Since 2000, changes in top-of-atmosphere (TOA) energy fluxes can be tracked from space using CERES satellite observations (Figure 7.3). The variations in TOA energy fluxes reflect the influence of internal climate variability, particularly that of El Niño–Southern Oscillation (ENSO), in addition to radiative forcing of the climate system and climate feedbacks (Allan et al., 2014; Loeb et al., 2018b). For example, globally, the reduction in both outgoing thermal and reflected solar radiation during La Niña conditions in 2008/2009 led to an energy gain for the climate system, whereas enhanced outgoing thermal and reflected solar radiation caused an energy loss during the El Niños of 2002/2003 and 2009/2010 (Figure 7.3; Loeb et al., 2018b). An ensemble of CMIP6 models is able to track the variability in global mean TOA fluxes observed by CERES, when driven with prescribed sea surface temperatures (SSTs) and sea ice concentrations (Figure 7.3; Loeb et al., 2020). Under cloud-free conditions, the CERES record shows a near zero trend in outgoing thermal radiation (Loeb et al., 2018b), which – combined with an increasing surface upwelling thermal flux – implies an increasing clear-sky greenhouse effect (Raghuraman et al., 2019). Conversely, clear-sky solar reflected TOA radiation in the CERES record covering March 2000 to September 2017 shows a decrease due to reductions in aerosol optical depth in the Northern Hemisphere and sea ice fraction (Loeb et al., 2018a; Paulot et al., 2018).

Figure 7.3 | Anomalies in global mean all-sky top-of-atmosphere (TOA) fluxes from CERES-EBAF Ed4.0 (solid black lines) and various CMIP6 climate models (coloured lines) in terms of (a) reflected solar, (b) emitted thermal and (c) net TOA fluxes. The multi-model means are additionally depicted as solid red lines. Model fluxes stem from simulations driven with prescribed sea surface temperatures (SSTs) and all known anthropogenic and natural forcings. Shown are anomalies of 12-month running means. All flux anomalies are defined as positive downwards, consistent with the sign convention used throughout this chapter. The correlations between the multi-model means (solid red lines) and the CERES records (solid black lines) for 12-month running means are: 0.85 for the global mean reflected solar; 0.73 for outgoing thermal radiation; and 0.81 for net TOA radiation. Figure adapted from Loeb et al. (2020). Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

Open figure

An effort to reconstruct variations in net TOA fluxes back to 1985, based on a combination of satellite data, atmospheric reanalysis and high-resolution climate model simulations (Allan et al., 2014; Liu et al., 2020), exhibits strong interannual variability associated with the volcanic eruption of Mount Pinatubo in 1991 and the ENSO events before 2000. The same reconstruction suggests that Earth’s energy imbalance increased by several tenths of a W m^–2 between the periods 1985–1999 and 2000–2016, in agreement with the assessment of changes in the global energy inventory (Section 7.2.2.2, and Box 7.2, Figure 1). Comparisons of year-to-year variations in Earth’s energy imbalance estimated from CERES and independent estimates based on ocean heat content change are significantly correlated with similar phase and magnitude (Johnson et al., 2016; Meyssignac et al., 2019), promoting confidence in both satellite and in situ-based estimates (Section 7.2.2.2).

In summary, variations in the energy exchange between Earth and space can be accurately tracked since the advent of improved observations since the year 2000 (high confidence), while reconstructions indicate that the Earth’s energy imbalance was larger in the 2000s than in the 1985–1999 period (high confidence).

The global energy inventory quantifies the integrated energy gain of the climate system associated with global ocean heat uptake, warming of the atmosphere, warming of the land, and melting of ice. Due to energy conservation, the rate of accumulation of energy in the Earth system (Section 7.1) is equivalent to the Earth energy imbalance (ΔN in Box 7.1, Equation 7.1). On annual and longer time scales, changes in the global energy inventory are dominated by changes in global ocean heat content (OHC; Rhein et al., 2013; Palmer and McNeall, 2014; Johnson et al., 2016). Thus, observational estimates and climate model simulations of OHC change are critical to the understanding of both past and future climate change (Sections 2.3.3.1, 3.5.1.3, 4.5.2.1 and 9.2.2.1).

Since AR5, both modelling and observation-based studies have established Earth’s energy imbalance (characterized by OHC change) as a more robust metric of the rate of global climate change than GSAT on interannual-to-decadal time scales (Palmer and McNeall, 2014; von Schuckmann et al., 2016; Wijffels et al., 2016; Cheng et al., 2018; Allison et al., 2020). This is because GSAT is influenced by large unforced variations, for example linked to ENSO and Pacific Decadal Variability (Roberts et al., 2015; Yan et al., 2016; Cheng et al., 2018). Measuring OHC change more comprehensively over the full ocean depth results in a higher signal-to-noise ratio and a time series that increases steadily over time (Box 7.2, Figure 1; Allison et al., 2020). In addition, understanding of the potential effects of historical ocean sampling on estimated global ocean heating rates has improved (Durack et al., 2014; Good, 2017; Allison et al., 2019) and there are now more estimates of OHC change available that aim to mitigate the effect of limited observational sampling in the Southern Hemisphere (Lyman and Johnson, 2008; Cheng et al., 2017; Ishii et al., 2017).

The assessment of changes in the global energy inventory for the periods 1971–2018, 1993–2018 and 2006–2018 draws upon the latest observational time series and the assessments presented in other chapters of this report. The estimates of OHC change come directly from the assessment presented in (Chapter 2 Section 2.3.3.1). The assessment of land and atmospheric heating comes from von Schuckmann et al. (2020), based on the estimates of Cuesta-Valero et al. (2021) and Steiner et al. (2020), respectively. Heating of inland waters, including lakes, reservoirs and rivers, is estimated to account for <0.1% of the total energy change, and is therefore omitted from this assessment (Vanderkelen et al., 2020). The cryosphere contribution from the melting of grounded ice is based on the mass-loss assessments presented in Chapter 9, Section 9.4.1 (Greenland Ice Sheet), Section 9.4.2 (Antarctic Ice Sheet) and (Section 9.5.1 (glaciers). Following AR5, the estimate of heating associated with loss of Arctic sea ice is based on a reanalysis (Schweiger et al., 2011), following the methods described by Slater et al. (2021). Chapter 9 Section 9.3.2) finds no significant trend in Antarctic sea ice area over the observational record, so a zero contribution is assumed. Ice melt associated with the calving and thinning of floating ice shelves is based on the decadal rates presented in Slater et al. (2021). For all cryospheric components, mass loss is converted to heat input using a latent heat of fusion of 3.34 × 10⁵J Kg^–1°C^–1 with the second-order contributions from variations associated with ice type and warming of ice from sub-freezing temperatures disregarded, as in AR5. The net change in energy, quantified in Zettajoules (1 ZJ = 10²¹Joules), is computed for each component as the difference between the first and last year of each period (Table 7.1). The uncertainties in the depth-interval contributions to OHC are summed to get the uncertainty in global OHC change. All other uncertainties are assumed to be independent and added in quadrature.

For the period 1971–2010, AR5 (Rhein et al., 2013) found an increase in the global energy inventory of 274 [196 to 351] ZJ with a 93% contribution from total OHC change, approximately 3% for both ice melt and land heating, and approximately 1% for warming of the atmosphere. For the same period, this Report finds an upwards revision of OHC change for the upper (<700 m depth) and deep (>700 m depth) ocean of approximately 8% and 20%, respectively, compared to AR5 and a modest increase in the estimated uncertainties associated with the ensemble approach of Palmer et al. (2021). The other substantive change compared to AR5 is the updated assessment of land heating, with values approximately double those assessed previously, based on a more comprehensive analysis of the available observations (von Schuckmann et al., 2020; Cuesta-Valero et al., 2021). The result of these changes is an assessed energy gain of 329 [224 to 434] ZJ for the period 1971–2010, which is consistent with AR5 within the estimated uncertainties, despite the systematic increase.

The assessed changes in the global energy inventory (Box 7.2, Figure 1, and Table 7.1) yields an average value for Earth’s energy imbalance (N in Box 7.1, Equation 7.1) of 0.57 [0.43 to 0.72] W m^–2 for the period 1971–2018, expressed relative to Earth’s surface area (high confidence). The estimates for the periods 1993–2018 and 2006–2018 yield substantially larger values of 0.72 [0.55 to 0.89] W m^–2 and 0.79 [0.52 to 1.06] W m^–2, respectively, consistent with the increased radiative forcing from GHGs (high confidence). For the period 1971–2006, the total energy gain was 282 [177 to 387] ZJ, with an equivalent Earth energy imbalance of 0.50 [0.32 to 0.69] W m^–2. To put these numbers in context, the 2006–2018 average Earth system heating is equivalent to approximately 20 times the annual rate of global energy consumption in 2018. ¹

Consistent with AR5 (Rhein et al., 2013), this Report finds that ocean warming dominates the changes in the global energy inventory (high confidence), accounting for 91% of the observed change for all periods considered (Table 7.1). The contributions from the other components across all periods are approximately 5% from land heating, 3% for cryosphere heating and 1% associated with warming of the atmosphere (high confidence). The assessed percentage contributions are similar to the recent study by von Schuckmann et al. (2020) and the total heating rates are consistent within the assessed uncertainties. Cross-validation of heating rates based on satellite and in situ observations (Section 7.2.2.1), and closure of the global sea level budget using consistent datasets (Cross-Chapter Box 9.1 and Table 9.5), strengthen scientific confidence in the assessed changes in the global energy inventory relative to AR5.

The AR5 (Hartmann et al., 2013) reported pronounced changes in multi-decadal records of in situ observations of surface solar radiation, including a widespread decline between the 1950s and 1980s, known as ‘global dimming’, and a partial recovery thereafter, termed ‘brightening’ Section 12.4). These changes have interacted with closely related elements of climate change, such as global and regional warming rates (Z. Li et al., 2016; Wild, 2016; Du et al., 2017; Zhou et al., 2018a), glacier melt (Ohmura et al., 2007; Huss et al., 2009), the intensity of the global water cycle (Wild, 2012) and terrestrial carbon uptake (Mercado et al., 2009). These observed changes have also been used as emergent constraints to quantify aerosol effective radiative forcing (Section 7.3.3.3).

Since AR5, additional evidence for dimming and/or subsequent brightening up to several percent per decade, based on direct surface observations, has been documented in previously less-studied areas of the globe, such as Iran, Bahrain, Tenerife, Hawaii, the Taklaman Desert and the Tibetan Plateau (Elagib and Alvi, 2013; You et al., 2013; Garcia et al., 2014; Longman et al., 2014; Rahimzadeh et al., 2015). Strong decadal trends in surface solar radiation remain evident after careful data quality assessment and homogenization of long-term records (Sanchez-Lorenzo et al., 2013, 2015; Manara et al., 2015, 2016; Wang et al., 2015; Z. Li et al., 2016; Wang and Wild, 2016; Y. He et al., 2018; Yang et al., 2018). Since AR5, new studies on the potential effects of urbanization on solar radiation trends indicate that these effects are generally small, with the exception of some specific sites in Russia and China (Wang et al., 2014; Imamovic et al., 2016; Tanaka et al., 2016). Also, surface-based solar radiation observations have been shown to be representative over large spatial domains of up to several degrees latitude/longitude on monthly and longer time scales (Hakuba et al., 2014; Schwarz et al., 2018). Thus, there is high confidence that the observed dimming between the 1950s and 1980s and the subsequent brightening are robust and do not arise from measurement artefacts or localized phenomena.

As noted in AR5 (Hartmann et al., 2013) and supported by recent studies, the trends in surface solar radiation are less spatially coherent since the beginning of the 21st century, with evidence for continued brightening in parts of Europe and the USA, some stabilization in China and India, and dimming in other areas (Augustine and Dutton, 2013; Sanchez-Lorenzo et al., 2015; Manara et al., 2016; Soni et al., 2016; Wang and Wild, 2016; Jahani et al., 2018; Pfeifroth et al., 2018; Yang et al., 2018; Schwarz et al., 2020). The CERES-EBAF satellite-derived dataset of surface solar radiation (Kato et al., 2018) does not indicate a globally significant trend over the short period 2001–2012 (Zhang et al., 2015), whereas a statistically significant increase in surface solar radiation of +3.4 W m⁻² per decade over the period 1996–2010 has been found in the Satellite Application Facility on Climate Monitoring (CM SAF) record of the geostationary satellite Meteosat, which views Europe, Africa and adjacent ocean (Posselt et al., 2014).

Since AR5, there is additional evidence that strong decadal changes in surface solar radiation have occurred under cloud-free conditions, as shown for long-term observational records in Europe, USA, China, India and Japan (Xu et al., 2011; Gan et al., 2014; Manara et al., 2016; Soni et al., 2016; Tanaka et al., 2016; Kazadzis et al., 2018; J. Li et al., 2018; Yang et al., 2019; Wild et al., 2021). This suggests that changes in the composition of the cloud-free atmosphere, primarily in aerosols, contributed to these variations, particularly since the second half of the 20th century (Wild, 2016). Water vapour and other radiatively active gases seem to have played a minor role (Wild, 2009; Mateos et al., 2013; Posselt et al., 2014; Yang et al., 2019). For Europe and East Asia, modelling studies also point to aerosols as an important factor for dimming and brightening by comparing simulations that include or exclude variations in anthropogenic aerosol and aerosol-precursor emissions (Golaz et al., 2013; Nabat et al., 2014; Persad et al., 2014; Folini and Wild, 2015; Turnock et al., 2015; Moseid et al., 2020). Moreover, decadal changes in surface solar radiation have often occurred in line with changes in anthropogenic aerosol emissions and associated aerosol optical depth (Streets et al., 2006; Wang and Yang, 2014; Storelvmo et al., 2016; Wild, 2016; Kinne, 2019). However, further evidence for the influence of changes in cloudiness on dimming and brightening is emphasized in some studies (Augustine and Dutton, 2013; Parding et al., 2014; Stanhill et al., 2014; Pfeifroth et al., 2018; Antuña-Marrero et al., 2019). Thus, the contribution of aerosol and clouds to dimming and brightening is still debated. The relative influence of cloud-mediated aerosol effects versus direct aerosol radiative effects on dimming and brightening in a specific region may depend on the prevailing pollution levels (Section 7.3.3; Wild, 2016).

ESMs and reanalyses often do not reproduce the full extent of observed dimming and brightening (Wild and Schmucki, 2011; Allen et al., 2013; Zhou et al., 2017a; Storelvmo et al., 2018; Moseid et al., 2020; Wohland et al., 2020), potentially pointing to inadequacies in the representation of aerosol mediated effects or related emissions data. The inclusion of assimilated aerosol optical depth inferred from satellite retrievals in the MERRA2 reanalysis (Buchard et al., 2017; Randles et al., 2017) helps to improve the accuracy of the simulated surface solar radiation changes in China (Feng and Wang, 2019). However, non-aerosol-related deficiencies in model representations of clouds and circulation, and/or an underestimation of natural variability, could further contribute to the lack of dimming and brightening in ESMs (Wild, 2016; Storelvmo et al., 2018).

The AR5 reported evidence for an increase in surface downward thermal radiation based on different studies covering 1964 to 2008, in line with what would be expected from an increased radiative forcing from GHGs and the warming and moistening of the atmosphere. Updates of the longest observational records from the Baseline Surface Radiation Network continue to show an increase at the majority of sites, in line with an overall increase predicted by ESMs of the order of 2 W m^–2 per decade (Wild, 2016). Upward longwave radiation at the surface is rarely measured but is expected to have increased over the same period due to rising surface temperatures.

Turbulent fluxes of latent and sensible heat are also an important part of the surface energy budget (Figure 7.2). Large uncertainties in measurements of surface turbulent fluxes continue to prevent the determination of their decadal changes. Nevertheless, over the ocean, reanalysis-based estimates of linear trends from 1948–2008 indicate high spatial variability and seasonality. Increases in magnitudes of 4 to 7 W m^–2 per decade for latent heat and 2 to 3 W m^–2 per decade for sensible heat in the western boundary current regions are mostly balanced by decreasing trends in other regions (Gulev and Belyaev, 2012). Over land, the terrestrial latent heat flux is estimated to have increased in magnitude by 0.09 W m^–2 per decade from 1989–1997, and subsequently decreased by 0.13 W m^–2 per decade from 1998–2005 due to soil-moisture limitation mainly in the Southern Hemisphere (derived from Mueller et al., 2013). These trends are small in comparison to the uncertainty associated with satellite-derived and in situ observations, as well as from land-surface models forced by observations and atmospheric reanalyses. Ongoing advances in remote sensing of evapotranspiration from space (Mallick et al., 2016; Fisher et al., 2017; McCabe et al., 2017a, b), as well as terrestrial water storage (Rodell et al., 2018) may contribute to future constraints on changes in latent heat flux.

In summary, since AR5, multi-decadal decreasing and increasing trends in surface solar radiation of up to several percent per decade have been detected at many more locations, even in remote areas. There is high confidence that these trends are widespread, and not localized phenomena or measurement artefacts. The origin of these trends is not fully understood, although there is evidence that anthropogenic aerosols have made a substantial contribution (medium confidence). There is medium confidence that downward and upward thermal radiation has increased since the 1970s, while there remains low confidence in the trends in surface sensible and latent heat.

The SARF for carbon dioxide (CO₂) has been slightly revised due to updates to spectroscopic data and inclusion of the absorption band overlaps between N₂O and CO₂ (Etminan et al., 2016). The formulae fitting to the Etminan et al. (2016) results in Meinshausen et al. (2020) are used. This increases the SARF due to doubling CO₂ slightly from 3.71 W m^–2 in AR5 to 3.75 W m^–2. Tropospheric responses to CO₂ in fSST experiments have been found to lead to an approximate balance in their radiative effects between an increased radiative forcing due to water vapour, cloud and surface-albedo adjustments and a decrease due to increased tropospheric temperature and land surface temperature response (Table 7.3; Vial et al., 2013; Zhang and Huang, 2014; Smith et al., 2018b, 2020b). The ΔF_fsst includes any effects represented within the ESMs on tropospheric adjustments due to changes in evapotranspiration or leaf area (mainly affecting surface and boundary-layer temperature, low-cloud amount, and albedo) from the CO₂ -physiological effects (Doutriaux-Boucher et al., 2009; Cao et al., 2010; T.B. Richardson et al., 2018). The effect on surface temperature (negative longwave response) is consistent with the expected physiological responses and needs to be removed for consistency with the ERF definition. The split between surface and tropospheric temperature responses was not reported in Vial et al. (2013) or Zhang and Huang (2014) but the total of surface and tropospheric temperature response agrees with Smith et al. (2018b, 2020b), givingmedium confidence in this decomposition. Doutriaux-Boucher et al. (2009) and Andrews et al. (2021) (using the same land surface model) find a 13% and 10% increase respectively in ERF due to the physiological responses to CO₂. The physiological adjustments are therefore assessed to make a substantial contribution to the overall tropospheric adjustment for CO₂ (high confidence), but there is insufficient evidence to provide a quantification of the split between physiological and thermodynamic adjustments. These forcing adjustments due to the effects of CO₂ on plant physiology differ from the biogeophysical feedbacks due to the effects of temperature changes on vegetation discussed in (Section 7.4.2.5. The adjustment is assumed to scale with the SARF in the absence of evidence for non-linearity. The tropospheric adjustment is assessed from Table 7.3 to be +5% of the SARF with an uncertainty of 5%, which is added to the Meinshausen et al. (2020) formula for SARF. Due to the agreement between the studies and the understanding of the physical mechanisms there is medium confidence in the mechanisms underpinning the tropospheric adjustment, but low confidence in its magnitude .

