude as
14   strong as the assessed best estimate and still match historical warming estimates. Both emulators have
15   medium to large differences compared to the TCRE and airborne fraction ranges (see note of Table 2).
16   Finally, there is also a slight overestimate of the low-end of the assessed historical GSAT range.
18   Overall, there is high confidence that emulated historical and future ranges of GSAT change can be
19   calibrated to be internally-consistent with the assessment of key physical-climate indicators in this Report:
20   greenhouse gas ERFs, ECS and TCR. When calibrated to match the assessed ranges of GSAT and multiple
21   physical climate indicators, physically-based emulators can reproduce the best estimate of GSAT change
22   over 1850–1900 to 1995–2014 to within 5% and very likely range of this GSAT change to within 10%.
23   MAGICC7 and FaIRv1.6.2 match at least two-thirds of the Chapter 4 assessed projected GSAT changes to
24   within these levels of precision.
29   Cross-Chapter Box 7.1, Table 2: Percentage differences between the emulator value and the WGI assessed best
30                                   estimate and range for key metrics. Values are given for four emulators in their
31                                   respective AR6-calibrated probabilistic setups. Absolute values of these indicators
32                                   are shown in Supplementary Table 7.SM.4.
      Emulator                                          CICERO-SCM                   FaIRv1.6.2                  MAGICC7                 OSCARv3.1.1

      Assessed range                              Lower    Central   Upper    Lowe    Centra      Upper   Lowe    Centra   Uppe   Lowe     Centra   Upper
                                                                              r       l                   r       l        r      r        l

      Key metrics

      ECS (oC)                                    26%      2%        –18%     3%      –2%         1%      –3%     –1%      –3%    –8%      –15%     –22%

      TCRE (oC per 1000 Gt C)**                                               29%     –7%         –21%    37%     5%       –5%    50%      –8%      –20%

      TCR (oC)                                    15%      –5%       –3%      14%     0%          3%      6%      4%       9%     26%      1%       –14%

      Historical warming and Effective Radiative Forcing

      GSAT warming (oC)              1995–
                                     2014 rel.
                                                  2%       0%        0%       7%      3%          4%      7%      1%       –1%    –0%      –8%      –0%

      Ocean heat content change      1971–                                                                                        –
                                                  –24%     –27%      –29%     5%      –4%         –9%     –1%     –3%      –6%             –39%     10%
      (ZJ)*                          2018                                                                                         47%

      Total Aerosol ERF (W m-2)      2005–
                                     2014 rel.    36%      37%       10%      16%     12%         0%      10%     8%       8%     38%      15%      –31%

      GHG ERF (W m-2)                2019 rel.
                                                  4%       –5%       –13%     1%      2%          1%      2%      1%       –0%    1%       3%       –3%

      Methane ERF (W m-2)            2019 rel.    31%      4%        –13%     3%      3%          3%      0%      –0%      3%     8%       –1%      –5%

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      Carbon Cycle metrics

      Airborne Fraction 1pctCO2    2×CO2                             8%      –3%    –11%   12%   6%    –1%   1%     –0%    8%

      Airborne Fraction 1pctCO2    4×CO2                             12%     1%     –9%    15%   4%    –6%   5%     –1%    –1%

      Future warming (GSAT) relative to 1995–2014

       SSP1-1.9 (oC)               2021–
                                                10%    –4%    10%    3%      1%     11%    2%    –0%   4%    12%    –9%    –25%

                                   2041–                             –
                                                8%     –9%    7%             –8%    6%     –1%   –1%   7%    12%    –8%    –31%
                                   2060                              11%

                                   2081–                             –                     –
                                                –12%   –25%   –2%            –15%   4%           –8%   3%    7%     –10%   –31%
                                   2100                              25%                   15%

       SSP1-2.6 (oC)               2021–
                                                7%     –5%    5%     2%      1%     8%     –1%   –2%   –0%   9%     –9%    –28%

                                                8%     –6%    2%     –2%     –2%    5%     0%    1%    2%    15%    –6%    –28%

                                                –2%    –14%   –5%    –8%     –7%    1%     –6%   –1%   1%    17%    –9%    –29%

       SSP2-4.5 (oC)               2021–
                                                8%     –5%    5%     7%      –1%    2%     3%    –3%   –2%   –5%    –14%   –30%

                                                4%     –4%    3%     1%      –1%    2%     1%    1%    2%    8%     –8%    –28%

                                                –1%    –10%   –3%    –2%     –3%    1%     –2%   1%    3%    8%     –4%    –25%

       SSP3-7.0 (oC)               2021–
                                                11%    –4%    1%     14%     1%     –1%    10%   1%    –0%   –5%    –15%   –29%

                                                4%     –5%    –0%    6%      0%     –1%    7%    4%    1%    7%     –8%    –26%

                                                –0%    –8%    –3%    3%      –1%    –1%    6%    3%    6%    5%     –6%    –25%

       SSP5-8.5 (oC)               2021–
                                                5%     –7%    2%     9%      2%     4%     7%    1%    2%    1%     –14%   –30%

                                                2%     –8%    –1%    4%      0%     4%     3%    2%    4%    10%    –6%    –24%

                                                4%     –7%    –3%    6%      –0%    1%     8%    4%    7%    9%     –4%    –25%

 2   Notes. Metrics calibrated against are equilibrium climate sensitivity, ECS (Section 7.5); transient climate response to
 3   cumulative emissions of carbon dioxide, TCRE (Chapter 5, Section 5.5); transient climate response, TCR (Section 7.5),
 4   historical GSAT change (Chapter 2, Section 2.3), ocean heat uptake (Section 7.2 and Chapter 2, Section 2.3) and
 5   effective radiative forcing, ERF (Section 7.3), carbon cycle metrics, namely airborne fractions of idealized CO2
 6   scenarios (taking the likely range as twice the standard deviation across the models analysed in Arora et al. (2020), see
 7   also Chapter 5, Table 5.7, cross-AR6 lines of evidence row) and GSAT projections under the concentration-driven SSP
 8   scenarios for the near-term (2021–2040), mid-term (2041–2060) and long-term (2081–2100) relative to 1995–2014
 9   (Chapter 4, Table 4.2). See Supplementary Table 7.SM.4 for a version of this table with the absolute values rather than
10   percentage differences. The columns labelled “upper” and “lower” indicate 5% to 95% ranges, except for the variables
11   demarcated with an asterisk or double asterisk (* or **), where they denote likely ranges from 17% to 83%. Note that
12   the TCRE assessed range (**) is wider than the combination of the TCR and airborne fraction to account for
13   uncertainties related to model limitations (Chapter 5, Table 5.7) hence it is expected that the emulators are too narrow
14   on this. particular metric and/or too wide on TCR and airborne fraction. For illustrative purposes, the cells are coloured
15   as follows: white cells indicate small differences (up to ±5% for the central value and +10% for the ranges), light blue
16   and light teal cells indicate medium differences (up to +10% and -10% for light blue and light teal for central values,
17   respectively; up to ±20% for the ranges) and darker cells indicate larger positive (blue) or negative (teal) differences
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 1   (note that values are rounded after the colours are applied).
 8   7.4     Climate feedbacks
10   The magnitude of global surface temperature change primarily depends on the strength of the radiative
11   forcings and feedbacks, the latter defined as the changes of the net energy budget at the top of atmosphere
12   (TOA) in response to a change in the GSAT (Box 7.1, Equation 7.1). Feedbacks in the Earth system are
13   numerous, and it can be helpful to categorise them into three groups: (1) physical feedbacks; (2)
14   biogeophysical and biogeochemical feedbacks; and (3) long-term feedbacks associated with ice sheets. The
15   physical feedbacks (for example, associated with changes in lapse-rate, water vapour, surface albedo, or
16   clouds; Sections and biogeophysical/biogeochemical feedbacks (for example, associated
17   with changes in methane, aerosols, ozone, or vegetation; Section act both on time scales that are
18   used to estimate the equilibrium climate sensitivity (ECS) in models (typically 150 years, see Box 7.1) and
19   on longer time scales required to reach equilibrium. Long-term feedbacks associated with ice sheets (Section
20 are relevant primarily after several centuries or more. The feedbacks associated with
21   biogeophysical/biogeochemical processes and ice sheets, often collectively referred to as Earth system
22   feedbacks, had not been included in conventional estimates of the climate feedback (e.g., Hansen et al.,
23   1984), but the former can now be quantified and included in the assessment of the total (net) climate
24   feedback. Feedback analysis represents a formal framework for the quantification of the coupled interactions
25   occurring within a complex Earth system in which everything influences everything else (e.g., Roe, 2009).
26   As used here and presented in Section 7.4.1, its primary objective is to identify and understand the key
27   processes that determine the magnitude of the surface temperature response to an external forcing. For each
28   feedback, the basic underlying mechanisms and their assessment are presented in Section 7.4.2.
30   Up until AR5, process understanding and quantification of feedback mechanisms were based primarily on
31   global climate models. Since AR5, the scientific community has undertaken a wealth of different alternative
32   approaches, including observational and fine-scale modelling approaches. This has in some cases led to more
33   constrained feedbacks and, on the other hand, uncovered shortcomings in global climate models, which are
34   starting to be corrected. Consequently, AR6 achieves a more robust assessment of feedbacks in the climate
35   system that is less reliant on global climate models than in earlier assessment reports.
37   It has long been recognized that the magnitude of climate feedbacks can change as the climate state evolves
38   over time (Manabe and Bryan, 1985; Murphy, 1995), but the implications for projected future warming have
39   been investigated only recently. Since AR5, progress has been made in understanding the key mechanisms
40   behind this time- and state-dependence. Specifically, the state-dependence is assessed by comparing climate
41   feedbacks between warmer and colder climate states inferred from paleoclimate proxies and model
42   simulations (Section 7.4.3). The time-dependence of the feedbacks is evident between the historical period
43   and future projections and is assessed to arise from the evolution of the surface warming pattern related to
44   changes in zonal and meridional temperature gradients (Section 7.4.4).
47   7.4.1    Methodology of the feedback assessment
49   The global surface temperature changes of the climate system are generally analysed with the classical
50   forcing-feedback framework as described in Box 7.1 (Equation 7.1). In this equation α is the net feedback
51   parameter (W m-2 °C–1). As surface temperature changes in response to the TOA energy imbalance, many
52   other climate variables also change, thus affecting the radiative flux at the TOA. The aggregate feedback
53   parameter can then be decomposed into an approximate sum of terms 𝛼𝛼 = ∑𝑥𝑥 𝛼𝛼𝑥𝑥 , where x is a vector
                                                                                                 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑
54   representing variables that have a direct effect on the net TOA radiative flux N and 𝛼𝛼𝑥𝑥 = 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑 . Following

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 1   the conventional definition, the physical climate feedbacks are here decomposed into terms associated with a
 2   vertically uniform temperature change (Planck response, P), changes in the water vapour plus temperature
 3   lapse rate (WV+LR), surface albedo (A) and clouds (C). The water vapour plus temperature lapse rate
 4   feedback is further decomposed using two different approaches, one based on changes in specific humidity,
 5   the other on changes in relative humidity. Biogeochemical feedbacks arise due to changes in aerosols and
 6   atmospheric chemical composition in response to changes in surface temperature, and Gregory et al. (2009)
 7   and Raes et al. (2010) show that they can be analysed using the same framework as for the physical climate
 8   feedbacks (see Chapter 5, Section 5.4 and Chapter 6, Section 6.4.5 Similarly, feedbacks associated with
 9   biogeophysical and ice sheet changes can also be incorporated.
11   In global climate models, the feedback parameters 𝛼𝛼𝑥𝑥 in global warming conditions are often estimated as
12   the mean differences in the radiative fluxes between atmosphere-only simulations in which the change in
13   SST is prescribed (Cess et al., 1990), or as the regression slope of change in radiation flux against change in
14   global-mean surface air temperature using atmosphere-ocean coupled simulations with abrupt CO2 changes
15   (abrupt4xCO2) for 150 years (Gregory et al., 2004; Andrews et al., 2012; Caldwell et al., 2016; see Box 7.1).
16   Neither method is perfect, but both are useful and yield consistent results (Ringer et al., 2014). In the
17   regression method, the radiative effects of land warming are excluded from the effective radiative forcing
18   due to doubling of CO2 (Section 7.3.2), which may overestimate feedback values by about 10%. At the same
19   time, the feedback calculated using the regression over years 1–150 ignores its state-dependence on multi-
20   centennial time scales (Section 7.4.3), probably giving an underestimate of 𝛼𝛼 by about 10% (Rugenstein et
21   al., 2019a). These effects are both small and cancel each other in the ensemble mean, justifying the use of
22   regression over 150 years as an approximation to feedbacks in ESMs.
24   The change of the TOA radiative flux N as a function of the change of a climate variable x (such as water
25   vapour) is commonly computed using the ‘radiative kernel’ method (Soden et al., 2008). In this method, the
26   kernel 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 is evaluated by perturbing x within a radiation code. Then multiplying the kernel by dx/dT
27   inferred from observations, meteorological analysis or GCMs produces a value of 𝛼𝛼𝑥𝑥 .
29   Feedback parameters from lines of evidence other than global models are estimated in various ways. For
30   example, observational data combined with GCM simulations could produce an emergent constraint on a
31   particular feedback (Hall and Qu, 2006; Klein and Hall, 2015), or the observed interannual fluctuations in
32   the global-mean TOA radiation and the surface air temperature, to which the linear regression analysis is
33   applied, could generate a direct estimate of the climate feedback assuming that the feedback associated with
34   internal climate variability at short time scales can be a surrogate of the feedback to CO2-induced warming
35   (Dessler, 2013; Loeb et al., 2016). The assumption is not trivial, but can be justified given that the climate
36   feedbacks are fast enough to occur at the interannual time scale. Indeed, a broad agreement has been
37   obtained in estimates of individual physical climate feedbacks based on interannual variability and longer
38   climate change timescales in GCMs (Zhou et al., 2015; Colman and Hanson, 2017). This means that the
39   climate feedbacks estimated from the observed interannual fluctuations are representative of the longer-term
40   feedbacks (decades to centuries). Care must be taken for these observational estimates because they can be
41   sensitive to details of the calculation such as data sets and periods used (Dessler, 2013; Proistosescu et al.,
42   2018). In particular, there would be a dependence of physical feedbacks on the surface warming pattern at
43   the interannual time scale due, for example, to El Niño-Southern Oscillation. However, this effect both
44   amplifies and suppresses the feedback when data include the positive and negative phases of the interannual
45   fluctuation, and therefore the net bias will be small.
47   In summary, the classical forcing-feedback framework has been extended to include biogeophysical and non-
48   CO2-biogeochemical feedbacks in addition to the physical feedbacks. It has also been used to analyse
49   seasonal and interannual to decadal climate variations in observations and ESMs, in addition to long-term
50   climate changes as seen in abrupt4xCO2 experiments. These developments allow an assessment of the
51   feedbacks based on a larger variety of lines of evidence compared to AR5.
54   7.4.2   Assessing climate feedbacks
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 1   This section provides an overall assessment of individual feedback parameters, αx, by combining different
 2   lines of evidence from observations, theory, process models and ESMs. To achieve this, we review the
 3   understanding of the key processes governing the feedbacks, why the feedback estimates differ among
 4   models, studies or approaches, and the extent to which these approaches yield consistent results. The
 5   individual terms assessed are the Planck response (Section and feedbacks associated with changes in
 6   water vapour and lapse rate (Section, surface albedo (Section, clouds (Section,
 7   biogeophysical and non-CO2 biogeochemical processes (Section, and ice sheets (Section A
 8   synthesis is provided in Section Climate feedbacks in CMIP6 models are then evaluated in Section
 9, with an explanation of how they have been incorporated into the assessment.
12   Planck response
14   The Planck response represents the additional thermal or longwave (LW) emission to space arising from
15   vertically uniform warming of the surface and the atmosphere. The Planck response 𝛼𝛼𝑃𝑃 , often called the
16   Planck feedback, plays a fundamental stabilizing role in Earth’s climate and has a value that is strongly
17   negative: a warmer planet radiates more energy to space. A crude estimate of 𝛼𝛼𝑃𝑃 can be made using the
18   normalized greenhouse effect 𝑔𝑔 ̃, defined as the ratio between the greenhouse effect G and the upwelling LW
19   flux at the surface (Raval and Ramanathan, 1989). Current estimates (Section 7.2, Figure 7.2) give G = 159
20   W m-2 and 𝑔𝑔 ̃ ≈ 0.4. Assuming 𝑔𝑔� is constant, one obtains for a surface temperature Ts = 288K, 𝛼𝛼𝑃𝑃 = (𝑔𝑔� −
21   1) 4 𝜎𝜎 𝑇𝑇𝑠𝑠3 ≈ –3.3 W m-2 °C–1, where 𝜎𝜎 is the Stefan-Boltzmann constant. This parameter 𝛼𝛼𝑃𝑃 is estimated
22   more accurately using kernels obtained from meteorological reanalysis or climate simulations (Soden and
23   Held, 2006; Dessler, 2013; Vial et al., 2013; Caldwell et al., 2016; Colman and Hanson, 2017; Zelinka et al.,
24   2020). Discrepancies among estimates primarily arise because differences in cloud distributions make the
25   radiative kernels differ (Kramer et al., 2019). Using six different kernels, Zelinka et al. (2020) obtained a
26   spread of ±0.1 W m–2 °C–1 (one standard deviation). Discrepancies among estimates secondarily arise from
27   differences in the pattern of equilibrium surface temperature changes among ESMs. For the CMIP5 and
28   CMIP6 models this introduces a spread of ±0.04 W m-2 °C–1 (one standard deviation). The multi-kernel and
29   multi-model mean of 𝛼𝛼𝑃𝑃 is equal to –3.20 W m-2 °C–1 for the CMIP5 and –3.22 W m-2 °C–1 for the CMIP6
30   models (Supplementary Table 7.SM.5). Overall, there is high confidence in the estimate of the Planck
31   response, which is assessed to be 𝛼𝛼𝑃𝑃 = –3.22 W m-2 °C–1 with a very likely range of –3.4 to –3.0 W m–2 °C–1
32   and a likely range of –3.3 to –3.1 W m–2 °C–1.
34   The Planck temperature response ΔTP is the equilibrium temperature change in response to a forcing ΔF
35   when the net feedback parameter is equal to the Planck response parameter: ΔTP = –ΔF / 𝛼𝛼𝑃𝑃 .
38   Water vapour and temperature lapse rate feedbacks
40   Two decompositions are generally used to analyse the feedbacks associated with a change in the water
41   vapour and temperature lapse rate in the troposphere. As in any system, many feedback decompositions are
42   possible, each of them highlighting a particular property or aspect of the system (Ingram, 2010; Held and
43   Shell, 2012; Dufresne and Saint-Lu, 2016). The first decomposition considers separately the changes (and
44   therefore feedbacks) in the lapse rate (LR) and specific humidity (WV). The second decomposition considers
45   changes in the lapse rate assuming constant relative humidity (LR*) separately from changes in relative
46   humidity (RH).
48   The specific humidity (WV) feedback, also known as the water vapour feedback, quantifies the change in
49   radiative flux at the TOA due to changes in atmospheric water vapour concentration associated with a
50   change in global mean air surface temperature. According to theory, observations and models, the water
51   vapour increase approximately follows the Clausius-Clapeyron relationship at the global scale with regional
52   differences dominated by dynamical processes (Chapter 8, Section 8.2.1; Sherwood et al., 2010b; Chung et
53   al., 2014; Romps, 2014; Liu et al., 2018; Schröder et al., 2019). Greater atmospheric water vapour content,
54   particularly in the upper troposphere, results in enhanced absorption of LW and SW radiation and reduced
55   outgoing radiation. This is a positive feedback. Atmospheric moistening has been detected in satellite records
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 1   (Chapter 2, Section, is simulated by climate models (Chapter 3, Section, and the estimates
 2   agree within model and observational uncertainty (Soden et al., 2005; Dessler, 2013; Gordon et al., 2013;
 3   Chung et al., 2014). The estimate of this feedback inferred from satellite observations is αWV = 1.85 ± 0.32
 4   W m–2 °C–1 (Liu et al., 2018). This is consistent with the value αWV = 1.77 ± 0.20 W m–2 °C–1 (one standard
 5   deviation) obtained with CMIP5 and CMIP6 models (Zelinka et al., 2020).
 7   The lapse rate (LR) feedback quantifies the change in radiative flux at the TOA due to a non­uniform change
 8   in the vertical temperature profile. In the tropics, the vertical temperature profile is mainly driven by moist
 9   convection and is close to a moist adiabat. The warming is larger in the upper troposphere than in the lower
10   troposphere (Manabe and Wetherald, 1975; Santer et al., 2005; Bony et al., 2006), leading to a larger
11   radiative emission to space and therefore a negative feedback. This larger warming in the upper troposphere
12   than at the surface has been observed over the last twenty years thanks to the availability of sufficiently
13   accurate observations (Chapter 2, Section In the extra-tropics, the vertical temperature profile is
14   mainly driven by a balance between radiation, meridional heat transport and ocean heat uptake (Rose et al.,
15   2014). Strong wintertime temperature inversions lead to warming that is larger in the lower troposphere
16   (Payne et al., 2015; Feldl et al., 2017a) and a positive lapse rate feedback in polar regions (Manabe and
17   Wetherald, 1975; Bintanja et al., 2012; Pithan and Mauritsen, 2014; Section However, the tropical
18   contribution dominates, leading to a negative global mean lapse rate feedback (Soden and Held, 2006;
19   Dessler, 2013; Vial et al., 2013; Caldwell et al., 2016). The LR feedback has been estimated at interannual
20   time scales using meteorological reanalysis and satellite measurements of TOA fluxes (Dessler, 2013). These
21   estimates from climate variability are consistent between observations and ESMs (Dessler, 2013; Colman
22   and Hanson, 2017). The mean and standard deviation of this feedback under global warming based on the
23   cited studies are αLR = –0.50 ± 0.20 W m–2 °C–1 (Dessler, 2013; Caldwell et al., 2016; Colman and Hanson,
24   2017; Zelinka et al., 2020).
26   The second decomposition was proposed by Held and Shell (2012) to separate the response that would occur
27   under the assumption that relative humidity remains constant from that due to the change in relative
28   humidity. The feedback is decomposed into three: (1) change in water vapour due to an identical
29   temperature increase at the surface and throughout the troposphere assuming constant relative humidity,
30   which will be called the Clausius­Clapeyron (CC) feedback here; (2) change in lapse rate assuming constant
31   relative humidity (LR*); (3) change in relative humidity (RH). Since AR5 it has been clarified that by
32   construction, the sum of the temperature lapse rate and specific humidity (LR+WV) feedbacks is equal to the
33   sum of the Clausius­Clapeyron, lapse rate assuming constant relative humidity, and changes in relative
34   humidity (CC+LR*+RH) feedbacks. Therefore, each of these two sums may simply be referred to as the
35   "water vapour plus lapse rate" feedback.
37   The CC feedback has a large positive value due to well understood thermodynamic and radiative processes:
38   αCC = 1.36 ± 0.04 W m–2 °C–1 (one standard deviation) (Held and Shell, 2012; Zelinka et al., 2020). The lapse
39   rate feedback assuming a constant relative humidity LR* in CMIP6 models has small absolute values (αLR* =
40   -0.10 ± 0.07 W m–2 °C–1 (one standard deviation)), as expected from theoretical arguments (Ingram, 2010,
41   2013). It includes the pattern effect of surface warming that modulates the lapse rate and associated specific
42   humidity changes (Po-Chedley et al., 2018a). The relative humidity feedback is close to zero (αRH = 0.00 ±
43   0.06 W m–2 °C–1 (one standard deviation)) and the spread among models is confined to the tropics (Sherwood
44   et al., 2010a; Vial et al., 2013; Takahashi et al., 2016; Po-Chedley et al., 2018a). The change in upper
45   tropospheric RH is closely related to model representation of current climate (Sherwood et al., 2010a; Po‐
46   Chedley et al., 2019), and a reduction in model RH biases is expected to reduce the uncertainty of the RH
47   feedback. At inter-annual time scales, it has been shown that the change in RH in the tropics is related to the
48   change of the spatial organisation of deep convection (Holloway et al., 2017; Bony et al., 2020).
50   Both decompositions allow estimates of the sum of the lapse rate and specific humidity feedbacks αLR+WV.
51   The multi-kernel and multi-model mean of αLR+WV is equal to 1.24 and 1.26 W m-2 °C–1 respectively for
52   CMIP5 and CMIP6 models, with a standard deviation of 0.10 W m-2 °C–1 (Zelinka et al., 2020). These values
53   are larger than the recently assessed value of 1.15 W m-2 °C–1 by Sherwood et al. (2020) as a larger set of
54   kernels, including those obtained from meteorological reanalysis, are used here.
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 1   Since AR5, the effect of the water vapour increase in the stratosphere with global warming has been
 2   investigated by different studies. This increase produces a positive feedback between 0.1 and 0.3 W m–2 °C–1
 3   if the stratospheric radiative response is computed assuming temperatures that are adjusted with fixed
 4   dynamical heating (Dessler et al., 2013; Banerjee et al., 2019). However, various feedbacks reduce this
 5   temperature adjustment and the overall physical (water vapour, temperature and dynamical) stratospheric
 6   feedback becomes much smaller (0.0 to 0.1 W m–2 °C–1) (Huang et al., 2016, 2020; Li and Newman, 2020),
 7   with uncertainty arising from limitations of current ESMs in simulating stratospheric processes. The total
 8   stratospheric feedback is assessed at 0.05 ± 0.1 W m–2 °C–1 (one standard deviation).
10   The combined water vapour plus lapse rate feedback is positive. The main physical processes that drive this
11   feedback are well understood and supported by multiple lines of evidence including models, theory and
12   observations. The combined water vapour plus lapse rate feedback parameter is assessed to be αLR+WV = 1.30
13   W m–2 °C–1, with a very likely range of 1.1 to 1.5 W m–2 °C–1 and a likely range of 1.2 to 1.4 W m–2 °C–1 with
14   high confidence.
17   Surface albedo feedback
19   Surface albedo is determined primarily by reflectance at Earth’s surface, but also by the spectral and angular
20   distribution of incident solar radiation. Changes in surface albedo result in changes in planetary albedo that
21   are roughly reduced by two-thirds, owing to atmospheric absorption and scattering, with variability and
22   uncertainty arising primarily from clouds (Bender, 2011; Donohoe and Battisti, 2011; Block and Mauritsen,
23   2013). Temperature change induces surface albedo change through several direct and indirect means. In the
24   present climate and at multidecadal time scales, the largest contributions by far are changes in the extent of
25   sea ice and seasonal snow cover, as these media are highly reflective and are located in regions that are close
26   to the melting temperature (Chapter 2, Sections and Reduced snow cover on sea ice may
27   contribute as much to albedo feedback as reduced extent of sea ice (Zhang et al., 2019). Changes in the snow
28   metamorphic rate, which generally reduces snow albedo with warmer temperature, and warming-induced
29   consolidation of light absorbing impurities near the surface, also contribute secondarily to the albedo
30   feedback (Flanner and Zender, 2006; Qu and Hall, 2007; Doherty et al., 2013; Tuzet et al., 2017). Other
31   contributors to albedo change include vegetation state (assessed separately in Section, soil wetness,
32   and ocean roughness.
34   Several studies have attempted to derive surface albedo feedback from observations of multidecadal changes
35   in climate, but only over limited spatial and inconsistent temporal domains, inhibiting a purely observational
36   synthesis of global αA. Flanner et al. (2011) applied satellite observations to determine that the northern
37   hemisphere (NH) cryosphere contribution to global αA over 1979–2008 was 0.48 [likely range 0.29 to 0.78]
38   W m-2 °C-1, with roughly equal contributions from changes in land snow cover and sea ice. Since AR5, and
39   over similar periods of observation, Crook and Forster (2014) found an estimate of 0.8 ± 0.3 W m-2 °C-1 (one
40   standard deviation) for the total NH extratropical surface albedo feedback, when averaged over global
41   surface area. For the Arctic sea ice alone, Pistone et al. (2014) and Cao et al. (2015) estimated the
42   contribution to global αA to be 0.31 ± 0.04 W m–2 °C–1 (one standard deviation) and 0.31 ± 0.08 W m–2 °C–1
43   (one standard deviation), respectively, whereas Donohoe et al. (2020) estimated it to be only 0.16 ± 0.04 W
44   m–2 °C–1 (one standard deviation). Much of this discrepancy can be traced to different techniques and data
45   used for assessing the attenuation of surface albedo change by Arctic clouds. For the NH land snow, Chen et
46   al. (2016) estimated that observed changes during 1982–2013 contributed (after converting from NH
47   temperature change to global mean temperature change) by 0.1 W m–2 °C–1 to global αA, smaller than the
48   estimate of 0.24 W m-2 °C-1 from Flanner et al. (2011). The contribution of the southern hemisphere (SH) to
49   global αA is expected to be small because seasonal snow cover extent in the SH is limited, and trends in SH
50   sea ice extent are relatively flat over much of the satellite record (Chapter 2, Section 2.3.2).
52   CMIP5 and CMIP6 models show moderate spread in global αA determined from century timescale changes
53   (Qu and Hall, 2014; Schneider et al., 2018; Thackeray and Hall, 2019; Zelinka et al., 2020), owing to
54   variations in modelled sea-ice loss and snow cover response in boreal forest regions. The multi-model mean
55   global-scale αA (from all contributions) over the 21st century in CMIP5 models under the RCP8.5 scenario
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 1   was derived by Schneider et al. (2018) to be 0.40 ± 0.10 W m–2 °C–1 (one standard deviation). Moreover,
 2   they found that modelled αA does not decline over the 21st century, despite large losses of snow and sea ice,
 3   though a weakened feedback is apparent after 2100. Using the idealized abrupt4xCO2 as for the other
 4   feedbacks, the estimate of the global-scale albedo feedback in the CMIP5 models is 0.35± 0.08 W m–2°C–1
 5   (one standard deviation) (Vial et al., 2013; Caldwell et al., 2016). The CMIP6 multi-model mean varies from
 6   0.3 to 0.5 W m–2°C–1 depending on the kernel used (Zelinka et al., 2020). Donohoe et al. (2020) derived a
 7   multi-model mean αA and its inter-model spread of 0.37 ± 0.19 W m–2 °C–1 from the CMIP5 abrupt4xCO2
 8   ensemble, employing model-specific estimates of atmospheric attenuation and thereby avoiding bias
 9   associated with use of a single radiative kernel.
11   The surface albedo feedback estimates using centennial changes have been shown to be highly correlated to
12   those using seasonal regional changes for NH land snow (Qu and Hall, 2014) and Arctic sea ice (Thackeray
13   and Hall, 2019). For the NH land snow, the physics underpinning this relationship being credible, this opens
14   the possibility to use it as an emergent constraint (Qu and Hall, 2014). Considering only the 8 models whose
15   seasonal cycle of albedo feedback falls within the observational range does not change the multi-model mean
16   contribution to global αA (0.08 W m–2°C–1) but decreases the inter-model spread by a factor of two (from ±
17   0.03 to ± 0.015 W m–2°C–1) (Qu and Hall, 2014). For the Arctic sea-ice, Thackeray and Hall (2019) show
18   that the seasonal cycle also provides an emergent constraint, at least until mid-century when the relationship
19   degrades. They find that the CMIP5 multi-model mean of the Arctic sea-ice contribution to αA is 0.13 W
20   m–2 °C–1 and that the inter-model spread is reduced by a factor of two (from ± 0.04 to ± 0.02 W m–2 °C–1)
21   when the emergent constraint is used. This model estimate is smaller than observational estimates (Pistone et
22   al., 2014; Cao et al., 2015) except those of Donohoe et al. (2020). This can be traced to CMIP5 models
23   generally underestimating the rate of Arctic sea ice loss during recent decades (Stroeve et al., 2012; Flato et
24   al., 2013; Chapter 9, Section 9.3.1), though this may also be an expression of internal variability, since the
25   observed behaviour is captured within large ensemble simulations (Notz, 2015). CMIP6 models better
26   capture the observed Arctic sea ice decline (Chapter 3, Section 3.4.1). In the SH the opposite situation is
27   observed. Observations show relatively flat trends in SH sea ice over the satellite era (Chapter 2, Section
28 whereas CMIP5 models simulate a small decrease (Chapter 3, Section 3.4.1). SH αA is presumably
29   larger in models than observations but only contribute to about one quarter of the global αA. Thus, we assess
30   that αA estimates are consistent, at global scale, in CMIP5 and CMIP6 models and satellite observations,
31   though hemispheric differences and the role of internal variability need to be further explored.
33   Based on the multiple lines of evidence presented above that include observations, CMIP5 and CMIP6
34   models and theory, the global surface albedo feedback is assessed to be positive with high confidence. The
35   basic phenomena that drive this feedback are well understood and the different studies cover a large variety
36   of hypotheses or behaviours, including how the evolution of clouds affects this feedback. The value of the
37   global surface albedo feedback is assessed to be αA = 0.35 W m-2 °C-1, with a very likely range from 0.10 to
38   0.60 W m–2 °C–1 and a likely range from 0.25 to 0.45 W m–2 °C–1 with high confidence.
41   Cloud feedbacks
43 Decomposition of clouds into regimes
44   Clouds can be formed almost anywhere in the atmosphere when moist air parcels rise and cool, enabling the
45   water vapour to condense. The cloud droplets, ice crystals frozen from small water droplets, and their
46   mixture may further grow into large particles of rain, snow, or drizzle. These microphysical processes
47   interact with aerosols, radiation and atmospheric circulation, resulting in a highly complex set of processes
48   governing cloud formation and lifecycles that operate across a wide range of spatial and temporal scales.
50   Clouds have various types, from optically thick convective clouds to thin stratus and cirrus clouds,
51   depending upon thermodynamic conditions and large-scale circulation (Figure 7.9). Over the equatorial
52   warm pool and inter-tropical convergence zone (ITCZ) regions, high SSTs stimulate the development of
53   deep convective cloud systems, which are accompanied by anvil and cirrus clouds near the tropopause where
54   the convective air outflows. The large-scale circulation associated with these convective clouds leads to
55   subsidence over the subtropical cool ocean, where deep convection is suppressed by a lower tropospheric
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 1   inversion layer maintained by the subsidence and promoting the formation of shallow cumulus and
 2   stratocumulus clouds. In the extratropics, mid-latitude storm tracks control cloud formation, which occurs
 3   primarily in the frontal bands of extratropical cyclones. Since liquid droplets do not freeze spontaneously at
 4   temperatures warmer than approximately –40°C and ice nucleating particles that can aid freezing at warmer
 5   temperatures are scarce (see Section 7.3.3), extratropical clouds often consist both of super-cooled liquid and
 6   ice crystals, resulting in mixed-phase clouds.
 8   In the global energy budget at TOA, clouds affect SW radiation by reflecting sunlight due to their high
 9   albedo (cooling the climate system) and also LW radiation by absorbing the energy from the surface and
10   emitting at a lower temperature to space, i.e., contributing to the greenhouse effect, warming the climate
11   system. In general, the greenhouse effect of clouds strengthens with height whereas the SW reflection
12   depends on the cloud optical properties. The effects of clouds on Earth’s energy budget are measured by the
13   cloud radiative effect (CRE), which is the difference in the TOA radiation between clear and all skies (see
14   Section 7.2.1). In the present climate, the SW CRE tends to be compensated by the LW CRE over the
15   equatorial warm pool, leading to the net CRE pattern showing large negative values over the eastern part of
16   the subtropical ocean and the extratropical ocean due to the dominant influence of highly reflective marine
17   low clouds.
19   In a first attempt to systematically evaluate ECS based on fully coupled GCMs in AR4, diverging cloud
20   feedbacks were recognized as a dominant source of uncertainty. An advance in understanding the cloud
21   feedback was to assess feedbacks separately for different cloud regimes (Gettelman and Sherwood, 2016). A
22   thorough assessment of cloud feedbacks in different cloud regimes was carried out in AR5 (Boucher et al.,
23   2013), which assigned high or medium confidence for some cloud feedbacks but low or no confidence for
24   others (Table 7.9). Many studies that estimate the net cloud feedback using CMIP5 simulations (Vial et al.,
25   2013; Caldwell et al., 2016; Zelinka et al., 2016; Colman and Hanson, 2017) show different values
26   depending on the methodology and the set of models used, but often report a large inter-model spread of the
27   feedback, with the 90% confidence interval spanning both weak negative and strong positive net feedbacks.
28   Part of this diversity arises from the dependence of the model cloud feedbacks on the parameterization of
29   clouds and their coupling to other sub-grid scale processes (Zhao et al., 2015).
31   Since AR5, community efforts have been undertaken to understand and quantify the cloud feedbacks in
32   various cloud regimes coupled with large-scale atmospheric circulation (Bony et al., 2015). For some cloud
33   regimes, alternative tools to ESMs, such as observations, theory, high-resolution cloud resolving models
34   (CRMs), and Large Eddy Simulations (LES), help quantify the feedbacks. Consequently, the net cloud
35   feedback derived from ESMs has been revised by assessing the regional cloud feedbacks separately and
36   summing them with weighting by the ratio of fractional coverage of those clouds over the globe to give the
37   global feedback, following an approach adopted in Sherwood et al. (2020). This “bottom-up” assessment is
38   explained below with a summary of updated confidence of individual cloud feedback components (Table
39   7.9). Dependence of cloud feedbacks on evolving patterns of surface warming will be discussed in Section
40   7.4.4 and is not explicitly taken into account in the assessment presented in this section.
45   Figure 7.9: Schematic cross section of diverse cloud responses to surface warming from the tropics to polar
46               regions. Thick solid and dashed curves indicate the tropopause and the subtropical inversion layer in the
47               current climate, respectively. Thin grey text and arrows represent robust responses in the thermodynamic
48               structure to greenhouse warming, of relevance to cloud changes. Text and arrows in red, orange and green
49               show the major cloud responses assessed with high, medium and low confidence, respectively, and the
50               sign of their feedbacks to the surface warming is indicated in the parenthesis. Major advances since AR5
51               are listed in a box.
53   [END FIGURE 7.9 HERE]

