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Observational datasets for the period from January 2003 to December 2012 are utilized in our study to evaluate the performance of CMIP6 models. Monthly-mean radiative fluxes from the Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) dataset are used for assessing top-of-atmosphere (TOA) cloud radiative properties, including the longwave cloud radiative effect (LW CRE), shortwave cloud radiative effect (SW CRE), and net cloud radiative effect (CRE). Furthermore, the Surface Data Ocean Fraction Coverage from CERES SYN1deg Products are also used as a filter in our study to avoid the inconsistency between land and ocean surface retrievals. Hence, the pixels with ocean fraction of more than 95% are chosen in this study. We also use retrieved Level-3 cloud physical properties from Moderate Resolution Imaging Spectroradiometer (MODIS) instruments onboard the Aqua satellite (MYD08_M3), including the CF, liquid cloud fraction (LCF), re, LWP, and COD. The details of the MODIS dataset are shown in Table 1. Note that satellite-derived LWP is an in-cloud property. To match up with the climate models’ definition, which is averaged over the grid box, we multiply the satellite LWP by the satellite CF to get the grid-scale LWP for all the analyses below. To explore the relationship between aerosols and clouds over the SO, the Level-3 AOD product from MODIS is also analyzed in this study.
Parameter Variable Name CF Cloud_Fraction_Mean_Mean LCF Cloud_Retrieval_Fraction_Liquid_FMean LWP Cloud_Water_Path_Liquid_Mean_Mean COD Cloud_Optical_Thickness_Combined_Mean_Mean re Cloud_Effective_Radius_Liquid_Mean_Mean AOD Aerosol_Optical_Depth_Average_Ocean_Mean_Mean Table 1. Dataset and parameters used from the MYD08_M3 dataset
The uncertainty of satellite-derived variables needs to be emphasized, specifically for any model evaluation study. Based on prior research, the uncertainty of global monthly mean TOA fluxes can be separated into two parts. The difference of all-sky radiative fluxes can be 2.5–3 W m–2, while the discrepancies of clear-sky fluxes can reach 5–6 W m–2 and 4.5–5 W m–2 for SW and LW fluxes, respectively (Loeb et al., 2018a,b). Compared with in situ aircraft observations, the MODIS cloud retrieval product overestimates re near cloud top by 26%–31% over the SO (Zhao et al., 2020). Kang et al. (2021) further suggested that re is overestimated by satellite for non- or light precipitation and underestimated for heavy precipitation. Considering the possible existing uncertainty in satellite-derived variables, corresponding statistic strategies (Weatherhead et al., 1998; Shea et al., 2017) are used in this study. σvar is the standard deviation of the variable’s regional, annual, or monthly mean time series. κvar is the autocorrelation time of natural variability. It is calculated as: κvar=
$ \sqrt{(1+\rho )/(1-\rho )} $ , where ρ is the lag-1 autocorrelation. The uncertainty of MODIS-derived cloud physical properties used in this study is presented in Table 2.Mean κvar (yr) σvar (yr) κvar (mon) σvar (mon) LW CRE 30.64 1.29 0.22 2.45 3.20 SW CRE −70.11 0.97 0.20 2.35 42.31 Net CRE −39.47 0.97 0.31 2.36 43.73 CF 88.36% 1.73 0.121% 2.41 1.48% LCF 43.45% 0.98 0.346% 2.50 7.49% re 13.33 0.98 0.06 2.37 1.27 LWP 142.03 1.99 1.88 2.56 40.95 COD 14.99 2.20 0.21 2.65 4.17 AOD 0.09 1.40 0.0032 2.64 0.02 Table 2. Annual and monthly variability parameters calculated for cloud radiative effect and cloud properties over the SO from the CERES and MODIS satellite products. σvar is the standard deviation of the variable’s annual and monthly mean time series. κvar is the autocorrelation time of natural variability.
Model Name Modeling Center Horizontal Grids CESM2 National Center for Atmospheric Research, USA 288 × 192 GISS-E2-1-G Goddard Institute for Space Studies, USA 144 × 90 MPI-ESM-1-2-HAM* Max Planck Institut fur Meteorologie, Germany 192 × 96 NorESM2-LM** NorESM Climate modeling Consortium, Norway 144 × 96 UKESM1-0-LL Met Office Hadley Centre, UK 192 × 144 *re is multiplied by a factor of 10, as the original re is on the order of 1 μm.