The ERF from doubling CO₂ (2×CO₂) from the 1750 level (278 ppm; Section 2.2.3.3) is assessed to be 3.93 ± 0.47 W m^–2(high confidence). Its assessed components are given in Table 7.4. The combined spectroscopic and radiative transfer modelling uncertainties give an uncertainty in the CO₂ SARF of around 10% or less (Etminan et al., 2016; Mlynczak et al., 2016). The overall uncertainty in CO₂ ERF is assessed as ±12%, as the more uncertain adjustments only account for a small fraction of the ERF (Table 7.3). The 2×CO₂ ERF estimate is 0.2 W m^–2 larger than using the AR5 formula (Myhre et al., 2013b) due to the combined effects of tropospheric adjustments which were assumed to be zero in AR5. CO₂ concentrations have increased from 278 ppm in 1750 to 410 ppm in 2019 Section 2.2.3.3). The historical ERF estimate from CO₂ is revised upwards from the AR5 value of 1.82 ± 0.38 W m^–2(1750–2011) to 2.16 ± 0.26 W m^–2(1750–2019) in this assessment, from a combination of the revisions described above (0.06 W m^–2) and the 19 ppm rise in atmospheric concentrations between 2011 and 2019 (0.27 W m^–2). The ESM estimates of 2×CO₂ ERF (Table 7.2) lie within ±12% of the assessed value (apart from CESM2). The definition of ERF can also include further physiological effects – for instance on dust, natural fires and biogenic emissions from the land and ocean – but these are not typically included in the modelling setup for 2×CO₂ ERF.

The SARF for methane (CH₄) has been substantially increased due to updates to spectroscopic data and inclusion of shortwave absorption (Etminan et al., 2016). Adjustments have been calculated in nine climate models by Smith et al. (2018b). Since CH₄ is found to absorb in the shortwave near infrared, only adjustments from those models including this absorption are taken into account. For these models the adjustments act to reduce the ERF because the shortwave absorption leads to tropospheric heating and reductions in upper tropospheric cloud amounts. The adjustment is –14% ± 15%, which counteracts much of the increase in SARF identified by Etminan et al. (2016). Modak et al. (2018) also found negative forcing adjustments from a methane perturbation including shortwave absorption in the NCAR CAM5 model, in agreement with the above assessment. The uncertainty in the shortwave component leads to a higher radiative modelling uncertainty (14%) than for CO₂ (Etminan et al., 2016). When combined with the uncertainty in the adjustment, this gives an overall uncertainty of ±20%. There is high confidence in the spectroscopic revision but only medium confidence in the adjustment modification. CH₄ concentrations have increased from 729 ppb in 1750 to 1866 ppb in 2019 Section 2.2.3.3). The historical ERF estimate from AR5 of 0.48 ± 0.10 W m^–2(1750–2011) is revised to 0.54 ± 0.11 W m^–2(1750 to 2019) in this assessment from a combination of spectroscopic radiative efficiency revisions (+0.12 W m^–2), adjustments (–0.08 W m^–2) and the 63 ppb rise in atmospheric CH₄ concentrations between 2011 and 2019 (+0.03 W m^–2). As the adjustments are assessed to be small, there is high confidence in the overall assessment of ERF from methane. Increased methane leads to tropospheric ozone production and increased stratospheric water vapour, so that an attribution of forcing to methane emissions gives a larger effect than that directly from the methane concentration itself. This is discussed in detail in (Chapter 6 (Section 6.4.2) and shown in Figure 6.12.

The tropospheric adjustments to nitrous oxide (N₂O) have been calculated from 5 ESMs as 7% ± 13% of the SARF (Hodnebrog et al., 2020b). This value is therefore taken as the assessed adjustment, but with low confidence. The radiative modelling uncertainty is ±10% (Etminan et al., 2016), giving an overall uncertainty of ±16%. Nitrous oxide concentrations have increased from 270 ppb in 1750 to 332 ppb in 2019 Section 2.2.3.3). The historical ERF estimate from N₂O is revised upwards from 0.17 ± 0.06 W m^–2(1750–2011) in AR5 to 0.21 ± 0.03 W m^–2(1750–2019) in this assessment, of which 0.02 W m^–2 is due to the 7 ppb increase in concentrations, and 0.02 W m^–2 to the tropospheric adjustment. As the adjustments are assessed to be small there remains high confidence in the overall assessment.

Increased nitrous oxide leads to ozone depletion in the upper stratosphere which will make a positive contribution to the direct ERF here (Section 6.4.2 and Figure 6.12) when considering emissions-based estimates of ERF.

The stratospheric-temperature-adjusted radiative efficiencies (SARF per ppb increase in concentration) for halogenated compounds are reviewed extensively in Hodnebrog et al. (2020a) , an update to those used in AR5. Many halogenated compounds have lifetimes short enough that they can be considered short-lived climate forcers (SLCFs; Table 6.1). As such, they are not completely ‘well-mixed’ and their vertical distributions are taken into account when determining their radiative efficiencies. The World Meteorological Organization (WMO, 2018) updated the lifetimes of many halogenated compounds and these were used in Hodnebrog et al. (2020a) .

The tropospheric adjustments to chlorofluorocarbons (CFCs), specifically CFC-11 and CFC-12, have been quantified as 13% ± 10% and 12% ± 14% of the SARF, respectively (Hodnebrog et al., 2020b). The assessed adjustment to CFCs is therefore 12% ± 13% with low confidence due to the lack of corroborating studies. There have been no calculations for other halogenated species so for these the tropospheric adjustments are therefore assumed to be 0 ± 13% with low confidence. The radiative modelling uncertainties are 14% and 24% for compounds with lifetimes greater than and less than five years, respectively (Hodnebrog et al., 2020a). The overall uncertainty in the ERFs of halogenated compounds is therefore assessed to be 19% and 26% depending on the lifetime. The ERF from CFCs is slowly decreasing, but this is compensated for by the increased forcing from the replacement species (HCFCs and HFCs). The ERF from HFCs has increased by 0.028 ± 0.05 W m^–2. Thus, the concentration changes mean that the total ERF from halogenated compounds 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 is due to increased radiative efficiencies and tropospheric adjustments, and 0.014 W m^–2 is due to increases in concentrations. As the adjustments are assessed to be small there remains high confidence in the overall assessment.

Halogenated compounds containing chlorine and bromine lead to ozone depletion in the stratosphere which will reduce the associated ERF (Morgenstern et al., 2020). Chapter 6 (Section 6.4 and Figure 6.12) assesses the ERF contributions due to the chemical effects of reactive gases.

Estimates of the pre-industrial to present-day tropospheric ozone radiative forcing are based entirely on models. The lack of pre-industrial ozone measurements prevents an observational determination. There have been limited studies of ozone ERFs (MacIntosh et al., 2016; Xie et al., 2016; Skeie et al., 2020). Skeie et al. (2020) found little net contribution to the ERF from tropospheric adjustment terms for 1850–2000 change in ozone (tropospheric and stratospheric ozone combined), although MacIntosh et al. (2016) suggested that increases in stratospheric or upper tropospheric ozone reduces high-cloud and increases low-cloud, whereas an increase in lower tropospheric ozone reduces low-cloud. Further studies suggest that changes in circulation due to decreases in stratospheric ozone affect Southern Hemisphere clouds and the atmospheric levels of sea salt aerosol that would contribute additional adjustments, possibly of comparable magnitude to the SARF from stratospheric ozone depletion (Grise et al., 2013, 2014; Xia et al., 2016, 2020). ESM responses to changes in ozone-depleting substances (ODS) in CMIP6 show a much more negative ERF than would be expected from offline calculations of SARF (Morgenstern et al., 2020; Thornhill et al., 2021b) again suggesting a negative contribution from adjustments. However there is insufficient evidence available to quantify this effect.

Without sufficient information to assess whether the ERFs differ from SARF, this assessment relies on offline radiative transfer calculations of SARF for both tropospheric and stratospheric ozone. Checa-Garcia et al. (2018) found SARF of 0.30 W m^–2 for changes in ozone (1850–1860 to 2009–2014). These were based on precursor emissions and ODS concentrations from the Coupled Chemistry Model Initiative (CCMI) project (Morgenstern et al., 2017). Skeie et al. (2020) calculated an ozone SARF of 0.41 ± 0.12 W m^–2(1850–2010; from five climate models and one chemistry transport model) using CMIP6 precursor emissions and ODS concentrations (excluding models without fully interactive ozone chemistry and one model with excessive ozone depletion). The ozone precursor emissions are higher in CMIP6 than in CCMI, which explains much of the increase compared to Checa-Garcia et al. (2018).

Previous assessments have split the ozone forcing into tropospheric and stratospheric components. This does not correspond to the division between ozone production and ozone depletion and is sensitive to the choice of tropopause (high confidence) (Myhre et al., 2013b). The contributions to total SARF in CMIP6 (Skeie et al., 2020) are 0.39 ± 0.07 and 0.02 ± 0.07 W m^–2 for troposphere and stratosphere respectively (using a 150 ppb ozone tropopause definition). This small positive (but with uncertainty encompassing negative values) stratospheric ozone SARF is due to contributions from ozone precursors to lower stratospheric ozone and some of the CMIP6 models showing ozone depletion in the upper stratosphere, where depletion contributes a positive radiative forcing (medium confidence).

As there is insufficient evidence to quantify adjustments, for total ozone the assessed central estimate for ERF is assumed to be equal to SARF (low confidence) and follows Skeie et al. (2020), since that study uses the most recent emissions data. The dataset is extended over the entire historical period following Skeie et al. (2020), with a SARF for 1750–1850 of 0.03 W m^–2 and for 2010–2018 of 0.03 W m^–2, to give 0.47 [0.24 to 0.70] W m^–2 for 1750–2019. This maintains the 50% uncertainty (5–95% range) from AR5 which is largely due to the uncertainty in pre-industrial emissions (Rowlinson et al., 2020). There is also high confidence that this range includes uncertainty due to the adjustments. The CMIP6 SARF is more positive than the AR5 value of 0.31 W m^–2 for the period 1850–2011 (Myhre et al., 2013b) which was based on the Atmospheric Chemistry and Climate Intercomparison Project (ACCMIP; Shindell et al., 2013). The assessment is sensitive to the assumptions on precursor emissions used to drive the models, which are larger in CMIP6 than ACCMIP.

In summary, although there is insufficient evidence to quantify adjustments, there is high confidence in the assessed range of ERF for ozone changes over the 1750–2019 period, giving an assessed ERF of 0.47 [0.24 to 0.70] W m^–2.

This section considers direct anthropogenic effects on stratospheric water vapour by oxidation of methane. Since AR5 the SARF from methane-induced stratospheric water vapour changes has been calculated in Winterstein et al., 2019, corresponding to 0.09 W m^–2 when scaling to 1850 to 2014 methane changes. This is marginally larger than the AR5 assessed value of 0.07 ± 0.05 W m^–2(Myhre et al., 2013b). Wang and Huang (2020) quantified the adjustment terms to a stratospheric water vapour change equivalent to a forcing from a 2×CO₂ warming (which has a different vertical profile). They found that the ERF was less than 50% of the SARF due to high-cloud decrease and upper tropospheric warming. The assessed ERF is therefore 0.05 ± 0.05 W m^–2 with a lower limit reduced to zero and the central value and upper limit reduced to allow for adjustment terms. This still encompasses the two recent SARF studies. There is medium confidence in the SARF from agreement with the recent studies and AR5. There is low confidence in the adjustment terms.

Stratospheric water vapour may also change as an adjustment to species that warm or cool the upper troposphere–lower stratosphere region (Forster and Joshi, 2005; Stuber et al., 2005), in which case it should be included as part of the ERF for that compound. Changes in GSAT are also associated with changes in stratospheric water vapour as part of the water-vapour–climate feedback (Section 7.4.2.2).

The ERF of GHGs (excluding ozone and stratospheric water vapour) over 1750–2019 is assessed to be 3.32 ± 0.29 W m^–2. It has increased by 0.49 W m^–2 compared to AR5 (reference year 2011) (high confidence). Most of this has been due to an increase in CO₂ concentration since 2011 [0.27 ± 0.03] W m^–2, with concentration increases in CH₄, N₂O and halogenated compounds adding 0.02, 0.02 and 0.01 W m^–2 respectively (Table 7.5). Changes in the radiative efficiencies (including adjustments) of CO₂, CH₄, N₂O and halogenated compounds have increased the ERF by an additional 0.15 W m^–2 compared to the AR5 values (high confidence). Note that the ERFs in this section do not include chemical effects of GHGs on production or destruction of ozone or aerosol formation (Section 6.2.2). The ERF for ozone is considerably increased compared to AR5 due to an increase in the assumed ozone precursor emissions in CMIP6 compared to CMIP5, and better accounting for the effects of both ozone precursors and ODSs in the stratosphere. The ERF for stratospheric water vapour is slightly reduced. The combined ERF from ozone and stratospheric water vapour has increased since AR5 by 0.10 ± 0.50 W m^–2(high confidence), although the uncertainty ranges still include the AR5 values.

Since AR5, deeper understanding of the processes that govern aerosol radiative properties, and thus IRFari, has emerged. Combined with new insights into adjustments to aerosol forcing, this progress has informed new observation- and model-based estimates of ERFari and associated uncertainties.

Anthropogenic aerosol particles primarily affect water clouds by serving as additional cloud condensation nuclei (CCN) and thus increasing cloud drop number concentration (N_d; Twomey, 1959). Increasing N_d while holding liquid water content constant reduces cloud drop effective radius (r_e), increases the cloud albedo, and induces an instantaneous negative radiative forcing (IRFaci). The clouds are thought to subsequently adjust by a slowing of the drop coalescence rate, thereby delaying or suppressing rainfall. Rain generally reduces cloud lifetime and thereby liquid water path (LWP, i.e., the vertically integrated cloud water) and/or cloud fractional coverage (Cf; Albrecht, 1989), thus any aerosol-induced rain delay or suppression would be expected to increase LWP and/or Cf. Such adjustments could potentially lead to an ERFaci considerably larger in magnitude than the IRFaci alone. However, adding aerosols to non-precipitating clouds has been observed to have the opposite effect (i.e., a reduction in LWP and/or Cf) (Lebsock et al., 2008; Christensen and Stephens, 2011). These findings have been explained by enhanced evaporation of the smaller droplets in the aerosol-enriched environments, and resultant enhanced mixing with ambient air, leading to cloud dispersal.

A small subset of aerosols can also serve as ice nucleating particles (INPs) that initiate the ice phase in supercooled water clouds, and thereby alter cloud radiative properties and/or lifetimes. However, the ability of anthropogenic aerosols (specifically BC) to serve as INPs in mixed-phase clouds has been found to be negligible in recent laboratory studies (e.g., Vergara-Temprado et al., 2018). No assessment of the contribution to ERFaci from cloud phase changes induced by anthropogenic INPs will therefore be presented.

In ice (cirrus) clouds (cloud temperatures less than –40°C), INPs can initiate ice crystal formation at relative humidity much lower than that required for droplets to freeze spontaneously. Anthropogenic INPs can thereby influence ice crystal numbers and thus cirrus cloud radiative properties. At cirrus temperatures, certain types of BC have in fact been demonstrated to act as INPs in laboratory studies (Ullrich et al., 2017; Mahrt et al., 2018), suggesting a non-negligible anthropogenic contribution to INPs in cirrus clouds. Furthermore, anthropogenic changes to drop number also alter the number of droplets available for spontaneous freezing, thus representing a second pathway through which anthropogenic emissions could affect cirrus clouds.

Energy balance models of reduced complexity have in recent years increasingly been combined with Monte Carlo approaches to provide valuable ‘top-down’ (also called inverse) observational constraints on the total aerosol ERF. These top-down approaches report ranges of aerosol ERF that are found to be consistent with the global mean temperature record and, in some cases, also observed ocean heat uptake. However, the total aerosol ERF is also used together with the historical temperature record in (Section 7.5 to constrain equilibrium climate sensitivity (ECS) and transient climate response (TCR). Using top-down estimates as a separate line of evidence also for the total aerosol ERF would therefore be circular. Nevertheless, it is useful to examine the development of these estimates since AR5, and the degree to which these estimates are consistent with the upper and lower bounds of the assessments of total aerosol ERF (ERFari+aci).

When the first top-down estimates emerged (e.g., Knutti et al., 2002), it became clear that some of the early (‘bottom-up’) ESM estimates of total aerosol ERF were inconsistent with the plausible top-down range. However, as more inverse estimates have been published, it has increasingly become clear that they too are model-dependent and span a wide range of ERF estimates, with confidence intervals that in some cases do not overlap (Forest, 2018). It has also become evident that these methods are sensitive to revised estimates of other forcings and/or updates to observational datasets. A recent review of 19 such estimates reported a mean of –0.77 W m^–2 for the total aerosol ERF, and a 95% confidence interval of [–1.15 to –0.31] W m^–2(Forest, 2018). Adding to that review, a more recent study using the same approach reported an estimate of total aerosol ERF of –0.89 [–1.82 to –0.01] W m^–2(Skeie et al., 2018). However, in the same study, an alternative way of incorporating ocean heat content in the analysis produced a total aerosol ERF estimate of –1.34 [–2.20 to –0.46] W m^–2, illustrating the sensitivity to the manner in which observations are included. A new approach to inverse estimates took advantage of independent climate radiative response estimates from eight prescribed SST and sea ice-concentration simulations over the historical period to estimate the total anthropogenic ERF. From this a total aerosol ERF of –0.8 [–1.6 to +0.1] W m^–2 was derived (valid for near-present relative to the late 19th century). This range was found to be more invariant to parameter choices than earlier inverse approaches (Andrews and Forster, 2020).

Beyond the inverse estimates described above, other efforts have been made since AR5 to constrain the total aerosol ERF. For example, Stevens (2015) used a simple (one-dimensional) model to simulate the historical total aerosol ERF evolution consistent with the observed temperature record. Given the lack of temporally extensive cooling trends in the 20th-century record and the fact that the historical evolution of GHG forcing is relatively well constrained, the study concluded that a more negative total aerosol ERF than –1.0 W m^–2 was incompatible with the historical temperature record. This was countered by Kretzschmar et al. (2017), who argued that the model employed in Stevens (2015) was too simplistic to account for the effect of geographical redistributions of aerosol emissions over time. Following the logic of Stevens (2015), but basing their estimates on a subset of CMIP5 models as opposed to a simplified modelling framework, Kretzschmar et al. argued that a total aerosol ERF as negative as –1.6 W m^–2 was consistent with the observed temperature record. Similar arguments were put forward by Booth et al. (2018), who emphasized that the degree of non-linearity of the total aerosol ERF with aerosol emissions is a central assumption in Stevens (2015).

The historical temperature record was also the key observational constraint applied in two additional studies (Rotstayn et al., 2015; Shindell et al., 2015) based on a subset of CMIP5 models. Rotstayn et al. (2015) found a strong temporal correlation (>0.9) between the total aerosol ERF and the global surface temperature. They used this relationship to produce a best estimate for the total aerosol ERF of –0.97 W m^–2, but with considerable unquantified uncertainty, in part due to uncertainties in the TCR. Shindell et al. (2015) came to 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 W m^–2 but based this on spatial temperature and ERF patterns in the models in comparison with observed spatial temperature patterns.

A separate observational constraint on the total ERF was proposed by Cherian et al. (2014), who compared trends in downward fluxes of solar radiation observed at surface stations across Europe (described in (Section 7.2.2.3) to those simulated by a subset of CMIP5 models. Based on the relationship between solar radiation trends and the total aerosol ERF in the models, they inferred a total aerosol ERF of –1.3 W m^–2 and a standard deviation of ± 0.4 W m^–2.

Based solely on energy balance considerations or other observational constraints, it is extremely likely that the total aerosol ERF is negative (high confidence), butextremely unlikely that the total aerosol ERF is more negative than –2.0 W m^–2(high confidence).

