A Refined Understanding of the Ice Cloud Longwave Scattering Effects in Climate Model

Because longwave (LW) absorption by greenhouse gases and clouds is more significant than the LW scattering effect by clouds, most climate models neglect cloud LW scattering to save computational costs. Ignoring cloud LW scattering directly overestimates outgoing longwave radiation (OLR). This study included ice‐cloud LW scattering treatment in the Exascale Energy Earth System Model (E3SM) version 2 and ran fully‐coupled simulations, prescribed sea surface temperature simulations, and offline radiative transfer calculations to comprehensively assess the impact of ice‐cloud LW scattering on global climate simulation. The instantaneous effect due to ice‐cloud LW scattering reduces the OLR by ∼1 W/m2 on the global average and 2 W/m2 on the tropical average. Tropospheric warming and high cloud amount reduction act to partially compensate for such instantaneous OLR reduction caused by the inclusion of LW scattering. When the simulation reaches the equilibrium, the surface warms by 0.66 K on average with respect to the simulation without LW scattering, with the Arctic surface temperature differences more than twice as large as that of the global mean. The impact of including LW scattering on the simulated climate change in response to 4 × CO2 is also assessed. While including the cloud LW scattering does not significantly modify radiative forcing and total radiative feedback under such a scenario, it results in a 10% more positive cloud feedback.

Photons scattered by clouds will take a longer path to reach the top of the atmosphere (TOA), increasing the probability of being absorbed by greenhouse gas molecules, cloud particles, or the surface.This can further lead to a different atmospheric radiative cooling rate and a different surface downward LW flux (FLDS) (Ritter & Geleyn, 1992).Several parameterization schemes have been proposed to include multiple scattering of LW fluxes by clouds in climate models (Chou et al., 1999;Fu et al., 1997;Li & Fu, 2000).Using atmospheric profiles from model simulations or reanalysis, these studies estimated that when cirrus LW scattering is included, the instantaneous OLR can be reduced by 6-8 W/m 2 under the overcast conditions, and the FLDS can be increased by 2-4 W/m 2 correspondingly.(Chou et al., 1999;Fu et al., 1997;Joseph & Min, 2003;Ritter & Geleyn, 1992).Aside from cirrus clouds, which were believed to induce the most prominent LW scattering effect, some studies also highlighted the importance of scattered LW fluxes for radiation budget over the marine stratocumulus cloud regions (Costa & Shine, 2006;Kuo et al., 2017;Schmidt et al., 2006).It was estimated that, without LW scattering, the global mean OLR is overestimated by 1.5-3 W/m 2 (Costa & Shine, 2006;Kuo et al., 2017).
Beyond estimating the direct impact of cloud LW scattering on the radiation budget, efforts have been made to include cloud LW scattering in climate models to investigate how this can affect the overall simulated climate (Jin et al., 2019;Zhao et al., 2018).By examining prescribed sea surface temperature (SST) simulations, they estimated a global-mean OLR reduction of ∼2.6 W/m 2 when the effect of cloud LW scattering is considered, which is 0.8 W/m 2 larger than the estimated instantaneous effect.Zhao et al. (2018) attributed it to the water vapor increase in response to the warming atmosphere.However, such prescribed-SST simulations cannot evaluate the impact of cloud LW scattering on surface climate as the surface-atmosphere coupling is constrained.To address this, Chen et al. (2020) used the Community Earth System Model (CESM) 1.1 slab-ocean model with a modified LW scheme to study the ice cloud LW scattering effect.They argued that cloud LW scattering is especially important over polar regions due to the small amount of water vapor in such regions.Their simulations showed a 1.0-2.0K increase in the seasonal-mean surface air temperature over the polar region, which is at least twice as much as the increase in the tropics.Such temperature increases in the polar regions are mostly absent in their prescribed-SST simulations, highlighting the importance of surface-atmosphere coupling when evaluating the impact of cloud LW scattering on simulated climate.However, the analysis by Chen et al. (2020) is largely confined to the polar region without examining possible connections between extra-polar and polar regions (Holland & Bitz, 2003;Stuecker et al., 2018).
To the best of our knowledge, no study has run fully-coupled simulations to assess the effect of cloud LW scattering on the simulated climate.Unlike the slab-ocean models that do not include ocean dynamics and prescribe the meridional heat transport by oceans, the fully-coupled models have full ocean dynamics.They thus can represent the ocean's responses better.With these simulations, we can analyze the fast adjustment (i.e., atmospheric and land processes when SST is fixed) and slow adjustment (i.e., when SST is allowed to change) in response to the initial TOA flux change caused by cloud LW scattering.Previous modeling studies have also limited their scope to the mean state climate difference after including cloud LW scattering.Modification of cloud optics could affect how the climate system responds to the increase of greenhouse gases.In this study, we incorporate the same ice-cloud LW scattering treatment in Chen et al. (2020) into the Exascale Energy Earth System Model (E3SM) version 2, a flagship climate model developed by the Department of Energy (Golaz et al., 2022).Note that LW scattering by liquid water clouds is not included here to be consistent with the treatment in Chen et al. (2020).The OLR reduction caused by liquid cloud LW scattering is only ∼1/2 of the reduction caused by ice cloud LW scattering, although the FLDS increase caused by them is comparable (Kuo et al., 2017).This study focuses on understanding the impact of ice cloud LW scattering, which also includes the LW scattering of the ice portion of mixed-phase clouds.Hereafter, cloud LW scattering refers to ice cloud LW scattering only.Using the modified model, we ran fully coupled simulations and prescribed-SST simulations with cloud LW scattering on and off to evaluate how the inclusion of cloud LW scattering can affect the simulated mean-state climate.The central question to answer is, for a climate model without scattering, how the fast processes (i.e., direct atmospheric responses) and slow processes respond to the inclusion of LW scattering to attain a new mean state.Moreover, we ran additional pairs of 4 × CO 2 simulations, with LW scattering on and off, to investigate how enabling cloud LW scattering affects the simulated radiative feedback and climate sensitivity.
Section 2 describes the model we used, our modifications, and the details of the numerical experiments.After a brief analysis of the total mean-climate state change when cloud LW scattering is included in Section 3, Section 4 delineates the instantaneous effect due to the inclusion of cloud LW scattering, the fast response to such instantaneous effect, and the relationship between them.The impact on radiative feedback and long-term surface

