1. Introduction
Clouds are crucial to Earth’s energy budget due to their effect on outgoing longwave radiation (OLR) (e.g., Norris et al. 2016; Zelinka et al. 2012; Ramanathan et al. 1989b). The representation of clouds and their variations in climate models is one of the most difficult issues affecting the understanding of the climate system and climatic change (Boucher et al. 2013). Thus, the improvement of our understanding and representation of clouds is essential for the credible prediction of future climatic change (Zhou et al. 2015).
Cloud particle size and water path play important roles in the parameterization of cloud albedo (Han et al. 1998). The horizontal resolutions of global climate models (GCMs) are usually dozens to hundreds of kilometers; thus, the parameterization of cloud microphysical properties usually cover only portions of grid cells (Lu et al. 2013). The relationship between the cloud fraction and cloud albedo has been explored in many studies (e.g., Betts and Viterbo 2005; Charlock and Ramanathan 1985; Liu et al. 2011; Xie and Liu 2013; Xie et al. 2014; Feingold et al. 2017). Based on the effective single cloud layer assumption, Liu et al. (2011) derived the relationships of relative cloud radiative forcing (RCRF), cloud fraction, and cloud albedo and proposed that RCRF could be used to estimate cloud albedo.
For multilayer clouds, the cloud albedo and cloud fraction also depend on the cloud vertical overlapping structure. The effect of the cloud overlap representation on the cloud fraction has been studied extensively. Most traditional cloud vertical overlap models incorporate fixed forms of overlap assumption, commonly the maximum overlap and/or random overlap (Geleyn and Hollingsworth 1979; Tian and Curry 1989; Chou et al. 1998; Hogan and Illingworth 2000). However, these cloud overlapping treatments cannot represent real cloud structures in the atmosphere. An innovative approach to unify the treatment of cloud overlap via the observation-based decorrelation length scales (Lcf) has been proposed (e.g., Hogan and Illingworth 2000; Mace and Benson-Troth 2002; Bergman and Rasch 2002). Following these studies, various methods have been applied to obtain Lcf from observations or cloud-resolving simulations (e.g., Kato et al. 2010; Shonk and Hogan 2010; Shonk et al. 2010; Oreopoulos et al. 2012; Zhang et al. 2013; Di Giuseppe and Tompkins 2015; Jing et al. 2016, 2018; Li et al. 2018, 2019).
According to Liu et al. (2011), the cloud albedo can be calculated from RCRF and the cloud fraction. To better address multilayer clouds, in this study, we first extend the formula of Liu et al. (2011) to link cloud albedo directly to Lcf. We then apply the new formula to BCC_AGCM2.0_CUACE/Aero (Wu et al. 2010) model data and Clouds and the Earth’s Radiation Energy System (CERES) (Wielicki et al. 1996; Smith et al. 2004) measurements to calculate the cloud fraction, RCRF, and cloud albedo, and evaluate the model performance against the CERES results. The effects of different cloud vertical overlap structures on the calculated cloud albedos are further investigated by comparing the model and observational results as a function of Lcf.
The rest of this paper is organized as follows. Section 2 briefly introduces the data, model, and methods. The influences of cloud vertical overlap on the calculated cloud albedo in the models and satellite observations are discussed in section 3. The conclusions are presented in section 4.
