UNDERSTANDING ALBRECHT MODEL OF TRADE CUMULUS CLOUD FIELDS

Using Albrecht's model, approximate analytical formulas are found for the dependence of the steady-state mean thermodynamic structure of a p artly cloudy convective marine boundary layer on external parameters. Our goals are 1) to understand the physical factors that influence the vertical profiles of mean relative humidity, temperature, and fractio nal cloudiness within the cloud layer using the model to gain insight into the stratocumulus-trade cumulus transition in the subtropical tra de wind regime, and 2) to understand the sensitivity of the model to t unable internal parameters. The model, a prototype for bulk models of trade cumulus boundary layers, consists of a well-mixed subcloud layer topped by a cumulus layer and a sharp trade inversion. In the simples t formulation discussed here, precipitation is ignored and simple para meterizations for radiative cooling and fractional cloudiness are used . The analytical approximation agrees well with exact steady-state num erical solutions of Albrecht's model. The cloud-base and trade-inversi on heights are not strongly dependent on adjustable parameters within the cloud model and are largely determined by bulk balances of radiati ve fluxes, surface fluxes, and subsidence in a manner similar to the m ore empirical model of Betts and Ridgway. The cloud-layer sounding and the cloud fraction are affected by external parameters only through c hanges in the cloud-base latent heat flux and the cloud thickness. The cloud fraction is quite sensitive to two tunable internal constants i n the cloud model that affect rates of cloud entrainment and detrainme nt, respectively. For most choices of SST and upper-air conditions, th ese constants can be tuned to produce either a mainly saturated (strat ocumulus-like) cloud layer or a trade cumulus-like layer with no envir onmental saturation. The sensitivity of cloud fraction to SST and mean subsidence is explored for two choices of these constants and the eff ect of unsteadiness due to downstream changes in external conditions a re considered.