To compare with Sun et al. (2021), the GCM used in this study is NCAR CESM1.2. The atmospheric component is the Community Atmosphere Model, version 5 (CAM5). The land model is the Community Land Model, version 4 (CLM4). The spatial land surface heterogeneity in the default CLM4 is represented as a nested subgrid hierarchy in which the grid cells are composed of multiple land units, snow and soil columns, and plant functional types (PFTs) (Oleson et al., 2010). All of the fluxes to and from the surface, including the heat fluxes, are defined at the PFT level. Since the subgrid heat fluxes exported to the CAM5 are weighted averages and their weights depend on the fractional coverage of each PFT within the grid cell, the subgrid variations in the land surface fluxes are missing during the land–atmosphere coupling process (Sun et al., 2021).

To consider the influences of the heterogeneity of the subgrid heat fluxes to the atmosphere in CESM1.2, a parameterization scheme is developed and implemented in CLM4. This scheme establishes the truncated normal distributions of the subgrid sensible and latent heat fluxes independently within the grid cell at each time step. The probability density function (PDF) of subgrid sensible and latent heat fluxes in a given grid cell is calculated by 1f(x|F¯,σ,Fmin⁡,Fmax⁡)=1σϕx-F¯σΨFmax⁡-F¯σ-ΨFmin⁡-F¯σ,x∈[Fmin⁡,Fmax⁡] where F¯ is the weighted average value of all subgrid heat fluxes, σ is the standard deviation, Fmin⁡ and Fmax⁡ are the minima and maxima of the subgrid heat fluxes, respectively, and ϕ and Ψ are the PDF and the cumulative distribution function (CDF) of the standard normal distribution, respectively. N (i.e., the maximum number of PFTs coexisting in the grid cell) samples of sensible and latent heat fluxes are independently and randomly paired with each other to drive N independent groups of the PBL and the deep convection parameterization schemes in CAM5. The outputs from these N calls of the schemes are then averaged with equal weights as the inputs of the other schemes.

The stochastic sampling implicitly parameterizes the uncertainties of the PBL and convection processes to a certain degree. As stated in Sun et al. (2021), the sampled fluxes from a statistical distribution rather than the fluxes directly from individual PFTs can represent the mix of subgrid fluxes from mixed land cover types in reality. Moreover, the distribution of the sampled subgrid surface heat fluxes based on the assumed normal distribution resembles the distribution of realistic subgrid PFT heat fluxes within the grid cell in long-term statistics. As shown in Fig. 1, for the sensible heat flux, over the grid cells with 16 and 8 PFTs, the two distributions are highly consistent, in terms of mean value, variance and skewness. The latent heat flux has similar results (not shown). Given that those grid cells are stochastically selected and cover different climatic regimes (Fig. S1 in the Supplement), the assumed normal distribution works well and thus the sampled samples can represent the realistic features for climate simulation.

Note that the closure of the surface energy balance at the grid scale is not affected by the stochastic sampling method. The surface energy balance is closed at the grid scale in the default land–atmosphere coupling way. Therefore, the stochastic sampling at the subgrid scale based on the truncated normal distributions with mean values equal to the default grid averages calculated by the weighted fluxes on each PFT within the grid cell (Fig. 1) can assure that the grid-scale surface energy balance is closed as well in the long-term statistics, although at a given time step this might be broken up.

In the stochastic scheme proposed by Sun et al. (2021), the sampled subgrid sensible heat and latent heat fluxes are stochastically paired, without considering the underlying relationship between them. However, we can compute the correlation coefficients between the subgrid sensible and latent heat fluxes within each grid cell at every time step (i.e., 30 min) using the following equation: 2r=∑i=1nwi(FSHi-F¯SH)(FLHi-F¯LH)σSHσLH, where n is the number of PFTs within a grid cell in the land model, wi is the area percentage of each PFT within the grid cell, FSHi and FLHi are the subgrid surface sensible and latent heat fluxes of each PFT, respectively, F¯SH and F¯LH are their weighted averages, and σSH and σLH are their standard deviations. The correlation coefficients vary with time. Figure 2a shows the annual mean distribution of the energy partitioning between the sensible heat and latent heat fluxes at the subgrid scale. There are negative correlations at low latitudes in the Northern Hemisphere (NH) and most of the Southern Hemisphere (SH), whereas most regions have positive correlations in the middle and high latitudes in the NH and on the TP. In boreal summer (June–July–August, JJA) (Fig. 2b), the sensible and latent heat fluxes in most regions of the world are negatively correlated, except for the TP, Greenland, the central US and southern Australia (Fig. 2b). In boreal winter (December–January–February, DJF) (Fig. 2c), the global distribution is similar to that of the annual mean, showing larger positive correlation coefficients but smaller negative correlation coefficients. Positive correlation coefficients in both summer and winter mainly persist in high latitudes and altitudes. This is because as snow melts in summer the land surface gains more water for evaporation (i.e., latent heat flux). Sensible heat flux increases synchronously from enhanced surface net radiation as a result of increased incoming solar radiation and reduced snow albedo. In winter, decreased solar radiation and increased snow cover reduce both sensible and latent heat fluxes.

