Decomposing Effective Radiative Forcing Due to Aerosol Cloud Interactions by Global Cloud Regimes

Quantifying effective radiative forcing due to aerosol‐cloud interactions (E ERFACI ) remains a largely uncertain process, and the magnitude remains unconstrained in general circulation models. Previous studies focus on the magnitude of ERFACI arising from all cloud types, or examine it in the framework of dynamical regimes. Aerosol forcing due to aerosol‐cloud interactions in the HadGEM3‐GA7.1 global climate model is decomposed into several global observational cloud regimes. Regimes are assigned to model gridboxes and forcing due to aerosol‐cloud interactions is calculated on a regime‐by‐regime basis with a 20‐year averaging period. Patterns of regime occurrence are in good agreement with satellite observations. ERFACI is then further decomposed into three terms, representing radiative changes within a given regime, transitions between different cloud regimes, and nonlinear effects. The total global mean ERFACI is −1.03 Wm−2. When decomposed, simulated ERFACI is greatest in the thick stratocumulus regime (−0.51 Wm−2).

2 of 9 insight into the way cloud processes are modeled, and provides a pathway to incorporate results from observations and high resolution modeling, as these will make predictions relating to specific cloud regimes.
Regime-based analysis of clouds uses joint histograms of cloud top pressure (CTP) and cloud optical depth (COD), and was pioneered by Jakob and Tselioudis (2003), using the data produced by the International Satellite Cloud Climatology Project (ISCCP [Rossow & Schiffer, 1999]). This analysis has had success when applied to observations. For instance, several studies have determined the sensitivity of different cloud properties to AOD in a regime-based framework (Gryspeerdt & Stier, 2012;Oreopoulos et al., 2020). In addition, Schuddeboom et al. (2018) examined differences in the cloud radiative effect (CRE) between models and observations. What has not been done, however, is to examine on a regime-by-regime basis the indirect radiative forcing by aerosol. It is reasonable to believe, in light of these papers, that different cloud regimes may react differently to an increase in aerosol emissions, and hence have varying total contributions to the aerosol forcing. When decomposed into regimes, it will also be possible to examine the modeled sensitivities of each regime, for instance the sensitivity of cloud albedo to aerosol loading. This paper sets out a framework to analyze indirect aerosol forcing by cloud regime, and applies this methodology to analyze the forcing from HadGEM3. This methodology can provide useful insights into how different models calculate aerosol processes. In addition, the forcing can be quantified in terms of changes in the average properties of each regime, and also to account for differing relative frequency of occurence (RFO) of regimes between present-day and preindustrial time periods.

Model and Experimental Design
This study makes use of 2 different model runs of HadGEM3 GA7.1 global model and the Global Land configuration version 7.1 (GL7.1) (Walters et al., 2019). A 20-year run is performed for both a present-day  and preindustrial (1850 emissions) time period, both at N96 resolution (1.875 1.25 E   ) with 85 vertical levels. The aerosol-cloud interactions are handled by the Unified Model Physics scheme, described in Mulcahy et al. (2018). Cloud droplet number concentrations are diagnosed by the UK Chemistry and Aerosol model, using the Global Model of Aerosol Processes (GLOMAP-mode) (Mann et al., 2010) coupled to the PC2 cloud scheme with the Wilson and Ballard microphysics scheme (Wilson et al., 2008;Wilson & Ballard, 1999), via the Abdul-Razzak Ghan activation scheme (Abdul-Razzak & Ghan, 2000) as described in West et al. (2014). The emissions used are the present day Coupled Model Intercomparison Project Phase 6 (CMIP6) emissions data sets (Hoesly et al., 2018). For the 1850 emissions, anthropogenic aerosol emissions were reverted to their preindustrial estimates, while natural emissions, sea ice coverage, and sea surface temperatures were kept identical to the present day run.
The CFMIP Observational Simulator Package (COSP; Bodas-Salcedo et al. [2011]) is used to generate model simulations of the joint histograms of CTP and COD ( E  ) available from the ISCCP D1 products (Rossow & Schiffer, 1999). As COSP is designed to mimic the output of ISCCP, these histograms are only available on sunlit points.
Data are generated at every radiation time step (1 h), and regimes can be assigned on daylit points only. As COSP only produces data on daylit points, the nighttime LW forcing is calculated for all cloud types, and then divided amongst the regimes proportionally to their daytime RFO.
The Wilson and Ballard cloud microphysics scheme does not include interactions between aerosol and either the convective or ice microphysics, however, there are interactions between convective clouds and the large-scale microphysics, as condensate is detrained from the convective cloud into the large-scale cloud, affecting cloud liquid and ice water content. This means that while aerosols in the region of deep convective regimes will not directly interact with the clouds as they would in an LES model, they will produce a signal, although this signal could be difficult to interpret accurately.

