Editing IPCC:AR6/WGI/Chapter-7 (section)

==== 7.3.3.2 Aerosol–Cloud Interactions ====

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Anthropogenic aerosol particles primarily affect water clouds by serving as additional cloud condensation nuclei (CCN) and thus increasing cloud drop number concentration (N <sub>d</sub> ; [[#Twomey--1959|Twomey, 1959]] ). Increasing N <sub>d</sub> while holding liquid water content constant reduces cloud drop effective radius (r <sub>e</sub> ), 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|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--2008|Lebsock et al., 2008]] ; [[#Christensen--2011|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--2018|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--2017|Ullrich et al., 2017]] ; [[#Mahrt--2018|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.

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<span id="observation-based-evidence"></span>
===== 7.3.3.2.1 Observation-based evidence =====

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Since AR5, the analysis of observations to investigate aerosol–cloud interactions has progressed along several axes: (i) The framework of forcing and adjustments introduced rigorously in AR5 has helped better categorize studies; (ii) the literature assessing statistical relationships between aerosol and cloud in satellite retrievals has grown, and retrieval uncertainties are better characterized; (iii) advances have been made to infer causality in aerosol–cloud relationships.

In AR5 the statistical relationship between cloud microphysical properties and aerosol index (AI; AOD multiplied by Ångström exponent) was used to make inferences about IRFaci were assessed alongside other studies which related cloud quantities to AOD. However, it is now well-documented that the latter approach leads to low estimates of IRFaci since AOD is a poor proxy for cloud-base CCN ( [[#Penner--2011|Penner et al., 2011]] ; [[#Stier--2016|Stier, 2016]] ). [[#Gryspeerdt--2017|Gryspeerdt et al. (2017)]] demonstrated that the statistical relationship between droplet concentration and AOD leads to an inferred IRFaci that is underestimated by at least 30%, while the use of AI leads to estimates of IRFaci to within ±20%, if the anthropogenic perturbation of AI is known.

Further, studies assessed in AR5 mostly investigated linear relationships between cloud droplet concentration and aerosol ( [[#Boucher--2013|Boucher et al., 2013]] ). Since in most cases the relationships are not linear, this leads to a bias ( [[#Gryspeerdt--2016|Gryspeerdt et al., 2016]] ). Several studies did not relate cloud droplet concentration, but cloud droplet effective radius, to the aerosol ( [[#Brenguier--2000|Brenguier et al., 2000]] ). This is problematic because in order to infer IRFaci, stratification by cloud LWP is required ( [[#McComiskey--2012|McComiskey and Feingold, 2012]] ). Where LWP positively co-varies with aerosol retrievals (which is often the case), IRFaci inferred from such relationships is biased towards low values. Also, it is increasingly evident that different cloud regimes show different sensitivities to aerosols ( [[#Stevens--2009|Stevens and Feingold, 2009]] ). Averaging statistics over regimes thus biases the inferred IRFaci ( [[#Gryspeerdt--2014b|Gryspeerdt et al., 2014b]] ). The AR5 concluded that IRFaci estimates tied to satellite studies generally show weak IRFaci ( [[#Boucher--2013|Boucher et al., 2013]] ), but when correcting for the biases discussed above, this is no longer the case.

