1 Robustness, uncertainties, and emergent constraints in the radiative

2 responses of stratocumulus cloud regimes to future warming

3

4 Yoko Tsushima¹, Mark A. Ringer¹, Tsuyoshi Koshiro², Hideaki Kawai², Romain Roehrig³,

5 Jason Cole⁴, Masahiro Watanabe⁵, Tokuta Yokohata⁶, Alejandro Bodas-Salcedo¹, Keith D.

6 Williams¹, and Mark J. Webb¹

7 1. Met Office Hadley Centre, UK

8 2. Meteorological Research Institute (MRI), JMA, Japan

9 3. Centre National de Recherches Météorologiques, France

10 4. Canadian Centre for Climate Modelling and Analysis, Canada

11 5. Atmosphere and Ocean Research Institute (AORI), University of Tokyo, Japan

12 6. National Institute for Environmental Studies, Japan

13

14 Corresponding author's address and e-mail

15 FitzRoy Road, Exeter, Devon, EX1 3PB, United Kingdom

16 yoko.tsushima@metoffice.gov.uk

17 Tel: +44 (0)1392 885258

18 Fax: +44 (0)1392 885681

19
20 ABSTRACT

21 Future responses of cloud regimes are analyzed for five CMIP5 models forced with observed
22 SSTs and subject to a patterned SST perturbation. Correlations between cloud properties in
23 the control climate and changes in the warmer climate are investigated for each of a set of
24 cloud regimes defined using a clustering methodology. The only significant (negative)
25 correlation found is in the in-regime net cloud radiative effect (CRE) for the stratocumulus
26 regime. All models overestimate the in-regime albedo of the stratocumulus regime. Reasons
27 for this bias and its relevance to the future response are investigated. A detailed evaluation of
28 the models' daily-mean contributions to the albedo from stratocumulus clouds with different
29 cloud cover fractions reveals that all models systematically underestimate the relative
30 occurrence of overcast cases but overestimate those of broken clouds. In the warmer climate
31 the relative occurrence of overcast cases tends to decrease while that of broken clouds
32 increases. This suggests a decrease in the climatological in-regime albedo with increasing
33 temperature (a positive feedback); this is opposite to the feedback suggested by the analysis
34 of the bulk in-regime albedo. Furthermore we find that the inter-model difference in the sign
35 of the in-cloud albedo feedback is consistent with the difference in sign of the in-cloud liquid
36 water path response, and there is a strong positive correlation between the in-regime liquid
37 water path in the control climate and its response to warming. We therefore conclude that
38 further breakdown of the in-regime properties into cloud cover and in-cloud properties is
39 necessary to better understand the behavior of the stratocumulus regime. Since cloud water is
40 a physical property and is independent of a model's radiative assumptions, it could
41 potentially provide a useful emergent constraint on cloud feedback.

42

43 Key words: stratocumulus; liquid water path; cloud feedback; cloud radiative effect;
44 climate model

45
## 1. Introduction

Clouds continue to contribute the largest uncertainty to estimates and interpretations of the Earth's changing energy budget (Boucher et al., 2013, Flato et al., 2013). The evaluation and improvement of cloud performance in climate models are considered necessary prerequisites for reducing this uncertainty. Stephens (2005) suggested that progress in understanding cloud feedbacks requires a carefully orchestrated and systematic combination of models and observations. Various cloud metrics and diagnostics have been developed (e.g. Klein et al., 2013; Nam et al., 2012; Qu et al., 2014; Tsushima et al., 2013; Williams and Webb, 2009), and the Cloud Feedback Model Intercomparison Project (CFMIP) Diagnostics Code Repository<fnref n="1" /> now provides a repository of cloud metrics and diagnostics, including programs to calculate them.

Many cloud regimes simulated by models are biased compared to observations and most of these biases include compensating errors (Tsushima et al., 2013). Low clouds have the largest errors (Williams and Webb, 2009), primarily a compensation between too small cloud amount and larger albedo than observations (Nam et al., 2012; Tsushima et al., 2013; Williams and Webb, 2009). It is clearly necessary to investigate how these errors could be related to model-simulated cloud feedbacks.

On the other hand, emergent constraints (e.g. correlations between a variable in the historical period and its behavior in response to projected future changes) are increasingly being sought in order to make reliable projections of climate change (e.g. Sherwood et al., 2014; Fasullo and Trenberth, 2012). This approach assumes the existence of observable variables that are strongly related to climate sensitivity or climate feedback. However, the reasons for such relationships are not always clear because of the obvious complexity of the climate system. In order for such correlations to be used with confidence as a robust emergent

<footnote n="1">¹ http://www.cfmip.net</footnote>
constraint, understanding of the physical mechanisms underpinning the relationships found is critical.

To make the interpretation of model differences in present day and future climate more straightforward several idealized experiments were designed in CFMIP Phase 2 (CFMIP2). Several studies have since proposed mechanisms in which a variable in the present day climate could be related to the future response (Bony et al., 2015; Sherwood et al., 2014; Brient and Bony, 2012). These efforts form part of the World Climate Research Program (WCRP) Grand Challenge on Clouds, Circulation and Climate Sensitivity (http://www.wcrp-climate.org/grand-challenges/gc-clouds).

Here we investigate robust responses and uncertainties under the same patterned SST change among models, as well as correlations between the inter-model differences in cloud regime properties in the control climate and in response to future warming. The questions we address are:

1. What are the uncertainties and robust responses of cloud regimes among current models?

2. Are inter-model differences of cloud properties in the control climate correlated to inter-model differences of their responses to future warming? If significant correlations are found in any of the cloud regimes, then two further questions follow:

3. What are the possible mechanisms that are responsible for the inter-model spread of the feedback?

4. Which values of the feedback are most consistent with the observations?

Our main aim is to investigate whether we can obtain any quantitative constraint on the cloud regime response to a warming climate.
## 2. Data and Analysis Method

### 2-1. Cloud Regime Analysis

We apply the clustering method of Williams and Webb (2009) (hereafter WW09) to ISCCP observations and comparable Global Climate Model (GCM) output produced with the ISCCP simulator (Klein and Jakob 1999; Webb et al. 2001). The ISCCP simulator and the analysis code used by WW09 are both freely available for research use from the CFMIP website (http://www.cfmip.net).