Regime Assignment
Cloud regime definitions were taken from the work of Tselioudis et al. (2013), which defined a set of 11 (Global) Weather States (WS) from ISCCP observations using a k-means clustering algorithm (Anderberg, 2014), which clusters on 6 7 E  joint histograms of cloud top pressure (CTP) and cloud optical depth (COD). These are depicted visually in Figure 1. The average properties of each of these centroids, which are used for regime assignment, are shown in Table S1.
These cloud regimes can be seen to somewhat mimic classical cloud types. Gridboxes with CF 0.5% E  are assigned to a separate clear-sky regime. In this analysis, several regimes with similar geographical distributions and cloud vertical structures are merged together. This is done by first assigning the regimes to the original 11 weather states defined by Tselioudis et al. (2013), and then not distinguishing between the merged states. These merged states are: This method has the advantage that the ERF ACI of regimes with a low RFO appears amplified by grouping together physically similar regimes (e.g., Cirrus and Anvil Cirrus), without changing the initial cluster definitions.
Cloud regimes are assigned based on the methodology of Williams and Webb (2009

Definitions
In this paper, we examine the indirect effects of aerosol on clouds, as modeled by the Wilson and Ballard single moment cloud microphysics scheme within HadGEM3. All functions unless stated otherwise are assumed to be functions of latitude and longitude, and will have these arguments omitted for conciseness.
Following the methods and terminology of Ghan (2013), we define the cloud radiative forcing due to aerosols ( clean E C  ) as: where E  denotes the difference between present-day and preindustrial emissions periods, clean E C denotes the clean-cloud radiative effect, E F denotes the net top-of-atmosphere (TOA) radiative flux, the difference between incoming and outgoing flux for both SW and LW radiation, and subscripts clean & clear denote the TOA fluxes when the model removes the direct radiative effects of aerosol and cloud, respectively.
Relative frequency of occurrence of the E kth cloud regime is denoted by ( ) k E R T , and we denote present-day and preindustrial time periods by 1 E T and 0 E T respectively. Finally, the cloud radiative effect of the ( 2) where ( ) E R t is a discrete 10-valued function indicating which cloud regime is seen in each gridbox, E  is the Kronecker delta, and the sum is performed over all time steps t in the model run representing time period E T. ( ) E R t references the cloud regimes post-merge, rather than the 12 observational regimes found in (Tselioudis et al., 2013).

