Underestimated marine stratocumulus cloud feedback associated with overly active deep convection in models

Cloud feedback remains the largest source of uncertainty in equilibrium climate sensitivity (ECS). Many studies have attempted to narrow uncertainties in cloud feedback and ECS by proposing observable metrics with high skill at predicting future climate, referred to as emergent constraints. These constraints are often associated with clouds, convection, and circulation, and are interrelated. However, physical explanations for these connections remain unclear. Here, we propose a new mechanism relating convection and clouds across multiple climate models. Some models show overly active deep convection on daily timescales in the subtropical low cloud regions, which contributes to weaker subsidence inversion and smaller amounts of low-level clouds. Such models predict smaller shortwave (SW) cloud feedback. Using precipitation frequency in these regions as an emergent constraint, encapsulating this mechanism, models with lower SW cloud feedback (<0.50 W m−2 °C−1) are found to exhibit erroneously frequent convection. Our results suggest that further improvements in understanding and better modeling of cloud and convective systems are necessary for accurate climate predictions.


Introduction
Large variations in cloud feedback across different climate models are by far the largest source of uncertainty in equilibrium climate sensitivity (ECS) (Bony and Dufresne 2005, Zelinka et al 2013, Ceppi et al 2017, the equilibrium global surface temperature response to atmospheric CO 2 doubling. In particular, the importance of low-level cloud responses to global warming over the subtropical oceans has been emphasized (Bony and Dufresne 2005). Because low-level clouds cover a large portion of tropical subsidence regions and effectively reflect shortwave (SW) solar radiation, their cloud radiative effects (CREs) exert significant influence on the global energy budget. Numerical experiments have suggested that representations of convection in climate models can significantly influence cloud feedback and ECS (Zhao 2014, Webb et al 2015. For example, when radiation, turbulence, convection, cloud, and surface scheme model parameters were perturbed within their uncertainty ranges, ECS values were most sensitive to convection scheme parameters (Stainforth et al 2005, Shiogama et al 2012. A possible explanation for the link between low-level clouds and convection is that convection mixes air between the cloud-topped boundary layer and the drier free troposphere, which disturbs inversion layers and disrupts low-level cloud formation Bony 2012, Sherwood et al 2014). This hypothesis is consistent with previous research demonstrating that models with lower ECS values tend to overestimate convective precipitation over the southeastern Pacific (Hirota and Takayabu 2012, Tian 2015, Lutsko and Cronin 2018, Webb and Lock 2020. The precipitation bias over a low cloud region of the southeastern Pacific is known as 'the double ITCZ bias' and has long been recognized as one of the major deficiencies in climate models (e.g. Xie et al 2007, Fiedler et al 2020, Tian and Dong 2020.

Results
We first examine the SW cloud feedback, which is approximated by changes in SW CRE values (the difference in radiative flux between all sky and clear sky conditions) per 1 • C of global surface temperature warming in the climate models participating in phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6). Figure  E1 (available online at stacks.iop.org/ERL/16/074015/ mmedia) shows the correlation between SW cloud feedback and ECS across the CMIP models. Consistent with previous studies, variations in the cloud feedback and ECS are shown to be correlated over the subtropical subsidence regions. In these regions, convective activities are limited, and a strong inversion layer in the lower troposphere (∼800 hPa) and associated low-level clouds are observed (Wood and Bretherton 2006). In this study, the subtropical low cloud regions are defined as corresponding to the tropical oceans (30 • S-30 • N) where the estimated inversion strength (EIS) (Wood and Bretherton 2006) on annual climatologies is larger than 3 • C (black contours in figure E1(a)) according to the European Center for Medium-Range Weather Forecasts Interim Re-Analysis (ERAI). EIS is calculated from the following formula: where θ 700 and θ sfc are the potential temperatures at the 700 hPa and the surface, respectively, Γ 850 m is the moist adiabatic lapse rate at 850 hPa, Z 700 is the height of the 700 hPa, and Z lcl is the lifting condensation level. The correlation between SW cloud feedback averaged over the subtropical low cloud regions (hereafter referred to as dSW EIS>3 • C ) and ECS is 0.56 ( figure E1(b)). Note that we used EIS of ERAI rather than that of models in defining the subtropical low cloud regions. We are investigating model's performance in representing the subtropical low cloud regimes with a strong inversion layer and suppressed convection in the observation.
