Evaluation and Attribution of Shortwave Feedbacks to ENSO in CMIP6 models

The shortwave (SW) feedback to El Niño – Southern Oscillation (ENSO) is one of the largest biases in climate models, as the feedback includes atmosphere – ocean interactions and cloud processes. In this study, the performance of SW feedback in 19 models from the 6th Coupled Model Intercomparison Project (CMIP6) is evaluated and the biases are attributed using the historical and Atmospheric Model Intercomparison Project (AMIP) runs. The results demonstrate that most CMIP6 models underestimate the strength of SW feedback, although 11 models (~58%) show the observed negative signs in the Niño-3 region, a superior result to that (7 of 17, ~41%) of CMIP5. The underestimates of SW feedback arise mainly from the biased feedbacks to El Niño in the four models with relatively better skills, while from both underestimated negative feedbacks to El Niño and overestimated positive feedbacks to La Niña in other 15 models, which reproduce better seasonal variations than corresponding CMIP5 models. Furthermore, the SW feedback bias is connected to weak convective/stratiform rainfall feedback, which is sensitive/insensitive to sea surface temperature (SST) biases during El Niño/La Niña. There are different biases among the factors contributing to SW feedback, such as erroneous compensations between underestimated cloud fraction feedback and overestimated liquid water path feedback in the four best-performing models, whereas both are underestimated in the other models, and weakened dynamical feedbacks are observed in all models. The rainfall feedbacks in the AMIP runs are much closer to the observations than those in CMIP5, although they are greatly reduced in the historical runs, indicating that the atmospheric models may be over-tuning under given observed SSTs.


Introduction
As an important component of the climate system, cloud strongly influences global climate as well as its change by modifying the energy budget and hydrological cycle.
Moreover, cloud feedback to increasing CO2 is the greatest source of uncertainty for climate sensitivity (e.g., Zelinka et al. 2016;Wang et al. 2022).Cloud radiative effects can be separated into two parts: longwave and shortwave cloud radiation effects (L/SWCRE), measured as the all-sky minus clear-sky longwave and shortwave fluxes, respectively.At the top of the atmosphere (TOA), the global average SWCRE is about −50 W m −2 , greater in strength than that of LWCRE (about 30 W m −2 ), giving a net cooling effect of nearly −20 W m −2 (Zelinka et al. 2017;Tang et al. 2020).
The SW feedback (  ) to El Niño-Southern Oscillation (ENSO), defined as the regression coefficient between the net SW radiation flux anomalies at the surface and the sea surface temperature anomaly (SSTA), is the main source of uncertainty in ENSO-related atmospheric feedbacks (Bellenger et al. 2014;Rädel et al. 2016) and may influence both the degree of thermodynamic damping of ENSO as well as the anomalous Walker circulation in the central tropical Pacific (Bellenger et al. 2014;Li et al. 2014;Ferrett et al. 2018).During El Niño, the atmospheric ascent response to warm SSTA leads to an increasing convective cloud, which suppresses downward SW flux as well as sea surface warming, exhibiting negative SW feedback.During La Niña, the atmospheric descent response to cool SSTA enhances lower tropospheric static stability and leads to an increase in stratiform cloud that further reflects SW radiation, and the cooling effect at the surface is enhanced, corresponding to a positive SW feedback (Ramanathan and Collins 1991;Klein et al. 1993;Bony et al. 1996;Philander et al. 1996;Park and Leovy 2003;Xie 2004;Li et al. 2015).
Shortwave feedback is asymmetric in these two phases but is negative on average (Vanniere et al. 2013;Li et al. 2015;Ceppi et al. 2017).
Current general circulation models (GCMs) do not adequately reproduce the spatial distribution and magnitude of   in the tropical Pacific, especially its negative values over the central−eastern equatorial Pacific (Sun et al. 2006;Dommenget et al. 2014;Hua et al. 2018).Almost all CMIP3 models underestimate the negative   strength over the central−eastern equatorial Pacific, and a few of them overestimate it over the western equatorial Pacific (Lloyd et al. 2009;Lloyd et al. 2012;Chen et al. 2013).Although model skills are somewhat improved in CMIP5, notable differences between models and observations and spread among models remain, especially in coupled GCMs (CGCMs), and many share the same systematic mean-state biases; e.g., the excessive westward extension of the seasonal equatorial cold tongue associated with strong trade winds in the eastern Pacific (Davey et al. 2001;AchutaRao and Sperber 2006;Lin 2007).Identifying the origin of these biases remains challenging because of the complex interactions between the feedbacks and mean states that lead to ENSO (SST) evolution, such as surface heat flux, wind forcing, and eddies (Wyrtki 1981;Wang and Mcphaden 1999;Vialard et al. 2001;Nam et al. 2012;Vanniere et al. 2013;Ceppi et al. 2017;Bayr et al. 2018;Wengel et al. 2018;Wang et al. 2020).Both CMIP3 and CMIP5 models have large biases in the nonlinearity of SW feedback.Bellenger et al. (2014) indicated that only one third of CMIP3+CMIP5 ensemble models simulate the shift from positive feedback to negative under the effect of seasonal and interannual variations in the tropical Pacific and strong relationship can be found between SW feedback nonlinearity and ENSO amplitude; i.e., the models with strong nonlinearity in SW feedback are also those with strong ENSO.Using 24 ENSO-relevant metrics, Planton et al. (2021) indicated that CMIP6 models significantly outperform CMIP5 models in eight metrics, including double-intertropical convergence zone (ITCZ) bias, ENSO pattern and diversity, and teleconnections.However there has been little improvement in the surface heat flux feedbacks.As such, it remains unclear whether the SW feedbacks, as one of the most uncertain components of heat flux feedback, have also failed to improve in the CMIP6 models.
In order to unravel the origin of the biases in simulating   , Lloyd et al. (2012) proposed an idealized decomposition method for SW feedback using a chain rule under the assumption that the individual response is local [see eq.(3) in Lloyd et al. (2012)].Under such an assumption, the SW flux response to SST can be divided into three parts: (1)