In AR5 (Boucher et al., 2013), the overall assessment of total aerosol ERF (ERFari+aci) used the median of 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 confidence in a subset of models that were deemed more complete in their representation of aerosol–cloud interactions. These models, which included aerosol effects on mixed-phase, ice and/or convective clouds, produced a smaller estimate of –1.38 W m^–2. Likewise, studies that constrained models with satellite observations (five in total), which produced a median estimate of –0.85 W m^–2, were given extra weight. Furthermore, a longwave ERFaci of 0.2 W m^–2 was added to studies that only reported shortwave ERFaci values. Finally, based on higher resolution models, doubt was raised regarding the ability of ESMs to represent the cloud-adjustment component of ERFaci with fidelity. The expert judgement was therefore that aerosol effects on cloud lifetime were too strong in the ESMs, further reducing the overall ERF estimate. The above lines of argument resulted in a total aerosol assessment of –0.9 [–1.9 to –0.1] W m^–2 in AR5.

Here, the best estimate and range is revised relative to AR5 (Boucher et al., 2013), partly based on updates to the above lines of argument. Firstly, the studies that included aerosol effects on mixed-phase clouds in AR5 relied on the assumption that anthropogenic black carbon (BC) could act as INPs in these clouds, which has since been challenged by laboratory experiments (Kanji et al., 2017; Vergara-Temprado et al., 2018). There is no observational evidence of appreciable ERFs associated with aerosol effects on mixed-phase and ice clouds (Section 7.3.3.2.1), and modelling studies disagree when it comes to both their magnitude and sign (Section 7.3.3.2.2). Likewise, very few ESMs incorporate aerosol effects on deep convective clouds, and cloud-resolving modelling studies report different effects on cloud radiative properties depending on environmental conditions (Tao et al., 2012). Thus, it is not clear whether omitting such effects from ESMs would lead to any appreciable ERF biases, or if so, what the sign of such biases would be. As a result, all ESMs are given equal weight in this assessment. Furthermore, there is now a considerably expanded body of literature which suggests that early modelling studies that incorporated satellite observations may have resulted in overly conservative estimates of the magnitude of ERFaci (Section 7.3.3.2.1). Finally, based on an assessment of the longwave ERFaci in the CMIP5 models, the offset of +0.2 W m^–2 applied in AR5 appears to be too large (Heyn et al., 2017). As in AR5, there is still reason to question the ability of ESMs to simulate adjustments in LWP and cloud cover in response to aerosol perturbation, but it is not clear that this will result in biases that exclusively increase the magnitude of the total aerosol ERf (Section 7.3.3.2.2).

The assessment of total aerosol ERF here uses the following lines of evidence: satellite-based evidence for IRFari; model-based evidence for IRFari and ERFari; satellite-based evidence of IRFaci and ERFaci; and finally model-based evidence for ERFaci. Based on this, ERFari and ERFaci for 2014 relative to 1750 are assessed to be –0.3 ± 0.3 W m^–2 and –1.0 ± 0.7 W m^–2, respectively. There is thus strong evidence for a substantive negative total aerosol ERF, which is supported by the broad agreement between observation-based and model-based lines of evidence for both ERFari and ERFaci that has emerged since AR5 (Gryspeerdt et al., 2020). However, considerable uncertainty remains, particularly with regards to the adjustment contribution to ERFaci, as well as missing processes in current ESMs, notably aerosol effects on mixed-phase, ice and convective clouds. This leads to amedium confidence in the estimate of ERFari+aci and a slight narrowing of the uncertainty range. Because the estimates informing the different lines of evidence are generally valid for approximately 2014 conditions, the total aerosol ERF assessment is considered valid for 2014 relative to 1750.

Combining the lines of evidence and adding uncertainties in quadrature, the ERFari+aci estimated for 2014 relative to 1750 is assessed to be –1.3 [–2.0 to –0.6] W m^–2(medium confidence). The corresponding range from Bellouin et al. (2019) is –3.15 to –0.35 W m^–2, thus there is agreement for the upper bound while the lower bound assessed here is less negative. A lower bound more negative than –2.0 W m^–2 is not supported by any of the assessed lines of evidence. There is high confidence that ERFaci contributes most (75–80%) to the total aerosol effect (ERFari+aci). In contrast to AR5 (Boucher et al., 2013), it is nowvirtually certain that the total aerosol ERF is negative. Figure 7.5 depicts the aerosol ERFs from the different lines of evidence along with the overall assessments.

Figure 7.5 | Net aerosol effective radiative forcing (ERF) from different lines of evidence. The headline AR6 assessment of –1.3 [–2.0 to –0.6] W m^–2 is highlighted in purple for 1750–2014 and compared to the AR5 assessment of –0.9 [–1.9 to –0.1] W m^–2 for 1750–2011. The evidence comprising the AR6 assessment is shown below this: energy balance constraints [–2 to 0 W m^–2 with no best estimate]; observational evidence from 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] W m^–2. Estimates from individual CMIP5 (Zelinka et al., 2014) and CMIP6 (Smith et al., 2020b and Table 7.6) models are depicted by blue and red crosses respectively. For each line of evidence the assessed best-estimate contributions from ERFari and ERFaci are shown with darker and paler shading respectively. The observational assessment for ERFari is taken from the IRFari. Uncertainty ranges are represented by black bars for the total aerosol ERF and depictvery likely ranges. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

Open figure

As most modelling and observational estimates of aerosol ERF have end points in 2014 or earlier, there is limited evidence available for the assessment of how aerosol ERF has changed from 2014 to 2019. However, based on a general reduction in global mean AOD over this period (Section 2.2.6 and Figure 2.9), combined with a reduction in emissions of aerosols and their precursors in updated emissions inventories (Hoesly et al., 2018), the aerosol ERF is assessed to have decreased in magnitude from about 2014 to 2019 (medium confidence). Consistent with Figure 2.10, the change in aerosol ERF from about 2014 to 2019 is assessed to be +0.2 W m^–2, but with low confidence due tolimited evidence. Aerosols are therefore assessed to have contributed an ERF of –1.1 [–1.7 to –0.4] W m^–2 over 1750–2019 (medium confidence).

Land-use forcing is defined as those changes in land-surface properties directly caused by human activity rather than by climate processes (see also Section 2.2.7). Land-use change affects the surface albedo. For example, deforestation typically replaces darker forested areas with brighter cropland, and thus imposes a negative radiative forcing on climate, while afforestation and reforestation can have the opposite effect. Precise changes depend on the nature of the forest, crops and underlying soil. Land-use change also affects the amount of water transpired by vegetation (Devaraju et al., 2015). Irrigation of land directly affects evaporation (Sherwood et al., 2018), causing a global increase of 32,500 m³s⁻¹due to human activity. Changes in evaporation and transpiration affect the latent heat budget, but do not directly affect the top-of-atmosphere (TOA) radiative fluxes. The lifetime of water vapour is so short that the effect of changes in evaporation on the greenhouse contribution of water vapour are negligible (Sherwood et al., 2018). However, evaporation can affect the ERF through adjustments, particularly through changes in low-cloud amounts. Land management affects the emissions or removal of GHGs from the atmosphere (such as CO₂, CH₄, N₂O). These emissions changes have the greatest effect on climate (Ward et al., 2014), however they are already included in GHG inventories. Land-use change also affects the emissions of dust and biogenic volatile organic compounds (BVOCs), which form aerosols and affect the atmospheric concentrations of ozone and methane (Section 6.2.2). The effects of land use on surface temperature and hydrology were recently assessed in SRCCL (Jia et al., 2019).

Using the definition of ERF from (Section 7.1, the adjustment in land-surface temperature is excluded from the definition of ERF, but changes in vegetation and snow cover (resulting from land-use change) are included (Boisier et al., 2013). Land-use change in the mid-latitudes induces a substantial amplifying adjustment in snow cover. Few climate model studies have attempted to quantify the ERF of land-use change. T. Andrews et al. (2017) calculated a very large surface albedo ERF (–0.47 W m^–2) from 1860 to 2005 in the HadGEM2-ES model, although they did not separate out the surface albedo change from snow cover change. HadGEM2-ES is known to overestimate the amount of boreal trees and shrubs in the unperturbed state (Collins et al., 2011) so will tend to overestimate the ERF associated with land-use change. The increases in dust in HadGEM2-ES contributed an extra –0.25 W m^–2, whereas cloud cover changes added a small positive adjustment (0.15 W m^–2) consistent with a reduction in transpiration. A multi-model quantification of land-use forcing in CMIP6 models (excluding one outlier) (Smith et al., 2020b) found an IRF of –0.15 ± 0.12 W m^–2(1850–2014), and an ERF (correcting for land-surface temperature change) of –0.11 ± 0.09 W m^–2. This shows a small positive adjustment term (mainly from a reduction in cloud cover). CMIP5 models show an IRF of –0.11 [–0.16 to –0.04] W m^–2(1850–2000) after excluding unrealistic models (Lejeune et al., 2020).

The contribution of land-use change to albedo changes has recently been investigated using MODIS and AVHRR to attribute surface albedo to geographically specific land-cover types (Ghimire et al., 2014). When combined with a historical land-use map (Hurtt et al., 2011) this gives a SARF of –0.15 ± 0.01 W m^–2 for the period 1700–2005, of which approximately –0.12 W m^–2 is from 1850. This study accounted for correlations between vegetation type and snow cover, but not the adjustment in snow cover identified in T. Andrews et al. (2017).

The indirect contributions of land-use change through biogenic emissions is very uncertain. Decreases in BVOCs reduce ozone and methane (Unger, 2014), but also reduce the formation of organic aerosols and their effects on clouds (Scott et al., 2017). Adjustments through changes in aerosols and chemistry are model dependent (Zhu et al., 2019b; Zhu and Penner, 2020), and it is not yet possible to make an assessment based on a limited number of studies.

The contribution of irrigation (mainly to low-cloud amount) is assessed as –0.05[–0.1 to 0.05] W m^–2 for the historical period (Sherwood et al., 2018).

Because the CMIP5 and CMIP6 modelling studies are in agreement with Ghimire et al. (2014), that study is used as the assessed albedo ERF. Adding the irrigation effect to this gives an overall assessment of the ERF from land-use change of –0.20 ± 0.10 W m^–2(medium confidence). Changes in ERF since 2014 are assumed to be small compared to the uncertainty, so this ERF applies to the period 1750–2019. The uncertainty range includes uncertainties in the adjustments.

ERF from contrails and aviation-induced cirrus is taken from the assessment of Lee et al. (2020), at 0.057 [0.019 to 0.098] W m^–2 in 2018 (see Section 6.6.2 for an assessment of the total effects of aviation). This is rounded up to address its low confidence and the extra year of air traffic to give an assessed ERF over 1750–2019 of 0.06 [0.02 to 0.10] W m^–2. This assessment is given low confidence due to the potential that processes missing from the assessment would affect the magnitude of contrails and aviation-induced cirrus ERF.

In AR5, it was assessed that the effects of light-absorbing particles (LAPs) did probably not significantly contribute to recent reductions in Arctic ice and snow (Vaughan et al., 2013). The SARF from LAPs on snow and ice was assessed to 0.04 [0.02 to 0.09] W m^–2(Boucher et al., 2013), a range appreciably lower than the estimates given in AR4 (Forster et al., 2007). This effect was assessed to be low confidence (medium evidence, low agreement) (Table 8.5 in Myhre et al., 2013b).

Since AR5 there has been progress in the understanding of the physical state and processes in snow that govern the albedo reduction by black carbon (BC). The SROCC (IPCC, 2019a) assessed that there is high confidence that darkening of snow by deposition of BC and other light-absorbing aerosol species increases the rate of snow melt (Section 2.2 in Hock et al., 2019; Section 3.4 in Meredith et al., 2019). C. He et al. (2018) found that taking into account both the non-spherical shape of snow grains and internal mixing of BC in snow significantly altered the effects of BC on snow albedo. The reductions of snow albedo by dust and BC have been measured and characterized in the Arctic, the Tibetan Plateau, and mid-latitude regions subject to seasonal snowfall, including North America and northern and eastern Asia (Qian et al., 2015).

Since AR5, two further studies of global IRF from black carbon on snow deposition are available, with best estimates of 0.01 W m^–2(Lin et al., 2014) and 0.045 W m^–2(Namazi et al., 2015). Organic carbon deposition on snow and icehas been estimated to contribute a small positive IRF of 0.001 to 0.003 W m^–2(Lin et al., 2014). No comprehensive global assessments of mineral dust deposition on snow are available, although the effects are potentially large in relation to the total effect of LAPs on snow and ice forcing (Yasunari et al., 2015).

Most radiative forcing estimates have a regional emphasis. The regional focus makes estimating a global mean radiative forcing from aggregating different studies challenging, and the relative importance of each region is expected to change if the global pattern of emissions sources changes (Bauer et al., 2013). The lower bound of the assessed range of BC on snow and ice is extended to zero to encompass Lin et al. (2014), with the best estimate unchanged, resulting in 0.04 [0.00 to 0.09] W m^–2. The efficacy of BC on snow forcing was estimated to be 2 to 4 times as large as for an equivalent CO₂ forcing as the effects are concentrated at high latitudes in the cryosphere (Bond et al., 2013). However, it is unclear how much of this effect is due to radiative adjustments leading to a higher ERF, and how much comes from a less negative feedback α due to the high-latitude nature of the forcing. To estimate the overall ERF, the IRF is doubled assuming that part of the increased efficacy is due to adjustments. This gives an overall assessed ERF of +0.08 [0.00 to 0.18] W m^–2, with low confidence.

Variations in the total solar irradiance (TSI) represent a natural external forcing agent. The dominant cycle is the solar 11-year activity cycle, which is superimposed on longer cycles (Section 2.2). Over the last three 11-year cycles, the peak-to-trough amplitude in TSI has differed by about 1 W m^–2 between solar maxima and minima (Figure 2.2).

The fractional variability in the solar irradiance, over the solar cycle and between solar cycles, is much greater at short wavelengths in the 200–400 nanometre (nm) band than for the broad visible/infrared band that dominates TSI (Krivova et al., 2006). The IRF can be derived simply by ΔTSI× (1 – albedo)/4 irrespective of wavelength, where the best estimate of the planetary albedo is usually taken to be 0.29 and ΔTSIrepresents the change in total solar irradiance (Stephens et al., 2015). (The factor 4 arises because TSI is per unit area of Earth cross section presented to the Sun and IRF is per unit area of Earth’s surface). The adjustments are expected to be wavelength dependent. Gray et al. (2009) determined a stratospheric temperature adjustment of –22% to spectrally resolved changes in the solar radiance over one solar cycle. This negative adjustment is due to stratospheric heating from increased absorption by ozone at the short wavelengths, increasing the outgoing longwave radiation to space. A multi-model comparison (Smith et al., 2018b) calculated adjustments of –4% due to stratospheric temperatures and –6% due to tropospheric processes (mostly clouds), for a change in TSI across the spectrum (Figure 7.4). The smaller magnitude of the stratospheric temperature adjustment is consistent with the broad spectral change rather than the shorter wavelengths characteristic of solar variation. A single-model study also found an adjustment that acts to reduce the forcing (Modak et al., 2016). While there has not yet been a calculation based on the appropriate spectral change, the –6% tropospheric adjustment from Smith et al. (2018b) is adopted along with the Gray et al. (2009) stratospheric temperature adjustment. The ERF due to solar variability over the historical period is therefore represented by 0.72 × ΔTSI× (1 – albedo)/4 using the TSI timeseries from (Chapter 2 Section 2.2.1).

The 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 which was computed from the seven-year mean around the solar minima in 1745 (being closest to 1750) and 2008 (being the most recent solar minimum). The inclusion of tropospheric adjustments that reduce ERF (compared to SARF in AR5) has a negligible effect on the overall forcing. Prior to the satellite era, proxy records are used to reconstruct historical solar activity. In AR5, historical records were constructed using observations of solar magnetic features. In this assessment historical time series are constructed from radiogenic compounds in the biosphere and in ice cores that are formed from cosmic rays (Steinhilber et al., 2012).

In this assessment the TSI from the Paleoclimate Model Intercomparison Project Phase 4 (PMIP4) reconstruction is used (Section 2.2.1; Jungclaus et al., 2017). Proxies constructed from the¹⁴C and¹⁰Be radiogenic records for the SATIRE-M model (Vieira et al., 2011) and¹⁴C record for the PMOD model (Shapiro et al., 2011) for the 1745 solar minimum provide ERFs for 1745–2008 of –0.01, –0.02 and 0.00 W m^–2 respectively. An independent dataset from the National Oceanic and Atmospheric Administration’s Climate Data Record (Coddington et al., 2016; Lean, 2018) provides an ERF for 1745–2008 of +0.03 W m^–2. One substantially higher ERF estimate of +0.35 W m^–2 derived from TSI reconstructions is provided by Egorova et al. (2018). However, the estimate from Egorova et al. (2018) hinges on assumptions about long-term changes in the quiet Sun for which there is no observed evidence. Lockwood and Ball (2020) analysed the relationship between observed changes in cosmic ray fluxes and recent, more accurate, TSI data and derived ERF between –0.01 and +0.02 W m^–2, and Yeo et al. (2020) modelling showed the maximum possible ERF to be 0.26 ± 0.09 W m^–2. Hence the Egorova et al. (2018) estimate is not explicitly taken into account in the assessment presented in this section.

In contrast to AR5, the solar ERF in this assessment uses full solar cycles rather than solar minima. The pre-industrial TSI is defined as the mean from all complete solar cycles from the start of the¹⁴C SATIRE-M proxy record in 6755 BCE to 1744 CE. The mean TSI from solar cycle 24 (2009–2019) is adopted as the assessment period for 2019. The best estimate solar ERF is assessed to be 0.01 W m^–2, using the¹⁴C reconstruction from SATIRE-M, with a likely range of –0.06 to +0.08 W m^–2(medium confidence). The uncertainty range is adopted from the evaluation of Lockwood and Ball (2020) using a Monte Carlo analysis of solar activity from the Maunder Minimum to 2019 from several datasets, leading to an ERF of –0.12 to +0.15 W m^–2. The Lockwood and Ball (2020) full uncertainty range is halved as the period of reduced solar activity in the Maunder Minimum had ended by 1750 (medium confidence).

Variations in the flux of galactic cosmic rays (GCR) reaching the atmosphere are modulated by solar activity and affect new particle formation in the atmosphere through their link to ionization of the troposphere (Lee et al., 2019). It has been suggested that periods of high GCR flux correlate with increased aerosol and CCN concentrations and therefore also with cloud properties (e.g., Dickinson, 1975; Kirkby, 2007).

Since AR5, the link between GCR and new particle formation has been more thoroughly studied, particularly by experiments in the CERN CLOUD chamber (Cosmics Leaving OUtdoor Droplets; Dunne et al., 2016; Kirkby et al., 2016; Pierce, 2017). By linking the GCR-induced new particle formation from CLOUD experiments to CCN, Gordon et al. (2017) found that the CCN concentration for low-clouds differed by 0.2–0.3% between solar maximum and solar minimum. Combined with relatively small variations in the atmospheric ion concentration over centennial time scales (Usoskin et al., 2015), it is therefore unlikely that cosmic ray intensity affects present-day climate via nucleation (Yu and Luo, 2014; Dunne et al., 2016; Pierce, 2017; Lee et al., 2019).

Studies continue to seek a relationship between GCR and properties of the climate system based on correlations and theory. Svensmark et al. (2017) proposed a new mechanism for ion-induced increase in aerosol growth rate and subsequent influence on the CCN concentration. The study does not include an estimate of the resulting effect on atmospheric CCN concentration and cloud radiative properties. Furthermore, Svensmark et al. (2009, 2016) find correlations between GCRs and aerosol and cloud properties in satellite and ground-based data. Multiple studies investigating this link have challenged such correlations (Kristjánsson et al., 2008; Calogovic et al., 2010; Laken, 2016).

