2.1 Forcing decomposition

To decompose the aerosol forcing into components, two separate model simulations are required: one with PI aerosol emissions and another with PD emissions. The ERFaer is taken as the difference in top-of-atmosphere (TOA) radiation between these two simulations. Cloudy-sky quantities (x_c) are computed from the all-sky (x) and clear sky (x_clr) quantities and the cloud fraction (f_c).

The ERFaer is split into longwave (LW) and shortwave (SW) components. The changes in the SW TOA radiation can be attributed to changes in the cloudy-sky albedo, clear-sky albedo (Δα_clr), and changes in the cloud fraction (Eq. 3). The change in the longwave component (ΔLW) can be similarly decomposed into a cloudy-sky (ΔOLR_c), clear sky (ΔOLR_clr), and cloud fraction change. Throughout this work, a Δ signifies PI to PD changes. NoA (no aerosol) indicates an albedo determined in a clean atmosphere (no radiative effect of aerosol; Ghan, 2013). F^↓ is the TOA incoming solar radiation. Note that all of the steps in this decomposition are performed at the grid-box scale.

The terms can then be connected to the decomposition of the aerosol forcing in Boucher et al. (2013). The aerosol direct effect or RFari can be approximated as SWari_cs+ LWari_cs. This ignores changes in the surface (ΔSurf) and the impact of aerosol above cloud (SWari_cld), but it provides a comparable value to the RFari estimated using observations (e.g. Quaas et al., 2008). The remaining terms can then be considered the ERFaci (plus cloudy-sky components of the RFari), with terms due to changes in cloud properties (ΔSW_c) and cloud amount (ΔSW_cf).

These cloud terms can be further decomposed into changes in liquid and ice cloud (Eqs. 5–7), resulting in forcings from changes in liquid (ΔSW_cl) and ice-cloud albedo (ΔSW_ci) as well as the forcings from changes in cloud fraction (ΔSW_cfl, ΔSW_cfi). The liquid cloud albedo is determined using only grid boxes with an ice-cloud fraction of less than 2 %. A similar criterion is used for the ice-cloud albedo. The forcing from changes in liquid cloud albedo (ΔSW_cl, the “intrinsic” forcing; Chen et al., 2014) can then be further decomposed into a forcing from changes in ℒ and a change in N_d. Using the strong dependence of cloud albedo on ℒ (Engström et al., 2015), the ERFaci due to ℒ changes can be determined by a linear regression to determine the sensitivity of liquid cloud albedo to ℒ (Eq. 8), combined with a known PI to PD change in ℒ. Similar results are obtained when using ln ℒ instead of ℒ. The forcing due to N_d changes (the RFaci) is the residual of liquid cloud albedo forcing with the ℒ forcing removed (Eq. 9).

In many situations, the ice-cloud fraction includes clouds with a low optical depth. This means that in situations where a thin ice cloud overlies a thick low-level liquid cloud, changes in the low-level liquid cloud albedo might be misattributed as changes in the ice-cloud albedo. To avoid this issue, a threshold in-cloud ice water path (IWP) of 8.7 g m⁻² is required for a grid box to be classed as an ice-cloud grid box. This threshold is approximately equal to the MODIS cloud mask sensitivity of an optical depth of 0.4 (Ackerman et al., 2008), following the relationship from Heymsfield et al. (2003). The shortwave forcing from these optically thin cases is assigned to underlying liquid clouds, assuming that the ratio of the RFaci to the forcing from ℒ adjustments is the same as in the ice-cloud-free regions. The longwave forcing is assumed to originate from the ice clouds, due to the emissivity of these thin clouds. The sensitivity of the decomposition to the IWP sensitivity is investigated in this work.

Changes in overlying ice cloud create a change in the liquid cloud fraction (f_l), but observational estimates of the forcing from liquid cloud adjustments typically assume no change in the ice-cloud fraction f_i (Gryspeerdt et al., 2016; Christensen et al., 2017). To get a closer agreement between models and observations, the change in liquid cloud fraction (Δf_l) is adjusted in the model output for changes in the ice-cloud fraction (Δf_i) following Eq. (10), assuming that the changes in ice-cloud fraction are uncorrelated to the occurrence of liquid cloud.