E3SM Version 2
E3SMv2 (Golaz et al., 2022) is the successor of the first version of the E3SM model (E3SMv1) developed by the Department of Energy (Golaz et al., 2019).Although the first version was initially branched from CESM1, the second one is different from CESM as many components have been replaced or heavily modified, including the atmosphere dynamical core, ocean model, sea ice model, and river routing.Atmospheric physics in E3SMv2 still shares similarities with CESM2.To evaluate the model, the E3SM team conducted experiments according to a standard set of the Coupled Model Intercomparison Project Phase 6 (CMIP6) Diagnosis, Evaluation, and Characterization of Klima (DECK) simulations (Eyring et al., 2016).Compared to its predecessor, E3SMv2 doubles its speed and alleviates some issues.For example, it simulates better clouds and precipitation climatology and, consequently, improves the estimates of cloud feedbacks and equilibrium climate sensitivity (ECS).While E3SMv1 estimates an ECS of 5.3 K, which is deemed too high, E3SMv2 estimates a more realistic ECS value of 4.0 K (Golaz et al., 2022).
Our new fully-coupled simulations were branched from year 101 of the 500-year E3SMv2 pre-industrial control run (v2.LR.piControl), one of the standard runs in the CMIP6 DECK experiment.These simulations run on a horizontal grid of ∼100 km in the atmosphere and land components, ½ degree in the river component, and 60 to 30 km in the ocean and sea-ice components.The atmosphere has 72 vertical layers from the surface to approximately 60 km.Note that the model runs on separate dynamics and column parameterization grids to improve computational efficiency.As a result, the dynamics grid has an average horizontal grid of 110 km, while the parameterization grid and the land grid have an average grid size of 165 km.