AR5 concluded that the GCR effect on CCN is too weak to have any detectable effect on climate and no robust association was found between GCR and cloudiness (Boucher et al., 2013). Published literature since AR5 robustly supports these conclusions with key laboratory, theoretical and observational evidence. There is high confidence that GCRs contribute a negligible ERF over the period 1750–2019.

There is large episodic negative radiative forcing associated with sulphur dioxide (SO­­₂) being ejected into the stratosphere from explosive volcanic eruptions, accompanied by more frequent smaller eruptions (Figure 2.2 and Cross-Chapter Box 4.1). From SO₂ gas, reflective sulphate aerosol is formed in the stratosphere where it may persist for months to years, reducing the incoming solar radiation. The volcanic SARF in AR5 (Myhre et al., 2013b) was derived by scaling the stratospheric aerosol optical depth (SAOD) by a factor of –25 W m^–2 per unit SAOD from Hansen et al. (2005b). Quantification of the adjustments to SAOD perturbations from climate model simulations have determined a significant positive adjustment driven by a reduction in cloud amount (Figure 7.4; Marshall et al., 2020). Analysis of CMIP5 models provides a mean ERF of –20 W m^–2 per unit SAOD (Larson and Portmann, 2016). Single-model studies with successive generations of Hadley Centre climate models produce estimates between –17 and –19 W m^–2 per unit SAOD (Gregory et al., 2016; Marshall et al., 2020), with some evidence that ERF may be non-linear with SAOD for large eruptions (Marshall et al., 2020). Analysis of the volcanically active periods of 1982–1985 and 1990–1994 using the CESM1(WACCM) aerosol–climate model provided an SAOD-to-ERF relationship of –21.5 (± 1.1) W m^–2 per unit SAOD (Schmidt et al., 2018). Volcanic SO₂ emissions may contribute a positive forcing through effects on upper tropospheric ice clouds, due to additional ice nucleation on volcanic sulphate particles (Friberg et al., 2015; Schmidt et al., 2018), although one observational study found no significant effect (Meyer et al., 2015). Due to low agreement, the contribution of sulphate aerosol effects on ice clouds to volcanic ERF is not included in the overall assessment.

Non-explosive volcanic eruptions generally yield negligible global ERFs due to the short atmospheric lifetimes (a few weeks) of volcanic aerosols in the troposphere. However, as discussed in (Section 7.3.3.2, the massive fissure eruption in Holuhraun, Iceland persisted for months in 2014 and 2015 and did in fact result in a marked and persistent reduction in cloud droplet radii and a corresponding increase in cloud albedo regionally (Malavelle et al., 2017). This shows that non-explosive fissure eruptions can lead to strong regional and even global ERFs, but because the Holuhraun eruption occurred in Northern Hemisphere winter, solar insolation was weak and the observed albedo changes therefore did not result in an appreciable global ERF (Gettelman et al., 2015).

The ERF for volcanic stratospheric aerosols is assessed to be –20 ± 5 W m^–2 per unit SAOD (medium confidence) based on the CMIP5 multi-model mean from the Larson and Portmann (2016) SAOD forcing efficiency calculations combined with the single-model results of Gregory et al. (2016), Schmidt et al. (2018) and Marshall et al. (2020). This is applied to the SAOD time series from (Chapter 2 Section 2.2.2) to generate a time series of ERF and temperature response shown in (Chapter 2 (Figure 2.2 and Figure 7.8, respectively). The period from 500 BCE to 1749 CE, spanning back to the start of the record of Toohey and Sigl (2017), is defined as the pre-industrial baseline and the volcanic ERF is calculated using an SAOD anomaly from this long-term mean. As in AR5, a pre-industrial to present-day ERF assessment is not provided due to the episodic nature of volcanic eruptions.

The AR5 introduced the concept of effective radiative forcing (ERF) and radiative adjustments, and made a preliminary assessment that the tropospheric adjustments were zero for all species other than the effects of aerosol–cloud interaction and black carbon. Since AR5, new studies have allowed for a tentative assessment of values for tropospheric adjustments to CO₂, CH₄, N₂O, some CFCs, solar forcing, and stratospheric aerosols, and to place a tighter constraint on adjustments from aerosol–cloud interaction (Sections 7.3.2, 7.3.3 and 7.3.4). In AR6, the definition of ERF explicitly removes the land-surface temperature change as part of the forcing, in contrast to AR5 where only sea surface temperatures were fixed. The ERF is assessed to be a better predictor of modelled equilibrium temperature change (i.e., less variation in feedback parameter) than SARf (Section 7.3.1).

As discussed in (Section 7.3.2, the radiative efficiencies for CO₂, CH₄ and N₂O have been updated since AR5 (Etminan et al., 2016). There has been a small (1%) increase in the stratospheric-temperature-adjusted CO₂ radiative efficiency, and a +5% tropospheric adjustment has been added. The stratospheric-temperature-adjusted radiative efficiency for CH₄ is increased by approximately 25% (high confidence). The tropospheric adjustment is tentatively assessed to be –14% (low confidence). A +7% tropospheric adjustment has been added to the radiative efficiency for N₂O and +12% to CFC-11 and CFC-12 (low confidence).

For aerosols there has been a convergence of model and observational estimates of aerosol forcing, and the partitioning of the total aerosol ERF has changed. Compared to AR5 a greater fraction of the ERF is assessed to come from ERFaci compared to the ERFari. It is now assessed as virtually certain that the total aerosol ERF (ERFari+aci) is negative.

Figure 7.6 shows the industrial-era ERF estimates for 1750 to 2019 for the concentration change in different forcing agents. The assessed uncertainty distributions for each individual component are combined with a 100,000-member Monte Carlo simulation that samples the different distributions, assuming they are independent, to obtain the overall assessment of total present-day ERF (Supplementary Material 7.SM.1). The corresponding emissions-based ERF figure is shown in (Chapter 6 (Figure 6.12).

Figure 7.6 | Change in effective radiative forcing (ERF) from 1750 to 2019 by contributing forcing agents (carbon dioxide, other well-mixed greenhouse gases (WMGHGs), ozone, stratospheric water vapour, surface albedo, contrails and aviation-induced cirrus, aerosols, anthropogenic total, and solar). Solid bars represent best estimates, and very likely (5–95%) ranges are given by error bars. Non-CO₂ WMGHGs are further broken down into contributions from methane (CH₄), nitrous oxide (N₂O) and halogenated compounds. Surface albedo is broken down into land-use changes and light-absorbing particles on snow and ice. Aerosols are broken down into contributions from aerosol–cloud interactions (ERFaci) and aerosol–radiation interactions (ERFari). For aerosols and solar, the 2019 single-year values are given (Table 7.8), which differ from the headline assessments in both cases. Volcanic forcing is not shown due to the episodic nature of volcanic eruptions. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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The total anthropogenic ERF over the industrial era (1750–2019) is estimated as 2.72 [1.96 to 3.48] W m^–2(high confidence) (Table 7.8 and Annex III). This represents a 0.43 W m^–2 increase over the assessment made in AR5 (Myhre et al., 2013b) for the period 1750–2011. This increase is a result of compensating effects. Atmospheric concentration increases of GHGs since 2011 and upwards revisions of their forcing estimates have led to a 0.59 W m^–2 increase in their ERF. However, the total aerosol ERF is assessed to be more negative compared to AR5, due to revised estimates rather than trends (high confidence).

Greenhouse gases, including ozone and stratospheric water vapour from methane oxidation, are estimated to contribute an ERF of 3.84 [3.46 to 4.22] W m^–2 over 1750–2019. Carbon dioxide continues to contribute the largest part (56 ± 16%) of this GHG ERF (high confidence).

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 1750–2019 (medium confidence). Aerosol–cloud interactions contribute approximately 75–80% of this ERF with the remainder due to aerosol–radiation interactions (Table 7.8).

For the purpose of comparing forcing changes with historical temperature change (Section 7.5.2), longer averaging periods are useful. The change in ERF from the second half of the 19th century (1850–1900) 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 is due to CO₂.

The estimated contribution of forcing agents to the 2019 global surface air temperature (GSAT) change relative to 1750 is shown in Figure 7.7. These estimates were produced using the concentration-derived ERF time series presented in Figure 2.10 and described in Supplementary Material 7.SM.1.3. The resulting GSAT changes over time are shown in Figure 7.8. The historical time series of ERFs for the WMGHGs can be derived by applying the ERF calculations of Section 7.3.2 to the observed time series of WMGHG concentrations in Chapter 2 Section 2.2.

Figure 7.7 | The contribution of forcing agents to 2019 temperature change relative to 1750 produced using the two-layer emulator (Supplementary Material 7.SM.2), constrained to assessed ranges for key climate metrics described in Cross-Chapter Box 7.1. The results are from a 2237-member ensemble. Temperature contributions are expressed for carbon dioxide, other well-mixed greenhouse gases (WMGHGs), ozone, stratospheric water vapour, surface albedo, contrails and aviation-induced cirrus, aerosols, solar, volcanic, and total. Solid bars represent best estimates, and very likely (5–95%) ranges are given by error bars. Dashed error bars show the contribution of forcing uncertainty alone, using best estimates of ECS (3.0°C), TCR (1.8°C) and two-layer model parameters representing the CMIP6 multi-model mean. Solid error bars show the combined effects of forcing and climate response uncertainty using the distribution of ECS and TCR from Tables 7.13 and 7.14, and the distribution of calibrated model parameters from 44 CMIP6 models. Non-CO₂WMGHGs are further broken down into contributions from methane (CH₄), nitrous oxide (N₂O) and halogenated compounds. Surface albedo is broken down into land-use changes and light-absorbing particles on snow and ice. Aerosols are broken down into contributions from aerosol–cloud interactions (ERFaci) and aerosol–radiation interactions (ERFari). Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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These ERF timeseries are combined with a two-layer emulator (Cross-Chapter Box 7.1 and Supplementary Material 7.SM.2) using a 2237-member constrained Monte Carlo sample of both forcing uncertainty (by sampling ERF ranges) and climate response (by sampling ECS, TCR and ocean heat capacity ranges). The net model warming over the historical period is matched to the assessment of historical GSAT warming from 1850–1900 to 1995–2014 of 0.85 [0.67 to 0.98] °C (Cross-Chapter Box 2.3) and ocean heat content change from 1971 to 2018 Section 7.2.2.2). Therefore the model gives the breakdown of the GSAT trend associated with different forcing mechanisms that are consistent with the overall GSAT change. The model assumes that there is no variation in feedback parameter across forcing mechanisms (Section 7.3.1) and variations in the effective feedback parameter over the historical record (Section 7.4.4). The distribution of ECS was informed bySection 7.5.5 and chosen to approximately maintain the best estimate and likely /very likely ranges assessed in that section (see also Supplementary Material 7.SM.2). The TCR has an ensemble median value of 1.81°C, in good agreement with (Section 7.5.5. Two error bars are shown in Figure 7.7. The dashed error bar shows the contribution of ERF uncertainty (as assessed in the subsections of (Section 7.3) employing the best estimate of climate response with an ECS of 3.0°C. The solid bar is the total response uncertainty using the (Section 7.5.5 assessment of ECS. The uncertainty in the historical temperature contributions ofthe different forcing agents is mostly due to uncertainties in ERF, yet for the WMGHG the uncertainty is dominated by the climate response as its ERF is relatively well known (Figure 7.7). From the assessment of emulator responses in Cross-Chapter Box 7.1, there is high confidence that calibrated emulators such as the one employed here can represent the historical GSAT change between 1850–1900 and 1995–2014 to within 5% for the best estimate and 10% for the very likely range (Supplementary Material, Table 7.SM.4). This gives high confidence in the overall assessment of GSAT change for the response to ERFs over 1750–2019 derived from the emulator.

The total human forced GSAT change from 1750 to 2019 is calculated to be 1.29 [1.00 to 1.65] °C (high confidence). Although the total emulated GSAT change has high confidence, the confidence of the individual contributions matches those given for the ERF assessment in the subsections of (Section 7.3. The calculated GSAT change is comprised of a WMGHG warming of 1.58 [1.17 to 2.17] °C (high confidence), a warming from ozone changes of 0.23 [0.11 to 0.39] °C (high confidence), and a cooling of –0.50 [–0.22 to –0.96] °C from aerosol effects (medium confidence). The aerosol cooling has considerable regional time dependence (Section 6.4.3) but has weakened slightly over the last 20 years in the global mean (Figures 2.10 and 7.8). There is also a –0.06 [–0.15 to +0.01] °C contribution from surface reflectance changes which is dominated by land-use change (medium confidence). Changes in solar and volcanic activity are assessed to have together contributed a small change of –0.02 [–0.06 to +0.02] °C since 1750 (medium confidence).

The total (anthropogenic + natural) emulated GSAT between 1850–1900 and 2010–2019 is 1.14 [0.89 to 1.45] °C, compared to the assessed GSAT of 1.06 [0.88 to 1.21] °c (Section 2.3.1 and Cross Chapter Box 2.3). The emulated response is slightly warmer than the observations and has a larger uncertainty range. As the emulated response attempts to constrain to multiple lines of evidence (Supplementary Material 7.SM.2), only one of which is GSAT, they should not necessarily be expected to exactly agree. The larger uncertainty range in the emulated GSAT compared to the observations is reflective of the uncertainties in ECS, TCR and ERF (particularly the aerosol ERF) that drive the emulator response.

The emulator gives a range of GSAT response for the period 1750 to 1850–1900 of 0.09 [0.04 to 0.14] °C from anthropogenic ERFs. These results are used as a line of evidence for the assessment of this change in (Chapter 1 (Cross-Chapter Box 1.2), which gives an overall assessment of 0.1°C [likely range –0.1 to +0.3] °C.

Figure 7.8 presents the GSAT time series using ERF time series for individual forcing agents rather than their aggregation. It shows that for most of the historical period the long time scale total GSAT trend estimate from the emulator closely follows the CO₂ contribution. The GSAT estimate from non-CO₂ greenhouse gas forcing (from other WMGHGs and ozone) has been approximately cancelled out in the global average by a cooling GSAT trend from aerosols. However, since 1980 the aerosol cooling trend has stabilized and may have started to reverse, so that over the last few decades the long-term warming has been occurring at a faster rate than would be expected due to CO₂ alone (high confidence) (see also Sections 2.2.6 and 2.2.8). Throughout the record, but especially prior to 1930, periods of volcanic cooling dominate decadal variability. These estimates of the forced response are compared with model simulations and attributable warming estimates in (Chapter 3 Section 3.3.1).

Figure 7.8 | Attributed global surface air temperature change (GSAT) from 1750 to 2019 produced using the two-layer emulator (Supplementary Material 7.SM.2), forced with ERF derived in this chapter (displayed in Figure 2.10) and climate response constrained to assessed ranges for key climate metrics described in Cross-Chapter Box 7.1. The results shown are the medians from a 2237-member ensemble that encompasses uncertainty in forcing and climate response (year-2019 best estimates and uncertainties are shown in Figure 7.7 for several components). Temperature contributions are expressed for carbon dioxide (CO₂), methane (CH₄), nitrous oxide (N₂O), other well-mixed greenhouse gases (WMGHGs), ozone (O₃), aerosols, and other anthropogenic forcings, as well as total anthropogenic, solar, volcanic, and total forcing. Shaded uncertainty bands showvery likely (5–95%)ranges. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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The Planck response represents the additional thermal or longwave (LW) emission to space arising from vertically uniform warming of the surface and the atmosphere. The Planck response α P, often called the Planck feedback, plays a fundamental stabilizing role in Earth’s climate and has a value that is strongly negative: a warmer planet radiates more energy to space. A crude estimate of α Pcan be made using the normalized greenhouse effect g̃, defined as the ratio between the greenhouse effectG and the upwelling LW flux at the surface (Raval and Ramanathan, 1989). Current estimates (Section 7.2, Figure 7.2) give G= 159 W m^–2 and g̃≈ 0.4. Assumingg̃ is constant, one obtains for a surface temperature Ts= 288 K, α P= (g– 1) 4σT³s≈ –3.3 W m^–2°C^–1, whereσ is the Stefan–Boltzmann constant. This parameter α P is estimated more accurately using kernels obtained from meteorological reanalysis or climate simulations (Soden and Held, 2006; Dessler, 2013; Vial et al., 2013; Caldwell et al., 2016; Colman and Hanson, 2017; Zelinka et al., 2020). Discrepancies among estimates primarily arise because differences in cloud distributions make the radiative kernels differ (Kramer et al., 2019). Using six different kernels, Zelinka et al. (2020) obtained a spread of ±0.1 W m^–2°C^–1(one standard deviation). Discrepancies among estimates secondarily arise from differences in the pattern of equilibrium surface temperature changes among ESMs. For the CMIP5 and CMIP6 models this introduces a spread of ±0.04 W m^–2°C^–1(one standard deviation). The multi-kernel and multi-model mean of α P is equal to –3.20 W m^–2°C^–1for the CMIP5 and –3.22 W m^–2°C^–1for the CMIP6 models (Supplementary Material, Table 7.SM.5). Overall, there is high confidence in the estimate of the Planck response, which is assessed to be α P= –3.22 W m^–2°C^–1 with avery likely range of –3.4 to –3.0 W m^–2°C^–1and a likely range of –3.3 to –3.1 W m^–2°C^–1.

The Planck temperature response ΔTP is the equilibrium temperature change in response to a forcing ΔF when the net feedback parameter is equal to the Planck response parameter: ΔTP= –ΔF / α P.

Two decompositions are generally used to analyse the feedbacks associated with a change in the water-vapour and temperature lapse-rate in the troposphere. As in any system, many feedback decompositions are possible, each of them highlighting a particular property or aspect of the system (Ingram, 2010; Held and Shell, 2012; Dufresne and Saint-Lu, 2016). The first decomposition considers separately the changes (and therefore feedbacks) in the lapse rate (LR) and specific humidity (WV). The second decomposition considers changes in the lapse rate assuming constant relative humidity (LR*) separately from changes in relative humidity (RH).

The specific humidity (WV) feedback, also known as the water-vapour feedback, quantifies the change in radiative flux at the TOA due to changes in atmospheric water vapour concentration associated with a change in global mean surface air temperature. According to theory, observations and models, the water vapour increase approximately follows the Clausius–Clapeyron relationship at the global scale with regional differences dominated by dynamical processes (Section 8.2.1; Sherwood et al., 2010a; Chung et al., 2014; Romps, 2014; R. Liu et al., 2018; Schröder et al., 2019). Greater atmospheric water vapour content, particularly in the upper troposphere, results in enhanced absorption of LW and SW radiation and reduced outgoing radiation. This is a positive feedback. Atmospheric moistening has been detected in satellite records (Section 2.3.1.3.3), it is simulated by climate models (Section 3.3.2.2), and the estimates agree within model and observational uncertainty (Soden et al., 2005; Dessler, 2013; Gordon et al., 2013; Chung et al., 2014). The estimate of this feedback inferred from satellite observations is α WV= 1.85 ± 0.32 W m^–2°C^–1(R. Liu et al., 2018). This is consistent with the value α WV= 1.77 ± 0.20 W m^–2°C^–1(one standard deviation) obtained with CMIP5 and CMIP6 models (Zelinka et al., 2020).

