An Analysis of Diagnostic Cloud Mass Flux Models

Abstract

The use of the Arakawa-Schubert cloud model to diagnose cloud mass fluxes from the large-scale budgets is becoming an increasingly popular technique in observational tropical meteorology. The results of such studies are now being widely quoted in discussions of convective parameterization and of convective scale-larger scale interactions. In this paper a concise summary is presented of the technique's methodology and a comparison is made of solutions obtained from different versions of the model (i.e., the basic model, the model with downdrafts, the model with lateral detrainment, etc.) A comparison also is made of solutions obtained on different tropical data sets (cloud clusters from the tropical Northwest Pacific and convective systems from the GARP Atlantic Tropical Experiment). A simple algebraic analysis on the model equations yields some interesting relationships between the mass flux distribution and the large-scale parameters. In particular: 1) Once QR h, h?* are specified, the deep cumulonimbus mass flux is related only to the upper level large-scale vertical velocity. 2) The lack of convection with tops in the middle troposphere is a result of the shape of the tropical vertical profile of h. The mid-tropospheric minimum means that ?c(hc?h) for deep clouds is of the same order at middle levels as w??h??. 3) For a given amount of upper level divergence and deep convection, the shallow convective activity is inversely related to the magnitude of the low-level convergence. 4) For the diagnostic cloud model to have a solution, strong low-level convergence requires small low-level values of moist static energy. These relationships follow mathematically from the insertion of the Arakawa-Schubert cloud model into the large-scale equations, but they are not obvious from the initial formulation of the model. The validity of the original model assumptions is dependent on the validity of these model input-output relationships. The paper also includes some discussion of the physical interpretation of the large-scale input parameters used in the technique.