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 1 Assessment for individual cloud regimes
 2   High-cloud altitude feedback.
 3   It has long been argued that cloud top altitude rises under global warming, concurrent with the rising of the
 4   tropopause at all latitudes (Marvel et al., 2015; Thompson et al., 2017). This increasing altitude of high
 5   clouds was identified in early generation GCMs and the tropical high-cloud altitude feedback was assessed
 6   to be positive with high confidence in AR5 (Boucher et al., 2013). This assessment is supported by a
 7   theoretical argument called the fixed anvil temperature mechanism, which ensures that the temperature of the
 8   convective detrainment layer does not change when the altitude of high-cloud tops increases with the rising
 9   tropopause (Hartmann and Larson, 2002). Because the cloud top temperature does not change significantly
10   with global warming, cloud longwave emission does not increase even though the surface warms, resulting
11   in an enhancement of the high-cloud greenhouse effect (a positive feedback; Yoshimori et al. (2020)). The
12   upward shift of high clouds with surface warming is detected in observed interannual variability and trends
13   in satellite records for recent decades (Chepfer et al., 2014; Norris et al., 2016; Saint-Lu et al., 2020). The
14   observational detection is not always successful (Davies et al., 2017), but the cloud altitude shifts similarly in
15   many CRM experiments (Khairoutdinov and Emanuel, 2013; Tsushima et al., 2014; Narenpitak et al., 2017).
16   The high-cloud altitude feedback was estimated to be 0.5 W m–2°C–1 based on GCMs in AR5, but is revised,
17   using a recent re-evaluation that excludes aliasing effects by reduced low-cloud amounts, downward to 0.22
18   ± 0.12 W m–2 °C–1 (one standard deviation) (Zhou et al., 2014; Zelinka et al., 2020). In conclusion, there is
19   high confidence in the positive high-cloud altitude feedback simulated in ESMs as it is supported by
20   theoretical, observational, and process modelling studies.
22   Tropical high-cloud amount feedback.
23   Updrafts in convective plumes lead to detrainment of moisture at a level where the buoyancy diminishes, and
24   thus deep convective clouds over high SSTs in the tropics are accompanied by anvil and cirrus clouds in the
25   upper troposphere. These clouds, rather than the convective plumes themselves, play a substantial role in the
26   global TOA radiation budget. In the present climate, the net CRE of these clouds is small due to a
27   cancellation between the SW and LW components (Hartmann et al., 2001). However, high clouds with
28   different optical properties could respond to surface warming differently, potentially perturbing this radiative
29   balance and therefore leading to a non-zero feedback.
31   A thermodynamic mechanism referred to as the ‘stability iris effect’ has been proposed to explain that the
32   anvil cloud amount decreases with surface warming (Bony et al., 2016). In this mechanism, a temperature-
33   mediated increase of static stability in the upper troposphere, where convective detrainment occurs, acts to
34   balance a weakened mass outflow from convective clouds, and thereby reduce anvil cloud areal coverage
35   (Figure 7.9). The reduction of anvil cloud amount is accompanied by enhanced convective aggregation that
36   causes a drying of the surrounding air and thereby increases the LW emission to space that acts as a negative
37   feedback (Bony et al., 2020). This phenomenon is found in many CRM simulations (Emanuel et al., 2014;
38   Wing and Emanuel, 2014; Wing et al., 2020) and also identified in observed interannual variability (Stein et
39   al., 2017; Saint-Lu et al., 2020).
41   Despite the reduction of anvil cloud amount supported by several lines of evidence, estimates of radiative
42   feedback due to high-cloud amount changes is highly uncertain in models. The assessment presented here is
43   guided by combined analyses of TOA radiation and cloud fluctuations at interannual time scale using
44   multiple satellite data sets. The observationally based local amount feedback associated with optically thick
45   high clouds is negative, leading to its global contribution (by multiplying the mean tropical anvil cloud
46   fraction of about 8%) of –0.24 ± 0.05 W m-2 °C–1 (one standard deviation) for LW (Vaillant de Guélis et al.,
47   2018). Also, there is a positive feedback due to increase of optically thin cirrus clouds in the tropopause
48   layer, estimated to be 0.09 ± 0.09 W m-2 °C–1 (one standard deviation) (Zhou et al., 2014). The negative LW
49   feedback due to reduced amount of thick high clouds is partly compensated by the positive SW feedback
50   (due to less reflection of solar radiation), so that the tropical high-cloud amount feedback is assessed to be
51   equal to or smaller than their sum. Consistently, the net high cloud feedback in the tropical convective
52   regime, including a part of the altitude feedback, is estimated to have the global contribution of –0.13 ± 0.06
53   W m-2 °C–1 (one standard deviation) (Williams and Pierrehumbert, 2017). The negative cloud LW feedback
54   is considerably biased in CMIP5 GCMs (Mauritsen and Stevens, 2015; Su et al., 2017; Li et al., 2019) and
55   highly uncertain primarily due to differences in the convective parameterization (Webb et al., 2015).
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 1   Furthermore, high-resolution CRM simulations cannot alone be used to constrain uncertainty because the
 2   results depend on parametrized cloud microphysics and turbulence (Bretherton et al., 2014; Ohno et al.,
 3   2019). Therefore, the tropical high-cloud amount feedback is assessed as negative but with low confidence
 4   given the lack of modelling evidence. Taking observational estimates altogether and methodological
 5   uncertainty into account, the global contribution of the high-cloud amount feedback is assessed to –0.15 ±
 6   0.2 W m–2 °C–1 (one standard deviation).
 8   Subtropical marine low-cloud feedback.
 9   It has long been argued that the response of marine boundary layer clouds over the subtropical ocean to
10   surface warming was the largest contributor to the spread among GCMs in the net cloud feedback (Boucher
11   et al., 2013). However, uncertainty of the marine low-cloud feedback has been reduced considerably since
12   AR5 through combined knowledge from theoretical, modelling, and observational studies (Klein et al.,
13   2017). Processes that control the low clouds are complex and involve coupling with atmospheric motions on
14   multiple scales, from the boundary layer turbulence to the large-scale subsidence, which may be represented
15   by a combination of shallow and deep convective mixing (Sherwood et al., 2014).
17   In order to disentangle the large-scale processes that cause the cloud amount either to increase or decrease in
18   response to the surface warming, the cloud feedback has been expressed in terms of several ‘cloud
19   controlling factors’ (Qu et al., 2014, 2015; Zhai et al., 2015; Brient and Schneider, 2016; Myers and Norris,
20   2016; McCoy et al., 2017b). The advantage of this approach over conventional calculation of cloud
21   feedbacks is that the temperature-mediated cloud response can be estimated without using information of the
22   simulated cloud responses that are less well-constrained than the changes in the environmental conditions.
23   Two dominant factors are identified for the subtropical low clouds: a thermodynamic effect due to rising
24   SST that acts to reduce low cloud by enhancing cloud-top entrainment of dry air, and a stability effect
25   accompanied by an enhanced inversion strength that acts to increase low cloud (Qu et al., 2014, 2015; Kawai
26   et al., 2017). These controlling factors compensate with a varying degree in different ESMs, but can be
27   constrained by referring to the observed seasonal or interannual relationship between the low-cloud amount
28   and the controlling factors in the environment as a surrogate. The analysis leads to a positive local feedback
29   that has the global contribution of 0.14–0.36 W m–2 °C–1 (Klein et al., 2017), to which the feedback in the
30   stratocumulus regime dominates over the feedback in the trade cumulus regime (Cesana et al., 2019; Radtke
31   et al., 2020). The stratocumulus feedback may be underestimated because explicit simulations using LES
32   show a larger local feedback of up to 2.5 W m–2 °C–1, corresponding to the global contribution of 0.2 W m-2
33   °C–1 by multiplying the mean tropical stratocumulus fraction of about 8% (Bretherton, 2015). Supported by
34   different lines of evidence, the subtropical marine low-cloud feedback is assessed as positive with high
35   confidence. Based on the combined estimate using LESs and the cloud controlling factor analysis, the global
36   contribution of the feedback due to marine low clouds equatorward of 30° is assessed to be 0.2 ± 0.16 W m–2
37   °C–1 (one standard deviation), for which the range reflects methodological uncertainties.
39   Land cloud feedback.
40   Intensification of the global hydrological cycle is a robust feature of global warming, but at the same time,
41   many land areas in the subtropics will experience drying at the surface and in the atmosphere (Chapter 8,
42   Section 8.2.2). This occurs due to a limited water availability in these regions, where the cloudiness is
43   consequently expected to decrease. Reduction in clouds over land are consistently identified in the CMIP5
44   models and also in a GCM with explicit convection (Bretherton et al., 2014; Kamae et al., 2016). Because
45   low clouds make up the majority of subtropical land clouds, this reduced amount of low clouds reflects less
46   solar radiation and leads to a positive feedback similar to the marine low clouds. The mean estimate of the
47   global land cloud feedback in CMIP5 models is smaller than the marine low cloud feedback, 0.08 ± 0.08 W
48   m–2 °C–1 (Zelinka et al., 2016). These values are nearly unchanged in CMIP6 (Zelinka et al., 2020). However,
49   ESMs still have considerable biases in the climatological temperature and cloud fraction over land and the
50   magnitude of this feedback has not yet been supported by observational evidence. Therefore, the feedback
51   due to decreasing land clouds is assessed to be 0.08 ± 0.08 W m–2 °C–1 (one standard deviation) with low
52   confidence.
54   Mid-latitude cloud amount feedback.
55   Poleward shifts in the mid-latitude jets are evident since the 1980s (Chapter 2, Section and are a
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 1   feature of the large-scale circulation change in future projections (Chapter 4, Section Because mid-
 2   latitude clouds over the North Pacific, North Atlantic, and Southern Ocean are induced mainly by
 3   extratropical cyclones in the storm tracks along the jets, it has been suggested that the jet shifts should be
 4   accompanied by poleward shifts in the mid-latitude clouds, which would result in a positive feedback
 5   through the reduced reflection of insolation (Boucher et al., 2013). However, studies since AR5 have
 6   revealed that this proposed mechanism does not apply in practice (Ceppi and Hartmann, 2015). While a
 7   poleward shift of mid-latitude cloud maxima in the free troposphere has been identified in satellite and
 8   ground-based observations (Bender et al., 2012; Eastman and Warren, 2013), associated changes in net CRE
 9   are small because the responses in high and low clouds to the jet shift act to cancel each other (Grise and
10   Medeiros, 2016; Tselioudis et al., 2016; Zelinka et al., 2018). This cancellation is not well captured in ESMs
11   (Lipat et al., 2017), but the above findings show that the mid-latitude cloud feedback is not dynamically
12   driven by the poleward jet shifts, which are rather suggested to occur partly in response to high cloud
13   changes (Li et al., 2018b).
15   Thermodynamics play an important role in controlling extratropical cloud amount equatorward of about 50°
16   latitude. Recent studies showed using observed cloud controlling factors that the mid-latitude low cloud
17   fractions decrease with rising SST, which also acts to weaken stability of the atmosphere unlike the
18   subtropics (McCoy et al., 2017b). ESMs consistently show a decrease of cloud amounts and a resultant
19   positive shortwave feedback in the 30°–40° latitude bands, which can be constrained using observations of
20   seasonal migration of cloud amount (Zhai et al., 2015). Based on the qualitative agreement between
21   observations and ESMs, the mid-latitude cloud amount feedback is assessed as positive with medium
22   confidence. Following these emergent constraint studies using observations and CMIP5/6 models, the global
23   contribution of net cloud amount feedback over 30°–60° ocean areas, covering 27% of the globe, is assigned
24   0.09 ± 0.1 W m–2 °C–1 (one standard deviation), in which the uncertainty reflects potential errors in models’
25   low cloud response to changes in thermodynamic conditions.
27   Extratropical cloud optical depth feedback.
28   Mixed-phase clouds that consist of both liquid and ice are dominant over the Southern Ocean (50°–80°S),
29   which accounts for 20% of the net CRE in the present climate (Matus and L’Ecuyer, 2017). It has been
30   argued that the cloud optical depth (opacity) will increase over the Southern Ocean as warming drives the
31   replacement of ice-dominated clouds with liquid-dominated clouds (Tan et al., 2019). Liquid clouds
32   generally consist of many small cloud droplets, while the crystals in ice clouds are orders of magnitudes
33   fewer in number and much larger, causing the liquid clouds to be optically thicker and thereby resulting in a
34   negative feedback (Boucher et al., 2013). However, this phase change feedback works effectively only below
35   freezing temperature (Lohmann and Neubauer, 2018; Terai et al., 2019) and other processes that increase or
36   decrease liquid water path (LWP) may also affect the optical depth feedback (McCoy et al., 2019).
38   Due to insufficient amounts of super-cooled liquid water in the simulated atmospheric mean state, many
39   CMIP5 models overestimated the conversion from ice to liquid clouds with climate warming and the
40   resultant negative phase change feedback (Kay et al., 2016a; Tan et al., 2016; Lohmann and Neubauer,
41   2018). This feedback can be constrained using satellite-derived LWP observations over the past 20 years that
42   enable estimates of both long-term trends and the interannual relationship with SST variability (Gordon and
43   Klein, 2014; Ceppi et al., 2016; Manaster et al., 2017). The observationally-constrained SW feedback ranges
44   from –0.91 to –0.46 W m–2 °C–1 over 40°–70°S depending on the methodology (Ceppi et al., 2016; Terai et
45   al., 2016). In some CMIP6 models, representation of super-cooled liquid water content has been improved,
46   leading to weaker negative optical depth feedback over the Southern Ocean closer to observational estimates
47   (Bodas-Salcedo et al., 2019; Gettelman et al., 2019). This improvement at the same time results in a positive
48   optical depth feedback over other extratropical ocean where LWP decreased in response to reduced stability
49   in those CMIP6 models (Zelinka et al., 2020). Given the accumulated observational estimates and an
50   improved agreement between ESMs and observations, the extratropical optical depth feedback is assessed to
51   be small negative with medium confidence. Quantitatively, the global contribution of this feedback is
52   assessed to have a value of –0.03 ± 0.05 W m–2 °C–1 (one standard deviation) by combining estimates based
53   on observed interannual variability and the cloud controlling factors.
55   Arctic cloud feedback.
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 1   Clouds in polar regions, especially over the Arctic, form at low altitude above or within a stable to neutral
 2   boundary layer and are known to co-vary with sea-ice variability beneath. Because the clouds reflect sunlight
 3   during summer but trap longwave radiation throughout the year, seasonality plays an important role for cloud
 4   effects on Arctic climate (Kay et al., 2016b). AR5 assessed that Arctic low cloud amount will increase in
 5   boreal autumn and winter in response to declining sea ice in a warming climate, due primarily to an
 6   enhanced upward moisture flux over open water. The cloudier conditions during these seasons result in more
 7   downwelling longwave radiation, acting as a positive feedback on surface warming (Kay and Gettelman,
 8   2009). Over recent years, further evidence of the cloud contribution to the Arctic amplification has been
 9   obtained (Goosse et al., 2018; Section Space-borne lidar observations show that the cloud response
10   to summer sea-ice loss is small and cannot overcome the cloud effect in autumn (Taylor et al., 2015;
11   Morrison et al., 2018). The seasonality of the cloud response to sea-ice variability is reproduced in GCM
12   simulations (Laîné et al., 2016; Yoshimori et al., 2017). The agreement between observations and models
13   indicates that the Arctic cloud feedback is positive at the surface. This leads to an Arctic cloud feedback at
14   TOA that is likely positive, but very small in magnitude as found in some climate models (Pithan and
15   Mauritsen, 2014; Morrison et al., 2018). The observational estimates are sensitive to the analysis period and
16   the choice of reanalysis data, and a recent estimate of the TOA cloud feedback over 60°–90°N using
17   atmospheric reanalysis data and CERES satellite observations suggests a regional value ranging from –0.3 to
18   0.5 W m–2 °C–1, which corresponds to a global contribution of –0.02 to 0.03 W m–2 °C–1 (Zhang et al.,
19   2018b). Based on the overall agreement between ESMs and observations, the Arctic cloud feedback is
20   assessed small positive and has the value of 0.01 ± 0.05 W m–2 °C–1 (one standard deviation). The assessed
21   range indicates that a negative feedback is almost as probable as a positive feedback, and the assessment that
22   the Arctic cloud feedback is positive is therefore given low confidence.
25 Synthesis for the net cloud feedback
26   The understanding of the response of clouds to warming and associated radiative feedback has deepened
27   since AR5 (Figure 7.9, FAQ7.2). Particular progress has been made in the assessment of the marine low-
28   cloud feedback, which has historically been a major contributor to the cloud feedback uncertainty but is no
29   longer the largest source of uncertainty. Multiple lines of evidence (theory, observations, emergent
30   constraints and process modelling) are now available in addition to ESM simulations, and the positive low-
31   cloud feedback is consequently assessed with high confidence.
33   The best estimate of net cloud feedback is obtained by summing feedbacks associated with individual cloud
34   regimes and assessed to be αC = 0.42 W m–2 °C–1. By assuming that uncertainty of individual cloud
35   feedbacks is independent of each other, their standard deviations are added in quadrature, leading to the
36   likely range of 0.12 to 0.72 W m–2 °C–1 and the very likely range of –0.10 to 0.94 W m–2 °C–1 (Table 7.10).
37   This approach potentially misses feedbacks from cloud regimes that are not assessed, but almost all the
38   major cloud regimes were taken into consideration (Gettelman and Sherwood, 2016) and therefore additional
39   uncertainty will be small. This argument is also supported by an agreement between the net cloud feedback
40   assessed here and the net cloud feedback directly estimated using observations. The observational estimate,
41   which is sensitive to the period considered, based on two atmospheric reanalyses (ERA-Interim and
42   MERRA) and TOA radiation budgets derived from the CERES satellite observations for the years 2000–
43   2010 is 0.54 ± 0.7 W m–2 °C–1 (one standard deviation) (Dessler, 2013) and overlaps with the assessed range
44   of the net cloud feedback. The assessed very likely range is reduced by about 50% compared to AR5, but is
45   still wide compared to those of other climate feedbacks (Table 7.10). The largest contribution to this
46   uncertainty range is the estimate of tropical high-cloud amount feedback which is not yet well quantified
47   using models.
49   In reality, different types of cloud feedback may occur simultaneously in one cloud regime. For example, an
50   upward shift of high clouds associated with the altitude feedback could be coupled to an increase/decrease of
51   cirrus/anvil cloud fractions associated with the cloud amount feedback. Alternatively, slowdown of the
52   tropical circulation with surface warming (Chapter 4, Section 4.5.3; Figure 7.9) could affect both high and
53   low clouds so that their feedbacks are co-dependent. Quantitative assessments of such covariances require
54   further knowledge about cloud feedback mechanisms, which will further narrow the uncertainty range.
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 1   In summary, deepened understanding of feedback processes in individual cloud regimes since AR5 leads to
 2   an assessment of the positive net cloud feedback with high confidence. A small probability (less than 10%)
 3   of a net negative cloud feedback cannot be ruled out, but this would require an extremely large negative
 4   feedback due to decreases in the amount of tropical anvil clouds or increases in optical depth of extratropical
 5   clouds over the Southern Ocean; neither is supported by current evidence.
10   Table 7.9:     Assessed sign and confidence level of cloud feedbacks in difference regimes, compared between AR5
11                  and AR6. For some cloud regimes, the feedback was not assessed in AR5, indicated by N/A.
     Feedback                                   AR5                                  AR6
     High-cloud altitude feedback               Positive (high confidence)           Positive (high confidence)
     Tropical high-cloud amount feedback        N/A                                  Negative (low confidence)
     Subtropical marine low-cloud
                                                N/A (low confidence)                 Positive (high confidence)
     Land cloud feedback                        N/A                                  Positive (low confidence)
     Mid-latitude cloud amount feedback         Positive (medium confidence)         Positive (medium confidence)
     Extratropical cloud optical depth                                               Small negative (medium
     feedback                                                                        confidence)
                                                Small positive (very low
     Arctic cloud feedback                                                           Small positive (low confidence)
     Net cloud feedback                         Positive (medium confidence)         Positive (high confidence)
14   [END TABLE 7.9 HERE]
17      Biogeophysical and non-CO2 biogeochemical feedbacks
19   The feedbacks presented in the previous sections (Sections– are directly linked to physical
20   climate variables (for example temperature, water vapour, clouds, or sea ice). The central role of climate
21   feedbacks associated with these variables has been recognised since early studies of climate change.
22   However, in addition to these physical climate feedbacks, the Earth system includes feedbacks for which the
23   effect of global mean surface temperature change on the TOA energy budget is mediated through other
24   mechanisms, such as the chemical composition of the atmosphere, or by vegetation changes. Among these
25   additional feedbacks, the most important is the CO2 feedback that describes how a change of the global
26   surface temperature affects the atmospheric CO2 concentration. In ESM simulations in which CO2 emissions
27   are prescribed, changes in surface carbon fluxes affect the CO2 concentration in the atmosphere, the TOA
28   radiative energy budget, and eventually the global mean surface temperature. In ESM simulations in which
29   the CO2 concentration is prescribed, changes in the carbon cycle allow compatible CO2 emissions to be
30   calculated, i.e., the CO2 emissions that are compatible with both the prescribed CO2 concentration and the
31   representation of the carbon cycle in the ESM. The CO2 feedback is assessed in Chapter 5, Section 5.4. The
32   framework presented in this chapter assumes that the CO2 concentration is prescribed, and our assessment of
33   the net feedback parameter, α, does not include carbon-cycle feedbacks on the atmospheric CO2
34   concentration (Section 7.1; Box 7.1). However, our assessment of α does include non-CO2 biogeochemical
35   feedbacks (Section; including effects due to changes in atmospheric methane concentration) and
36   biogeophysical feedbacks (Section A synthesis of the combination of biogeophysical and non-
37   CO2 biogeochemical feedbacks is given in Section

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 1 Non-CO2 biogeochemical feedbacks
 2   The chemical composition of the atmosphere (beyond CO2 and water vapour changes) is expected to change
 3   in response to a warming climate. These changes in greenhouse gases (CH4, N2O, and ozone) and aerosol
 4   amount (including dust) have the potential to alter the TOA energy budget and are collectively referred to as
 5   non-CO2 biogeochemical feedbacks. CH4 and N2O feedbacks arise partly from changes in their emissions
 6   from natural sources in response to temperature change; these are assessed in Chapter 5, Section 5.4.7 (see
 7   also Figure 5.29c). Here we exclude the permafrost CH4 feedback (Chapter 5, Section because,
 8   although associated emissions are projected to increase under warming on multi-decadal to centennial
 9   timescales, on longer timescales these emissions would eventually substantially decline as the permafrost
10   carbon pools were depleted (Schneider von Deimling et al., 2012, 2015). This leaves the wetland CH4, land
11   N2O, and ocean N2O feedbacks, the assessed mean values of which sum to a positive feedback parameter of
12   +0.04 [0.02 to 0.06] W m–2 °C–1 (Chapter 5, Section 5.4.7). Other non-CO2 biogeochemical feedbacks that
13   are relevant to the net feedback parameter are assessed in Chapter 6, Section 6.4.5 (Table 6.8). These
14   feedbacks are associated with sea salt, dimethyl sulphide, dust, ozone, biogenic volatile organic compounds,
15   lightning, and CH4 lifetime, and sum to a negative feedback parameter of –0.20 [–0.41 to +0.01] W m–2 °C–1.
16   The overall feedback parameter for non-CO2 biogeochemical feedbacks is obtained by summing the Chapter
17   5 and Chapter 6 assessments, which gives –0.16 [–0.37 to +0.05] W m–2 °C–1. However, there is low
18   confidence in the estimates of both the individual non-CO2 biogeochemical feedbacks as well as their total
19   effect, as evident from the large range in the magnitudes of α from different studies, which can be attributed
20   to diversity in how models account for these feedbacks and limited process-level understanding.
23 Biogeophysical feedbacks
24   Biogeophysical feedbacks are associated with changes in the spatial distribution and/or biophysical
25   properties of vegetation, induced by surface temperature change and attendant hydrological cycle change.
26   These vegetation changes can alter radiative fluxes directly via albedo changes, or via surface momentum or
27   moisture flux changes and hence changes in cloud properties. However, the direct physiological response of
28   vegetation to changes in CO2, including changes in stomatal conductance, is considered part of the CO2
29   effective radiative forcing rather than a feedback (Section The timescale of response of vegetation
30   to climate change is relatively uncertain but can be from decades to hundreds of years (Willeit et al., 2014),
31   and could occur abruptly or as a tipping point (Chapter 5, Section; Chapter 8, Sections and
32; equilibrium only occurs when the soil system and associated nutrient and carbon pools equilibrate,
33   which can take millennia (Brantley, 2008; Sitch et al., 2008). The overall effects of climate-induced
34   vegetation changes may be comparable in magnitude to those from anthropogenic land-use and land cover
35   change (Davies-Barnard et al., 2015). Climate models that include a dynamical representation of vegetation
36   (e.g., Reick et al., 2013; Harper et al., 2018) are used to explore the importance of biogeophysical feedbacks
37   (Notaro et al., 2007; Brovkin et al., 2009; O’ishi et al., 2009; Port et al., 2012; Willeit et al., 2014; Alo and
38   Anagnostou, 2017; Zhang et al., 2018c; Armstrong et al., 2019). In AR5, it was discussed that such model
39   experiments predicted that expansion of vegetation in the high latitudes of the Northern Hemisphere would
40   enhance warming due to the associated surface albedo change, and that reduction of tropical forests in
41   response to climate change would lead to regional surface warming, due to reduced evapotranspiration
42   (Collins et al., 2013a), but there was no assessment of the associated feedback parameter. SRCCL stated that
43   regional climate change can be dampened or enhanced by changes in local land cover, but that this depends
44   on the location and the season; however, in general the focus was on anthropogenic land cover change, and
45   no assessment of the biogeophysical feedback parameter was carried out. There are also indications of a
46   marine biogeophysical feedback associated with surface albedo change due to changes in phytoplankton
47   (Frouin and Iacobellis, 2002; Park et al., 2015), but there is not currently enough evidence to quantitatively
48   assess this feedback.
50   Since AR5, several studies have confirmed that a shift from tundra to boreal forests and the associated
51   albedo change leads to increased warming in Northern Hemisphere high latitudes (Willeit et al., 2014; Zhang
52   et al., 2018c; Armstrong et al., 2019) (high confidence). However, regional modelling indicates that
53   vegetation feedbacks may act to cool climate in the Mediterranean (Alo and Anagnostou, 2017), and in the
54   tropics and subtropics the regional response is in general not consistent across models. On a global scale,
55   several modelling studies have either carried out a feedback analysis (Stocker et al., 2013; Willeit et al.,
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 1   2014) or presented simulations that allow a feedback parameter to be estimated (O’ishi et al., 2009;
 2   Armstrong et al., 2019), in such a way that the physiological response can be accounted for as a forcing
 3   rather than a feedback. The central estimates of the biogeophysical feedback parameter from these studies
 4   range from close to zero (Willeit et al., 2014) to +0.13 W m-2 °C-1 (Stocker et al., 2013). An additional line of
 5   evidence comes from the mid-Pliocene warm period (MPWP, Chapter 2, Cross-Chapter Box 2.1), for which
 6   paleoclimate proxies provide evidence of vegetation distribution and CO2 concentrations. Model simulations
 7   that include various combinations of modern versus MPWP vegetation and CO2 allow an associated
 8   feedback parameter to be estimated, as long as account is also taken of the orographic forcing (Lunt et al.,
 9   2010, 2012b). This approach has the advantage over pure modelling studies in that the reconstructed
10   vegetation is based on (paleoclimate) observations, and is in equilibrium with the CO2 forcing. However,
11   there are uncertainties in the vegetation reconstruction in regions with little or no proxy data, and it is
12   uncertain how much of the vegetation change is associated with the physiological response to CO2. This
13   paleoclimate approach gives an estimate for the biogeophysical feedback parameter of +0.3 W m-2 °C-1.
15   Given the limited number of studies, we take the full range of estimates discussed above for the
16   biogeophysical feedback parameter, and assess the very likely range to be from zero to +0.3 W m-2 °C-1, with
17   a central estimate of +0.15 W m-2 °C-1 (low confidence). Although this assessment is based on evidence from
18   both models and paleoclimate proxies, and the studies above agree on the sign of the change, there is
19   nonetheless limited evidence. Higher confidence could be obtained if there were more studies that allowed
20   calculation of a biogeophysical feedback parameter (particularly from paleoclimates), and if the partitioning
21   between biogeophysical feedbacks and physiological forcing were clearer for all lines of evidence.
24 Synthesis of biogeophysical and non-CO2 biogeochemical feedbacks
25   The non-CO2 biogeochemical feedbacks are assessed in Section to be –0.16 [–0.37 to +0.05] W m–
26     °C–1 and the biogeophysical feedbacks are assessed in Section to be +0.15 [0 to +0.3] W m-2 °C-1.
27   The sum of the biogeophysical and non-CO2 biogeochemical feedbacks is assessed to have a central value of
28   -0.01 W m–2 °C–1 and a very likely range from –0.27 to +0.25 W m–2 °C–1 (see Table 7.10). Given the
29   relatively long timescales associated with the biological processes that mediate the biogeophysical and many
30   of the non-CO2 biogeochemical feedbacks, in comparison with the relatively short timescale of many of the
31   underlying model simulations, combined with the small number of studies for some of the feedbacks, and the
32   relatively small signals, this overall assessment has low confidence.
34   Some supporting evidence for this overall assessment can be obtained from the CMIP6 ensemble, which
35   provides some pairs of instantaneous 4×CO2 simulations carried out using related models with and without
36   biogeophysical and non-CO2 biogeochemical feedbacks. This is not a direct comparison because these pairs
37   of simulations may differ by more than just their inclusion of these additional feedbacks; furthermore, not all
38   biogeophysical and non-CO2 biogeochemical feedbacks are fully represented. However, a comparison of the
39   pairs of simulations does provide a first-order estimate of the magnitude of these additional feedbacks.
40   Séférian et al. (2019) find a slightly more negative feedback parameter in CNRM-ESM2-1 (with additional
41   feedbacks) then in CNRM-CM6-1 (a decrease of 0.02 W m-2 °C-1, using the linear regression method from
42   years 10-150). Andrews et al. (2019) also find a slightly more negative feedback parameter when these
43   additional feedbacks are included (a decrease of 0.04 W m-2○C-1 in UKESM1 compared with HadGEM3-
44   GC3.1). Both of these studies suggest a small but slightly negative feedback parameter for the combination
45   of biogeophysical and non-CO2 biogeochemical feedbacks, but with relatively large uncertainty given (a)
46   interannual variability and (b) that feedbacks associated with natural terrestrial emissions of CH4 and N2O
47   were not represented in either pair.
50   Long term radiative feedbacks associated with ice sheets
52   Although long-term radiative feedbacks associated with ice sheets are not included in our definition of ECS
53   (Box 7.1), the relevant feedback parameter is assessed here because the timescales on which these feedbacks
54   act are relatively uncertain, and the long-term temperature response to CO2 forcing of the entire Earth system
55   may be of interest.
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 2   Earth’s ice sheets (Greenland and Antarctica) are sensitive to climate change (Chapter 9, Section 9.4; Pattyn
 3   et al., 2018). Their time evolution is determined by both their surface mass balance and ice dynamic
 4   processes, with the latter being particularly important for the West Antarctic Ice Sheet. Surface mass balance
 5   depends on the net energy and hydrological fluxes at their surface, and there are mechanisms of ice sheet
 6   instability that depend on ocean temperatures and basal melt rates (Chapter 9, Section The presence
 7   of ice sheets affects Earth’s radiative budget, hydrology, and atmospheric circulation due to their
 8   characteristic high albedo, low roughness length, and high altitude, and they influence ocean circulation
 9   through freshwater input from calving and melt (e.g., Fyke et al., 2018). Ice sheet changes also modify
10   surface albedo through the attendant change in sea level and therefore land area (Abe-Ouchi et al., 2015).
11   The timescale for ice sheets to reach equilibrium is on the order of thousands of years (Clark et al., 2016).
12   Due to the long timescales involved, it is a major challenge to run coupled climate-ice sheet models to
13   equilibrium, and as a result, long-term simulations are often carried out with lower complexity models,
14   and/or are asynchronously coupled.
16   In AR5, it was described that both the Greenland and Antarctic ice sheets would continue to lose mass in a
17   warming world (Collins et al., 2013a), with a continuation in sea level rise beyond the year 2500 assessed as
18   virtually certain. However, there was low confidence in the associated radiative feedback mechanisms, and
19   as such, there was no assessment of the magnitude of long-term radiative feedbacks associated with ice
20   sheets. That assessment is consistent with SROCC, wherein it was stated that ‘with limited published studies
21   to draw from and no simulations run beyond 2100, firm conclusions regarding the net importance of
22   atmospheric versus ocean melt feedbacks on the long-term future of Antarctica cannot be made.’
24   The magnitude of the radiative feedback associated with changes to ice sheets can be quantified by
25   comparing the global mean long-term equilibrium temperature response to increased CO2 concentrations in
26   simulations that include interactive ice sheets with that of simulations that do not include the associated ice-
27   sheet climate interactions (Swingedouw et al., 2008; Vizcaíno et al., 2010; Goelzer et al., 2011; Bronselaer et
28   al., 2018; Golledge et al., 2019). These simulations indicate that on multi-centennial timescales, ice sheet
29   mass loss leads to fresh water fluxes that can modify ocean circulation (Swingedouw et al., 2008; Goelzer et
30   al., 2011; Bronselaer et al., 2018; Golledge et al., 2019). This leads to reduced surface warming (by about
31   0.2°C in the global mean after 1000 years; Goelzer et al., 2011; see also Section, although other
32   work suggests no net global temperature effect of ice sheet mass loss (Vizcaíno et al., 2010). However,
33   model simulations in which the Antarctic ice sheet is removed completely in a paleoclimate context indicate
34   a positive global mean feedback on multi-millennial timescales due primarily to the surface albedo change
35   (Goldner et al., 2014a; Kennedy-Asser et al., 2019); in Chapter 9 (Section 9.6.3) it is assessed that such ice-
36   free conditions could eventually occur given 7–13°C of warming. This net positive feedback due to ice
37   sheets on long timescales is also supported by model simulations of the mid-Pliocene warm period (MPWP,
38   Chapter 2, Cross-chapter Box 2.1) in which the volume and area of the Greenland and West Antarctic ice
39   sheets are reduced in model simulations in agreement with geological data (Chandan and Peltier, 2018),
40   leading to surface warming. As such, overall, on multi-centennial timescales the feedback parameter
41   associated with ice sheets is likely negative (medium confidence), but on multi-millennial timescales by the
42   time the ice sheets reach equilibrium, the feedback parameter is very likely positive (high confidence; see
43   Table 7.10). However, a relative lack of models carrying out simulations with and without interactive ice
44   sheets over centennial to millennial timescales means that there is currently not enough evidence to quantify
45   the magnitude of these feedbacks, or the timescales on which they act.
48   Synthesis
50   Table 7.10 summarises the estimates and the assessment of the individual and the net feedbacks presented in
51   the above sections. The uncertainty range of the net climate feedback was obtained by adding standard
52   deviations of individual feedbacks in quadrature, assuming that they are independent and follow the
53   Gaussian distribution. It is virtually certain that the net climate feedback is negative, primarily due to the
54   Planck temperature response, indicating that climate acts to stabilise in response to radiative forcing imposed
55   to the system. Supported by the level of confidence associated with the individual feedbacks, it is also
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 1   virtually certain that the sum of the non-Planck feedbacks is positive. Based on Table 7.10 these climate
 2   feedbacks amplify the Planck temperature response by about 2.8 [1.9 to 5.9] times. Cloud feedback remains
 3   the largest contributor to uncertainty of the net feedback, but the uncertainty is reduced compared to AR5. A
 4   secondary contribution to the net feedback uncertainty is the biogeophysical and non-CO2 biogeochemical
 5   feedbacks, which together are assessed to have a central value near zero and thus do not affect the central
 6   estimate of ECS. The net climate feedback is assessed to be –1.16 W m–2 °C–1, likely from –1.54 to –0.78 W
 7   m–2 °C–1, and very likely from –1.81 to –0.51 W m–2°C–1.
 9   Feedback parameters in climate models are calculated assuming that they are independent of each other,
10   except for a well-known co-dependency between the WV and LR feedbacks. When the inter-model spread of
11   the net climate feedback is computed by adding in quadrature the inter-model spread of individual feedbacks,
12   it is 17% wider than the spread of the net climate feedback directly derived from the ensemble. This
13   indicates that the feedbacks in climate models are partly co-dependent. Two possible co-dependencies have
14   been suggested (Huybers, 2010; Caldwell et al., 2016). One is a negative covariance between the LR and
15   longwave cloud feedbacks, which may be accompanied by a deepening of the troposphere (O’Gorman and
16   Singh, 2013; Yoshimori et al., 2020) leading both to greater rising of high clouds and a larger upper-
17   tropospheric warming. The other is a negative covariance between albedo and shortwave cloud feedbacks,
18   which may originate from the Arctic regions: a reduction in sea ice enhances the shortwave cloud radiative
19   effect because the ocean surface is darker than sea ice (Gilgen et al., 2018). This covariance is reinforced as
20   the decrease of sea-ice leads to an increase in low-level clouds (Mauritsen et al., 2013). However, the
21   mechanism causing these co-dependences between feedbacks is not well understood yet and a quantitative
22   assessment based on multiple lines of evidence is difficult. Therefore, this synthesis assessment does not
23   consider any co-dependency across individual feedbacks.
25   The assessment of the net climate feedback presented above is based on a single approach (i.e., process
26   understanding) and directly results in a value for ECS given in Section 7.5.1; this is in contrast to the
27   synthesis assessment of ECS in Section 7.5.5 which combines multiple approaches. The total (net) feedback
28   parameter consistent with the final synthesis assessment of the ECS and Equation 7.1 is provided there.
31   [START TABLE 7.10 HERE]
33   Table 7.10: Synthesis assessment of climate feedbacks (central estimate shown by boldface). The mean values and
34               their 90% ranges in CMIP5/6 models, derived using multiple radiative kernels (Zelinka et al., 2020), are
35               also presented for comparison.
      Feedback           CMIP5 GCMs            CMIP6 ESMs          AR6 assessed ranges
      parameter 𝛼𝛼𝑥𝑥     Mean and the          Mean and the         Central    Very likely      Likely            Level of
      (W m-2 °C-1)       5–95% interval        5–95% interval       estimate   interval         interval          confidence
      Planck             –3.20 [–3.3 to –      –3.22 [–3.3 to –     –3.22      –3.4 to –3.0     –3.3 to –3.1      high
                         3.1]                  3.1]
      WV+LR              1.24 [1.08 to 1.35]   1.25 [1.14 to 1.45] 1.30        1.1 to 1.5       1.2 to 1.4        high
      Surface albedo     0.41 [0.25 to 0.56]   0.39 [0.26 to 0.53] 0.35        0.10 to 0.60     0.25 to 0.45      medium
      Clouds             0.41 [–0.09 to 1.1]   0.49 [–0.08 to 1.1] 0.42        –0.10 to 0.94    0.12 to 0.72      high
      Biogeophysical     Not evaluated         Not evaluated        –0.01      –0.27 to 0.25    –0.16 to 0.14     low
      and non-CO2