A three element vector of in-cloud mean cloud albedo ($\alpha$), in-cloud mean cloud top pressure (CTP) and total cloud cover (TCC) is calculated for each daily mean GCM grid point. This is assigned to the closest observed regime based on the reference values of (CTP, $\alpha$, TCC) in Table 3 in WW09 using a normalized minimum root-sum-square measure of distance. Cloud Radiative Effect (CRE) is the difference between the outgoing radiative flux in the clear-sky and the total-sky (Charlock and Ramanathan, 1985), and the CRE within each regime (in-regime CRE) is calculated as the average of the values when that regime is assigned. As described in Tsushima et al., (2013), we define the relative frequency of occurrence (RFO) as the number of points assigned in each regime relative to the number of data points in the whole period.

### 2-2. Observed Data and Analysis Period

Daily mean values of the CRE are obtained from the top-of-the-atmosphere (TOA) fluxes from the ISCCP-FD product (Zhang et al. 1995) for the period March 1985-June 2007 except March 1990-June 1994, ERBE-S4G (Harrison et al. 1990) for March 1985-February 1990, CERES-aqua for July 2002-June 2007 (Loeb et al. 2009). The cloud data used for the present analysis are the daily averaged grid-box means of cloud top pressure (CTP), cloud albedo ($\alpha$), and total cloud cover (TCC) provided by the International Satellite Cloud Climatology Project (ISCCP; Rossow and Schiffer 1999). The exclusion of March 1990-June 1994 from the ISCCP-FD data is to remove the period which is most affected by the Mt. Pinatubo
eruption and is necessary because ISCCP-FD double counts radiative effects of aerosols from the eruption. The choice of the period is based on Murphy et al. (2009)

## 2-3. Model Data

We use the Coupled Model Intercomparison Project (CMIP5) multi-model ensemble outputs of Atmospheric Model Intercomparison Project (AMIP) simulations as well as AMIP Future simulations. In the latter experiment, a patterned SST perturbation based on the multi-model mean from the CMIP3 1%/year CO₂ increase experiments is used as a perturbation to the AMIP SST. As part of CFMIP2, modeling groups have archived daily-mean ISCCP simulator outputs of CTP, α, and TCC from the AMIP CMIP5 experiments using the CFMIP Observation Simulator Package (COSP; Bodas-Salcedo et al. 2011). These are analyzed here, along with CRE values and cloud properties for which daily mean data are available. The CMIP5 variable names used are pctisccp (for CTP), albisccp (for α), cltisccp (for TCC), rsut (for TOA Outgoing Shortwave Radiation), rsutcs (TOA Outgoing Clear-Sky Shortwave Radiation), rlut (for TOA Outgoing Longwave Radiation) and rlutcs (for TOA Outgoing Clear-Sky Longwave Radiation), clwvi (for vertically integrated cloud water), clivi (for vertically integrated cloud ice).

Five models are used for the analysis. The main restriction on the number of models is the availability of the daily-mean data. The models are CanAM4, CNRM-CM5, MIROC5, MRI-CGCM3-org, MRI-CGCM3-mod, and HadGEM2-A (see http://cmip-pcmdi.llnl.gov/cmip5/citation.html for the names of the institutions identified by the acronyms listed here). MRI-CGCM3-org is the official submitted version: however, a bug was found in the equations for cloud droplet and ice crystal number concentrations (Kawai et al., 2015), which makes the cloud effective radius too sensitive to cloud water amount. The same simulations were performed with a modified version of this model (MRI-CGCM3-mod) and these are also included in our analysis. The analysis period for the models is chosen to be consistent with ISCCP-FD, which is available for the longest period.
147

148 **3. Future Response of Cloud Regimes**

149 To answer question 1, the cloud radiative effect feedback from each model is broken down
150 into contributions from different cloud regimes. Firstly, contributions of different cloud
151 regimes to the net cloud radiative effect (net CRE) feedback are shown in the top panel in
152 Fig.1. To provide a global summary of the seven regimes in the tropics (20°S-20°N), the
153 seven in the ice-free extra-tropics, and the six in the snow/ice covered extra-tropics, we
154 combine cloud regimes defined in different regions but which have the same name. The
155 global cloud regimes presented are: shallow cumulus, thin cirrus, anvil, deep convective,
156 mid-level, transition, stratocumulus and frontal cloud. The thin mid-level regime and thick
157 mid-level regime over snow/ice covered regions are shown as a combined mid-level regime.

158 The cloud regime which has the largest ensemble-mean change is the stratocumulus regime
159 (+0.11Wm⁻²K⁻¹) followed by the shallow cumulus regime (−0.09Wm⁻²K⁻¹) and the frontal
160 regime (−0.09Wm⁻²K⁻¹). The three regimes which have the largest inter-model spread of the
161 net CRE feedback are the deep convective regime, the shallow cumulus regime, and the
162 stratocumulus regime. In the shallow cumulus regime and the mid-level regime the net CRE
163 feedback is systematically negative, but for the other regimes the sign of the feedback is not
164 consistent among models.

165 The net CRE response can be decomposed into changes in relative frequency of occurrence
166 (RFO) and changes in in-regime net CRE (NCREO) (see Eqn. A-1-1 in Appendix 1). The
167 definition of the RFO is the number of days when a cloud regime occurs normalized by a
168 number of days used in the analysis. Several cloud regimes are found to have robust signs in
169 response either in the RFO (Fig. 1b) or in the in-regime net CRE (Fig.1c). All models show a
170 decrease in the RFO for the stratocumulus regime but an increase for the frontal regime. The
171 in-regime net CRE feedback is negative in the shallow cumulus and mid-level regimes in all
172 models, consistent with the systematic negative net CRE feedback in these regimes. Fig. 1d
shows the contributions of RFO and in-regime NCRE to the global-mean NCRE change. The
inter-model spread in the RFO contributions to the NCRE change is larger than that in the in-
regime net CRE although the magnitude is roughly comparable.

Examining the change in statistical characteristics of a cloud regime gives a different
perspective to looking at a specific location in the control simulation and seeing how the
characteristics of the cloud there change in response to warming. By definition, variations of
cloud cover, in-cloud albedo, and cloud top pressure within a cloud regime are limited so that
these values meet the criteria of the regime. We first verified that the RFO changes found in
the cloud regimes do not result from an artifact of changes in cloud properties (i.e. cloud
thickening, or increase in cloud top pressure). We checked the spatial distributions of each
cloud regime in areas dominated by stratocumulus and confirmed that the largest change in
RFO is for the stratocumulus regime itself. We also found that there was no systematic
increase or decrease of any of the other regimes accompanying this change in stratocumulus,
i.e. there is no evidence for a transition from stratocumulus to another cloud regime.