Here we propose two methods below based on the subgrid surface energy partitioning between sensible and latent heat fluxes.

Arrange the randomly selected N subgrid sensible heat fluxes and N subgrid latent heat fluxes in each grid cell from largest to smallest and pair them in turn to drive the atmosphere independently. In this case, a large (small) sensible heat flux corresponds to a large (small) latent heat flux.

Three Atmospheric Model Intercomparison Project (AMIP)-type experiments with a finite-volume dynamical core at a horizontal resolution of 1.9∘ × 2.5∘ (∼ 2∘) and 30 vertical levels from the surface to 3.6 hPa are conducted using observed climatological (1982–2001 mean) monthly sea surface temperature and sea ice extent data (Stone et al., 2018). The control simulation (CTL) uses the standard CESM1.2, the experimental simulation (EXP) uses the Sun et al. (2021) parameterization in CESM1.2 (also the same as the EXP run in their study) and the EXP_COR run uses the modifications as described in Sect. 2.2. All of the simulations were run for 6 years, with the first year discarded as the spin-up stage. The value of N in each grid cell was fixed to 16, which equals the maximum number of PFTs ever coexisting on a single column in the land model, although different grid cells have different numbers of PFTs (Sun et al., 2021). As noted by Sun et al. (2021), further increasing N has negligible impacts on the model performance compared with setting N to 16 and enhances computational loading instead.

To evaluate the model performance, the simulation results are compared with the available observation and reanalysis datasets. The Tropical Rainfall Measuring Mission (TRMM; Huffman et al., 2014) observations (0.25∘ × 0.25∘) and the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2; Gelaro et al., 2017) reanalysis (0.5∘ × 0.625∘) are used for precipitation. The other datasets include surface radiative fluxes from the Clouds and the Earth's Radiation Energy Systems (CERES) Energy Balanced and Filled (1.0∘ × 1.0∘) (EBAF; Loeb et al., 2012), sensible heat and latent heat fluxes from the Global Land Data Assimilation System version 2.1 (GLDAS-2.1) Noah monthly data (1.0∘ × 1.0∘) (Rodell et al., 2004) and 2 m air temperature from the Climatic Research Unit with a 0.5∘ resolution (CRU; Harris et al., 2020). For consistency, all of the observation and reanalysis datasets are regridded to the same grid size as CAM5.

Sun et al. (2021) (i.e., the EXP run) improved the simulation of summer precipitation over eastern China and the coastal areas of the Bay of Bengal (Fig. 3b–d), which is attributed to altered vertical diffusion and convection. In particular, it still produces excessive precipitation on the eastern and southern margins of the TP. After taking the subgrid energy partitioning into account in the EXP_COR run, the overall performance in terms of the root-mean-square error (RMSE) and the spatial correlation coefficient (COR) is comparable to that of the EXP run (Fig. 3d and f). The long-standing overestimations of precipitation on the southern and eastern margins of the TP are alleviated by up to -2.5 mm d-1 (Fig. 3b–f), although the simulated precipitation is still excessive. Over other regions such as southern China, the Middle East and Indonesia, there are some slight degradations.