      Residual of        0.06 [–0.17 to        0.05 [–0.18 to 0.28
      kernel estimates   0.29]                 ]
      Net (i.e.,         –1.08 [–1.61 to –     –1.03 [–1.54 to –   –1.16       –1.81 to –0.51   –1.54 to –        medium
      relevant for       0.68]                 0.62]                                            0.78
      Long-term ice                                                            > 0.0                              high
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      sheet feedbacks
      (millennial scale)
 2   [END TABLE 7.10 HERE]
 5   Climate feedbacks in ESMs
 7   Since AR5, many modelling groups have newly participated in CMIP experiments, leading to an increase in
 8   the number of models in CMIP6 (Chapter 1, Section 1.5.4). Other modelling groups that contributed to
 9   CMIP5 also updated their ESMs for carrying out CMIP6 experiments. While some of the CMIP6 models
10   share components and are therefore not independent, they are analysed independently when calculating
11   climate feedbacks. This, and more subtle forms of model inter-dependence, creates challenges when
12   determining appropriate model weighting schemes (Chapter 1, Section 1.5.4). Additionally, it must be kept
13   in mind that the ensemble sizes of the CMIP5 and CMIP6 models are not sufficiently large to sample the full
14   range of model uncertainty.
16   The multi-model mean values of all physical climate feedbacks are calculated using the radiative kernel
17   method (Section 7.4.1) and compared with the assessment in the previous sections (Figure 7.10). For CMIP
18   models, there is a discrepancy between the net climate feedback calculated directly using the time evolutions
19   of ∆T and ∆Ν in each model and the accumulation of individual feedbacks, but it is negligibly small
20   (Supplementary Material 7.SM.4). Feedbacks due to biogeophysical and non-CO2 biogeochemical processes
21   are included in some models but neglected in the kernel analysis. In the AR6, biogeophysical and non-CO2
22   biogeochemical feedbacks are explicitly assessed (Section
24   All the physical climate feedbacks apart from clouds are very similar to each other in CMIP5 and CMIP6
25   model ensembles (see also Table 7.10). These values, where possible supported by other lines of evidence,
26   are used for assessing feedbacks in Sections– A difference found between CMIP5 and CMIP6
27   models is the net cloud feedback, which is larger in CMIP6 by about 20%. This change is the major cause of
28   less-negative values of the net climate feedback in CMIP6 than in CMIP5 and hence an increase in modelled
29   ECS (Section 7.5.1).
31   A remarkable improvement of cloud representation in some CMIP6 models is the reduced error of the too
32   weak negative SW CRE over the Southern Ocean (Bodas-Salcedo et al., 2019; Gettelman et al., 2019) due to
33   a more realistic simulation of supercooled liquid droplets and associated cloud optical depths that were
34   biased low commonly in CMIP5 models (McCoy et al. 2014a; 2014b). Because the negative cloud optical
35   depth feedback occurs due to ‘brightening’ of clouds via phase change from ice to liquid cloud particles in
36   response to surface warming (Cesana and Storelvmo, 2017), the extratropical cloud SW feedback tends to be
37   less negative or even slightly positive in models with reduced errors (Bjordal et al., 2020; Zelinka et al.,
38   2020). The assessment of cloud feedbacks in Section incorporates estimates from these improved
39   ESMs. Yet, there still remain other shared model errors such as in the subtropical low clouds (Calisto et al.,
40   2014) and tropical anvil clouds (Mauritsen and Stevens, 2015), hampering an assessment of feedbacks
41   associated with these cloud regimes based only on ESMs (Section
46   Figure 7.10: Global-mean climate feedbacks estimated in abrupt4xCO2 simulations of 29 CMIP5 models (light
47                blue) and 49 CMIP6 models (orange), compared with those assessed in this Report (red). Individual
48                feedbacks for CMIP models are averaged across six radiative kernels as computed in Zelinka et al.
49                (2020). The white line, black box and vertical line indicate the mean, 66% and 90% ranges, respectively.
50                The shading represents the probability distribution across the full range of GCM/ESM values and for the
51                2.5-97.5 percentile range of the AR6 normal distribution. The unit is W m–2 °C–1. Feedbacks associated
52                with biogeophysical and non-CO2 biogeochemical processes are assessed in AR6, but they are not
53                explicitly estimated from GCMs/ESMs in CMIP5 and CMIP6. Further details on data sources and
54                processing are available in the chapter data table (Table 7.SM.14).
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 2   [END FIGURE 7.10 HERE]
 5   7.4.3     Dependence of feedbacks on climate mean state
 7   In the standard framework of forcings and feedbacks (Section 7.4.1; Box 7.1), the approximation is made
 8   that the strength of climate feedbacks is independent of the background global surface mean temperature.
 9   More generally, the individual feedback parameters, αx, are often assumed to be constant over a range of
10   climate states, including those reconstructed from the past (encompassing a range of states warmer and
11   colder than today, with varying continental geographies) or projected for the future. If this approximation
12   holds, then the equilibrium global surface temperature response to a fixed radiative forcing will be constant,
13   regardless of the climate state to which that forcing is applied.
15   This approximation will break down if climate feedbacks are not constant, but instead vary as a function of,
16   e.g., background temperature (Roe and Baker, 2007; Zaliapin and Ghil, 2010; Roe and Armour, 2011;
17   Bloch-Johnson et al., 2015), continental configuration (Farnsworth et al., 2019), or configuration of ice
18   sheets (Yoshimori et al., 2009). If the real climate system exhibits this state dependence, then the future
19   equilibrium temperature change in response to large forcing may be different from that inferred using the
20   standard framework, and/or different to that inferred from paleoclimates. Such considerations are important
21   for the assessment of ECS (Section 7.5). Climate models generally include representations of feedbacks that
22   allow state-dependent behaviour, and so model results may also differ from the predictions from the standard
23   framework.
25   In AR5 (Boucher et al., 2013), there was a recognition that climate feedbacks could be state dependent
26   (Colman and McAvaney, 2009), but modelling studies that explored this (e.g., Manabe and Bryan, 1985;
27   Voss and Mikolajewicz, 2001; Stouffer and Manabe, 2003; Hansen, 2005b) were not assessed in detail. Also
28   in AR5 (Masson-Delmotte et al., 2013), it was assessed that some models exhibited weaker sensitivity to
29   Last Glacial Maximum (LGM, Cross-Chapter Box 2.1) forcing than to 4×CO2 forcing, due to state-
30   dependence in shortwave cloud feedbacks.
32   Here, recent evidence for state-dependence in feedbacks from modelling studies (Section and from
33   the paleoclimate record (Section are assessed, with an overall assessment in Section The
34   focus is on temperature-dependence of feedbacks when the system is in equilibrium with the forcing;
35   evidence for transient changes in the net feedback parameter associated with evolving spatial patterns of
36   warming is assessed separately in Section 7.4.4.
39    State-dependence of feedbacks in models
41   There are several modelling studies since AR5 in which ESMs of varying complexity have been used to
42   explore temperature dependence of feedbacks, either under modern (Hansen et al., 2013; Jonko et al., 2013;
43   Meraner et al., 2013; Good et al., 2015; Duan et al., 2019; Mauritsen et al., 2019; Rohrschneider et al., 2019;
44   Rugenstein et al., 2019b; Stolpe et al., 2019; Bloch‐Johnson et al., 2020) or paleo (Caballero and Huber,
45   2013; Zhu et al., 2019b) climate conditions, typically by carrying out multiple simulations across successive
46   CO2 doublings. A non-linear temperature response to these successive doublings may be partly due to
47   forcing that increases more (or less) than expected from a purely logarithmic dependence (Section 7.3.2;
48   Etminan et al., 2016), and partly due to state-dependence in feedbacks; however, not all modelling studies
49   have partitioned the non-linearities in temperature response between these two effects. Nonetheless, there is
50   general agreement amongst ESMs that the net feedback parameter, α, increases (i.e., becomes less negative)
51   as temperature increases from pre-industrial levels (i.e., sensitivity to forcing increases as temperature
52   increases; e.g., Meraner et al., 2013; see Figure 7.11). The associated increase in sensitivity to forcing is, in
53   most models, due to the water vapour (Section and cloud (Section feedback parameters
54   increasing with warming (Caballero and Huber, 2013; Meraner et al., 2013; Rugenstein et al., 2019b; Zhu et
55   al., 2019b; Sherwood et al., 2020b). These changes are offset partially by the surface albedo feedback
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 1   parameter decreasing (Jonko et al., 2013; Meraner et al., 2013; Rugenstein et al., 2019b), as a consequence
 2   of a reduced amount of snow and sea ice cover in a much warmer climate. At the same time, there is little
 3   change in the Planck response (Section, which has been shown in one model to be due to competing
 4   effects from increasing Planck emission at warmer temperatures and decreasing planetary emissivity due to
 5   increased CO2 and water vapour (Mauritsen et al., 2019). Analysis of the spatial patterns of the non-
 6   linearities in temperature response (Good et al., 2015) suggests that these patterns are linked to a reduced
 7   weakening of the AMOC, and changes to evapotranspiration. The temperature dependence of α is also found
 8   in model simulations of high-CO2 paleoclimates (Caballero and Huber, 2013; Zhu et al., 2019b). The
 9   temperature dependence is not only evident at very high CO2 concentrations in excess of 4×CO2, but also
10   apparent in the difference in temperature response to a 2×CO2 forcing compared with to a 4×CO2 forcing
11   (Mauritsen et al., 2019; Rugenstein et al., 2019b), and as such is relevant for interpreting century-scale
12   climate projections.
14   Despite the general agreement that α increases as temperature increases from pre-industrial levels (Figure
15   7.11), other modelling studies have found the opposite (Duan et al., 2019; Stolpe et al., 2019). Modelling
16   studies exploring state dependence in climates colder than today, including in cold paleoclimates such as the
17   LGM, provide conflicting evidence of either decreased (Yoshimori et al., 2011) or increased (Kutzbach et
18   al., 2013; Stolpe et al., 2019) temperature response per unit forcing during cold climates compared to the
19   modern era.
21   In contrast to most ESMs, the majority of Earth system models of intermediate complexity (EMICs) do not
22   exhibit state dependence, or have a net feedback parameter that decreases with increasing temperature
23   (Pfister and Stocker, 2017). This is unsurprising since EMICs usually do not include process-based
24   representations of water vapour and cloud feedbacks. Although this shows that care must be taken when
25   interpreting results from current generation EMICs, Pfister and Stocker (2017) also suggest that non-
26   linearities in feedbacks can take a long time to emerge in model simulations due slow adjustment timescales
27   associated with the ocean; longer simulations also allow better estimates of equilibrium warming (Bloch‐
28   Johnson et al., 2020). This implies that multi-century simulations (Rugenstein et al., 2019b) could increase
29   confidence in ESM studies examining state dependence.
31   The possibility of more substantial changes in climate feedbacks, sometimes accompanied by hysteresis
32   and/or irreversibility, has been suggested from some theoretical and modelling studies. It has been postulated
33   that such changes could occur on a global scale and across relatively narrow temperature changes (Popp et
34   al., 2016; von der Heydt and Ashwin, 2016; Steffen et al., 2018; Schneider et al., 2019; Ashwin and von der
35   Heydt, 2020; Bjordal et al., 2020). However, the associated mechanisms are highly uncertain, and as such
36   there is low confidence as to whether such behaviour exists at all, and in the temperature thresholds at which
37   it might occur.
39   Overall, the modelling evidence indicates that there is medium confidence that the net feedback parameter, α,
40   increases (i.e., becomes less negative) with increasing temperature (i.e., that sensitivity to forcing increases
41   with increasing temperature), under global surface background temperatures at least up to 40°C (Meraner et
42   al., 2013; Seeley and Jeevanjee, 2021), and medium confidence that this temperature dependence primarily
43   derives from increases in the water vapour and shortwave cloud feedbacks. This assessment is further
44   supported by recent analysis of CMIP6 model simulations (Bloch‐Johnson et al., 2020) in the framework of
45   nonlinMIP (Good et al., 2016), which showed that out of ten CMIP6 models, seven of them showed an
46   increase of the net feedback parameter with temperature, primarily due to the water vapour feedback.
49   State-dependence of feedbacks in the paleoclimate proxy record
51   Several studies have estimated ECS from observations of the glacial-interglacial cycles of the last
52   approximately 2 million years, and found a state dependence, with more-negative α (i.e., lower sensitivity to
53   forcing) during colder periods of the cycles and less-negative α during warmer periods (von der Heydt et al.,
54   2014; Köhler et al., 2015, 2017; Friedrich et al., 2016; Royer, 2016; Snyder, 2019); see summaries in
55   Skinner (2012) and von der Heydt et al. (2016). However, the nature of the state dependence derived from
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 1   these observations is dependent on the assumed ice sheet forcing (Köhler et al., 2015; Stap et al., 2019),
 2   which is not well known, due to a relative lack of proxy indicators of ice sheet extent and distribution prior
 3   to the LGM (Cross-Chapter Box 2.1). Furthermore, many of these glacial-interglacial studies estimate a very
 4   strong temperature-dependence of α (Figure 7.11) that is hard to reconcile with the other lines of evidence,
 5   including proxy estimates from warmer paleoclimates. However, if the analysis excludes time periods when
 6   the temperature and CO2 data are not well correlated, which occurs in general at times when sea level is
 7   falling and obliquity is decreasing, the state-dependence reduces (Köhler et al., 2018). Despite these
 8   uncertainties, due to the agreement in the sign of the temperature-dependence from all these studies, there is
 9   medium confidence from the paleoclimate proxy record that the net feedback parameter, α, was less negative
10   in the warm periods than in the cold periods of the glacial-interglacial cycles.
12   Paleoclimate proxy evidence from past high-CO2 time periods much warmer than present (the early Eocene
13   and PETM; Cross-Chapter Box 2.1) show that the feedback parameter increases as temperature increases
14   (Anagnostou et al., 2016, 2020; Shaffer et al., 2016). However, such temperature-dependence of feedbacks
15   was not found in the warm Pliocene relative to the cooler Pleistocene (Martínez-Botí et al., 2015), although
16   the temperature changes are relatively small at this time, making temperature-dependence challenging to
17   detect given the uncertainties in reconstructing global mean temperature and forcing. Overall, the
18   paleoclimate proxy record provides medium confidence that the net feedback parameter, α, was less negative
19   in these past warm periods than in the present day.
22   Synthesis of state-dependence of feedbacks from modelling and paleoclimate records
24   Overall, independent lines of evidence from models (Section and from the paleoclimate proxy record
25   (Section lead to high confidence that the net feedback parameter, α, increases (i.e., becomes less
26   negative) as temperature increases; i.e., that sensitivity to forcing increases as temperature increases; see
27   Figure 7.11. This temperature-dependence should be considered when estimating ECS from ESM
28   simulations in which CO2 is quadrupled (Section 7.5.5) or from paleoclimate observations from past time
29   periods colder or warmer than today (Section 7.5.4). Although individual lines of evidence give only medium
30   confidence, the overall high confidence comes from the multiple models that show the same sign of the
31   temperature-dependence of α, the general agreement in evidence from the paleo proxy and modelling lines of
32   evidence, and the agreement between proxy evidence from both cold and warm past climates. However, due
33   to the large range in estimates of the magnitude of the temperature-dependence of α across studies (Figure
34   7.11), a quantitative assessment cannot currently be given, which provides a challenge for including this
35   temperature-dependence in emulator-based future projections (Cross-Chapter Box 7.1). Greater confidence
36   in the modelling lines of evidence could be obtained from simulations carried out for several hundreds of
37   years (Rugenstein et al., 2019b), substantially longer than in many studies, and from more models carrying
38   out simulations at multiple CO2 concentrations. Greater confidence in the paleoclimate lines of evidence
39   would be obtained from stronger constraints on atmospheric CO2 concentrations, ice sheet forcing, and
40   temperatures, during past warm climates.
45   Figure 7.11: Feedback parameter, α (W m–2 °C–1), as a function of global mean surface air temperature anomaly
46                relative to preindustrial, for ESM simulations (red circles and lines) (Caballero and Huber, 2013;
47                Jonko et al., 2013; Meraner et al., 2013; Good et al., 2015; Duan et al., 2019; Mauritsen et al., 2019;
48                Stolpe et al., 2019; Zhu et al., 2019b), and derived from paleoclimate proxies (grey squares and lines)
49                (von der Heydt et al., 2014; Anagnostou et al., 2016, 2020; Friedrich et al., 2016; Royer, 2016; Shaffer et
50                al., 2016; Köhler et al., 2017; Snyder, 2019; Stap et al., 2019). For the ESM simulations, the value on the
51                x-axis refers to the average of the temperature before and after the system has equilibrated to a forcing (in
52                most cases a CO2 doubling), and is expressed as an anomaly relative to an associated pre-industrial global
53                mean temperature from that model. The light blue shaded square extends across the assessed range of α
54                (Table 7.10) on the y-axis, and on the x-axis extends across the approximate temperature range over
55                which the assessment of α is based (taken as from zero to the assessed central value of ECS (Table 7.13).
56                Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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 2   [END FIGURE 7.11 HERE]
 5   7.4.4     Relationship between feedbacks and temperature patterns
 7   The large-scale patterns of surface warming in observations since the 19th century (Chapter 2, Section 2.3.1)
 8   and climate model simulations (Chapter 4, Section 4.3.1; Figure 7.12a) share several common features. In
 9   particular, surface warming in the Arctic is greater than for the global average and greater than in the
10   southern hemisphere (SH) high latitudes; and surface warming is generally greater over land than over the
11   ocean. Observations and climate model simulations also show some notable differences. ESMs generally
12   simulate a weakening of the equatorial Pacific Ocean zonal (east-west) SST gradient on multi-decadal to
13   centennial timescales, with greater warming in the east than the west, but this trend has not been seen in
14   observations (Chapter 2, Figure 2.11b; Chapter 9, Section 9.2.1).
16   Chapter 4, Section 4.5.1 discusses patterns of surface warming for 21st century climate projections under the
17   Shared Socioeconomic Pathways (SSP) scenarios. Chapter 9, Section 9.2.1 assesses historical SST trends
18   and the ability of coupled ESMs to replicate the observed changes. Chapter 4, Section 4.5.1 discusses the
19   processes that cause the land to warm more than the ocean (land-ocean warming contrast). This section
20   assesses process understanding of the large-scale patterns of surface temperature response from the
21   perspective of a regional energy budget. It then assesses evidence from the paleoclimate proxy record for
22   patterns of surface warming during past time periods associated with changes in atmospheric CO2
23   concentrations. Finally, it assesses how radiative feedbacks depend on the spatial pattern of surface
24   temperature, and thus how they can change in magnitude as that pattern evolves over time, with implications
25   for the assessment of ECS based on historical warming (Sections and
28    Polar amplification
30   Polar amplification describes the phenomenon where surface temperature change at high latitudes exceeds
31   the global average surface temperature change in response to radiative forcing of the climate system. Arctic
32   amplification, often defined as the ratio of Arctic to global surface warming, is a ubiquitous emergent feature
33   of climate model simulations (Holland and Bitz, 2003; Pithan and Mauritsen, 2014; Chapter 4, Section 4.5.1;
34   Figure 7.12a) and is also seen in observations (Chapter 2, Section 2.3.1). However, both climate models and
35   observations show relatively less warming of the SH high latitudes compared to the northern hemisphere
36   (NH) high latitudes over the historical record (Chapter 2, Section 2.3.1); a characteristic that is projected to
37   continue over the 21st century (Chapter 4, Section 4.5.1). Since AR5 there is a much-improved understanding
38   of the processes that drive polar amplification in the NH and delay its emergence in the SH (Section
39 Furthermore, the paleoclimate record provides evidence for polar amplification from multiple
40   time periods associated with changes in CO2 (Hollis et al., 2019; Cleator et al., 2020; McClymont et al.,
41   2020; Tierney et al., 2020b), and allows an evaluation of polar amplification in model simulations of these
42   periods (Section Research since AR5 identifies changes in the degree of polar amplification over
43   time, particularly in the SH, as a key factor affecting how radiative feedbacks may evolve in the future
44   (Section
49   Figure 7.12: Contributions of effective radiative forcing, ocean heat uptake, atmospheric heat transport, and
50                radiative feedbacks to regional surface temperature changes at year 100 of abrupt4xCO2
51                simulations of CMIP6 ESMs. (a) Pattern of near-surface air temperature change. (b-d) Contributions to
52                net Arctic (>60°N), tropical (30°S – 30°N), and Antarctic (<60°S) warming calculated by dividing
53                regional-average energy inputs by the magnitude of the regional-average Planck response. The
54                contributions from radiative forcing, changes in moist, dry-static, and total atmospheric energy transport,
55                ocean heat uptake, and radiative feedbacks (orange bars) all sum to the value of net warming (grey bar).
56                Inset shows regional warming contributions associated with individual feedbacks, all summing to the
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 1                total feedback contribution. Uncertainties show the interquartile range (25th and 75th percentiles) across
 2                models. The warming contributions (units of °C) for each process are diagnosed by calculating the energy
 3                flux (units of W m–2) that each process contributes to the atmosphere over a given region, either at the
 4                TOA or surface, then dividing that energy flux by the magnitude of the regional Planck response (around
 5                3.2 W m–2 °C–1 but varying with region). By construction, the individual warming contributions sum to
 6                the total warming in each region. Radiative kernel methods (see Section 7.4.1) are used to decompose the
 7                net energy input from radiative feedbacks into contributions from changes in atmospheric water vapour,
 8                lapse-rate, clouds, and surface albedo (Zelinka et al. (2020) using the Huang et al. (2017) radiative
 9                kernel). The CMIP6 models included are those analysed by Zelinka et al. (2020) and the warming
10                contribution analysis is based on that of Goosse et al. (2018). Further details on data sources and
11                processing are available in the chapter data table (Table 7.SM.14).
13   [END FIGURE 7.12 HERE]
16 Critical processes driving polar amplification
17   Several processes contribute to polar amplification under greenhouse gas forcing including the loss of sea ice
18   and snow (an amplifying surface-albedo feedback), the confinement of warming to near the surface in the
19   polar atmosphere (an amplifying lapse-rate feedback), and increases in poleward atmospheric and oceanic
20   heat transport (Pithan and Mauritsen, 2014; Goosse et al., 2018; Dai et al., 2019; Feldl et al., 2020).
21   Modelling and process studies since AR5 have led to an improved understanding of the combined effect of
22   these different processes in driving polar amplification and how they differ between the hemispheres.
24   Idealized modelling studies suggest that polar amplification would occur even in the absence of any
25   amplifying polar surface-albedo or lapse-rate feedbacks owing to changes in poleward atmospheric heat
26   transport under global warming (Hall, 2004; Alexeev et al., 2005; Graversen and Wang, 2009; Alexeev and
27   Jackson, 2013; Graversen et al., 2014; Roe et al., 2015; Merlis and Henry, 2018; Armour et al., 2019).
28   Poleward heat transport changes reflect compensating changes in the transport of latent energy (moisture)
29   and dry-static energy (sum of sensible and potential energy) by atmospheric circulations (Alexeev et al.,
30   2005; Held and Soden, 2006; Hwang and Frierson, 2010; Hwang et al., 2011; Kay et al., 2012; Huang and
31   Zhang, 2014; Feldl et al., 2017a; Donohoe et al., 2020). ESMs project that within the mid-latitudes, where
32   eddies dominate the heat transport, an increase in poleward latent energy transport arises from an increase in
33   the equator-to-pole gradient in atmospheric moisture with global warming, with moisture in the tropics
34   increasing more than at the poles as described by the Clausius-Clapeyron relation (Chapter 8, Section 8.2).
35   This change is partially compensated by a decrease in dry-static energy transport arising from a weakening
36   of the equator-to-pole temperature gradient as the polar regions warm more than the tropics.
38   Energy balance models that approximate atmospheric heat transport in terms of a diffusive flux down the
39   meridional gradient of near-surface moist static energy (sum of dry-static and latent energy) are able to
40   reproduce the atmospheric heat transport changes seen within ESMs (Flannery, 1984; Hwang and Frierson,
41   2010; Hwang et al., 2011; Rose et al., 2014; Roe et al., 2015; Merlis and Henry, 2018), including the
42   partitioning of latent and dry-static energy transports (Siler et al., 2018b; Armour et al., 2019). These models
43   suggest that polar amplification is driven by enhanced poleward latent heat transport and that the magnitude
44   of polar amplification can be enhanced or diminished by the latitudinal structure of radiative feedbacks.
45   Amplifying polar feedbacks enhance polar warming and in turn cause a decrease in the dry-static energy
46   transport to high latitudes (Alexeev and Jackson, 2013; Rose et al., 2014; Roe et al., 2015; Bonan et al.,
47   2018; Merlis and Henry, 2018; Armour et al., 2019; Russotto and Biasutti, 2020). Poleward latent heat
48   transport changes act to favour polar amplification and inhibit tropical amplification (Armour et al., 2019),
49   resulting in a strongly polar-amplified warming response to polar forcing and a more latitudinally-uniform
50   warming response to tropical forcing within ESMs (Alexeev et al., 2005; Rose et al., 2014; Stuecker et al.,
51   2018). The important role for poleward latent energy transport in polar amplification is supported by studies
52   of atmospheric reanalyses and ESMs showing that episodic increases in latent heat transport into the Arctic
53   can enhance surface downwelling radiation and drive sea-ice loss on sub-seasonal timescales (Woods and
54   Caballero, 2016; Gong et al., 2017; Lee et al., 2017; Luo et al., 2017a), however this may be a smaller driver
55   of sea-ice variability than atmospheric temperature fluctuations (Olonscheck et al., 2019).
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 1   Regional energy budget analyses are commonly used to diagnose the relative contributions of radiative
 2   feedbacks and energy fluxes to polar amplification as projected by ESMs under increased CO2
 3   concentrations (Figure 7.12; Feldl and Roe, 2013; Pithan and Mauritsen, 2014; Goosse et al., 2018; Stuecker
 4   et al., 2018). These analyses suggest that a primary cause of amplified Arctic warming in ESMs is the
 5   latitudinal structure of radiative feedbacks, which warm the Arctic more than the tropics (Figure 7.12b), and
 6   enhanced latent energy transport into the Arctic. That net atmospheric heat transport into the Arctic does not
 7   change substantially within ESMs, on average, under CO2 forcing (Figure 7.12b) reflects a compensating
 8   decrease in poleward dry-static energy transport as a response to polar amplified warming (Hwang et al.,
 9   2011; Armour et al., 2019; Donohoe et al., 2020). The latitudinal structure of radiative feedbacks primarily
10   reflects that of the surface-albedo and lapse-rate feedbacks, which preferentially warm the Arctic (Graversen
11   et al., 2014; Pithan and Mauritsen, 2014; Goosse et al., 2018). Latitudinal structure in the lapse-rate feedback
12   reflects weak radiative damping to space with surface warming in polar regions, where atmospheric warming
13   is constrained to the lower troposphere owing to stably stratified conditions, and strong radiative damping in
14   the tropics, where warming is enhanced in the upper troposphere owing to moist convective processes. This
15   is only partially compensated by latitudinal structure in the water vapour feedback (Taylor et al., 2013),
16   which favours tropical warming (Pithan and Mauritsen, 2014). While cloud feedbacks have been found to
17   play little role in Arctic amplification in CMIP5 models (Pithan and Mauritsen, 2014; Goosse et al., 2018;
18   Figure 7.12b), less-negative cloud feedbacks at high latitude as seen within some CMIP6 models (Zelinka et
19   al., 2020) tend to favour stronger polar amplification (Dong et al., 2020). A weaker Planck response at high
20   latitudes, owing to less efficient radiative damping where surface and atmospheric temperatures are lower,
21   also contributes to polar amplification (Pithan and Mauritsen, 2014). The effective radiative forcing of CO2
22   is larger in the tropics than at high latitudes, suggesting that warming would be tropically amplified if not for
23   radiative feedbacks and poleward latent heat transport changes (Stuecker et al., 2018; Figure 7.12b-d).
25   While the contributions to regional warming can be diagnosed within ESM simulations (Figure 7.12),
26   assessment of the underlying role of individual factors is limited by interactions inherent to the coupled
27   climate system. For example, polar feedback processes are coupled and influenced by warming at lower
28   latitudes (Screen et al., 2012; Alexeev and Jackson, 2013; Graversen et al., 2014; Graversen and Burtu,
29   2016; Rose and Rencurrel, 2016; Feldl et al., 2017a; Yoshimori et al., 2017; Garuba et al., 2018; Po-Chedley
30   et al., 2018a; Stuecker et al., 2018; Dai et al., 2019; Feldl et al., 2020), while atmospheric heat transport
31   changes are in turn influenced by the latitudinal structure of regional feedbacks, radiative forcing, and ocean
32   heat uptake (Hwang et al., 2011; Zelinka and Hartmann, 2012; Feldl and Roe, 2013; Huang and Zhang,
33   2014; Merlis, 2014; Rose et al., 2014; Roe et al., 2015; Feldl et al., 2017b; Stuecker et al., 2018; Armour et
34   al., 2019). The use of different feedback definitions, such as a lapse-rate feedback partitioned into upper and
35   lower tropospheric components (Feldl et al., 2020) or including the influence of water vapour at constant
36   relative humidity (Held and Shell, 2012; Section 7.4.2), would also change the interpretation of which
37   feedbacks contribute most to polar amplification.
39   The energy budget analyses (Figure 7.12) suggest that greater surface warming in the Arctic than the
40   Antarctic under greenhouse gas forcing arises from two main processes. The first is large surface heat uptake
41   in the Southern Ocean (Figure 7.12c) driven by the upwelling of deep waters that have not yet felt the effects
42   of the radiative forcing; the heat taken up is predominantly transported away from Antarctica by northward-
43   flowing surface waters (Marshall et al., 2015; Armour et al., 2016; Chapter 9, Section 9.2.1). Strong surface
44   heat uptake also occurs in the subpolar North Atlantic Ocean under global warming (Chapter 9, Section
45   9.2.1). However, this heat is partially transported northward into the Arctic which leads to increased heat
46   fluxes into the Arctic atmosphere (Rugenstein et al., 2013; Jungclaus et al., 2014; Koenigk and Brodeau,
47   2014; Marshall et al., 2015; Nummelin et al., 2017; Singh et al., 2017; Oldenburg et al., 2018; Figure 7.12b).
48   The second main process contributing to differences in Arctic and Antarctic warming is the asymmetry in
49   radiative feedbacks between the poles (Yoshimori et al., 2017; Goosse et al., 2018). This primarily reflects
50   the weaker lapse-rate and surface-albedo feedbacks and more-negative cloud feedbacks in the SH high
51   latitudes (Figure 7.12). However, note the SH cloud feedbacks are uncertain due to possible biases in the
52   treatment of mixed phase clouds (Hyder et al., 2018). Idealized modelling suggests that the asymmetry in the
53   polar lapse-rate feedback arises from the height of the Antarctic ice sheet precluding the formation of deep
54   atmospheric inversions that are necessary to produce the stronger positive lapse-rate feedbacks seen in the
55   Arctic (Salzmann, 2017; Hahn et al., 2020). ESM projections of the equilibrium response to CO2 forcing
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 1   show polar amplification in both hemispheres, but generally with less warming in the Antarctic than the
 2   Arctic (Li et al., 2013a; Yoshimori et al., 2017).
 4   Because multiple processes contribute to polar amplification, it is a robust feature of the projected long-term
 5   response to greenhouse gas forcing in both hemispheres. At the same time, contributions from multiple
 6   processes make projections of the magnitude of polar warming inherently more uncertain than global mean
 7   warming (Holland and Bitz, 2003; Roe et al., 2015; Bonan et al., 2018; Stuecker et al., 2018). The magnitude
 8   of Arctic amplification ranges from a factor of two to four in ESM projections of 21st century warming
 9   (Chapter 4, Section 4.5.1). While uncertainty in both global and tropical warming under greenhouse gas
10   forcing is dominated by cloud feedbacks (Vial et al., 2013; Section 7.5.7), uncertainty in polar warming
11   arises from polar surface-albedo, lapse-rate, and cloud feedbacks, changes in atmospheric and oceanic
12   poleward heat transport, and ocean heat uptake (Hwang et al., 2011; Mahlstein and Knutti, 2011; Pithan and
13   Mauritsen, 2014; Bonan et al., 2018).
15   The magnitude of polar amplification also depends on the type of radiative forcing applied (Stjern et al.,
16   2019; Chapter 4, Section, with Chapter 6, Section 6.4.3 discussing changes in sulphate aerosol
17   emissions and the deposition of black carbon aerosols on ice and snow as potential drivers of amplified
18   Arctic warming. The timing of the emergence of SH polar amplification remains uncertain due to insufficient
19   knowledge of the timescales associated with Southern Ocean warming and the response to surface wind and
20   freshwater forcing (Bintanja et al., 2013; Kostov et al., 2017, 2018; Pauling et al., 2017; Purich et al., 2018).
21   ESM simulations indicate that freshwater input from melting ice shelves could reduce Southern Ocean
22   warming by up to several tenths of a °C over the 21st century by increasing stratification of the surface ocean
23   around Antarctica (Bronselaer et al., 2018; Golledge et al., 2019; Lago and England, 2019; Section;
24   Chapter 9, Section 9.2.1 and Box 9.3) (low confidence due to medium agreement but limited evidence).
25   However, even a large reduction in the Atlantic meridional overturning circulation (AMOC) and associated
26   northward heat transport due, for instance, to greatly increased freshwater runoff from Greenland would be
27   insufficient to eliminate Arctic amplification (Liu et al., 2017a, 2017b; Wen et al., 2018) (medium confidence
28   based on to medium agreement and medium evidence).
30   Arctic amplification has a distinct seasonality with a peak in early winter (Nov–Jan) owing to sea-ice loss
31   and associated increases in heat fluxes from the ocean to the atmosphere resulting in strong near-surface
32   warming (Pithan and Mauritsen, 2014; Dai et al., 2019). Surface warming may be further amplified by
33   positive cloud and lapse-rate feedbacks in autumn and winter (Burt et al., 2016; Morrison et al., 2018; Hahn
34   et al., 2020). Arctic amplification is weak in summer owing to surface temperatures remaining stable as
35   excess energy goes into thinning the summertime sea-ice cover, which remains at the melting point, or into
36   the ocean mixed layer. Arctic amplification can also be interpreted through changes in the surface energy
37   budget (Burt et al., 2016; Woods and Caballero, 2016; Boeke and Taylor, 2018; Kim et al., 2019), however
38   such analyses are complicated by the finding that a large portion of the changes in downward longwave
39   radiation can be attributed to the lower troposphere warming along with the surface itself (Vargas Zeppetello
40   et al., 2019).
43 Polar amplification from proxies and models during past climates associated with CO2 change
44   Paleoclimate proxy data provide observational evidence of large-scale patterns of surface warming in
45   response to past forcings, and allow an evaluation of the modelled response to these forcings (Chapter 3,
46   Section; Section In particular, paleoclimate data provide evidence for long-term changes in
47   polar amplification during time periods in which the primary forcing was a change in atmospheric CO2,
48   although data sparsity means that for some time periods this evidence may be limited to a single hemisphere
49   or ocean basin, or the evidence may come primarily from the mid-latitudes as opposed to the polar regions.
50   In this context, there has been a modelling and data focus on the Last Glacial Maximum (LGM) in the
51   context of PMIP4 (Cleator et al., 2020; Tierney et al., 2020b; Kageyama et al., 2021), the mid-Pliocene
52   warm period (MPWP) in the context of PlioMIP2 (Chapter 2, Cross-Chapter Box 2.4; Salzmann et al., 2013;
53   Haywood et al., 2020; McClymont et al., 2020), the early Eocene climatic optimum (EECO) in the context of
54   DeepMIP (Hollis et al., 2019; Lunt et al., 2021), and there is growing interest in the Miocene (Goldner et al.,
55   2014b; Steinthorsdottir et al., 2020) (for definitions of time periods see Chapter 2, Cross-Chapter Box 2.1).
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 1   For all these time periods, in addition to the CO2 forcing there are long-term feedbacks associated with ice
 2   sheets (Section, and in particular for the early Eocene there is a forcing associated with
 3   paleogeographic change (Farnsworth et al., 2019). However, because these non-CO2 effects can all be
 4   included as boundary conditions in model simulations, these time periods allow an assessment of the patterns
 5   of modelled response to known forcing (although uncertainty in the forcing increases further back in time).
 6   Because these changes to boundary conditions can be complex to implement in models, and because long
 7   simulations (typically >500 years) are required to approach equilibrium, these simulations have been carried
 8   out mostly by pre-CMIP6 models, with relatively few (or none for the early Eocene) fully coupled CMIP6
 9   models in the ensembles.
11   At the time of AR5, polar amplification was evident in proxy reconstructions of paleoclimate SST and SAT
12   from the LGM, MPWP and the early Eocene, but uncertainties associated with proxy calibrations
13   (Waelbroeck et al., 2009; Dowsett et al., 2012; Lunt et al., 2012a) and the role of orbital forcing (for the
14   MPWP; Lisiecki and Raymo, 2005) meant that the degree of polar amplification during these time periods
15   was not accurately known. Furthermore, although some models (CCSM3; Winguth et al., 2010; Huber and
16   Caballero, 2011) at that time were able to reproduce the strong polar amplification implied by temperature
17   proxies of the early Eocene, this was achieved at higher CO2 concentrations (>2000 ppm) than those
18   indicated by CO2 proxies (<1500 ppm; Beerling and Royer, 2011).
20   Since AR5 there has been progress in improving the accuracy of proxy temperature reconstructions of the
21   LGM (Cleator et al., 2020; Tierney et al., 2020b), the MPWP (McClymont et al., 2020), and the early
22   Eocene (Hollis et al., 2019) time periods. In addition, reconstructions of the MPWP have been focused on a
23   short time slice with an orbit similar to modern-day (isotopic stage KM5C; Haywood et al., 2013, 2016b).
24   Furthermore, there are more robust constraints on CO2 concentrations from the MPWP (Martínez-Botí et al.,
25   2015; de la Vega et al., 2020) and the early Eocene (Anagnostou et al., 2016, 2020). As such, polar
26   amplification during the LGM, MPWP, and early Eocene time periods can now be better quantified than at
27   the time of AR5, and the ability of climate models to reproduce this pattern can be better assessed; model-
28   data comparisons for SAT and SST for these three time periods are shown in Figure 7.13.
33   Figure 7.13: Polar amplification in paleo proxies and models of the early Eocene climatic optimum (EECO), the
34                mid-Pliocene warm period (MPWP), and the Last Glacial Maximum (LGM). Temperature
35                anomalies compared with pre-industrial (equivalent to CMIP6 simulation piControl) are shown for the
36                high-CO2 EECO and MPWP time periods, and for the low-CO2 LGM (expressed as pre-industrial minus
37                LGM). (a,b,c) Modelled near-surface air temperature anomalies for ensemble-mean simulations of the (a)
38                EECO (Lunt et al., 2021), (b) MPWP (Haywood et al., 2020; Zhang et al., 2021), and (c) LGM
39                (Kageyama et al., 2021; Zhu et al., 2021). Also shown are proxy near-surface air temperature anomalies
40                (coloured circles). (d,e,f) Proxy near-surface air temperature anomalies (grey circles), including published
41                uncertainties (grey vertical bars), model ensemble mean zonal mean anomaly (solid red line) for the same
42                model ensembles as in (a,b,c), light red lines show the modelled temperature anomaly for the individual
43                models that make up each ensemble (LGM, N=9; MPWP, N=17; EECO, N=5). Black dashed lines show
44                the average of the proxy values in each latitude bands 90°S to 30°S, 30°S to 30°N, and 30°N to 90°N.
45                Red dashed lines show the same banded average in the model ensemble mean, calculated from the same
46                locations as the proxies. Black and red dashed lines are only shown if there are 5 or more proxy points in
47                that band. Mean differences between the 90°S/N to 30°S/N and 30°S to 30°N bands are quantified for the
48                models and proxies in each plot. Panels (g,h,i) are like panels (d,e,f) but for SST instead of near-surface
49                air temperature. Panels (j,k,l) are like panels (a,b,c) but for SST instead of near-surface air temperature.
50                For the EECO maps (a,j), the anomalies are relative to the zonal mean of the pre-industrial, due to the
51                different continental configuration. Proxy datasets are (a,d) Hollis et al. (2019), (b,e) Salzmann et al.
52                (2013); Vieira et al. (2018), (c,f) Cleator et al. (2020) at the sites defined in Bartlein et al. (2011), (g,j) )
53                Hollis et al. (2019), (h,k) McClymont et al. (2020) (i,l) Tierney et al. (2020b). Where there are multiple
54                proxy estimations at a single site, a mean is taken. Model ensembles are (a,d,g,j) DeepMIP (only model
55                simulations carried out with a mantle-frame paleogeography, and carried out under CO2 concentrations
56                within the range assessed in Chapter 2, Table 2.2, are shown), (b,e,h,k) PlioMIP, and (c,f,i,l) PMIP4.
57                Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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 2   [END FIGURE 7.13 HERE]
 5   Since AR5, there has been progress in the simulation of polar amplification by paleoclimate models of the
 6   early Eocene. Initial work indicated that changes to model parameters associated with aerosols and/or clouds
 7   could increase simulated polar amplification and improve agreement between models and paleoclimate data
 8   (Kiehl and Shields, 2013; Sagoo et al., 2013), but such parameter changes were not physically based. In
 9   support of these initial findings, a more recent (CMIP5) climate model, that includes a process-based
10   representation of cloud microphysics, exhibits polar amplification in better agreement with proxies when
11   compared to the models assessed in AR5 (Zhu et al., 2019b). Since then, some other CMIP3 and CMIP5
12   models in the DeepMIP multi-model ensemble (Lunt et al., 2021) have obtained polar amplification for the
13   EECO that is consistent with proxy indications of both polar amplification and CO2. Although there is a lack
14   of tropical proxy SAT estimates, both proxies and DeepMIP models show greater terrestrial warming in the
15   high latitudes than the mid-latitudes in both Hemispheres (Figure 7.13a,d). SST proxies also exhibit polar
16   amplification in both Hemispheres, but the magnitude of this polar amplification is too low in the models, in
17   particular in the southwest Pacific (Figure 7.13g,j).
19   For the MPWP, model simulations are now in better agreement with proxies than at the time of AR5
20   (Haywood et al., 2020; McClymont et al., 2020). In particular, in the tropics new proxy reconstructions of
21   SSTs are warmer and in better agreement with the models, due in part to the narrower time window in the
22   proxy reconstructions. There is also better agreement at higher latitudes (primarily in the North Atlantic),
23   due in part to the absence of some very warm proxy SSTs due to the narrower time window (McClymont et
24   al., 2020), and in part to a modified representation of Arctic gateways in the most recent Pliocene model
25   simulations (Otto-Bliesner et al., 2017), which have resulted in warmer modelled SSTs in the North Atlantic
26   (Haywood et al., 2020). Furthermore, as for the Eocene, improvements in the representation of aerosol-cloud
27   interactions has also led to improved model-data consistency at high latitudes (Feng et al., 2019). Although
28   all PlioMIP2 models exhibit polar amplification of SAT, due to the relatively narrow time window there are
29   insufficient terrestrial proxies to assess this (Figure 7.13b,e). However, polar SST amplification in the
30   PlioMIP2 ensemble mean is in reasonably good agreement with that from SST proxies in the Northern
31   Hemisphere (Figure 7.13h,k).
33   The Last Glacial Maximum (LGM) also gives an opportunity to evaluate model simulation of polar
34   amplification under CO2 forcing, albeit under colder conditions than today (Kageyama et al., 2021).
35   Terrestrial SAT and marine SST proxies exhibit clear polar amplification in the Northern Hemisphere, and
36   the PMIP4 models capture this well (Figure 7.13c,f,i,l), in particular for SAT. There is less proxy data in the
37   mid to high latitudes of the Southern Hemisphere, but here the models exhibit polar amplification of both
38   SST and SAT. LGM regional model-data agreement is also assessed in Chapter 3, Section 3.8.2.
40   Overall, the proxy reconstructions give high confidence that there was polar amplification in the LGM,
41   MPWP and EECO, and this is further supported by model simulations of these time periods (Zhu et al.,
42   2019b; Haywood et al., 2020; Kageyama et al., 2021; Lunt et al., 2021; Figure 7.13). For both the MPWP
43   and EECO, models are more consistent with the temperature and CO2 proxies than at the time of AR5 (high
44   confidence). For the LGM Northern Hemisphere, which is the region with the most data and the time period
45   with the least uncertainty in model boundary conditions, polar amplification in the PMIP4 ensemble mean is
46   in good agreement with the proxies, especially for SAT (medium confidence). Overall, the confidence in the
47   ability of models to accurately simulate polar amplification is higher than at the time of AR5, but a more
48   complete model evaluation could be carried out if there were more CMIP6 paleoclimate simulations included
49   in the assessment.
52 Overall assessment of polar amplification
53   Based on mature process understanding of the roles of poleward latent heat transport and radiative feedbacks
54   in polar warming, a high degree of agreement across a hierarchy of climate models, observational evidence,
55   paleoclimate proxy records of past climates associated with CO2 change, and ESM simulations of those past
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 1   climates, there is high confidence that polar amplification is a robust feature of the long-term response to
 2   greenhouse gas forcing in both hemispheres. Stronger warming in the Arctic than in the global average has
 3   already been observed (Chapter 2, Section 2.3.1) and its causes are well understood. It is very likely that the
 4   warming in the Arctic will be more pronounced than on global average over the 21st century (high
 5   confidence) (Chapter 4, Section This is supported by models’ improved ability to simulate polar
 6   amplification during past time periods, compared with at the time of AR5 (high confidence); although this is
 7   based on an assessment of mostly non-CMIP6 models.
 9   Southern Ocean SSTs have been slow to warm over the instrumental period, with cooling since about 1980
10   owing to a combination of upper-ocean freshening from ice-shelf melt, intensification of surface westerly
11   winds from ozone depletion, and variability in ocean convection (Chapter 9, Section 9.2.1). This stands in
12   contrast to the equilibrium warming pattern either inferred from the proxy record or simulated by ESMs
13   under CO2 forcing. There is high confidence that the SH high latitudes will warm more than the tropics on
14   centennial timescales as the climate equilibrates with radiative forcing and Southern Ocean heat uptake is
15   reduced. However, there is only low confidence that this feature will emerge this century.
18   Tropical Pacific sea-surface temperature gradients
20   Research published since AR5 identifies changes in the tropical Pacific Ocean zonal SST gradient over time
21   as a key factor affecting how radiative feedbacks may evolve in the future (Section There is now a
22   much-improved understanding of the processes that govern the tropical Pacific SST gradient (Section
23 and the paleoclimate record provides evidence for its equilibrium changes from time periods
24   associated with changes in CO2 (Section
27 Critical processes determining changes in tropical Pacific sea-surface temperature gradients
28   A weakening of the equatorial Pacific Ocean east-west SST gradient, with greater warming in the East than
29   the west, is a common feature of the climate response to greenhouse gas forcing as projected by ESMs on
30   centennial and longer timescales (e.g., Figure 7.14b) (Chapter 4, Section 4.5.1). There are thought to be
31   several factors contributing to this pattern. In the absence of any changes in atmospheric or oceanic
32   circulations, the east-west surface temperature difference is theorized to decrease owing to weaker
33   evaporative damping, and thus greater warming in response to forcing, where climatological temperatures
34   are lower in the eastern Pacific cold tongue (Xie et al., 2010; Luo et al., 2015). Within atmospheric ESMs
35   coupled to mixed-layer ocean, this gradient in damping has been linked to the rate of change with warming
36   of the saturation specific humidity, which is set by the Clausius-Clapeyron relation (Merlis and Schneider,
37   2011). Gradients in low-cloud feedbacks may also favour eastern equatorial Pacific warming (DiNezio et al.,
38   2009).
40   In the coupled climate system, changes in atmospheric and oceanic circulations will influence the east-west
41   temperature gradient as well. It is expected that as global temperature increases and as the east-west
42   temperature gradient weakens, east-west sea-level pressure gradients and easterly trade winds (characterizing
43   the Walker circulation) will weaken as well (Vecchi et al., 2006, 2008; Figure 7.14b; Chapter 8, Sections
44 and; Chapter 4, Section 4.5.3). This would, in turn, weaken the east-west temperature gradient
45   through a reduction of equatorial upwelling of cold water in the east Pacific and a reduction in the transport
46   of warmer water to the western equatorial Pacific and Indian Ocean (England et al., 2014; Dong and
47   McPhaden, 2017; Li et al., 2017; Maher et al., 2018).
49   Research published since AR5 (Burls and Fedorov, 2014a; Fedorov et al., 2015; Erfani and Burls, 2019) has
50   built on an earlier theory (Liu and Huang, 1997; Barreiro and Philander, 2008) linking the east-west
51   temperature gradient to the north-south temperature gradient. In particular, model simulations suggest that a
52   reduction in the equator-to-pole temperature gradient (polar amplification) increases the temperature of water
53   subducted in the extra-tropics, which in turn is upwelled in the eastern Pacific. Thus, polar amplified
54   warming, with greater warming in the mid-latitudes and subtropics than in the deep tropics, is expected to
55   contribute to the weakening of the east-west equatorial Pacific SST gradient on decadal to centennial
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 1   timescales.
 3   The transient adjustment of the equatorial Pacific SST gradient is influenced by upwelling waters which
 4   delay surface warming in the east since they have not been at the surface for years-to-decades to experience
 5   the greenhouse gas forcing. This ‘thermostat mechanism’ (Clement et al., 1996; Cane et al., 1997) is not
 6   thought to persist to equilibrium since it does not account for the eventual increase in temperatures of
 7   upwelled waters (Liu et al., 2005; Xie et al., 2010; Luo et al., 2017b) which will occur as the subducting
 8   waters in mid-latitudes warm by more than the tropics on average as polar amplification emerges. An
 9   individual CMIP5 ESM (GFDL’s ESM2M) has been found to exhibit a La Niña–like pattern of Pacific
10   temperature change through the 21st century, similar to the SST trends seen over the historical record
11   (Chapter 9, Section 9.2.1; Figure 7.14a), owing to a weakening asymmetry between El Niño and La Niña
12   events (Kohyama et al., 2017), but this pattern of warming may not persist to equilibrium (Paynter et al.,
13   2018).
15   Since 1870, observed SSTs in the tropical western Pacific Ocean have increased while those in the tropical
16   eastern Pacific Ocean have changed less (Figure 7.14a; Chapter 9, Section 9.2.1). Much of the resultant
17   strengthening of the equatorial Pacific temperature gradient has occurred since about 1980 due to strong
18   warming in the west and cooling in the east (Chapter 2, Figure 2.11b) concurrent with an intensification of
19   the surface equatorial easterly trade winds and Walker Circulation (England et al., 2014; Chapter 3, Section
20, Section 3.7.6, Figure 3.16f, Figure 3.39f; Chapter 8, Section; Chapter 9, Section 9.2). This
21   temperature pattern is also reflected in regional ocean heat content trends and sea level changes observed
22   from satellite altimetry since 1993 (Bilbao et al., 2015; Richter et al., 2020). The observed changes may have
23   been influenced by one or a combination of temporary factors including sulphate aerosol forcing (Smith et
24   al., 2016; Takahashi and Watanabe, 2016; Hua et al., 2018), internal variability within the Indo-Pacific
25   Ocean (Luo et al., 2012; Chung et al., 2019), teleconnections from multi-decadal tropical Atlantic SST trends
26   (Kucharski et al., 2011, 2014, 2015; McGregor et al., 2014; Chafik et al., 2016; Li et al., 2016a; Kajtar et al.,
27   2017; Sun et al., 2017), teleconnections from multi-decadal Southern Ocean SST trends (Hwang et al.,
28   2017), and coupled ocean–atmosphere dynamics which slow warming in the equatorial eastern Pacific
29   (Clement et al., 1996; Cane et al., 1997; Seager et al., 2019). CMIP3 and CMIP5 ESMs have difficulties
30   replicating the observed trends in the Walker Circulation and Pacific Ocean SSTs over the historical record
31   (Sohn et al., 2013; Zhou et al., 2016; Coats and Karnauskas, 2017), possibly due to model deficiencies
32   including insufficient multi-decadal Pacific Ocean SST variability (Laepple and Huybers, 2014; Bilbao et al.,
33   2015; Chung et al., 2019), mean state biases affecting the forced response or the connection between Atlantic
34   and Pacific basins (Kucharski et al., 2014; Kajtar et al., 2018; Luo et al., 2018; McGregor et al., 2018;
35   Seager et al., 2019), and/or a misrepresentation of radiative forcing (Chapter 9, Section 9.2.1 and Chapter 3,
36   Section 3.7.6). However, the observed trends in the Pacific Ocean SSTs are still within the range of internal
37   variability as simulated by large initial condition ensembles of CMIP5 and CMIP6 models (Olonscheck et
38   al., 2020; Watanabe et al., 2020a). Because the causes of observed equatorial Pacific temperature gradient
39   and Walker circulation trends are not well understood (Chapter 3, Section, there is low confidence in
40   their attribution to anthropogenic influences (Chapter 8, Section, while there is medium confidence
41   that the observed changes have resulted from internal variability (Chapter 8, Section; Chapter 3,
42   Section 3.7.6).
45 Tropical Pacific temperature gradients in past high-CO2 climates
46   AR5 stated that paleoclimate proxies indicate a reduction in the longitudinal SST gradient across the
47   equatorial Pacific during the mid-Pliocene warm period (MPWP; Cross-Chapter Box 2.1; Cross-Chapter Box
48   2.4; Masson-Delmotte et al., 2013). This assessment was based on SST reconstructions between two sites
49   situated very close to the equator in the heart of the western Pacific warm pool and eastern Pacific cold
50   tongue, respectively. Multiple SST reconstructions based on independent paleoclimate proxies generally
51   agreed that during the Pliocene the SST gradient between these two sites was reduced compared with the
52   modern long-term mean (Wara et al., 2005; Dekens et al., 2008; Fedorov et al., 2013).
54   Since AR5, the generation of new SST records has led to a variety of revised gradient estimates, specifically
55   the generation of a new record for the warm pool (Zhang et al., 2014), the inclusion of SST reconstructions
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 1   from sites in the South China Sea as warm pool estimates (O’Brien et al., 2014; Zhang et al., 2014), and the
 2   inclusion of several new sites from the eastern Pacific as cold tongue estimates (Zhang et al., 2014; Fedorov
 3   et al., 2015). Published estimates of the reduction in the longitudinal SST difference for the Late Pliocene,
 4   relative to either Late Quaternary (0-0.5Ma) or pre-industrial values, include 1 to 1.5°C (Zhang et al., 2014),
 5   0.1 to 1.9°C (Tierney et al., 2019), and about 3°C (Ravelo et al., 2014; Fedorov et al., 2015; Wycech et al.,
 6   2020). All of these studies report a further weakening of the longitudinal gradient based on records extending
 7   into the Early Pliocene. While these revised estimates differ in magnitude due to differences in the sites and
 8   SST proxies used, they all agree that the longitudinal gradient was weaker, and this is supported by the
 9   probabilistic approach of Tierney et al. (2019). However, given that there are currently relatively few
10   western equatorial Pacific records from independent site locations, and due to uncertainties associated with
11   the proxy calibrations (Haywood et al., 2016a), there is only medium confidence that the average longitudinal
12   gradient in the tropical Pacific was weaker during the Pliocene than during the Late Quaternary.
14   To avoid the influence of local biases, changes in the longitudinal temperature difference within Pliocene
15   model simulations are typically evaluated using domain-averaged SSTs within chosen east and west Pacific
16   regions and as such there is sensitivity to methodology. Unlike the reconstructed estimates, longitudinal
17   gradient changes simulated by the Pliocene Model Intercomparison Project Phase 1 (PlioMIP1) models do
18   not agree on the change in sign and are reported as spanning approximately –0.5 to 0.5 °C by Brierley et al.
19   (2015) and approximately –1 to 1 °C by Tierney et al. (2019). Initial PlioMIP Phase 2 (PlioMIP2) analysis
20   suggests responses similar to PlioMIP1 (Feng et al., 2019; Haywood et al., 2020). Models that include
21   hypothetical modifications to cloud albedo or ocean mixing are required to simulate the substantially weaker
22   longitudinal differences seen in reconstructions of the early Pliocene (Fedorov et al., 2013; Burls and
23   Fedorov, 2014b).
25   While more western Pacific warm pool temperature reconstructions are needed to refine estimates of the
26   longitudinal gradient, several Pliocene SST reconstructions from the east Pacific indicate enhanced warming
27   in the centre of the eastern equatorial cold tongue upwelling region (Liu et al., 2019). This enhanced
28   warming in the east Pacific cold tongue appears to be dynamically consistent with reconstruction of
29   enhanced subsurface warming (Ford et al., 2015) and enhanced warming in coastal upwelling regions,
30   suggesting that the tropical thermocline was deeper and/or less stratified during the Pliocene. The Pliocene
31   data therefore suggests that the observed cooling trend over the last 60 years in parts of the eastern equatorial
32   Pacific (Seager et al., 2019; Chapter 9, Section; Figure 9.3), whether forced or due to internal
33   variability, involves transient processes that are probably distinct from the longer-timescale process (Burls
34   and Fedorov, 2014a, 2014b; Luo et al., 2015; Heede et al., 2020) that maintained warmer eastern Pacific SST
35   during the Pliocene.
38 Overall assessment of tropical Pacific sea-surface temperature gradients under CO2 forcing
39   The paleoclimate proxy record and ESM simulations of the MPWP, process understanding, and ESM
40   projections of climate response to CO2 forcing provide medium evidence and a medium degree of agreement
41   and thus medium confidence that equilibrium warming in response to elevated CO2 will be characterized by a
42   weakening of the east-west tropical Pacific SST gradient.
44   Overall the observed pattern of warming over the instrumental period, with a warming minimum in the
45   eastern tropical Pacific Ocean (Figure 7.14a), stands in contrast to the equilibrium warming pattern either
46   inferred from the MPWP proxy record or simulated by ESMs under CO2 forcing. There is medium
47   confidence that the observed strengthening of the east-west SST gradient is temporary and will transition to a
48   weakening of the SST gradient on centennial timescales. However, there is only low confidence that this
49   transition will emerge this century owing to a low degree of agreement across studies about the factors
50   driving the observed strengthening of the east-west SST gradient and how those factors will evolve in the
51   future. These trends in tropical Pacific SST gradients reflect changes in the climatology, rather than changes
52   in ENSO amplitude or variability, which are assessed in Chapter 4, Section 4.3.3.
55   Dependence of feedbacks on temperature patterns
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 2   The expected time-evolution of the spatial pattern of surface warming in the future has important
 3   implications for values of ECS inferred from the historical record of observed warming. In particular,
 4   changes in the global TOA radiative energy budget can be induced by changes in the regional variations of
 5   surface temperature, even without a change in the global mean temperature (Zhou et al., 2016; Ceppi and
 6   Gregory, 2019). Consequently, the global radiative feedback, characterizing the net TOA radiative response
 7   to global surface warming, depends on the spatial pattern of that warming. Therefore, if the equilibrium
 8   warming pattern under CO2 forcing (similar to CMIP6 projections in Fig. 7.12a) is distinct from that
 9   observed over the historical record or indicated by paleoclimate proxies (Sections and, then
10   ECS will be different from the effective ECS (Box 7.1) that is inferred from those periods. Accounting for
11   the dependence of radiative feedbacks on the spatial pattern of warming has helped to reconcile values of
12   ECS inferred from the historical record with values of ECS based on other lines of evidence and simulated
13   by climate models (Armour, 2017; Proistosescu and Huybers, 2017; Andrews et al., 2018; Section
14   but has not yet been examined in the paleoclimate context.
16   This temperature “pattern effect” (Stevens et al., 2016) can result from both internal variability and radiative
17   forcing of the climate system. Importantly, it is distinct from potential radiative feedback dependencies on
18   the global surface temperature, which are assessed in Section 7.4.3. While changes in global radiative
19   feedbacks under transient warming have been documented in multiple generations of climate models
20   (Williams et al., 2008; Andrews et al., 2015; Ceppi and Gregory, 2017; Dong et al., 2020), research
21   published since AR5 has developed a much-improved understanding of the role of evolving SST patterns in
22   driving feedback changes (Armour et al., 2013; Andrews et al., 2015, 2018, Zhou et al., 2016, 2017b;
23   Gregory and Andrews, 2016; Proistosescu and Huybers, 2017; Ceppi and Gregory, 2017; Haugstad et al.,
24   2017; Andrews and Webb, 2018; Silvers et al., 2018; Marvel et al., 2018; Dong et al., 2019, 2020). This
25   section assesses process understanding of the pattern effect, which is dominated by the evolution of SSTs.
26   Section describes how potential feedback changes associated with the pattern effect are important to
27   interpreting ECS estimates based on historical warming.
29   The radiation changes most sensitive to warming patterns are those associated with the low-cloud cover
30   (affecting global albedo) and the tropospheric temperature profile (affecting thermal emission to space)
31   (Ceppi and Gregory, 2017; Zhou et al., 2017b; Andrews et al., 2018; Dong et al., 2019). The mechanisms
32   and radiative effects of these changes are illustrated in Figure 7.14a,b. SSTs in regions of deep convective
33   ascent (e.g., in the western Pacific warm pool) govern the temperature of the tropical free troposphere and, in
34   turn, affect low clouds through the strength of the inversion that caps the boundary layer (i.e., the lower-
35   tropospheric stability) in subsidence regions (Wood and Bretherton, 2006; Klein et al., 2017). Surface
36   warming within ascent regions thus warms the free troposphere and increases low-cloud cover, causing an
37   increase in emission of thermal radiation to space and a reduction in absorbed solar radiation. In contrast,
38   surface warming in regions of overall descent preferentially warms the boundary layer and enhances
39   convective mixing with the dry free troposphere, decreasing low-cloud cover (Bretherton et al., 2013; Qu et
40   al., 2014; Zhou et al., 2015). This leads to an increase in absorption of solar radiation but little change in
41   thermal emission to space. Consequently, warming in tropical ascent regions results in negative lapse-rate
42   and cloud feedbacks while warming in tropical descent regions results in positive lapse-rate and cloud
43   feedbacks (Figure 7.14; Rose and Rayborn, 2016; Zhou et al., 2017b; Andrews and Webb, 2018; Dong et al.,
44   2019). Surface warming in mid-to-high latitudes causes a weak radiative response owing to compensating
45   changes in thermal emission (Planck and lapse-rate feedbacks) and absorbed solar radiation (shortwave
46   cloud and surface-albedo feedbacks) (Rose and Rayborn, 2016; Dong et al., 2019), however this
47   compensation may weaken due to less-negative shortwave cloud feedbacks at high warming (Frey and Kay,
48   2018; Bjordal et al., 2020; Dong et al., 2020).
53   Figure 7.14: Illustration of tropospheric temperature and low-cloud response to observed and projected Pacific
54                Ocean sea-surface temperature trends; adapted from Mauritsen (2016). (a) Atmospheric response to
55                linear sea-surface temperature trend observed over 1870–2019 (HadISST1 dataset; Rayner et al., 2003).