Since AR5, several studies assessed the global IRFaci from satellite observations using different methods (Table 7.7). All studies relied on statistical relationships between aerosol and cloud quantities to infer sensitivities. Four studies inferred IRFaci by estimating the anthropogenic perturbation of N <sub>d</sub> (cloud drop number concentration). For this, [[#Bellouin--2013b|Bellouin et al. (2013b)]] and [[#Rémy--2018|Rémy et al. (2018)]] made use of regional-seasonal regressions between satellite-derived N <sub>d</sub> and AOD following [[#Quaas--2008|Quaas et al. (2008)]] , while [[#Gryspeerdt--2017|Gryspeerdt et al. (2017)]] used AI instead of AOD in the regression to infer IRFaci. [[#McCoy--2017b|McCoy et al. (2017b)]] instead used the sulphate-specific mass derived in the MERRA aerosol reanalysis that assimilated MODIS AOD ( [[#Rienecker--2011|Rienecker et al., 2011]] ). All approaches have in common the need to identify the anthropogenic perturbation of the aerosol to assess IRFaci. [[#Gryspeerdt--2017|Gryspeerdt et al. (2017)]] and [[#Rémy--2018|Rémy et al. (2018)]] used the same approach as [[#Bellouin--2013b|Bellouin et al. (2013b)]] , while [[#McCoy--2017b|McCoy et al. (2017b)]] used an anthropogenic fraction from the AEROCOM multi-model ensemble ( [[#Schulz--2006|Schulz et al., 2006]] ). [[#Chen--2014|Chen et al. (2014)]] , [[#Christensen--2016a|Christensen et al. (2016a)]] and [[#Christensen--2017|Christensen et al. (2017)]] derived the combination of IRFaci and the LWP adjustment to IRFaci (‘intrinsic forcing’ in their terminology). They relate AI and cloud albedo statistically and use the anthropogenic aerosol fraction from [[#Bellouin--2013b|Bellouin et al. (2013b)]] . This was further refined by [[#Hasekamp--2019|Hasekamp et al. (2019)]] who used additional polarimetric satellite information over ocean to obtain a better proxy for CCN. They derived an IRFaci of –1.14 [–1.72 to –0.84] W m <sup>–2</sup> . The variant by [[#Christensen--2017|Christensen et al. (2017)]] is an update compared to the [[#Chen--2014|Chen et al. (2014)]] and [[#Christensen--2016a|Christensen et al. (2016a)]] studies in that it better accounts for ancillary influences on the aerosol retrievals such as aerosol swelling and three-dimensional radiative effects. [[#McCoy--2020|McCoy et al. (2020)]] used the satellite-observed hemispheric difference in N <sub>d</sub> as an emergent constraint on IRFaci as simulated by GCMs to obtain a range of –1.2 to –0.6 W m <sup>–2</sup> (95% confidence interval). [[#Diamond--2020|Diamond et al. (2020)]] analysed the difference in clouds affected by ship emissions with unperturbed clouds and based on this inferred a global IRFaci of –0.69 [–0.99 to –0.44] W m <sup>–2</sup> .

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'''Table 7.''' '''7 |''' '''Studies quantifying aspects of the global effective radiative forcing due to aerosol–cloud interactions ERFaci that are mainly based on satellite retrievals and were published since AR5.''' All forcings/adjustments are presented as global annual mean values in W m <sup>–2</sup> . Most studies split the ERFaci into instantaneous radiative forcing (IRFaci) and adjustments in liquid water path (LWP) and cloud fraction (Cf) separately. All published studies only considered liquid clouds. Some studies assessed the IRFaci and the LWP adjustment together and called this ‘intrinsic forcing’ ( [[#Christensen--2017|Christensen et al., 2017]] ) and the cloud fraction adjustment ‘extrinsic forcing’. Published uncertainty ranges are converted to 5–95% confidence intervals, and ‘n/a’ indicates that the study did not provide an estimate for the relevant IRF/ERF.

{| class="wikitable"
|-
| IRFaci (W m <sup>–2</sup> )

| Liquid Water Path (LWP) Adjustment (W m <sup>–2</sup> )

| Cloud Fraction (Cf) Adjustment (W m <sup>–2</sup> )

| Reference

|-
| –0.6 ± 0.6

| n/a

| n/a

| [[#Bellouin--2013b|Bellouin et al. (2013b)]]

|-
| –0.4 [–0.2 to –1.0]

| n/a

| n/a

| [[#Gryspeerdt--2017|Gryspeerdt et al. (2017)]]

|-
| –1.0 ± 0.4

| n/a

| n/a

| [[#McCoy--2017b|McCoy et al. (2017b)]]

|-
| n/a

| n/a

| –0.5 [–0.1 to –0.6]

| [[#Gryspeerdt--2016|Gryspeerdt et al. (2016)]]

|-
| n/a

| +0.3 to 0.0

| n/a

| [[#Gryspeerdt--2019|Gryspeerdt et al. (2019)]]

|-
| –0.8 ± 0.7

| n/a

| n/a

| [[#Rémy--2018|Rémy et al. (2018)]]

|-
| –0.53

–1.14 [–1.72 to –0.84]