It should be noted that large correlations between SW cloud feedback and ECS are also found in the middle and high latitudes (figure E1(a)). When correlations for sub-model ensembles of CMIP5 and CMIP6 are calculated separately, we found that values in middle and high latitudes are mostly associated with variations in the CMIP6 models ( figure E2). Recent studies showed that cloud feedback in the subtropics is the dominant source of ECS uncertainty in CMIP5; however, middle-and high-latitude processes also play important roles in CMIP6 (Zelinka et al 2020). The correlation between ECS and dSW EIS>3 • C is reduced from 0.70 in CMIP5 to 0.48 Figure 1. Relationship between precipitation frequency and EIS. Scatter plot showing the precipitation frequency metric α versus EIS in the subtropical low cloud regions. The orange line shows the α value for the observations. A, S, 5 and 6 denote the ensemble average of ACM, SCM, CMIP5, and CMIP6, respectively, with crosses indicating +/− one standard error. Note that these standard errors are very small, and the differences between the model groups are statistically significant. E denotes the ERAI. Black and white dots denote individual CMIP5 and 6 models, respectively. Correlation across all CMIP models, CMIP5 models, and CMIP6 models are indicated in the figure, with asterisks denoting significance at the 95% level.
in CMIP6 ( figure E1(b)). Middle-and high-latitude processes are, however, beyond the scope of this study, in which we focus on understanding cloud feedback in the subtropical low cloud regions.
Next, we investigate how convection influences inversion strength in the subtropical low cloud regions. A typical temperature profile in these regions is close to a moist adiabat with a sharp temperature increase in the lower troposphere (∼800 hPa), which corresponds to the inversion layer (figure E3) (Wood and Bretherton 2006). A convective parcel ascending from the lifting condensation level into the free troposphere follows a moist adiabat. As a result, convection adjusts the temperature profile closer to a moist adiabat of the parcel, resulting in weaker inversion and fewer low-level clouds.
To determine the quantitative importance of convection in EIS variation across climate models, a scatter plot of EIS and a metric of convection frequency in the subtropical low cloud regions (hereafter referred to as α) is shown in figure 1. The metric α is defined as the percentage of days in which daily mean precipitation rate was greater than 5 mm d −1 in the subtropical low cloud regions (see definition above) and is shown for observations and models in figure E4. EIS and α are closely related, having a correlation coefficient of −0.68 (figure 1). When the correlation of precipitation frequency and EIS is examined at different precipitation intensities (figure E5), large negative values are found at intensities greater than 5 mm d −1 , suggesting that relatively strong precipitation is responsible for the relationships between EIS and convection. Although we have emphasized that active convection reduces inversion strength, weaker inversion also results in more active convection. The causal relationship between convection and inversion should further be examined in future work.
We compare convection, inversion, and clouds in the present-day climate between model groups with the 30 highest and 30 lowest values of α, which are named as active convection models (ACMs) and suppressed convection models (SCM), respectively (figure E4). Figures 2(a) and (b) shows probability distribution functions (PDFs) for precipitation rate and vertical pressure velocity at 500 hPa (ω500) in the subtropical low cloud regions (Bony et al 2004). These figures are based on daily average statistics on the T42 Gaussian (∼2.8 • ) grid with a 1 mm d −1 bin width for precipitation and a 20 hPa d −1 bin width for ω500. The frequency of strong precipitation (>5 mm d −1 ) and upward motions (ω500 < −70 hPa d −1 ), indicating the occurrence of deep convection, are smaller in SCM than in ACM. These differences are larger than the standard errors (shading in the figures) of ACM and SCM and are significant at the 95% level using a two-tailed t-test. The PDFs of observed precipitation from the Global Precipitation Measurement (GPM) mission and ω500 from ERAI are also shown. Although the PDFs of SCM are more realistic relative than those of ACM, SCM nevertheless still overestimates the occurrence of convection relative to observations. EIS and cloud water content are shown in figures 2(c) and (d). Consistent with the proposed mechanism described in figure E3, EIS and associated , and (d) cloud water content (10 −6 kg kg −1 • C −1 ) in the subtropical low cloud regions for ACM and SCM. Tick marks in (a) and shadings in (b) and (c) indicate +/− one standard error for ACM and SCM. low level cloud water contents are larger in SCM than in ACM. These differences are also significant at the 95% level using a two-tailed t-test.