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 1                (b) Atmospheric response to linear sea-surface temperature trend over 150 years following abrupt4xCO2
 2                forcing as projected by CMIP6 ESMs (Dong et al., 2020). Relatively large historical warming in the
 3                western tropical Pacific has been communicated aloft (a shift from grey to red atmospheric temperature
 4                profile), remotely warming the tropical free troposphere and increasing the strength of the inversion in
 5                regions of the tropics where warming has been slower, such as the eastern equatorial Pacific. In turn, an
 6                increased inversion strength has increased the low-cloud cover (Zhou et al., 2016) causing an
 7                anomalously-negative cloud and lapse-rate feedbacks over the historical record (Andrews et al., 2018;
 8                Marvel et al., 2018). Relatively large projected warming in the eastern tropical Pacific is trapped near the
 9                surface (shift from grey to red atmospheric temperature profile), decreasing the strength of the inversion
10                locally. In turn, a decreased inversion strength combined with surface warming is projected to decrease
11                the low-cloud cover, causing the cloud and lapse-rate feedbacks to become less negative in the future.
12                Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).
14   [END FIGURE 7.14 HERE]
17   The spatial pattern of SST changes since 1870 shows relatively little warming in key regions of less-negative
18   radiative feedbacks, including the eastern tropical Pacific Ocean and Southern Ocean (Sections and
19; Figure 7.14a; Chapter 2, Figure 2.11b). Cooling in these regions since 1980 has occurred along with
20   an increase in the strength of the capping inversion in tropical descent regions, resulting in an observed
21   increase in low-cloud cover over the tropical eastern Pacific (Zhou et al., 2016; Ceppi and Gregory, 2017;
22   Fueglistaler and Silvers, 2021; Figure 7.14a). Thus, tropical low-cloud cover increased over recent decades
23   even as global surface temperature increased, resulting in a negative low-cloud feedback which is at odds
24   with the positive low-cloud feedback expected for the pattern of equilibrium warming under CO2 forcing
25   (Section; Figure 7.14b).
27   Andrews et al. (2018) analysed available CMIP5/6 ESM simulations (six in total) comparing effective
28   feedback parameters diagnosed within atmosphere-only ESMs using prescribed historical SST and sea-ice
29   concentration patterns with the equilibrium feedback parameters as estimated within coupled ESMs (using
30   identical atmospheres) driven by abrupt 4×CO2 forcing. The atmosphere-only ESMs show pronounced
31   multi-decadal variations in their effective feedback parameters over the last century, with a trend toward
32   strongly negative values since about 1980 owing primarily to negative shortwave cloud feedbacks driven by
33   warming in the western equatorial Pacific Ocean and cooling in the eastern equatorial Pacific Ocean (Zhou et
34   al., 2016; Andrews et al., 2018; Marvel et al., 2018; Dong et al., 2019). Yet, all six models show a less-
35   negative net feedback parameter under abrupt4xCO2 than for the historical period (based on regression since
36   1870 following Andrews et al., 2018). The average change in net feedback parameter between the historical
37   period and the equilibrium response to CO2 forcing, denoted here as α’, for these simulations is α’ = +0.6 W
38   m–2 °C–1 (+0.3 to +1.0 W m–2 °C–1 range across models) (Figure 7.15b). These feedback parameter changes
39   imply that the value of ECS may be substantially larger than that inferred from the historical record (Section
40 These findings can be understood from the fact that, due to a combination of internal variability and
41   transient response to forcing (Section, historical sea-surface warming has been relatively large in
42   regions of tropical ascent (Figure 7.14a), leading to an anomalously large net negative radiative feedback;
43   however, future warming is expected to be largest in tropical descent regions, such as the eastern equatorial
44   Pacific, and at high latitudes (Sections and; Figure 7.14b), leading to a less-negative net
45   radiative feedback and higher ECS.
47   A similar behaviour is seen within transient simulations of coupled ESMs, which project SST warming
48   patterns that are initially characterised by relatively large warming rates in the western equatorial Pacific
49   Ocean on decadal timescales and relatively large warming in the eastern equatorial Pacific and Southern
50   Ocean on centennial timescales (Andrews et al., 2015; Proistosescu and Huybers, 2017; Dong et al., 2020).
51   Recent studies based on simulations of 1% yr–1 CO2 increase (1pctCO2) or abrupt4xCO2 as analogues for
52   historical warming suggest characteristic values of α’ = +0.05 W m–2 °C–1 (–0.2 to +0.3 W m–2 °C–1 range
53   across models) based on CMIP5 and CMIP6 ESMs (Armour 2017, Lewis and Curry 2018, Dong et al. 2020).
54   Using historical simulations of one CMIP6 ESM (HadGEM3-GC3.1-LL), Andrews et al., (2019) find an
55   average feedback parameter change of α’ = +0.2 W m–2 °C–1(–0.2 to +0.6 W m–2 °C–1 range across four
56   ensemble members). Using historical simulations from another CMIP6 ESM (GFDL CM4.0), Winton et al.
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 1   (2020) find an average feedback parameter change of α’ = +1.5 W m–2 °C–1(+1.2 to +1.7 W m–2 °C–1 range
 2   across three ensemble members). This value is larger than the α’ = +0.7 W m–2 °C–1 within GFDL CM4.0 for
 3   historical CO2 forcing only, suggesting that the value of α’ may depend on historical non-CO2 forcings such
 4   as those associated with tropospheric and stratospheric aerosols (Marvel et al., 2016; Gregory et al., 2020;
 5   Winton et al., 2020).
 7   The magnitude of the net feedback parameter change α’ found within coupled CMIP5 and CMIP6 ESMs is
 8   generally smaller than that found when prescribing observed warming patterns within atmosphere-only
 9   ESMs (Andrews et al., 2018; Figure 7.15). This arises from the fact that the forced spatial pattern of
10   warming within transient simulations of most coupled ESMs are distinct from observed warming patterns
11   over the historical record in key regions such as the equatorial Pacific Ocean and Southern Ocean (Sections
12 and, while being more similar to the equilibrium pattern simulated under abrupt4xCO2.
13   However, historical simulations with HadGEM3-GC3.1-LL (Andrews et al., 2019) and GFDL CM4.0
14   (Winton et al., 2020) show substantial spread in the value of α’ across ensemble members, indicating a
15   potentially important role for internal variability in setting the magnitude of the pattern effect over the
16   historical period. Using the 100-member historical simulation ensemble of MPI- ESM1.1, Dessler et al.
17   (2018) find that internal climate variability alone results in a 0.5 W m–2 °C–1 spread in the historical effective
18   feedback parameter, and thus also in the value of α’. Estimates of α’ using prescribed historical warming
19   patterns provide a more realistic representation of the historical pattern effect because they account for the
20   net effect of the transient response to historical forcing and internal variability in the observed record
21   (Andrews et al., 2018).
23   The magnitude of α’, as quantified by ESMs, depends on the accuracy of both the projected patterns of SST
24   and sea-ice concentration changes in response to CO2 forcing and the radiative response to those patterns
25   (Andrews et al., 2018). Model biases that affect the long-term warming pattern (e.g., SST and relative
26   humidity biases in the equatorial Pacific cold tongue as suggested by Seager et al. (2019)) will affect the
27   value of α’. The value of α’ also depends on the accuracy of the historical SST and sea-ice concentration
28   conditions prescribed within atmosphere-only versions of ESMs to quantify the historical radiative feedback
29   (Figure 7.15b). Historical SSTs are particularly uncertain for the early portion of the historical record
30   (Chapter 2, Section 2.3.1), and there are few constraints on sea-ice concentration prior to the satellite era.
31   Using alternative SST datasets, Andrews et al. (2018) found little change in the value of α’ within two
32   models (HadGEM3 and HadAM3), while Lewis and Mauritsen (2020) found a smaller value of α’ within
33   two other models (ECHAM6.3 and CAM5). The sensitivity of results to the choice of dataset represents a
34   major source of uncertainty in the quantification of the historical pattern effect using atmosphere-only ESMs
35   that has yet to be systematically explored, but the preliminary findings of Lewis and Mauritsen (2020) and
36   Fueglistaler and Silvers (2021) suggest that α’ could be smaller than the values reported in Andrews et al.
37   (2018).
42   Figure 7.15: Relationship between historical and abrupt4xCO2 net radiative feedbacks in ESMs. (a) Radiative
43                feedbacks in CMIP6 ESMs estimated under historical forcing (values for GFDL CM4.0 and HadGEM3-
44                CG3.1-LL from Winton et al. (2020) and Andrews et al. (2019), respectively); horizontal lines show the
45                range across ensemble members. The other points show effective feedback values for 29 ESMs estimated
46                using regression over the first 50 years of abrupt4xCO2 simulations as an analogue for historical
47                warming (Dong et al., 2020). (b) Historical radiative feedbacks estimated from atmosphere-only ESMs
48                with prescribed observed sea-surface temperature and sea-ice concentration changes (Andrews et al.
49                2018) based on a linear regression of global TOA radiation against global near-surface air temperature
50                over the period 1870–2010 (pattern of warming similar to Figure 7.14a) and compared with equilibrium
51                feedbacks in a abrupt4xCO2 simulations of coupled versions of the same ESMs (pattern of warming
52                similar to Figure 7.14b). In all cases, the equilibrium feedback magnitudes are estimated as CO2 ERF
53                divided by ECS where ECS is derived from regression over years 1–150 of abrupt4xCO2 simulations
54                (Box 7.1); similar results are found if the equilibrium feedback is estimated directly from the slope of the
55                linear regression. Further details on data sources and processing are available in the chapter data table
56                (Table 7.SM.14).

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 2   [END FIGURE 7.15 HERE]
 5   While there are not yet direct observational constraints on the magnitude of the pattern effect, satellite
 6   measurements of variations in TOA radiative fluxes show strong co-variation with changing patterns of
 7   SSTs, with a strong dependence on SST changes in regions of deep convective ascent (e.g., in the western
 8   Pacific warm pool) (Loeb et al., 2018b; Fueglistaler, 2019). Cloud and TOA radiation responses to observed
 9   warming patterns in atmospheric models have been found to compare favourably with those observed by
10   satellite (Zhou et al., 2016; Loeb et al., 2020; Section; Figure 7.3). This observational and modelling
11   evidence indicates the potential for a strong pattern effect in nature that will only be negligible if the
12   observed pattern of warming since pre-industrial levels persists to equilibrium – an improbable scenario
13   given that Earth is in a relatively early phase of transient warming and that reaching equilibrium would take
14   multiple millennia (Li et al., 2013a). Moreover, paleoclimate proxies, ESM simulations, and process
15   understanding indicate that strong warming in the eastern equatorial Pacific Ocean (with medium confidence)
16   and Southern Ocean (with high confidence) will emerge on centennial timescales as the response to CO2
17   forcing dominates temperature changes in these regions (Sections;; Chapter 9, Section 9.2.1).
18   However, there is low confidence that these features, which have been largely absent over the historical
19   record, will emerge this century (Sections;; Chapter 9, Section 9.2.1). This leads to high
20   confidence that radiative feedbacks will become less negative as the CO2-forced pattern of surface warming
21   emerges (α’ > 0 W m–2 °C–1), but low confidence that these feedback changes will be realized this century.
22   There is also substantial uncertainty in the magnitude of the net radiative feedback change between the
23   present warming pattern and the projected equilibrium warming pattern in response to CO2 forcing owing to
24   the fact that its quantification currently relies solely on ESM results and is subject to uncertainties in
25   historical SST patterns. Thus, based on the pattern of warming since 1870, α’ is estimated to be in the range
26   0.0 to 1.0 W m–2 °C–1 but with a low confidence in the upper end of this range. A value of α’ = +0.5 ± 0.5
27   W m–2 °C –1 is used to represent this range in Box 7.2 and Section 7.5.2, which respectively assess the
28   implications of changing radiative feedbacks for Earth’s energy imbalance and estimates of ECS based on
29   the instrumental record. The value of α’ is larger if quantified based on the observed pattern of warming
30   since 1980 (Chapter 2, Figure 2.11b) which is more distinct from the equilibrium warming pattern expected
31   under CO2 forcing (similar to CMIP6 projections shown in Figure 7.12a) (Andrews et al., 2018) (high
32   confidence).
35   7.5   Estimates of ECS and TCR
37   Equilibrium climate sensitivity (ECS) and transient climate response (TCR) are metrics of the global surface
38   air temperature (GSAT) response to forcing, as defined in Section 7.1; Box 7.1. ECS is the magnitude of the
39   long-term GSAT increase in response to a doubling of atmospheric CO2 concentration after the planetary
40   energy budget is balanced, though leaving out feedbacks associated with ice sheets; whereas the TCR is the
41   magnitude of GSAT increase at year 70 when CO2 concentration is doubled in a 1% yr–1 increase scenario.
42   Both are idealised quantities, but can be inferred from paleoclimate or observational records or estimated
43   directly using climate simulations, and are strongly correlated with the climate response in realistic future
44   projections (Grose et al., 2018; Chapter 4, Section 4.3.4; Section 7.5.7).
46   TCR is always smaller than ECS because ocean heat uptake acts to reduce the rate of surface warming. Yet,
47   TCR is related with ECS across CMIP5 and CMIP6 models (Grose et al., 2018; Flynn and Mauritsen, 2020)
48   as expected since TCR and ECS are inherently measures of climate response to forcing; both depend on
49   effective radiative forcing (ERF) and the net feedback parameter, α. The relationship between TCR and ECS
50   is, however, non-linear and becomes more so for higher ECS values (Hansen et al., 1985; Knutti et al., 2005;
51   Millar et al., 2015; Flynn and Mauritsen, 2020; Tsutsui, 2020) owing to ocean heat uptake processes and
52   surface temperature pattern effects temporarily reducing the rate of surface warming. When α is small in
53   magnitude, and correspondingly ECS is large (recall that ECS is inversely proportional to α), these
54   temporary effects are increasingly important in reducing the ratio of TCR to ECS.
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 1   Before the AR6, the assessment of ECS relied on either CO2-doubling experiments using global atmospheric
 2   models coupled with mixed-layer ocean or standardized CO2-quadrupling (abrupt4xCO2) experiments using
 3   fully coupled ocean-atmosphere models or Earth system models (ESMs). The TCR has similarly been
 4   diagnosed from ESMs in which the CO2 concentration is increased at 1% yr–1 (1pctCO2, an approximately
 5   linear increase in ERF over time) and is in practice estimated as the average over a 20–year period centred at
 6   the time of atmospheric CO2 doubling, i.e., year 70. In the AR6, the assessments of ECS and TCR are made
 7   based on multiple lines of evidence, with ESMs representing only one of several sources of information. The
 8   constraints on these climate metrics are based on radiative forcing and climate feedbacks assessed from
 9   process understanding (Section 7.5.1), climate change and variability seen within the instrumental record
10   (Section 7.5.2), paleoclimate evidence (Section 7.5.3), emergent constraints (Section 7.5.4), and a synthesis
11   of all lines of evidence (Section 7.5.5). In AR5, these lines of evidence were not explicitly combined in the
12   assessment of climate sensitivity, but as demonstrated by Sherwood et al. (2020) their combination narrows
13   the uncertainty ranges of ECS compared to that assessed in AR5. ECS values found in CMIP6 models, some
14   of which exhibit values higher than 5 °C (Meehl et al., 2020; Zelinka et al., 2020), are discussed in relation
15   to the AR6 assessment in section 7.5.6.
18   7.5.1     Estimates of ECS and TCR based on process understanding
20   This section assesses the estimates of ECS and TCR based on process understanding of the ERF due to a
21   doubling of CO2 concentration and the net climate feedback (Sections 7.3.2 and 7.4.2). This process-based
22   assessment is made in Section and applied to TCR in Section
25    ECS estimated using process-based assessments of the forcing and feedbacks
27   The process-based assessment is based on the global energy budget equation (Box 7.1, Equation 7.1), where
28   the ERF (∆F) is set equal to the effective radiative forcing due to a doubling of CO2 concentration (denoted
29   as ∆𝐹𝐹2×CO2 ) and the climate state reaches a new equilibrium, i.e., Earth’s energy imbalance averages to zero
30   (∆N = 0). ECS is calculated as the ratio between the ERF and the net feedback parameter: ECS =
31   –∆𝐹𝐹2×CO2 /α. Estimates of ∆𝐹𝐹2×CO2 and α are obtained separately based on understanding of the key
32   processes that determine each of these quantities. Specifically, ∆𝐹𝐹2×CO2 is estimated based on instantaneous
33   radiative forcing that can be accurately obtained using line-by-line calculations, to which uncertainty due to
34   adjustments are added (Section 7.3.2). The range of α is derived by aggregating estimates of individual
35   climate feedbacks based not only on ESMs but also on theory, observations, and high-resolution process
36   modelling (Section 7.4.2).
38   The effective radiative forcing of CO2 doubling is assessed to be ∆𝐹𝐹2×CO2 = 3.93 ± 0.47 W m–2 (Section
39, while the net feedback parameter is assessed to be α = –1.16 ± 0.40 W m–2 °C–1 (Section,
40   Table 7.10), where the ranges indicate one standard deviation. These values are slightly different from those
41   directly calculated from ESMs because more information is used to assess them, as explained above.
42   Assuming ∆𝐹𝐹2×CO2 and α each follow an independent normal distribution, the uncertainty range of ECS can
43   be obtained by substituting the respective probability density function into the expression of ECS (red curved
44   bar in Figure 7.16). Since α is in the denominator, the normal distribution leads to a long tail in ECS toward
45   high values, indicating the large effect of uncertainty in α in estimating the likelihood of a high ECS (Roe
46   and Baker, 2007; Knutti and Hegerl, 2008).
48   The wide range of the process-based ECS estimate is not due solely to uncertainty in the estimates of
49   ∆𝐹𝐹2×CO2 and α, but is partly explained by the assumption that ∆𝐹𝐹2×CO2 and α are independent in this
50   approach. In CMIP5 and CMIP6 ensembles, ∆𝐹𝐹2×CO2 and α are negatively correlated when they are
51   calculated using linear regression in abrupt4xCO2 simulations (r2 = 0.34) (Andrews et al., 2012; Webb et al.,
52   2013; Zelinka et al., 2020). The negative correlation leads to compensation between the inter-model spreads
53   of these quantities, thereby reducing the ECS range estimated directly from the models. If the process-based
54   ECS distribution is reconstructed from probability distributions of ∆𝐹𝐹2×CO2 and α assuming that they are
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 1   correlated as in CMIP model ensembles, the range of ECS will be narrower by 14% (pink curved bar in
 2   Figure 7.16). If, however, the covariance between ∆𝐹𝐹2×CO2 and α is not adopted, there is no change in the
 3   mean, but the wide range still applies.
 5   A significant correlation between ∆𝐹𝐹2×CO2 and α also occurs when the two parameters are estimated
 6   separately from AGCM fixed-SST experiments (Section 7.3.1) or fixed CO2 concentration experiments
 7   (Ringer et al., 2014; Chung and Soden, 2018; Section 7.4.1). Hence the relationship is not expected to be an
 8   artefact of calculating them using linear regression in abrupt4xCO2 simulations. A possible physical cause
 9   of the correlation may be a compensation between the cloud adjustment and the cloud feedback over the
10   tropical ocean (Ringer et al., 2014; Chung and Soden, 2018). It has been shown that the change in the
11   hydrological cycle is a controlling factor for the low-cloud adjustment (Dinh and Fueglistaler, 2019) and for
12   the low-cloud feedback (Watanabe et al., 2018), and therefore the responses of these clouds to the direct CO2
13   radiative forcing and to the surface warming may not be independent. However, robust physical mechanisms
14   are not yet established, and furthermore, the process-based assessment of the tropical low-cloud feedback is
15   only indirectly based on ESMs given that physical processes which control the low clouds are not
16   sufficiently well-simulated in models (Section For these reasons, the co-dependency between
17   ∆𝐹𝐹2×CO2 and α is assessed to have low confidence and, therefore, the more conservative assumption that they
18   are independent for the process-based assessment of ECS is retained.
20   In summary, the ECS based on the assessed values of ∆𝐹𝐹2×CO2 and α is assessed to have a median value of
21   3.4°C with a likely range of 2.5–5.1 °C and very likely range of 2.1–7.7 °C. To this assessed range of ECS,
22   the contribution of uncertainty in α is approximately three times as large as the contribution of uncertainty in
23   ∆𝐹𝐹2×CO2 .
28   Figure 7.16: Probability distributions of ERF to CO2 doubling (∆𝑭𝑭𝟐𝟐×𝐂𝐂𝐂𝐂𝐂𝐂 , top) and the net climate feedback (𝛂𝛂,
29                right), derived from process-based assessments in Sections 7.3.2 and 7.4.2. Middle panel shows the
30                joint probability density function calculated on a two-dimensional plane of ∆𝐹𝐹2×CO2 and α (red), on which
31                the 90% range shown by an ellipse is imposed to the background theoretical values of ECS (colour
32                shading). The white dot, thick and thin curves in the ellipse represent the mean, likely and very likely
33                ranges of ECS. An alternative estimation of the ECS range (pink) is calculated by assuming that ∆𝐹𝐹2×CO2
34                and α have a covariance. The assumption about the co-dependence between ∆𝐹𝐹2×CO2 and α does not alter
35                the mean estimate of ECS but affects its uncertainty. Further details on data sources and processing are
36                available in the chapter data table (Table 7.SM.14).
38   [END FIGURE 7.16 HERE]
41   Emulating process-based ECS to TCR
43   ECS estimated using the ERF due to a doubling of CO2 concentration and the net feedback parameter (ECS =
44   –∆𝐹𝐹2×CO2 /α) can be translated into the TCR so that both climate sensitivity metrics provide consistent
45   information about the climate response to forcing. Here a two-layer energy budget emulator is used to
46   transfer the process-based assessment of forcing, feedback, efficacy and heat uptake to TCR (Supplementary
47   Material 7.SM.2.1, Cross-Chapter Box 7.1). The emulator can reproduce the transient surface temperature
48   evolution in ESMs under 1pctCO2 simulations and other climate change scenarios, despite the very low
49   number of degrees of freedom (Held et al., 2010; Geoffroy et al., 2012, 2013a; Palmer et al., 2018). Using
50   this model with parameters given from assessments in the previous sections, TCR is assessed based on the
51   process-based understanding.
53   In the two-layer energy balance emulator, additional parameters are introduced: heat capacities of the upper
54   and deep ocean, heat uptake efficiency (γ), and the so-called efficacy parameter (ε) that represents the
55   dependence of radiative feedbacks and heat uptake on the evolving SST pattern under CO2 forcing alone
56   (Section 7.4.4). In the real world, natural internal variability and aerosol radiative forcing also affect the
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 1   efficacy parameter, but these effects are excluded for the current discussion.
 3   The analytical solution of the energy balance emulator reveals that the global surface temperature change to
 4   abrupt increase of the atmospheric CO2 concentration is expressed by a combination of a fast adjustment of
 5   the surface components of the climate system and a slow response of the deep ocean, with time scales of
 6   several years and several centuries, respectively (grey curves in Figure 7.17). The equilibrium response of
 7   upper ocean temperature, approximating SST and the surface air temperature response, depends, by
 8   definition, only on the radiative forcing and the net feedback parameter. Uncertainty in α dominates
 9   (80–90%) the corresponding uncertainty range for ECS in CMIP5 models (Vial et al., 2013), and also an
10   increase of ECS in CMIP6 models (Section 7.5.5) is attributed by about 60–80% to a change in α (Zelinka et
11   al., 2020). For the range of TCR, the contribution from uncertainty in α is reduced to 50–60% while
12   uncertainty in ∆𝐹𝐹2×CO2 becomes relatively more important (Geoffroy et al., 2012; Lutsko and Popp, 2019).
13   TCR reflects the fast response occurring approximately during the first 20 years in the abrupt4xCO2
14   simulation (Held et al., 2010), but the fast response is not independent of the slow response because there is a
15   nonlinear co-dependence between them (Andrews et al., 2015). The nonlinear relationship between ECS and
16   TCR indicates that the probability of high TCR is not very sensitive to changes in the probability of high
17   ECS (Meehl et al., 2020).
19   Considering an idealized time evolution of ERF (1% increase per year until CO2 doubling and held fixed
20   afterwards, see Figure 7.17a), the TCR defined by the surface temperature response at year 70 is derived by
21   substituting the process-based ECS into the analytical solution of the emulator (Figure 7.17b, see also
22   Supplementary Material 7.SM.2.1). When additional parameters in the emulator are prescribed by using
23   CMIP6 multi-model mean values of those estimates (Smith et al., 2020a), this calculation translates the range
24   of ECS in Section to the range of TCR. The transient temperature response, in reality, varies with
25   different estimates of the ocean heat uptake efficiency (γ) and efficacy (ε). When the emulator was calibrated
26   to the transient responses in CMIP5 models, it shows that uncertainty in heat capacities is negligible and
27   differences in γ and ε explain 10–20% of the inter-model spread of TCR among GCMs (Geoffroy et al.,
28   2012). Specifically, their product, κ = γε, appearing in a simplified form of the solution, i.e., TCR ≅
29   −∆𝐹𝐹2×CO2 /(α − κ), gives a single parameter quantifying the damping effects of heat uptake (Jiménez-de-la-
30   Cuesta and Mauritsen, 2019). This parameter is positive and acts to slow down the temperature response in a
31   similar manner to the ‘pattern effect’ (Sections and The ocean heat uptake in nature is
32   controlled by multiple processes associated with advection and mixing (Exarchou et al., 2014; Kostov et al.,
33   2014; Kuhlbrodt et al., 2015) but is simplified to be represented by a single term of heat exchange between
34   the upper- and deep-ocean in the emulator. Therefore, it is challenging to constrain γ and ε from process-
35   based understanding (Section 7.5.2). Because the estimated values are only weakly correlated across models,
36   the mean value and one standard deviation of κ are calculated as κ = 0.84 ± 0.38 W m–2 °C–1 (one standard
37   deviation) by ignoring their covariance (the mean value is very similar to that used for Chapter 4, Box 4.1,
38   Figure 1) (see Supplementary Material 7.SM.2.1). By incorporating this inter-model spread in κ, the range of
39   TCR is widened by about 10% (blue bar in Figure 7.17b). Yet, the dominant contribution to the uncertainty
40   range of TCR arises from the net feedback parameter α, consistent with analyses of CMIP6 models
41   (Williams et al., 2020), and this assessment remains unchanged from AR5 stating that uncertainty in ocean
42   heat uptake is of secondary importance.
44   In summary, the process-based estimate of TCR is assessed to have the central value of 2.0°C with the likely
45   range from 1.6 to 2.7°C and the very likely range from 1.3 to 3.1°C (high confidence). The upper bound of
46   the assessed range was slightly reduced from AR5 but can be further constrained using multiple lines of
47   evidence (Section 7.5.5).
52   Figure 7.17: (a) Time evolution of the effective radiative forcing (ERF) to the CO2 concentration increased by
53                1% per year until the year 70 (equal to the time of doubling) and kept fixed afterwards (white line).
54                The likely and very likely ranges of ERF indicated by light and dark orange have been assessed in Section
55       (b) Surface temperature response to the CO2 forcing calculated using the emulator with a given