2.2 Datasets

The decomposition is applied to pairs of simulations from the AeroCom and CMIP5 intercomparisons. The simulation pairs have prescribed sea surface temperatures and sea ice, differing only in their aerosol emissions. Three-hourly model output from the AeroCom indirect effect experiment simulations (Zhang et al., 2016; Ghan et al., 2016) is used, with 5-year simulations nudged to present-day meteorology for the years 2006–2010. The CMIP5 models make use of the “sstClim” and “sstClimAerosol” simulations, which are 30-year-long free-running simulations with climatological sea surface temperature (SST) fields. Further details on the AeroCom and CMIP5 models can be found in Zhang et al. (2016) and Zelinka et al. (2014), respectively. As a descendent of the HadGEM2-A and HadGEM3-UKCA models, UKESM1-A (Sellar, 2019) has also been included to provide an additional comparison between different versions of the same model (futher details in Mulcahy et al., 2018). It is run in the same configuration at the AeroCom simulations.

To test the accuracy of the decomposition, two additional sets of model simulations were performed using ECHAM6–HAM2.2. The “anthsca” simulations are the same as the base AeroCom setup but with present-day anthropogenic aerosol emissions scaled by a factor given in the simulation name. While both the aerosol distribution and the parameterisations vary between the models used in this work, the “anthsca” simulations demonstrate the impact of changing the aerosol distribution alone. The CND (constant N_d) simulation replaces the N_d value used in the autoconversion parameterisation with a climatological value, selected to agree with the global mean N_d in the full two-moment run. This removes any aerosol-dependent cloud adjustments, such that change in liquid cloud albedo is the result of the Twomey effect alone.

Table 1The ERFaer (global mean differences between the PI and PD TOA radiation) from the AeroCom (top section) and CMIP5 (bottom section) models in watts per square metre (W m⁻²). CMIP5 physics ensemble members are shown with the “-p” suffix. The third column identifies the nature of the aerosol parameterisation in the model, (0 – direct effect only; 1 – RFaci in liquid clouds, no adjustments; 2 – with liquid cloud adjustments; 3 – parameterised aerosol impacts on ice cloud) following Heyn et al. (2017). Models in italics are sensitivity studies and not included in averages. The icons are used in scatter plots and models of the same family have the same colour. UKESM is not an AeroCom model but has been run in a similar configuration.

Ensemble key: ¹ constant climatological N_d in autoconversion. ² scaled anthropogenic emissions. ³ updated cloud scheme. ⁴ different aerosol forcing data.

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3.1 Decomposition comparisons

The total ERFaer in the AeroCom and CMIP5 models varies from −0.36 to −2.30W m⁻² (Table 1), with the majority of models having a stronger SW component that is partially offset by a smaller positive LW forcing. There is a significant variation in the magnitude and even the sign of the components of the forcing calculated using the method from the previous section (Table S2 in the Supplement). However, the residual of the sum of the components of decomposition compared to the total ERFaer calculated is small (typically less than 10 %), increasing confidence in the completeness of the decomposition as each term is calculated independently.

The decomposition in this work also compares well to other methods. By removing the aerosol-dependent cloud adjustments using a climatological N_d (CND), the RFaci is isolated from the adjustments and is found to be within 10 % of the value calculated through the decomposition in this work, with the forcing from the cloud adjustments decreasing to close to zero as the adjustments are removed (Table 2). Similarly, the three components of the ERFaci in liquid clouds determined using the sophisticated partial radiative perturbation (PRP) method (Mülmenstädt et al., 2019) match the results of this work to within 15 % (Table 2). There is also a close match in the spatial patterns of the forcing from the components between the different methods (Fig. S2). Due to the variability in the cloud field, a higher threshold of 40 g m⁻² gives very similar forcing values when using daily mean data for the AeroCom models (not shown), although only the 3-hourly AeroCom data are used in this work. The similarity of the results between methods suggest that the method introduced in this work is capable of accurately identifying the individual components of the ERFaer.