Model Modifications to Enable Ice-Cloud LW Scattering
This study employed the same ice-cloud optics and longwave radiation schemes as described in Chen et al. (2020).In brief, a hybrid two-stream and four-stream (2S/4S) radiative transfer solver is implemented into the LW radiation scheme to enable cloud LW scattering.Compared to other solvers, the hybrid 2S/4S solver has a better compromise between accuracy and computational efficiency (Fu et al., 1997).The default ice-cloud optics in the E3SMv2 do not include ice-cloud scattering properties in the LW.In this study, cloud optical properties, including cloud extinction coefficients, single-scattering albedo, and asymmetry factors, are based on a cloud habit model (Yang et al., 2018) consistent with that used for the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection six operational cloud products (Platnick et al., 2015(Platnick et al., , 2017)).When cloud LW scattering is disabled, the extinction coefficient is set equal to the absorption coefficient.Details about the LW radiative transfer solver and ice-cloud optics can be found in Kuo et al. (2020) and Chen et al. (2020).

Numerical Experiment Design and Data Analysis
The scheme described in the previous subsection has been ported to the E3SMv2.We carried out four fully-coupled simulations, each one consisting of 105 years (i.e., year 0101-0205): • Control: fully-coupled simulation without cloud LW scattering; • Scat: fully-coupled simulation with cloud LW scattering; • Control_4 × CO 2 : same as Control, but the CO 2 concentration is set to four times of the piControl value, that is, instantaneous quadrupling CO 2 experiment.• Scat_4 × CO 2 : same as Scat, but the CO 2 concentration is set to four times of the piControl value.
The other specifications of the four simulations are identical.By comparing the Scat case and the Control case, we can study the effects of cloud LW scattering on the simulated mean climate.With 4 × CO 2 cases, we can further contrast climate feedbacks when cloud LW scattering is enabled or disabled.Note that the Control run is not the same as the standard E3SMv2 piControl run because the default ice-cloud optics are replaced with MODIS Collection six ice optics, and the radiative transfer solver is replaced by the hybrid 2S/4S solver with the LW scattering capability.
Figure 1 shows the time series of global-mean net TOA radiative flux imbalance and surface temperature of the four simulations.Because we replaced the ice-cloud optics and the radiative transfer solver, the Control run has a small TOA energy loss after branching from the equilibrated piControl run.Long-term mean TOA energy imbalance is −0.19 W/m 2 .The Scat case, on the other hand, is closer to the equilibrium state (−0.01 W/m 2 ).The difference in surface temperature between the Scat and the Control case accumulates to ∼0.6 K after about 30 years.Both Control_4 × CO 2 and Scat_4 × CO 2 have more than 1 W/m 2 net TOA energy imbalance throughout the simulations.However, the surface temperature in both cases becomes stable after about 70 years.For the last 30 years (year 0176-0205), the absolute trend of net TOA energy imbalance in all simulations is less than 0.02 W/m 2 per year, and the absolute trend of surface temperature is within 0.01 K per year.Therefore, we used the last 30 years of those simulations in all climatology calculations in the following sections.Note that the difference in global-mean surface temperature (Figure 1b) between Scat and Control is similar to that between Scat_4 × CO2 and Control_4 × CO2.

