Understanding Albrecht's model of trade cumulus cloud fields

Abstract

Using Albrecht's model, approximate analytical formulas are found for the dependence of the steady-state mean thermodynamic structure of a partly cloudy convective marine boundary layer on external parameters. In the simplest formulation discussed here, precipitation is ignored and simple parameterizations for radiative cooling and fractional cloudiness are used. The analytical approximation agrees well with exact steady-state numerical solutions of Albrecht's model. The cloud-base and trade-inversion heights are not strongly dependent on adjustable parameters within the cloud model and are largely determined by bulk balances of radiative fluxes, surface fluxes, and subsidence. The cloud-layer sounding and the cloud fraction are affected by external parameters only through changes in the cloud-base latent heat flux and the cloud thickness. The cloud fraction is quite sensitive to two tunable internal constants in the cloud model that affect rates of cloud entrainment and detrainment, respectively. The sensitivity of cloud fraction to SST and mean subsidence is explored for two choices of these constants and the effect of unsteadiness due to downstream changes in external conditions are considered. -from Author