The estimate of the RFaci is also found to be insensitive to the value chosen for the IWP threshold used to identify ice clouds (Table 2). Although there is a significant change in the RFaci when a 1 g m⁻² threshold is introduced, this is likely due to the occurrence of clouds in the model that have little condensed water and hence are not optically active. However, for larger values of the IWP threshold, the variations in the RFaci are within 10 % of the value used in this work. Even with a very large threshold value of 100 g m⁻², the adjustments as a percentage of the RFaci are within 20 % of the best estimate, showing that this method is relatively insensitive to the choice of threshold and hence is a suitable method to account for the effect of thin ice clouds.

Table 2The impact of ice water path thresholds on the RFaci estimate, the forcing from ℒ and f_l adjustments and the ℒ and f_l enhancements of the RFaci. The row in bold represents the threshold value used throughout the rest of this work. The bottom rows show the liquid forcing estimates from a simulation with no parameterised cloud adjustment and determined from the standard simulation using the PRP method (Mülmenstädt et al., 2019). Values are in watts per square metre (W m⁻²) unless otherwise specified.

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Figure 1(a) The RFaci related to the fractional change in aerosol optical depth (AOD) and N_d. Colours and symbols are given in Table 1; vertical lines link the RFaci estimates to the “intrinsic” (RFaci+LWP adjustment) forcing. The black points are the observation-based estimates from A – Gryspeerdt et al. (2017), B – Fiedler et al. (2017), C – McCoy et al. (2017), D – Bellouin et al. (2013), E – Stevens (2015), and F – Hasekamp et al. (2019). (b) Forcing from adjustments in ℒ and liquid f_c. Other estimates from G – Andersen et al. (2017), H – Gryspeerdt et al. (2016), I – Christensen et al. (2017), J – Gryspeerdt et al. (2019), K – Sato et al. (2018), and L – Toll et al. (2019) are shown. Not all studies provide a central estimate (black point). (c) The percentage enhancement of the RFaci by ℒ and liquid f_c changes. Diagonal lines are contours of constant total RFaci enhancement.

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Figure 2(a) The ensemble mean shortwave RFaci. (b) ERFaci contribution from f_l changes. (c) ERFaci contribution from ℒ changes.

3.2 The RFaci

Previous observation-based studies estimating the RFaci have used a limited number of methods. A sample of these estimates using various methods and estimates of the anthropogenic aerosol fraction are included in Fig. 1a. A – Gryspeerdt et al. (2017) is representative of studies (e.g. Quaas et al., 2008) using relationships between satellite observations of aerosol and N_d along with observed cloud properties to convert this to estimate the RFaci. B – Fiedler et al. (2017) use a similar method but incorporate the observed relationship in a climate model to calculate the RFaci (e.g. Quaas et al., 2006). C – McCoy et al. (2017) use reanalysis aerosol instead of observed aerosol properties. D – Bellouin et al. (2013) use a model strongly constrained by satellite observations to estimate the RFaci. E – Stevens (2015) combine several lines of evidence that are distinct from the other studies. F – Hasekamp et al. (2019) use a polarimetric retrieval of aerosol to include more size information and account for the detectability limit in satellite retrievals of aerosol. Although other studies place an implicit limit on the RFaci by constraining the total ERFaer (Cherian et al., 2014) or a combination of the RFaci and the ℒ adjustments (Lebsock et al., 2008; Christensen et al., 2017), they are not included here due to the weak constraint they provide on RFaci. Together the observation-based studies suggest a central estimate for the RFaci in the range −0.2 to −1.0 W m⁻² (Fig. 1a).

All the models considered in the present study show a significant ΔSW_c, typically dominated by changes in liquid clouds (Table S2). This forcing varies significantly, from −0.06 to −1.44 W m⁻², outside the range of plausible RFaci generated by many observational constraints (Fig. 1a – crossbars). However, when the forcing due to ℒ adjustments is removed, the variability is reduced, with a lower bound of −1.26 W m⁻² and many of the models producing an RFaci estimate around −0.75 W m⁻² or smaller (Fig. 1a – markers). Considering the models as a whole, there is a weak relationship between the aerosol optical depth (AOD) perturbation and the RFaci (Fig. 1a), due to the weak relationship between AOD and CCN (Stier, 2016). A stronger relationship between ΔN_d and the RFaci is seen for the individual models (Fig. 1a), with the remaining variation being due to differences in the cloud field (Zelinka et al., 2014).