Figure 4 zooms in on the region (20–50∘ N, 75–125∘ E) where the simulated precipitation exhibits obvious improvements in the EXP_COR run. In the CTL run, the wet bias over the southern margin of the TP can exceed 11 mm d-1, while that over the eastern margin of the TP is approximately 7 mm d-1. In CMIP5&6 models, the biases along the TP are much larger than those in the rest of the world (Fig. 3) (Su et al., 2013; Yu et al., 2015; Zhu and Yang, 2020; Lun et al., 2021). In contrast, in the EXP_COR run, the reduced biases over these two regions can be as much as 2.5 mm d-1 accounting for a reduction of approximately 25 %, especially over the southern margin of the TP. Given that there are many causes (e.g., unrealistic water vapor advection and the absence of subgrid topographic effects) for the severe overestimation of precipitation along the TP, the improvement in this study, to some extent, is impressive. The regionally averaged RMSE decreases from 4.51 in the CTL run and 4.07 in the EXP run to 3.71 in the EXP_COR run, and the COR increases from 0.48 in the CTL run to 0.60 in both the EXP and EXP_COR runs.

Total precipitation in the model consists of convective and large-scale components. Their contributions are analyzed accordingly. Compared with the EXP run, large-scale precipitation is significantly suppressed on the southern fringe (Fig. 5a and b), and more large-scale precipitation and convective precipitation are reduced on the eastern margin in the EXP_COR run.

A moisture budget analysis widely used in previous studies (Gao et al., 2017; Wang et al., 2016) is conducted to examine the causes of precipitation changes. Following Sun et al. (2021), the atmospheric water vapor budget equation is given below: 3∂W∂t=-W∇⋅V+-V⋅∇W-P+E, where P is precipitation and E is evaporation. W is the column-integrated moisture given by ∫PtopPbotqdp/g, in which q is the specific humidity, Ptop and Pbot are the top and surface pressures, respectively, and g is the acceleration due to gravity. The vector V (with units of m s-1), given by W-1∫PtopPbot(qu)dp/g, represents the total horizontal moisture transport normalized to the column-integrated moisture, where u is the horizontal wind vector. The first term on the right-hand side of Eq. (3) is the moisture convergence Qcnvg, and the second term is the moisture advection Qadvt. The tendency of the term ∂W∂t on the left-hand side of Eq. (3) is negligible for seasonal averages of multiple years.

Compared with the CTL run, moisture convergence weakens on the eastern edge of the TP, while moisture advection increases in the EXP_COR run (Fig. 5e and f). On the southern edge of the TP, moisture advection decreases, and moisture convergence slightly increases. Overall, consistent with the change in total precipitation, the total water vapor contributions decrease on the eastern and southern edges of the TP (Fig. 5h). We note that the spatial pattern of Qcnvg changes in the EXP_COR run relative to the CTL run and resembles that in the EXP run (Fig. 4d and f in Sun et al., 2021), which is linked with the changes in the heating rate due to vertical diffusion in the PBL caused by the subgrid variations in land surface heat fluxes. In comparison with the EXP run, the negative moisture convergence anomaly is further aggravated, and the positive bias of moisture advection on the eastern margin of the TP is smaller (Sun et al., 2021). The negative maximum of the total contribution thus shifts westward to the eastern margin of the TP. Overall, moisture convergence dominates the change in precipitation on the eastern border of the TP (Fig. 5e and h). On the southern edge of the TP, the main term contributing to precipitation changes is the reduced moisture advection (Fig. 5f and h).

The causes of the altered moisture convergence and advection are illustrated in Figs. 6 and S2, where the MERRA-2 reanalysis is included for reference. In the EXP run, the subgrid variations of the land surface heat fluxes increase (decrease) PBL heating over southern (northern) China (Fig. 6a). With the partitioning of subgrid surface heat fluxes included, the increase (decrease) in the heating rate over southern (northern) China is strengthened (Fig. 6b). Therefore, destabilization (stabilization) in the lower atmosphere is further enhanced, promoting (suppressing) local convection. Lower (higher) sea level pressure (SLP) anomalies over southern (northern) China are generated in the EXP_COR run than in the EXP run. In particular, compared with the EXP run, the anomalous high SLP over northern China extends further to the south and to the eastern border of the TP, with the anomalous low SLP over southern China retreating (Fig. 6d–h). The anomalous anticyclonic moisture transport associated with downdraft expands accordingly, which engenders decreased precipitation on the eastern border of the TP and slight dry biases over southern China. Similar to the EXP run, convective precipitation dominates the changes in total precipitation over eastern China and the eastern margin of the TP in the EXP_COR run. In the EXP run, negative SLP anomalies appear along the Bay of Bengal, leading to cyclonic moisture transport from the ocean in the south (Fig. 6e). As a result, excessive moisture is transported to the southern edge of the TP producing overestimated rainfall there. In contrast, in the EXP_COR run (Fig. 6g), the easterly anomaly along 25–30∘ N partly blocks moisture transport from the ocean in the south to the southern margin of the TP, and hence the decrease in large-scale precipitation plays a first-order role on the southern margin of the TP.