Total Response in Equilibrium
Compared to a simulated climate system without LW scattering, the instantaneous effect of LW scattering is to reduce the global-mean OLR (Costa & Shine, 2006;Kuo et al., 2017).Therefore, more energy would be retained in the climate system and a warming climate can be expected.
Figure 2 summarizes the impacts on the surface climatology due to cloud LW scattering, where the differences in global mean surface air temperature and downward longwave flux at surface (FLDS) are plotted in each row.Panels (b) and (d) show the zonal mean differences of the corresponding variables.In addition to the annual mean value (black), these panels also show the changes in boreal summers (red) and boreal winters (blue).Globally speaking, the cloud LW scattering effect results in a warmer surface by 0.66 K on average.The largest warming occurs in the Arctic, where the annual-mean maximum exceeds 2 K.It is amplified in winters (∼4 K) and damped in summers (∼0.5 K).Such seasonal variation is a typical feature of the polar amplification phenomenon and can be explained by feedback processes in the Arctic region (Boeke et al., 2021;Stuecker et al., 2018) Figures 3a-3c show the vertical temperature profile difference when the cloud LW scattering effect is enabled.For pure comparison purpose, the differences caused by the 4 × CO 2 effect are also presented in Figures 3d-3f.Please note Figures 3a-3c is the mean-state difference caused by including a physical process in the model while Figures 3d-3f is the difference caused by abrupt 4 × CO 2 increases in the original model without LW scattering.Regardless of the scale difference (2 vs. 20 K), they share some common features including the large warming of the upper troposphere in the tropics (Manabe & Stouffer, 1980;Manabe & Wetherald, 1975) and the confined near-surface warming in the Arctic.However, when cloud LW scattering is activated, the stratosphere does not cool as much as the one in the case of 4 × CO 2 concentration.This can be explained by the fact that CO 2 has a strong stratospheric radiative cooling effect and, thus, increase of CO 2 directly affects the radiative equilibrium in the stratosphere; but enabling cloud longwave scattering would not directly affect the radiative cooling in the stratosphere.

