Improving Representation of Tropical Cloud (5)

Fig. 9. As in Fig. 8, but for (a, c, e) LWSFC and (b, d, f) SWSFC.

Figures 10 and 11 are scatter diagrams comparing the generated and reference radiation fields at the TOA and surface, respectively. Systematically negative biases in LWTOA and positive biases in SWTOA are shown for the MRO assumption (Figs. 10a, d) and the opposite for G2KM (Figs. 10b, e). PARA shows little systematic bias in LWTOA and SWTOA—that is, the points are distributed more symmetrically around the reference lines(Figs. 10c, f). Similar features are also shown at the surface (Fig. 11), except that G2KM and PARA resemble each other for the LWSFC (Figs. 11b, c), consistent with their similarity in Fig. 9.

Figure 12 shows the tropical-averaged radiation biases for all areas (solid fill) and areas of ascent only(hatched fill). As expected, the MRO assumption shows the largest errors relative to the reference, especially for the shortwave fluxes (about 16 W m-2 at both the TOA and the surface). G2KM performs much better than the MRO assumption, with absolute errors of approximately 2 W m-2 for LWTOA and SWTOA. PARA reduces the errors more significantly, especially for shortwave fluxes. The error in LWSFC of PARA is more negative than that of G2KM (Fig. 12c); this is because PARA reduces the positive errors in the ITCZ (as shown in Fig. 9)that compensate for negative errors in other regions. It should be stressed that, for most of these variables,PARA reduces the all-area mean errors as effectively as it does in the areas of ascent only, implying that unrealistic cloud overlap treatment in areas of ascent is a major source of radiation error in tropical areas. Considering that these areas typically have large radiation biases in GCM simulations (Lauer and Hamilton, 2013), the introduction of PARA-like overlap treatment could possibly reduce the uncertainty in tropical radiation calculations.

The treatment of vertical cloud overlap also influences the radiative heating rate in the atmosphere, a property important for atmospheric stability and 13 compares the effects of different overlap treatments on the ascending area mean longwave (LWHTR)and shortwave (SWHTR) heating rates. The LWHTRs of different overlap treatments are similar to each other in the middle to higher troposphere, but near the surface the MRO assumption shows remarkable longwave cooling(Fig. 13b) and G2KM and PARA show overestimated longwave heating. This is probably due to the underestimated (overestimated) cloud fraction of the MRO assumption (G2KM and PARA) over these regions (as shown in Fig. 7). For the SWHTR, the MRO assumption underestimates heating around altitudes of 2 and 10 km,whereas G2KM overestimates heating around 10 km height and underestimates heating in the lower troposphere. PARA has a similar SWHTR to G2KM, but the bias in the upper troposphere is remarkably reduced and the bias in the lower troposphere is also reduced to some extent. These changes in the radiative heating rates caused by applying PARA, when coupled with a circulation model, will exert an influence on atmospheric stability in the vertical direction and consequently change the dynamic circulation. These aspects will be explored in future studies.

Fig. 10. Comparisons between LWTOA and SWTOA calculated from generated cloud fields with different cloud overlap treatments (MRO,G2KM, and PARA) and the values calculated directly from the CRM fields (REF) for the tropical areas.

4. Discussion and conclusions

The treatment of cloud overlap plays a crucial part in radiation calculations in GCMs. However, it is difficult to achieve a unified description of this highly variable(both spatially and temporally) property of clouds. By using the simulation of a CRM isolated to the tropical region, a statistical relationship between cloud overlap and convective strength was found and a dynamic representation of Lcf (which determines the extent of cloud overlap)was established. A simple linear regression of Lcf as a function of vertical velocity in the mid-troposphere is capable of partly capturing the cloud overlap dynamic connection and thus remarkably reduces biases in the cloud fraction and radiation fields in tropical convective regions. These regions are where major cloud fraction and radiation biases exist and therefore a reduction in these biases would make a significant contribution to the reduction of the overall bias in the tropics.

Fig. 11. As in Fig. 10, but for (a, b, c) LWSFC and (d, e, f) SWSFC.

Fig. 12. Tropical mean biases in (a) LWTOA, (b) SWTOA, (c) LWSFC, and (d) SWSFC for generated clouds fields with different cloud overlap treatments (MRO, G2KM, and PARA) compared with those for the CRM fields (REF) over all areas (solid fill) and areas of ascent only(hatched fill).

In spite of the improvement in cloud fraction and radiation fields by implementing the convection-dependent overlap treatment, the results rely on the fidelity of the intrinsic physical and dynamic properties of the overlap characteristics also depend on other meteorological conditions in addition to convection, such as wind shear and atmospheric instability (Naud et al.,2008; Di Giuseppe and Tompkins, 2015), even in the tropical deep convection region. Thus the method derived here should not be regarded as a perfect deterministic relationship between cloud overlap and convection,but an empirical, statistical approximation of the contribution of convection to cloud overlap. Other meteorological conditions are virtually ignored in the overlap treatment in this study. The treatment of cloud overlap in extratropical areas was not addressed in this work because the overlap of clouds in such areas relates to large-scale meteorological conditions in a more complex manner than in the tropics. Another aspect of sub-grid cloud structures, i.e., the horizontally inhomogeneous distribution of cloud water, is also highly important in radiation calculations (Barker et al., 1996; Wu and Liang, 2005a);this aspect was excluded in the overlap treatment of this study.

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