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 1                 value of ECS, considering uncertainty in ΔF2×CO2, α, and 𝜅𝜅 associated with the ocean heat uptake and
 2                 efficacy (white line). The likely and very likely ranges are indicated by cyan and blue. For comparison, the
 3                 temperature response to abrupt doubling of the CO2 concentration is displayed by a grey curve. The
 4                 mean, likely and very likely ranges of ECS and TCR are shown at the right (the values of TCR also
 5                 presented in the panel). Further details on data sources and processing are available in the chapter data
 6                 table (Table 7.SM.14).
 8   [END FIGURE 7.17 HERE]
11   7.5.2     Estimates of ECS and TCR based on the instrumental record
13   This section assesses the estimates of ECS and TCR based on the instrumental record of climate change and
14   variability with an emphasis on new evidence since AR5. Several lines of evidence are assessed including
15   the global energy budget (Section, the use of simple climate models evaluated against the historical
16   temperature record (Section, and internal variability in global temperature and TOA radiation
17   (Section Section provides an overall assessment of TCR and ECS based on these lines of
18   evidence from the instrumental record.
21    Estimates of ECS and TCR based on the global energy budget
23   The GSAT change from 1850–1900 to 2006–2019 is estimated to be 1.03 [0.86 to 1.18] °C (Cross-chapter
24   Box 2.3). Together with estimates of Earth’s energy imbalance (Section 7.2.2) and the global ERF that has
25   driven the observed warming (Section 7.3), the instrumental temperature record enables global energy
26   budget estimates of ECS and TCR. While energy budget estimates use instrumental data, they are not based
27   purely on observations. A conceptual model typically based on the global-mean forcing and response energy
28   budget framework (Box 7.1) is needed to relate ECS and TCR to the estimates of global warming, ERF and
29   Earth’s energy imbalance (Forster, 2016; Knutti et al., 2017). Moreover, ESM simulations partly inform
30   estimates of the historical ERF (Section 7.3) as well as Earth’s energy imbalance in the 1850-1900 climate
31   (the period against which changes are measured) (Forster, 2016; Lewis and Curry, 2018). ESMs are also
32   used to estimate uncertainty due the internal climate variability that may have contributed to observed
33   changes in temperature and energy imbalance (e.g., Palmer and McNeall, 2014; Sherwood et al., 2020).
34   Research since AR5 has shown that global energy budget estimates of ECS may be biased low when they do
35   not take into account how radiative feedbacks depend on the spatial pattern of surface warming (Section
36 or when they do not incorporate improvements in the estimation of global surface temperature trends
37   which take better account of data-sparse regions and are more consistent in their treatment of surface
38   temperature data (Chapter 2, Section 2.3.1). Together with updated estimates of global ERF and Earth’s
39   energy imbalance, these advances since AR5 have helped to reconcile energy budget estimates of ECS with
40   estimates of ECS from other lines of evidence.
42   The traditional global-mean forcing and response energy budget framework (Gregory et al., 2002; Section
43   7.4.1; Box 7.1) relates the difference between the ERF (ΔF) and the radiative response to observed global
44   warming (αΔT) to the Earth’s energy imbalance (ΔN): ΔN = αΔT + ΔF. Given the relationship ECS = –
45   ΔF2×CO2/α, where ΔF2×CO2 is the ERF from CO2 doubling, ECS can be estimated from historical estimates of
46   ΔT, ΔF, ΔN and ΔF2×CO2: ECS = ΔF2×CO2 ΔT/(ΔF – ΔN). Since TCR is defined as the temperature change at
47   the time of CO2 doubling under an idealized 1% yr–1 CO2 increase, it can be inferred from the historical
48   record as: TCR = ΔF2×CO2 ΔT/ΔF, under the assumption that radiative forcing increases quickly compared to
49   the adjustment timescales of the deep ocean, but slowly enough and over a sufficiently long time that the
50   upper ocean is adjusted, so that ΔT and ΔN increases approximately in proportion to ΔF. Because ΔN is
51   positive, TCR is always smaller than ECS, reflecting weaker transient warming than equilibrium warming.
52   TCR is better constrained than ECS owing to the fact that the denominator of TCR, without the quantity ΔN,
53   is more certain and further from zero than is the denominator of ECS. The upper bounds of both TCR and
54   ECS estimated from historical warming are inherently less certain than their lower bounds because ΔF is
55   uncertain and in the denominator.

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 2   The traditional energy budget framework lacks a representation of how radiative feedbacks depend on the
 3   spatial pattern of warming. Thus, studies employing this framework (Otto et al., 2013; Lewis and Curry,
 4   2015, 2018; Forster, 2016) implicitly assume that the net radiative feedback has a constant magnitude,
 5   producing an estimate of the effective ECS (defined as the value of ECS that would occur if α does not
 6   change from its current value) rather than of the true ECS. As summarized in Section, there are now
 7   multiple lines of evidence providing high confidence that the net radiative feedback will become less
 8   negative as the warming pattern evolves in the future (the pattern effect). This arises because historical
 9   warming has been relatively larger in key negative feedback regions (e.g., western tropical Pacific Ocean)
10   and relatively smaller in key positive feedback regions (e.g., eastern tropical Pacific Ocean and Southern
11   Ocean) than is projected in the near-equilibrium response to CO2 forcing (Held et al., 2010; Proistosescu and
12   Huybers, 2017; Dong et al., 2019; Section, implying that the true ECS will be larger than the
13   effective ECS inferred from historical warming. This section first assesses energy budget constraints on TCR
14   and the effective ECS based on updated estimates of historical warming, ERF, and Earth’s energy imbalance.
15   It then assesses what these energy budget constraints imply for values of ECS once the pattern effect is
16   accounted for.
18   Energy budget estimates of TCR and ECS have evolved in the literature over recent decades. Prior to AR4,
19   the global energy budget provided relatively weak constraints, primarily due to large uncertainty in the
20   tropospheric aerosol forcing, giving ranges of the effective ECS that typically included values above 10°C
21   (Forster, 2016; Knutti et al., 2017). Revised estimates of aerosol forcing together with a larger greenhouse-
22   gas forcing by the time of AR5 led to an estimate of ΔF that was more positive and with reduced uncertainty
23   relative to AR4. Using energy budget estimates and radiative forcing estimates updated to 2009, Otto et al.
24   (2013) estimated that TCR was 1.3 [0.9 to 2.0] °C, and that the effective ECS was 2.0 [1.2 to 3.9] °C. This
25   AR5-based energy budget estimate of ECS was lower than estimates based on other lines of evidence,
26   leading AR5 to expand the assessed likely range of ECS to include lower values relative to AR4. Studies
27   since AR5 using similar global energy budget methods have produced similar or slightly narrower ranges for
28   TCR and effective ECS (Forster, 2016; Knutti et al., 2017).
30   Energy budget estimates of TCR and ECS assessed here are based on improved observations and
31   understanding of global surface temperature trends extended to the year 2020 (Chapter 2, Section 2.3.1),
32   revised estimates of Earth’s energy imbalance (Section 7.2), and revised estimates of ERF (Section 7.3).
33   Accurate, in situ-based estimates of Earth’s energy imbalance can be made from around 2006 based on near-
34   global ocean temperature observations from the ARGO array of autonomous profiling floats (Chapter 2
35   Section 2.3, Section 7.2). Over the period 2006 to 2018 the Earth’s energy imbalance is estimated to be 0.79
36   ± 0.27 W m–2 (Section 7.2) and it is assumed that this value is also representative for the period 2006 to
37   2019. Anomalies are taken with respect to the baseline period 1850-1900, although other baselines could be
38   chosen to avoid major volcanic activity (Otto et al., 2013; Lewis and Curry, 2018). Several lines of evidence,
39   including ESM simulations (Lewis and Curry, 2015), energy balance modelling (Armour, 2017), inferred
40   ocean warming given observed SSTs using ocean models (Gebbie and Huybers, 2019; Zanna et al., 2019),
41   and ocean warming reconstructed from noble gas thermometry (Baggenstos et al., 2019) suggest a 1850-
42   1900 Earth energy imbalance of 0.2 ± 0.2 W m–2. Combined with estimates of internal variability in Earth’s
43   energy imbalance, calculated using periods of equivalent lengths of years as used in unforced ESM
44   simulations (Palmer and McNeall, 2014; Sherwood et al., 2020b), the anomalous energy imbalance between
45   1850–1900 and 2006–2019 is estimated to be ΔN = 0.59 ± 0.35 W m-2. GSAT change between 1850–1900
46   and 2006–2019 is estimated to be ΔT = 1.03°C ± 0.20 °C (Chapter 2, Cross-Chapter Box 2.3; Box 7.2) after
47   accounting for internal temperature variability derived from unforced ESM simulations (Sherwood et al.,
48   2020b). The ERF change between 1850–1900 and 2006–2019 is estimated to be ΔF = 2.20 [1.53 to 2.91]
49   W m–2 (Section 7.3.5) and the ERF for a doubling of CO2 is estimated to be ΔF2×CO2 = 3.93 ± 0.47 W m–2
50   (Section 7.3.2). Employing these values within the traditional global energy balance framework described
51   above (following the methods of Otto et al. (2013) and accounting for correlated uncertainties between ΔF
52   and ΔF2×CO2) produces a TCR of 1.9 [1.3 to 2.7]°C and an effective ECS of 2.5 [1.6–4.8] °C. These TCR and
53   effective ECS values are higher than those in the recent literature (Otto et al., 2013; Lewis and Curry, 2015,
54   2018) but are comparable to those of Sherwood et al. (2020) who also used updated estimates of observed
55   warming, Earth’s energy imbalance, and ERF.
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 2   The trend estimation method applied to global surface temperature affects derived values of ECS and TCR
 3   from the historical record. In this Report, the effective ECS is inferred from estimates that use global
 4   coverage of GSAT to estimate the surface temperature trends. The GSAT trend is assessed to have the same
 5   best estimate as the observed global mean surface temperature (GMST), although the GSAT trend is
 6   assessed to have larger uncertainty (see Cross-Chapter Box 2.3). Many previous studies have relied on
 7   HadCRUT4 GMST estimates that used the blended observations and did not interpolate over regions of
 8   incomplete observational coverage such as the Arctic. As a result, the ECS and TCR derived from these
 9   studies has smaller ECS and TCR values than those derived from model-inferred estimates (Richardson et
10   al., 2016, 2018a). The energy budget studies assessing ECS in AR5 employed HadCRUT4 or similar
11   measures of GMST trends. As other lines of evidence in that report used GSAT trends, this could partly
12   explain why AR5-based energy budget estimates of ECS were lower than those estimated from other lines of
13   evidence, adding to the overall disparity in Collins et al. (2013a). In this report, GSAT is chosen as the
14   standard measure of global surface temperature to aid comparison with previous model and process-based
15   estimates of ECS, TCR and climate feedbacks (see Cross-Chapter Box 2.3).
17   The traditional energy budget framework has been evaluated within ESM simulations by comparing the
18   effective ECS estimated under historical forcing with the ECS estimated using regression methods (Box 7.1)
19   under abrupt4xCO2 (Andrews et al., 2019; Winton et al., 2020). For one CMIP6 model (GFDL-CM4.0), the
20   value of effective ECS derived from historical energy budget constraints is 1.8°C while ECS is estimated to
21   be 5.0°C (Winton et al., 2020). For another model (HadGEM3-GC3.1-LL) the effective ECS derived from
22   historical energy budget constraints is 4.1°C (average of four ensemble members) while ECS is estimated to
23   be 5.5°C (Andrews et al., 2019). These modelling results suggest that the effective ECS under historical
24   forcing could be lower than the true ECS owing to differences in radiative feedbacks induced by the distinct
25   patterns of historical and equilibrium warming (Section Using GFDL-CM4, Winton et al. (2020)
26   also find that the value of TCR estimated from energy budget constraints within a historical simulation
27   (1.3°C) is substantially lower than the true value of TCR (2.1°C) diagnosed within a 1pctCO2 simulation
28   owing to a combination of the pattern effect and differences in the efficiency of ocean heat uptake between
29   historical and 1pctCO2 forcing. This section next considers how the true ECS can be estimated from the
30   historical energy budget by accounting for the pattern effect. However, owing to limited evidence this
31   section does not attempt to account for these effects in estimates of TCR.
33   Research since AR5 has introduced extensions to the traditional energy budget framework that account for
34   the feedback dependence on temperature patterns by allowing for multiple radiative feedbacks operating on
35   different timescales (Armour et al., 2013; Geoffroy et al., 2013a; Armour, 2017; Proistosescu and Huybers,
36   2017; Goodwin, 2018; Rohrschneider et al., 2019), by allowing feedbacks to vary with the spatial pattern or
37   magnitude of ocean heat uptake (Winton et al., 2010; Rose et al., 2014; Rugenstein et al., 2016a), or by
38   allowing feedbacks to vary with the type of radiative forcing agent (Kummer and Dessler, 2014; Shindell,
39   2014; Marvel et al., 2016; Winton et al., 2020). A direct way to account for the pattern effect is to use the
40   relationship ECS = ΔF2×CO2/(–α + α’), where α = (ΔN – ΔF)/ΔT is the effective feedback parameter (Box 7.1)
41   estimated from historical global energy budget changes and α’ represents the change in the feedback
42   parameter between the historical period and the equilibrium response to CO2 forcing, which can be estimated
43   using ESMs (Armour, 2017; Andrews et al., 2018, 2019; Lewis and Curry, 2018; Dong et al., 2020; Winton
44   et al., 2020; Section
46   The net radiative feedback change between the historical warming pattern and the projected equilibrium
47   warming pattern in response to CO2 forcing (α’) is estimated to be in the range 0.0 to 1.0 W m–2 °C–1 (Figure
48   7.15). Using the value α’ = +0.5 ± 0.5 W m–2 °C –1 to represent this range illustrates the effect of changing
49   radiative feedbacks on estimates of ECS. While the effective ECS inferred from historical warming is 2.5
50   [1.6–4.8] °C , ECS = ΔF2×CO2/(–α + α’) is 3.5 [1.7–13.8] °C. For comparison, values of α’ derived from the
51   response to historical and idealized CO2 forcing within coupled climate models (Armour, 2017; Lewis and
52   Curry, 2018; Andrews et al., 2019; Dong et al., 2020; Winton et al., 2020) can be approximated as α’ = +0.1
53   ± 0.3 W m–2 °C–1 (Section, corresponding to a value of ECS of 2.7 [1.7–5.9] °C. In both cases, the
54   low end of the ECS range is similar to that of the effective ECS inferred using the traditional energy balance
55   model framework that assumes α’ = 0, reflecting a weak dependence on the value of α’ when ECS is small
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 1   (Armour, 2017; Andrews et al., 2018); the low end of the ECS range is robust even in the hypothetical case
 2   that α’ is slightly negative. However, the high end of the ECS range is substantially larger than that of the
 3   effective ECS and strongly dependent on the value of α’.
 5   The values of ECS obtained from the techniques outlined above are all higher than those estimated from both
 6   AR5 and recently published estimates (Collins et al., 2013a; Otto et al., 2013; Lewis and Curry, 2015;
 7   Forster, 2016; Lewis and Curry, 2018). Four revisions made in this Report are responsible for this increase:
 8   (1) An upwards revision of historic global surface temperature trends from newly published trend estimates
 9   (Chapter 2, Section 2.3.1); (2) An 8% increase in the ERF for ΔF2×CO2 (Section 7.3.2); (3) A more negative
10   central estimate of aerosol ERF, which acts to reduce estimates of historical ERF trends; and (4) Accounting
11   for the pattern effect in ECS estimates. Values of ECS provided here are similar to those based on the
12   historical energy budget found in Sherwood et al. (2020), with small differences owing to methodological
13   differences and the use of different estimates of observed warming, Earth’s energy imbalance, and ERF.
15   Overall, there is high confidence that the true ECS is higher than the effective ECS as inferred from the
16   historical global energy budget, but there is substantial uncertainty in how much higher because of limited
17   evidence regarding how radiative feedbacks may change in the future. While several lines of evidence
18   indicate that α’ > 0, the quantitative accuracy of feedback changes is not known at this time (Section
19   Global energy budget constraints thus provide high confidence in the lower bound of ECS which is not
20   sensitive to the value of α’: ECS is extremely unlikely to be less than 1.6°C. Estimates of α’ that are informed
21   by idealized CO2 forcing simulations of coupled ESMs (Armour, 2017; Lewis and Curry, 2018; Andrews et
22   al., 2019; Dong et al., 2020; Winton et al., 2020) indicate a median value of ECS of around 2.7°C while
23   estimates of α’ that are informed by observed historical sea surface temperature patterns (Andrews et al.,
24   2018) indicate a median value of ECS of around 3.5°C. Owing to large uncertainties in future feedback
25   changes, the historical energy budget currently provides little information about the upper end of the ECS
26   range.
29   Estimates of ECS and TCR based on climate model emulators
31   Energy budget emulators are far less complex than comprehensive ESMs (see Chapter 1, Section 1.5.3 and
32   Cross-Chapter Box 7.1). For example, an emulator could represent the atmosphere, ocean, and land using a
33   small number of connected boxes (e.g., Goodwin, 2016), or it could represent the global mean climate using
34   two connected ocean layers (e.g., Cross-Chapter Box 7.1, Supplementary Material 7.SM.2). The numerical
35   efficiency of emulators means that they can be empirically constrained by observations: a large number of
36   possible parameter values (e.g., feedback parameter, aerosol radiative forcing, and ocean diffusivity) are
37   randomly drawn from prior distributions; forward integrations of the model are performed with these
38   parameters and weighted against observations of surface or ocean warming, producing posterior estimates of
39   quantities of interest such as TCR, ECS and aerosol forcing (see Section 7.3). Owing to their reduced
40   complexity, emulators lack full representations of the spatial patterns of sea surface temperature and
41   radiative responses to changes in those patterns (discussed in Section and many represent the net
42   feedback parameter using a constant value. The ranges of ECS reported by studies using emulators are thus
43   interpreted here as representative of the effective ECS over the historical record rather than of the true ECS.
45   Improved estimates of ocean heat uptake over the past two decades (Section 7.2) have diminished the role of
46   ocean diffusivity in driving uncertainty in ECS estimates, leaving the main trade-off between posterior
47   ranges in ECS and aerosol radiative forcing (Forest, 2002; Knutti et al., 2002; Frame et al., 2005). AR5
48   (Bindoff et al., 2013) assessed a variety of estimates of ECS based on emulators and found that they were
49   sensitive to the choice of prior parameter distributions and temperature datasets used, particularly for the
50   upper end of the ECS range, though priors can be chosen to minimize the effect on results (e.g., Lewis,
51   2013). Emulators generally produced estimates of effective ECS between 1°C and 5°C and ranges of TCR
52   between 0.9°C and 2.6°C. Padilla et al. (2011) use a simple global-average emulator with two timescales
53   (see Supplementary Material 7.SM.2 and Section to estimate a TCR of 1.6 [1.3 to 2.6] °C. Using the
54   same model, Schwartz (2012) finds TCR in the range 0.9–1.9°C while Schwartz (2018) finds that an
55   effective ECS of 1.7°C provides the best fit to the historical global surface temperature record while also
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 1   finding a median aerosol forcing that is smaller than that assessed in Section 7.3. Using an eight-box
 2   representation of the atmosphere–ocean–terrestrial system constrained by historical warming, Goodwin
 3   (2016) found an effective ECS of 2.4 [1.4 to 4.4] °C while Goodwin (2018) found effective ECS to be in the
 4   range 2–4.3°C when using a prior for ECS based on paleoclimate constraints.
 6   Using an emulator comprised of northern and southern hemispheres and an upwelling-diffusive ocean
 7   (Aldrin et al., 2012), with surface temperature and ocean heat content datasets updated to 2014, Skeie et al.
 8   (2018) estimate a TCR of 1.4 [0.9 to 2.0] °C and a median effective ECS of 1.9 [1.2 to 3.1] °C. Using a
 9   similar emulator comprised of land and ocean regions and an upwelling-diffusive ocean, with global surface
10   temperature and ocean heat content datasets through 2011, Johansson et al. (2015) find an effective ECS of
11   2.5 [2.0 to 3.2] °C. The estimate is found to be sensitive to the choice of dataset endpoint and the
12   representation of internal variability meant to capture the El Niño–Southern Oscillation and Pacific Decadal
13   Variability. Differences between these two studies arise, in part, from their different global surface
14   temperature and ocean heat content datasets, different radiative forcing uncertainty ranges, different priors
15   for model parameters, and different representations of internal variability. This leads to different estimates of
16   effective ECS, with the median estimate of Skeie et al. (2018) lying below the 5% to 95% range of effective
17   ECS from Johansson et al. (2015). Moreover, while the Skeie et al. (2018) emulator has a constant value of
18   the net feedback parameter, the Johansson et al. (2015) emulator allows distinct radiative feedbacks for land
19   and ocean, contributing to the different results.
21   The median estimates of TCR and effective ECS inferred from emulator studies generally lie within the 5%
22   to 95% ranges of the those inferred from historical global energy budget constraints (1.3 to 2.7°C for TCR
23   and 1.6 to 4.8°C for effective ECS). Their estimates would be consistent with still higher values of ECS
24   when accounting for changes in radiative feedbacks as the spatial pattern of global warming evolves in the
25   future (Section Cross-Chapter Box 7.1 and references therein show that four very different
26   physically-based emulators can be calibrated to match the assessed ranges of historical GSAT change, ERF,
27   ECS and TCR from across the report. Therefore, the fact that the emulator effective ECS values estimated
28   from previous studies tend to lie at the lower end of the range inferred from historical global energy budget
29   constraints may reflect that the energy budget constraints in Section use updated estimates of Earth’s
30   energy imbalance, GSAT trends and ERF, rather than any methodological differences between the lines of
31   evidence. The ‘emergent constraints’ on ECS based on observations of climate variability used in
32   conjunction with comprehensive ESMs are assessed in Section
35   Estimates of ECS based on variability in Earth’s top-of-atmosphere radiation budget
37   While continuous satellite measurements of TOA radiative fluxes (Figure 7.3) do not have sufficient
38   accuracy to determine the absolute magnitude of Earth’s energy imbalance (Section 7.2.1), they provide
39   accurate estimates of its variations and trends since the year 2002 that agree well with estimates based on
40   observed changes in global ocean heat content (Loeb et al., 2012; Johnson et al., 2016; Palmer, 2017). When
41   combined with global surface temperature observations and simple models of global energy balance, satellite
42   measurements of TOA radiation afford estimates of the net feedback parameter associated with recent
43   climate variability (Tsushima and Manabe, 2013; Donohoe et al., 2014; Dessler and Forster, 2018). These
44   feedback estimates, derived from the regression of TOA radiation on surface temperature variability, imply
45   values of ECS that are broadly consistent with those from other lines of evidence (Forster, 2016; Knutti et
46   al., 2017). A history of regression-based feedbacks and their uncertainties is summarized in (Bindoff et al.,
47   2013; Forster, 2016; Knutti et al., 2017).
49   Research since AR5 has noted that regression-based feedback estimates depend on whether annual- or
50   monthly-mean data are used and on the choice of lag employed in the regression, complicating their
51   interpretation (Forster, 2016). The observed lead-lag relationship between global TOA radiation and global
52   surface temperature, and its dependence on sampling period, is well replicated within unforced simulations
53   of ESMs (Dessler, 2011; Proistosescu et al., 2018). These features arise because the regression between
54   global TOA radiation and global surface temperature reflects a blend of different radiative feedback
55   processes associated with several distinct modes of variability acting on different time scales (Annex IV),
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 1   such as monthly atmospheric variability and inter-annual El Niño–Southern Oscillation (ENSO) variability
 2   (Lutsko and Takahashi, 2018; Proistosescu et al., 2018). Regression-based feedbacks thus provide estimates
 3   of the radiative feedbacks that are associated with internal climate variability (e.g., Brown et al., 2014), and
 4   do not provide a direct estimate of ECS (high confidence). Moreover, variations in global surface
 5   temperature that do not directly affect TOA radiation may lead to a positive bias in regression-based
 6   feedback, although this bias appears to be small, particularly when annual-mean data are used (Murphy and
 7   Forster, 2010; Spencer and Braswell, 2010, 2011; Proistosescu et al., 2018). When tested within ESMs,
 8   regression-based feedbacks have been found to be only weakly correlated with values of ECS (Chung et al.,
 9   2010), although cloudy-sky TOA radiation fluxes have been found to be moderately correlated with ECS at
10   ENSO timescales within CMIP5 models (Lutsko and Takahashi, 2018).
12   Finding such correlations within models requires simulations that span multiple centuries, suggesting that the
13   satellite record may not be of sufficient length to produce robust feedback estimates. However, correlations
14   between regression-based feedbacks and long-term feedbacks have been found to be higher when focused on
15   specific processes or regions, such as for cloud or the water vapour feedback (Dessler, 2013; Zhou et al.,
16   2015; Section 7.4.2). Assessing the global radiative feedback in terms of the more stable relationship
17   between tropospheric temperature and TOA radiation offers another potential avenue for constraining ECS.
18   The ‘emergent constraints’ on ECS based on variability in the TOA energy budget are assessed in Section
22   Estimates of ECS based on the climate response to volcanic eruptions
24   A number of studies consider the observed climate response to volcanic eruptions over the 20th century
25   (Knutti et al., 2017; Chapter 3 Section 3.3.1, Cross-Chapter Box 4.1). However, the direct constraint on ECS
26   is weak, particularly at the high end, because the temperature response to short-term forcing depends only
27   weakly on radiative feedbacks and because it can take decades of a sustained forcing before the magnitude of
28   temperature changes reflects differences in ECS across models (Geoffroy et al., 2013b; Merlis et al., 2014).
29   It is also a challenge to separate the response to volcanic eruptions from internal climate variability in the
30   years that follow them (Wigley et al., 2005). Based on ESM simulations, radiative feedbacks governing the
31   global surface temperature response to volcanic eruptions can be substantially different than those governing
32   long-term global warming (Merlis et al., 2014; Marvel et al., 2016; Ceppi and Gregory, 2019). Estimates
33   based on the response to volcanic eruptions agree with other lines of evidence (Knutti et al., 2017), but they
34   do not constitute a direct estimate of ECS (high confidence). The ‘emergent constraints’ on ECS based on
35   climate variability, including volcanic eruptions, are summarized in Section
38   Assessment of ECS and TCR based on the instrumental record
40   Evidence from the instrumental temperature record, including estimates using global energy budget changes
41   (Section, climate emulators (Section, variability in the TOA radiation budget (Section
42, and the climate response to volcanic eruptions (Section produce median ECS estimates that
43   range between 2.5°C and 3.5°C, but a best estimate value cannot be given owing to a strong dependence on
44   assumptions about how radiative feedbacks will change in the future. However, there is robust evidence and
45   high agreement across the lines of evidence that ECS is extremely likely greater than 1.6°C (high
46   confidence). There is robust evidence and medium agreement across the lines of evidence that ECS is very
47   likely greater than 1.8°C and likely greater than 2.2°C (high confidence). These ranges of ECS correspond to
48   estimates based on historical global energy budget constraints (Section under the assumption of no
49   feedback dependence on evolving SST patterns (i.e., α’ = 0) and thus represent an underestimate of the true
50   ECS ranges that can be inferred from this line of evidence (high confidence). Historical global energy budget
51   changes do not provide constraints on the upper bound of ECS, while the studies assessed in Section
52   based on climate variability provide low confidence in its value owing to limited evidence.
54   Global energy budget constraints indicate a central estimate (median) TCR value of 1.9°C and that TCR is
55   likely in the range 1.5°C to 2.3°C and very likely in the range 1.3°C to 2.7°C (high confidence). Studies that
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 1   constrain TCR based on the instrumental temperature record used in conjunction with ESM simulations are
 2   summarized in Section
 5   7.5.3     Estimates of ECS based on paleoclimate data
 7   Estimates of ECS based on paleoclimate data are complementary to, and largely independent from, estimates
 8   based on process-based studies (Section 7.5.1) and the instrumental record (Section 7.5.2). The strengths of
 9   using paleoclimate data to estimate ECS include: (1) the estimates are based on observations of a real-world
10   Earth system response to a forcing, in contrast to using estimates from process-based modelling studies or
11   directly from models; (2) the forcings are often relatively large (similar in magnitude to a CO2 doubling or
12   more), in contrast to data from the instrumental record; (3) the forcing often changes relatively slowly so the
13   system is close to equilibrium; as such, all individual feedback parameters, αx, are included, and
14   complications associated with accounting for ocean heat uptake are reduced or eliminated, in contrast to the
15   instrumental record. However, there can be relatively large uncertainties on estimates of both the paleo
16   forcing and paleo global surface temperature response, and care must be taken to account for long-term
17   feedbacks associated with ice sheets (Section, which often play an important role in the paleoclimate
18   response to forcing, but which are not included in the definition of ECS. Furthermore, the state-dependence
19   of feedbacks (Section 7.4.3) means that climate sensitivity during Earth’s past may not be the same as it is
20   today, which should be accounted for when interpreting paleoclimate estimates of ECS.
22   AR5 stated that data and modelling of the Last Glacial Maximum (LGM, Cross-Chapter Box 2.1) indicated
23   that it was very unlikely that ECS lay outside the range 1–6°C (Masson-Delmotte et al., 2013). Furthermore,
24   AR5 reported that climate records of the last 65 million years indicated an ECS 95% confidence interval of
25   1.1–7.0°C.
27   Compared with AR5, there are now improved constraints on estimates of ECS from paleoclimate evidence.
28   The strengthened understanding and improved lines of evidence come in part from the use of high-resolution
29   paleoclimate data across multiple glacial-interglacial cycles, taking into account state-dependence (von der
30   Heydt et al., 2014; Köhler et al., 2015, 2017, 2018; Friedrich et al., 2016; Snyder, 2019; Stap et al., 2019;
31   Section 7.4.3) and better constrained pre-ice core estimates of atmospheric CO2 concentrations (Martínez-
32   Botí et al., 2015; Anagnostou et al., 2016, 2020; de la Vega et al., 2020) and surface temperature (Hollis et
33   al., 2019; Inglis et al., 2020; McClymont et al., 2020).
35   Overall, the paleoclimate lines of evidence regarding climate sensitivity can be broadly categorised into two
36   types: estimates of radiative forcing and temperature response from paleo proxy measurements, and
37   emergent constraints on paleoclimate model simulations. This section focuses on the first type only; the
38   second type (emergent constraints) are discussed in Section 7.5.4.
40   In order to provide estimates of ECS, evidence from the paleoclimate record can be used to estimate forcing
41   (ΔF) and global surface temperature response (ΔT) in Equation 7.1, Box 7.1, under the assumption that the
42   system is in equilibrium (i.e. ΔN=0). However, there are complicating factors when using the paleoclimate
43   record in this way, and these challenges and uncertainties are somewhat specific to the time period being
44   considered.
47    Estimates of ECS from the Last Glacial Maximum
49   The LGM (Cross-Chapter Box 2.1) has been used to provide estimates of ECS (Sherwood et al., 2020b;
50   Tierney et al., 2020b) (see Table 7.11 for estimates since AR5). The major forcings and feedback processes
51   that led to the cold climate at that time (e.g., CO2, non-CO2 greenhouse gases, and ice sheets) are relatively
52   well-known (Chapter 5, Section 5.1), orbital forcing relative to pre-industrial was negligible, and there are
53   relatively high spatial resolution and well-dated paleoclimate temperature data available for this time period
54   (Chapter 2, Section 2.3.1). Uncertainties in deriving global surface temperature from the LGM proxy data
55   arise partly from uncertainties in the calibration from the paleoclimate data to local annual mean surface
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 1   temperature, and partly from uncertainties in the conversion of the local temperatures to an annual mean
 2   global surface temperature. Overall, the global mean LGM cooling relative to pre-industrial is assessed to be
 3   very likely from 5–7°C (Chapter 2, Section 2.3.1). The LGM climate is often assumed to be in full
 4   equilibrium with the forcing, such that ΔN in Equation 7.1, Box 7.1, is zero. A calculation of sensitivity
 5   using solely CO2 forcing, and assuming that the LGM ice sheets were in equilibrium with that forcing, would
 6   give an Earth System Sensitivity (ESS) rather than an ECS (see Box 7.1). In order to calculate an ECS,
 7   which is defined here to include all feedback processes except ice sheets, the approach of Rohling et al.
 8   (2012) can be used. This approach introduces an additional forcing term in Equation 7.1, Box 7.1, that
 9   quantifies the resulting forcing associated with the ice sheet feedback (primarily an estimate of the radiative
10   forcing associated with the change in surface albedo). However, differences between studies as to which
11   processes are considered as forcings (for example, some studies also include vegetation and/or aerosols, such
12   as dust, as forcings), means that published estimates are not always directly comparable. Additional
13   uncertainty arises from the magnitude of the ice sheet forcing itself (Stap et al., 2019; Zhu and Poulsen,
14   2021), which is often estimated using ESMs. Furthermore, the ECS at the LGM may differ from that of
15   today due to state-dependence (see Section 7.4.3). Here, only studies that report values of ECS that have
16   accounted for the long-term feedbacks associated with ice sheets, and therefore most closely estimate ECS as
17   defined in this chapter, are assessed here (see Table 7.11).
20   Estimates of ECS from glacial-interglacial cycles
22   Since AR5, several studies have extended the Rohling et al. (2012) approach (described above for the LGM)
23   to the glacial-interglacial cycles of the last ~1 to 2 million years (von der Heydt et al., 2014; Köhler et al.,
24   2015; Friedrich et al., 2016; Royer, 2016; Köhler et al., 2017, 2018; Snyder, 2019; Stap et al., 2019;
25   Friedrich and Timmermann, 2020; Table 7.11). Compared to the LGM, uncertainties in the derived ECS
26   from these periods are in general greater, due to greater uncertainty in global surface temperature (due to
27   fewer individual sites with proxy temperature records), ice sheet forcing (due to a lack of detailed ice sheet
28   reconstructions), and CO2 forcing (for those studies that include the pre-ice core period, where CO2
29   reconstructions are substantially more uncertain). Furthermore, accounting for varying orbital forcing in the
30   traditional global-mean forcing and response energy budget framework (Box 7.1) is challenging (Schmidt et
31   al., 2017b), due to seasonal and latitudinal components of the forcing that, despite a close-to-zero orbital
32   forcing in the global annual mean, can directly result in responses in annual mean global surface temperature
33   (Liu et al., 2014), ice volume (Abe-Ouchi et al., 2013), and feedback processes such as those associated with
34   methane (Singarayer et al., 2011). In addition, for time periods in which the forcing relative to the modern
35   era is small (interglacials), the inferred ECS has relatively large uncertainties because the forcing and
36   temperature response (ΔF and ΔT in Equation 7.1 in Box 7.1) are both close to zero.
39   Estimates of ECS from warm periods of the pre-Quaternary
41   In the pre-Quaternary (prior to about 2.5 million years ago), the forcings and response are generally of the
42   same sign and similar magnitude as future projections of climate change (Burke et al., 2018; Tierney et al.,
43   2020a). Similar uncertainties as for the LGM apply, but in this case a major uncertainty relates to the forcing,
44   because prior to the ice core record there are only indirect estimates of CO2 concentration. However,
45   advances in pre-ice-core CO2 reconstruction (e.g., Foster and Rae, 2016; Super et al., 2018; Witkowski et al.,
46   2018) mean that the estimates of pre-Quaternary CO2 have less uncertainty than at the time of AR5, and
47   these time periods can now contribute to an assessment of climate sensitivity (see Table 7.11). The mid-
48   Pliocene warm period (MPWP; Cross-Chapter Box 2.1; Cross-Chapter Box 2.4) has been targeted for
49   constraints on ECS (Martínez-Botí et al., 2015; Sherwood et al., 2020b), due to the fact that CO2
50   concentrations were relatively high at this time (350–425 ppm) and because the MPWP is sufficiently recent
51   that topography and continental configuration are similar to modern-day. As such, a comparison of the
52   MPWP with the pre-industrial climate provides probably the closest natural geological analogue for the
53   modern day that is useful for assessing constraints on ECS, despite the effects of different geographies not
54   being negligible (global surface temperature patterns; ocean circulation). Furthermore, the global surface
55   temperature of the MPWP was such that non-linearities in feedbacks (Section 7.4.3) were relatively modest.
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 1   Within the MPWP, the KM5c interglacial has been identified as a particularly useful time period for
 2   assessing ECS (Haywood et al., 2013, 2016b) because Earth’s orbit during that time was very similar to that
 3   of the modern-day.
 5   Further back in time, in the early Eocene (Cross-Chapter Box 2.1), uncertainties in forcing and temperature
 6   change become larger, but the signals are generally larger too (Anagnostou et al., 2016, 2020; Shaffer et al.,
 7   2016; Inglis et al., 2020). Caution must be applied when estimating ECS from these time periods, due to
 8   differing continental position and topography/bathymetry (Farnsworth et al., 2019), and due to temperature-
 9   dependence of feedbacks (Section 7.4.3). On even longer timescales of the last 500 million years (Royer,
10   2016) the temperature and CO2 measurements are generally asynchronous, presenting challenges in using
11   this information for assessments of ECS.
14   Synthesis of ECS based on paleo radiative forcing and temperature
16   The lines of evidence directly constraining ECS from paleoclimates are summarised in Table 7.11. Although
17   some of the estimates in Table 7.11 are not independent because they use similar proxy records to each other
18   (e.g., von der Heydt et al., 2014; Köhler et al., 2015, 2017; Stap et al., 2019), there are still multiple
19   independent lines of paleoclimate evidence regarding ECS, from differing past time periods (LGM
20   (Sherwood et al., 2020b; Tierney et al., 2020b); glacial-interglacial (Royer, 2016; Köhler et al., 2017;
21   Snyder, 2019; Friedrich and Timmermann, 2020), Pliocene (Martínez-Botí et al., 2015; Sherwood et al.,
22   2020b) and the Eocene (Anagnostou et al., 2016, 2020; Shaffer et al., 2016; Inglis et al., 2020), with
23   differing proxies for estimating forcing (e.g., CO2 from ice cores or boron isotopes) and response (e.g.,
24   global surface temperature from δ18O, Mg/Ca or Antarctic δD). Furthermore, although different studies have
25   uncertainty estimates that account for differing sources of uncertainty, some studies (Snyder, 2019; Inglis et
26   al., 2020; Sherwood et al., 2020b; Tierney et al., 2020b) do consider many of the uncertainties discussed in
27   Sections All the studies based on glacial-interglacial cycles account for some aspects of the
28   state-dependence of climate sensitivity (Section 7.4.3) by considering only the warm phases of the
29   Pleistocene, although what constitutes a warm phase is defined differently across the studies.
32   [START TABLE 7.11 HERE]
34   Table 7.11: Estimates of ECS derived from paleoclimates; from AR5 (above double lines) and from post-AR5 studies
35               (below double lines). Many studies provide an estimate of ECS that includes only CO2 and the ice sheet
36               feedback as forcings, providing an estimate of S[CO2, LI] using the notation of Rohling et al. (2012), which
37               is equivalent to our definition of ECS (Box 7.1). However, some studies provide estimates of other types
38               of sensitivity (column 4). Different studies (column 1) focus on different time periods (column 2) and
39               use a variety of different paleoclimate proxies and models (column 3) to give a best estimate (column 5)
40               and/or a range (column 5). The published ranges given account for varying sources of uncertainty
41               (column 6). See Cross-Chapter Box 2.1 for definition of time periods. All temperature values in column
42               (5) are shown to a precision of 1 decimal place.
      (1) Study       (2) Time period          (3) Proxies/models        (4) Climate       (5) Published     (6) Range
                                               used for CO2,             sensitivity       best estimate     accounts for:
                                               temperature (T), and      classification    of ECS
                                               global scaling (GS).      according to      [and/or
                                                                         Rohling et al.    range]