Instantaneous Radiative Effect and Fast Response
Analogous to the concepts in radiative forcing and feedback analysis, in this section, we decomposed the total TOA flux changes (i.e., total response) due to the inclusion of cloud LW scattering into three parts: instantaneous radiative effect (analogous to IRF, instantaneous radiative forcing), fast adjustment (corresponding to rapid adjustment), and slow adjustment.The sum of the first two parts is termed the fast response (analogous to ERF, effective radiative forcing).We also decomposed FLDS into the same three parts to attribute the FLDS increase to physical processes.
The instantaneous radiative effect is defined as the radiative flux change when we only include the cloud LW scattering physics; all atmospheric and surface state variables are fixed.In this case, shortwave flux is unmodified.Similar to the approach in Zhao et al. (2018) to quantitatively derive the scattered LW flux by clouds, we ran a short 3-year simulation configured similar to the Scat case.While these runs evolve with cloud LW scattering enabled, the model outputs additional longwave radiative fluxes and longwave heating rates computed in parallel but without the cloud LW scattering effect.The instantaneous radiative effect is the difference between these extra outputs (without scattering) and the original flux outputs (with scattering).Over the course of 3 years, this difference shows a small seasonal variation (∼1 W/m 2 for OLR and ∼0.2 W/m 2 for FLDS) and an even smaller annual variation (Figure S1 in Supporting Information S1).Hence, we think this derived instantaneous radiative effect is applicable to interpret our fully-coupled simulation results.
Figure 4 shows the zonal mean instantaneous OLR change and FLDS change, as well as the total response, due to the cloud LW scattering effect.Here, cloud LW scattering reduces the OLR by 1.13 W/m 2 globally on average.The largest decrease is seen in the tropics by 2 W/m 2 , while the smallest decrease occurs in the polar region and the subtropical region (<1 W/m 2 ).Such latitudinal distribution is consistent with Kuo et al. (2017) and Costa and Shine (2006).Note that the instantaneous FLDS increase due to the scattered LW flux by ice clouds is only 0.08 Wm −2 , only ∼2% of the FLDS increase for the total response (3.95 W/m 2 globally), suggesting that climate feedbacks must play an important role in the change of FLDS.
Fast response here is defined as the TOA flux changes when SST and sea ice conditions are fixed.This is equal to the instantaneous radiative effect plus the fast adjustment due to changes in atmospheric temperature, land temperature, water vapor concentration, and clouds.To derive this quantity, we ran two 35-year prescribed-SST simulations, one with cloud LW scattering and one without.Only the atmosphere component is active, while SST and sea ice are prescribed using historical observations from 1980 to 2014.The zonal mean OLR and FLDS differences between these two runs are plotted as blue curves in Figure 4. We also calculated the contributions to the flux changes from individual components of the atmosphere-surface system using a radiative kernel (Huang et al., 2017) except clouds.Cloud adjustments are directly calculated from all-sky and clear-sky fluxes output from the model.The impact on the TOA fluxes is summarized in Table 1.
Following the instantaneous OLR reduction due to the LW scattering effect, fast adjustments increase the OLR by 0.44 W/m 2 .The sum of individual fast adjustment terms is 0.45 W/m 2 , close to the amount above, which confirms the validity of using a radiative kernel to decompose the fast adjustment.Major contributors to the OLR increase include cloud LW radiative effect (0.283 W/m 2 ), tropospheric warming (0.260 W/m 2 ), and land surface warming (0.028 W/m 2 ).Stratospheric temperature change only leads to a small change in OLR by −0.013 W/m 2 .This phenomenon is a typical feature of increased absorption in the troposphere but nearly unchanged absorption in the stratosphere, as this is comparable to the pattern of the rapid adjustment when black carbon is injected into the troposphere (Smith et al., 2018).Consequently, the TOA flux imbalance becomes smaller, and the peak in the tropics is also shaved (Figure 4a).The FLDS change after fast adjustments increases by 0.35 W/m 2 , primarily due to tropospheric warming (Figure 4b).The increase in the Arctic is larger than the global mean (∼1 W/m 2 ).
As for the slow adjustment to further compensate for the TOA flux imbalance of 0.67 W/m 2 (the imbalance caused by the instantaneous effect of the inclusion of cloud LW scattering and the fast response to such inclusion together), it consists of the surface temperature increase and the subsequent state variable changes via various feedback mechanisms.As a result, the global-mean OLR in the Scat case now exceeds the one in the Control case (Figure 4a) and the global-mean shortwave flux in the Scat case is smaller than it in the control case (thus the net TOA imbalance becomes closer to zero).Ultimately, cloud LW scattering induces a small warming effect globally.The ratio of net TOA flux changes and surface temperature increase (0.66 K) in the slow process is approximately −0.9 W/m 2 /K, a value that is close to the one in the case of CO 2 concentration increase (which will be discussed in the next section).Driven by surface warming, FLDS in total response is significantly stronger, especially in the Arctic where the magnitude exceeds 10 W/m 2 (Figure 4b).This suggests that the large increase of FLDS in the Arctic is dominantly caused by the slow adjustment.Because of the positive correlation between FLDS and TS, it can be inferred that the strong warming in the Arctic region should be attributed to the slow adjustments instead of the instantaneous radiative effect.Total responses seen in cloud fraction and properties are also the consequence of slow adjustments, including ice-to-liquid transition in tropical mid-troposphere (Figure S2 in Supporting Information S1), elevated deep convective clouds (Figure S3 in Supporting Information S1), reduced anvil cloud coverage (Figure S3 in Supporting Information S1), and increased stratiform low cloud coverage (Figure S4 in Supporting Information S1).