Calculation
It must be possible to recover total clean cloud forcing ACI ERF E simply by summing over each regime.
ACI ERF E is decomposed into a contribution by each regime so that it can be written out as: Having done this, it makes sense to define the total forcing by each cloud regime clean k E C  , to be the summand of Equation 3. However, this definition is a little nonphysical and it makes more sense to further break down the forcing into individual effects. These proposed effects are: Multiplying out the terms of  Figure 2 shows the RFO of the 9 regimes used in the analysis in the present-day simulation. This shows that HadGEM3 broadly reproduces the satellite retrieved patterns seen in Tselioudis et al. (2013) throughout the tropics, especially in the cases of deep convection and the low CF regime, which represents regimes with a mixture of shallow cumulus and cirrus clouds. The k-means algorithm also does a good job distinguishing between storms seen in the ITCZ (WS1) and those in the midlatitudes (WS2). The dominant cloud regimes are the low CF regime, and the thick stratocumulus regime, primarily seen over the southern ocean and in the marine stratocumulus regions off the west coasts of Africa, North, and South America. The model fails to reproduce the very high observational RFO of the thick stratocumulus regimes seen in marine stratocumulus decks. Similarly, thin stratocumulus/shallow cumulus clouds are globally underrepresented, particularly over equatorial landmasses. This indicates that the model has difficulty simulating very thin cloud. The clear-sky regime is also over-represented by 5.2% globally, lending further evidence to this conclusion. Figure S3 shows the increase in CCN at cloud base between PD and PI simulations. CCN is defined by the dry particle cutoff radius being larger than 50 nm. The strongest increase is seen over land, predominantly over China and south-east Asia, and the Indian subcontinent, with other more localized perturbations seen elsewhere over areas with high emissions. The Southern ocean sees very little aerosol perturbation, and the north Atlantic and Pacific see a perturbation an order of magnitude smaller than the one seen over land. Figure 3 shows the total forcing produced by each cloud regime before any decomposition into individual effects,

Results
. This figure shows that approximately 50% of the total forcing comes from the thick stratocumulus regime.  . The data are aggregated for each month, and then subjected to a 2-tailed t-test. The data shown are significant at the 5% level. The forcing is dominated by the shortwave contribution by the thick stratocumulus regime, particularly in the marine stratocumulus decks off the coast of Africa and North & South America, and in the north Pacific and north Atlantic shipping lanes. The longwave contribution is much smaller than the shortwave, and is more pronounced in regimes with high CF, for instance the thick stratocumulus or thick midlevel cloud regimes. As the cloud fraction in the merged thick stratocumulus regime is already very high, it is likely that this forcing is arising from an increase in optical thickness of these clouds.
The Cirrus regime shows almost no shortwave forcing, however, it does present the highest longwave forcing of all regimes (−0.10 E Wm −2 ). Figure 5 shows the shortwave and longwave contributions to the forcing produced by changes in occurrence of each cloud regime. Once again, this effect is dominated by the shortwave contribution, this time with a roughly equal weighting between the thick midlevel and thick stratocumulus regimes for both SW and LW radiation. Because of the predominantly negative sign of cloud radiative effects, it is easy to see how changes in RFO manifest themselves in forcings. An increased RFO of a particular regime, broadly speaking, will result in an increased negative shortwave forcing, and an increased positive longwave forcing. The RFO of the clear regime is not preserved between experiments, however, as can be seen in Figure S1, the change of the clear-sky RFO is only −0.1% from present-day to preindustrial conditions. This effect is most visible in the midlevel cloud, where the forcing patterns in the thin and thick midlevel cloud regimes map onto each other fairly well. This indicates that for midlevel clouds, HadGEM3 predicts that the increased anthropogenic emissions are not causing a fundamental shift in which types of cloud are predominant over a given area, but merely an optical thickening of the pre-existing clouds, causing a shift from thin midlevel to thick midlevel clouds. As can be seen from  The cirrus regime shows strong effects arising from regime transitions, which is not seen in the effects shown in Figure 4. This can be attributed to a strong decrease in the RFO of the cirrus regime over land and most of the Pacific Ocean (see Figure S1).
Two regimes neglected in discussion so far have been the deep convective and midlatitude storm regimes. The reason for this is that the aerosol scheme in HadGEM does not interact directly with the convection scheme, meaning that theoretically there should be no change in the properties of convective clouds between the two simulations. However, there are indirect interactions between the two schemes, and this means that while the forcing produced by these regimes are not attributable to noise, these figures may not be reliable and a specific experiment must be run to accurately diagnose the forcing for the convective regimes. In these simulations, the deep convective regime contributes a total of −0.08 E Wm −2 to the global indirect aerosol forcing.
and so generally is not a dominant contribution to the overall forcing. The one exception to this is the cirrus regime, which exhibits −0.06 E Wm −2 to the global forcing via nonlinear effects. This, however, almost cancels out the linear effects shown by the cirrus regime, such that it only contributes −0.02 E Wm −2 to the global forcing.