      AR5             LGM                      Assessment of             Sa = ECS          [very likely >    Multiple
      (Masson-                                 multiple lines of                           1.0 ; very        sources of
      Delmotte et                              evidence                                    unlikely >        uncertainty
      al., 2013)                                                                           6.0 °C]
      AR5             Cenozoic (last 65        Assessment of             S[CO2,LI]         [95% range:       Multiple
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 (Masson-        million years)         multiple lines of                         1.1 to 7.0 °C] sources of
 Delmotte et                            evidence                                                 uncertainty
 al., 2013)
 Tierney et      LGM                    CO2: ice core           S[CO2,LI,CH4,     3.8 °C           Multiple
 al. (2020b)                            T: multiproxy           N2O]              [68% range:      sources of
                                                                                  3.3 to 4.3°C]    uncertainty
 Sherwood        LGM                    CO2: ice core           S[CO2, LI, CH4,   maximum          Multiple
 et al.                                 T: multiple lines of    N2O, dust, VG]    likelihood:      sources of
 (2020)                                 evidence                                  2.6 °C           uncertainty
                                                                                  [likely range
                                                                                  depends on
                                                                                  chosen prior;
                                                                                  1.6 to 4.4°C]
 von der         Warm states of         CO2: ice core           S[CO2,LI]         3.5°C            Varying
 Heydt et al.    glacial-interglacial   T: ice core δD,                           [range: 3.1 to   LGM global
 (2014)          cycles of last 800     benthic δ18O.                             5.4°C]*          mean
                 kyrs.                  GS: Annan and                                              temperatures
                                        Hargreaves,                                                used for
                                        Schneider von                                              scaling.

 Köhler et       Warm states of         CO2: ice core           S[CO2,LI]         5.7 °C           Temporal
 al. (2015)      glacial-interglacial   alkenones and boron                       [68% range:      variability in
                 cycles of last 2       isotopes                                  3.7 to 8.1       records.
                 Myrs.                  T: benthic δ18O                           °C]*
                                        GS: PMIP LGM and
                                        PlioMIP MPWP
 Köhler et       Warm states of         CO2: boron isotopes     S[CO2,LI]         5.6 °C           Temporal
 al. (2017)      glacial-interglacial   T: benthic δ18O                           [16th to 84th    variability in
                 cycles of last 2       GS: PMIP LGM and                          percentile:      records.
                 Myrs.                  PlioMIP MPWP                              3.6 to 8.1

 Köhler et       Warm states of         CO2: ice cores          S[CO2, LI]        [range: 3.0 to   Varying
 al. (2018)      glacial-interglacial   T: benthic δ18O,                          5.9 °C]*         temperature
                 cycles of last 800     alkenone, Mg/Ca,                                           reconstructio
                 kyrs, excluding        MAT, and faunal                                            ns.
                 those for which        SST
                 CO2 and T diverge.     GS: PMIP3 LGM
 (Stap et al.,   States of glacial-     CO2: ice cores          S[CO2, LI]        [range: 6.1 to   Varying
 2019)           interglacial cycles    T: benthic δ18O                           11.0 °C]*        efficacies of
                 of last 800 kyrs for   GS: PMIP LGM and                                           ice sheet
                 which forcing is       PlioMIP MPWP                                               forcing
                 zero compared with
                 modern, excluding
                 those for which
                 CO2 and T diverge.
 Friedrich et    Warm states of         CO2: ice cores          S[GHG,LI,AE]      4.9 °C           Varying
 al. (2016)      glacial-interglacial   T: alkenone, Mg/Ca,                       [Likely          LGM global
                 cycles of last 780     MAT, and faunal                           range: 4.3 to    mean
                 kyrs.                  SST                                       5.4°C]*          temperatures,
                                        GS: PMIP3 LGM.                                             aerosol
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     Friedrich       Last glacial-            CO2: ice cores            S[GHG,LI,AE]       4.2°C            Varying
     and             interglacial cycle       T: alkenone, Mg/Ca,                          [range: 3.4 to   aerosol
     Timmerma                                 MAT                                          6.2°C]*          forcings
     nn (2020)
     Snyder          Interglacial periods     CO2: ice cores            S[GHG,LI,AE,VG]    3.1°C            Multiple
     (2019)          and intermediate         T: alkenone, Mg/Ca,                          [67% range :     sources of
                     glacial climates of      species assemblages                          2.6 to 3.7       uncertainty
                     last 800 kyrs            GS: PMIP models                              °C]*
     Royer           Glacial-interglacial     CO2: boron isotopes       S[CO2,LI]          10.2°C           Temporal
     (2016)          cycles of the            T: benthic δ18O                              [68% range:      variability in
                     Pliocene (3.4 to 2.9                                                  8.1 to           records.
                     Ma)                                                                   12.3°C]
     Martínez-       Pliocene                 CO2: boron isotopes       S[CO2,LI]          3.7 °C           Pliocene sea
     Botí et al.                              T: benthic δ18O                              [68% range:      level,
     (2015)                                                                                3.0 to           temporal
                                                                                           4.4°C]*          variability in
     Sherwood        Pliocene                 CO2: boron isotopes       S[CO2,             maximum          Multiple
     et al.                                   T: multiple lines of      LI,N2O,CH4,VG]     likelihood:      sources of
     (2020)                                   evidence                                     3.2°C            uncertainty
                                                                                           [likely range
                                                                                           depends on
                                                                                           chosen prior;
                                                                                           1.8 to 5.2°C]
     Anagnostou Early Eocene                  CO2: boron isotopes       S[CO2,LI]          3.6 °C         Varying
     et al.                                   T: various terrestrial                       [66% range:    calibrations
     (2016)                                   MAT, Mg/Ca, TEX,                             2.1 to 4.6 °C] for
                                              δ18O SST.                                                   temperature
                                                                                                          and CO2.

     Anagnostou Late Eocene (41.2             CO2: boron isotopes       S[CO2,LI]          3.0 °C           Temporal
     et al.     to 33.9 Ma)                   T: one SST record                            [68% range:      variability in
     (2020)                                   GS: CESM1                                    1.9 to 4.1 °C]   records.
     Shaffer et Pre-PETM                      CO2: mineralogical,       S[GHG,AE,VG,LI]    [range: 3.3 to   Varying
     al. (2016)                               carbon cycling, and                          5.6 °C]          calibration of
                                              isotope constraints                                           temperature
                                              T: various terrestrial                                        and CO2.
                                              MAT, Mg/Ca, TEX,
                                              δ18O SST.

     Inglis et al.   Mean of EECO,            CO2: boron isotopes       S[CO2,LI, VG,AE]   3.7 °C [likely   Multiple
     (2020)          PETM, and latest         T: multiproxy SST                            range : 2.2 to   sources of
                     Paleocene                and SAT                                      5.3°C]           uncertainty
                                              GS: EoMIP models
1   Notes:
2   (Note 1) Sa in this table denotes a classification of climate sensitivity following (Rohling et al., 2012).
3   (Note 2 ) * = Although our assessed value of ERF due to CO2 doubling is 3.93 W m-2 (Section, for these studies
4   the best estimate and range of temperature is calculated from the published estimate of sensitivity in units of °C (W m-
5    ) using an ERF of 3.7 W m-2, for consistency with the typical value used in the studies to estimate the paleo CO2
    2 -1

6   forcing.
8   [END TABLE 7.11 HERE]
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 2   None of the post-AR5 studies in Table 7.11 have an estimated lower range for ECS below 1.6 °C. As such,
 3   based solely on the paleoclimate record, it is assessed to be very likely that ECS is greater than 1.5°C (high
 4   confidence).
 6   In general, it is the studies based on the warm periods of the glacial-interglacial cycles (Section that
 7   give the largest values of ECS. Given the large uncertainties associated with estimating the magnitude of the
 8   ice sheet forcing during these intervals (Stap et al., 2019), and other uncertainties discussed in Section
 9, in particular the direct effect of orbital forcing on estimates of ECS, there is only low confidence in
10   estimates from the studies based on glacial-interglacial periods. This low confidence also results from the
11   temperature-dependence of the net feedback parameter, α, resulting from several of these studies (Figure
12   7.10), that is hard to reconcile with the other lines of evidence for α, including proxy estimates from warmer
13   paleoclimates (Section A central estimate of ECS, derived from the LGM (Section and
14   warm periods of the pre-Quaternary (Section, that takes into account some of the interdependencies
15   between the different studies, can be obtained by averaging across studies within each of these two time
16   periods, and then averaging across the two time periods; this results in a central estimate of 3.4°C. This
17   approach of focussing on the LGM and warm climates was also taken by Sherwood et al. (2020) in their
18   assessment of ECS from paleoclimates. An alternative method is to average across all studies, from all
19   periods, that have considered multiple sources of uncertainty (Table 7.11); this approach leads to a similar
20   central estimate of 3.3°C. Overall, we assess medium confidence for a central estimate of 3.3–3.4°C.
22   There is more variation in the upper bounds of ECS than in the lower bounds. Estimates of ECS from pre-
23   Quaternary warm periods have an average upper range of 4.9 °C, and from the LGM of 4.4°C; taking into
24   account the independence of the estimates from these two time periods, and accounting for state-dependence
25   (Section 7.4.3) and other uncertainties discussed in Section 7.5.3, the paleoclimate record on its own
26   indicates that ECS is likely less than 4.5 °C. Given the higher values from many glacial-interglacial studies,
27   this value has only medium confidence. Despite the large variation in individual studies at the extreme upper
28   end, all except two studies (both of which are from glacial-interglacial time periods associated with low
29   confidence) have central estimates that are below 6 °C; overall we assess that it is extremely likely that ECS
30   is below 8 °C (high confidence).
33   7.5.4   Estimates of ECS and TCR based on emergent constraints
35   ESMs exhibit substantial spread in ECS and TCR (Section 7.5.7). Numerous studies have leveraged this
36   spread in order to narrow estimates of Earth's climate sensitivity by employing methods known as “emergent
37   constraints” (Chapter 1, Section 1.5.4). These methods establish a relationship between an observable and
38   either ECS or TCR based on an ensemble of models, and combine this information with observations to
39   constrain the probability distribution of ECS or TCR. Most studies of this kind have clearly benefitted from
40   the international efforts to coordinate the CMIP and other multi-model ensembles.
42   A number of considerations must be taken into account when assessing the diverse literature on ECS and
43   TCR emergent constraints. For instance, it is important to have physical and theoretical basis for the
44   connection between the observable and modelled ECS or TCR since in model ensembles thousands of
45   relationships that pass statistical significance can be found simply by chance (Caldwell et al., 2014). It is also
46   important that the underlying model ensemble does not exhibit a shared bias that influences the simulation of
47   the observable quantity on which the emergent constraint is based. Also, correctly accounting for
48   uncertainties in both the observable (including measurement uncertainty and natural variability) and the
49   emergent constraint statistical relationship can be challenging, in particular in cases where the latter is not
50   expected to be linear (Annan et al., 2020a). A number of proposed emergent constraints leverage variations
51   in modelled ECS arising from tropical low clouds, which was the dominant source of inter-model spread in
52   the CMIP5 ensemble used in most emergent constraint studies. Since ECS is dependent on the sum of
53   individual feedbacks (Section 7.5.1) these studies implicitly assume that all other feedback processes in
54   models are unbiased and should therefore rather be thought of as constraints on tropical low-cloud feedback
55   (Klein and Hall, 2015; Qu et al., 2018; Schlund et al., 2020). The following sections go through a range of
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 1   emergent constraints and assess their strengths and limitations.
 4   Emergent constraints using global or near-global surface temperature change
 6   Perhaps the simplest class of emergent constraints regress past equilibrium paleoclimate temperature change
 7   against modelled ECS to obtain a relationship that can be used to translate a past climate change to ECS. The
 8   advantage is that these are constraints on the sum of all feedbacks, and furthermore unlike constraints on the
 9   instrumental record they are based on climate states that are at, or close to, equilibrium. So far, these
10   emergent constraints have been limited to the Last Glacial Maximum (LGM; Cross-Chapter Box 2.1)
11   cooling (Hargreaves et al., 2012; Schmidt et al., 2014; Renoult et al., 2020) and warming in the mid-Pliocene
12   Warm Period (MPWP, Hargreaves and Annan, 2016; Renoult et al., 2020; Cross-Chapter Box 2.1; Cross-
13   Chapter Box 2.4) due to the availability of sufficiently large multi-model ensembles for these two cases. The
14   paleoclimate emergent constraints are limited by structural uncertainties in the proxy-based global surface
15   temperature and forcing reconstructions (Section 7.5.3), possible differences in equilibrium sea-surface
16   temperature patterns between models and the real world, and a small number of model simulations
17   participating, which has led to divergent results. For example, Hopcroft and Valdes (2015) repeated the study
18   based on the LGM by Hargreaves et al. (2012) using another model ensemble and found that the emergent
19   constraint was not robust, whereas studies using multiple available ensembles retain useful constraints
20   (Schmidt et al., 2014; Renoult et al., 2020). Also, the results are somewhat dependent on the applied
21   statistical methods (Hargreaves and Annan, 2016). However, Renoult et al. (2020) explored this and found
22   95th percentiles of ECS below 6°C for LGM and Pliocene individually, regardless of statistical approach, and
23   by combining the two estimates the 95th percentile dropped to 4.0°C. The consistency between the cold LGM
24   and warm MPWP emergent constraint estimates increases confidence in these estimates, and further suggests
25   that the dependence of feedback on climate mean state (Section 7.4.3) as represented in PMIP models used
26   in these studies is reasonable.
28   Various emergent constraint approaches using global warming over the instrumental record have been
29   proposed. These benefit from more accurate data compared with paleoclimates, but suffer from the fact that
30   the climate is not in equilibrium, thereby assuming that ESMs on average accurately depict the ratio of short
31   term to long term global warming. Global warming in climate models over 1850 to the present day exhibits
32   no correlation with ECS, which is partly due to a substantial number of models exhibiting compensation
33   between a high climate sensitivity with strong historical aerosol cooling (Kiehl, 2007; Forster et al., 2013;
34   Nijsse et al., 2020). However, the aerosol cooling increased up until the 1970s when air quality regulations
35   reduced the emissions from Europe and North America whereas other regions saw increases resulting in a
36   subsequently reduced pace of global mean aerosol ERF increase (Chapter 2, Section 2.2.8, Figure 2.10).
37   Energy balance considerations over the 1970–2010 period gave a best estimate ECS of 2.0°C (Bengtsson and
38   Schwartz, 2013), however this estimate did not account for pattern effects. To address this limitation an
39   emergent constraint on 1970–2005 global warming was demonstrated to yield a best estimate ECS of 2.83
40   [1.72 to 4.12] °C (Jiménez-de-la-Cuesta and Mauritsen, 2019). The study was followed up using CMIP6
41   models yielding a best estimate ECS of 2.6 [1.5 to 4.0] °C based on 1975–2019 global warming (Nijsse et
42   al., 2020), thereby confirming the emergent constraint. Internal variability and forced or unforced pattern
43   effects may influence the results (Jiménez-de-la-Cuesta and Mauritsen, 2019; Nijsse et al., 2020). For
44   instance the Atlantic Multidecadal Oscillation changed from negative to positive anomaly, while the Indo-
45   Pacific Oscillation changed less over the 1970–2005 period, potentially leading to high-biased results
46   (Jiménez-de-la-Cuesta and Mauritsen, 2019), whereas during the later period 1975–2019 these anomalies
47   roughly cancel (Nijsse et al., 2020). Pattern effects may have been substantial over these periods (Andrews et
48   al., 2018), however the extent to which TOA radiation anomalies influenced surface temperature may have
49   been dampened by the deep ocean (Hedemann et al., 2017; Newsom et al., 2020). It is therefore deemed
50   more likely than not that these estimates based on post-1970s global warming are biased low by internal
51   variability.
53   A study that developed an emergent constraint based on the response to the Mount Pinatubo 1991 eruption
54   yielded a best estimate of 2.4 [likely range 1.7–4.1] °C (Bender et al., 2010). When accounting for ENSO
55   variations they found a somewhat higher best estimate of 2.7°C, which is in line with results of later studies
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 1   that suggest ECS inferred from periods with substantial volcanic activity are low-biased due to strong pattern
 2   effects (Gregory et al., 2020) and that the short-term nature of volcanic forcing could exacerbate possible
 3   underestimates of modelled pattern effects.
 5   Lagged-correlations present in short term variations in the global surface temperature can be linked to ECS
 6   through the fluctuation-dissipation theorem which is derived from a single heat reservoir model (Einstein,
 7   1905; Hasselmann, 1976; Schwartz, 2007; Cox et al., 2018a). From this it follows that the memory carried
 8   by the heat capacity of the ocean results in low-frequency global temperature variability (red noise) arising
 9   from high frequency (white noise) fluctuations in the radiation balance, e.g., caused by weather. Initial
10   attempts to apply the theorem to observations yielded a fairly low median ECS estimate of 1.1°C (Schwartz,
11   2007), a result that was disputed (Foster et al., 2008; Knutti et al., 2008). Recently it was proposed by Cox et
12   al. (2018a) to use variations in the historical experiments of the CMIP5 climate models as an emergent
13   constraint giving a median ECS estimate of 2.8 [1.6 to 4.0] °C. A particular challenge associated with these
14   approaches is to separate short-term from long-term variability, and slightly arbitrary choices regarding the
15   methodology of separating these in the global surface temperature from long-term signals in the historical
16   record, omission of the more strongly forced period after 1962, as well as input data choices, can lead to
17   median ECS estimates ranging from 2.5–3.5°C (Brown et al., 2018; Po-Chedley et al., 2018b; Rypdal et al.,
18   2018). Calibrating the emergent constraint using CMIP5 modelled internal variability as measured in
19   historical control simulations (Po-Chedley et al., 2018b) will inevitably lead to an overestimated ECS due to
20   externally forced short term variability present in the historical record (Cox et al., 2018b). Contrary to
21   constraints based on paleoclimates or global warming since the 1970s, when based on CMIP6 models a
22   higher, yet still well-bounded ECS estimate of 3.7 [2.6 to 4.8] °C is obtained (Schlund et al., 2020). A more
23   problematic issue is raised by (Annan et al., 2020b) who showed that the upper bound on ECS estimated this
24   way is less certain when considering deep ocean heat uptake. In conclusion, even if not inconsistent, these
25   limitations prevents us from directly using this type of constraint in the assessment.
27   Short term variations in the TOA energy budget, observable from satellites, arising from variations in the
28   tropical tropospheric temperature has been linked to ECS through models, either as a range of models
29   consistent with observations (those with ECS values between 2.0°C and 3.9°C ) (Dessler et al., 2018) or as a
30   formal emergent constraint by deriving further model-based relationships to yield a median of 3.3 [2.4 to
31   4.5] °C (Dessler and Forster, 2018). There are major challenges associated with short term variability in the
32   energy budget, in particular how it relates to the long-term forced response of clouds (Colman and Hanson,
33   2017; Lutsko and Takahashi, 2018), and variations in the surface temperature that are not directly affecting
34   the radiation balance lead to an overestimated ECS when using linear regression techniques where it appears
35   as noise in the independent variable (Proistosescu et al., 2018; Gregory et al., 2020). The latter issue is
36   largely overcome when using the tropospheric mean or mid-tropospheric temperature (Trenberth et al., 2015;
37   Dessler et al., 2018).
40   Emergent constraints focused on cloud feedbacks and present-day climate
42   A substantial number of emergent constraint studies focus on observables that are related to tropical low-
43   cloud feedback processes (Volodin, 2008; Sherwood et al., 2014; Zhai et al., 2015; Brient and Schneider,
44   2016; Brient et al., 2016). These studies yield median ECS estimates of 3.5–4°C and in many cases indicate
45   low likelihoods of values below 3°C. The approach has attracted attention since most of the spread in climate
46   sensitivity seen in CMIP5, and earlier climate model ensembles, arises from uncertainty in low cloud
47   feedbacks (Bony and Dufresne, 2005; Wyant et al., 2006; Randall et al., 2007; Vial et al., 2013).
48   Nevertheless, this approach assumes that all other feedback processes are unbiased (Klein and Hall, 2015;
49   Qu et al., 2018; Schlund et al., 2020), for instance the possibly missing negative anvil area feedback or the
50   possibly exaggerated mixed-phase cloud feedback (Section Thus, the subset of emergent constraints
51   that focus on low-level tropical clouds are not necessarily inconsistent with other emergent constraints of
52   ECS. Related emergent constraints that focus on aspects of the tropical circulation and ECS have led to
53   conflicting results (Su et al., 2014; Tian, 2015; Lipat et al., 2017; Webb and Lock, 2020), possibly because
54   these processes are not the dominant factors in causing the inter-model spread (Caldwell et al., 2018).
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 1   The fidelity of models in reproducing aspects of temperature variability or the radiation budget has also been
 2   proposed as emergent constraints on ECS (Covey et al., 2000; Knutti et al., 2006; Huber et al., 2010; Bender
 3   et al., 2012; Brown and Caldeira, 2017; Siler et al., 2018a). Here indices based on spatial or seasonal
 4   variability are linked to modelled ECS, and overall the group of emergent constraints yields best estimates of
 5   3.3°C to 3.7°C. Nevertheless, the physical relevance of present-day biases to the sum of long-term climate
 6   change feedbacks is unclear and therefore these constraints on ECS are not considered reliable.
 9   Assessed ECS and TCR based on emergent constraints
11   The available emergent constraint studies have been divided into two classes: (i) those that are based on
12   global or near-global indices, such as global surface temperature and the TOA energy budget; and (ii) those
13   that are more focussed on physical processes, such as the fidelity of phenomena related to low-level cloud
14   feedbacks or present-day climate biases. The former class is arguably superior in representing ECS, since it
15   is a global surface temperature or energy budget change, whereas the latter class is perhaps best thought of as
16   providing constraints on individual climate feedbacks, e.g., the determination that low-level cloud feedbacks
17   are positive. The latter result is consistent with and confirms process-based estimates of low cloud feedbacks
18   (Section, but are potentially biased as a group by missing or biased feedbacks in ESMs and is
19   accordingly not taken into account here. A limiting case here is Dessler and Forster (2018) which is focused
20   on monthly co-variability in the global TOA energy budget with mid-tropospheric temperature, at which
21   time scale the surface albedo feedback is unlikely to operate thus implicitly assuming it is unbiased in the
22   model ensemble.
24   In the first group of emergent constraints there is broad agreement on the best estimate of ECS ranging from
25   2.4–3.3°C. At the lower end, nearly all studies find lower bounds (5th percentiles) around 1.5°C, whereas
26   several studies indicate 95th percentiles as low as 4°C. Considering both classes of studies, none of them
27   yield upper very likely bounds above 5°C. Since several of the emergent constraints can be considered nearly
28   independent one could assume that emergent constraints provide very strong evidence on ECS by combining
29   them. Nevertheless, this is not done here because there are sufficient cross-dependencies, as for instance
30   models are re-used in many of the derived emergent constraints, and furthermore the methodology has not
31   yet reached a sufficient level of maturity since systematic biases may not have been accounted for.
32   Uncertainty is therefore conservatively added to reflect these potential issues. This leads to the assessment
33   that ECS inferred from emergent constraints is very likely 1.5 to 5°C with medium confidence.
35   Emergent constraints on TCR with a focus on the instrumental temperature record, though less abundant,
36   have also been proposed. These can be influenced by internal variability and pattern effects as discussed in
37   Section, although the influence is smaller because uncertainty in forced pattern effects correlate
38   between transient historical warming and TCR. In the simplest form Gillett et al. (2012) regressed the
39   response of one model to individual historical forcing components to obtain a tight range of 1.3–1.8°C, but
40   later when an ensemble of models was used the range was widened to 0.9–2.3°C (Gillett et al., 2013), and
41   updated by Schurer et al. (2018). A related data-assimilation based approach that accounted also for
42   uncertainty in response patterns gave 1.33–2.36°C (Ribes et al., 2021), but is dependent on the choice of
43   prior ensemble distribution (CMIP5 or CMIP6). Another study used the response to the Pinatubo volcanic
44   eruption to obtain a range of 0.8–2.3°C (Bender et al., 2010). A tighter range, notably at the lower end, was
45   found in an emergent constraint focusing on the post-1970s warming exploiting the lower spread in aerosol
46   forcing change over this period (Jiménez-de-la-Cuesta and Mauritsen, 2019). Their estimate was 1.67 [1.17
47   to 2.16] °C. Two studies tested this idea: Tokarska et al. (2020) estimates TCR was 1.60 [0.90 to 2.27] °C
48   based on CMIP6 models, whereas Nijsse et al. (2020) found 1.68 [1.0 to 2.3] °C, and in both cases there was
49   a small sensitivity to choice of ensemble with CMIP6 models yielding slightly lower values and ranges.
50   Combining these studies gives a best estimate of 1.7°C and a very likely range of TCR of 1.1–2.3°C with
51   high confidence.
54   [START TABLE 7.12 HERE]
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 1   Table 7.12: Emergent constraint studies used in the assessment of ECS. These are studies that rely on global or near-
 2               global temperature change as the observable.
      Study                Emergent constraint description                  Published best      Uncertainty estimate:
                                                                            estimate and
                                                                            uncertainty (°C)
      (Bender et al.,      Pinatubo integrated forcing normalized by        2.4                 5% to 95%
      2010)                CMIP3 models own forcing versus                  [1.7 to 4.1]
                           temperature change regressed against ECS
      (Dessler and         Emergent constraint on TOA radiation             3.3                 17% to 83%
      Forster, 2018)       variations linked to mid-tropospheric            [2.4 to 4.5]
                           temperature in CMIP5 models
      (Hargreaves et       Last Glacial Maximum tropical SSTs in            2.5                 5% to 95%
      al., 2012)           PMIP2 models                                     [1.3 to 4.2]
      (Hargreaves and      Pliocene tropical SSTs in PlioMIP models         [1.9 to 3.7]        5% to 95%
      Annan, 2016)
      (Jiménez-de-la-      Post–1970s global warming, 1995–2005             2.83                5% to 95%
      Cuesta and           relative to 1970–1989, CMIP5 models              [1.72 to 4.12]
      (Nijsse et al.,      Post–1970s global warming, 2009–2019             2.6                 5% to 95%
      2020)                relative to 1975–1985, CMIP6 models              [1.5 to 4.0]
      (Renoult et al.,     Combined Last Glacial Maximum and                2.5 [0.8 to 4.0]    5% to 95%
      2020)                Pliocene tropical SSTs in PMIP2, PMIP3,
                           PMIP4, PlioMIP and PlioMIP2 models
 5   [END TABLE 7.12 HERE]
 8   7.5.5    Combined assessment of ECS and TCR
10   Substantial quantitative progress has been made in interpreting evidence of Earth's climate sensitivity since
11   AR5, through innovation, scrutiny, theoretical advances and a rapidly evolving data base from current, recent
12   and paleo climates. It should be noted that, unlike AR5 and earlier reports, our assessment of ECS is not
13   directly informed by ESM simulations (Section 7.5.6). The assessments of ECS and TCR are focussed on the
14   following lines of evidence: process-understanding; the instrumental record of warming; paleoclimate
15   evidence; and emergent constraints. ESMs remain essential tools throughout establishing these lines of
16   evidence, for instance for estimating part of the feedback parameters and radiative forcings, and emergent
17   constraints rely on substantial model spread in ECS and TCR (Section 7.5.6).
19   A key advance over the AR5 assessment is the broad agreement across multiple lines of evidence. These
20   support a central estimates of ECS close to, or at least not inconsistent with, 3°C. This advance is foremost
21   following improvements in the understanding and quantification of Earth's energy imbalance, the
22   instrumental record of global temperature change, and the strength of anthropogenic radiative forcing.
23   Further advances include increased understanding of how the pattern effect influences ECS inferred from
24   historical global warming (Sections 7.4.4 and 7.5.3), improved quantification of paleo climate change from
25   proxy evidence and a deepened understanding of how feedback mechanisms increase ECS in warmer climate
26   states (Sections 7.4.3, 7.4.4 and 7.5.4), and also an improved quantification of individual cloud feedbacks
27   (Sections 7.4.2 and The assessment findings for ECS and TCR are summarized in Table 7.13 and
28   Table 7.14, respectively, and also visualized in Figure 7.18.
33   Figure 7.18: Summary of the equilibrium climate sensitivity (ECS) and transient climate response (TCR)
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 1                assessments using different lines of evidence. Assessed ranges are taken from Tables 7.13 and 7.14 for
 2                ECS and TCR respectively. Note that for the ECS assessment based on both the instrumental record and
 3                paleoclimates, limits (i.e. one-sided distributions) are given, which have twice the probability of being
 4                outside the maximum/minimum value at a given end, compared to ranges (i.e. two tailed distributions)
 5                which are given for the other lines of evidence. For example, the extremely likely limit of greater than
 6                95% probability corresponds to one side of the very likely (5% to 95%) range. Best estimates are given as
 7                either a single number or by a range represented by grey box. CMIP6 model values are not directly used
 8                as a line of evidence but presented on the Figure for comparison. ECS values are taken from Schlund et
 9                al. (2020) and TCR values from Meehl et al. (2020), see Supplementary Material 7.SM.4. Further details
10                on data sources and processing are available in the chapter data table (Table 7.SM.14).
12   [END FIGURE 7.18 HERE]
15   AR5 assessed ECS to have a likely range from 1.5 to 4.5°C (Collins et al., 2013a) based on the majority of
16   studies and evidence available at the time. The broader evidence base presented in this Report and the
17   general agreement among different lines of evidence means that they can be combined to yield a narrower
18   range of ECS values. This can be done formally using Bayesian statistics, though such a process is complex
19   and involves formulating likelihoods and priors (Annan and Hargreaves, 2006; Stevens et al., 2016;
20   Sherwood et al., 2020b). However, it can be understood that if two lines of independent evidence each give a
21   low probability of an outcome being true, e.g., that ECS is less than 2.0°C, then the combined probability
22   that ECS is less than 2.0°C is lower than that of either line of evidence. On the contrary, if one line of
23   evidence is unable to rule out an outcome, but another is able to assign a low probability, then there is a low
24   probability that the outcome is true (Stevens et al., 2016). This general principle applies even when there is
25   some dependency between the lines of evidence (Sherwood et al., 2020b), for instance between historical
26   energy budget constraints (Section and those emergent constraints that use the historically observed
27   global warming (Section Even in this case the combined constraint will be closer to the narrowest
28   range associated with the individual lines of evidence.
30   In the process of providing a combined and self-consistent ECS assessment across all lines of evidence, the
31   above principles were all considered. As in earlier reports, a 0.5°C precision is used. Starting with the very
32   likely lower bound, there is broad support for a value of 2.0°C, including process understanding and the
33   instrumental record (Table 7.13). For the very likely upper bound, emergent constraints give a value of 5.0°C
34   whereas the three other lines of evidence are individually less tightly constrained. Nevertheless, emergent
35   constraints are a relatively recent field of research, in part taken into account by adding uncertainty to the
36   upper bound (Section, and the underlying studies use, to a varying extent, information that is also
37   used in the other three lines of evidence causing statistical dependencies. However, omitting emergent
38   constraints and statistically combining the remaining lines of evidence likewise yields 95th percentiles close
39   to 5.0°C (Sherwood et al., 2020b). Information for the likely range is partly missing or one-sided, however it
40   must necessarily reside inside the very likely range and is therefore supported by evidence pertaining to both
41   the likely and very likely ranges. Hence, the upper likely bound is assessed to be about halfway between the
42   best estimate and the upper very likely bound while the lower likely bound is assessed to be about halfway
43   between the best estimate and the lower very likely bound. In summary, based on multiple lines of evidence
44   the best estimate of ECS is 3°C, it is likely within the range 2.5 to 4°C and very likely within the range 2 to
45   5°C. It is virtually certain that ECS is larger than 1.5°C. Whereas there is high confidence based on
46   mounting evidence that supports the best estimate, likely range and very likely lower end, a higher ECS than
47   5°C cannot be ruled out, hence there is medium confidence in the upper end of the very likely range. Note
48   that the best estimate of ECS made here corresponds to a feedback parameter of –1.3 W m–2 °C–1 which is
49   slightly more negative than the feedback parameter from process based evidence alone that is assessed in
50   Section
52   There has long been a consensus (Charney et al., 1979) supporting an ECS estimates of 1.5 to 4°C. In this
53   regard it is worth remembering the many debates challenging an ECS of this magnitude. These started as
54   early as Ångström (1900) criticizing the results of Arrhenius (1896) arguing that the atmosphere was already
55   saturated in infrared absorption such that adding more CO2 would not lead to warming. The assertion of
56   Ångström was understood half a century later to be incorrect. History has seen a multitude of studies (e.g.,
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 1   Svensmark, 1998; Lindzen et al., 2001; Schwartz, 2007) mostly implying lower ECS than the range assessed
 2   as very likely here. However, there are also examples of the opposite such as very large ECS estimates based
 3   on the Pleistocene records (Snyder, 2016), which has been shown to be overestimated due to a lack of
 4   accounting for orbital forcing and long term ice sheet feedbacks (Schmidt et al., 2017b), or suggestions that
 5   global climate instabilities may occur in the future (Steffen et al., 2018; Schneider et al., 2019). There is,
 6   however, no evidence for unforced instabilities of such magnitude occurring in the paleo record temperatures
 7   of the past 65 million years (Westerhold et al., 2020), possibly short of the PETM excursion (Chapter 5,
 8   Section that occurred at more than 10°C above present (Anagnostou et al., 2020). Looking back, the
 9   resulting debates have led to a deeper understanding, strengthened the consensus, and have been
10   scientifically valuable.
12   In the climate sciences, there are often good reasons to consider representing deep uncertainty, or what is
13   sometimes referred to as unknown unknowns. This is natural in a field that considers a system that is both
14   complex and at the same time challenging to observe. For instance, since emergent constraints represent a
15   relatively new line of evidence, important feedback mechanisms may be biased in process-level
16   understanding, pattern effects and aerosol cooling may be large and paleo evidence inherently builds on
17   indirect and incomplete evidence of past climate states, there certainly can be valid reasons to add
18   uncertainty to the ranges assessed on individual lines of evidence. This has indeed been addressed
19   throughout Sections 7.5.1–7.5.4. Since it is neither probable that all lines of evidence assessed here are
20   collectively biased nor is the assessment sensitive to single lines of evidence, deep uncertainty it is not
21   considered as necessary to frame the combined assessment of ECS.
24   [START TABLE 7.13 HERE]
26   Table 7.13: Summary of ECS assessment
      Equilibrium Climate            Central value    Likely            Very likely          Extremely likely
      Sensitivity (ECS)
      Process understanding
                                     3.4°C            2.5 to 5.1 °C     2.1 to 7.7 °C
      Warming over instrumental
                                                                                             > 1.6 °C
      record (7.5.2)                 2.5 to 3.5 °C    > 2.2°C           > 1.8 °C
      Paleoclimates (7.5.3)          3.3 to 3.4°C     < 4.5 °C          > 1.5°C              < 8 °C
      Emergent constraints
                                     2.4 to 3.3°C                       1.5 to 5.0 °C
      Combined assessment            3°C              2.5 to 4.0 °C     2.0 to 5.0 °C
29   [END TABLE 7.13 HERE]
32   The evidence for TCR is less abundant than for ECS, and focuses on the instrumental temperature record
33   (Sections 7.5.2 and 7.5.6), emergent constraints (Section and process understanding (Section 7.5.1).
34   AR5 assessed a likely range of 1.0 to 2.5°C. TCR and ECS are related, though, and in any case TCR is less
35   than ECS (see Section 7.5 introduction). Furthermore, estimates of TCR from the historical record are not as
36   strongly influenced by externally forced surface temperature pattern effects as estimates of ECS are since
37   both historical transient warming and TCR are affected by this phenomenon (Section 7.4.4). A slightly
38   higher weight is given to instrumental record warming and emergent constraints since these are based on
39   observed transient warming, whereas the process understanding estimate relies on pattern effects and ocean
40   heat uptake efficiency from ESMs to represent the transient dampening effects of the ocean. If these effects
41   are underestimated by ESMs then the resulting TCR would be lower. Given the interdependencies of the
42   other two lines of evidence, a conservative approach to combining them as reflected in the assessment is
43   adopted. Since uncertainty is substantially lower than in AR5 a 0.1°C precision is therefore used here.
44   Otherwise the same methodology for combining the lines of evidence as applied to ECS is used for TCR.
45   Based on process understanding, warming over the instrumental record and emergent constraints the best
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 1   estimate TCR is 1.8°C, it is likely 1.4 to 2.2°C and very likely 1.2 to 2.4°C. The assessed ranges are all
 2   assigned high confidence due to the high level of agreement among the lines of evidence.
 5   [START TABLE 7.14 HERE]
 7   Table 7.14: Summary of TCR assessment
                          Transient Climate           Central        Likely        Very likely
                          Response (TCR)              value          range         range
                          Process understanding       2.0 °C         1.6 to 2.7    1.3 to 3.1 °C
                          (7.5.1)                                    °C
                          Warming over                1.9 °C         1.5 to        1.3 to 2.7 °C
                          instrumental record                        2.3°C
                          Emergent constraints        1.7 °C                       1.1 to 2.3°C
                          Combined assessment         1.8 °C         1.4 to        1.2 to 2.4°C
10   [END TABLE 7.14 HERE]
13   7.5.6   Considerations on the ECS and TCR in global climate models and their role in the assessment
15   Coupled climate models, such as those participating in CMIP, have long played a central role in assessments
16   of ECS and TCR. In reports up to and including TAR, climate sensitivities derived directly from ESMs were
17   the primary line of evidence. However, since AR4, historical warming and paleoclimate information
18   provided useful additional evidence and it was noted that assessments based on models alone were
19   problematic (Knutti, 2010). As new lines of evidence have evolved, in AR6 various numerical models are
20   used where they are considered accurate, or in some cases the only available source of information, and
21   thereby support all four lines of evidence (Sections 7.5.1-7.5.4). However, AR6 differs from previous IPCC
22   reports in excluding direct estimates of ECS and TCR from ESMs in the assessed ranges (Section 7.5.5),
23   following several recent studies (Annan and Hargreaves, 2006; Stevens et al., 2016; Sherwood et al., 2020b).
24   The purpose of this section is to explain why this approach has been taken and to provide a perspective on
25   the interpretation of the climate sensitivities exhibited in CMIP6 models.
27   The primary consideration that led to excluding ECS and TCR directly derived from ESMs is that
28   information from these models is incorporated in the lines of evidence used in the assessment: ESMs are
29   partly used to estimate historical- and paleoclimate ERFs (Sections 7.5.2 and 7.5.3); to convert from local to
30   global mean paleo temperatures (Section 7.5.3), to estimate how feedbacks change with SST patterns
31   (Section; and to establish emergent constraints on ECS (Section 7.5.4). They are also used as
32   important evidence in the process understanding estimates of the temperature, water vapour, albedo,
33   biogeophysical, and non-CO2 biogeochemical feedbacks, whereas other evidence is primarily used for cloud
34   feedbacks where the climate model evidence is weak (Section 7.4.2). One perspective on this is that the
35   process understanding line of evidence builds on and replaces ESM estimates.
37   The ECS of a model is the net result of the model’s effective radiative forcing from a doubling of CO2 and
38   the sum of the individual feedbacks and their interactions. It is well known that most of the model spread in
39   ECS arises from cloud feedbacks, and particularly the response of low-level clouds (Bony and Dufresne,
40   2005; Zelinka et al., 2020). Since these clouds are small-scale and shallow, their representation in climate
41   models is mostly determined by sub-grid scale parameterizations. It is sometimes assumed that
42   parameterization improvements will eventually lead to convergence in model response and therefore a
43   decrease in the model spread of ECS. However, despite decades of model development, increases in model
44   resolution and advances in parametrization schemes, there has been no systematic convergence in model
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 1   estimates of ECS. In fact, the overall inter model spread in ECS for CMIP6 is larger than for CMIP5; ECS
 2   and TCR values are given for CMIP6 models in Supplementary Material 7.SM.4 based on Schlund et al.
 3   (2020) for ECS and Meehl et al. (2020) for TCR, see also Figure 7.18 and FAQ 7.3. The upward shift does
 4   not apply to all models traceable to specific modelling centres, but a substantial subset of models have seen
 5   an increase in ECS between the two model generations. The increased ECS values, as discussed in Section
 6, are partly due to shortwave cloud feedbacks (Flynn and Mauritsen, 2020) and it appears that in some
 7   models extra-tropical clouds with mixed ice and liquid phases are central to the behaviour (Zelinka et al.,
 8   2020), probably borne out of a recent focus on biases in these types of clouds (McCoy et al., 2016; Tan et al.,
 9   2016). These biases have recently been reduced in many ESMs, guided by process understanding from
10   laboratory experiments, field measurements, and satellite observations (Lohmann and Neubauer, 2018;
11   Bodas-Salcedo et al., 2019; Gettelman et al., 2019). However, this and other known model biases are already
12   factored into the process-level assessment of cloud feedback (Section, and furthermore the emergent
13   constraints used here focus on global surface temperature change, which are less susceptible to shared model
14   biases in individual feedback parameters than emergent constraints that focus on specific physical processes
15   (Section 7.5.4). The high values of ECS and TCR in some CMIP6 models lead to higher levels of surface
16   warming than CMIP5 simulations and also the AR6 projections based on the assessed ranges of ECS, TCR
17   and ERF (Chapter 4, Box 4.1; FAQ 7.3; Forster et al., 2019).
19   It is generally difficult to determine which information enters the formulation and development of
20   parameterizations used in ESMs. Climate models frequently share code components and in some cases entire
21   sub-model systems are shared and slightly modified. Therefore, models cannot be considered independent
22   developments, but rather families of models with interdependencies (Knutti et al., 2013). It is therefore
23   difficult to interpret the collection of models (Knutti, 2010), and it cannot be ruled out that there are common
24   limitations and therefore systematic biases to model ensembles that are reflected in the distribution of ECS as
25   derived from them. Although ESMs are typically well-documented, in ways that increasingly include
26   information on critical decisions regarding tuning (Mauritsen et al., 2012; Hourdin et al., 2017; Schmidt et
27   al., 2017a; Mauritsen and Roeckner, 2020), the full history of development decisions could involve both
28   process-understanding and sometimes also other information such as historical warming. As outlying or
29   poorly performing models emerge from the development process, they can become re-tuned, reconfigured or
30   discarded and so might not see publication (Hourdin et al., 2017; Mauritsen and Roeckner, 2020). In the
31   process of addressing such issues, modelling groups may, whether intentional or not, modify the modelled
32   ECS.
37   Figure 7.19: Global mean temperature anomaly in models and observations from 5 time periods. (a) Historical
38                (CMIP6 models), (b) post 1975 (CMIP6 models), (c) Last Glacial Maximum (LGM; Cross-Chapter Box
39                2.1; PMIP4 models; (Kageyama et al., 2021; Zhu et al., 2021), (d) mid Pliocene warm period (MPWP;
40                Cross-Chapter Box 2.4; PlioMIP models; Haywood et al., 2020; Zhang et al., 2021), (e) early Eocene
41                climatic optimum (EECO; Cross-Chapter Box 2.1; DeepMIP models; Zhu et al., 2020; Lunt et al., 2021).
42                Grey circles show models with ECS in the assessed very likely range; models in red have an ECS greater
43                than the assessed very likely range (>5°C), models in blue have an ECS lower than the assessed very
44                likely range (<2°C). Black ranges show the assessed temperature anomaly derived from observations
45                (Chapter 2, Section 2.3). The Historical anomaly in models and observations is calculated as the
46                difference between 2005–2014 and 1850–1900, and the post 1975 anomaly is calculated as the difference
47                between 2005–2014 and 1975–1984. For the LGM, MPWP, and EECO, temperature anomalies are
48                compared with pre-industrial (equivalent to CMIP6 simulation piControl). All model simulations of the
49                MPWP and LGM were carried out with atmospheric CO2 concentrations of 400 and 190 ppm
50                respectively. However, CO2 during the EECO is relatively more uncertain, and model simulations were
51                carried out at either 1120ppm or 1680 ppm (except for the one high-ECS EECO simulation which was
52                carried out at 560 ppm; Zhu et al., 2020). The one low-ECS EECO simulation was carried out at 1680
53                ppm. Further details on data sources and processing are available in the chapter data table (Table
54                7.SM.14).
56   [END FIGURE 7.19 HERE]
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 2   It is problematic and not obviously constructive to provide weights for, or rule out, individual CMIP6 model
 3   ensemble members based solely on their ECS and TCR values. Rather these models must be tested in a like-
 4   with-like way against observational evidence. Based on the currently published CMIP6 models we provide
 5   such an analysis, marking models with ECS above and below the assessed very likely range (Figure 7.19). In
 6   the long term historical warming (Figure 7.19a) both low and high ECS models are able to match the
 7   observed warming, presumably in part as a result of compensating aerosol cooling (Kiehl, 2007; Forster et
 8   al., 2013; Wang et al., 2021). In several cases of high ECS models that apply strong aerosol cooling it is
 9   found to result in surface warming and ocean heat uptake evolutions that are inconsistent with observations
10   (Golaz et al., 2019b; Andrews et al., 2020; Winton et al., 2020). Modelled warming since the 1970s is less
11   influenced by compensation between climate sensitivity and aerosol cooling (Jiménez-de-la-Cuesta and
12   Mauritsen, 2019; Nijsse et al., 2020) resulting in the high ECS models in general warming more than
13   observed, whereas low sensitivity models mostly perform better (Figure 7.19b); a result that may also have
14   been influenced by temporary pattern effects (Sections 7.4.4 and 7.5.4). Paleoclimates are not influenced by
15   such transient pattern effects, but are limited by structural uncertainties in the proxy-based temperature and
16   forcing reconstructions as well as possible differences in equilibrium sea-surface temperature patterns
17   between models and the real world (Section 7.5.4). Across the LGM, MPWP and EECO (Figure 7.19c-e),
18   the few high ECS models that simulated these cases were outside the observed very likely ranges; see also
19   (Feng et al., 2020; Renoult et al., 2020; Zhu et al., 2020). Also the low ECS model is either outside or on the
20   edge of the observed very likely ranges.
22   As a result of the above considerations, in this Report projections of global surface temperature are produced
23   using climate model emulators that are constrained by the assessments of ECS, TCR and ERF. In reports up
24   to and including AR5, ESM values of ECS did not fully encompass the assessed very likely range of ECS,
25   raising the possibility that past multi-model ensembles underestimated the uncertainty in climate change
26   projections that existed at the times of those reports (e.g., Knutti, 2010). However, due to an increase in the
27   modelled ECS spread and a decrease in the assessed ECS spread based on improved knowledge in multiple
28   lines of evidence, the CMIP6 ensemble encompasses the very likely range of ECS (2–5°C) assessed in
29   Section 7.5.5. Models outside of this range are useful for establishing emergent constraints on ECS and TCR
30   and provide useful examples of “tail risk” (Sutton, 2018), producing dynamically consistent realisations of
31   future climate change to inform impacts studies and risk assessments.
33   In summary, the distribution of CMIP6 models have higher average ECS and TCR values than the CMIP5
34   generation of models and the assessed values of ECS and TCR in Section 7.5.5. The high ECS and TCR
35   values can in some CMIP6 models be traced to improved representation of extra-tropical cloud feedbacks
36   (medium confidence). The ranges of ECS and TCR from the CMIP6 models are not considered robust
37   samples of possible values and the models are not considered a separate line of evidence for ECS and TCR.
38   Solely based on its ECS or TCR values an individual ESM cannot be ruled out as implausible, though some
39   models with high ( greater than 5°C) and low ( less than 2°C) ECS are less consistent with past climate
40   change (high confidence). High model climate sensitivity leads to generally higher projected warming in
41   CMIP6 compared to both CMIP5 and that assessed based on multiple lines of evidence (Chapter 4, Sections
42   4.3.1 and 4.3.4; FAQ 7.3).
45   7.5.7   Processes underlying uncertainty in the global temperature response to forcing
47   While the magnitude of global warming by the end of the 21st century is dominated by future greenhouse gas
48   emissions, the uncertainty in warming for a given ERF change is dominated by the uncertainty in ECS and
49   TCR (Chapter 4, Section 4.3.4). The proportion of variation explained by ECS and TCR varies with scenario
50   and the time period considered, but within CMIP5 models around 60% to 90% of the globally averaged
51   projected surface warming range in 2100 can be explained by the model range of these metrics (Grose et al.,
52   2018). Uncertainty in the long-term global surface temperature change can further be understood in terms of
53   the processes affecting the global TOA energy budget, namely the ERF, the radiative feedbacks which
54   govern the efficiency of radiative energy loss to space with surface warming, and the increase in the global
55   energy inventory (dominated by ocean heat uptake) which reduces the transient surface warming. A variety
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 1   of studies evaluate the effect of each of these processes on surface changes within coupled ESM simulations
 2   by diagnosing so-called ‘warming contributions’ (Dufresne and Bony, 2008; Crook et al., 2011; Feldl and
 3   Roe, 2013; Vial et al., 2013; Pithan and Mauritsen, 2014; Goosse et al., 2018). By construction, the
 4   individual warming contributions sum to the total global surface warming (Figure 7.19b). For long-term
 5   warming in response to CO2 forcing in CMIP5 models, the energy added to the climate system by radiative
 6   feedbacks is larger than the ERF of CO2 (Figure 7.19a), implying that feedbacks more than double the
 7   magnitude of global warming (Figure 7.19b). Radiative kernel methods (see Section 7.4.1) can be used to
 8   decompose the net energy input from radiative feedbacks into its components. The water-vapour, cloud and
 9   surface-albedo feedbacks enhance global warming, while the lapse-rate feedback reduces global warming.
10   Ocean heat uptake reduces the rate of global surface warming by sequestering heat at depth away from the
11   ocean surface. Section shows the warming contributions from these factors at the regional scale.
16   Figure 7.20: Contributions of effective radiative forcing, ocean heat uptake and radiative feedbacks to global
17                atmospheric energy input and near-surface air temperature change at year 100 of abrupt4xCO2
18                simulations of CMIP6 models. (a) The energy flux to the global atmosphere associated with the
19                effective CO2 forcing, global ocean heat uptake, Planck response, and radiative feedbacks, which together
20                sum to zero. The inset shows energy input from individual feedbacks, summing to the total feedback
21                energy input. (b) Contributions to net global warming are calculated by dividing the energy inputs by the
22                magnitude of the global Planck response (3.2 W m–2 °C–1), with the contributions from radiative forcing,
23                ocean heat uptake, and radiative feedbacks (orange bars) summing to the value of net warming (grey bar).
24                The inset shows warming contributions associated with individual feedbacks, summing to the total
25                feedback contribution. Uncertainties show the interquartile range (25% and 75% percentiles) across
26                models. Radiative kernel methods (see Section 7.4.1) were used to decompose the net energy input from
27                radiative feedbacks into contributions from changes in atmospheric water vapour, lapse-rate, clouds, and
28                surface albedo (Zelinka et al. (2020) using the Huang et al. (2017) radiative kernel). The CMIP6 models
29                included are those analysed by Zelinka et al. (2020) and the warming contribution analysis is based on
30                that of Goosse et al. (2018). Further details on data sources and processing are available in the chapter
31                data table (Table 7.SM.14).
33   [END FIGURE 7.20 HERE]
36   Differences in projected transient global warming across ESMs are dominated by differences in their
37   radiative feedbacks, while differences in ocean heat uptake and radiative forcing play secondary roles
38   (Figure 7.20b; Vial et al., 2013). The uncertainty in projected global surface temperature change associated
39   with inter-model differences in cloud feedbacks is the largest source of uncertainty in CMIP5 and CMIP6
40   models (Figure 7.20b), just as they were for CMIP3 models (Dufresne and Bony, 2008). Extending this
41   energy budget analysis to equilibrium surface warming suggests that about 70% of the inter-model
42   differences in ECS arises from uncertainty in cloud feedbacks, with the largest contribution to that spread
43   coming from shortwave low-cloud feedbacks (Vial et al., 2013; Zelinka et al., 2020).
45   Interactions between different feedbacks within the coupled climate system pose a challenge to our ability to
46   understand global warming and its uncertainty based on energy budget diagnostics (Section 7.4.2). For
47   example, water-vapour and lapse-rate feedbacks are correlated (Held and Soden, 2006) owing to their joint
48   dependence on the spatial pattern of warming (Po-Chedley et al., 2018a). Moreover, feedbacks are not
49   independent of ocean heat uptake because the uptake and transport of heat by the ocean influences the SST
50   pattern on which global feedbacks depend (Section However, alternative decompositions of
51   warming contributions that better account for correlations between feedbacks produce similar results
52   (Caldwell et al., 2016). The key role of radiative feedbacks in governing the magnitude of global warming is
53   also supported by the high correlation between radiative feedbacks (or ECS) and transient 21st century
54   warming within ESMs (Grose et al., 2018).
56   Another approach to evaluating the roles of forcing, feedbacks, and ocean heat uptake in projected warming