**re values that are too large (greater than 25 μm) are excluded.Table 3. CMIP6 AMIP models evaluated in this study.
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Considering the availability of datasets within the CMIP6 project, five CMIP6 climate models (CESM2, GISS-E2-1-G, MPI-ESM-1-2-HAM, NorESM2-LM, and UKESM1-0-LL) participating in the Atmospheric Model Intercomparison Project (AMIP) are chosen. Some detailed information on these five models is listed in Table 3. The CMIP6 dataset is from “historical*” experiments. The radiative properties in five CMIP6 models are incoming shortwave radiation (rsdt), outgoing longwave radiation (rlut), outgoing shortwave radiation (rsut), upwelling clear-sky longwave radiation (rlutcs), and outgoing clear-sky shortwave radiation (rsutcs). The total CF for the whole atmospheric column is called clt, and the LCF (the mass of cloud liquid water) seen by MODIS, including the large-scale and convective clouds, is called clwmodis. The cloud physical properties in the models include LWP, re, and COD. The parameters of LWP are calculated by clwvi minus clivi, which corresponds to column integrated condensed water minus that of ice. The variables of re are named as reffclwtop, representing the effective radius of liquid droplets seen from satellite. Note that re in GISS-E2-1-G is calculated from the averaged reffclws (the effective radius of stratiform cloud liquid water) in multiple layers. The cod of CMIP6 models is the integral of scattering, absorption, and attenuation coefficients along the radiative path. The od550aer of CMIP6 models refers to the AOD from ambient aerosols. All available “r1i1p1f1” ensemble runs from three CMIP6 models (CESM2, MPI-ESM-1-2-HAM, and NorESM2-LM) are used in our study. Owing to the unavailability in the AMIP experiment, the “r1i1p3f1” ensemble run from GISS-E2-1-G and the “r1i1p1f4” ensemble run from UKESM1-0-LL are used here. The time period of CMIP6 datasets used in this study is from January 2003 to December 2012, consistent with our satellite product time period.
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In this study, the evaluations are developed using the following statistical methods. The regional averaged variables over the SO are calculated by Eq. (1):
where Xi is the ith value of the multiyear averaged corresponding variable and k is the total number of samples.
The regional root-mean-square Error (RMSE) is calculated from Eq. (2), where m is the sum of grid samples covering the SO and Xi is the corresponding value of grid i.
$ \overline{X} $ is the averaged value of the grid over the SO.The correlation coefficient is used for evaluations in this study. In Eq. (3), X and Y represent the corresponding variables of observation and the CMIP6 models, respectively,
$ \mathrm{C}\mathrm{o}\mathrm{v}(X,Y) $ is the covariance, and$ \mathrm{V}\mathrm{a}\mathrm{r}\left|X\right| $ and$ \mathrm{V}\mathrm{a}\mathrm{r}\left|Y\right| $ denote the variance of X and Y separately.The normalization method used in this study is calculated by using the ratio of the ith variable and the maximum of values to show the temporal change of corresponding variables. Note that all the grid data used in this study is latitude-weighted.
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To explore the possible influence of cloud physical properties on the net CRE, the correlation coefficients of spatial distributions between individual cloud physical properties and net CRE are calculated from three sources: the satellite observation, the CMIP6 multimodel mean, and the differences between models and observations (Fig. 10). Generally, all cloud physical properties examined here are positively correlated with SW CRE. For CF, the observations show a high correlation coefficient of about 0.6, while the modeled climatological means and biases do not show strong relationships between CF and SW CRE. In contrast, the models all agree well with observations on the strong positive relationship between LCF and SW CRE. For COD and LWP, the observations only show a moderate positive correlation, with coefficients no larger than 0.3, while much stronger correlations between COD/LWP and SW CRE are found in the CMIP6 models. It indicates that the radiation simulations of those CMIP6 models over the SO are too sensitive to LWP and COD. The positive correlation between CRE and re is unexpected to some extent, and it implies that some other co-varying factors dictate such a relationship.