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188 4. Constraining Future Stratocumulus Responses by Their Present-day Characteristics

To answer question 2, correlations between the control climate and the changes in the
warmer climate are calculated for the cloud radiative properties (net CRE, RFO, and in-
regime net CRE) of each of the cloud regimes. No correlation is found for either present-
future RFO or net CRE for all nine regimes shown in Figure 1. No correlation is found for in-
regime NCRE for all regimes except one: a strong correlation is found for the in-regime net
CRE of the stratocumulus regime (Fig. 2a). The larger the in-regime net CRE, the more
positive the feedback, and the smaller the in-regime net CRE, the more negative the feedback.
The negative bias and the correlation are seen even if the region is broken down into the
tropics (20°S-20°N) and the extra-tropics (See Fig. 2b for the tropics). The shortwave (SW)
CRE drives the negative bias and the strong correlation (r=0.96).
Since we found a significant correlation in the stratocumulus regime, we address question 3. We focus on the tropical region and analyze the bulk properties first and then the contributions from different cloud cover conditions to the bulk properties.

**4-1. Bulk cloud properties of the tropical stratocumulus regime**

A scatter plot (which corresponds to the Fig. 2) is plotted for the in-regime albedo, which is an output from the ISCCP simulator (Fig.3). The in-regime albedo is overestimated in all models. Figures2 and 3 look roughly similar, but the order of the models along the two axes is not the same. Inter-model differences in the zonal-mean distribution of stratocumulus clouds could be responsible for the disagreement, because the difference in the zonal distribution is important for the SW CRE – because of the different solar insolation (Appendix 2) - but not for the albedo.

The in-regime albedo is a product of cloud cover and albedo within clouds (Appendix 2).
Figure 4a shows the total cloud cover and in-cloud albedo of the stratocumulus regime in the control climate and the amipFuture experiments. Each dashed line is the line at constant in-regime albedo. This figure clearly shows that there is a compensation of errors in the in-regime albedo of the stratocumulus regime: an underestimate of the total cloud cover and an overestimate the in-cloud albedo. Although the biases in the total cloud cover and the in-cloud albedo are worse in MIROC5, its product (in-regime albedo) is in best agreement with the observations. This suggests that evaluating only the in-regime albedo would miss the errors in the cloud cover and the in-cloud albedo. Fig. 4b shows the total cloud cover and the cloud top pressure of the stratocumulus regime in the control climate and the future. Cloud tops are too high in all models, and the smaller the cloud cover, the lower the cloud top pressure (Fig 4b. According to WW09, the average cloud top pressure of the stratocumulus regime in the observations is 722 hPa. The stratocumulus regime tends to have the largest population in the ISCCP cloud top pressure bin between 800 hPa and 680 hPa, as well as a contribution in the bin between 680 hPa and 560 hPa. These characteristics are also found in
other cloud regime studies which use the ISCCP data (e.g. Tselioudis et al., 2013). In a warming climate, the signs of the changes in the cloud top pressure and the cloud cover are related, i.e. four models show deepening with decreasing cloudiness and one model shows lowering with increasing cloudiness. However, there is no significant quantitative correlation between the changes in these variables in response to warming. Brient and Bony (2012) found a correlation between the low cloud amount in the control climate and the future response in a range of configurations of their model, and they proposed that atmospheric CRE could be the controlling factor. We looked at the inter-model difference in the atmospheric CRE in the control climate and the future response, but no clear correlation was found (not shown).

## 4-2. Contributions of Cloud Properties from Different Cloud Covers

### 4-2-1. Initial analysis

To further understand the biases found in the cloud properties in the stratocumulus regime and their future responses, the ISCCP cloud property data are analyzed more in detail. Cloud cover gives an indication of the degree to which the stratocumulus is overcast or broken. We sort the various cloud data by the cloud cover and take the average for each cloud cover bin. First, the in-regime albedo data are broken down into different cloud cover bins for the control climate (Fig. 5a) and the future response (Fig. 5b). According to the observations, cloud cover is larger than 0.6, and the larger the cloud cover, the larger the contribution to the in-regime albedo. It is found that the models systematically underestimate the contributions from clouds on fully overcast days and overestimate the contributions from broken stratocumulus clouds. This figure further reveals that the overestimate of the in-regime albedo in the stratocumulus regime is not from clouds with larger cloud cover but from clouds with smaller cloud cover. These results suggest that GCMs are not good at producing fully-overcast stratocumulus clouds, instead having broken stratocumulus too frequently. In a warming climate, the in-regime albedo tends to decrease in the bins with cloud cover larger
than 0.8, but tends to increase in the bins with cloud cover smaller than 0.7, except for
CNRM-CM5 which shows small responses in the opposite sense (Fig. 5b).

To see which cloud property is responsible for this bias, RFO, cloud top pressure, in-cloud
albedo and in-cloud liquid water path are plotted in different cloud cover bins (Fig. 6). It is
found that the RFO is responsible for the distribution of the in-regime albedo and the bias in
models. According to the observations, the cloud cover is larger than 0.7 whenever this
regime occurs. All models fail to produce clouds with large cloud cover as frequently as the
observations. The in-cloud albedo is found to be overestimated in all models. The models
tend to have highly reflective broken cloud (i.e. high in-cloud albedo with smaller cloud
cover) frequently, but such highly reflective broken clouds are not found in the observations
(not shown). Although the overestimate contributes to models' overestimate of the in-regime
albedo to some extent, replacing the models' stronger in-cloud albedo with the observational
value does not resolve the stronger in-regime albedo bias (not shown). Both observations and
models suggest a quadratic relationship between in-cloud albedo and increasing cloud cover,
with the minimum in-cloud albedo occurring at cloud covers around 0.7-0.8. Models
reproduce this effect. These characteristics can be interpreted as follows. Clouds with the
largest cloud cover will occur in overcast conditions in cool, moist boundary layers with
thicker clouds and lower cloud bases. On the other hand, more broken clouds will occur in
warmer, drier boundary layers, where the decrease and subsequent increase of in-cloud
albedo for smaller cloud cover could then be explained by an initial rising of cloud base
whose effect on cloud thickening is later overtaken by a more rapid increase in cloud top
height. The smaller the cloud cover, the smaller the cloud top pressure, i.e. the higher the
cloud top. Distributions of the LWP are similar to the in-cloud albedo, but the ordering of the
models in terms of in-cloud LWP is different from the ordering in terms of in-cloud albedo.
For example, CanAM4 has the largest in-cloud liquid water path in all cloud cover bins, but
this model has one of the smallest in-cloud albedos. The difference in the ordering of the
models between the LWP and the albedo indicates that radiative parameterizations which relate radiative effects of the LWP to the albedo are different in different models and that they are very likely responsible for the inter-model difference in the albedo.