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 1   employs idealized energy balance models that emulate the response of ESMs, and which preserve the
 2   interactions between system components. One such emulator, used in Section, resolves the heat
 3   capacity of both the surface components of the climate system and the deep ocean (Held et al., 2010;
 4   Geoffroy et al., 2013a, 2013b; Kostov et al., 2014; Armour, 2017). Using this emulator, Geoffroy et al.
 5   (2012) find that: under an idealized 1% per year increase in atmospheric CO2, radiative feedbacks constitute
 6   the greatest source of uncertainty (about 60% of variance) in transient warming beyond several decades;
 7   ERF uncertainty plays a secondary but important role in warming uncertainty (about 20% of variance) that
 8   diminishes beyond several decades; and ocean heat uptake processes play a minor role in warming
 9   uncertainty (less than 10% of variance) at all timescales.
11   More computationally intensive approaches evaluate how the climate response depends on perturbations to
12   key parameter or structural choices within ESMs. Large ‘perturbed parameter ensembles’ wherein a range of
13   parameter settings associated with cloud physics are explored within atmospheric ESMs produce a wide
14   range of ECS due to changes in cloud feedbacks, but often produce unrealistic climate states (Joshi et al.,
15   2010). Rowlands et al. (2012) generated a ESM perturbed-physics ensemble of several thousand members by
16   perturbing model parameters associated with radiative forcing, cloud feedbacks, and ocean vertical
17   diffusivity (an important parameter for ocean heat uptake). After constraining the ensemble to have a
18   reasonable climatology and to match the observed historical surface warming, they found a wide range of
19   projected warming by the year 2050 under the SRES A1B scenario (1.4–3°C relative to the 1961–1990
20   average) that is dominated by differences in cloud feedbacks. The finding that cloud feedbacks are the
21   largest source of spread in the net radiative feedback has since been confirmed in perturbed parameter
22   ensemble studies using several different ESMs (Gettelman et al., 2012; Tomassini et al., 2015; Kamae et al.,
23   2016; Rostron et al., 2020; Tsushima et al., 2020). By swapping out different versions of the atmospheric or
24   oceanic components in a coupled ESM, Winton et al. (2013) found that TCR and ECS depend on which
25   atmospheric component was used (using two versions with different atmospheric physics), but that only TCR
26   is sensitive to which oceanic component of the model was used (using two versions with different vertical
27   coordinate systems, among other differences); TCR and ECS changed by 0.4°C and 1.4°C, respectively,
28   when the atmospheric model component was changed, while TCR and ECS changed by 0.3°C and less than
29   0.05°C, respectively, when the oceanic model component was changed. By perturbing ocean vertical
30   diffusivities over a wide range, Watanabe et al. (2020b) found that TCR changed by 0.16°C within the model
31   MIROC5.2 while Krasting et al. (2018) found that ECS changed by about 0.6°C within the model GFDL-
32   ESM2G, with this difference linked to different radiative feedbacks associated with different spatial patterns
33   of sea-surface warming (see Section By comparing simulations of CMIP6 models with and without
34   the effects of CO2 on vegetation, (Zarakas et al., 2020) find a physiological contribution to TCR of 0.12°C
35   (range 0.02–0.29°C across models) owing to physiological adjustments to the CO2 ERF (Section
37   There is robust evidence and high agreement across a diverse range of modelling approaches and thus high
38   confidence that radiative feedbacks are the largest source of uncertainty in projected global warming out to
39   2100 under increasing or stable emissions scenarios, and that cloud feedbacks in particular are the dominant
40   source of that uncertainty. Uncertainty in radiative forcing plays an important but generally secondary role.
41   Uncertainty in global ocean heat uptake plays a lesser role in global warming uncertainty, but ocean
42   circulation could play an important role through its effect on sea-surface warming patterns which in turn
43   project onto radiative feedbacks through the pattern effect (Section
45   The spread in historical surface warming across CMIP5 ESMs shows a weak correlation with inter-model
46   differences in radiative feedback or ocean heat uptake processes but a high correlation with inter-model
47   differences in radiative forcing owing to large variations in aerosol forcing across models (Forster et al.,
48   2013). Likewise, the spread in projected 21st century warming across ESMs depends strongly on emissions
49   scenario (Hawkins and Sutton, 2012; Chapter 4, Section 4.3.1). Strong emissions reductions would remove
50   aerosol forcing (Chapter 6, Section 6.7.2) and this could dominate the uncertainty in near-term warming
51   projections (Armour and Roe, 2011; Mauritsen and Pincus, 2017; Schwartz, 2018; Smith et al., 2019). On
52   post 2100 timescales carbon cycle uncertainty such as that related to permafrost thawing could become
53   increasingly important, especially under high emission scenarios (Chapter 5, Figure 5.30).
55   In summary, there is high confidence that cloud feedbacks are the dominant source of uncertainty for late 21st
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 1   century projections of transient global warming under increasing or stable emissions scenarios, whereas
 2   uncertainty is dominated by aerosol ERF in strong mitigation scenarios. Global ocean heat uptake is a
 3   smaller source of uncertainty in long-term surface warming. (high confidence).
 6   7.6     Metrics to evaluate emissions
 8   Emission metrics are used to compare the relative effect of emissions of different gases over time in terms of
 9   radiative forcing, global surface temperature or other climate effects. They are introduced in Chapter 1, Box
10   1.3. Chapter 8 of AR5 (Myhre et al., 2013b) comprehensively discussed different emission metrics so this
11   section focuses on updates since that report. Section 7.6.1 updates the physical assessment. Section 7.6.2
12   assesses developments in the comparison of emissions of short- and long-lived gases. Box 7.3 assesses
13   physical aspects of emission metric use within climate policy.
16   7.6.1     Physical description of metrics
18   This section discusses metrics that relate emissions to physical changes in the climate system. Other metrics,
19   for instance relating to economic costs or ‘damage’ are discussed in WG III Chapter 2. The same Chapter
20   also assesses literature examining to what extent different physical metrics are linked to cost-benefit and
21   cost-effectiveness metrics. One metric, the 100-year Global Warming Potential (GWP-100), has extensively
22   been employed in climate policy to report emissions of different greenhouse gases on the same scale. Other
23   physical metrics exist, which are discussed in this section.
25   Emission metrics can be quantified as the magnitude of the effect a unit mass of emission of a species has on
26   a key measure of climate change. This section focuses on physical measures such as the radiative forcing,
27   GSAT change, global average precipitation change, and global mean sea level rise (Myhre et al., 2013b;
28   Sterner et al., 2014; Shine et al., 2015). When used to represent a climate effect, the metrics are referred to as
29   absolute metrics and expressed in units of effect per kg (e.g., Absolute Global Warming Potential, AGWP or
30   Absolute Global Temperature-change Potential, AGTP). More commonly, these are compared with a
31   reference species (almost always CO2 in kg(CO2)), to give a dimensionless factor (written as e.g., Global
32   Warming Potential (GWP) or Global Temperature-change Potential (GTP)). The unit mass is usually taken
33   as a 1 kg instantaneous “pulse” (Myhre et al., 2013b), but can also refer to a “step” in emission rate of 1 kg
34   yr-1.
36   There is a cause-effect chain that links human activity to emissions, then from emissions to radiative forcing,
37   climate response, and climate impacts (Fuglestvedt et al., 2003). Each step in the causal chain requires an
38   inference or modelling framework that maps causes to effects. Emission metrics map from emissions of
39   some compound to somewhere further down the cause and effect chain, radiative forcing (e.g., GWP) or
40   temperature (e.g., GTP) or other effects (such as sea-level rise or socioeconomic impacts). While variables
41   later in the chain have greater policy or societal relevance, they are also subject to greater uncertainty
42   because each step in the chain includes more modelling systems, each of which brings its own uncertainty
43   (Balcombe et al., 2018; Chapter 1, Figure 1.15).
45   Since AR5, understanding of the radiative effects of emitted compounds has continued to evolve and these
46   changes are assessed in Section Metrics relating to precipitation and sea level have also been
47   quantified (Section Understanding of how the carbon-cycle response to temperature effects
48   emission metrics has improved. This allows the carbon cycle response to temperature to be more fully
49   included in the emission metrics presented here (Section There have also been developments in
50   approaches for comparing short-lived greenhouse gases to CO2 in the context of mitigation and global
51   surface temperature change (Section Emission metrics for selected key compounds are presented in
52   Section
55    Radiative properties and lifetimes.
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 2   The radiative properties and lifetimes of compounds are the fundamental component of all emission metrics.
 3   Since AR5, there have been advances in the understanding of the radiative properties of various compounds
 4   (see Sections 7.3.1, 7.3.2 and 7.3.3), and hence their effective radiative efficiencies (ERFs per unit change in
 5   concentration). For CO2, CH4 and N2O, better accounting of the spectral properties of these gases has led to
 6   re-evaluation of their SARF radiative efficiencies and their dependence on the background gas
 7   concentrations (Section 7.3.2). For CO2, CH4, N2O, CFC-11 and CFC-12 the tropospheric adjustments
 8   (Sections 7.3.1 and 7.3.2) are assessed to make a non-zero contribution to ERF. There is insufficient
 9   evidence to include tropospheric adjustments for other halogenated compounds. The re-evaluated effective
10   radiative efficiency for CO2 will affect all emission metrics relative to CO2.
12   The effective radiative efficiencies (including adjustments from Section 7.3.2) for 2019 background
13   concentrations for CO2, CH4 and N2O are assessed to be 1.36×10–5, 3.77×10–4 and 3.11×10–3 W m–2 ppb–1
14   respectively (see Table 7.15 for uncertainties), compared to AR5 assessments of 1.37×10–5, 3.63×10–4 and
15   3.00×10–3 W m–2 ppb–1. For CO2, increases due to the re-evaluated radiative properties and adjustments
16   balance the decreases due to the increasing background concentration. For CH4, increases due to the re-
17   evaluated radiative properties more than offset the decreases due to the increasing background concentration.
18   For N2O the addition of tropospheric adjustments increases the effective radiative efficiency. Radiative
19   efficiencies of halogenated species have been revised slightly (Section and for CFCs include
20   tropospheric adjustments.
22   The perturbation lifetimes of CH4 (Chapter 6, Section 6.3.1). and N2O (Chapter 5, Section have been
23   slightly revised since AR5 to be 11.8 ± 1.8 years and 109 ± 10 years (Table 7.15). The lifetimes of
24   halogenated compounds have also been slightly revised (Hodnebrog et al., 2020a).
26   Although there has been greater understanding since AR5 of the carbon cycle responses to CO2 emissions
27   (Chapter 5, Sections 5.4 and 5.5), there has been no new quantification of the response of the carbon-cycle
28   to an instantaneous pulse of CO2 emission since Joos et al. (2013).
31   Physical indicators
33   The basis of all the emission metrics is the time profile of effective radiative forcing (ERF) following the
34   emission of a particular compound. The emission metrics are then built up by relating the forcing to the
35   desired physical indicators. These forcing-response relationships can either be generated from emulators
36   (Tanaka et al., 2013; Gasser et al., 2017b; Cross-Chapter Box 7.1), or from analytical expressions based on
37   parametric equations (response functions) derived from more complex models (Myhre et al., 2013b).
39   To illustrate the analytical approach, the ERF time evolution following a pulse of emission can be considered
40   an Absolute Global Forcing Potential AGFP (similar to the Instantaneous Climate Impact of Edwards and
41   Trancik (2014)). This can be transformed into an Absolute Global Temperature Potential (AGTP) by
42   combining the radiative forcing with a global surface temperature response function. This temperature
43   response is typically derived from a two-layer energy balance emulator (Supplementary Material 7.SM.5;
44   Myhre et al., 2013b). For further physical indicators further response functions are needed based on the
45   radiative forcing or temperature, for instance. Sterner et al. (2014) used an upwelling-diffusion energy
46   balance model to derive the thermosteric component of sea level rise (SLR) as response functions to
47   radiative forcing or global surface temperature. A metric for precipitation combines both the radiative
48   forcing (AGFP) and temperature (AGTP) responses to derive an Absolute Global Precipitation Potential
49   AGPP (Shine et al., 2015). The equations relating these metrics are given in the Supplementary Material
50   7.SM.5.
52   The physical emission metrics described above are functions of time since typically the physical effects
53   reach a peak and then decrease in the period after a pulse emission as the concentrations of the emitted
54   compound decay. The value of the metrics can therefore be strongly dependent on the time horizon of
55   interest. All relative metrics (GWP, GTP etc) are also affected by the time dependence of the CO2 metrics in
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 1   the denominator. Instantaneous or endpoint metrics quantify the change (in radiative forcing, global surface
 2   temperature, global mean sea level) at a particular time after the emission. These can be appropriate when
 3   the goal is to not exceed a fixed target such as a temperature or global mean sea-level rise level at a specific
 4   time. Emission metrics can also be integrated from the time of emission. The most common of these is the
 5   Absolute Global Warming Potential (AGWP), which is the integral of the AGFP. The physical effect is then
 6   in units of forcing-years, degree-years or metre-years for forcing, temperature, or sea-level rise, respectively.
 7   These can be appropriate for trying to reduce the overall damage potential when the effect depends on how
 8   long the change occurs for, not just how large the change is. The integrated metrics still depend on the time
 9   horizon, though for the shorter-lived compounds this dependence is somewhat smoothed by the integration.
10   The integrated version of a metric is often denoted as iAGxx, although the integral of the forcing-based
11   metric (iAGFP) is known as the AGWP. Both the endpoint and integrated absolute metrics for non-CO2
12   species can be divided by the equivalent for CO2 to give relative emission metrics (e.g., GWP (=iGFP), GTP,
13   iGTP).
15   Each step from radiative forcing to global surface temperature to SLR introduces longer timescales and
16   therefore prolongs further the contributions to climate change of short-lived greenhouse gases (Myhre et al.,
17   2013b). Thus, short-lived greenhouse gases become more important (relative to CO2) for SLR than for
18   temperature or radiative forcing (Zickfeld et al., 2017). Integrated metrics include the effects of a pulse
19   emission from the time of emission up to the time horizon, whereas endpoint metrics only include the effects
20   that persist out to the time horizon. Because the largest effects of short-lived greenhouse gases occur shortly
21   after their emission and decline towards the end of the time period, short-lived greenhouse gases have
22   relatively higher integrated metrics than their corresponding endpoint metrics (Peters et al., 2011; Levasseur
23   et al., 2016).
25   For species perturbations that lead to a strong regional variation in forcing pattern, the regional temperature
26   response can be different to that for CO2. Regional equivalents to the global metrics can be derived by
27   replacing the global surface temperature response function with a regional response matrix relating forcing
28   changes in one region to temperature changes in another (Collins et al., 2013b; Aamaas et al., 2017; Lund et
29   al., 2017).
31   For the research discussed above, metrics for several physical variables can be constructed that are linear
32   functions of radiative forcing. Similar metrics could be devised for other climate variables provided they can
33   be related by response functions to radiative forcing or global surface temperature change. The radiative
34   forcing does not increase linearly with emissions for any species, but the non-linearities (for instance
35   changes in CO2 radiative efficiency) are small compared to other uncertainties.
38   Carbon cycle responses and other indirect contributions
40   The effect of a compound on climate is not limited to its direct radiative forcing. Compounds can perturb the
41   carbon cycle affecting atmospheric CO2 concentrations. Chemical reactions from emitted compounds can
42   produce or destroy other greenhouse gases or aerosols.
44   Any agent that warms the surface perturbs the terrestrial and oceanic carbon fluxes (Chapter 5, Sections
45   5.4.3 and 5.4.4), typically causing a net flux of CO2 into the atmosphere and hence further warming. This
46   aspect is already included in the carbon cycle models that are used to generate the radiative effects of a pulse
47   of CO2 (Joos et al., 2013), but was neglected for non-CO2 compounds in the conventional metrics so this
48   introduces an inconsistency and bias in the metric values (Gillett and Matthews, 2010; MacDougall et al.,
49   2015; Tokarska et al., 2018). A simplistic account of the carbon cycle response was tentatively included in
50   AR5 based on a single study (Collins et al., 2013b). Since AR5 this understanding has been revised (Gasser
51   et al., 2017b; Sterner and Johansson, 2017) using simple parameterised carbon cycle models to derive the
52   change in CO2 surface flux for a unit temperature pulse as an impulse response function to temperature. In
53   Collins et al. (2013a) this response function was assumed to be simply a delta function, whereas the newer
54   studies include a more complete functional form accounting for subsequent re-uptake of CO2 after the
55   removal of the temperature increase. Accounting for re-uptake has the effect of reducing the carbon-cycle
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 1   responses associated with the metrics compared to AR5, particularly at large time horizons. The increase in
 2   any metric due to the carbon cycle response can be derived from the convolution of the global surface
 3   temperature response with the CO2 flux response to temperature and the equivalent metric for CO2 (equation
 4   7.SM.5.5 in the Supplementary Material). Including this response also increases the duration of the effect of
 5   short-lived greenhouse gases on climate (Fu et al., 2020). An alternative way of accounting for the carbon
 6   cycle temperature response would be to incorporate it into the temperature response function (the response
 7   functions used here and given in Supplementary Material 7.SM.5.2 do not explicitly do this). If this were
 8   done, the correction could be excluded from both the CO2 and non-CO2 forcing responses as in Hodnebrog et
 9   al. (2020a).
11   Including the carbon cycle response for non-CO2 treats CO2 and non-CO2 compounds consistently and
12   therefore we assess that its inclusion more accurately represents the climate effects of non-CO2 species.
13   There is high confidence in the methodology of using carbon cycle models for calculating the carbon cycle
14   response. The magnitude of the carbon cycle response contributions to the emission metrics vary by a factor
15   of two between Sterner and Johansson (2017) and Gasser et al. (2017b). The central values are taken from
16   Gasser et al. (2017b) as the OSCAR 2.2 model used is based on parameters derived from CMIP5 models,
17   and the climate-carbon feedback magnitude is therefore similar to the CMIP5 multi-model mean (Arora et
18   al., 2013; Lade et al., 2018). As values have only been calculated in two simple parameterised carbon cycle
19   models the uncertainty is assessed to be ±100%. Due to few studies and a factor of two difference between
20   them, there is low confidence that the magnitude of the carbon cycle response is within the higher end of this
21   uncertainty range, but high confidence that the sign is positive. Carbon cycle responses are included in all the
22   metrics presented in Tables 7.15 and Supplementary Table 7.SM.7. The carbon cycle contribution is lower
23   than in AR5, but there is high confidence in the need for its inclusion and the method by which it is
24   quantified.
26   Emissions of non-CO2 species can affect the carbon cycle in other ways: emissions of ozone precursors can
27   reduce the carbon uptake by plants (Collins et al., 2013b); emissions of reactive nitrogen species can fertilize
28   plants and hence increase the carbon uptake (Zaehle et al., 2015); and emissions of aerosols or their
29   precursors can affect the utilisation of light by plants (Cohan et al., 2002; Mercado et al., 2009; Mahowald et
30   al., 2017) (see Chapter 6, Section 6.4.4 for further discussion). There is robust evidence that these processes
31   occur and are important, but insufficient evidence to determine the magnitude of their contributions to
32   emission metrics. Ideally, emission metrics should include all indirect effects to be consistent, but limits to
33   our knowledge restrict how much can be included in practice.
35   Indirect contributions from chemical production or destruction of other greenhouse gases are quantified in
36   Chapter 6, Section 6.4. For methane, AR5 (Myhre et al., 2013b) assessed that the contributions from effects
37   on ozone and stratospheric water vapour add 50% ± 30% and 15% ± 11% to the emission-based ERF, which
38   were equivalent to 1.8 ± 0.7 ×10–4 and 0.5 ± 0.4 ×10–4 W m-2 ppb (CH4)-1. In AR6 the radiative efficiency
39   formulation is preferred as it is independent of the assumed radiative efficiency for methane. The assessed
40   contributions to the radiative efficiency for methane due to ozone are 1.4 ± 0.7 ×10–4 W m-2 ppb (CH4)-1,
41   based on 0.14 W m-2 forcing from a 1023 ppb (1850 to 2014) methane change (Thornhill et al., 2021b). The
42   contribution from stratospheric water vapour is 0.4 ± 0.4 ×10–4 W m-2 ppb (CH4)-1, based on 0.05 W m-2
43   forcing from a 1137 ppb (1750 to 2019) methane change (Section N2O depletes upper stratospheric
44   ozone (a positive forcing) and reduces the methane lifetime. In AR5 the methane lifetime effect was assessed
45   to reduce methane concentrations by 0.36 ppb per ppb increase in N2O, with no assessment of the effective
46   radiative forcing from ozone. This is now increased to –1.7 ppb methane per ppb N2O (based on a methane
47   lifetime decrease of 4% ± 4% for a 55 ppb increase in N2O (Thornhill et al., 2021b) and a radiative
48   efficiency of 5.5 ± 0.4 ×10–4 W m-2 ppb (N2O)-1 through ozone (Thornhill et al., 2021b). In summary, GWPs
49   and GTPs for methane and nitrous oxide are slightly lower than in AR5 (medium confidence) due to
50   revisions in their lifetimes and updates to their indirect chemical effects.
52   Methane can also affect the oxidation pathways of aerosol formation (Shindell et al., 2009) but the available
53   literature is insufficient to make a robust assessment of this. Hydrocarbon and molecular hydrogen oxidation
54   also leads to tropospheric ozone production and change in methane lifetime (Collins et al., 2002; Hodnebrog
55   et al., 2018). For reactive species the emission metrics can depend on where the emissions occur, and the
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 1   season of emission (Aamaas et al., 2016; Lund et al., 2017; Persad and Caldeira, 2018). AR5 included a
 2   contribution to the emission metrics for ozone-depleting substances (ODSs) from the loss of stratospheric
 3   ozone. The assessment of ERFs from ODSs in Chapter 6 (Section 6.4.2) suggests the quantification of these
 4   terms may be more uncertain than the formulation in AR5 so these are not included here.
 6   Oxidation of methane leads ultimately to the net production of atmospheric CO2 (Boucher et al., 2009). This
 7   yield is less than 100% (on a molar basis) due to uptake by soils and some of the reaction products (mainly
 8   formaldehyde) being directly removed from the atmosphere before being completely oxidised. Estimates of
 9   the yield are 61% (Boucher et al., 2009) and 88% (Shindell et al., 2017), so the assessed range is 50-100%
10   with a central value of 75% (low confidence). For methane and hydrocarbons from fossil sources, this will
11   lead to additional fossil CO2 in the atmosphere whereas for biogenic sources of methane or hydrocarbons,
12   this replaces CO2 that has been recently removed from the atmosphere. Since the ratio of molar masses is
13   2.75, 1 kg of methane generates 2.1± 0.7 kg CO2 for a 75% yield. For biogenic methane the soil uptake and
14   removal of partially-oxidised products is equivalent to a sink of atmospheric CO2 of 0.7 ± 0.7 kg per kg
15   methane. The contributions of this oxidation effect to the methane metric values allow for the time delay in
16   the oxidation of methane. Methane from fossil fuel sources has therefore slightly higher emission metric
17   values than those from biogenic sources (high confidence). The CO2 can already be included in carbon
18   emission totals (Muñoz and Schmidt, 2016) so care needs to be taken when applying the fossil correction to
19   avoid double counting.
22   Comparing long-lived with short-lived greenhouse gases
24   Since AR5 there have been developments in how to account for the different behaviours of short-lived and
25   long-lived compounds. Pulse-based emission metrics for short-lived greenhouse gases with lifetimes less
26   than twenty years are very sensitive to the choice of time horizon (e.g. Pierrehumbert, 2014). Global surface
27   temperature changes following a pulse of CO2 emissions are roughly constant in time (the principle behind
28   TCRE, Figure 7.21b, Chapter 5, Section 5.5.1) whereas the temperature change following a pulse of short-
29   lived greenhouse gas emission declines with time. In contrast to a one-off pulse, a step change in short-lived
30   greenhouse gas emissions that is maintained indefinitely causes a concentration increase that eventually
31   equilibrates to a steady state in a way that is more comparable to a pulse of CO2. Similarly the resulting
32   change in global surface temperature from a step change in short-lived greenhouse gases (Figure 7.21a) after
33   a few decades increases only slowly (due to accumulation of heat in the deep ocean) and hence its effects are
34   more similar to a pulse of CO2 (Smith et al., 2012; Lauder et al., 2013; Allen et al., 2016, 2018b). The
35   different time dependence of short-lived and long-lived compounds can be accounted for exactly with the
36   CO2 forcing equivalent metric (Wigley, 1998; Allen et al., 2018b; Jenkins et al., 2018) that produces a CO2
37   emission time profile such that the radiative forcing matches the time evolution of that from the non-CO2
38   emissions. But other metric approaches can approximate this exact approach.
40   The similarity in behaviour of step changes in short-lived greenhouse gas emissions and pulses of CO2
41   emissions has recently been used to formulate new emissions metric concepts (Collins et al., 2020). For
42   short-lived greenhouse gases, these new concepts use a step change in the rate of emissions, in contrast to an
43   instantaneous pulse in a given year that is typically used (e.g. Myhre et al., 2013b). Metrics for step emission
44   changes are denoted here by a superscript “S” (e.g., 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑋𝑋𝑆𝑆 is the absolute global surface temperature
45   change potential from a unit step change in emissions of species “X”). These can be derived by integrating
46   the more standard pulse emission changes up to the time horizon. The response to a step emission change is
47   therefore equivalent to the integrated response to a pulse emission (𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑋𝑋𝑆𝑆 = 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑋𝑋 ); and the radiative
48   forcing response to a step emission change 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑋𝑋𝑆𝑆 is equivalent to the integrated forcing
49   response 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑋𝑋 which is the AGWP. The step metric for short-lived greenhouse gases can then be
50   compared with the pulse metric for CO2 in a ratio 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑋𝑋𝑆𝑆 /𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐶𝐶𝐶𝐶2 (Collins et al., 2020). This is referred to
51   as a combined-GTP (CGTP) in Collins et al. (2020), and has units of years (the standard GTP is
52   dimensionless). This CGTP shows less variation with time than the standard GTP (comparing Figure 7.21c
53   with Figure 7.21d) and provides a scaling for comparing a change in emission rate (in kg yr-1) of short-lived
54   greenhouse gases with a pulse emission or change in cumulative CO2 emissions (in kg). Cumulative CO2
55   equivalent emissions are given by CGTP × emission rate of short-lived greenhouse gases. The CGTP can be
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 1   calculated for any species, but it is least dependent on the chosen time horizon for species with lifetimes less
 2   than half the time horizon of the metric (Collins et al., 2020). Pulse-step metrics can therefore be useful
 3   where time dependence of pulse metrics, like GWP or GTP, complicates their use (see Box 7.3).
 5   For a stable global warming from non-CO2 climate agents (gas or aerosol) their effective radiative forcing
 6   needs to gradually decrease (Tanaka and O’Neill, 2018). Cain et al. (2019) find this decrease to be around
 7   0.3% yr-1 for the climate response function in AR5 (Myhre et al., 2013b). To account for this, a quantity
 8   referred to as GWP* has been defined that combines emissions (pulse) and changes in emission levels (step)
 9   approaches (Cain et al., 2019; Smith et al., 2021) 2. The emission component accounts for the need for
10   emissions to decrease to deliver a stable warming. The step (sometimes referred to as flow or rate) term in
11   GWP* accounts for the change in global surface temperature that arises in from a change in short-lived
12   greenhouse gas emission rate, as in CGTP, but here approximated by the change in emissions over the
13   previous 20 years.
15   Cumulative CO2 emissions and GWP*-based cumulative CO2 equivalent greenhouse gas (GHG) emissions
16   multiplied by TCRE closely approximate the global warming associated with emissions timeseries (of CO2
17   and GHG, respectively) from the start of the time-series (Lynch et al., 2020). Both the CGTP and GWP*
18   convert short-lived greenhouse gas emission rate changes into cumulative CO2 equivalent emissions, hence
19   scaling these by TCRE gives a direct conversion from short-lived greenhouse gas emission to global surface
20   temperature change. By comparison expressing methane emissions as CO2 equivalent emissions using GWP-
21   100 overstates the effect of constant methane emissions on global surface temperature by a factor of 3-4 over
22   a 20-year time horizon (Lynch et al., 2020, their Figure 5), while understating the effect of any new methane
23   emission source by a factor of 4-5 over the 20 years following the introduction of the new source (Lynch et
24   al., 2020, their Figure 4).
28   Figure 7.21: Emission metrics for two short-lived greenhouse gases: HFC-32 and CH4, (lifetimes of 5.4 and 11.8
29                years). The temperature response function comes from Supplementary Material 7.SM.5.2. Values for
30                non-CO2 species include the carbon cycle response (Section Results for HFC-32 have been
31                divided by 100 to show on the same scale. (a) temperature response to a step change in short-lived
32                greenhouse gas emission. (b) temperature response to a pulse CO2 emission. (c) conventional GTP
33                metrics (pulse vs pulse). (d) combined-GTP metric (step versus pulse). Further details on data sources and
34                processing are available in the chapter data table (Table 7.SM.14).
36   [END FIGURE 7.21 HERE]
39   Figure 7.22 explores how cumulative CO2 equivalent emissions estimated for methane vary under different
40   emission metric choices and how estimates of the global surface air temperature (GSAT) change deduced
41   from these cumulative emissions compare to the actual temperature response computed with the two-layer
42   emulator. Note that GWP and GTP metrics were not designed for use under a cumulative carbon dioxide
43   equivalent emission framework (Shine et al., 1990, 2005), even if they sometimes are (e.g. Cui et al., 2017;
44   Howard et al., 2018) and analysing them in this way can give useful insights into their physical properties.
45   Using these standard metrics under such frameworks, the cumulative CO2 equivalent emission associated
46   with methane emissions would continue to rise if methane emissions were substantially reduced but
47   remained above zero. In reality, a decline in methane emissions to a smaller but still positive value could
48   cause a declining warming. GSAT changes estimated with cumulative CO2 equivalent emissions computed
49   with GWP-20 matches the warming trend for a few decades but quickly overestimates the response.
50   Cumulative emissions using GWP-100 perform well when emissions are increasing but not when they are
51   stable or decreasing. Cumulative emissions using GTP-100 consistently underestimate the warming.
52   Cumulative emissions using either CGTP or GWP* approaches can more closely match the GSAT evolution
53   (Allen et al., 2018b; Cain et al., 2019; Collins et al., 2020; Lynch et al., 2020).