Models and observational datasets
The 19 CMIP6 models that provide the variables required for the analyses were chosen, and the first realizations (r1i1p1f1) of their historical runs (1950( -2014( ) and AMIP runs (1984( -2008) ) were used (Table 1

Methodology
For a variable F (e.g., SW flux, cloud fraction), the feedback to ENSO is measured as the linear regression coefficient : where FA is the anomaly of variable F with the annual cycle removed.Here < SSTA > is the SST anomaly averaged over the Niño-3 region (5°S-5°N, 150°-90°W).As proposed in Li et al. (2014), the shortwave flux feedback (  ) is decomposed into two parts as follows: where CLD SST ⁄ and LWP SST ⁄ represent cloud fraction feedback and LWP feedback, respectively.The cloud fraction feedback is further decomposed as follows: where 500 SST ⁄ and RH SST ⁄ stand for dynamical feedback and RH feedback, respectively.
In this study, we adopt the method of Lloyd et al. (2012), in which feedbacks to El Niño are calculated for SSTA > 0 at each grid point and feedbacks to La Niña for SSTA < 0, and then averaged over the Niño-3 region.

Biases in the historical runs
In  The spatial distribution of   and   , the regression coefficients between total cloud fraction and LWP anomaly and the Niño-3 index, are well correlated with those of   in observations and the models (Fig. 3).The SCCs between   and   and between   and   over the Niño-3+4 (region includes both Niño-3 and Niño-4 regions) are both −0.90 in the observations.In the models, the SCCs for   range from −0.97 (NorESM2-LM) to −0.68 (BCC-ESM1) with two low SCC models, KACE-1-0-G (−0.19) and TaiESM1 (−0.13), and those for   range from −0.99 (MRI-ESM2-0) to −0.53 (IPSL-CM6A-LR) with one low SCC model, SAM0-UNICON (−0.26).All SCCs exceed the 0.01 significance level; i.e., −0.13.The high correlation coefficients between   and   as well as   indicate that both   and   are associated with   ; in other words, the biases in   are derived from both   and   .For instance, in the Niño-3 region, 4 of the 19 models (FGOALS-g3, MIROC6, MRI-ESM2-0, and EC-Earth3-Veg) simulate more reasonable   (falling within 50% of the observations), but only EC-Earth3-Veg simulates both   and   well (also within 50% of the observations) and in the other three models, there is error compensation between underestimated   and overestimated   .The remaining models with relatively large   biases, especially those with incorrect signs in the Niño-3 region (the eight models mentioned above), underestimate both   and   .When compared with the feedbacks in Niño-3, the feedback biases in Niño-4 are greatly reduced, especially in the models with incorrect signs (Figs.2b, 2c, and 3).To further understand the biases, the models are divided into two groups based on the strength of Niño-3 averaged   .One is the "strong group" of models that simulate strong negative feedbacks (EC-Earth3-Veg, FGOALS-g3, MIROC6, and MRI-ESM2-0) over the Niño-3 region, and the other is the "weak group" of models that simulate weak negative or even positive feedbacks (all models apart from the four in the strong group).The strong group has stronger positive cloud fraction and LWP feedbacks than the weak group.Both groups have similar positive ice water content (IWC) feedback distributed above 600 hPa (Fig. 4).In particular, the negative cloud fraction and LWP feedbacks below 850 hPa in the weak group are too strong, contributing to the positive SW feedback; this is also observed in many CMIP5 models with large biases in   .Furthermore, the profile of cloud fraction feedback may be connected to the feedbacks of relative humidity (  ) and vertical velocity (  ; Fig. 5).The strong group has stronger   and   (much closer to ERA5) than the weak group, in agreement with the difference of   between the two groups.The negative   and weak   below 850 hPa in the weak group appear to contribute negative   and, ultimately, less negative or more positive   than in the strong group, as also demonstrated by Ferrett et al. (2018).Note that the positive   and negative   in both groups extends too far west, reaching the region around 135°E compared with ~160°E in ERA5, consistent with the westward extensions of   and   .ENSO amplitude (or phase lock) in both groups and observations (Fig. 6).For both the feedback sign and strength, the strong group mean is closer to that of the observations than the weak group, and both groups have