## 4-2-2. Understanding physical mechanisms of the in-regime albedo response in different models

It has been found that the RFO distribution is responsible for the error in the distribution of the in-regime albedo and the positive bias in the in-cloud albedo contributes to making the cloud too bright. Here, quantitative contributions of the cloud cover and the in-cloud albedo to the in-regime albedo response are estimated and mechanisms that could contribute to the inter-model difference in the in-regime albedo response are investigated. Fig. 7 shows a breakdown of in-regime cloud albedo change into the change from the cloud cover distributions and that from the in-cloud albedo. The former is a product of in-cloud albedo in the control climate and the change in the RFO for each cloud cover. The latter is a product of the change in in-cloud albedo and the RFO in the control climate. All models except CNRM-CM5 show a decrease in the cloud cover component. On the other hand, all models except HadGEM2 show an increase in the in-cloud albedo component. The spread of the in-regime albedo change in the models depends on the relative contribution of these two responses in the models.

Figure 8 shows the change in cloud properties with different cloud covers in response to warming. The Fig. 8a shows the change in RFO. The change in RFO distribution is similar to the change in the in-regime albedo distribution. There is less overcast stratocumulus but more broken cloud in the warming climate. CNRM-CM5 is an exception: clouds with cloud cover smaller than 0.6 decrease and those with large cloud cover increase in this model. The inter-model differences in the change in the relative occurrence of overcast cases and broken cases are consistent with these differences in signs of the cloud cover component in Fig. 7. In all models except CNRM-CM5, the cloud top becomes higher almost in all cloud cover bins (not
shown). Figure 8b shows the change in the in-cloud albedo. The inter-model differences in sign as well as ordering of the models in terms of the in-cloud albedo responses is the same in all cloud cover bins above 0.6 and explain those of the in-cloud albedo component in Fig. 7.

The top-right panel in Fig. 8 shows the difference of the in-cloud LWP in the amipFuture experiment from the amip experiment. Although the ordering of the models in terms of the increases in the albedo and in the LWP is different, it is found that the inter-model differences in the sign of the in-cloud albedo feedback are consistent to those of the in-cloud LWP response in cloud cover bins above 0.7 (except MRICGCM3-org). This indicates that not only radiative parameterizations but also cloud physical properties contribute to the inter-model differences in the in-regime albedo feedback of the stratocumulus regime.

We investigated to what extent the inter-model differences in the in-cloud albedo response can be explained by this inter-model difference in the in-cloud LWP response. Using two basic physical equations which relate in-cloud LWP to in-cloud albedo (see Appendix 2 for the details), we estimated a change in the in-cloud albedo expected from the change in the in-cloud LWP for each model. It was found that the inter-model differences of the estimated in-cloud albedo are rather similar to those of in-cloud LWP (Fig. 8d) hence the inter-model difference in the LWP response cannot explain the actual in-cloud albedo response. The inter-model difference in cloud radiative parameterizations should also affect the magnitude of the in-regime albedo response. Information on the cloud parameterizations used in the models is summarized in Table 1, and can be used to investigate the impact on the inter-model differences in the in-cloud LWP, in-cloud albedo, and the feedbacks. Models which have radiative interaction in all condensation process (HadGEM2 and MIROC5) tend to have smaller LWP and smaller $R_e$; small in amount but efficient in reflectivity. However we could not find a process which has a clear impact on the inter-model differences in the in-cloud LWP, in-cloud albedo, or the feedbacks.
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## 4-3. Toward emergent constraints

330

Finally, we address question 4. According to the evaluation in section 4-2-1, those models whose in-regime albedo agrees less with the observations actually agree better in the distributions of in-regime albedo contributions from different cloud cover bins because of the RFO distributions. All GCMs have less overcast cases and more broken clouds than the observations in the stratocumulus regime. In the warming climate, overcast cases further decrease and broken cases increase further. Because the magnitude of this redistribution is related to the distribution in the control climate, reproducibility of the distribution in the control climate is regarded to be more important than the bulk value.

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In which case, what does the performance of the distribution suggest about the in-regime net CRE feedback of stratocumulus regime in the warmer climate? In Fig. 9, the horizontal axis shows an RMS error of in-regime albedo in different cloud cover bins for the stratocumulus regime, and the vertical axis shows the in-regime albedo feedback. The RMS error measures the contributions from different cloud cover bins to the in-regime albedo: this value quantifies the error of the in-regime albedo distribution in different cloud cover bins. In models whose bulk in-regime albedo agrees better with the observations the in-regime albedo contributions from overcast cloud are too small and those from broken clouds are too large. As suggested in Fig.5, models whose distribution agrees better with the observations (e.g. HadGEM2 and MRI-CGCM3-mod), show a decrease in the albedo, while the remainder show an increase. The best guess (the y value at x=0) suggests a small positive feedback (-0.015/K), i.e. a decrease in the in-regime albedo with temperature increase.

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Since we found that a physical property, LWP, contributes to the inter-model difference in the in-regime albedo feedback of the stratocumulus regime, we further investigate whether there is any correlation between the inter-model difference in LWP in the control climate and the future response. We find a strong positive correlation in the in-regime LWP of the stratocumulus regime (Fig.10). Even MRI-CGCM3-org (which has a bug in the cloud droplet

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355 number calculations, see above) is consistent with this relationship. Models with larger
356 (smaller) in-regime liquid water path in the control climate show an increase (a decrease) in
357 the liquid water path in the warming climate. Since LWP is a physical property, it will be
358 useful to understand the role of physical processes in the inter-model difference in cloud
359 feedback, such as possible future thickening or thinning of cloud layers and its relevance to
360 the thickness of the cloud layer and/or the relationship to the atmospheric profile in the
361 control climate.

362

363 **5. Summary and Discussion**

364 Cloud regimes are analyzed for five CMIP5 models forced with observed SSTs and a
365 patterned SST perturbation. Under the constrained surface temperature increase all models
366 show a decrease in the frequency of occurrence of the stratocumulus regime and an increase
367 in the occurrence of the frontal regime.