2. Methodology and data
a. Model and experiments
The BCC_AGCM2.0_CUACE/Aero model is used in this work. The BCC_AGCM2.0 was developed by the Beijing Climate Center (BCC) of the Chinese Meteorological Administration (Wu et al. 2010). CUACE/Aero was added by the Institute of Atmospheric Composition and Environmental Meteorology (Gong et al. 2002, 2003). The coupled model employs a horizontal T42 spectral resolution (about 2.8° × 2.8°) and a hybrid vertical coordinate with 26 levels, the top of which is located at about 2.9 hPa (Zhao et al. 2018). This model is well known for its ability to describe cloud overlapping structures and their radiative transfer (Zhang et al. 2012). In this model, hydrometeor types are not assumed in advance, and it mainly depends on physical quantities such as temperature and cloud water content. The radiation scheme developed by Zhang (2016) (named BCC_RAD) is incorporated in the model, with a correlated k-distribution method adopted to treat gas absorption (Zhang et al. 2006a,b). The optical properties of water and ice clouds are given by Lu et al. (2011) and Zhang et al. (2015). The Monte Carlo independent column approximation (McICA) approach (Pincus et al. 2003; Zhang et al. 2014) is applied to treat subgrid cloud structures, such as the vertical overlapping of fractional clouds and horizontal inhomogeneity of cloud condensate. A subgrid random cloud generator (Räisänen et al. 2004) is used in the McICA approach to create unresolved cloud distributions based on the grid mean cloud profile and auxiliary assumptions about vertical and horizontal cloud alignment. A detailed evaluation of the combined application of BCC_RAD and McICA to calculate cloud-mediated radiation fields is given in Zhang et al. (2014). Wang et al. (2014) incorporates a two-moment cloud microphysical scheme (Morrison and Gettelman 2008) into the BCC_AGCM2.0_CUACE/Aero, and showed that this model simulated the properties of the cloud and radiation balance at the top of the atmosphere more accurately than did previous simulations. A more detailed introduction to the model physics and framework can be found in Zhang (2016) and Zhang et al. (2020). Jing et al. (2016) obtained a set of satellite-based representations of Lcf and incorporated them into the BCC_AGCM2.0 model with a one-moment scheme to consider aerosol–cloud interactions without aerosol feedback processes. In Jing et al. (2016), the 2B-GEOPROF and 2B-GEOPROF-lidar products from CloudSat/Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellites during 2007–10 were used. Then, CPR_Cloud_mask, cloud fraction, and Z obtained from the above products were used to identify a cloudy volume. Finally, the gridded climatology of Lcf calculated by stochastic cloud generator (SCG) was applied in BCC_AGCM2.0_CUACE/Aero. Following this work, Wang et al. (2022) incorporates the above satellite-based representations of Lcf into the online coupled BCC_AGCM2.0_CUACE/Aero model with a two-moment scheme to consider aerosol–cloud interactions and their feedback (see Wang et al. 2014). Both studies have improved cloud fraction simulations regionally and globally relative to the fixed decorrelation length scales method (Barker 2008). Thus, the version of the model developed by Wang et al. (2022) is used for all analyses performed in this study.
The model (Wang et al. 2022) is run for 35 years with prescribed SSTs and sea ice of the AMIP dataset (Hurrell et al. 2008) from 1970 to 2000, and satellite-based Lcf from Jing et al. (2016), and all of the variables needed to calculate RCRF (e.g., cloud albedo, including all-sky and clear-sky surface downwelling shortwave radiation fluxes, and the total cloud fraction) are output. We use the most recent 30-yr results for the analyses performed in this work.
b. Satellite data
The CERES project provides satellite-based observations of Earth radiation budget (ERB) and clouds. It uses measurements from CERES instruments flying on several satellites along with data from many other instruments to produce a comprehensive set of ERB data products for climate, weather, and applied science research. The cloud fraction from CERES SYN1deg–level 3 (https://ceres-tool.larc.nasa.gov/ord-tool/jsp/SYN1degEd41Selection.jsp) and radiation fluxes from CERES EBAF–level 3b (https://ceres-tool.larc.nasa.gov/ord-tool/jsp/EBAFTOA42Selection.jsp) are used to calculate observation-based RCRF and cloud albedo (Wielicki et al. 1996; Smith et al. 2004; Minnis et al. 2011; Loeb et al. 2018). The data used here are monthly mean fields for both products over the period of 2006–15, with a horizontal resolution of 1° × 1°. These data are interpolated to a 2.8° × 2.8° latitude–longitude resolution based on bilinear interpolation to maintain the same resolution as our model. Therefore, these datasets can be used to calculate RCRF and cloud albedo using Eq. (8) for the observational references to evaluate the modeling results.