–1.2 to –0.6

–0.69 [–0.99 to –0.44]

| +0.15

n/a

n/a

n/a

| n/a

n/a

n/a

n/a

| [[#Toll--2019|Toll et al. (2019)]]

[[#Hasekamp--2019|Hasekamp et al. (2019)]]

[[#McCoy--2020|McCoy et al. (2020)]]

[[#Diamond--2020|Diamond et al. (2020)]]

|-
| colspan="2"| ‘Intrinsic Forcing’

|
|-
| colspan="2"| –0.5 ± 0.5

| –0.5 ± 0.5

| [[#Chen--2014|Chen et al. (2014)]]

|-
| colspan="2"| –0.4 ± 0.3

| n/a

| [[#Christensen--2016a|Christensen et al. (2016a)]]

|-
| colspan="2"| –0.3 ± 0.4

| –0.4 ± 0.5

| [[#Christensen--2017|Christensen et al. (2017)]]

|}

Summarizing the above findings related to statistical relationships and causal aerosol effects on cloud properties, there is ''high confidence'' that anthropogenic aerosols lead to an increase in cloud droplet concentrations. Taking the average across the studies providing IRFaci estimates discussed above and considering the general agreement among estimates (Table 7.7), IRFaci is assessed to be –0.7 ± 0.5 W m <sup>–2</sup> ( ''medium confidence'' ).

Multiple studies have found a positive relationship between cloud fraction and/or cloud LWP and aerosols (e.g., Nakajimaet al., 2001; [[#Kaufman--2006|Kaufman and Koren, 2006]] ; [[#Quaas--2009|Quaas et al., 2009]] ). Since AR5, however, it has been documented that factors independent of causal aerosol–cloud interactions heavily influence such statistical relationships. These include the swelling of aerosols in the high relative humidity in the vicinity of clouds ( [[#Grandey--2013|Grandey et al., 2013]] ) and the contamination of aerosol retrievals next to clouds by cloud remnants and cloud-side scattering ( [[#Várnai--2015|Várnai and Marshak, 2015]] ; [[#Christensen--2017|Christensen et al., 2017]] ). Stratifying relationships by possible influencing factors such as relative humidity ( [[#Koren--2010|Koren et al., 2010]] ) does not yield satisfying results since observations of the relevant quantities are not available at the resolution and quality required. Another approach to tackle this problem was to assess the relationship of cloud fraction with droplet concentration ( [[#Gryspeerdt--2016|Gryspeerdt et al., 2016]] ; [[#Michibata--2016|Michibata et al., 2016]] ; [[#Sato--2018|Sato et al., 2018]] ). The relationship between satellite-retrieved cloud fraction and N <sub>d</sub> was found to be positive ( [[#Christensen--2016a|Christensen et al., 2016a]] , 2017; [[#Gryspeerdt--2016|Gryspeerdt et al., 2016]] ), implying an overall adjustment that leads to a more negative ERFaci. However, since retrieved N <sub>d</sub> is biased low for broken clouds this result has been called into question ( [[#Grosvenor--2018|Grosvenor et al., 2018]] ). [[#Zhu--2018|Zhu et al. (2018)]] proposed to circumvent this problem by considering N <sub>d</sub> of only continuous thick cloud covers, on the basis of which [[#Rosenfeld--2019|Rosenfeld et al. (2019)]] still obtained a positive relationship between cloud fraction and N <sub>d</sub> relationship.