368 Our study has found that the stratocumulus in-regime albedo in all models is biased: the
369 cloud cover is too small, the in-cloud albedo is too high, and the cloud top is too high. This is
370 consistent with Nam et al. (2012), even though their definition of the stratocumulus regime is
371 dependent on dynamical regime sorting and independent of the cloud characteristics. The fact
372 that the results are consistent despite this different definition strengthens the credibility of our
373 results. Our study also showed that clouds in the stratocumulus regime become more shallow
374 convective in the warming climate, consistent with Webb and Lock, (2013). We further found
375 that there is a strong correlation between the inter-model difference in the in-regime albedo in
376 the control climate and the difference in the future feedback. The sample size is limited
377 because not many modeling centers submitted all of the daily-mean cloud data which are
378 necessary for this analysis. Although our analysis is based on much more than correlations,
379 and attempts to interpret what we see in the models in terms of the physics of low cloud
380 behavior correlations obtained from them should be subject to further corroboration in the future
because our results are obtained from a small number of models. We would like to strongly encourage modeling centres to submit these data in Phase 3 of CFMIP.

The correlation noted above suggests that an evaluation of the in-regime albedo performance with the observations could provide an emergent constraint on the feedback, but our results highlight the importance of evaluating the bulk properties in detail, such as distributions of each component, to ensure that a compensation of errors in the bulk property is revealed. All models have too reflective in-regime albedos, but it has been found that this is because all models systematically underestimate the relative occurrence of overcast cases but overestimate that of broken clouds, and that the overestimate of the in-regime albedo is due to the latter issue. A detailed evaluation of the contributions of clouds with different cloud covers to the in-regime albedo suggests a decrease in the in-regime albedo and positive contribution to the overall feedback, which is different from that implied by the evaluation of the bulk property of in-regime albedo.

These results suggest that GCMs have biases which are not good at producing stratiform clouds, having convective process too frequently, and the magnitude of these biases is related to the magnitude of the future change in relative increase in broken clouds. The biases found in this study are consistent with the findings from a comparative study of single-column models with Large-Eddy Simulations (LES) (Bretherton et al., 2013). Low clouds tend to have the cloud cover fully covered in the LES, (Bretherton et al., 2013; Van Del Dussen et al., 2014), but single column experiments using GCMs cannot produce clouds with fully covered grid cells (Dal Gesso et al., 2014). Further, climate change sensitivities of subtropical cloud-topped marine boundary layers have been analyzed using LES of three CFMIP-GCSS Intercomparison of Large-Eddy and Single-Column Models (CGILS) cases of well-mixed stratocumulus, cumulus under stratocumulus, and shallow cumulus cloud regimes, respectively (Bretherton et al., 2013). The LES results suggest that the low cloud feedback is positive: the stratocumulus clouds tend to get physically thinner with the cloud cover being
407 kept fully covered in the warming climate (Bretherton et al., 2013). The stratocumulus layer
408 thins as cloud base rises more than cloud top, and this physical thinning of the layer decreases
409 the LWP (Van Der Dussen et al., 2015; Dal Gesso et al., 2015). In our study, cloud cover
410 tends to change in all GCMs. Interestingly, the inter-model difference in sign of the in-cloud
411 albedo feedback among the GCMs agrees with the inter-model difference in sign of in-cloud
412 LWP response, and also a significant correlation is found in the inter-model difference in the
413 in-regime liquid water path in the control climate and the future response. The correlation
414 suggests that thermodynamic processes partly contribute to the inter-model differences in
415 cloud feedback. A recent LES sensitivity study has found that the steady state LWP is rather
416 insensitive to the LTS, but increases significantly and almost linearly with the free
417 tropospheric humidity (Van Der Dussen et al., 2015). Investigation of the different
418 mechanisms between the GCMs with different sign of the response in LWP would be useful.
419 Also it is important to understand mechanisms of the common biases in the GCMs and their
420 relevance to the responses so that the robustness of such emergent constraints can be
421 addressed. For this purpose, investigations between LES and the GCMs and analysis of more
422 detailed observational cloud data from a field campaign in comparison with models such as
423 VOCALS and Transpose-AMIP would be useful. Since LWP is a value from the physical
424 variable of cloud water, it will be helpful to evaluate LWP as well as the radiative properties
425 of clouds.

426 The LWP amount controls whether the in-regime LWP and the in-regime albedo increase or
427 decrease in the warming climate. Models with more broken clouds tend to become more so in
428 the warming climate. A sensitivity study using mixed-layer model found that future increase
429 or decrease of the stratocumulus LWP is sensitive to the entrainment rate (De Roode et al.,
430 2014), and they argued that inter-model differences in the sign of the LWP response in
431 GCMs may be well attributable to differences in the entrainment response, because the
432 entrainment response to changes in the large-scale forcing conditions depends on the details
433

of the parameterization of turbulent and convective transport. Investigations of how

434

convective processes act to modify cloudiness in the stratocumulus regime will be useful.

435

The inter-model difference in cloud radiative parameterizations also affects the magnitude

436

of the in-regime albedo response. If clouds and tendency terms including radiative heating

437

data are provided separately for convective clouds and large-scale clouds, as well as CCN

438

data to cloud optical thickness conversion, the inter-model difference in LWP could better

439

explain the inter-model difference in the in-cloud albedo and its response to warming. These

440

data were not requested as daily-mean data in CMIP5 and requesting these data in the next

441

phase of CFMIP would be useful.

442

Models which have radiative interaction in all condensation process (HadGEM2 and

443

MIROC5) tend to have smaller LWP and smaller Re: small amount but efficiently reflective

444

clouds. This indicates that radiative processes in convective condensation process influence

445

large-scale condensation. Detailed process analysis may be helpful.

446

Nam et al., (2012) showed that CanAM4 minimizes the overestimate of the low-cloud

447

optical thickness, which is consistent with the largest estimated effective radius in our study.

448

They also noted that CanAM4 includes state-of-the-art representations of the cloud overlap as

449

well as the horizontal inhomogeneity of cloud optical properties (Cole et al., 2011) and

450

argued that mis-representation of the horizontal inhomogeneity of cloud optical properties

451

and the vertical overlap of cloud layers may contribute to the models' overestimate of low-

452

cloud radiative effects. However, the inter-model difference cannot explain the inter-model

453

difference in their clouds' effectiveness to the reflectivity (which is represented by estimated

454

effective radius in the Table 1. In MRI-CGCM3-mod, the estimated Re is also larger (23 µm).

455

However, this model does not introduce any horizontal inhomogeneity. Also, MRI-CGCM3

456

uses a maximum-random normalized random overlap assumption, i.e. clouds overlap

457

randomly but the total cloud cover is normalized by the one based on the maximum-random

458

assumption. The normalized random overlap assumption should give a larger albedo than the
459 maximum-random overlap assumption for the same cloud vertical distribution because of the
460 non-linearity of cloud albedo with cloud water amount. In this model a considerably large
461 decrease in the number of cloud droplets is found in the warming simulation. Comparison of
462 more detailed data such as cloud droplet size in different models will be necessary to better
463 understand the different albedo responses.