Figure 10. Correlation coefficients of spatial distributions between SW CRE and cloud physical properties or AOD in satellite products, multimodel mean, and the model biases (model minus observation).
The relative importance of each factor in contributing to SW CRE can be partly revealed by comparing the correlation coefficients across all parameters in their relationship with SW CRE. In observations, CF and LCF exhibit the largest correlation, indicating highest relevance to SW CRE. However, for the CMIP6 models, COD, LWP, and re are the more relevant variables compared with CF and LCF, corroborating the notion that the SW CRE controlling factors are quite different between the models and observations. For the biases in the modeled SW CRE, the potential largest contributors include LCF, LWP, and COD, as their biases resemble those of SW CRE well in space with high correlation coefficients. Furthermore, AOD–SW CRE relationships are found to be positive in both observations and models. However, the biases in the modeled SW CRE cannot be explained by those in the aerosol field, as there is a small correlation coefficient between aerosol and SW CRE biases.
The two key parameters in controlling CRE are CF and LWP. To quantitatively estimate their joint and relative contributions to CRE errors, we adopt a multivariate linear regression model to link CRE with CF and LWP. The regression slopes of CREs versus CF (
$ {\partial }_{\mathrm{C}\mathrm{F}} $ ) and LWP ($ {\partial }_{\mathrm{L}\mathrm{W}\mathrm{P}} $ ) can be derived from Eq. (5),where CRE represents the LW, SW, or net CRE. r is the residual of the corresponding regression.
Following Dolinar et al. (2015), the CRE sensitivity to CF or LWP (
${\varepsilon }_{\mathrm{s}\mathrm{e}\mathrm{n}}$ ), the CRE errors from CF or LWP bias (${\varepsilon }_{\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}}$ ), the co-variations (${\varepsilon }_{\mathrm{c}\mathrm{o}\mathrm{v}}$ ), and the total errors (${\varepsilon }_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ ) are computed as follows:where X is CF or LWP, the subscript obs means the observation, and m represents the simulated value.
Four errors (
${\varepsilon }_{\mathrm{s}\mathrm{e}\mathrm{n}}$ ,${\varepsilon }_{\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}}$ ,${\varepsilon }_{\mathrm{c}\mathrm{o}\mathrm{v}}$ ,${\varepsilon }_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ ) for SW, LW, and net CRE are shown in Table 4. The SW CRE sensitivity to CF and LWP can reach 187.6 W m–2 and –104.9 W m–2, respectively. The different signs of the sensitivity errors and biases from CF and LWP once again corroborate the notions that there are compensating errors in the modeled SW CRE calculation, and the cancellation of those errors result in smaller error in CRE. Similar with SW CRE, the net CRE is sensitive to CF and LWP with sensitivity magnitudes of 209.2 W m–2 and –106.4 W m–2, respectively. LW CRE sensitivities to CF or LWP, the biases in CF and LWP, and the co-variations are much smaller than the ones in SW and net CRE, indicating that simulated SW sensitivity contributes most to the total errors. With larger magnitudes in all four errors, CF generally exhibits a larger influence on CRE in comparison with LWP.SW CRE LW CRE net CRE CF sensitivity error 187.56 21.61 209.18 CF biases 8.22 0.12 8.34 CF co-variations −10.93 −1.26 −12.19 LWP sensitivity error −104.86 −1.95 −106.41 LWP biases −6.18 −1.55 −6.56 LWP co-variations 21.41 0.32 21.73 Total 95.22 17.29 114.09 Note: Error are in units of W m−2. Table 4. Individual errors and total error in SW, LW, and net CRE of the CMIP6 models as indicated by CRE sensitivities to CF or LWP, biases of CF or LWP, and co-variations.
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As is discussed in section 3, the modeled spatial distributions of LWP, COD, and re have different characteristics compared to the MODIS observations. Even though LWP and COD in the CMIP6 models share similar spatial patterns (Figs. 6 and 7), that of re is largely different from them (Fig. 8). This motivates us to explore how COD is calculated in each model. Employing the canonical formula of the COD calculation in Eq. (10), we compare COD provided by the CMIP6 models with those calculated as a function of LWP and re.