The responses (feedback) of EIS, temperature, humidity, and clouds to global surface warming are examined in figure 3. Low-level cloud is shown to increase in ACM but decrease in SCM (figure 3(d)). This difference in cloud response is likely related to differences in the atmospheric temperature change. The warming in boundary layer is larger in SCM than ACM (figure 3(b)), which is consistent with the smaller increases of EIS (figure 3(a)). The warmer boundary layer with larger saturated water vapor also suggests smaller increase in relative humidity (figure 3(c)). Smaller changes in stability and boundary layer relative humidity in SCM are consistent with low-level cloud reduction in contrast to cloud increases in ACM. Moreover, changes in SCM are favorable for the development of convection, which may further reduce low-level clouds. Note that the causal relationship between boundary layer warming and changes in low clouds is still unclear.
Based on the association between deep convection in the present-day climate and cloud feedback in a changed climate, we use α as a new emergent constraint. As shown in figure 4(a), correlation between our constraint and dSW EIS>3 • C is −0.59, explaining a significant part of inter-model spread in SW cloud feedback. The observed value of α from GPM is 2.2%, which is very small compared to its value in ACM. Using linear regression and standard deviation of dSW EIS>3 • C in the CMIP models, the likely range (>66% probability) of dSW EIS>3 • C is estimated at 0.50-3.44 W m −2 • C −1 .
To examine important regions for the relationship between convection and SW cloud feedback, the spatial distributions of correlation of α versus local SW cloud feedback and local precipitation frequency (>5 mm d −1 ) are shown in figure E6. Interestingly, precipitation frequency in the subtropical low cloud regions seems to affect SW cloud feedback in the larger areas in low-and mid-latitude oceans.
We also examined an alternative metric defined as the 95th percentile of daily mean precipitation rate averaged over the subtropical low cloud regions. The correlation between this alternative metric and α is 0.99 and very similar results are obtained ( figure E7). This result support robustness of the relationship between relatively strong convection and dSW EIS>3 • C .
Our constraint of α is significantly correlated with ECS in CMIP5 but not in CMIP6 ( figure 4(b)). As discussed above (figure E2), ECS spread in CMIP6 is not dominated by SW cloud feedback in the subtropical low cloud regions (Zelinka et al 2020).
Some CMIP6 models have very high ECS values larger than 4.5 • , the upper bound of the likely range proposed in the 5th assessment report by the Intergovernmental Panel on Climate Change (Collins et al 2013). This is an issue of great interest (Pendergrass 2020, Zelinka et al 2020 and is worth investigating using our proposed mechanism. We examined a group of five models with high climate sensitivity (ECS > 5 • ) and suppressed convection (α < 4%) and a group of four models with high climate sensitivity (ECS > 4.3 • C) and active convection (α > 6%) named HSC and HAC, respectively ( figure 4(b)). EIS and low-level cloud in the present climate are larger in HSC than in HAC, and cloud responses are negative in HSC but positive in HAC (figure E8). These results are qualitatively consistent with comparisons between SCM and ACM. However, even if low clouds in HSC and HAC are similar to those in SCM and ACM, respectively (figure E8(b)), ECS is very large in both HSC and HAC ( figure 4(b)), indicating that our mechanism does not explain very high ECS values. Further exploration, including investigation of middle-and high-latitude processes, is needed to understand these very high ECS values (Zelinka et al 2020). . The orange line shows the α value for observations. A, S, 5 and 6 denote the ensemble average of ACM, SCM, CMIP5, and CMIP6, respectively, with crosses indicating +/− one standard error. Note that these standard errors are very small, and the differences between the model groups are statistically significant. Black and white dots denote individual CMIP5 and 6 models, respectively. Correlations across all CMIP models, CMIP5 models, and CMIP6 models are indicated with asterisks indicating significance at the 95% level. The pink line shows the best linear fit to the data with the upper and lower lines plotted at +/− one standard deviation of the y-axis for all CMIP models.