464 The perturbed SST experiment analyzed in this study is different from fully coupled
465 simulations. Comparative analysis of these experiments will also be the subject of future
466 work.

467 Our study demonstrates the usefulness of cloud regime analysis to understand and
468 constrain cloud feedbacks. In addition, our results highlight the importance of evaluating not
469 only the bulk characteristics of clouds, such as CRE, but also more detailed cloud properties
470 and their distributions.

471

472
473 Acknowledgements

474 We are very grateful to Drs. Gill Martin, Adrian Lock, William Ingram, and Malcolm

475 Roberts who gave useful comments. We thank the international climate modeling groups

476 ((listed in Section 2-3 of this paper), the WCRP's Working Group on Coupled Modeling for

477 making available the multi-model data set obtained from the Phase 5 of the Coupled Model

478 Intercomparison Project (CMIP5). The data set has been indispensable for the study

479 conducted here. For CMIP5 the U.S. Department of Energy's Program for Climate Model

480 Diagnosis and Intercomparison provides coordinating support and led development of

481 software infrastructure in partnership with the Global Organization for Earth System Science

482 Portals. The research leading to these results has received funding from the European Union,

483 Seventh Framework Programme (FP7/2007-2013) under grant agreement no 244067 via the

484 EU Cloud Intercomparison and Process Study Evaluation Project (EUCLIPSE) and the Joint

485 DECC / Defra Met Office Hadley Centre Climate Programme (GA01101).

486
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Appendix 1: Breakdown of net CRE into contributions from cloud regimes

619

620

$$netCRE = \sum_{i=1}^{R} netCRE_{i} \qquad (A-1-1)$$

R is the total number of the regimes, netCRE<sub>i</sub> is the mean contribution of regime i to the net CRE.

623 netCRE<sub>i</sub> is broken down into the relative frequency of occurrence of regime i (RFO<sub>i</sub>) and the in-regime netCRE (netCREO<sub>i</sub>),

625

626

$$netCRE_{i} = RFO_{i} \cdot netCREO_{i} \qquad (A-1-2)$$

627 The future response of net CRE from each cloud regime (ΔNCRE<sub>i</sub>) is from contributions from changes in the RFO and changes in the in-regime net CRE (NCREO<sub>i</sub>), based on the following equation.

630

631

$$\Delta NCRE_{i} = \Delta RFO_{i} \cdot NCREO_{i} + RFO_{i} \cdot \Delta NCREO_{i} + \Delta RFO_{i} \cdot \Delta NCREO_{i} \qquad (A-1-3)$$

632 The definitions of RFO<sub>i</sub> and netCREO<sub>i</sub> are as follows.

633

$$RFO_{i} = \frac{\sum_{j=1}^{n(i)} w(j)}{\sum_{j=1}^{N} w(j)} \qquad (A-1-4)$$

634 , here n(i) is the number of points which are assigned to the cloud regime i and N is the total number of points.

636

$$N = \sum_{i=1}^{R} n(i) \qquad (A-1-5)$$

637

$$netCREO_{i} = \frac{\sum_{j=1}^{n(i)} w(j) \cdot netCRE(j)}{\sum_{j=1}^{n(i)} w(j)} \qquad (A-1-6)$$

638

639

640 w(j) is the area weight of the point normalized by the total area of interest.
The average SW CRE for regime i is $swCRE_i$ and is defined as follows,

$$swCREO_i = \frac{\sum_{j=1}^{n(i)} w(j) \cdot swCRE(j)}{\sum_{j=1}^{n(i)} w(j)} \qquad (A-2-1)$$

$n(i)$ is the number of points which are assigned to the cloud regime i, and $w(j)$ is an area

weight of the point normalized by the total area of the interest. As defined in Eq.A-1-6, $N$ is

the total number of data points.

$swCRE(j)$ is affected by the solar insolation $S_0(j)$ and the cloud albedo effect $CAE(j)$.

$$swCRE(j) = S_0(j) \cdot CAE(j) \qquad (A-2-2)$$

$CAE$ is defined as the difference of the all-sky albedo ($A_{total}$) from the clear sky albedo ($A_{clr}$)

at the TOA.

$$CAE(j) = A_{clr}(j) - A_{total}(j) \qquad (A-2-3)$$

Further, $CAE$ can be expressed in terms of cloud cover ($c$) and in-cloud TOA albedo ($A_{ic}$).

$$\begin{aligned} CAE(j) &= A_{clr}(j) - \{(1-c(j)) \cdot A_{clr}(j) + c(j) \cdot A_{ic}(j)\} \\ &= c(j) \cdot (A_{clr}(j) - A_{ic}(j)) \end{aligned} \qquad (A-2-4)$$

An in-regime $CAE$ of regime i ($CAEO_i$) is defined as follows.

$$CAEO_i = \frac{-\sum_{j=1}^{n(i)} w(j) \cdot c(j) \cdot (A_{ic}(j) - A_{clr}(j))}{\sum_{j=1}^{n(i)} w(j)} \qquad (A-2-5)$$

For the stratocumulus regime, scatter plots of the in-regime SW CRE for the stratocumulus

regime in amip run and their feedback in amipFuture for stratocumulus regime for the tropics
663 [20°S, 20°N] is similar to that of in-regime CAE. Hence the inter-model difference in the
664 swCREO is dominated by the difference in CAEO.

665 On the other hand, a regime's average in-regime albedo ($A_i$) is expressed by the average
666 cloud cover ($c_i$) and the average in-cloud albedo ($A_{ic,i}$) as follows.

$$668 \qquad c_i = \frac{\sum_{j=1}^{n(i)} w(j) \cdot c(j)}{\sum_{j=1}^{n(i)} w(j)} \qquad (A-2-6)$$

$$669 \qquad A_{ic,i} = \frac{\sum_{j=1}^{n(i)} w(j) \cdot c(j) \cdot A_{ic}(j)}{\sum_{j=1}^{n(i)} w(j) \cdot c(j)} \qquad (A-2-7)$$

$$670 \qquad A_{ic,i} = \frac{\sum_{j=1}^{n(i)} w(j) \cdot c(j) \cdot A_{ic}(j)}{\sum_{j=1}^{n(i)} w(j)} \qquad (A-2-8)$$

673 By definition, the in-regime albedo is a product of the $c_i$ and $A_{ic,i}$.

$$675 \qquad A_i = c_i \cdot A_{ic,i} \qquad (A-2-9)$$

676

677

678

679
## Appendix 3: Basic physical equations relating in-cloud LWP to in-cloud albedo