Figure 11 uses scatter density maps to show the relationship between model-simulated COD and calculated COD based on model output and MODIS retrieved and calculated COD. In Fig. 11a, the correlation between MODIS retrieved and calculated COD reaches 0.9, with RMSE of 1.7. As is shown in Figs. 11b and c, the simulated COD values in CESM2 and UKESM1-0-LL have better consistency with the predicted values. In particular, the correlation coefficient R in CESM2 can reach 0.99. In the comparison of CRE (Figs. 2 and 3), the better inner relationship among the physical properties in CESM2 and UKESM1-0-LL can determine the simulation appearance of CRE. However, the simulated COD and calculated COD in GISS-E2-1-G, MPI_ESM_1-2_HAM, and NorESM2-LM shows weaker correlations, with a correlation coefficient R of 0.53, 0.63, and 0.45, respectively (Figs. 11d–f). Specifically, MPI_ESM_1-2_HAM tends to simulate smaller COD than calculated COD. Such a discrepancy can be explained by the “reduction factor” introduced in the radiation scheme of the MPI model (Mauritsen et al., 2019). Its purpose is to account for the cloud heterogenicity within a grid cell, but it is poorly constrained. The disagreement between calculated and online simulated COD may stem from the re choice in the calculation based on the model output, as mentioned in section 2.
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As a possible source of bias contributing to the modeled cloud radiative effect and physical properties in the CMIP6 models over the SO, aerosol fields in the CMIP6 models are evaluated with satellite products. Here, we focus on AOD, which is output by all models. Among the five CMIP6 models, the GISS model is an outlier, as its AOD values are about six times the MODIS observations. The other four models only differ from MODIS by 0.04 (Figs. 12a and b). However, the spatial correlations of AOD between the other four CMIP6 models and MODIS are rather poor, with coefficients smaller than 0.2. It implies the models have difficulty in predicting the sources of aerosols of the SO and related transport processes. Interestingly, even with the largely biased AOD magnitude, the GISS model shows good agreement with MODIS on the spatial pattern of AOD (Fig. 12c), showing much larger AOD in the Atlantic and Indian oceans of the SO than in the Pacific Ocean. The high AOD over the southern Pacific near 150°W is also captured by the GISS model. Note that the satellite-retrieved AOD is also subject to large uncertainty over the SO, as the highly frequent clouds make it difficult for the instruments to distinguish aerosol from cloud. Overall, a poor ability of aerosol simulation in the CMIP6 models is identified, and the biases can be propagated to simulating cloud physical properties over the SO.
Figure 12. Spatial distribution of multiyear mean aerosol optical depth (AOD) over the SO from CMIP6 models and MODIS (a–c). Taylor Diagram of multiyear AOD spatial average of CMIP6 to MODIS (d). The axis is the standard deviation of CMIP6 simulated AOD and MODIS AOD. The RMSE of difference between CMIP6 and MODIS is represented as green dotted line. The arc refers the correlation coefficient between the four CMIP6 models and observation.
The relationships between re and AOD from MODIS and the five individual CMIP6 models are shown in Fig. 13. From Fig. 13a, the satellite-derived re is dominated by cloud droplet radii between 13–15 μm, with AOD ranging from 0.04 to 0.19. The correlation between MODIS AOD and MODIS re is 0.05, indicating that the signal of aerosol–cloud interaction is not strong in this long-time averaged spatial pattern of re over the SO, and there should be some other more relevant factors. Three models predict a positive correlation between AOD and re, while NorESM2-LM and GISS-E2-1-G simulate a negative correlation (Figs. 13d and e). The weak relationship in the observation and diverse relationships in the model simulations reveal that it is not a feasible way to identify aerosol–cloud interactions by simply correlating AOD with cloud properties through their spatial patterns.
Parameter | Variable Name |
CF | Cloud_Fraction_Mean_Mean |
LCF | Cloud_Retrieval_Fraction_Liquid_FMean |
LWP | Cloud_Water_Path_Liquid_Mean_Mean |
COD | Cloud_Optical_Thickness_Combined_Mean_Mean |
re | Cloud_Effective_Radius_Liquid_Mean_Mean |
AOD | Aerosol_Optical_Depth_Average_Ocean_Mean_Mean |