The lapse-rate (LR) feedback quantifies the change in radiative flux at the TOA due to a non­uniform change in the vertical temperature profile. In the tropics, the vertical temperature profile is mainly driven by moist convection and is close to a moist adiabat. The warming is larger in the upper troposphere than in the lower troposphere (Manabe and Wetherald, 1975; Santer et al., 2005; Bony et al., 2006), leading to a larger radiative emission to space and therefore a negative feedback. This larger warming in the upper troposphere than at the surface has been observed over the last 20 years thanks to the availability of sufficiently accurate observations (Section 2.3.1.2.2). In the extratropics, the vertical temperature profile is mainly driven by a balance between radiation, meridional heat transport and ocean heat uptake (Rose et al., 2014). Strong winter temperature inversions lead to warming that is larger in the lower troposphere (Payne et al., 2015; Feldl et al., 2017a) and a positive LR feedback in polar regions (Section 7.4.4.1; Manabe and Wetherald, 1975; Bintanja et al., 2012; Pithan and Mauritsen, 2014). However, the tropical contribution dominates, leading to a negative global mean LR feedback (Soden and Held, 2006; Dessler, 2013; Vial et al., 2013; Caldwell et al., 2016). The LR feedback has been estimated at interannual time scales using meteorological reanalysis and satellite measurements of TOA fluxes (Dessler, 2013). These estimates from climate variability are consistent between observations and ESMs (Dessler, 2013; Colman and Hanson, 2017). The mean and standard deviation of this feedback under global warming based on the cited studies are α LR= –0.50 ± 0.20 W m^–2°C^–1(Dessler, 2013; Caldwell et al., 2016; Colman and Hanson, 2017; Zelinka et al., 2020).

The second decomposition was proposed by Held and Shell (2012) to separate the response that would occur under the assumption that relative humidity remains constant from that due to the change in relative humidity. The feedback is decomposed into three: (i) change in water vapour due to an identical temperature increase at the surface and throughout the troposphere assuming constant relative humidity, which will be called the Clausius–Clapeyron (CC) feedback here; (ii) change in LR assuming constant relative humidity (LR*); (iii) change in relative humidity (RH). Since AR5 it has been clarified that by construction, the sum of the temperature lapse rate and specific humidity (LR + WV) feedbacks is equal to the sum of the Clausius–Clapeyron feedback, the lapse rate feedback assuming constant relative humidity, and the feedback from changes in relative humidity (that is, CC + LR* + RH). Therefore, each of these two sums may simply be referred to as the ‘water-vapour plus lapse-rate’ feedback.

The CC feedback has a large positive value due to well understood thermodynamic and radiative processes: α CC= 1.36 ± 0.04 W m^–2°C^–1(one standard deviation; Held and Shell, 2012; Zelinka et al., 2020). The lapse-rate feedback assuming a constant relative humidity (LR*) in CMIP6 models has small absolute values ( α LR_*= –0.10 ± 0.07 W m^–2°C^–1(one standard deviation)), as expected from theoretical arguments (Ingram, 2010, 2013). It includes the pattern effect of surface warming that modulates the lapse rate and associated specific humidity changes (Po-Chedley et al., 2018b). The relative humidity feedback is close to zero ( α RH= 0.00 ± 0.06 W m^–2°C^–1(one standard deviation)) and the spread among models is confined to the tropics (Sherwood et al., 2010b; Vial et al., 2013; Takahashi et al., 2016; Po-Chedley et al., 2018b). The change in upper tropospheric RH is closely related to model representation of current climate (Sherwood et al., 2010b; Po-Chedley et al., 2019), and a reduction in model RH biases is expected to reduce the uncertainty of the RH feedback. At interannual time scales, it has been shown that the change in RH in the tropics is related to the change of the spatial organization of deep convection (Holloway et al., 2017; Bony et al., 2020).

Both decompositions allow estimates of the sum of the lapse-rate and specific humidity feedbacks α LR+WV. The multi-kernel and multi-model mean of α LR+WV is equal to 1.24 and 1.26 W m^–2°C^–1respectively for CMIP5 and CMIP6 models, with a standard deviation of 0.10 W m^–2°C^–1(Zelinka et al., 2020). These values are larger than the recently assessed value of 1.15 W m^–2°C^–1by Sherwood et al. (2020) as a larger set of kernels, including those obtained from meteorological reanalysis, are used here.

Since AR5, the effect of the water vapour increase in the stratosphere as a result of global warming has been investigated by different studies. This increase produces a positive feedback between 0.1 and 0.3 W m^–2°C^–1if the stratospheric radiative response is computed assuming temperatures that are adjusted with fixed dynamical heating (Dessler et al., 2013; Banerjee et al., 2019). However, various feedbacks reduce this temperature adjustment and the overall physical (water vapour, temperature and dynamical) stratospheric feedback becomes much smaller (0.0 to 0.1 W m^–2°C^–1; Huang et al., 2016, 2020; Li and Newman, 2020), with uncertainty arising from limitations of current ESMs in simulating stratospheric processes. The total stratospheric feedback is assessed at 0.05 ± 0.1 W m^–2°C^–1(one standard deviation).

The combined ‘water-vapour plus lapse-rate’ feedback is positive. The main physical processes that drive this feedback are well understood and supported by multiple lines of evidence including models, theory and observations. The combined ‘water-vapour plus lapse-rate’ feedback parameter is assessed to be α LR+WV= 1.30 W m^–2°C^–1, with avery likely range of 1.1 to 1.5 W m^–2°C^–1and a likely range of 1.2 to 1.4 W m^–2°C^–1 with high confidence.

Surface albedo is determined primarily by reflectance at Earth’s surface, but also by the spectral and angular distribution of incident solar radiation. Changes in surface albedo result in changes in planetary albedo that are roughly reduced by two-thirds, owing to atmospheric absorption and scattering, with variability and uncertainty arising primarily from clouds (Bender, 2011; Donohoe and Battisti, 2011; Block and Mauritsen, 2013). Temperature change induces surface-albedo change through several direct and indirect means. In the present climate and at multi-decadal time scales, the largest contributions by far are changes in the extent of sea ice and seasonal snow cover, as these media are highly reflective and are located in regions that are close to the melting temperature (Sections 2.3.2.1 and 2.3.2.2). Reduced snow cover on sea ice may contribute as much to albedo feedback as reduced extent of sea ice (Zhang et al., 2019). Changes in the snow metamorphic rate, which generally reduces snow albedo with warmer temperature, and warming-induced consolidation of light-absorbing impurities near the surface, also contribute secondarily to the albedo feedback (Flanner and Zender, 2006; Qu and Hall, 2007; Doherty et al., 2013; Tuzet et al., 2017). Other contributors to albedo change include vegetation state (assessed separately in (Section 7.4.2.5), soil wetness and ocean roughness.

Several studies have attempted to derive surface-albedo feedback from observations of multi-decadal changes in climate, but only over limited spatial and inconsistent temporal domains, inhibiting a purely observational synthesis of global surface-albedo feedback ( α A). Flanner et al. (2011) applied satellite observations to determine that the northern hemisphere (NH) cryosphere contribution to global α Aover the period 1979–2008 was 0.48 [likely range 0.29 to 0.78] W m^–2°C^–1, with roughly equal contributions from changes in land snow cover and sea ice. Since AR5, and over similar periods of observation, Crook and Forster (2014) found an estimate of 0.8 ± 0.3 W m^–2°C^–1(one standard deviation) for the total NH extratropical surface-albedo feedback, when averaged over global surface area. For Arctic sea ice alone, Pistone et al. (2014) and Cao et al. (2015) estimated the contribution to global α Ato be 0.31 ± 0.04 W m^–2°C^–1(one standard deviation) and 0.31 ± 0.08 W m^–2°C^–1(one standard deviation), respectively, whereas Donohoe et al. (2020) estimated it to be only 0.16 ± 0.04 W m^–2°C^–1(one standard deviation). Much of this discrepancy can be traced to different techniques and data used for assessing the attenuation of surface-albedo change by Arctic clouds. For the NH land snow, Chen et al. (2016) estimated that observed changes during 1982–2013 contributed (after converting from NH temperature change to global mean temperature change) by 0.1 W m^–2°C^–1to global α A, smaller than the estimate of 0.24 W m^–2°C^–1from Flanner et al. (2011). The contribution of the Southern Hemisphere (SH) to global α A is expected to be small because seasonal snow cover extent in the SH is limited, and trends in SH sea ice extent are relatively flat over much of the satellite record (Section 2.3.2).

CMIP5 and CMIP6 models show moderate spread in global α A, determined from century time scale changes(Qu and Hall, 2014; Schneider et al., 2018; Thackeray and Hall, 2019; Zelinka et al., 2020), owing to variations in modelled sea ice loss and snow cover response in boreal forest regions. The multi-model mean global-scale α A(from all contributions) over the 21st century in CMIP5 models under the RCP8.5 scenario was derived by Schneider et al. (2018) to be 0.40 ± 0.10 W m^–2°C^–1(one standard deviation). Moreover, they found that modelled α Adoes not decline over the 21st century, despite large losses of snow and sea ice, though a weakened feedback is apparent after 2100. Using the idealized abrupt 4xCO2 , as for the other feedbacks, the estimate of the global-scale albedo feedback in the CMIP5 models is 0.35 ± 0.08 W m^–2°C^–1(one standard deviation; Vial et al., 2013; Caldwell et al., 2016). The CMIP6 multi-model mean varies from 0.3 to 0.5 W m^–2°C^–1depending on the kernel used (Zelinka et al., 2020). Donohoe et al. (2020) derived a multi-model mean α Aand its inter-model spread of 0.37 ± 0.19 W m^–2°C^–1from the CMIP5abrupt 4xCO2 ensemble, employing model-specific estimates of atmospheric attenuation and thereby avoiding bias associated with use of a single radiative kernel.

The surface-albedo feedback estimates using centennial changes have been shown to be highly correlated to those using seasonal regional changes for NH land snow (Qu and Hall, 2014) and Arctic sea ice (Thackeray and Hall, 2019). For the NH land snow, because the physics underpinning this relationship are credible, this opens the possibility to use it as an emergent constraint (Qu and Hall, 2014). Considering only the eight models whose seasonal cycle of albedo feedback falls within the observational range does not change the multi-model mean contribution to global α A(0.08 W m^–2°C^–1) but decreases the inter-model spread by a factor of two (from ±0.03 to ±0.015 W m^–2°C^–1; Qu and Hall, 2014). For Arctic sea ice, Thackeray and Hall (2019) show that the seasonal cycle also provides an emergent constraint, at least until mid-century when the relationship degrades. They find that the CMIP5 multi-model mean of the Arctic sea ice contribution to α A is 0.13 W m^–2°C^–1and that the inter-model spread is reduced by a factor of two (from ±0.04 to ±0.02 W m^–2°C^–1) when the emergent constraint is used. This model estimate is smaller than observational estimates (Pistone et al., 2014; Cao et al., 2015) except those of Donohoe et al. (2020). This can be traced to CMIP5 models generally underestimating the rate of Arctic sea ice loss during recent decades (Section 9.3.1; Stroeve et al., 2012; Flato et al., 2013), though this may also be an expression of internal variability, since the observed behaviour is captured within large ensemble simulations (Notz, 2015). CMIP6 models better capture the observed Arctic sea ice decline (Section 3.4.1). In the SH the opposite situation is observed. Observations show relatively flat trends in SH sea ice over the satellite era (Section 2.3.2.1) whereas CMIP5 models simulate a small decrease (Section 3.4.1). SH α A is presumably larger in models than observations but only contributes about one quarter of the global α A. Thus, we assess that α Aestimates are consistent, at global scale, in CMIP5 and CMIP6 models and satellite observations, though hemispheric differences and the role of internal variability need to be further explored.

Based on the multiple lines of evidence presented above that include observations, CMIP5 and CMIP6 models and theory, the global surface-albedo feedback is assessed to be positive with high confidence. The basic phenomena that drive this feedback are well understood and the different studies cover a large variety of hypotheses or behaviours, including how the evolution of clouds affects this feedback. The value of the global surface-albedo feedback is assessed to be α A= 0.35 W m^–2°C^–1, with avery likely range from 0.10 to 0.60 W m^–2°C^–1and a likely range from 0.25 to 0.45 W m^–2°C^–1 with high confidence.

The feedbacks presented in the previous sections (Sections 7.4.2.1–7.4.2.4) are directly linked to physical climate variables (for example temperature, water vapour, clouds, or sea ice). The central role of climate feedbacks associated with these variables has been recognized since early studies of climate change. However, in addition to these physical climate feedbacks, the Earth system includes feedbacks for which the effect of global mean surface temperature change on the TOA energy budget is mediated through other mechanisms, such as the chemical composition of the atmosphere, or by vegetation changes. Among these additional feedbacks, the most important is the CO₂ feedback that describes how a change of the global surface temperature affects the atmospheric CO₂ concentration. In ESM simulations in which CO₂ emissions are prescribed, changes in surface carbon fluxes affect the CO₂ concentration in the atmosphere, the TOA radiative energy budget, and eventually the global mean surface temperature. In ESM simulations in which the CO₂ concentration is prescribed, changes in the carbon cycle allow compatible CO₂ emissions to be calculated, that is, the CO₂ emissions that are compatible with both the prescribed CO₂ concentration and the representation of the carbon cycle in the ESM. The CO₂ feedback is assessed in (Chapter 5 Section 5.4). The framework presented in this chapter assumes that the CO₂ concentration is prescribed, and our assessment of the net feedback parameter, α , does not include carbon cycle feedbacks on the atmospheric CO₂ concentration (Section 7.1 and Box 7.1). However, our assessment of α does include non-CO₂ biogeochemical feedbacks (including effects due to changes in atmospheric methane concentration; Section 7.4.2.5.1) and biogeophysical feedbacks (Section 7.4.2.5.2). A synthesis of the combination of biogeophysical and non-CO₂ biogeochemical feedbacks is given in Section 7.4.2.5.3.

Although long-term radiative feedbacks associated with ice sheets are not included in our definition of ECS (Box 7.1), the relevant feedback parameter is assessed here because the time scales on which these feedbacks act are relatively uncertain, and the long-term temperature response to CO₂ forcing of the entire Earth system may be of interest.

Earth’s ice sheets (Greenland and Antarctica) are sensitive to climate change (Section 9.4; Pattyn et al., 2018). Their time evolution is determined by both their surface mass balance and ice dynamic processes, with the latter being particularly important for the West Antarctic Ice Sheet. Surface mass balance depends on the net energy and hydrological fluxes at their surface, and there are mechanisms of ice-sheet instability that depend on ocean temperatures and basal melt rates (Section 9.4.1.1). The presence of ice sheets affects Earth’s radiative budget, hydrology, and atmospheric circulation due to their characteristic high albedo, low roughness length, and high altitude, and they influence ocean circulation through freshwater input from calving and melt (e.g., Fyke et al., 2018). Ice-sheet changes also modify surface albedo through the attendant change in sea level and therefore land area (Abe-Ouchi et al., 2015). The time scale for ice sheets to reach equilibrium is of the order of thousands of years (Clark et al., 2016). Due to the long time scales involved, it is a major challenge to run coupled climate–ice sheet models to equilibrium, and as a result, long-term simulations are often carried out with lower complexity models, and/or are asynchronously coupled.

In AR5, it was described that both the Greenland and Antarctic ice sheets would continue to lose mass in a warming world (M. Collins et al., 2013), with a continuation in sea level rise beyond the year 2500 assessed as virtually certain. However, there was low confidence in the associated radiative feedback mechanisms, and as such, there was no assessment of the magnitude of long-term radiative feedbacks associated with ice sheets. That assessment is consistent with SROCC, wherein it was stated that ‘with limited published studies to draw from and no simulations run beyond 2100, firm conclusions regarding the net importance of atmospheric versus ocean melt feedbacks on the long-term future of Antarctica cannot be made.’

The magnitude of the radiative feedback associated with changes to ice sheets can be quantified by comparing the global mean long-term equilibrium temperature response to increased CO₂ concentrations in simulations that include interactive ice sheets with that of simulations that do not include the associated ice sheet–climate interactions (Swingedouw et al., 2008; Vizcaíno et al., 2010; Goelzer et al., 2011; Bronselaer et al., 2018; Golledge et al., 2019). These simulations indicate that on multi-centennial time scales, ice-sheet mass loss leads to freshwater fluxes that can modify ocean circulation (Swingedouw et al., 2008; Goelzer et al., 2011; Bronselaer et al., 2018; Golledge et al., 2019). This leads to reduced surface warming (by about 0.2°C in the global mean after 1000 years; Section 7.4.4.1.1; Goelzer et al., 2011), although other work suggests no net global temperature effect of ice-sheet mass loss (Vizcaíno et al., 2010). However, model simulations in which the Antarctic Ice Sheet is removed completely in a paleoclimate context indicate a positive global mean feedback on multi-millennial time scales due primarily to the surface-albedo change (Goldner et al., 2014a; Kennedy-Asser et al., 2019); in (Chapter 9 Section 9.6.3) it is assessed that such ice-free conditions could eventually occur given 7°C–13°C of warming. This net positive feedback from ice-sheet mass loss on long time scales is also supported by model simulations of the mid-Pliocene Warm Period (MPWP; Cross-chapter Box 2.1) in which the volume and area of the Greenland and West Antarctic ice sheets are reduced in model simulations in agreement with geological data (Chandan and Peltier, 2018), leading to surface warming. As such, overall, on multi-centennial time scales the feedback parameter associated with ice sheets is likely negative (medium confidence), but on multi-millennial time scales by the time the ice sheets reach equilibrium, the feedback parameter is very likely positive (high confidence) (Table 7.10). However, a relative lack of models carrying out simulations with and without interactive ice sheets over centennial to millennial time scales means that there is currently not enough evidence to quantify the magnitude of these feedbacks, or the time scales on which they act.

Table 7.10 summarizes the estimates and the assessment of the individual and the net feedbacks presented in the above sections. The uncertainty range of the net climate feedback was obtained by adding standard deviations of individual feedbacks in quadrature, assuming that they are independent and follow the Gaussian distribution. It is virtually certain that the net climate feedback is negative, primarily due to the Planck temperature response, indicating that climate acts to stabilize in response to radiative forcing imposed to the system. Supported by the level of confidence associated with the individual feedbacks, it is also virtually certain that the sum of the non-Planck feedbacks is positive. Based on Table 7.10 these climate feedbacks amplify the Planck temperature response by about 2.8 [1.9 to 5.9] times . Cloud feedback remains the largest contributor to uncertainty of the net feedback, but the uncertainty is reduced compared to AR5. A secondary contribution to the net feedback uncertainty is the biogeophysical and non-CO₂ biogeochemical feedbacks, which together are assessed to have a central value near zero and thus do not affect the central 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 m^–2°C^–1, and very likely from –1.81 to –0.51 W m^–2°C^–1.

Feedback parameters in climate models are calculated assuming that they are independent of each other, except for a well-known co-dependency between the water vapour (WV) and lapse rate (LR) feedbacks. When the inter-model spread of the net climate feedback is computed by adding in quadrature the inter-model spread of individual feedbacks, it is 17% wider than the spread of the net climate feedback directly derived from the ensemble. This indicates that the feedbacks in climate models are partly co-dependent. Two possible co-dependencies have been suggested (Huybers, 2010; Caldwell et al., 2016). One is a negative covariance between the LR and longwave cloud feedbacks, which may be accompanied by a deepening of the troposphere (O’Gorman and Singh, 2013; Yoshimori et al., 2020) leading both to greater rising of high-clouds and a larger upper-tropospheric warming. The other is a negative covariance between albedo and shortwave cloud feedbacks, which may originate from the Arctic regions: a reduction in sea ice enhances the shortwave cloud radiative effect because the ocean surface is darker than sea ice (Gilgen et al., 2018). This covariance is reinforced as the decrease of sea ice leads to an increase in low-level clouds (Mauritsen et al., 2013). However, the mechanism causing these co-dependences between feedbacks is not well understood yet and a quantitative assessment based on multiple lines of evidence is difficult. Therefore, this synthesis assessment does not consider any co-dependency across individual feedbacks.