In a plane-parallel cloud, in-cloud LWP (W) and in-cloud optical thickness ($\tau$) can be related to cloud effective radius ($R_e$) (Stephens, 1978).

$$ \tau = \frac{2 W}{3 R_e} \quad (A-3-0) $$

Also, in-regime LWP (cW, c is cloud cover) can be expressed in terms of $R_e$, number of cloud condensation nuclei (N·z) and a scaling parameter k.

$$ c \cdot W = \frac{4}{3} k \cdot \pi \cdot N \cdot z \cdot R_e^3 \quad (A-3-1) $$

The number of cloud condensation nuclei is strongly related to aerosol number concentration, which in turn is strongly related to aerosol emissions. In the amip and amipFuture experiments the aerosol emissions are fixed to be the same. The aerosol number concentrations and also the $N_z$ are assumed to remain the same in amip and amipFuture experiments, under the current circumstance that the daily-mean data for these variables were not requested in CMIP5. We also assume that k is the same in cloud water from large-scale processes and cloud water from convective processes because LWP data from large-scale processes and convective processes were not separately requested and only combined data are available in CMIP5. The conversion from the optical thickness to albedo is based on the ISCCP-simulator. Using each model's in-cloud LWP data and in-cloud albedo data in the control climate simulation, each model's $R_e$ are estimated. Using the $R_e$, $kN_z$ can be estimated. Then $R_e$ in the future experiment is estimated with each model's $kN_z$ and the in-cloud LWP data. Finally, the future in-cloud albedo expected from the in-cloud LWP is estimated.
## Appendix 4: Formulations to constrain the net CRE feedback using observations and models

Here we describe formulations to estimate a possible change in a cloud regime's contribution to net CRE feedback if models could simulate the regime in a manner consistent with the observations.

Errors in modeled cloud regimes could affect the regime's contribution to cloud radiative feedback in two ways. Firstly, an error in $NCREO_i$ or $RFO_i$ in the control climate could intensify or weaken the contribution of the responses $\Delta RFO_i$ or $\Delta NCREO_i$ to $\Delta NCRE_i$ by weighting the first or the second terms in Eq. A-1-3 in a different way from the observations. This error in the $\Delta NCRE_i$ can be removed by replacing the $NCREO_i$ and $RFO_i$ in the Eq. A-1-3 to the observational values i.e. $NCREO_i^{obs}$ and $RFO_i^{obs}$, respectively.

$$ \Delta NCRE_i^{ctl\_obs} = \Delta RFO_i \cdot NCREO_i^{obs} + RFO_i^{obs} \cdot \Delta NCREO_i + \Delta RFO_i \cdot \Delta NCREO_i \quad (A-4-1) $$

A second possible error in the estimated feedback is that the magnitude of a cloud regime property (e.g. RFO or in-regime net CRE) in the current climate could be related to the amplitude of the response in climate change. We can estimate an 'observationally-based' cloud property feedback of the regime by putting the observational value in the equation of the regression line by assuming that a strong correlation found in a cloud regime is based on a mechanism which operates in reality. If a correlation is found either in RFO or in-regime netCRE, the estimated changes from the regression line are $\Delta RFO_i^{robs}$, $\Delta NCREO_i^{robs}$, respectively. This error in the $\Delta NCRE_i$ can be removed by replacing $\Delta NCREO_i$ to $\Delta NCREO_i^{robs}$ or $\Delta RFO_i$ to $\Delta RFO_i^{robs}$ in the Eq. A-4-1, e.g.

$$ \Delta netCRE_i^{ctl\_obs,dNCREO\_robs} = \Delta RFO_i \cdot NCREO_i^{obs} + RFO_i^{obs} \cdot \Delta NCREO_i^{robs} + \Delta RFO_i \cdot \Delta NCREO_i^{robs} \quad (A-4-2) $$

A change in net CRE feedback is the difference of $\Delta NCRE_i^{ctl\_obs,dNCREO\_robs}$ from $\Delta NCRE_i$.
<table><caption>**Table 1** Cloud parameterizations in models and estimated cloud effective radius using Eq. 1 from in-cloud optical thickness and in-cloud LWP.</caption><thead><tr><th></th><th>Condensation processes</th><th>Contribution to cloud water</th><th>Radiative interaction</th><th>Horizontal Inhomogeneity</th><th>Cloud overlap assumption</th><th>Estimated effective Radius [µm] *</th></tr></thead><tbody><tr><td rowspan="3">CanAM4</td><td>Large-scale, Shallow convection</td><td>Y</td><td>Y</td><td rowspan="3">Cole et al., (2011)</td><td rowspan="3">Cole et al., (2011)</td><td rowspan="3">34</td></tr><tr><td>Deep convection</td><td>Y</td><td>Y</td></tr><tr><td></td><td>N</td><td>N</td></tr><tr><td>CNRM-CM5</td><td>Large-scale, Convection</td><td>Y</td><td>Either of which with maximum cloud cover</td><td>Scaling factor 0.7</td><td>Maximum-Random</td><td>18</td></tr><tr><td rowspan="3">HadGEM2</td><td>Large-scale, Shallow convection</td><td>Y</td><td>Y</td><td rowspan="3">Scaling factor 0.8 (ocean), 0.67 (land)</td><td rowspan="3">Maximum-Random</td><td rowspan="3">12</td></tr><tr><td>Deep convection</td><td>Y</td><td>Y</td></tr><tr><td></td><td></td><td></td></tr><tr><td rowspan="3">MIROC5</td><td>Large-scale, Convection</td><td>Y</td><td>Y</td><td rowspan="3">No</td><td rowspan="3">Maximum-Random</td><td rowspan="3">17</td></tr><tr><td></td><td>Y</td><td>Y</td></tr><tr><td></td><td></td><td></td></tr><tr><td rowspan="3">MRI-CGCM3 -mod</td><td>Large-scale Convection</td><td>Y</td><td>Y</td><td rowspan="3">No</td><td rowspan="3">Yukimoto et al., (2012)</td><td rowspan="3">23</td></tr><tr><td></td><td>N</td><td>N</td></tr><tr><td></td><td></td><td></td></tr></tbody></table>

<footnote>*Plane-parallel is assumed, all cloud water is assumed to be radiatively visible. The value is averaged over all cloud cover bins.</footnote>
731 **Figure Captions**

732 Figure 1 (a) Contributions of cloud regimes to net CRE feedback [$Wm^{-2}K^{-1}$], (b) the changes in RFO, (c) in-regime net CRE [$Wm^{-2}K^{-1}$], and (d) contributions from RFO and in-regime net CRE to net CRE feedback [$Wm^{-2}K^{-1}$]. The ordering of the models is following the global mean NET CRE feedback.

