Understanding Albrecht's Model of Trade Cumulus Cloud Fields

Christopher S. Bretherton Applied Mathematics Department, University of Washington, Seattle, Washington

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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. Our goals are 1) to understand the physical factors that influence the vertical profiles of mean relative humidity, temperature, and fractional cloudiness within the cloud layer using the model to gain insight into the strato-cumulus-trade cumulus transition in the subtropical trade wind regime, and 2) to understand the sensitivity of the model to tunable internal parameters. The model, a prototype for bulk models of trade cumulus boundary layer, consists of a well-mixed subcloud layer topped by a cumulus layer and a sharp trade inversion. 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 in a manner similar to the more empirical model of Betts and Ridgway. 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. For most choices of SST and upper-air conditions, these constants can be tuned to produce either a mainly saturated (stratocumulus-like) cloud layer or a trade cumulus-like layer with no environmental saturation. 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.

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. Our goals are 1) to understand the physical factors that influence the vertical profiles of mean relative humidity, temperature, and fractional cloudiness within the cloud layer using the model to gain insight into the strato-cumulus-trade cumulus transition in the subtropical trade wind regime, and 2) to understand the sensitivity of the model to tunable internal parameters. The model, a prototype for bulk models of trade cumulus boundary layer, consists of a well-mixed subcloud layer topped by a cumulus layer and a sharp trade inversion. 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 in a manner similar to the more empirical model of Betts and Ridgway. 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. For most choices of SST and upper-air conditions, these constants can be tuned to produce either a mainly saturated (stratocumulus-like) cloud layer or a trade cumulus-like layer with no environmental saturation. 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.

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