The relationship between LWP and cloud droplet number is debated. Most recent studies (primarily based on MODIS data) find negative statistical relationships ( [[#Michibata--2016|Michibata et al., 2016]] ; [[#Toll--2017|Toll et al., 2017]] ; [[#Sato--2018|Sato et al., 2018]] ; [[#Gryspeerdt--2019|Gryspeerdt et al., 2019]] ), while [[#Rosenfeld--2019|Rosenfeld et al. (2019)]] obtained a modest positive relationship. To increase confidence that observed relationships between aerosol emissions and cloud adjustments are causal, known emissions of aerosols and aerosol precursor gases into otherwise pristine conditions have been exploited. Ship exhaust is one such source. [[#Goren--2014|Goren and Rosenfeld (2014)]] suggested that both LWP and Cf increase in response to ship emissions, contributing approximately 75% to the total ERFaci in mid-latitude stratocumulus. [[#Christensen--2011|Christensen and Stephens (2011)]] found that such strong adjustments occur for open-cell stratocumulus regimes, while adjustments are comparatively small in closed-cell regimes. Volcanic emissions have been identified as another important source of information ( [[#Gassó--2008|Gassó, 2008]] ). From satellite observations, [[#Yuan--2011|Yuan et al. (2011)]] documented substantially larger Cf, higher cloud tops, reduced precipitation likelihood, and increased albedo in cumulus clouds in the plume of the Kīlauea volcano in Hawaii. [[#Ebmeier--2014|Ebmeier et al. (2014)]] confirmed the increased LWP and albedo for other volcanoes. In contrast, for the large Holuhraun eruption in Iceland, [[#Malavelle--2017|Malavelle et al. (2017)]] did not find any large-scale change in LWP in satellite observations. However, when accounting for meteorological conditions, [[#McCoy--2018|McCoy et al. (2018)]] concluded that for cyclonic conditions, the extra Holuhraun aerosol did enhance LWP. [[#Toll--2017|Toll et al. (2017)]] examined a large sample of volcanoes and found a distinct albedo effect, but only modest LWP changes, on average. [[#Gryspeerdt--2019|Gryspeerdt et al. (2019)]] demonstrated that the negative LWP–N <sub>d</sub> relationship becomes very small when conditioned on a volcanic eruption, and therefore concluded that LWP adjustments are small in most regions. Similarly, [[#Toll--2019|Toll et al. (2019)]] studied clouds downwind of various anthropogenic aerosol sources using satellite observations and inferred an IRFaci of –0.52 W m <sup>–2</sup> that was partly offset by 29% due to aerosol-induced LWP decreases.

Apart from adjustments involving LWP and Cf, several studies have also documented a negative relationship between cloud-top temperature and AOD/AI in satellite observations (e.g., [[#Koren--2005|Koren et al., 2005]] ). [[#Wilcox--2016|Wilcox et al. (2016)]] proposed that this could be explained by black-carbon (BC) absorption reducing boundary-layer turbulence, which in turn could lead to taller clouds. However, it has been demonstrated that the satellite-derived relationships are affected by spurious co-variation ( [[#Gryspeerdt--2014a|Gryspeerdt et al., 2014a]] ), and it therefore remains unclear whether a systematic causal effect exists.

Identifying relationships between INP concentrations and cloud properties from satellites is intractable because the INPs generally represent a very small subset of the overall aerosol population at any given time or location. For ice clouds, only a few satellite studies have so far investigated responses to aerosol perturbations. [[#Gryspeerdt--2018|Gryspeerdt et al. (2018)]] find a positive relationship between aerosol and ice crystal number for cold cirrus under strong dynamical forcing, which could be explained by an overall larger number of solution droplets available for homogeneous freezing in polluted regions. [[#Zhao--2018|Zhao et al. (2018)]] conclude that the sign of the relationship between ice crystal size and aerosol depends on humidity. While these studies support modelling results finding that ice clouds do respond to anthropogenic aerosols ( [[#7.3.3.2.2|Section 7.3.3.2.2]] ), no quantitative conclusions about IRFaci or ERFaci for ice clouds can be drawn based on satellite observations.