The above analysis indicates that the precipitation simulation is improved through the adjustment of large-scale atmospheric circulation in the lower atmosphere, which is highly linked with grid-scale surface heating or cooling (Sun et al., 2021). The following analyses will evaluate the performance of other variables such as surface energy budgets, clouds and 2 m air temperature in JJA globally.

The evaluations of the latent heat flux simulation are shown in Fig. 7. In those regions with large latent heat fluxes in GLDAS (e.g., the eastern US, northern South America, eastern China), the simulated values are generally underestimated in the CTL run, while in the regions with relatively small latent fluxes (e.g., the Arabian Peninsula, the Sahara and the northwestern TP), CTL tends to overestimate values. Overall, the three simulations have similar distributions and comparable CORs. This is probably because the low accuracy of land cover data in CLM is the major culprit for those biases (Liu et al., 2021). In the regions with small correlation coefficients r (Australia, the Arabian Peninsula, the Sahara Desert) (Fig. 2a), there are no improvements noticed in the EXP_COR run even with the simulation degraded.

For the sensible heat flux simulation (Fig. 8) over those regions with large and small values in GLDAS, the CTL run underestimates and overestimates them, respectively. Similar to latent heat fluxes, the three experiments resemble each other, except that EXP_COR further alleviates the overestimation along 45–60∘ N over the Eurasian continent where sensible heat fluxes and latent heat fluxes are highly correlated (Fig. 2b). The positive changes over the southern and eastern margins of the TP in the EXP_COR run are more significant than those in the EXP run (Fig. 8e and f). Nonetheless, we note some degradations from EXP to EXP_COR (e.g., over southern China).

As indicated in Sect. 3.1, large-scale atmospheric circulation in the lower atmosphere and local convection are altered as PBL heating changes, which affects clouds as well. The changes in clouds in turn influence surface radiation and thus surface heat fluxes. The cloud properties affecting cloud radiative effects include their macrostructures (e.g., fraction, top and base heights, and vertical overlap) and microphysical properties (e.g., particle size distribution and geometric configuration, cloud phase, and water condensation). As shown in Fig. 9c, the EXP_COR run reduces low clouds over northern China and southeastern Russia and increases them over southern China and along 45–60∘ N in comparison with the CTL run. The EXP run has a similar pattern of changes but with smaller magnitudes compared with the EXP_COR run (Fig. 9a–c). Low clouds reflect a large amount of incoming solar radiation and emit longwave radiation at relatively high temperatures, so they exert an overall net cooling effect on the Earth (Klein and Hartmann, 1993; Hartmann, 1994). Compared with the CTL run, the middle and high clouds on the TP are dramatically decreased in the EXP_COR run. Especially for high clouds, the decrease in the EXP_COR run is much larger than that in the EXP run.

The simulations of the total cloud water path (vertically integrated cloud liquid and ice water content, CWP) are shown in Fig. 10d–f. A higher cloud water content reflects more solar radiation. The EXP run increases the total CWP over southern China and along the Bay of Bengal. Northern China, the TP and southeastern Russia feature CWP decreases. In the EXP_COR run, the simulated CWP is further decreased on the TP and over northern China, while it is increased in southern China and along 45–60∘ N, especially over the Eurasian continent. The spatial distribution of the total ice water path (IWP) changes resembles that of the total CWP changes (Fig. 10g–i).

Generally, the radiative effect of clouds is quantified by cloud radiative forcing (CRF) (the difference in the surface net flux between all-sky and clear-sky conditions). It includes shortwave cloud forcing (SWCF) and longwave cloud forcing (LWCF). Realistic simulation of the CRF is another important measure of the performance of climate models (Sun et al., 2016). SWCF is negative, and a smaller value indicates a stronger reflection of solar shortwave radiation. The strengthened SWCF over the central US, the Eurasian continent along 45–60∘ N and southern China in EXP_COR (Fig. 10c) originates from the increased cloud water (Fig. 10f) and low clouds (Fig. 9c). Similarly, the decreased SWCF over northern China, the TP and southeastern Russia is due to their reductions. LWCF is positive, and a larger value means a stronger warming effect on the land surface. The LWCF increases over southern China and decreases over northern China in EXP_COR (figure not shown). The distribution of the net CRF (figure not shown) resembles that of the SWCF, which implies that the SWCF changes dominate the CRF variations.