larger biases in the first six months than in the following six months.In the strong group, the compensation between underestimation of   and  500 and overestimation of   is more serious in the first six months, which is also a problem in CMIP5 models (Bellenger et al. 2014;Li et al. 2015).The weak group broadly reproduces the seasonal evolutions of   and its feedback components (although with weaker strength and/or the incorrect sign during the following six months), somewhat better than the CMIP5 weak group which has nearly unchanging seasonal variations except for  500 (Li et al. 2015).The incorrect signs of the simulated   in the second six months are attributed to incorrect signs of   and   in the weak group.The strong and weak groups both simulate weaker-amplitude  500 than the observations and show little differences in magnitude and sign, indicating that weak dynamical feedback is a serious problem in most CMIP6 models.

Biases in the AMIP runs
The AMIP runs are analyzed in this section to investigate whether the biases of   in coupled models come from the atmospheric model or coupling processes or from other sources.The spatial pattern (figure not shown) and magnitude (Fig. 7a) of   are well reproduced by more atmospheric component models than coupled models.For instance, 12 of the 19 models fall within 50% of the observed   strength in Niño-3, ranging from −7.07 W m −2 K −1 (FGOALS-g3) to −2.78 W m −2 K −1 (BCC-ESM1); in Niño-4, 18 of the models (NESM3 is the exception: The SCCs between the observations and the models range from 0.22 (CanESM5) to 0.95 (EC-Earth3-Veg) over Niño-3, and from 0.93 (MPI-ESM-1-2-HAM) to 0.99 (KACE-1-0-G) over the Niño-4 region, higher than in the historical runs.The correct negative sign is obtained in all but one model in the Niño-3 region, surpassing the eight models for the historical runs., 7c, and 8) and enhanced dynamical feedbacks (Fig. 7d), which are mostly underestimated in the CMIP runs.The SCCs between   and   and between   and   range from −0.96 (FGOALS-g3) to −0.46 (KACE-1-0-G) and from −0.98 (FGOALS-g3) to −0.32 (SAM0-UNICON) over the Niño-3+4 regions (Fig. 8), closer to those in the historical runs.In addition, SCCs between the observations and models range from −0.25 (IPSL-CM6A-LR) to 0.98 (EC-Earth3) for   and −0.67 (SAM0-UNICON) to 0.96 (FGOALS-g3) for   over the Niño-3 region, higher than those in the historical runs (from −0.77 for IPSL-CM6A-LR to 0.95 for MRI-ESM2-0 for   and from −0.80 for NorESM2-LM to 0.86 for MRI-ESM2-0 for   ).Therefore, improvements of   in the AMIP runs are linked mainly to improvements in the spatial distribution and intensity of   and   .BCC-ESM1 simulates both area-averaged   and   well in Niño-3 but does not give better   .This is because the overestimation of   and   in the west of the Niño-3 region and the underestimation in the east (Fig. 8b) cancel each other out, leading to seemingly plausible area-averaged   and   but not   .From this point of view, area averaging can be a measurement of model performance but is not a complete picture.Figure 9 shows the feedbacks of   ,   ,   , and  500 during El Niño and La Niña.In the observational/reanalysis data, the   is negative (positive) during El Niño (La Niña), whereas   and   are positive (negative).The  500 is always negative during both conditions with greater magnitude during El Niño.In the historical runs, the   ,   , and   in the strong group models (EC-Earth3-Veg, FGOALS-g3, MIROC6, and MRI-ESM2-0) are dominated by the feedbacks during El Niño, the same as in the observations, though somewhat underestimated.However, in many weak group models, the underestimates are greater and some feedbacks are even opposite in sign to those observed during El Niño and are overestimated in strength during La Niña.Consistent with the underestimation of  500 , all CMIP6 models underestimate dynamical feedbacks to El Niño to different extents (Fig. 9d) and show larger biases than the CMIP5 models (Li et al. 2015).In the AMIP runs, all feedbacks to El Niño are enhanced compared with those in the historical runs, especially in the weak group, indicating these feedback biases are closely related to the SST biases/coupling processes during El Niño.During La Niña, however, the feedback change is smaller than in the historical runs, suggesting the feedback biases are insensitive to the SST biases and come mainly from the atmospheric models.