Only a handful of studies have estimated the LWP and Cf adjustments that are needed for satellite-based estimates of ERFaci. [[#Chen--2014|Chen et al. (2014)]] and [[#Christensen--2017|Christensen et al. (2017)]] used the relationship between cloud fraction and AI to infer the cloud fraction adjustment. [[#Gryspeerdt--2017|Gryspeerdt et al. (2017)]] used a similar approach but tried to account for non-causal coorelations between aerosols and cloud fraction by using N <sub>d</sub> <sup></sup> as a mediating factor. These three studies together suggest a global Cf adjustment that augments ERFaci relative to IRFaci by –0.5 ± 0.4 W m <sup>–2</sup> ( ''medium confidence'' ). For global estimates of the LWP adjustment, evidence is even scarcer. [[#Gryspeerdt--2019|Gryspeerdt et al. (2019)]] derived an estimate of the LWP adjustment using a method similar to [[#Gryspeerdt--2016|Gryspeerdt et al. (2016)]] . They estimated that the LWP adjustment offsets 0–60% of the (negative) IRFaci (0.0 to +0.3 W m <sup>–2</sup> ). Supporting an offsetting LWP adjustment, [[#Toll--2019|Toll et al. (2019)]] estimated a moderate LWP adjustment of 29% (+0.15 W m <sup>–2</sup> ). The adjustment due to LWP is assessed to be small, with a central estimate and ''very likely'' range of 0.2 ± 0.2 W m <sup>–2</sup> , but with ''low confidence'' due to the limited number of studies available.

Combining IRFaci and the associated adjustments in Cf and LWP (adding uncertainties in quadrature), considering only liquid-water clouds and evidence from satellite observations alone, the central estimate and ''very likely'' range for ERFaci is assessed to be –1.0 ± 0.7 W m <sup>–2</sup> ( ''medium confidence'' ). The confidence level and wider range for ERFaci compared to IRFaci reflect the relatively large uncertainties that remain in the adjustment contribution to ERFaci.

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<span id="model-based-evidence"></span>
===== 7.3.3.2.2 Model-based evidence =====

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As in AR5, the representation of aerosol–cloud interactions in ESMs remains a challenge, due to the limited representation of important sub-gridscale processes, from the emissions of aerosols and their precursors to precipitation formation. ESMs that simulate ERFaci typically include aerosol–cloud interactions in liquid stratiform clouds only, while very few include aerosol interactions with mixed-phase, convective and ice clouds. Adding to the spread in model-derived estimates of ERFaci is the fact that model configurations and assumptions vary across studies, for example when it comes to the treatment of oxidants, which influence aerosol formation, and their changes through time ( [[#Karset--2018|Karset et al., 2018]] ).

In AR5, ERFaci was assessed as the residual of the total aerosol ERF and ERFari, as the total aerosol ERF was easier to calculate based on available model simulations ( [[#Boucher--2013|Boucher et al., 2013]] ). The central estimates of total aerosol ERF and ERFari in AR5 were –0.9 W m <sup>–2</sup> and –0.45 W m <sup>–2</sup> , respectively, yielding an ERFaci estimate of –0.45 W m <sup>–2</sup> . This value is much less negative than the bottom-up estimate of ERFaci from ESMs presented in AR5 (–1.4 W m <sup>–2</sup> ) and efforts have been made since to reconcile this difference. [[#Zelinka--2014|Zelinka et al. (2014)]] estimated ERFaci to be –0.96 ± 0.55 W m <sup>–2</sup> (including semi-direct effects, and with land-surface cooling effect applied), based on nine CMIP5 models (Table 7.6). The corresponding ERFaci estimate based on 17 RFMIP models from CMIP6 is slightly less negative at –0.86 ± 0.57 W m <sup>–2</sup> (Table 7.6). Other post-AR5 estimates of ERFaci based on single-model studies are either in agreement with or slightly larger in magnitude than the CMIP6 estimate ( [[#Gordon--2016|Gordon et al., 2016]] ; [[#Fiedler--2017|Fiedler et al., 2017]] , 2019; [[#Neubauer--2017|Neubauer et al., 2017]] ; [[#Karset--2018|Karset et al., 2018]] ; [[#Regayre--2018|Regayre et al., 2018]] ; [[#Zhou--2018b|Zhou et al., 2018b]] ; [[#Golaz--2019|Golaz et al., 2019]] ; [[#Diamond--2020|Diamond et al., 2020]] ).