The assessment of the net climate feedback presented above is based on a single approach (i.e., process understanding) and directly results in a value for ECS given in (Section 7.5.1; this is in contrast to the synthesis assessment of ECS in (Section 7.5.5 which combines multiple approaches. The total (net) feedback parameter consistent with the final synthesis assessment of the ECS and Equation 7.1 (Box 7.1) is provided there.

Since AR5, many modelling groups have newly participated in CMIP experiments, leading to an increase in the number of models in CMIP6 Section 1.5.4). Other modelling groups that contributed to CMIP5 also updated their ESMs for carrying out CMIP6 experiments. While some of the CMIP6 models share components and are therefore not independent, they are analysed independently when calculating climate feedbacks. This, and more subtle forms of model inter-dependence, creates challenges when determining appropriate model weighting schemes (Section 1.5.4). Additionally, it must be kept in mind that the ensemble sizes of the CMIP5 and CMIP6 models are not sufficiently large to sample the full range of model uncertainty.

The multi-model mean values of all physical climate feedbacks are calculated using the radiative kernel method (Section 7.4.1) and compared with the assessment in the previous sections (Figure 7.10). For CMIP models, there is a discrepancy between the net climate feedback calculated directly using the time evolutions of ΔT and ΔN in each model and the accumulation of individual feedbacks, but it is negligibly small (Supplementary Material 7.SM.4). Feedbacks due to biogeophysical and non-CO₂ biogeochemical processes are included in some models but neglected in the kernel analysis. In AR6, biogeophysical and non-CO₂ biogeochemical feedbacks are explicitly assessed (Section 7.4.2.5).

Figure 7.10 | Global mean climate feedbacks estimated in abrupt 4xCO2 simulations of 29 CMIP5 models (light blue) and 49 CMIP6 models (orange), compared with those assessed in this Report (red). Individual feedbacks for CMIP models are averaged across six radiative kernels as computed in Zelinka et al. (2020). The white line, black box and vertical line indicate the mean, 66% and 90% ranges, respectively. The shading represents the probability distribution across the full range of GCM/ESM values and for the 2.5–97.5 percentile range of the AR6 normal distribution. The unit is W m^–2°C^–1. Feedbacks associated with biogeophysical and non-CO₂ biogeochemical processes are assessed in AR6, but they are not explicitly estimated from general circulation models (GCMs)/Earth system models (ESMs) in CMIP5 and CMIP6. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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All the physical climate feedbacks apart from clouds are very similar in the CMIP5 and CMIP6 model ensembles (see also Table 7.10). These values, where possible supported by other lines of evidence, are used for assessing feedbacks in Sections 7.4.2.1–7.4.2.3. A difference found between CMIP5 and CMIP6 models is the net cloud feedback, which is larger in CMIP6 by about 20%. This change is the major cause of less-negative values of the net climate feedback in CMIP6 than in CMIP5 and hence an increase in modelled ECs (Section 7.5.1).

A remarkable improvement of cloud representation in some CMIP6 models is the reduced error of the too-weak negative shortwave CRE over the Southern Ocean (Bodas-Salcedo et al., 2019; Gettelman et al., 2019) due to a more realistic simulation of supercooled liquid droplets and associated cloud optical depths that were biased low commonly in CMIP5 models (McCoy et al., 2014a, b). Because the negative cloud optical depth feedback occurs due to ‘brightening’ of clouds via phase change from ice to liquid cloud particles in response to surface warming (Cesana and Storelvmo, 2017), the extratropical cloud shortwave feedback tends to be less negative or even slightly positive in models with reduced errors (Bjordal et al., 2020; Zelinka et al., 2020). The assessment of cloud feedbacks in (Section 7.4.2.4 incorporates estimates from these improved ESMs. Yet, there still remain other shared model errors, such as in the subtropical low-clouds (Calisto et al., 2014) and tropical anvil clouds (Mauritsen and Stevens, 2015), hampering an assessment of feedbacks associated with these cloud regimes based only on ESMs (Section 7.4.2.4).

There are several modelling studies since AR5 in which ESMs of varying complexity have been used to explore temperature dependence of feedbacks, either under modern (Hansen et al., 2013; Jonko et al., 2013; Meraner et al., 2013; Good et al., 2015; Duan et al., 2019; Mauritsen et al., 2019; Rohrschneider et al., 2019; Stolpe et al., 2019; Bloch-Johnson et al., 2020; Rugenstein et al., 2020) or paleo (Caballero and Huber, 2013; Zhu et al., 2019a) climate conditions, typically by carrying out multiple simulations across successive CO₂ doublings. A non-linear temperature response to these successive doublings may be partly due to forcing that increases more (or less) than expected from a purely logarithmic dependence (Section 7.3.2; Etminan et al., 2016), and partly due to state-dependence in feedbacks; however, not all modelling studies have partitioned the non-linearities in temperature response between these two effects. Nonetheless, there is general agreement among ESMs that the net feedback parameter, α , increases (i.e., becomes less negative) as temperature increases from pre-industrial levels (i.e., sensitivity to forcing increases as temperature increases; e.g., Meraner et al., 2013; see Figure 7.11). The associated increase in sensitivity to forcing is, in most models, due to the water vapour (Section 7.4.2.2) and cloud (Section 7.4.2.4) feedback parameters increasing with warming (Caballero and Huber, 2013; Meraner et al., 2013; Zhu et al., 2019a; Rugenstein et al., 2020; Sherwood et al., 2020). These changes are offset partially by the surface-albedo feedback parameter decreasing (Jonko et al., 2013; Meraner et al., 2013; Rugenstein et al., 2020), as a consequence of a reduced amount of snow and sea ice cover in a much warmer climate. At the same time, there is little change in the Planck response (Section 7.4.2.1), which has been shown in one model to be due to competing effects from increasing Planck emission at warmer temperatures and decreasing planetary emissivity due to increased CO₂ and water vapour (Mauritsen et al., 2019). Analysis of the spatial patterns of the non-linearities in temperature response (Good et al., 2015) suggests that these patterns are linked to a reduced weakening of the AMOC, and changes to evapotranspiration. The temperature dependence of α is also found in model simulations of high-CO₂ paleoclimates (Caballero and Huber, 2013; Zhu et al., 2019a). The temperature dependence is not only evident at very high CO₂ concentrations in excess of 4×CO₂, but also apparent in the difference in temperature response to a 2×CO₂ forcing compared with to a 4×CO₂ forcing (Mauritsen et al., 2019; Rugenstein et al., 2020), and as such is relevant for interpreting century-scale climate projections.

Despite the general agreement that α increases as temperature increases from pre-industrial levels (Figure 7.11), other modelling studies have found the opposite (Duan et al., 2019; Stolpe et al., 2019). Modelling studies exploring state-dependence in climates colder than today, including in cold paleoclimates such as the LGM, provide conflicting evidence of either decreased (Yoshimori et al., 2011) or increased (Kutzbach et al., 2013; Stolpe et al., 2019) temperature response per unit forcing during cold climates compared to the modern era.

In contrast to most ESMs, the majority of Earth system models of intermediate complexity (EMICs) do not exhibit state-dependence, or have a net feedback parameter that decreases with increasing temperature (Pfister and Stocker, 2017). This is unsurprising since EMICs usually do not include process-based representations of water-vapour and cloud feedbacks. Although this shows that care must be taken when interpreting results from current generation EMICs, Pfister and Stocker (2017) also suggest that non-linearities in feedbacks can take a long time to emerge in model simulations due to slow adjustment time scales associated with the ocean; longer simulations also allow better estimates of equilibrium warming (Bloch-Johnson et al., 2020). This implies that multi-century simulations (Rugenstein et al., 2020) could increase confidence in ESM studies examining state-dependence.

The possibility of more substantial changes in climate feedbacks, sometimes accompanied by hysteresis and/or irreversibility, has been suggested from some theoretical and modelling studies. It has been postulated that such changes could occur on a global scaleand across relatively narrow temperature changes (Popp et al., 2016; von der Heydt and Ashwin, 2016; Steffen et al., 2018; Schneider et al., 2019; Ashwin and von der Heydt, 2020; Bjordal et al., 2020). However, the associated mechanisms are highly uncertain, and as such there is low confidence as to whether such behaviour exists at all, and in the temperature thresholds at which it might occur.

Overall, the modelling evidence indicates that there is medium confidence that the net feedback parameter, α , increases (i.e., becomes less negative) with increasing temperature (i.e., that sensitivity to forcing increases with increasing temperature), under global surface background temperatures at least up to 40°C (Meraner et al., 2013; Seeley and Jeevanjee, 2021), and medium confidence that this temperature dependence primarily derives from increases in the water-vapour and shortwave cloud feedbacks. This assessment is further supported by recent analysis of CMIP6 model simulations (Bloch-Johnson et al., 2020) in the framework of nonlinMIP (Good et al., 2016), which showed that out of 10 CMIP6 models, seven of them showed an increase of the net feedback parameter with temperature, primarily due to the water-vapour feedback.

Several studies have estimated ECS from observations of the glacial–interglacial cycles of the last approximately 2 million years, and found a state-dependence, with more-negative α (i.e., lower sensitivity to forcing) during colder periods of the cycles and less-negative α during warmer periods (von der Heydt et al., 2014; Köhler et al., 2015, 2017; Friedrich et al., 2016; Royer, 2016; Snyder, 2019); see summaries in Skinner (2012) and von der Heydt et al. (2016). However, the nature of the state-dependence derived from these observations is dependent on the assumed ice-sheet forcing (Köhler et al., 2015; Stap et al., 2019), which is not well known, due to a relative lack of proxy indicators of ice-sheet extent and distribution prior to the LGM (Cross-Chapter Box 2.1). Furthermore, many of these glacial–interglacial studies estimate a very strong temperature-dependence of α (Figure 7.11) that is hard to reconcile with the other lines of evidence, including proxy estimates from warmer paleoclimates. However, if the analysis excludes time periods when the temperature and CO₂ data are not well correlated, which occurs in general at times when sea level is falling and obliquity is decreasing, the state-dependence reduces (Köhler et al., 2018). Despite these uncertainties, due to the agreement in the sign of the temperature-dependence from all these studies, there is medium confidence from the paleoclimate proxy record that the net feedback parameter, α , was less negative in the warm periods than in the cold periods of the glacial–interglacial cycles.

Paleoclimate proxy evidence from past high-CO₂ time periods much warmer than present (the early Eocene and Paleocene–Eocene Thermal Maximum, PETM; Cross-Chapter Box 2.1) show that the feedback parameter increases as temperature increases (Anagnostou et al., 2016, 2020; Shaffer et al., 2016). However, such temperature-dependence of feedbacks was not found in the warm Pliocene relative to the cooler Pleistocene (Martínez-Botí et al., 2015), although the temperature changes are relatively small at this time, making temperature-dependence challenging to detect given the uncertainties in reconstructing global mean temperature and forcing. Overall, the paleoclimate proxy record provides medium confidence that the net feedback parameter, α , was less negative in these past warm periods than in the present day.

Figure 7.11 | Feedback parameter, α (W m–2°C–1), as a function of global mean surface air temperature anomaly relative to pre-industrial, for ESM simulations (red circles and lines) (Caballero and Huber, 2013; Jonko et al., 2013; Meraner et al., 2013; Good et al., 2015; Duan et al., 2019; Mauritsen et al., 2019; Stolpe et al., 2019; Zhu et al., 2019a), and derived from paleoclimate proxies (grey squares and lines) (von der Heydt et al., 2014; Anagnostou et al., 2016, 2020; Friedrich et al., 2016; Royer, 2016; Shaffer et al., 2016; Köhler et al., 2017; Snyder, 2019; Stap et al., 2019). For the ESM simulations, the value on The x-axis refers to the average of the temperature before and after the system has equilibrated to a forcing (in most cases a CO₂ doubling), and is expressed as an anomaly relative to an associated pre-industrial global mean temperature from that model. The light blue shaded square extends across the assessed range of α (Table 7.10) on The y-axis, and on The x-axis extends across the approximate temperature range over which the assessment of α is based (taken as from zero to the assessed central value of ECS; see Table 7.13). Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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Overall, independent lines of evidence from models (Section 7.4.3.1) and from the paleoclimate proxy record (Section 7.4.3.2) lead to high confidence that the net feedback parameter, α , increases (i.e., becomes less negative) as temperature increases; that is, that sensitivity to forcing increases as temperature increases (Figure 7.11). This temperature-dependence should be considered when estimating ECS from ESM simulations in which CO₂ is quadrupled (Section 7.5.5) or from paleoclimate observations from past time periods colder or warmer than today (Section 7.5.4). Although individual lines of evidence give only medium confidence, the overall high confidence comes from the multiple models that show the same sign of the temperature-dependence of α , the general agreement in evidence from the paleo proxy and modelling lines of evidence, and the agreement between proxy evidence from both cold and warm past climates. However, due to the large range in estimates of the magnitude of the temperature-dependence of α across studies (Figure 7.11), a quantitative assessment cannot currently be given, which provides a challenge for including this temperature-dependence in emulator-based future projections (Cross-Chapter Box 7.1). Greater confidence in the modelling lines of evidence could be obtained from simulations carried out for several hundreds of years (Rugenstein et al., 2020), substantially longer than in many studies, and from more models carrying out simulations at multiple CO₂ concentrations. Greater confidence in the paleoclimate lines of evidence would be obtained from stronger constraints on atmospheric CO₂ concentrations, ice-sheet forcing, and temperatures, during past warm climates.

Polar amplification describes the phenomenon where surface temperature change at high latitudes exceeds the global average surface temperature change in response to radiative forcing of the climate system. Arctic amplification, often defined as the ratio of Arctic to global surface warming, is a ubiquitous emergent feature of climate model simulations (Section 4.5.1 and Figure 7.12a; Holland and Bitz, 2003; Pithan and Mauritsen, 2014) and is also seen in observations (Section 2.3.1). However, both climate models and observations show relatively less warming of the SH high latitudes compared to the Northern Hemisphere (NH) high latitudes over the historical record (Section 2.3.1), a characteristic that is projected to continue over the 21st century (Section 4.5.1). Since AR5 there is a much-improved understanding of the processes that drive polar amplification in the NH and delay its emergence in the Sh (Section 7.4.4.1.1). Furthermore, the paleoclimate record provides evidence for polar amplification from multiple time periods associated with changes in CO₂ (Hollis et al., 2019; Cleator et al., 2020; McClymont et al., 2020; Tierney et al., 2020b), and allows an evaluation of polar amplification in model simulations of these periods (Section 7.4.4.1.2). Research since AR5 identifies changes in the degree of polar amplification over time, particularly in the SH, as a key factor affecting how radiative feedbacks may evolve in the future (Section 7.4.4.3).

Figure 7.12 | Contributions of effective radiative forcing, ocean heat uptake, atmospheric heat transport, and radiative feedbacks to regional surface temperature changes at year 100 of abrupt 4xCO2 simulations of CMIP6 Earth system models (ESMs). Figure 7.12: (a) Pattern of near-surface air temperature change. (b–d) Contributions to net Arctic (>60°N), tropical (30°S–30°N), and Antarctic (<60°S) warming calculated by dividing regional-average energy inputs by the magnitude of the regional-average Planck response. The contributions from radiative forcing, changes in moist, dry-static, and total atmospheric energy transport, ocean heat uptake, and radiative feedbacks (orange bars) all sum to the value of net warming (grey bar). Inset shows regional warming contributions associated with individual feedbacks, all summing to the total feedback contribution. Uncertainties (represented by black whiskers) show the interquartile range (25th and 75th percentiles) across models. The warming contributions (units of °C) for each process are diagnosed by calculating the energy flux (units of W m^–2) that each process contributes to the atmosphere over a given region, either at the top-of-atmosphere or surface, then dividing that energy flux by the magnitude of the regional Planck response (around 3.2 W m^–2°C^–1but varying with region). By construction, the individual warming contributions sum to the total warming in each region. Radiative kernel methods (Section 7.4.1) are used to decompose the net energy input from radiative feedbacks into contributions from changes in atmospheric water vapour, lapse rate, clouds, and surface albedo (Zelinka et al. (2020) using the Huang et al. (2017) radiative kernel). The CMIP6 models included are those analysed by Zelinka et al. (2020) and the warming contribution analysis is based on that of Goosse et al. (2018). Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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Research published since AR5 identifies changes in the tropical Pacific Ocean zonal SST gradient over time as a key factor affecting how radiative feedbacks may evolve in the future (Section 7.4.4.3). There is now a much-improved understanding of the processes that govern the tropical Pacific SST gradient (Section 7.4.4.2.1) and the paleoclimate record provides evidence for its equilibrium changes from time periods associated with changes in CO₂ Section 7.4.4.2.2).

7.4.4.2.1 Critical processes determining changes in tropical Pacific sea surface temperature gradients

A weakening of the equatorial Pacific Ocean east–west SST gradient, with greater warming in the east than the west, is a common feature of the climate response to greenhouse gas forcing as projected by ESMs on centennial and longer time scales (e.g., Figure 7.14b; see (Section 4.5.1). There are thought to be several factors contributing to this pattern. In the absence of any changes in atmospheric or oceanic circulations, the east–west surface temperature difference is theorized to decrease owing to weaker evaporative damping, and thus greater warming in response to forcing, where climatological temperatures are lower in the eastern Pacific cold tongue (Xie et al., 2010; Luo et al., 2015). Within atmospheric ESMs coupled to a mixed-layer ocean, this gradient in damping has been linked to the rate of change with warming of the saturation specific humidity, which is set by the Clausius–Clapeyron relation (Merlis and Schneider, 2011). Gradients in low-cloud feedbacks may also favour eastern equatorial Pacific warming (DiNezio et al., 2009).

Figure 7.14 | Illustration of tropospheric temperature and low-cloud response to observed and projected Pacific Ocean sea surface temperature trends. (a) Atmospheric response to linear sea surface temperature trend observed over 1870–2019 (HadISST1 dataset; Rayner et al., 2003). (b) Atmospheric response to linear sea-surface temperature trend over 150 years followingabrupt 4xCO2 forcing as projected by CMIP6 ESMs (Dong et al., 2020). Relatively large historical warming in the western tropical Pacific has been communicated aloft (a shift from grey to red atmospheric temperature profile), remotely warming the tropical free troposphere and increasing the strength of the inversion in regions of the tropics where warming has been slower, such as the eastern equatorial Pacific. In turn, an increased inversion strength has increased the low-cloud cover (Zhou et al., 2016) causing an anomalously negative cloud and lapse-rate feedbacks over the historical record (Andrews et al., 2018; Marvel et al., 2018). Relatively large projected warming in the eastern tropical Pacific is trapped near the surface (shift from grey to red atmospheric temperature profile), decreasing the strength of the inversion locally. In turn, a decreased inversion strength combined with surface warming is projected to decrease the low-cloud cover, causing the cloud and lapse-rate feedbacks to become less negative in the future. Figure adapted from Mauritsen (2016). Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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In the coupled climate system, changes in atmospheric and oceanic circulations will influence the east-west temperature gradient as well. It is expected that as global temperature increases and as the east–west temperature gradient weakens, east–west sea level pressure gradients and easterly trade winds (characterizing the Walker circulation) will weaken as well (Sections 4.5.3, 8.2.2.2 and 8.4.2.3, and Figure 7.14b; Vecchi et al., 2006, 2008). This would, in turn, weaken the east–west temperature gradient through a reduction of equatorial upwelling of cold water in the east Pacific and a reduction in the transport of warmer water to the western equatorial Pacific and Indian Ocean (England et al., 2014; Dong and McPhaden, 2017; Li et al., 2017; Maher et al., 2018).