Impact on the Simulated Climate Change Under 4 × CO 2 Scenario
In addition to the impact on the simulated mean-state climatology, a more scientifically intriguing question is to what extent the inclusion of cloud LW scattering can affect the simulated climate change in response to the increase of greenhouse gases.This section discusses this effect in the context of abrupt 4 × CO 2 simulations.We adopted the regression approach to calculate the ERF and total climate feedback for the cases with or without cloud LW scattering (Gregory et al., 2004).Figure 5 shows the scatterplot of annual-mean net TOA radiation with respect to surface temperature (a.k.a., Gregory plot) for both cases.The scatter points for both Control and Scat cases mix with each other.While the inclusion of cloud LW scattering tends to decrease the ERF and increase the total feedback, the differences are statistically negligible: the slopes of two corresponding regression lines (i.e., Control and Scat) only differ by 0.03 W/m 2 /K, with a large overlap between their 95% confidence intervals (i.e., −0.74 ± 0.08 vs. −0.71± 0.09 W/m 2 /K); the intercept difference is 0.24 W/m 2 , also with a large overlap between their 95% confidence intervals (i.e., 6.28 ± 0.49 vs. 6.04 ± 0.54) W/m 2 .Thus, two regression results are statistically indistinguishable.Consistent with such assessment, the global-mean surface temperature changes due Note.Wherever applicable, flux changes are separated into longwave and shortwave components.The instantaneous effect, fast response, and total response are shown, as well as their differences.Fast adjustment is decomposed into six terms using a radiative kernel.The sum of these individual terms is shown in the last row, which can be compared to the fast adjustment term in the fifth row (both rows are highlighted in the table ).10.1029/2023MS003810 9 of 13 to 4 × CO 2 , as inferred from the last 30 years of simulations (Figure 1), are 6.8 K for the Control case and 6.7 K for the Scat case, also suggesting that the cloud LW scattering affects little on such climate projection simulation.
To gain a detailed understanding of how the LW scattering affects individual radiative feedback strength, we decompose the total feedback into different components using the radiative kernel approach.We employed the same radiative kernel used in Section 4 to derive Planck feedback, lapse rate feedback, water vapor feedback, and surface albedo feedback.Cloud feedbacks are calculated using cloud radiative kernels similar to Zelinka et al. (2012aZelinka et al. ( , 2012b)).As the kernel in Zelinka et al. (2012aZelinka et al. ( , 2012b) ) was built without LW cloud scattering, we calculated a correction term based on offline radiative transfer calculations with LW scattering turning on and off, and derived two sets of LW cloud radiative kernels using the approach described in Zelinka et al. (2012a).Then, we took the difference between the two kernels and deemed it as the correction term to the original Zelinka's LW cloud radiative kernel.Figure 6a visualizes the kernel without cloud LW scattering, and Figure 6b shows the correction term.The correction term can exceed 10% for high clouds with optical depth ≤3.6.each individual term has a much better agreement with the change in total feedback strength estimated from the regression method (lower right panel in Figure 7).Nevertheless, given the uncertainty of climate feedback estimation and because the ice cloud LW scattering effect on feedback terms is small in magnitude, few differences shown in Figure 7 are likely to be statistically significant.