c. Calculation of cloud albedo
1) Single-layer clouds
2) Multilayer clouds
3. Results
a. Four cloud overlapping groups according to Lcf
To obtain the cloud albedo under different cloud vertical overlap structures, we divide the decorrelation length scales acquired from CloudSat/CALIPSO satellites into four consecutive ranges (0 ≤ Lcf < 2 km, 2 ≤ Lcf < 4 km, 4 ≤ Lcf < 6 km, and Lcf ≥ 6 km). We focus on the decorrelation length scales during December–February (DJF) and June–August (JJA) because of the relatively flat variation of decorrelation length scales in March–May (MAM) and September–November (SON). Here, it should be noted that the distribution of decorrelation length scales here is slightly different from previous studies, such as the decorrelation length scales over the SGP area does not correspond to those based on observations in Mace and Benson-Troth (2002) and Li et al. (2019) due to probably using different data. However, the results of this work are consistent with those of Jing et al. (2016). Figure 1 shows the global distribution of Lcf in DJF (Fig. 1a) and JJA (Fig. 1b), which is obtained from satellite data, as mentioned above. As shown in Fig. 1, the group with the largest values in DJF (Lcf ≥ 6 km) is distributed over the Eurasian continent with a stable atmosphere and thick clouds. The group with the smallest values (0 ≤ Lcf < 2 km) is linked primarily to marine stratiform clouds over the eastern subtropical oceans. The two intermediate ranges (2 ≤ Lcf < 4 km and 4 ≤ Lcf < 6 km) are often associated with the tropical deep convection zone, where clouds usually develop from the lower levels up to the tropopause (Wang et al. 1998). Figure 2 lists the number of grid points corresponding to the different groups of Lcf in DJF and JJA. The frequencies of occurrence are consistent for these two seasons, indicating that the smallest and largest number of samples occurred for Lcf ≥ 6 km and 2 ≤ Lcf < 4 km, respectively.
Global distribution of Lcf in (a) DJF and (b) JJA.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-22-0219.1
Classification of Lcf calculated by stochastic cloud generator and frequency of occurrence in DJF (blue) and JJA (orange).
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-22-0219.1
b. Global distribution of cloud albedo and differences between simulations and observations
Figures 3 and 4 show the global distribution of the cloud albedo, RCRF, and cloud fraction based on the model results, CERES data and their differences in DJF and JJA. The simulations and observations present a generally consistent regional distribution of cloud albedo, cloud fraction, and RCRF. In Eurasia, the observation-based cloud albedo ranges from 0.1 to 0.5 in DJF, which is consistent with the value obtained from geostationary satellite data (Mueller et al. 2011). The model-based cloud albedo behaves similarly to the observations in Eurasia in DJF, but it is larger than the observational results in JJA. In North America, most observation-based cloud albedos exceeded 0.4, with cloud fractions exceeding 0.6, especially in DJF. Cloud albedo are much smaller over the subtropical central oceans, such as the central Pacific and central Atlantic than over the adjacent coasts and continents due to the year-round small cloud fractions over these regions (Figs. 3d and 4d). In addition, there are some typical regional discrepancies. In Antarctica and Arctic north, there are large discrepancies between model-based and the observation-based cloud fraction caused by errors in the model itself (Figs. 3f and 4f). Differences in Alaska’s cloud albedo between simulations and observation are attributed to differences in RCRF (Figs. 3c,i and 4c,i). During DJF, the differences between model-based and observation-based cloud fractions are relatively apparent in northern and southern India.
Spatial distributions of (top) cloud albedo, (middle) cloud fraction, and (bottom) RCRF based on (left) the model results, (center) CERES data, and (right) their difference in DJF.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-22-0219.1
As in Fig. 3, but for JJA.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-22-0219.1
A persistent belt of high albedo and large cloud fraction exist over the mid- to high-latitude ocean in the Southern Hemisphere (SH), where mid- to low-level clouds are mostly predominant and highly shortwave reflective (see Figs. 3a,b,d,e and 4a,b,d,e). In these areas, the modeled cloud albedos show systematic biases compared to the CERES results (Figs. 3c and 4c), which is most likely due to sea ice and the complex mixed-phase cloud processes in the Southern Ocean, which are poorly represented in the model (Tan et al. 2016; Flynn and Mauritsen 2020). In particular and as shown in Fig. 2, we find large differences between the simulated and observed cloud fraction and RCRF in regions where Lcf ≥ 4 km. These differences may introduce errors in the calculation of cloud albedo.