Attribution
To further attribute the SW feedback biases, the relationships between the feedbacks of SW and precipitation as well as the mean state SST and precipitation, includes convective and stratiform (non-convective) components, are analyzed in this section.Both the SW and rainfall feedbacks in the AMIP runs are closer to the observation than those in the historical runs (Fig. 10a), implying that most models reproduce the feedback strength at given observed SST.However, the seemingly accurate rainfall simulations in the AMIP runs result from erroneous compensations between an overestimated convective component and underestimated stratiform component (Figs.10b and c).The total rainfall underestimates in the historical runs are present in both convective and stratiform components, and the total and convective rainfall feedbacks are highly correlated to the SW feedbacks, with linear correlation coefficients (LCCs) of −0.72 and −0.64 (Figs.10b and c), respectively.Comparing the AMIP and historical runs, the total and convective rainfall feedbacks appear to be sensitive to the SST biases and/or the atmosphere-ocean coupling processes, whereas the stratiform rainfall feedback appears insensitive to these factors.The differences of convective (total) rainfall feedbacks between the AMIP and historical runs correspond well with those of SW feedbacks, with LCC of −0.74 (−0.77) (figure not shown), suggesting that the weakened convective feedback due to the SST biases is a major cause of the underestimated SW feedbacks in the historical runs.In the historical runs, the high correlations between SW feedback and total and convective rainfall feedbacks result mainly from the feedbacks during El Niño conditions, although the feedbacks are underestimated by most models, especially the weak group models (Fig. 11).During La Niña, LCC between SW feedback and total rainfall feedback is −0.50, contributed largely by the stratiform component.In particular, the changes of stratiform rainfall feedback between the historical and AMIP runs are minor during both El Niño and La Niña (figure not shown), consistent with their minor changes in Fig. 10c.Combined with the nonlinearity shown in Fig. 9, the SW feedback biases and its components are connected with the convective feedback during El Niño, and all are affected by the SST biases/atmosphere-ocean interaction processes, and during La Niña, the SW biases appear linked to the stratiform feedback, which is dominated by internal atmospheric processes.The rainfall feedbacks are directly related to their mean states, with LCCs of 0.9 for the total and 0.89 and 0.82 for the convective and stratiform components, respectively and the underestimates of mean stratiform rainfall are clear in most models (Fig. 12).
The total and convective rainfall feedbacks are well correlated to the mean SST with LCCs of 0.64 and 0.54, whereas the stratiform feedbacks are insensitive to the mean SST.Note also that the cold SST biases are insignificant in about half of the CMIP6 models, which is an improvement on CMIP5 (Jiang et al. 2021).The strong correlations between both mean state total and convective rainfall and SST indicate that improvements in mean state SST lead to advances in mean state total/convective rainfall and vice versa (Fig. 13).However, for the stratiform component, only the mean state stratiform rainfall is connected to its feedback, and the mean state SST is not significantly correlated with either the mean state stratiform rainfall or its feedback.To summarize, the biases in rainfall feedbacks may be attributed to the biases in both mean state rainfall and SST; i.e., the mean SST may directly influence the total rainfall feedback, especially the convective component.The mean SST may also indirectly affect the rainfall feedbacks by interacting with the mean rainfall, which is highly correlated to the rainfall feedback, and the rainfall feedback is further connected to the SW feedback through the dynamical (  ) and thermodynamic (i.e.,   and   ) feedbacks.