Research published since AR5 (Burls and Fedorov, 2014b; Fedorov et al., 2015; Erfani and Burls, 2019) has built on an earlier theory (Liu and Huang, 1997; Barreiro and Philander, 2008) linking the east–west temperature gradient to the north–south temperature gradient. In particular, model simulations suggest that a reduction in the equator-to-pole temperature gradient (polar amplification) increases the temperature of water subducted in the extra-tropics, which in turn is upwelled in the eastern Pacific. Thus, polar amplified warming, with greater warming in the mid-latitudes and subtropics than in the deep tropics, is expected to contribute to the weakening of the east–west equatorial Pacific SST gradient on decadal to centennial time scales.

The transient adjustment of the equatorial Pacific SST gradient is influenced by upwelling waters which delay surface warming in the east since they have not been at the surface for years-to-decades to experience the greenhouse gas forcing. This ‘thermostat mechanism’ (Clement et al., 1996; Cane et al., 1997) is not thought to persist to equilibrium since it does not account for the eventual increase in temperatures of upwelled waters (Liu et al., 2005; Xie et al., 2010; Y. Luo et al., 2017) which will occur as the subducting waters in mid-latitudes warm by more than the tropics on average as polar amplification emerges. An individual CMIP5 ESM (GFDL’s ESM2M) has been found to exhibit a La Niña-like pattern of Pacific temperature change through the 21st century, similar to the SST trends seen over the historical record (Section 9.2.1 and Figure 7.14a), owing to a weakening asymmetry between El Niño and La Niña events (Kohyama et al., 2017), but this pattern of warming may not persist to equilibrium (Paynter et al., 2018).

Since 1870, observed SSTs in the tropical western Pacific Ocean have increased while those in the tropical eastern Pacific Ocean have changed less (Figure 7.14a and (Section 9.2.1). Much of the resultant strengthening of the equatorial Pacific temperature gradient has occurred since about 1980 due to strong warming in the west and cooling in the east (Figure 2.11b) concurrent with an intensification of the surface equatorial easterly trade winds and Walker circulation (Sections 3.3.3.1, 3.7.6, 8.3.2.3 and 9.2, and Figures 3.16f and 3.39f; England et al., 2014). This temperature pattern is also reflected in regional ocean heat content trends and sea level changes observed from satellite altimetry since 1993 (Bilbao et al., 2015; Richter et al., 2020). The observed changes may have been influenced by one or a combination of temporary factors including sulphate aerosol forcing (Smith et al., 2016; Takahashi and Watanabe, 2016; Hua et al., 2018), internal variability within the Indo-Pacific Ocean (Luo et al., 2012; Chung et al., 2019), teleconnections from multi-decadal tropical Atlantic SST trends (Kucharski et al., 2011, 2014, 2015; McGregor et al., 2014; Chafik et al., 2016; X. Li et al., 2016; Kajtar et al., 2017; Sun et al., 2017), teleconnections from multi-decadal Southern Ocean SST trends (Hwang et al., 2017), and coupled ocean–atmosphere dynamics which slow warming in the equatorial eastern Pacific (Clement et al., 1996; Cane et al., 1997; Seager et al., 2019). CMIP3 and CMIP5 ESMs have difficulties replicating the observed trends in the Walker circulation and Pacific Ocean SSTs over the historical record (Sohn et al., 2013; Zhou et al., 2016; Coats and Karnauskas, 2017), possibly due to model deficiencies including insufficient multi-decadal Pacific Ocean SST variability (Laepple and Huybers, 2014; Bilbao et al., 2015; Chung et al., 2019), mean state biases affecting the forced response or the connection between Atlantic and Pacific basins (Kucharski et al., 2014; Kajtar et al., 2018; Luo et al., 2018; McGregor et al., 2018; Seager et al., 2019), and/or a misrepresentation of radiative forcing (Sections 9.2.1 and 3.7.6). However, the observed trends in the Pacific Ocean SSTs are still within the range of internal variability as simulated by large initial condition ensembles of CMIP5 and CMIP6 models (Olonscheck et al., 2020; Watanabe et al., 2021). Because the causes of observed equatorial Pacific temperature gradient and Walker circulation trends are not well understood (Section 3.3.3.1), there is low confidence in their attribution to anthropogenic influences (Section 8.3.2.3), while there is medium confidence that the observed changes have resulted from internal variability (Sections 3.7.6 and 8.2.2.2).

The expected time-evolution of the spatial pattern of surface warming in the future has important implications for values of ECS inferred from the historical record of observed warming. In particular, changes in the global top-of-atmosphere (TOA) radiative energy budget can be induced by changes in the regional variations of surface temperature, even without a change in the global mean temperature (Zhou et al., 2016; Ceppi and Gregory, 2019). Consequently, the global radiative feedback, characterizing the net TOA radiative response to global surface warming, depends on the spatial patternof that warming. Therefore, if the equilibrium warming pattern under CO₂ forcing (similar to CMIP6 projections in Figure 7.12a) is distinct from that observed over the historical record or indicated by paleoclimate proxies (Sections 7.4.4.1 and 7.4.4.2), then ECS will be different from the effective ECS (Box 7.1) that is inferred from those periods. Accounting for the dependence of radiative feedbacks on the spatial pattern of warming has helped to reconcile values of ECS inferred from the historical record with values of ECS based on other lines of evidence and simulated by climate models (Section 7.5.2.1; Armour, 2017; Proistosescu and Huybers, 2017; Andrews et al., 2018) but has not yet been examined in the paleoclimate context.

This temperature ‘pattern effect’ (Stevens et al., 2016) can result from both internal variability and radiative forcing of the climate system. Importantly, it is distinct from potential radiative feedback dependencies on the global surface temperature, which are assessed in (Section 7.4.3. While changes in global radiative feedbacks under transient warming have been documented in multiple generations of climate models (Williams et al., 2008; Andrews et al., 2015; Ceppi and Gregory, 2017; Dong et al., 2020), research published since AR5 has developed a much-improved understanding of the role of evolving SST patterns in driving feedback changes (Armour et al., 2013; Andrews et al., 2015, 2018; Gregory and Andrews, 2016; Zhou et al., 2016, 2017b; Ceppi and Gregory, 2017; Haugstad et al., 2017; Proistosescu and Huybers, 2017; Andrews and Webb, 2018; Marvel et al., 2018; Silvers et al., 2018; Dong et al., 2019, 2020). This section assesses process understanding of the pattern effect, which is dominated by the evolution of SSTs. Section 7.5.2.1 describes how potential feedback changes associated with the pattern effect are important to interpreting ECS estimates based on historical warming.

Figure 7.13 | Polar amplification in paleo proxies and models of the Early Eocene Climatic Optimum (EECO), the Mid-Pliocene Warm Period (MPWP) and the Last Glacial Maximum (LGM). Figure 7.13: Temperature anomalies compared with pre-industrial (equivalent to CMIP6 simulation ‘piControl’) are shown for the high-CO₂ EECO and MPWP time periods, and for the low-CO₂ LGM (expressed as pre-industrial minus LGM). (a), (b) and (c) Modelled near-surface air temperature anomalies for ensemble-mean simulations of the (a) EECO (Lunt et al., 2021); (b) MPWP (Haywood et al., 2020; Zhang et al., 2021); and (c) LGM (Kageyama et al., 2021; Zhu et al., 2021). Also shown are proxy near-surface air temperature anomalies (coloured circles). (d), (e) and (f) Proxy near-surface air temperature anomalies (grey circles), including published uncertainties (grey vertical bars), model ensemble mean zonal mean anomaly (solid red line) for the same model ensembles as in (a–c), light-red lines show the modelled temperature anomaly for the individual models that make up each ensemble (LGM, N=9; MPWP, N=17; EECO, N=5). Black dashed lines show the average of the proxy values in each latitude band: 90°S–30°S, 30°S–30°N, and 30°N–90°N. Red dashed lines show the same banded average in the model ensemble mean, calculated from the same locations as the proxies. Black and red dashed lines are only shown if there are five or more proxy points in that band. Mean differences between the 90°S/N to 30°S/N and 30°S to 30°N bands are quantified for the models and proxies in each plot. Panels (g), (h) and (i) are like panels (d–f) but for sea surface temperature (SST) instead of near-surface air temperature. Panels (j), (k) and (l) are like panels (a–c) but for SST instead of near-surface air temperature. For the EECO maps – (a) and (j) – the anomalies are relative to the zonal mean of the pre-industrial, due to the different continental configuration. Proxy datasets are: (a) and (d) Hollis et al. (2019); (b) and (e) Salzmann et al. (2013); Vieira et al. (2018), (c) and (f) Cleator et al. (2020) at the sites defined in Bartlein et al. (2011); (g) and (j) Hollis et al. (2019); (h) and (k) McClymont et al. (2020); (i) and (l) Tierney et al. (2020b). Where there are multiple proxy estimations at a single site, a mean is taken. Model ensembles are (a), (d), (g) and (j) DeepMIP (only model simulations carried out with a mantle-frame paleogeography, and carried out under CO₂ concentrations within the range assessed in Table 2.2, are shown); (b), (e), (h) and (k) PlioMIP; and (c), (f), (i) and (l) PMIP4. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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The radiation changes most sensitive to warming patterns are those associated with low-cloud cover (affecting global albedo) and the tropospheric temperature profile (affecting thermal emission to space) (Ceppi and Gregory, 2017; Zhou et al., 2017b; Andrews et al., 2018; Dong et al., 2019). The mechanisms and radiative effects of these changes are illustrated in Figure 7.14a,b. SSTs in regions of deep convective ascent (e.g., in the western Pacific warm pool) govern the temperature of the tropical free troposphere and, in turn, affect low-clouds through the strength of the inversion that caps the boundary layer (i.e., the lower-tropospheric stability) in subsidence regions (Wood and Bretherton, 2006; Klein et al., 2017). Surface warming within ascent regions thus warms the free troposphere and increases low-cloud cover, causing an increase in emission of thermal radiation to space and a reduction in absorbed solar radiation. In contrast, surface warming in regions of overall descent preferentially warms the boundary layer and enhances convective mixing with the dry free troposphere, decreasing low-cloud cover (Bretherton et al., 2013; Qu et al., 2014; Zhou et al., 2015). This leads to an increase in absorption of solar radiation but little change in thermal emission to space. Consequently, warming in tropical ascent regions results in negative lapse-rate and cloud feedbacks while warming in tropical descent regions results in positive lapse-rate and cloud feedbacks (Figure 7.14; Rose and Rayborn, 2016; Zhou et al., 2017b; Andrews and Webb, 2018; Dong et al., 2019). Surface warming in mid-to-high latitudes causes a weak radiative response owing to compensating changes in thermal emission (Planck and lapse-rate feedbacks) and absorbed solar radiation (shortwave cloud and surface-albedo feedbacks; Rose and Rayborn, 2016; Dong et al., 2019), however this compensation may weaken due to less-negative shortwave cloud feedbacks at high warming (Frey and Kay, 2018; Bjordal et al., 2020; Dong et al., 2020).

The spatial pattern of SST changes since 1870 shows relatively little warming in key regions of less-negative radiative feedbacks, including the eastern tropical Pacific Ocean and Southern Ocean (Sections 7.4.4.1 and 7.4.4.2, and Figures 2.11b and 7.14a). Cooling in these regions since 1980 has occurred along with an increase in the strength of the capping inversion in tropical descent regions, resulting in an observed increase in low-cloud cover over the tropical eastern Pacific (Figure 7.14a; Zhou et al., 2016; Ceppi and Gregory, 2017; Fueglistaler and Silvers, 2021). Thus, tropical low-cloud cover increased over recent decades even as global surface temperature increased, resulting in a negative low-cloud feedback which is at odds with the positive low-cloud feedback expected for the pattern of equilibrium warming under CO₂ forcing (Section 7.4.2.4 and Figure 7.14b).

Andrews et al. (2018) analysed available CMIP5/6 ESM simulations (six in total) comparing effective feedback parameters diagnosed within atmosphere-only ESMs using prescribed historical SST and sea ice concentration patterns with the equilibrium feedback parameters as estimated within coupled ESMs (using identical atmospheres) driven by abrupt 4×CO₂ forcing. The atmosphere-only ESMs show pronounced multi-decadal variations in their effective feedback parameters over the last century, with a trend towards strongly negative values since about 1980 owing primarily to negative shortwave cloud feedbacks driven by warming in the western equatorial Pacific Ocean and cooling in the eastern equatorial Pacific Ocean (Zhou et al., 2016; Andrews et al., 2018; Marvel et al., 2018; Dong et al., 2019). Yet, all six models show a less-negative net feedback parameter underabrupt 4xCO2 than for the historical period (based on regression since 1870 following Andrews et al., 2018). The average change in net feedback parameter between the historical period and the equilibrium response to CO₂ forcing, denoted here as α ’ , for these simulations is α ’ = +0.6 W m^–2°C^–1(+0.3 to +1.0 W m^–2°C^–1range across models; Figure 7.15b). These feedback parameter changes imply that the value of ECS may be substantially larger than that inferred from the historical record (Section 7.5.2.1). These findings can be understood from the fact that, due to a combination of internal variability and transient response to forcing (Section 7.4.4.2), historical sea surface warming has been relatively large in regions of tropical ascent (Figure 7.14a), leading to an anomalously large net negative radiative feedback; however, future warming is expected to be largest in tropical descent regions, such as the eastern equatorial Pacific, and at high latitudes (Sections 7.4.4.1 and 7.4.4.2 and Figure 7.14b), leading to a less-negative net radiative feedback and higher ECS.

Figure 7.15 | Relationship between historical and abrupt 4xCO2 net radiative feedbacks in ESMs. (a) Radiative feedbacks in CMIP6 ESMs estimated under historical forcing (values for GFDL CM4.0 and HadGEM3-CG3.1-LL from Winton et al. (2020) and Andrews et al. (2019), respectively); horizontal lines show the range across ensemble members. The other points show effective feedback values for 29 ESMs estimated using regression over the first 50 years ofabrupt 4xCO2 simulations as an analogue for historical warming (Dong et al., 2020). (b) Historical radiative feedbacks estimated from atmosphere-only ESMs with prescribed observed sea-surface temperature and sea-ice concentration changes (Andrews et al., 2018) based on a linear regression of global top-of-atmosphere (TOA) radiation against global near-surface air temperature over the period 1870–2010 (pattern of warming similar to Figure 7.14a) and compared with equilibrium feedbacks inabrupt 4xCO2 simulations of coupled versions of the same ESMs (pattern of warming similar to Figure 7.14b). In all cases, the equilibrium feedback magnitudes are estimated as CO₂ ERF divided by ECS where ECS is derived from regression over years 1–150 ofabrupt 4xCO2 simulations (Box 7.1); similar results are found if the equilibrium feedback is estimated directly from the slope of the linear regression. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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A similar behaviour is seen within transient simulations of coupled ESMs, which project SST warming patterns that are initially characterized by relatively large warming rates in the western equatorial Pacific Ocean on decadal time scales and relatively large warming in the eastern equatorial Pacific and Southern Ocean on centennial time scales (Andrews et al., 2015; Proistosescu and Huybers, 2017; Dong et al., 2020). Recent studies based on simulations of 1% yr^–1CO₂ increase (1pctCO2 ) orabrupt 4xCO2 as analogues for historical warming suggest characteristic values of α ’ = +0.05 W m^–2°C^–1(–0.2 to +0.3 W m^–2°C^–1range across models) based on CMIP5 and CMIP6 ESMs (Armour 2017, Lewis and Curry 2018, Dong et al. 2020). Using historical simulations of one CMIP6 ESM (HadGEM3-GC3.1-LL), Andrews et al. (2019) find an average feedback parameter change of α ’ = +0.2 W m^–2°C^–1(–0.2 to +0.6 W m^–2°C^–1range across four ensemble members). Using historical simulations from another CMIP6 ESM (GFDL CM4.0), Winton et al. (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^–1range across three ensemble members). This value is larger than The α ’ = +0.7 W m^–2°C^–1 within GFDL CM4.0 for historical CO₂ forcing only, suggesting that the value of α ’ may depend on historical non-CO₂ forcings such as those associated with tropospheric and stratospheric aerosols (Marvel et al., 2016; Gregory et al., 2020; Winton et al., 2020).

The magnitude of the net feedback parameter change α ’ found within coupled CMIP5 and CMIP6 ESMs is generally smaller than that found when prescribing observed warming patterns within atmosphere-only ESMs (Figure 7.15; Andrews et al., 2018). This arises from the fact that the forced spatial pattern of warming within transient simulations of most coupled ESMs are distinct from observed warming patterns over the historical record in key regions such as the equatorial Pacific Ocean and Southern Ocean (Sections 7.4.4.1 and 7.4.4.2), while being more similar to the equilibrium pattern simulated under abrupt 4xCO2 . However, historical simulations with HadGEM3-GC3.1-LL (Andrews et al., 2019) and GFDL CM4.0 (Winton et al., 2020) show substantial spread in the value of α ’ across ensemble members, indicating a potentially important role for internal variability in setting the magnitude of the pattern effect over the historical period. Using the 100-member historical simulation ensemble of MPI-ESM1.1, Dessler et al. (2018) find that internal climate variability alone results in a 0.5 W m^–2°C^–1spread in the historical effective feedback parameter, and thus also in the value of α ’ . Estimates of α ’ using prescribed historical warming patterns provide a more realistic representation of the historical pattern effect because they account for the net effect of the transient response to historical forcing and internal variability in the observed record (Andrews et al., 2018).

The magnitude of α ’ , as quantified by ESMs, depends on the accuracy of both the projected patterns of SST and sea ice concentration changes in response to CO₂ forcing and the radiative response to those patterns (Andrews et al., 2018). Model biases that affect the long-term warming pattern (e.g., SST and relative humidity biases in the equatorial Pacific cold tongue as suggested by Seager et al., 2019) will affect the value of α ’ . The value of α ’ also depends on the accuracy of the historical SST and sea ice concentration conditions prescribed within atmosphere-only versions of ESMs to quantify the historical radiative feedback (Figure 7.15b). Historical SSTs are particularly uncertain for the early portion of the historical record (Section 2.3.1), and there are few constraints on sea ice concentration prior to the satellite era. Using alternative SST datasets, Andrews et al. (2018) found little change in the value of α ’ within two models (HadGEM3 and HadAM3), while Lewis and Mauritsen (2021) found a smaller value of α ’ within two other models (ECHAM6.3 and CAM5). The sensitivity of results to the choice of dataset represents a major source of uncertainty in the quantification of the historical pattern effect using atmosphere-only ESMs that has yet to be systematically explored, but the preliminary findings of Lewis and Mauritsen (2021) and Fueglistaler and Silvers (2021) suggest that α ’ could be smaller than the values reported in Andrews et al. (2018).