Global patterns of the RFaci (Fig. 2a) show a weak RFaci over land and stronger effect over the ocean, particularly in regions with large amounts of low cloud. This is very similar to a number of observational estimates, which place the majority of the aerosol forcing over the ocean due to a high N_d sensitivity to aerosol and f_l (e.g. Quaas et al., 2008; Gryspeerdt et al., 2017; Christensen et al., 2017).

3.3 Liquid cloud adjustments

Uncertainties in the aerosol environment (source S1), droplet activation (S2), and cloud processes (S3) all contribute to the total uncertainty in forcing from liquid cloud adjustments, making model–observation comparisons difficult. However, uncertainties from both S1 and S2 apply to both the RFaci and the adjustments. By reporting cloud adjustments in f_l and ℒ as a percentage enhancement of the RFaci (Fig. 1c), the impact of S1 and S2 on the estimate of the adjustments can be reduced. This focuses on the uncertainty in the cloud response to N_d changes (S3), simplifying comparisons between models with different anthropogenic aerosol fractions and activation schemes.

The benefit of normalisation of the adjustments by the RFaci is demonstrated by the analysis of the ECHAM6-HAM ensemble with varying aerosol emissions (ECHAM6-HAM-anthsca, red). Although the forcing from both f_l and ℒ changes in these simulations is very different (Fig. 1b), the enhancement of the RFaci by both effects is the same to within 10 % (Fig. 1c). In contrast, the CAM5 microphysics ensemble (blue) has a similar aerosol environment (Fig. 1a) but very different cloud microphysics schemes for each of its members. As such, the variation in the RFaci enhancement from cloud adjustments is significant among members of this ensemble. This normalisation by RFaci allows the adjustments to be more closely compared with observation-based studies.

f_l adjustments. Three recent observational studies using different methods (Gryspeerdt et al., 2016; Andersen et al., 2017; Christensen et al., 2017) find an f_l adjustment that enhances the RFaci by around 130 % to 200 %. This remains the case when a different anthropogenic aerosol fraction (MACv2; Kinne, 2019) is used in the Gryspeerdt et al. (2016) estimate. The upper bound to the enhancement in Christensen et al. (2017) is unknown, as the RFaci is not reported separately from ℒ adjustment. This highlights the impact the RFaci uncertainty can have in observational estimates of the enhancement when the RFaci uncertainty is large.

Many of the models, particularly those from CMIP5, have a very small f_l adjustment, producing an RFaci enhancement close to 0 %. This explains the smaller mean forcing from liquid cloud adjustments in Zelinka et al. (2014), where only CMIP5 models were used. The largest model estimates of f_l adjustments are of a similar magnitude to the observational estimates, with an enhancement of around 100 %. While some models are more similar to the observation-based f_l adjustment forcing (Fig. 1b) than the f_l enhancement (Fig. 1c), this is due to the model RFaci estimates typically being stronger than the average observation-based estimates (Fig. 1a). The overall pattern of the forcing from f_l changes in models (Fig. 2b) is similar to that from Gryspeerdt et al. (2016), with a stronger forcing around the edges of the stratocumulus regions, but a weaker forcing in the North Pacific. This is likely related to the mean-state f_l, as increasing the f_l is difficult if the f_l is already high.

ℒ adjustments. Observational estimates of ℒ adjustments are difficult to interpret (Neubauer et al., 2017). Several studies have found a ℒ decrease with increased aerosol or N_d, suggesting a negative adjustment (Chen et al., 2014; Christensen et al., 2017; Sato et al., 2018). However, recent work has suggested that this decrease may overestimate the impact of aerosols on ℒ, supporting a weak ℒ response to aerosol (Malavelle et al., 2017; Gryspeerdt et al., 2019; Toll et al., 2019). In contrast, all the models with a significant RFaci also produce a positive ℒ adjustment, enhancing the ERFaci. As with the f_l adjustments, the ℒ adjustments are smaller in the CMIP5 models, due to the smaller change in ℒ but similar cloud radiative effects (Fig. 3). The CMIP5 models tend to have less sophisticated aerosol schemes (Table 1), which may explain these weaker adjustments. However, as some models with higher levels of sophistication (e.g. UKESM1-A, MRI-CGCM3) also have weak adjustments, model sophistication is not the only factor influencing the strength of the adjustments.