      To calculate CO2 equivalent emissions under GWP*, the short-lived greenhouse gas emissions are multiplied by GWP100 × 0.28
     and added to the net emission increase or decrease over the previous 20 years multiplied by GWP100 x 4.24 (Smith et al., 2021).
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 2   In summary, new emission metric approaches such as GWP* and CGTP are designed to relate emission
 3   changes in short-lived greenhouse gases to emissions of CO2 as they better account for the different physical
 4   behaviours of short and long-lived gases. Through scaling the corresponding cumulative CO2 equivalent
 5   emissions by the TCRE, the GSAT response from emissions over time of an aggregated set of gases can be
 6   estimated. Using either these new approaches, or treating short and long-lived GHG emission pathways
 7   separately, can improve the quantification of the contribution of emissions to global warming within a
 8   cumulative emission framework, compared to approaches that aggregate emissions of GHGs using standard
 9   CO2 equivalent emission metrics. As discussed in Box 7.3, there is high confidence that multi-gas emission
10   pathways with the same time dependence of aggregated CO2 equivalent emissions estimated from standard
11   approaches, such as weighting emissions by their GWP-100 values, rarely lead to the same estimated
12   temperature outcomes..
17   Figure 7.22: Explores how cumulative carbon dioxide equivalent emissions estimated for methane vary under
18                different emission metric choices and how estimates of the global surface air temperature (GSAT)
19                change deduced from these cumulative emissions compare to the actual temperature response
20                computed with the two-layer emulator (solid black lines). Panels a) and b) show the SSP4-6.0 and
21                SSP1-2.6 scenarios respectively. The panels show annual methane emissions as the dotted lines (left
22                axis) from 1750–2100. The solid lines can be read as either estimates of GSAT change or estimates of the
23                cumulative carbon dioxide equivalent emissions. This is because they are related by a constant factor, the
24                TCRE. Thus, values can be read using either of the right hand axes. Emission metric values are taken
25                from Table 7.15. The GWP* calculation is given in Section The two-layer emulator has been
26                calibrated to the central values of the report’s assessment (see Supplementary Material 7.SM.5.2). Further
27                details on data sources and processing are available in the chapter data table (Table 7.SM.14).
29   [END FIGURE 7.22 HERE]
31   Emission metrics by compounds
33   Emission metrics for selected compounds are presented in Table 7.15, with further compounds presented in
34   the Supplementary Material Table 7.SM.7. The evolution of the CO2 concentrations in response to a pulse
35   emission is as in AR5 (Joos et al., 2013; Myhre et al., 2013b), the perturbation lifetimes for CH4 and N2O are
36   from Section The lifetimes and radiative efficiencies for halogenated compounds are taken from
37   Hodnebrog et al. (2020a). Combined metrics (CGTPs) are presented for compounds with lifetimes less than
38   20 years. Note CGTP has units of years and is applied to a change in emission rate rather than a change in
39   emission amount. Changes since AR5 are due to changes in radiative properties and lifetimes (Section
40, and indirect contributions (Section Table 7.15 also gives overall emission uncertainties in
41   the emission metrics due to uncertainties in radiative efficiencies, lifetimes and the climate response function
42   (Supplementary Material Tables 7.SM.8 to 7.SM.13)
44   Following their introduction in AR5 the assessed metrics now routinely include the carbon-cycle response
45   for non-CO2 gases (Section As assessed in this earlier section, the carbon cycle contribution is
46   lower than in AR5. Contributions to CO2 formation are included for methane depending on whether or not
47   the source originates from fossil carbon, thus methane from fossil fuel sources has slightly higher emission
48   metric values than that from non-fossil sources.
51   [START TABLE 7.15 HERE]
53   Table 7.15: Emission metrics for selected species: Global Warming Potential (GWP), Global Temperature-change
54               Potential (GTP). All values include carbon cycle responses as described in Section Combined-
55               GTPs (CGTPs) are shown only for species with a lifetime less than 20 years (see Section Note
56               CGTP has units of years and is applied to a change in emission rate rather than a change in emission
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 1                  amount. The radiative efficiencies are as described in Section 7.3.2 and include tropospheric adjustments
 2                  where assessed to be non-zero in Section The climate response function is from Supplementary
 3                  Material 7.SM.5.2. Uncertainty calculations are presented in Supplementary Tables 7.SM.8 to 7.SM.13.
 4                  Chemical effects of CH4 and N2O are included (Section Contributions from stratospheric ozone
 5                  depletion to halogenated species metrics are not included. Supplementary Table 7.SM.7 presents the full
 6                  table.
           #           Lifetime     Radiative     GWP- GWP-         GWP-       GTP-    GTP-       CGTP-     CGTP-
           Species     (years)      efficiency    20   100          500        50      100        50        100
                                    (W m-2                                                        (years)   (years)
           CO2         Multiple    1.33±0.16      1.      1.000     1.000      1.000   1.000

           CH4-        11.8 ±1.8   5.7±1.4×10-4   82.5    29.8      10.0 ±3.8 13.2     7.5 ±2.9   2823      3531 ±1385
           fossil                                 ±25.8   ±11                 ±6.1                ±1060

           CH4-non 11.8 ±1.8       5.7±1.4×10-4   80.8    27.2      7.3 ±3.8   10.3    4.7 ±2.9   2701      3254 ±1364
           fossil                                 ±25.8   ±11                  ±6.1               ±1057

           N2O         109 ±10     2.8±1.1 ×10-3 273      273       130 ±64    290     233 ±110
                                                 ±118     ±130                 ±140

           HFC-32 5.4 ±1.1         1.1±0.2 ×10-1 2693     771       220 ±87    181     142 ±51    78175     92888
                                                 ±842     ±292                 ±83                ±29402    ±36534

           HFC-        14.0 ±2.8   1.67±0.32      4144    1526      436 ±173 733       306 ±119 146670      181408
           134a                    ×10-1          ±1160   ±577               ±410               ±53318      ±71365

           CFC-11 52.0 ±10.4       2.91±0.65      8321    6226      2093       6351    3536
                                   ×10-1          ±2419   ±2297     ±865       ±2342   ±1511

           PFC-14      50000       9.89±0.19      5301    7380      10587      7660    9055
                                   ×10-2          ±1395   ±2430     ±3692      ±2464   ±3128

 9   [END TABLE 7.15 HERE]
12   [START BOX 7.3 HERE]
14   BOX 7.3:       Physical considerations in emission-metric choice
16   Following AR5, this report does not recommend an emission metric because the appropriateness of the
17   choice depends on the purposes for which gases or forcing agents are being compared. Emission metrics can
18   facilitate the comparison of effects of emissions in support of policy goals. They do not define policy goals
19   or targets but can support the evaluation and implementation of choices within multi-component policies
20   (e.g., they can help prioritise which emissions to abate). The choice of metric will depend on which aspects
21   of climate change are most important to a particular application or stakeholder and over which time-
22   horizons. Different international and national climate policy goals may lead to different conclusions about
23   what is the most suitable emission metric (Myhre et al., 2013b).
25   GWP and GTP give the relative effect of pulse emissions, i.e. how much more energy is trapped (GWP) or
26   how much warmer (GTP) the climate would be when unit emissions of different compounds are compared
27   (Section Consequently, these metrics provide information on how much energy accumulation
28   (GWP) or how much global warming (GTP) could be avoided (over a given time period, or at a given future
29   point in time) by avoiding the emission of a unit of a short-lived greenhouse gas compared to avoiding a unit
30   of CO2. By contrast, the new metric approaches of Combined-GTP and GWP* closely approximate the
31   additional effect on climate from a time-series of short-lived greenhouse gas emissions, and can be used to
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 1   compare this to the effect on temperature from the emission or removal of a unit of CO2 (Allen et al., 2018b;
 2   Collins et al., 2020; Section
 4   If global surface temperature stabilization goals are considered, cumulative CO2 equivalent emissions
 5   computed with the GWP-100 emission metric would continue to rise when short-lived greenhouse gas
 6   emissions are reduced but remain above zero (Figure 7.22b). Such as rise would not match the expected
 7   global surface temperature stabilization or potential decline in warming that comes from a reduction in
 8   emissions of short-lived greenhouse gases (Pierrehumbert, 2014; Allen et al., 2018b; Cain et al., 2019;
 9   Collins et al., 2020; Lynch et al., 2020, 2021). This is relevant to net zero greenhouse gas emission goals
10   (See Section 7.6.2 and Chapter 1, Box 1.4).
12   When individual gases are treated separately in climate model emulators (Cross-Chapter Box 7.1), or
13   weighted and aggregated using an emission metric approach (such as CGTP or GWP*) which translate the
14   distinct behaviour from cumulative emissions of short-lived gases, ambiguity in the future warming
15   trajectory of a given emission scenario can be substantially reduced (Cain et al., 2019; Denison et al., 2019;
16   Collins et al., 2020; Lynch et al., 2021). The degree of ambiguity varies with the emissions scenario. For
17   mitigation pathways that limit warming to 2°C with an even chance, the ambiguity arising from using GWP-
18   100 as sole constraint on emissions of a mix of greenhouse gases (without considering their economic
19   implications or feasibility) could be as much as 0.17°C, which represents about one fifth of the remaining
20   global warming in those pathways (Denison et al., 2019). If the evolution of the individual GHGs are not
21   known, this can make it difficult to evaluate how a given global multi-gas emission pathway specified only
22   in CO2 equivalent emissions would achieve (or not) global surface temperature goals. This is potentially an
23   issue as Nationally Determined Contributions frequently make commitments in terms of GWP-100 based
24   CO2- equivalent emissions at 2030 without specifying individual gases (Denison et al., 2019). Clear and
25   transparent representation of the global warming implications of future emission pathways including
26   Nationally Determined Contributions could be achieved either by their detailing pathways for multiple gases
27   or by detailing a pathway of cumulative carbon dioxide equivalent emission approach aggregated across
28   greenhouse gases evaluated by either GWP* or CGTP metric approaches (Cain et al., 2019; Collins et al.,
29   2020; Lynch et al., 2021). Note that although the Paris Agreement Rulebook asks countries to report
30   emissions of individual greenhouse gases separately for the global stocktake (Decision 18/CMA.1, annex,
31   paragraph 38) which can allow the current effects of their emissions on global surface temperature to be
32   accurately estimated, estimates of future warming are potentially ambiguous where emissions are aggregated
33   using GWP-100 or other pulse metrics.
35   Although there is significant history of using single-basket approaches, supported by emission metrics such
36   as GWP-100, in climate policies such as the Kyoto Protocol, multi-basket approaches also have many
37   precedents in environmental management, including the Montreal Protocol (Daniel et al., 2012). Further
38   assessment of the performance of physical and economics-based metrics in the context of climate change
39   mitigation is provided in the contribution of Working Group III to the AR6.
41   [END BOX 7.3 HERE]
44   7.6.2   Applications of emission metrics
46   One prominent use of emission metrics is for comparison of efforts measured against climate change goals or
47   targets. One of the most commonly discussed goals are in Article 2 of the Paris Agreement which aims to
48   limit the risks and impacts of climate change by setting temperature goals. In addition, the Paris Agreement
49   has important provisions which relate to how the goals are to be achieved, including making emissions
50   reductions in a manner that does not threaten food production (Article 2), an early emissions peaking target,
51   and the aim to “achieve a balance between anthropogenic emissions by sources and removals by sinks of
52   greenhouse gases in the second half of this century” (Article 4). Article 4 also contains important context
53   regarding international equity, sustainable development, and poverty reduction. Furthermore, the United
54   Nations Framework Convention on Climate Change (UNFCCC) sets out as its ultimate objective, the
55   “stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous
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 1   anthropogenic interference with the climate system.”
 3   How the interpretation of the Paris Agreement and the meaning of “net zero” emissions, reflects on the
 4   appropriate choice of metric is an active area of research (Schleussner et al., 2016, 2019; Fuglestvedt et al.,
 5   2018; Collins et al., 2020). Several possible scientific interpretations of the Article 2 and 4 goals can be
 6   devised, and these along with emission metric choice have implications both for when a balance in GHG
 7   emissions, net zero CO2 emissions or net zero GHG emissions are achieved, and for their meaning in terms
 8   of temperature outcome (Fuglestvedt et al., 2018; Rogelj et al., 2018; Wigley, 2018). In AR6 net zero
 9   greenhouse gas emissions is defined as the condition in which metric-weighted anthropogenic GHG
10   emissions are balanced by metric-weighted anthropogenic GHG removals over a specified period (see
11   Chapter 1, Box 1.4, Appendix VII: Glossary). The quantification of net zero GHG emissions depends on the
12   GHG emission metric chosen to compare emissions and removals of different gases, as well as the time
13   horizon chosen for that metric. As the choice of emission metric affects the quantification of net zero GHG
14   emissions, it therefore affects the resulting temperature outcome after net zero emissions are achieved
15   (Lauder et al., 2013; Rogelj et al., 2015; Fuglestvedt et al., 2018; Schleussner et al., 2019). Schleussner et al.(
16   2019) note that declining temperatures may be a desirable outcome of net zero. Rogelj and Schleussner
17   (2019) also point out that the physical metrics raise questions of equity and fairness between developed and
18   developing countries.
20   Based on SR1.5 (Allen et al., 2018a), there is high confidence that achieving net zero CO2 emissions and
21   declining non-CO2 radiative forcing would halt human-induced warming. Based on (Bowerman et al., 2013;
22   Pierrehumbert, 2014; Fuglestvedt et al., 2018; Tanaka and O’Neill, 2018; Schleussner et al., 2019) there is
23   also high confidence that reaching net zero GHG emissions as quantified by GWP-100 typically leads to
24   reductions from peak global surface temperature after net zero GHGs emissions are achieved, depending on
25   the relative sequencing of mitigation of short-lived and long-lived species. If both short- and long-lived
26   species are mitigated together, then temperatures peak and decline. If mitigation of short-lived species occurs
27   much earlier than that of long-lived species, then temperatures stabilise very near peak values, rather than
28   decline. Temperature targets can be met even with positive net GHG emissions based on GWP-100 (Tanaka
29   and O’Neill, 2018). As demonstrated by Allen et al. (2018b), Cain et al. (2019), Schleussner et al. (2019) and
30   Collins et al. (2020) reaching net zero GHG emissions when quantified using the new emission metric
31   approaches such as CGTP or GWP* would lead to an approximately similar temperature evolution as
32   achieving net zero CO2. Hence, net zero CO2 and net zero GHG quantified using these new approaches
33   would both lead to approximately stable contributions to temperature change after net zero emissions are
34   achieved (high confidence).
36   Comparisons with emission or global surface temperature stabilisation goals are not the only role for
37   emissions metrics. Other important roles include those in pricing approaches where policymakers choose to
38   compare short-lived and long-lived climate forcers (e.g. Manne and Richels, 2001), and in life cycle analyses
39   (e.g. Hellweg and Milà i Canals, 2014). Several papers have reviewed the issue of metric choice for life
40   cycle analyses, noting that analysts should be aware of the challenges and value judgements inherent in
41   attempting to aggregate the effects of forcing agents with different timescales onto a common scale (e.g.
42   Mallapragada and Mignone, 2017) and recommend aligning metric choice with policy goals as well as
43   testing sensitivities of results to metric choice (Cherubini et al., 2016). Furthermore, life cycle analyses
44   approaches which are sensitive to choice of emission metric benefit from careful communication of the
45   reasons for the sensitivity (Levasseur et al., 2016).

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 1   Frequently Asked Questions
 3   [START FAQ7.1 HERE]
 5   FAQ 7.1:     What is the Earth’s energy budget, and what does it tell us about climate change?
 7   The Earth’s energy budget describes the flow of energy within the climate system. Since at least 1970 there
 8   has been a persistent imbalance in the energy flows that has led to excess energy being absorbed by the
 9   climate system. By measuring and understanding these energy flows and the role that human activities play
10   in changing them, we are better able to understand the causes of climate change and project future climate
11   change more accurately.
13   Our planet receives vast amounts of energy every day in the form of sunlight. Around a third of the sunlight
14   is reflected back to space by clouds, by tiny particles called aerosols, and by bright surfaces such as snow
15   and ice. The rest is absorbed by the ocean, land, ice, and atmosphere. The planet then emits energy back out
16   to space in the form of thermal radiation. In a world that was not warming or cooling, these energy flows
17   would balance. Human activity has caused an imbalance in these energy flows.
19   We measure the influence of various human and natural factors on the energy flows at the top of our
20   atmosphere in terms of radiative forcings, where a positive radiative forcing has a warming effect and a
21   negative radiative forcing has a cooling effect. In response to these forcings, the Earth system will either
22   warm or cool, so as to restore balance through changes in the amount of outgoing thermal radiation (the
23   warmer the Earth, the more radiations it emits). Changes in Earth’s temperature in turn lead to additional
24   changes in the climate system (known as climate feedbacks) that either amplify or dampen the original
25   effect. For example, Arctic sea-ice has been melting as the Earth warms, reducing the amount of reflected
26   sunlight and adding to the initial warming (an amplifying feedback). The most uncertain of those climate
27   feedbacks are clouds, as they respond to warming in complex ways that affect both the emission of thermal
28   radiation and the reflection of sunlight. However, we are now more confident that cloud changes, taken
29   together, will amplify climate warming (see FAQ 7.2).
31   Human activities have unbalanced these energy flows in two main ways. First, increases in greenhouse gas
32   levels have led to more of the emitted thermal radiation being absorbed by the atmosphere, instead of being
33   released to space. Second, increases in pollutants have increased the amount of aerosols such as sulphates in
34   the atmosphere (see FAQ 6.1). This has led to more incoming sunlight being reflected away, by the aerosols
35   themselves and through the formation of more cloud drops, which increases the reflectivity of clouds (see
36   FAQ 7.2).
38   Altogether, the global energy flow imbalance since the 1970s has been just over half a watt per square metre
39   of the Earth’s surface. This sounds small, but because the imbalance is persistent and because Earth’s surface
40   is large, this adds up to about 25 times the total amount of primary energy consumed by human society,
41   compared over 1971 to 2018. Compared to the IPCC Fifth Assessment Report, we are now better able to
42   quantify and track these energy flows from multiple lines of evidence, including satellite data, direct
43   measurements of ocean temperatures, and a wide variety of other Earth system observations (see FAQ 1.1).
44   We also have a better understanding of the processes contributing to this imbalance, including the complex
45   interactions between aerosols, clouds and radiation.
47   Research has shown that the excess energy since the 1970s has mainly gone into warming the ocean (91%),
48   followed by the warming of land (5%) and the melting ice sheets and glaciers (3%). The atmosphere has
49   warmed substantially since 1970, but because it is comprised of thin gases it has absorbed only 1% of the
50   excess energy (FAQ 7.1, Figure 1). As the ocean has absorbed the vast majority of the excess energy,
51   especially within their top two kilometres, the deep ocean is expected to continue to warm and expand for
52   centuries to millennia, leading to long-term sea level rise – even if atmospheric greenhouse gas levels were
53   to decline (see FAQ 5.3). This is in addition to the sea level rise expected from melting ice sheets and
54   glaciers.
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 1   Understanding the Earth’s energy budget also helps to narrow uncertainty in future projections of climate.
 2   By testing climate models against what we know about the Earth’s energy budget, we can make more
 3   confident projections of surface temperature changes we might expect this century and beyond.
 8   FAQ7.1, Figure 1: The Earth’s energy budget compares the flows of incoming and outgoing of energy that are
 9                     relevant for the climate system. Since the at least the 1970s, less energy is flowing out than is
10                     flowing in, which leads to excess energy being absorbed by the ocean, land, ice and atmosphere,
11                     with the ocean absorbing 91%.
15   [END FAQ 7.1 HERE]

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 1   [START FAQ 7.2 HERE]
 3   FAQ 7.2:     Clouds – What is the role in a warming climate?
 5   One of the biggest challenges in climate science has been to predict how clouds will change in a warming
 6   world and whether those changes will amplify or partially offset the warming caused by increasing
 7   concentrations of greenhouse gases and other human activities. Scientists have made significant progress
 8   over the past decade and are now more confident that changes in clouds will amplify, rather than offset,
 9   global warming in the future.
11   Clouds cover roughly two thirds of the Earth’s surface. They consist of small droplets and/or ice crystals,
12   which form when water vapour condenses or deposits around tiny particles called aerosols (such as salt,
13   dust, or smoke). Clouds play a critical role in the Earth’s energy budget at the top of atmosphere and
14   therefore influence Earth’s surface temperature (see FAQ 7.1) . The interactions between clouds and the
15   climate are complex and varied. Clouds at low altitudes tend to reflect incoming solar energy back to space,
16   preventing this energy from reaching and warming the Earth and causing a cooling effect. On the other hand,
17   higher clouds tend to trap (i.e., absorb and then emit at a lower temperature) some of the energy leaving the
18   Earth, leading to a warming effect. On average, clouds reflect back more incoming energy than the amount
19   of outgoing energy they trap, resulting in an overall net cooling effect on the present climate. Human
20   activities since the pre-industrial era have altered this climate effect of clouds in two different ways: by
21   changing the abundance of the aerosol particles in the atmosphere and by warming the Earth’s surface,
22   primarily as a result of increases in greenhouse gas emissions.
24   The concentration of aerosols in the atmosphere has markedly increased since the pre-industrial era, and this
25   has had two important effects on clouds. First, clouds now reflect more incoming energy because cloud
26   droplets have become more numerous and smaller. Second, smaller droplets may delay rain formation,
27   thereby making the clouds last longer, although this effect remains uncertain. Hence, aerosols released by
28   human activities have had a cooling effect, counteracting a considerable portion of the warming caused by
29   increases in greenhouse gases over the last century (see FAQ 3.1). Nevertheless, this cooling effect is
30   expected to diminish in the future, as air pollution policies progress worldwide, reducing the amount of
31   aerosols released into the atmosphere.
33   Since the pre-industrial period, the Earth’s surface and atmosphere have warmed, altering the properties of
34   clouds, such as their altitude, amount, and composition (water or ice), thereby affecting the Earth’s energy
35   budget and, in turn, changing temperature. This cascading effect of clouds, known as the cloud feedback,
36   could either amplify or offset some of the future warming and has long been the biggest source of
37   uncertainty in climate projections. The problem stems from the fact that clouds can change in many ways
38   and that their processes occur on much smaller scales than what global climate models can explicitly
39   represent. As a result, global climate models have disagreed on how clouds, particularly over the subtropical
40   ocean, will change in the future and whether the change will amplify or suppress the global warming.
42   Since the last IPCC Report in 2013, understanding of cloud processes has advanced with better observations,
43   new analysis approaches and explicit high-resolution numerical simulation of clouds. Also, current global
44   climate models simulate cloud behaviour better than previous models, due both to advances in computational
45   capabilities and process understanding. Altogether, this has helped to build a more complete picture of how
46   clouds will change as the climate warms (FAQ 7.2, Figure 1). For example, the amount of low clouds will
47   reduce over the subtropical ocean, leading to less reflection of incoming solar energy, and the altitude of
48   high clouds will rise, making them more prone to trapping outgoing energy; both processes have a warming
49   effect. In contrast, clouds in high latitudes will be increasingly made of water droplets rather than ice
50   crystals. This shift from fewer, larger ice crystals to smaller but more numerous water droplets will result in
51   more of the incoming solar energy being reflected back to space and produce a cooling effect. Better
52   understanding of how clouds respond to warming has led to more confidence than before that future changes
53   in clouds will, overall, cause additional warming (i.e., by weakening the current cooling effect of clouds).
54   This is called a positive net cloud feedback.
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 1   In summary, clouds will amplify rather than suppress the warming of the climate system in the future, as
 2   more greenhouse gases and fewer aerosols are released to the atmosphere by human activities.
 7   FAQ7.2, Figure 1: Interactions between clouds and the climate today and in a warmer future. Global warming is
 8                     expected to alter the altitude (left) and the amount (centre) of clouds, which will amplify warming.
 9                     On the other hand, cloud composition will change (right), offsetting some of the warming. Overall
10                     clouds are expected to amplify future warming.
12   [END FAQ7.2, FIGURE 1 HERE]
14   [END FAQ 7.2 HERE]

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 1   FAQ 7.3:     What is equilibrium climate sensitivity and how does it relate to future warming?
 3   For a given future scenario, climate models project a range of changes in global surface temperature. This
 4   range is closely related to equilibrium climate sensitivity, or ECS, which measures how climate models
 5   respond to a doubling of carbon dioxide in the atmosphere. Models with high climate sensitivity project
 6   stronger future warming. Some climate models of the new generation are more sensitive than the range
 7   assessed in the IPCC Sixth Assessment Report. This leads to end-of-century global warming in some
 8   simulations of up to 2°C–3°C above the current IPCC best estimate. Although these higher warming levels
 9   are not expected to occur, high-ECS models are useful for exploring high impact, low-likelihood futures.
11   The equilibrium climate sensitivity (ECS) is defined as the long-term global warming caused by a doubling
12   of carbon dioxide above its pre-industrial concentration. For a given emission scenario, much of the
13   uncertainty in projections of future warming can be explained by the uncertainty in ECS (FAQ 7.3, Figure
14   1). The significance of equilibrium climate sensitivity has long been recognised, and the first estimate was
15   presented by Swedish scientist Svante Arrhenius in 1896.
17   This Sixth Assessment Report concludes that there is a 90% or more chance (very likely) that the ECS is
18   between 2°C and 5°C. This represents a significant reduction in uncertainty compared to the Fifth
19   Assessment Report, which gave a 66% chance (likely) of ECS being between 1.5°C and 4.5°C. This
20   reduction in uncertainty has been possible not through a single breakthrough or discovery but instead by
21   combining evidence from many different sources and by better understanding their strengths and
22   weaknesses.
24   There are four main lines of evidence for ECS. First, the self-reinforcing processes, called feedback loops,
25   that amplify or dampen the warming in response to increasing carbon dioxide are now better understood. For
26   example, warming in the Arctic melts sea ice, resulting in more open ocean area, which is darker and
27   therefore absorbs more sunlight, further intensifying the initial warming. It remains challenging to represent
28   realistically all the processes involved in these feedback loops, particularly those related to clouds (see FAQ
29   7.2). Such identified model errors are now taken into account, and other known, but generally weak,
30   feedback loops that are usually not included in models are now included in the assessment of ECS.
32   Second, historical warming since early industrialisation provides strong evidence that climate sensitivity is
33   not small. Since 1850, the concentration of carbon dioxide and other greenhouse gases have increased, and
34   as a result the Earth has warmed by about 1.1ºC. However, relying on this industrial-era warming to
35   estimate ECS is challenging, partly because some of the warming from greenhouse gases was offset by
36   cooling from aerosol particles and partly because the ocean are still responding to past increases in carbon
37   dioxide.
39   Third, evidence from ancient climates that had reached equilibrium with greenhouse gas concentrations, such
40   as the coldest period of the last ice age around 20,000 years ago, or warmer periods further back in time,
41   provide useful data on the ECS of the climate system (see FAQ 1.3). Fourth, statistical approaches linking
42   model ECS values with observed changes, such as global warming since the 1970s, provide complementary
43   evidence.
45   All four lines of evidence rely, to some extent, on climate models, and interpreting the evidence often
46   benefits from model diversity and spread in modelled climate sensitivity. Furthermore, high-sensitivity
47   models can provide important insights into futures that have a low likelihood of occurring but that could
48   result in large impacts. But, unlike in previous assessments, climate models are not considered a line of
49   evidence in their own right in the IPCC Sixth Assessment Report.
51   The ECS of the latest climate models is, on average, higher than that of the previous generation of models
52   and also higher than this report’s best estimate of 3.0°C. Furthermore, the ECS values in some of the new
53   models are both above and below the 2°C to 5°C very likely range, and although such models cannot be ruled
54   out as implausible solely based on their ECS, some of them do display climate change that is inconsistent
55   with the observed when tested with ancient climates. A slight mismatch with models is only natural because
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 1   the IPCC Sixth Assessment Report is based on observations and an improved understanding of the climate
 2   system.
 6   FAQ7.3, Figure 1: Equilibrium climate sensitivity and future warming. (left) Equilibrium climate
 7                   sensitivities for the current generation (sixth climate model intercomparison project,
 8                   CMIP6) climate models, and the previous (CMIP5) generation. The assessed range in this
 9                   report (AR6) is also shown. (right) Climate projections of CMIP5, CMIP6, and AR6 for
10                   the very high-emission scenarios RCP8.5, and SSP5-8.5, respectively. The thick
11                   horizontal lines represent the multi-model average and the thin horizontal lines the results
12                   of individual models. The boxes represent the model ranges for CMIP5 and CMIP6 and
13                   the range assessed in AR6.
14   [END FAQ 7.3, FIGURE 1 HERE]
16   [END FAQ 7.3 HERE]

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