While there are not yet direct observational constraints on the magnitude of the pattern effect, satellite measurements of variations in TOA radiative fluxes show strong co-variation with changing patterns of SSTs, with a strong dependence on SST changes in regions of deep convective ascent (e.g., in the western Pacific warm pool; Loeb et al., 2018a; Fueglistaler, 2019). Cloud and TOA radiation responses to observed warming patterns in atmospheric models have been found to compare favourably with those observed by satellite (Section 7.2.2.1 and Figure 7.3; Zhou et al., 2016; Loeb et al., 2020). This observational and modelling evidence indicates the potential for a strong pattern effect in nature that will only be negligible if the observed pattern of warming since pre-industrial levels persists to equilibrium – an improbable scenario given that Earth is in a relatively early phase of transient warming and that reaching equilibrium would take multiple millennia (C. Li et al., 2013). Moreover, paleoclimate proxies, ESM simulations, and process understanding indicate that strong warming in the eastern equatorial Pacific Ocean (with medium confidence) and Southern Ocean (with high confidence) will emerge on centennial time scales as the response to CO₂ forcing dominates temperature changes in these regions (Sections 7.4.4.1, 7.4.4.2 and 9.2.1). However, there is low confidence that these features, which have been largely absent over the historical record, will emerge this century (Sections 7.4.4.1, 7.4.4.2 and (Section 9.2.1). This leads to high confidence that radiative feedbacks will become less negative as the CO₂-forced pattern of surface warming emerges ( α ’ > 0 W m^–2°C^–1), but low confidence that these feedback changes will be realized this century. There is also substantial uncertainty in the magnitude of the net radiative feedback change between the present warming pattern and the projected equilibrium warming pattern in response to CO₂ forcing owing to the fact that its quantification currently relies solely on ESM results and is subject to uncertainties in historical SST patterns. Thus, based on the pattern of warming since 1870, α ’ is estimated to be in the range 0.0 to 1.0 W m^–2°C^–1but with a low confidence in the upper end of this range. A value of α ’ = +0.5 ± 0.5 W m^–2°C^–1is used to represent this range in Box 7.2 and (Section 7.5.2, which respectively assess the implications of changing radiative feedbacks for Earth’s energy imbalance and estimates of ECS based on the instrumental record. The value of α ’ is larger if quantified based on the observed pattern of warming since 1980 (Figure 2.11b) which is more distinct from the equilibrium warming pattern expected under CO₂ forcing (high confidence) (similar to CMIP6 projections shown in Figure 7.12a; Andrews et al., 2018).

The process-based assessment is based on the global energy budget equation (Box 7.1, Equation 7.1), where the ERF (ΔF) is set equal to the effective radiative forcing due to a doubling of CO₂ concentration (denoted as ΔF2×CO2) and the climate state reaches a new equilibrium, that is, Earth’s energy imbalance averages to zero (ΔN= 0). ECS is calculated as the ratio between the ERF and the net feedback parameter: ECS = –ΔF2×CO2/ α . Estimates of ΔF2×CO2 and α are obtained separately based on understanding of the key processes that determine each of these quantities. Specifically, ΔF2×CO2 is estimated based on instantaneous radiative forcing that can be accurately obtained using line-by-line calculations, to which uncertainty due to adjustments are added (Section 7.3.2). The range of α is derived by aggregating estimates of individual climate feedbacks based not only on ESMs but also on theory, observations, and high-resolution process modelling (Section 7.4.2).

The effective radiative forcing of CO₂ doubling is assessed to be ΔF2×CO2= 3.93 ± 0.47 W m^–2Section 7.3.2.1), while the net feedback parameter is assessed to be α = –1.16 ± 0.40 W m^–2°C^–1(Table 7.10), where the ranges indicate one standard deviation. These values are slightly different from those directly calculated from ESMs because more information is used to assess them, as explained above. Assuming ΔF2×CO2 and α each follow an independent normal distribution, the uncertainty range of ECS can be obtained by substituting the respective probability density function into the expression of ECS (red curved bar in Figure 7.16). Since α is in the denominator, the normal distribution leads to a long tail in ECS towards high values, indicating the large effect of uncertainty in α in estimating the likelihood of a high ECS (Roe and Baker, 2007; Knutti and Hegerl, 2008).

Figure 7.16 | Probability distributions of ERF to CO₂ doubling (ΔF2×CO2; top) and the net climate feedback ( α ; right), derived from process-based assessments in Sections 7.3.2 and 7.4.2. Central panel shows the joint probability density function calculated on a two-dimensional plane ofΔF2×CO2 and α (red), on which the 90% range shown by an ellipse is imposed to the background theoretical values of ECS (colour shading). The white dot, and thick and thin curves inside the ellipse represent the mean, likely and very likely ranges of ECS. An alternative estimation of the ECS range (pink) is calculated by assuming thatΔF2×CO2 and α have a covariance. The assumption about the co-dependence betweenΔF2×CO2 and α does not alter the mean estimate of ECS but affects its uncertainty. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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The wide range of the process-based ECS estimate is not due solely to uncertainty in the estimates of ΔF2×CO2 and α , but is partly explained by the assumption thatΔF2×CO2 and α are independent in this approach. In CMIP5 and CMIP6 ensembles, ΔF2×CO2 and α are negatively correlated when they are calculated using linear regression inabrupt 4xCO2 simulations (r²= 0.34; Andrews et al., 2012; Webb et al., 2013; Zelinka et al., 2020). The negative correlation leads to compensation between the inter-model spreads of these quantities, thereby reducing the ECS range estimated directly from the models. If the process-based ECS distribution is reconstructed from probability distributions of ΔF2×CO2 and α assuming that they are correlated as in CMIP model ensembles, the range of ECS will be narrower by 14% (pink curved bar in Figure 7.16). If, however, the covariance between ΔF2×CO2 and α is not adopted, there is no change in the mean, but the wide range still applies.

A significant correlation between ΔF2×CO2 and α also occurs when the two parameters are estimated separately from atmospheric ESM fixed-SST experiments (Section 7.3.1) or fixed CO₂ concentration experiments (Section 7.4.1; Ringer et al., 2014; Chung and Soden, 2018). Hence the relationship is not expected to be an artefact of calculating the parameters using linear regression inabrupt 4xCO2 simulations. A possible physical cause of the correlation may be a compensation between the cloud adjustment and the cloud feedback over the tropical ocean (Ringer et al., 2014; Chung and Soden, 2018). It has been shown that the change in the hydrological cycle is a controlling factor for the low-cloud adjustment (Dinh and Fueglistaler, 2019) and for the low-cloud feedback (Watanabe et al., 2018), and therefore the responses of these clouds to the direct CO₂ radiative forcing and to the surface warming may not be independent. However, robust physical mechanisms are not yet established, and furthermore, the process-based assessment of the tropical low-cloud feedback is only indirectly based on ESMs given that physical processes which control the low-clouds are not sufficiently well-simulated in models (Section 7.4.2.4). For these reasons, the co-dependency between ΔF2×CO2 and α is assessed to have low confidence and, therefore, the more conservative assumption that they are independent for the process-based assessment of ECS is retained.

In summary, the ECS based on the assessed values of ΔF 2×CO2 and α is assessed to have a median value of 3.4°C with a likely range of 2.5 to 5.1 °C and very likely range of 2.1 to 7.7 °C. To this assessed range of ECS, the contribution of uncertainty in α is approximately three times as large as the contribution of uncertainty in ΔF2×CO2.

ECS estimated using the ERF due to a doubling of CO₂ concentration and the net feedback parameter (ECS = –ΔF2×CO2/ α ) can be translated into the TCR so that both climate sensitivity metrics provide consistent information about the climate response to forcing. Here a two-layer energy budget emulator is used to transfer the process-based assessment of forcing, feedback, efficacy and heat uptake to TCR (Supplementary Material 7.SM.2.1 and Cross-Chapter Box 7.1). The emulator can reproduce the transient surface temperature evolution in ESMs under 1pctCO2 simulations and other climate change scenarios, despite the very low number of degrees of freedom (Held et al., 2010; Geoffroy et al., 2012, 2013a; Palmer et al., 2018). Using this model with parameters given from assessments in Sections 7.2, 7.3, and 7.4, TCR is assessed based on the process-based understanding.

In the two-layer energy balance emulator, additional parameters are introduced: heat capacities of the upper and deep ocean, heat uptake efficiency (γ), and the so-called efficacy parameter (ε) that represents the dependence of radiative feedbacks and heat uptake on the evolving SST pattern under CO₂ forcing alone (Section 7.4.4). In the real world, natural internal variability and aerosol radiative forcing also affect the efficacy parameter, but these effects are excluded for the current discussion.

The analytical solution of the energy balance emulator reveals that the global surface temperature change to abrupt increase of the atmospheric CO₂ concentration is expressed by a combination of a fast adjustment of the surface components of the climate system and a slow response of the deep ocean, with time scales of several years and several centuries, respectively (grey curve in Figure 7.17b). The equilibrium response of upper ocean temperature, approximating SST and the surface air temperature response, depends, by definition, only on the radiative forcing and the net feedback parameter. Uncertainty in α dominates (80–90%) the corresponding uncertainty range for ECS in CMIP5 models (Vial et al., 2013), and also an increase of ECS in CMIP6 models (Section 7.5.5) is attributed by about 60–80% to a change in α (Zelinka et al., 2020). For the range of TCR, the contribution from uncertainty in α is reduced to 50–60% while uncertainty in ΔF2×CO2 becomes relatively more important (Geoffroy et al., 2012; Lutsko and Popp, 2019). TCR reflects the fast response occurring approximately during the first 20 years in the abrupt 4xCO2 simulation (Held et al., 2010), but the fast response is not independent of the slow response because there is a non-linear co-dependence between them (Andrews et al., 2015). The non-linear relationship between ECS and TCR indicates that the probability of high TCR is not very sensitive to changes in the probability of high ECS (Meehl et al., 2020).

Figure 7.17 | (a) Time evolution of the effective radiative forcing (ERF) to the CO₂ concentration increased by 1% per year until year 70 (equal to the time of doubling) and kept fixed afterwards (white line). The likely and very likely ranges of ERF indicated by light and dark orange have been assessed in (Section 7.3.2.1. (b) Surface temperature response to the CO₂ forcing calculated using the emulator with a given value of ECS, considering uncertainty in ΔF2×CO2, α , and κ associated with the ocean heat uptake and efficacy (white line). The likely and very likely ranges are indicated by cyan and blue, respectively. For comparison, the temperature response to abrupt doubling of the CO₂ concentration is displayed by a grey curve. The mean, likely and very likely ranges of ECS and TCR are shown at the right (the values of TCR also presented in the panel). Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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Considering an idealized time evolution of ERF (1% increase per year until CO₂ doubling and held fixed afterwards, see Figure 7.17a), the TCR defined by the surface temperature response at year 70 is derived by substituting the process-based ECS into the analytical solution of the emulator (Figure 7.17b, see also Supplementary Material 7.SM.2.1). When additional parameters in the emulator are prescribed by using CMIP6 multi-model mean values of those estimates (Smith et al., 2020b), this calculation translates the range of ECS in (Section 7.5.2.1 to the range of TCR. The transient temperature response, in reality, varies with different estimates of the ocean heat uptake efficiency (γ) and efficacy (ε). When the emulator was calibrated to the transient responses in CMIP5 models, it shows that uncertainty in heat capacities is negligible and differences in γ and εexplain 10–20% of the inter-model spread of TCR among GCMs (Geoffroy et al., 2012). Specifically, their product, κ =γε, appearing in a simplified form of the solution, that is, TCR≅–ΔF2×CO2/(α – κ ), gives a single parameter quantifying the damping effects of heat uptake (Jiménez-de-la-Cuesta and Mauritsen, 2019). This parameter is positive and acts to slow down the temperature response in a similar manner to the ‘pattern effect’ (Sections 7.4.4.3 and 7.5.2.1). The ocean heat uptake in nature is controlled by multiple processes associated with advection and mixing (Exarchou et al., 2014; Kostov et al., 2014; Kuhlbrodt et al., 2015) but is simplified to be represented by a single term of heat exchange between the upper and deep ocean in the emulator. Therefore, it is challenging to constrainγ and εfrom process-based understanding (Section 7.5.2). Because the estimated values are only weakly correlated across models, the mean value and one standard deviation of κ are calculated asκ =0.84 ± 0.38 W m^–2°C^–1(one standard deviation) by ignoring their covariance (the mean value is very similar to that used for Box 4.1, Figure 1; see Supplementary Material 7.SM.2.1). By incorporating this inter-model spread in κ , the range of TCR is widened by about 10% (blue bar in Figure 7.17b). Yet, the dominant contribution to the uncertainty range of TCR arises from the net feedback parameterα, consistent with analyses of CMIP6 models (Williams et al., 2020), and this assessment remains unchanged from AR5 stating that uncertainty in ocean heat uptake is of secondary importance.

In summary, the process-based estimate of TCR is assessed to have the central value of 2.0°C with the likely 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 the assessed range was slightly reduced from AR5 but can be further constrained using multiple lines of evidence (Section 7.5.5).

The GSAT change from 1850–1900 to 2006–2019 is estimated to be 1.03 [0.86 to 1.18] °C (Cross-chapter Box 2.3). Together with estimates of Earth’s energy imbalance (Section 7.2.2) and the global ERF that has driven the observed warming (Section 7.3), the instrumental temperature record enables global energy budget estimates of ECS and TCR. While energy budget estimates use instrumental data, they are not based purely on observations. A conceptual model typically based on the global mean forcing and response energy budget framework (Box 7.1) is needed to relate ECS and TCR to the estimates of global warming, ERF and Earth’s energy imbalance (Forster, 2016; Knutti et al., 2017). Moreover, ESM simulations partly inform estimates of the historical ERf (Section 7.3) as well as Earth’s energy imbalance in the 1850–1900 climate (the period against which changes are measured; Forster, 2016; Lewis and Curry, 2018). ESMs are also used to estimate uncertainty due the internal climate variability that may have contributed to observed changes in temperature and energy imbalance (e.g., Palmer and McNeall, 2014; Sherwood et al., 2020). Research since AR5 has shown that global energy budget estimates of ECS may be biased low when they do not take into account how radiative feedbacks depend on the spatial pattern of surface warming (Section 7.4.4.3) or when they do not incorporate improvements in the estimation of global surface temperature trends which take better account of data-sparse regions and are more consistent in their treatment of surface temperature data (Section 2.3.1). Together with updated estimates of global ERF and Earth’s energy imbalance, these advances since AR5 have helped to reconcile energy budget estimates of ECS with estimates of ECS from other lines of evidence.

The traditional global mean forcing and response energy budget framework (Section 7.4.1 and Box 7.1; Gregory et al., 2002) relates the difference between the ERF (ΔF) and the radiative response to observed global warming ( α ΔT) to the Earth’s energy imbalance (ΔN): ΔN= α ΔT+ ΔF. Given the relationship ECS = –ΔF2×CO2/ α , where ΔF2×CO2 is the ERF from CO₂ doubling, ECS can be estimated from historical estimates of ΔT, ΔF, ΔN and ΔF2×CO2: ECS = ΔF2×CO2ΔT/(ΔF– ΔN). Since TCR is defined as the temperature change at the time of CO₂ doubling under an idealized 1% yr^–1CO₂ increase, it can be inferred from the historical record as: TCR = ΔF2×CO2ΔT/ΔF, under the assumption that radiative forcing increases quickly compared to the adjustment time scales of the deep ocean, but slowly enough and over a sufficiently long time that the upper ocean is adjusted, so that ΔT and ΔN increases approximately in proportion to ΔF. Because ΔN is positive, TCR is always smaller than ECS, reflecting weaker transient warming than equilibrium warming. TCR is better constrained than ECS owing to the fact that the denominator of TCR, without the quantity ΔN, is more certain and further from zero than is the denominator of ECS. The upper bounds of both TCR and ECS estimated from historical warming are inherently less certain than their lower bounds because ΔF is uncertain and in the denominator.

The traditional energy budget framework lacks a representation of how radiative feedbacks depend on the spatial pattern of warming. Thus, studies employing this framework (Otto et al., 2013; Lewis and Curry, 2015, 2018; Forster, 2016) implicitly assume that the net radiative feedback has a constant magnitude, producing an estimate of the effective ECS (defined as the value of ECS that would occur if α does not change from its current value) rather than of the true ECS. As summarized in (Section 7.4.4.3, there are now multiple lines of evidence providing high confidence that the net radiative feedback will become less negative as the warming pattern evolves in the future (the pattern effect). This arises because historical warming has been relatively larger in key negative feedback regions (e.g., western tropical Pacific Ocean) and relatively smaller in key positive feedback regions (e.g., eastern tropical Pacific Ocean and Southern Ocean) than is projected in the near-equilibrium response to CO₂ forcing (Section 7.4.4.3; Held et al., 2010; Proistosescu and Huybers, 2017; Dong et al., 2019), implying that the true ECS will be larger than the effective ECS inferred from historical warming. This section first assesses energy budget constraints on TCR and the effective ECS based on updated estimates of historical warming, ERF, and Earth’s energy imbalance. It then assesses what these energy budget constraints imply for values of ECS once the pattern effect is accounted for.

Energy budget estimates of TCR and ECS have evolved in the literature over recent decades. Prior to AR4, the global energy budget provided relatively weak constraints, primarily due to large uncertainty in the tropospheric aerosol forcing, giving ranges of the effective ECS that typically included values above 10°C (Forster, 2016; Knutti et al., 2017). Revised estimates of aerosol forcing together with a larger greenhouse gas forcing by the time of AR5 led to an estimate of ΔF that was more positive and with reduced uncertainty relative to AR4. Using energy budget estimates and radiative forcing estimates updated to 2009, Otto et al. (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 AR5-based energy budget estimate of ECS was lower than estimates based on other lines of evidence, leading AR5 to expand the assessed likely range of ECS to include lower values relative to AR4. Studies since AR5 using similar global energy budget methods have produced similar or slightly narrower ranges for TCR and effective ECS (Forster, 2016; Knutti et al., 2017).

Energy budget estimates of TCR and ECS assessed here are based on improved observations and understanding of global surface temperature trends extended to the year 2020 Section 2.3.1), revised estimates of Earth’s energy imbalance (Section 7.2), and revised estimates of ERf (Section 7.3). Accurate, in situ-based estimates of Earth’s energy imbalance can be made from around 2006 based on near-global ocean temperature observations from the ARGO array of autonomous profiling floats (Sections 2.3 and 7.2). Over the period 2006–2018 the Earth’s energy imbalance is estimated to be 0.79 ± 0.27 W m^–2Section 7.2) and it is assumed that this value is also representative for the period 2006–2019. Anomalies are taken with respect to the baseline period 1850–1900, although other baselines could be chosen to avoid major volcanic activity (Otto et al., 2013; Lewis and Curry, 2018). Several lines of evidence, including ESM simulations (Lewis and Curry, 2015), energy balance modelling (Armour, 2017), inferred ocean warming given observed SSTs using ocean models (Gebbie and Huybers, 2019; Zanna et al., 2019), and ocean warming reconstructed from noble gas thermometry (Baggenstos et al., 2019) suggest a 1850–1900 Earth energy imbalance of 0.2 ± 0.2 W m^–2. Combined with estimates of internal variability in Earth’s energy imbalance, calculated using periods of equivalent lengths of years as used in unforced ESM simulations (Palmer and McNeall, 2014; Sherwood et al., 2020), the anomalous energy imbalance between 1850–1900 and 2006–2019 is estimated to be ΔN= 0.59 ± 0.35 W m^–2. GSAT change between 1850–1900 and 2006–2019 is estimated to be ΔT= 1.03°C ± 0.20 °C (Cross-Chapter Box 2.3 and Box 7.2) after accounting for internal temperature variability derived from unforced ESM simulations (Sherwood et al., 2020). The ERF change between 1850–1900 and 2006–2019 is estimated to be ΔF= 2.20 [1.53 to 2.91] W m^–2Section 7.3.5) and the ERF for a doubling of CO₂ is estimated to be ΔF2×CO2= 3.93 ± 0.47 W m^–2Section 7.3.2). Employing these values within the traditional global energy balance framework described above (following the methods of Otto et al. (2013) and accounting for correlated uncertainties between ΔF and ΔF2×CO2) produces a TCR of 1.9 [1.3 to 2.7] °C and an effective ECS of 2.5 [1.6 to 4.8] °C. These TCR and effective ECS values are higher than those in the recent literature (Otto et al., 2013; Lewis and Curry, 2015, 2018) but are comparable to those of Sherwood et al. (2020) who also used updated estimates of observed warming, Earth’s energy imbalance, and ERF.