Figure 3The relationship Δℒ (in-cloud) and the ℒ adjustment in each of the models.

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In almost all of the models, the ℒ and f_l adjustments have the same sign (Fig. 1b). The different sign of the f_l and ℒ adjustments in the observation-based studies therefore suggests that inclusion of missing processes controlling ℒ, such as aerosol-dependent entrainment (Ackerman et al., 2004; Xue and Feingold, 2006), may be necessary for models to reproduce the observed relationships (e.g. Salzmann et al., 2010; Guo et al., 2011; Zhou and Penner, 2017; Mülmenstädt and Feingold, 2018).

Although the models typically have stronger ℒ and weaker f_l enhancements to the RFaci that those from observation-based studies, the models with stronger adjustments have a similar magnitude for the total RFaci enhancement due to adjustments when compared to observations (Fig. 1c). This is an encouraging sign but highlights the potential for models to produce the right answer for the wrong reason.

Figure 4(a) The total ERFaer in the longwave as a function of the shortwave ERFaer. The grey range is the estimate from Cherian et al. (2014) and the black circle the expert assessment from Boucher et al. (2013). (b) The ERFaci due to changes in ice-cloud properties. Shortwave changes from the cloud albedo (ΔSW_ci) and ice f_c (f_i) (ΔSW_cfi) are shown in blue, including the impact of ice-cloud changes masking lower-level clouds. Longwave changes from changes in intrinsic cloud properties (ΔLW_c) and cloud fraction (ΔLW_cf) are in yellow and red, respectively. The cross is the total ERFaci from changes in ice clouds.

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3.4 Ice-cloud ERFaci

As shown in previous modelling studies (Zelinka et al., 2014; Heyn et al., 2017), the model shortwave (SW) and longwave (LW) total aerosol forcings are strongly correlated (Fig. 4a), indicating a strong role of ice clouds, which dominate the longwave aerosol forcing (Table S3). The magnitude of slope of this relationship is smaller than one, such that an increased negative SW forcing is not completely cancelled by a positive LW forcing.

All of the models show an increase in the albedo of ice clouds (Fig. 4b), due to a Twomey-like effect in ice clouds. This is in agreement with current observational studies that suggest an increase in N_i with an increased aerosol emissions (Gryspeerdt et al., 2018; Mitchell et al., 2018), although there are no current large-scale observational constraints on the forcing from ice clouds. This is offset by a decrease in the outgoing longwave radiation from clouds. These effects occur even in models with no parameterised effect of aerosol directly on convective clouds or ice processes, likely through processes such as droplet freezing.

There is a strong variation in the response of high cloud amount to aerosol between the models. The increase in ice-cloud fraction exhibited by some models produces a negative shortwave forcing (ΔSW_cfi), but this is closely offset by a positive longwave forcing (ΔLW_cf), such that the net effect from f_i changes in high clouds is close to zero. The balance between ΔSW_cfi and ΔLW_cf varies between the models. The AeroCom models tend to produce a larger longwave effect, resulting in a positive overall forcing (similar to  Gettelman et al., 2012), whilst the CMIP5 models generally have an overall forcing close to zero. This may be due to the more detailed representation of clouds and aerosols in the AeroCom models (Table 1). While the AeroCom models are nudged to PD horizontal winds (compared to the free-running CMIP5 models), previous studies show that this does not have a significant impact on the forcing (Zhang et al., 2014) and the negative forcing from UKESM1-A (run with the AeroCom setup) further suggests that model setup does not explain this difference. The variability in the ice-cloud ERFaci is in contrast to the constant adjustment of +0.2 W m⁻² used in Boucher et al. (2013), highlighting the current uncertainty in the contribution of ice clouds to the total ERFaer.