Summary and discussion
The shortwave feedbacks to ENSO in 19 CMIP6 models have been evaluated and the biases analyzed and attributed using the historical and AMIP runs.In the historical runs, the strength of   in both the Niño-3 and Niño-4 regions is underestimated by most CMIP6 models.In Niño-3, only four models fall within 50% of the observations, and 11 of the 19 models (~58%) have negative   , as in the observations, although this is an improvement on CMIP5 [7 of 17, ~41%; fig. 2 in Li et al. (2015)].However, in three of the four models that simulate   well (classified as the strong group), this arises from compensations between underestimated   and overestimated   (both feedbacks are well simulated only in EC-Earth3-Veg).For the other models with significant underestimations of   (the weak group), especially those with incorrect signs, both   and   are underestimated.The differences in liquid water content feedback and cloud fraction feedback between the two groups occur mainly in the layers below 400 hPa; in particular, the weak group simulates excessively strong negative liquid water content and cloud fraction feedbacks below 850 hPa, which are further associated with the negative   and weak   below 850 hPa.In the Niño-4 region, 15 of the 19 models fall within 50% of the observations, and all 19 models simulate the same sign of   as the observations.The relatively better SW flux feedbacks originate from improvements in   ,   , and  500 , together with smaller differences in the vertical distributions of cloud fraction and liquid water content feedbacks between the two groups in addition to improvements in dynamical and RH feedbacks.
In the AMIP runs, the biases in   are reduced.For instance, more models fall within 50% of the observations (12 out of 19 models, compared with 4 of 19 in the historical runs) in Niño-3, and both intensity and spatial distribution are more realistic, which should be attributed to improvements in   and   .In addition, there is an overall improvement of  500 compared with the weakened  500 in the historical runs, which has a role in improving the simulation of   in the AMIP runs.
Corresponding with the performances of   in the two runs, the rainfall feedbacks are well reproduced in the AMIP runs and underestimated in the historical runs.However, erroneous compensations between overestimated convective and underestimated stratiform rainfall feedbacks occur in the AMIP runs, and both convective and stratiform components are underestimated in the historical runs.The changes of total (convective) rainfall feedback between the two runs contribute to the changes of   with LCCs of −0.77(−0.74);these high LCCs between rainfall and SW feedbacks are mainly due to the relationship in the historical runs, implying that the biased SST in the historical runs may be a key factor.
The total rainfall feedback and the convective component are directly related to the mean state SST with LCCs of 0.64 and 0.54, and they are closely associated with the mean rainfall simulations that are highly correlated to the feedbacks (including total, convective, and stratiform rainfall).Hence, the rainfall feedbacks, especially the convective components, are the main links between the SW feedbacks and mean SST through the dynamical (  ) and thermodynamic (i.e.,   and   ) feedbacks.It is also noted that the mean stratiform rainfall and its feedback are underestimated and insensitive to the SST mean state in most models, suggesting that the stratiform rainfall is determined by the internal atmospheric processes.
Analysis of the nonlinearity reveals that underestimations of   are contributed mainly by the biased feedbacks to El Niño in the strong group, whereas in the weak group they arise from both the underestimated negative feedbacks to El Niño and overestimated positive feedbacks to La Niña.The close relationship between SW and rainfall feedbacks is mainly due to the correlation between SW and convective feedbacks during El Niño and partly from the stratiform feedback during La Niña.
Comparing the coupled and uncoupled simulations, the underestimated SW and (convective) rainfall feedbacks during El Niño in the coupled simulations are connected to the SST biases/coupling processes, whereas during La Niña, the biases of SW and stratiform feedbacks are insensitive to the coupling processes and are dominated by the internal atmospheric processes.
The possible mechanisms may be as follows.The links between the mean state and SW feedback are cloud and dynamic processes (Sun et al. 2006;Sun et al. 2009;Chen et al. 2013;Chen et al. 2019), though there are complicated interactions between the mean state SST and rainfall.Under cold biased SST conditions, the Walker circulation tends to be shifted westward, and atmosphere ascent is reduced (less negative dynamical feedback in Figs.2a and 5c); the relative humidity declines, and cloud fraction and LWP are reduced, especially at low levels (Figs.4b and 5c).
Ultimately, reduced cloud in the tropical Pacific leads to more downward SW flux; i.e., less negative (or even positive) SW feedbacks.Bayr and Latif (2022) reported a similar finding, that SW feedback becomes stronger owing to the increased vertical wind response over the Niño-3/Niño-4 regions under global warming, and the models with larger cold equatorial SST bias exhibit strongly biased SW-driven ENSO dynamics.Therefore, improving the mean state in the coupled simulations is key to improving SW feedback.
Note that the horizontal model resolution has an impact on the simulations of convective and stratiform rainfall (Huang et al. 2018;Yang et al. 2021) that then influence the rainfall feedbacks.In addition, the total rainfall responses are closely distributed around the observations in the AMIP runs, indicating that the atmospheric models may be over-tuned/trained for the observed SST conditions.Therefore, further consideration of the atmosphere-ocean coupling processes and use of convectionresolving atmospheric models should be targets of future work.