c. Evaluation of simulated cloud albedo for multilayer clouds
The cloud albedos are separated by Lcf and shown in Fig. 5. For 0 ≤ Lcf < 2 km (Figs. 5a,b), the two sets of cloud albedos correlate with each other reasonably well, with correlation coefficients of 0.84 in DJF and 0.77 in JJA. As seen by the best fit line, the model-based cloud albedos are always higher than the satellite-based albedos in DJF and JJA, with the discrepancy increasing slightly with the cloud albedo in DJF, especially for highly reflective clouds, as shown by the frequency of occurrence. Unlike 0 ≤ Lcf < 2 km, the results for 2 ≤ Lcf < 4 km show differing features (Figs. 5c,d). Although the correlation coefficient remained positive, the spread of the data points become larger. When the satellite-based cloud albedo is less than 0.6, the difference between the model and observations is small (<20%), especially during JJA. However, the simulated albedos are much smaller (∼0.2) when the satellite-based albedos are greater than 0.6. This striking discrepancy implies that some of the observed highly reflective clouds with 2 ≤ Lcf < 4 km are not captured well by the model. The frequency of occurrence indicated that a cluster of grid points is present around the observed cloud albedo of ∼0.3, where the simulated albedos are about 0.1 or larger (with albedos ∼ 0.4), in DJF. No such cluster is seen in JJA.
Comparison of model-based and satellite-based cloud albedos for the groups of (a),(b) 0 ≤ Lcf < 2 km, (c),(d) 2 ≤ Lcf < 4 km, (e),(f) 4 ≤ Lcf < 6 km, and (g),(h) Lcf ≥ 6 km in DJF and JJA. The red lines denote the linear fit to all data points. The color bar represents the frequency.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-22-0219.1
When Lcf ≥ 4 km, the coefficients of correlation between model-based and observation-based cloud albedo are poor (Figs. 5e–h), due mainly to the bad cloud fraction and RCRF simulations (see Figs. 3f,i and 4f,i). There are also fewer sample points for the two groups of Lcf ≥ 4 km than for the other two groups (see Figs. 1 and 2).
Figure 6 shows the Taylor diagrams of the simulated and observed RCRF, cloud fraction, and cloud albedo for the four Lcf ranges during DJF and JJA (Taylor 2001). The cosine of the azimuthal angle of each point gives the correlation between the model and observed results. The distance between each point and the reference point “Obs” represent the root-mean-square error (RMSE). As this distance approached zero, the model results approach the observations. In DJF, when 0 ≤ Lcf < 2 km, the coefficients of correlation between the simulated RCRF and cloud albedo and the observed values exceed 0.8. For the remaining three Lcf ranges, the correlation coefficients for the three variables are <0.8. In JJA, all correlation coefficients for the three variables are <0.8 for all Lcf ranges. The points of the three variables in the figure are closer to “Obs” when Lcf < 4 km than when Lcf ≥ 4 km, implying that the simulations using the former are closer to the observed results. Overall, the correlation coefficients, RMSEs, and normalized standard deviations of the three variables had large errors when Lcf ≥ 4 km and small errors when 0 ≤ Lcf < 4 km.
Taylor diagrams of cloud albedo (α), relative cloud radiative forcing (RCRF), and cloud fraction (f) differences between the model results and satellite observations for four Lcf ranges 0 < Lcf < 2 km (red), 2 < Lcf < 4 km (green), 4 < Lcf < 6 km (blue), and Lcf > 6 km (light blue) in (a) DJF and (b) JJA. The large gray circles indicate normalized root-mean-square errors. The blue and cyan points of cloud albedo for JJA are outside the figure due to their large differences. The red dashed circle indicates circled points that have the best simulation results.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-22-0219.1
To measure the overall performance of the model simulations of cloud albedo, RCRF, and cloud fraction, relative D values are determined for the four Lcf ranges in DJF and JJA (Fig. 7). Figure 7 illustrates two noteworthy points. First, the D values for the three variables decrease with decreasing Lcf, indicating that the model performed better when Lcf is smaller, only in JJA. This conclusion is consistent with the results given by the Taylor diagram (Fig. 6). Second, most D values of cloud albedo increase with the D values of the cloud fraction and RCRF (Fig. 7), suggesting that the accuracy of the simulated cloud albedo is related closely to that of the cloud fraction and RCRF according to Eq. (11). These results reinforce the importance of the adequate representation of cloud overlaps when calculating cloud albedo.