Previous studies have proposed numerous emergent constraints associated with certain features of present-day climate, such as temperature variability (Cox et al 2018), cloud characteristics (Volodin 2008, Qu et al 2014, Zhai et al 2015, Brient and Schneider 2016, and convection (Sherwood et al 2014, Tian 2015. We calculated correlations between our constraint and 11 other constraints examined in Bretherton and Caldwell (2020) (figure E9). Interestingly, the correlations with constraints in Volodin (2008), Qu et al (2014), Sherwood et al (2014), Tian (2015), Zhai et al (2015), and Brient and Schneider (2016) are significant at a 90% level using a two-tailed t-test. Tian's constraint is defined as precipitation averaged over the southeastern Pacific (100 • -150 • E, 0 • -30 • S), which is a measure of the double ITCZ bias. Because model precipitation bias in this region is associated with the erroneously overactive convection, the significant correlation with our constraint is unsurprising. The constraints of Volodin, Qu, Zhai, and Brient are all associated with low cloud dependency on sea surface temperature (SST), thus their significant correlation with our constraint is consistent with our proposed mechanism, in which convection affects low-cloud formation and cloud response to surface warming. Our constraint is also correlated with Sherwood's index, measuring the fraction of boundary layer air in ascending regions that leaves in the mid-troposphere rather than in the upper troposphere. When we examined these ascending regions, we found that convection in the SCM showed a shallower structure, potentially favorable for cloud reduction in a warming climate (Sherwood et al 2014). Based on these results, we argue that the new constraint in this study is a refinement of previously proposed constraints with a clearer physical relationship between convection, clouds, and cloud feedback. Note that emergent constraints developed in CMIP5 generally have lower correlations in CMIP6 (Schlund et al 2020).
Overly active deep convection is known to be a long-standing bias in climate models (Dai 2006, Lutsko and Cronin 2018, Fiedler et al 2020. In particular, the bias over the southeastern Pacific corresponds to the double ITCZ bias (Tian and Dong 2020). It is often associated with a warm SST bias in the subtropics (Xie et al 2007). Because warmer SST supplies energy and moisture for convection, the warm SST bias favors active convection. Meanwhile, overly active convection is also found in atmospheric models in which the observed SST is prescribed and attributed to convection-triggering conditions or the dilution of convective parcels with environmental air in convective schemes (Song andZhang 2009, Hirota et al 2014). This implies that the fewer low clouds could be a cause of the warm bias in the subtropics.
To discuss the relative importance of oceanic and atmospheric processes, scatter plots of dSW EIS>3 • C versus SST and α in the Atmospheric Model Intercomparison Project (AMIP) experiment are shown in figure E10. Correlations between dSW EIS>3 • C with SST and the AMIP α are −0.37 and −0.40, respectively. Therefore, both oceanic and atmospheric processes are likely to be contributing to the relationship between SW cloud feedback and overly active convection as shown in figure 4(a). Note that the correlation between dSW EIS>3 • C and SST is not significant in CMIP6.
We should emphasize that the causal relationship between convection, EIS and SW cloud feedback is still unclear, and further exploration is needed. For example, the overly active convection may be resulted from the weaker inversion. Furthermore, SW cloud feedback is also affected by cloud-top radiative processes and surface fluxes (Vial et al 2016). Convective dehydration of the boundary layer strengthens the surface latent heat flux, which damps the reduction in low clouds. Low cloud reductions stabilize the lower troposphere by decreasing the cloud-top radiative cooling, which in turn decreases the surface latent heat flux and induces further low cloud reductions. The relative importance of low cloud mixing versus radiative cooling, and the resulting sign of the latent heat flux response, depends on the convective schemes in models.