Conclusions
We modified the E3SM version 2, a fully-coupled climate model, to include the ice cloud LW scattering effect, a physical process omitted by most climate models.Based on the modified model, we ran simulations with our modifications enabled and disabled to study the impact of ice cloud LW scattering on the simulated climate system, for both the mean-state and climate-change simulations.Figure 8 summarizes the radiative and temperature responses to the inclusion of ice cloud LW scattering.
Compared to the simulation without longwave scattering, the instantaneous radiative effect due to ice cloud LW scattering reduces the OLR across all latitudes.The strongest OLR reduction occurs in the tropics.Most scattered fluxes are absorbed in the atmosphere instead of reflected to the surface, as the instantaneous increase of FLDS (downward longwave radiative flux at the surface) is negligible compared to the OLR reduction.The OLR reduction is compensated to some extent, primarily by the warming troposphere and cloud LW effect through fast adjustments.Stratosphere contributes little here as the LW scattering alters the radiative flux throughout the troposphere but has little effect on the stratosphere.The majority of the total FLDS increase, as well as the highly correlated surface temperature increase, is primarily due to the slow adjustment.Consequently, compared to the mean-state climate simulated by the model without LW scattering, the global-mean surface temperature difference is +0.66 K, with the difference in the Arctic at least twice as much as the global mean difference, especially in boreal winter.
In the scenario of abrupt 4 × CO 2 simulations, ice cloud LW scattering does not significantly modify ERF (effective radiative forcing) and climate feedbacks.The ERF and total feedback strengths inferred from two pairs of simulations, with and without ice cloud LW scattering, have no statistically significant differences.When total feedback is decomposed to individual feedback using the radiative kernel technique, the most notable change is the 10% increase of cloud feedback due to the inclusion of ice cloud LW scattering.Such a change might not be statistically significant, though, given the uncertainty of cloud feedback.
This study refines and deepens our understanding of the cloud LW scattering effect.The explanation in Chen et al. (2020) for the simulated responses of mean states in the polar region overlooked the global connections, especially the changes in the tropics caused by cloud LW scattering.We took advantage of fully-coupled simulations, prescribed simulations, and offline radiative transfer calculations to analyze the instantaneous effect, fast adjustment, and slow adjustment after including the scattering physics.These analyses delineate a full picture of how the inclusion of cloud LW scattering affects the simulation of the mean-state climate.This study revealed that the strong response in the Arctic is primarily due to the highly sensitive nature of the polar climate.The instantaneous OLR reduction due to cloud LW scattering is indeed relatively weak in the Arctic.In addition, we assessed how including cloud LW scattering physics can affect ERF and climate feedbacks caused by the increase of CO 2 .While the impacts on the ERF and climate feedbacks are statistically insignificant, the cloud LW scattering is more inclined to increase the total feedback via more positive cloud feedback.Note that liquid cloud LW scattering is not studied here.Considering the different spatial distributions of ice clouds and liquid clouds, liquid cloud LW scattering effect may have different structural impacts on mean-state climate and climate feedback.Future work is warranted to assess the impact of liquid cloud LW scattering on climate simulations.
Cloud LW scattering is one example of physical processes that are often neglected in climate modeling studies.A variety of compensating biases occur in any fully-coupled climate model simulations.The inclusion of cloud LW scattering reduces one type of structural uncertainties in the climate models.While such a reduction of structural uncertainties might not directly lead to improved climate simulations (as the modified model might need to be re-tuned), it could help expose other compensating errors.Future work is warranted to compare the historical runs based on this modified model to satellite observations and reanalysis products.It can also be beneficial in future studies to include cloud LW scattering in other climate models and assess the impact on multi-model mean state as well as individual model simulation.In terms of computational costs, the modifications cost 10% additional computational time compared to the original E3SMv2 model.
Because of the three-dimensional nature of scattering, it would be a meaningful follow-up study to examine the cloud LW scattering effect in the context of 3D radiative transfer (e.g., Kablick et al., 2011), especially for high-spatial-resolution global simulations such as those global storm-resolving models with a spatial resolution as high as 1-3 km (Stevens et al., 2019).The horizontal photon flux transport, which is entirely neglected in plane-parallel radiative transfer calculation, could become important for certain cloud regimes (e.g., cumulus and stratocumulus) in such global storm-resolving model simulations.

Figure 1 .
Figure 1.Annual-mean time series of (a) global mean energy imbalance at the top of the atmosphere (TOA), defined as net downward flux; and (b) global mean surface skin temperature.The Scat and Control cases are shown in blue and black, respectively.The cases under preindustrial control scenario are marked by dots, while the cases under 4 × CO 2 scenario are marked by stars.The yellow highlighted region indicates the time period we used in all climatological calculations.
. Correspondingly, FLDS increases by approximately 4 W/m 2 on global average.Its high correlation with surface air temperature is also consistent with what Chen et al. (2020) has revealed.