The simulation of the net surface shortwave flux is demonstrated in Fig. 11. Globally, the RMSE and COR values are similar to each other in the three simulations. In the EXP_COR run, the underestimation over the TP in both the CTL and EXP runs is alleviated, although it slightly degrades the simulation over eastern China. The negative biases over southeastern Russia in EXP_COR are also larger than those in EXP. The changes in the net surface shortwave flux (Fig. 11e and f) are very consistent with those in SWCF (Fig. 10b and c) implying that the net surface radiation fluxes are mainly controlled by the shortwave radiation reflected by the adjustment of clouds as a result of the altered PBL heating rates and the associated changes in local convection.

In response to the adjustment of the surface energy budget, the global distributions of JJA mean 2 m air temperature from CRU and the difference between the observations and the three experiments are shown in Fig. 12. The three simulations have comparable CORs and RMSEs globally. Compared with the CTL run, the EXP run alleviates the overestimations in the middle and high latitudes, although the performance over central Africa and northern South America is slightly degraded (Fig. 12b, c and e). In the EXP_COR run, the overestimations over the central US and the Eurasian continent are further alleviated, while the negative biases over central Africa and the positive biases over southern South America are worsened (Fig. 12b, d and f). The simulated 2 m air temperature over northern China and the TP is increased, reintroducing some positive biases. In short, in the EXP_COR run the decreased net surface shortwave flux associated with the increases in low clouds and cloud water content over southern China, over the central US, over the Eurasian continent along 45–60∘ N and along the Bay of Bengal might contribute to local cooling, while the warming over the TP and northern China is attributed to the opposite changes accordingly (Figs. 9–11).

The analyses presented above demonstrate that the introduction of the subgrid heat flux schemes (EXP and EXP_COR) improves the simulations of summer precipitation in eastern China in EXP and additional TP regions in EXP_COR compared to the default model. The improvements and degradations in simulated surface heat fluxes, cloud properties and 2 m air temperature in boreal summer at the global scale are also discussed. The precipitation improvements over eastern China are mainly from the consideration of subgrid variations in surface heat fluxes (i.e., the EXP run where the sampled subgrid sensible and latent heat fluxes are stochastically paired with each other), while the improved precipitation simulations on the southern and eastern margins of the TP are attributed to the further inclusion of the partitioning of the subgrid surface heat fluxes (the EXP_COR run). A thorough evaluation of the global annual and seasonal means of those variables is necessary because from the perspective of climate model development, the incorporation of a new parameterization scheme to improve some aspects should not obviously cause the degradation of other aspects (Wang et al., 2021b). As presented in Table 1 (global distributions shown in Figs. S3–S9), the overall simulation statistics of the EXP and EXP_COR runs are comparable to those of the CTL run, although they are slightly different in some seasons. When focusing on East Asia (Table S1 in the Supplement), the new schemes outperform the default scheme, implying the importance of parameterizing the subgrid land surface heat fluxes to the atmosphere in GCMs in regions with complex terrain (e.g., the TP) and multiple surface types (e.g., eastern China).

The zonal means of temperature and specific humidity from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis dataset and the model biases are shown in Fig. 13. In the CTL run, the temperature is overestimated at lower levels in the tropics and midlatitudes in the SH, whereas it is underestimated at higher levels in other latitudes (Fig. 13a). The EXP run reverses the positive biases to negative biases with an excessive reduction at lower levels, and the negative biases at higher altitudes are further exacerbated (Figs. 13b and S10b). In contrast, the biases in the EXP_COR run are comparable to those in the CTL run (Fig. 13a and c). The low-latitude overestimations in the lower troposphere and the high-latitude underestimations across the troposphere are alleviated (Fig. S10c). In the simulation of specific humidity, the main positive biases occur in the low latitudes and midlatitudes below 400 hPa. For the midlatitudes, there are negative biases in the lower troposphere (Fig. 13d). In general, there are no significant differences among the three simulations (Fig. 13d–f). In the EXP run, the positive biases in the lower and middle troposphere are alleviated (Fig. S10e). In contrast, the EXP_COR run is similar to the CTL run, with negligible differences (Fig. S10f). In summary, the performance of the mean state simulations does not change significantly when using the two modified schemes (the EXP and EXP_COR runs).