An Economical Analytical Equation for the Integrated Vertical Overlap of Cumulus and Stratus

Abstract

AbstractBy extending the previously proposed heuristic parameterization, the author derived an analytical equation computing the overlap areas between the precipitation (or radiation) areas and the cloud areas in a cloud system consisting of cumulus and stratus. The new analytical equation is accurate and much more efficient than the previous heuristic equation, which suffers from the truncation error in association with the digitalization of the overlap areas. Global test simulations with the new analytical formula in an offline mode showed that the maximum cumulus overlap simulates more surface precipitation flux than the random cumulus overlap. On the other hand, the maximum stratus overlap simulates less surface precipitation flux than random stratus overlap, which is due to the increase in the evaporation rate of convective precipitation from the random to maximum stratus overlap. The independent precipitation approximation (IPA) marginally decreases the surface precipitation flux, implying that IPA works well with other parameterizations. In contrast to the net production rate of precipitation and surface precipitation flux that increase when the cumulus and stratus are maximally and randomly overlapped, respectively, the global mean net radiative cooling and longwave cloud radiative forcing (LWCF) increase when the cumulus and stratus are randomly overlapped. On the global average, the vertical cloud overlap exerts larger impacts on the precipitation flux than on the radiation flux. The radiation scheme taking the subgrid variability of water vapor between the cloud and clear portions into account substantially increases the global mean LWCF in tropical deep convection and midlatitude storm track regions.