The adjustment contribution to the CMIP6 ensemble mean ERFaci is –0.20 W m <sup>–2</sup> , though with considerable differences between the models ( [[#Smith--2020b|Smith et al., 2020b]] ). Generally, this adjustment in ESMs arises mainly from LWP changes (e.g., [[#Ghan--2016|Ghan et al., 2016]] ), while satellite observations suggest that cloud cover adjustments dominate and that aerosol effects on LWP are overestimated in ESMs ( [[#Bender--2019|Bender et al., 2019]] ). Large-eddy-simulations also tend to suggest an overestimated aerosol effect on cloud lifetime in ESMs, but some report an aerosol-induced decrease in cloud cover that is at odds with satellite observations ( [[#Seifert--2015|Seifert et al., 2015]] ). Despite this potential disagreement when it comes to the dominant adjustment mechanism, a substantial negative contribution to ERFaci from adjustments is supported both by observational and modelling studies.

Contributions to ERFaci from anthropogenic aerosols acting as INPs are generally not included in CMIP6 models. Two global modelling studies incorporating parametrizations based on recent laboratory studies both found a negative contribution to ERFaci ( [[#Penner--2018|Penner et al., 2018]] ; [[#McGraw--2020|McGraw et al., 2020]] ), with central estimates of –0.3 and –0.13 W m <sup>–2</sup> , respectively. However, previous studies have produced model estimates of opposing signs ( [[#Storelvmo--2017|Storelvmo, 2017]] ). There is thus ''limited evidenc'' e and ''medium agreement'' for a small negative contribution to ERFaci from anthropogenic INP-induced cirrus modifications ( ''low confidence'' ).

Similarly, aerosol effects on deep convective clouds are typically not incorporated in ESMs. However, cloud-resolving modelling studies support non-negligible aerosol effects on the radiative properties of convective clouds and associated detrained cloud anvils ( [[#Tao--2012|Tao et al., 2012]] ). While global ERF estimates are currently not available for these effects, the fact that they are missing in most ESMs adds to the uncertainty range for the model-based ERFaci.

From model-based evidence, ERFaci is assessed to –1.0 ± 0.8 W m <sup>–2</sup> ( ''medium confidence'' ). This assessment uses the mean ERFaci in Table 7.6 as a starting point, but further allows for a small negative ERF contribution from cirrus clouds. The uncertainty range is based on those reported in Table 7.6, but widened to account for uncertain but ''likely'' non-negligible processes currently unaccounted for in ESMs.

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<span id="overall-assessment-of-erfaci"></span>
===== 7.3.3.2.3 Overall assessment of ERFaci =====

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The assessment of ERFaci based on observational evidence alone (–1.0 ± 0.7 W m <sup>–2</sup> ) is very similar to the one based on model evidence alone (–1.0 ± 0.8 W m <sup>–2</sup> ), in strong contrast to what was reported in AR5. This reconciliation of observation-based and model-based estimates is the result of considerable scientific progress and reflects comparable revisions of both model-based and observation-based estimates. The strong agreement between the two largely independent lines of evidence increases confidence in the overall assessment of the central estimate and ''very likely'' range for ERFaci of –1.0 ± 0.7 W m <sup>–2</sup> ( ''medium confidence'' ). The assessed range is consistent with but narrower than that reported by the review of [[#Bellouin--2020|Bellouin et al. (2020)]] of –2.65 to –0.07 W m <sup>–2</sup> . The difference is primarily due to a wider range in the adjustment contribution to ERFaci in [[#Bellouin--2020|Bellouin et al. (2020)]] , however adjustments reported relative to IRFaci ranging from 40% to 150% in that study are fully consistent with the ERFaci assessment presented here.

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<span id="energy-budget-constraints-on-the-total-aerosol-erf"></span>