Conclusions
Quantifying effective radiative forcing due to aerosol-cloud interactions remains a largely uncertain process, and the magnitude remains unconstrained in general circulation models. Previous studies focus on the magnitude of ACI ERF E arising from all cloud types, however, here the ACI ERF E from the HadGEM3-GA7.1 global climate model is decomposed into several global observational cloud regimes.
Simulated ERF ACI was broken down into contributions from a set of 10 observational cloud regimes using the methodology of Williams and Webb (2009). This is further broken down into both shortwave and longwave effects, and into two contributions with physically understandable definitions. This regime methodology has the key limitation of only being available on daylit points due to technical limitations of COSP, however, this has the advantage that the results can be easily compared with satellite data as a result of the design goal of COSP. Other regime classification methods exist, however, for instance Unglaub et al. (2020), which uses cloud base height, and cloud top height variability to classify clouds from CALIPSO and CloudSat. This has the advantage of not being limited to daytime data and the disadvantage of sparse spatio-temporal sampling.
From this analysis it can be concluded that a large majority of forcing in the HadGEM3 GA7.1 comes from changes to the thick stratocumulus and thick midlevel cloud regimes (amounting to a total of −0.51 E and −0.23 E Wm −2 , respectively). These two sets of regimes have a similar geographical distribution and there may be some crossover between the two regimes, owing to the simplicity of the regime assignment method.
There is a lesser contribution from the low CF regime, which contributes −0.07 E Wm −2 to the global ERF ACI . This means that efforts should be focused on constraining the forcing produced specifically by these cloud regimes.
Comparing Figure 3 with the forcing plots, it can be inferred that the sensitivity of ERF ACI to an increased aerosol loading is much greater in marine stratocumulus than in similar clouds seen over land.
The Cirrus regime shows strong individual effects that largely cancel each other out, however, these values must be taken with caution due to the lack of aerosol-ice interactions in the model. These large effects highlight the uncertain nature of ACI ERF E arising from ice clouds in GCMs and should encourage model developments to reduce the magnitude of uncertainty surrounding ACI ERF E from ice clouds.
The lack of correlation between the CCN perturbation and the total cloud forcing (seen in Figures 3 and S3 respectively) is the motivation for a detailed study of cloud sensitivities. The results of this study suggest that marine clouds are much more sensitive to aerosol perturbations than clouds seen over land.
This new tool can be used to gain insights into model representations of ACI ERF E . It is unclear whether the stratocumulus dominated ACI ERF E is a feature of all modern GCMs or whether aerosol-cloud interactions manifest themselves differently between different models, and this will be the topic of ongoing research.

Data Availability Statement
Raw simulation output data from the HadGEM3 model runs are available in the Met Office postprocessing data format (.pp; Met Office, 2013) from the JASMIN data infrastructure (http://www.jasmin.ac.uk) via the Met Office Managed Archive Storage System (MASS). The PI data are stored at moose:/crum/u-bg357/apk. pp and the PD data are stored at moose:/crum/u-bf393/apk.pp. Processed data used for all the results in this paper are publicly available at https://doi.org/10.5281/zenodo.4676264. The clusters used in this analysis were generated by George Tselioudis, William Rossow, Yuanchong Zhang, and Dimitri Konsta, and were made available for use at http://crest.ccny.cuny.edu/rscg/products.html.