736

737 Figure 2 Scatter plots of the in-regime NET CRE [$Wm^{-2}$] for the stratocumulus regime in amip run (horizontal axis) and their feedback [$Wm^{-2}K^{-1}$] in amipFuture for stratocumulus regime (a) for the whole globe and (b) tropics [20°S, 20°N] (bottom). Black solid line is a regression line out of models except MRI-CGCM3-org. The direction of two axes is larger (increase in) cooling effect toward the right (top). Grey lines indicate observational values.
740
741
742 The grey dotted lines are lower and upper bound of standard deviation out of the three observations.
743

744

745 Figure 3 Scatter plots of the tropical [20°S, 20°N] stratocumulus regime for the in-regime albedo in the amip run (horizontal axis) and their feedback in amipFuture. The black solid line is a regression line out of models except MRI-CGCM3-org.

748

749 Figure 4 Scatter plots of the tropical stratocumulus regime of its cloud cover in x-axis and (a) in-cloud albedo in y-axis, (b) cloud top pressure normalized by surface pressure in y-axis.

750

751 Amip run (open circle) and amipFuture run (plus). Navy blue for HadGEM2, light blue for CanAM4, red for MIROC5, green for CNRMCM5, orange for MRI-CGCM3-mod, orange with smaller mark for MRI-CGCM3-org, ISCCP data in black filled circle.

754
Figure 5 Different cloud cover bins' contributions of the tropical stratocumulus regime's in-regime albedo (a) in the control climate and (b) the change in future. Horizontal bins are cloud cover in the control climate and the future climate for each data.

Figure 6 (a) Relative frequency of occurrence, (b) normalized cloud top pressure, (c) in-cloud albedo, and (d) in-cloud LWP [kgm⁻²] of the tropical stratocumulus regime averaged over different cloud covers in amip run.

Figure 7 Contributions of the cloud cover distribution change and in-cloud albedo change to the in-regime albedo change in the tropical stratocumulus regime from the amip run to the amipFuture run.

Figure 8 (a) Change in RFO, (b) in-cloud albedo, (c) in-cloud LWP, and (d) estimated in-cloud albedo from LWP of the tropical stratocumulus regime binned by different cloud covers.

Figure 9 Scatter plots of stratocumulus regime for the RMS error of the in-regime albedo contributions from different cloud covers in amip run (horizontal axis) and their response in amipFuture for stratocumulus regime for the tropics [20°S, 20°N].

Figure 10 Scatter plot of stratocumulus regime for the in-regime LWP in amip run (horizontal axis) and their feedback in amipFuture for stratocumulus regime for the tropics [20°S, 20°N].

Black solid line is a regression line out of models except MRI-CGCM3-org.
<figure><img src="image_1.png" /><figcaption>(b) RFO change (global)</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>(c) In-regime NCRE change (global)</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>(d) Contributions from RFO and in-regime NCRE to NCRE change</figcaption></figure>

<figure><img src="image_4.png" /></figure>

779

780 Figure 1 (a) Contributions of cloud regimes to net CRE feedback [Wm⁻²K⁻¹], (b) the changes

781 in RFO, (c) in-regime net CRE [Wm⁻²K⁻¹], and (d) contributions from RFO and in-regime net

782 CRE to net CRE feedback [Wm⁻²K⁻¹]. The ordering of the models is following the global

783 mean NET CRE feedback.
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Figure 2 Scatter plots of the in-regime NET CRE [Wm⁻²] for the stratocumulus regime in amip run (horizontal axis) and their feedback [Wm⁻²K⁻¹] in amipFuture for stratocumulus regime (a) for the whole globe and (b) tropics [20°S, 20°N] (bottom). Black solid line is a regression line out of models except MRI-CGCM3-org. The direction of two axes is larger (increase in) cooling effect toward the right (top). Grey lines indicate observational values. The grey dotted lines are lower and upper bound of standard deviation out of the three observations.

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>
Figure 3 Scatter plots of the tropical [20°S, 20°N] stratocumulus regime for the in-regime albedo in the amip run (horizontal axis) and their feedback in amipFuture. The black solid line is a regression line out of models except MRI-CGCM3-org.

796

<figure><img src="image_7.png" /></figure>

797

798
799 Figure 4 Scatter plots of the tropical stratocumulus regime of its cloud cover in x-axis and (a)

800 in-cloud albedo in y-axis, (b) cloud top pressure normalized by surface pressure in y-axis.

801 Amip run (open circle) and amipFuture run (plus). Navy blue for HadGEM2, light blue for

802 CanAM4, red for MIROC5, green for CNRMCM5, orange for MRI-CGCM3-mod, orange

803 with smaller mark for MRI-CGCM3-org, ISCCP data in black filled circle.

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>
Figure 5 Different cloud cover bins' contributions of the tropical stratocumulus regime's in-regime albedo (a) in the control climate and (b) the change in future. Horizontal bins are 805 806 807 cloud cover in the control climate and the future climate for each data.

808

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

809
810 Figure 6 (a) Relative frequency of occurrence, (b) normalized cloud top pressure, (c) in-cloud albedo, and (d) in-cloud LWP [kgm⁻²] of the tropical stratocumulus regime averaged over different cloud covers in amip run.

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>
Figure 7 Contributions of the cloud cover distribution change and in-cloud albedo change to the in-regime albedo change in the tropical stratocumulus regime from the amip run to the amipFuture run.

818

<figure><img src="image_16.png" /></figure>

819

820
Figure 8 (a) Change in RFO, (b) in-cloud albedo, (c) in-cloud LWP, and (d) estimated in-cloud albedo from LWP of the tropical stratocumulus regime binned by different cloud covers.

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>
Figure 9 Scatter plots of stratocumulus regime for the RMS error of the in-regime albedo contributions from different cloud covers in amip run (horizontal axis) and their response in amipFuture for stratocumulus regime for the tropics [20°S, 20°N].

<figure><img src="image_21.png" /></figure>

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831 Figure 10 Scatter plots of stratocumulus regime for the in-regime LWP in amip run (horizontal axis) and their feedback in amipFuture for stratocumulus regime for the tropics [20°S, 20°N]. Black solid line is a regression line out of models except MRI-CGCM3-org.

834

<figure><img src="image_22.png" /></figure>

835