Figure 2 .
Figure 2. Comparison of the surface climatology between the Scat case and the Control case.(a) Annual-mean surface air temperature difference.(b) Zonal-mean surface air temperature difference in annual mean (black), boreal summer season (JJA; red), and boreal winter season (DJF; blue).(c, d) Same as (a, b) but for FLDS.Gray slat patches mask the region without statistically significant changes (1% significance level).

Figure 3 .
Figure 3. (a) Annual-and zonal-mean differences in vertical temperature profile resulting from the cloud LW scattering effect; (b) the same zonal-mean difference but in boreal winter seasons (DJF); (c) the same zonal-mean difference but in boreal summer seasons (JJA); (d-f) the same as (a-c), but the contour shows the vertical temperature profile change due to abrupt 4 × CO 2 concentration.Black dots indicate statistically significant temperature change at 1% significance level.

Figure 4 .
Figure 4. Zonal mean flux changes from instantaneous radiative effect (black), fast response (blue), and total response (red) caused by the inclusion of cloud LW scattering.(a) Outgoing longwave radiation, where net upward is positive; (b) downward longwave flux at surface, where net downward is positive.The global average of each component is indicated in the legend.

Figure 7
Figure 7 summarizes the decomposition of the total radiative feedback into individual terms.Two sets of cloud feedback are included using the original cloud radiative kernel and the new kernel with the correction term.Accounting for the correction due to cloud LW scattering, the largest absolute change in individual terms is the cloud feedback.Both LW and SW parts contribute to the increase in cloud feedback, together adding ∼10% of the total cloud feedback strength to the counterpart derived from the Control simulations (i.e., without cloud LW scattering).Lapse rate feedback and water vapor feedback are also modified when cloud LW scattering is included, but these changes almost cancel out.Surface albedo feedback also decreases by approximately 0.03 W/m 2 /K, or 6% of that in the Control case.With the correction term, the sum of changes from

Figure 5 .
Figure 5.The relationship between the net TOA radiative flux and surface temperature (a.k.a., the Gregory plot) in the Control case (black) and the Scat case (blue).The slope (i.e., climate sensitivity) and the intercept (i.e., ERF) of each regression line are marked in the legend.

Figure 6 .
Figure 6.(a) Global and annual mean of the cloud LW radiative kernel we built based on the Control case.(b) The difference of the two kernels based on the Scat case and the Control case (i.e., the correction term).τ is cloud optical thickness at a visible wavelength, and CTP is cloud top pressure.Flux sensitivity is defined as the TOA flux change when we put a cloud with a specific optical thickness at a specific pressure level (net downward is positive).

Figure 7 .
Figure 7. Effective radiative forcing and climate feedbacks estimated from the abrupt 4 × CO 2 experiment with and without cloud LW scattering.The first row shows the absolute quantities in the Control case, while the second row shows the differences between the Scat case and the Control case.Values of 2 × CO 2 ERF and total feedback are estimated from linear regression, while other values are from radiative kernel analysis.The standard errors associated with the linear regression in the Gregory plot (Figure 5) are attached as purple stems on the corresponding terms.As usual, standard errors of the differences between Scat and Control are the Euclidean norm of the errors in both cases (i.e.,  diff = (  2 Control +  2 Scat ) 1 2 ).Red slat bars in the second row show the updated values using the corrected cloud radiative kernel (i.e., when cloud LW scattering is considered).

Figure 8 .
Figure 8. Schematic summary of the instantaneous radiative effect (left), fast response (middle), and total responses (right) due to the inclusion of cloud LW scattering in the E3SMv2.Only prominent features are presented in the diagram.All red texts indicate a warming factor (i.e., increasing temperature and reducing outgoing longwave radiation (OLR)), while blue texts indicate a cooling factor (i.e., decreasing temperature and increasing OLR).

Table 1
Simulated Global-Mean Net Radiative Flux Change at the TOA (Unit of W/m 2 , Positive Downward) Due To the Inclusion of Cloud LW Scattering FAN ET AL.