Fig. 2
Fig. 2 Averaged values of (a)   , (b)   (% K −1 ), (c)   (g m −2 K −1 ), and (d)  500 (10 −2 Pa s −1 K −1 ) in the Niño-4 (blue dots) and Niño-3 (red dots) regions for observations (OBS) and the 19 CMIP6 models.Opacity indicates the absolute value of the spatial correlation coefficient with observations over the corresponding region: higher transparency means a smaller value and a black edge indicates a negative correlation.Red and blue dashed lines are from ISCCP in (a)-(c) and ERA-5 in (d).The x-axis of each plot is ordered by the strength of the Niño-3 averaged   of the observational data and the CMIP6 models

Fig. 3
Fig. 3 As in Fig. 1, but for   (color shading) and   (contours).Dashed (solid) contour lines represent negative (positive) values with an interval of 10 g m −2 K −1 .The values on the top-right of each plot are the correlation coefficients between   and   and between   and   , respectively, over the Niño-3+4 region

Fig. 6
Fig. 6 Seasonal cycle of (a)   , (b)   , (c)   , and (d)  500 for observations (black), the ensemble-mean of the strong group (red) and the weak group (blue).The group spread is shown using colored shading

Fig. 7
Fig. 7 As in Fig. 2, but for the AMIP runs The improved   in the AMIP runs is accompanied by stronger   and   (Figs.7b, 7c, and 8) and enhanced dynamical feedbacks (Fig.7d), which are mostly

Fig. 10
Fig. 10 Scatter plots of Niño-3 averaged SW feedback as a function of (a) total, (b) convective, and (c) stratiform rainfall feedbacks.Black dots indicate observations, deep (light) red and blue crosses are strong (weak) group models for the CMIP and AMIP runs, respectively, and light red and blue dots are for the ensemble means of the CMIP and AMIP models, respectively.Values separated by a forward slash in the top-right corner of each plot are the correlation coefficients between SW feedback and rainfall feedback in the AMIP and CMIP multi-models.A correlation coefficient of 0.46 (0.58) indicates significance at the 95% (99%) level, here and similarly in Figs.11-13

Fig. 11
Fig. 11 Scatter plots of Niño-3 averaged   vs (a) total, (b) convective, and (c) stratiform rainfall feedbacks to El Niño (yellow) and La Niña (green) in the CMIP models: deep colors show the strong group models and light colors indicate the weak group models.Yellow and green dots indicate observations for El Niño and La Niña, respectively.The values in the top right of each plot are LCCs between SW feedback and rainfall feedbacks during El Niño and La Niña

Fig. 12
Fig. 12 Scatter plots of Niño-3 averaged (a) total, (b) convective, and (c) stratiform rainfall feedbacks against their mean state rainfall and SST in the historical runs.Dots in each plot indicate observations, with red (blue) symbols corresponding to the red (blue) y-axis.Values in the top right of each plot are LCCs between rainfall feedbacks and mean rainfall/SST

Fig. 13
Fig. 13 Scatter plots of Niño-3 averaged (a) total, (b) convective, and (c) stratiform rainfall feedbacks against mean state SST in the historical runs.Black dots indicate observations Li et al. (2015)arge-scale circulation, represented by 500) response   .Furthermore,Li et al. (2014)indicated that, in reality, SWCRE is a function of liquid water path (LWP) and cloud cover, and the latter depends on atmospheric dynamics and relative humidity (RH).Using a similar decomposition,Li et al. (2015)found that the   biases of CMIP5 models are associated with the ⁄ ; and (3) the SW feedback response to clouds,   ⁄ .Lloyd et al. (2012) found that the dynamical response plays the most important role in underestimating

Table 1 .
List of CMIP6 models used in this study.Model letters refer to the panel in Fig.1