Concluding remarks
Representing cloud and convection has been a significant challenge since the development of the first climate model (Arakawa 2004, Bony et al 2015. Here we show that low-level clouds are underestimated compared with observations when deep convection is overly active (figure 2), and such models tend to underestimate SW cloud feedback in the subtropical low-cloud regions (figure 4). Although convection is expected to be more important over warmer oceans, it must also be appropriately represented in the subtropical low cloud regions.

Methods
This study used daily and monthly datasets of historical, pre-industrial, abrupt-4xCO 2 , and AMIP experiments from 27 CMIP5 models and 38 CMIP6 models (https://esgf-node.llnl.gov). Name of the models are listed in table E1. The variables analyzed included surface temperature, precipitation, atmospheric temperature, vertical pressure velocity (ω), cloud water (liquid and ice) content, and radiative fluxes at the top of the atmosphere for all sky and clear sky conditions.
The precipitation frequency metric α used in this study was defined as percentage of days with daily mean precipitation rate greater than 5 mm d −1 in the subtropical low cloud regions (see definition above): where H(z) = 1 for z > 0 and 0 otherwise. Daily data for all seasons of the analyzed periods (see below) are used. Precipitation, vertical velocity (circulation and convection), cloud cover, and inversion strength under present-day climate and changed climate were compared between model groups with the 30 highest and 30 lowest values of α, named the ACMs and SCMs, respectively. We confirmed that our results were not sensitive to the number of models selected. The significance of differences between model groups was tested at the 95% level using the two-tailed t-test. We also calculated inter-model correlation using all available models to examine the relationship across the CMIP models. Assuming samples of 65 models are independent, a correlation larger than 0.25 was considered significant at the 95% level using the twotailed t-test. For observational references of precipitation, this study used the version 06A product of the Dual-Frequency Precipitation Radar on the core GPM spacecraft (Hou et cp-daily-global-precipitation-climatology-project; 1997-2014). Values of α are 2.15% for TRMM PR and 2.68% for GPCP1DD. Although TRMM PR has a known disadvantage when evaluating weak precipitation (Behrangi et al 2012), its value of α is very similar to that of GPM with improved sensors for weak precipitation (2.17%; figure 4(a)), suggesting that daily precipitation rate greater than 5 mm d −1 is adequately captured by both GPM and TRMM. The value of GPCP1DD is slightly larger than that of GPM, but our conclusion that models with larger SW cloud feedback are more consistent with observation is unaffected. We considered that the value of the latest dataset of GPM is most reliable. We did not analyze precipitation retrieved from CloudSat because CloudSat observation is performed only around 1:30 and 13:30 local time, therefore estimating daily mean precipitation is difficult.
Present-day climate in the CMIP5 and CMIP6 models is defined as the 1981-2000 average of historical simulations. The feedback and ECS for the models were calculated following a standard regression procedure using difference in global surface temperatures between the abrupt-4xCO 2 and pre-industrial scenarios for 150 years (Gregory et al 2004). All calculations were made after data are linearly interpolated onto the T42 Gaussian grid (∼2.8 • ); components with total (zonal + meridional) wave numbers larger than 42 were truncated because we are investigating convection and clouds on large-scale (∼1000 km) variabilities. Without the horizontal smoothing of the T42 truncation, some relationships discussed in this study are slightly weakened (figure E12) due to smaller scale variabilities resolved in high resolution models.

Data availability statement
The data that support the findings of this study are openly available at the following URL: https://esgfnode.llnl.gov.

Code availability
The codes used to calculate the precipitation frequency metric α are available on Zenodo at https:/ /zenodo.org/record/4062782#.X32m_Wj7SUk, and the other codes are available on request from the corresponding authors.