Relative Euclidean distances of the cloud albedo (green), RCRF (yellow), and cloud fraction (blue) for 0 ≤ Lcf < 2 km, 2 ≤ Lcf < 4 km, 4 ≤ Lcf < 6 km, and Lcf ≥ 6 km during (a) DJF and (b) JJA.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-22-0219.1
Figure 8 shows the comparison of the correlation coefficients for the four Lcf ranges in DJF and JJA between the simulations and observations for the three variables (cloud albedo, RCRF, and cloud fraction). All correlation coefficients are larger with smaller Lcf, indicating that the model performs better when the Lcf is smaller, especially in JJA. This result is consistent with the above results of the relative Euclidean distance.
As in Fig. 7, but for the correlation coefficients.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-22-0219.1
4. Conclusions
This study is performed to investigate the effect of cloud vertical overlap on cloud albedo in the BCC_AGCM2.0_CUACE/Aero climate model and Clouds and the Earth’s Radiation Energy System (CERES) observations. We first develop a new expression that directly related the effective cloud albedo to relative cloud radiative forcing (RCRF) and the decorrelation length scales by coupling Liu et al.’s (2011) expression for cloud albedo with an equation for the cloud fraction that explicitly accounted for the general structure of cloud vertical overlapping through Lcf, as presented in Hogan and Illingworth (2000). We then use the new expression to explore the effects of cloud vertical overlapping on the calculated cloud albedo by comparing the BCC_AGCM2.0_CUACE/Aero model results and the CERES observational results under different Lcf, regimes for multilayered clouds. The simulated cloud fraction and RCRF are also compared with the values from the CERES observations to better understand the differences in model performance as a function of Lcf, or under different regimes of cloud vertical overlap.
The spatial distributions of modeled and observed cloud albedos show that the cloud albedo is generally smaller over the Southern Hemisphere (SH) oceans than over land. Compared with the CERES results, the simulations capture the overall regional distribution of cloud albedo, cloud fraction, and RCRF. The differences in cloud albedo, cloud fraction, and RCRF are located mainly in the middle- and high-latitude oceans of the SH.
For multilayer clouds, model performance depends on Lcf, generally declining as Lcf increased or the overlap changed from random to maximum. It could be that the model struggles to capture partial cloudiness and does better in regimes that are closer to overcast since random overlap is overall cloudier than maximum overlap. Further analysis revealed that the deterioration of simulated cloud albedo with increasing Lcf is related closely to the similar deterioration of the simulated cloud fraction and RCRF, reinforcing the importance of the accurate cloud fraction simulation in climate models.
The concepts and methods proposed in this work can be used to evaluate cloud albedo using multimodel approaches. Cloud albedo evaluation is useful because cloud albedo represents a key component of cloud radiative properties. Therefore, cloud albedo improvements may ultimately improve weather and climate forecasting.
Acknowledgments.
This work is supported by the National Key R&D Program of China (2017YFA0603502), the National Natural Science Foundation of China (42275039). Yangang Liu is supported by the U.S. Department of Energy (DOE)’s Office of Science Atmospheric Systems Research (ASR) Program under Contract DESC0012704. I would like to thank Wang Fei, a doctoral student from Nanjing University of Information Science and Technology, and He Jingyi, a master student from Chinese Academy of Meteorological Sciences, for revising the language of the article.
Data availability statement.
All of the modeling results will be openly available after this paper is published. CERES data are also openly available. The cloud fraction from CERES SYN1deg–level 3 (https://ceres-tool.larc.nasa.gov/ord-tool/jsp/SYN1degEd41Selection.jsp) and radiation fluxes from CERES EBAF–level 3b (https://ceres-tool.larc.nasa.gov/ord-tool/jsp/EBAFTOA42Selection.jsp) are monthly mean fields for both products over the period of 2006–15, with a horizontal resolution of 1° × 1°.
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