Stratocumulus-capped mixed layers derived from a three-dimensional model

Abstract

Results of a three-dimensional numerical model are analysed in a study of turbulence and entrainment within mixed layers containing stratocumulus with or without parameterized cloud-top radiative cooling. The model eliminates most of the assumptions invoked in theories of cloud-capped mixed layers, but suffers disadvantages which include poor resolution and large truncation errors in and above the capping inversion.For relatively thick mixed layers with relatively thick capping inversions, the cloud-top radiative cooling is found to be lodged mostly within the capping inversion when the cooling is confined locally to the upper 50 m or less of the cloud. It does not then contribute substantially towards increased buoyancy flux and turbulence within the well mixed layer just below.The optimal means of correlating the entrainment rate, or mixed-layer growth rate, for mixed layers of variable amounts of stratocumulus is found to be through functional dependence upon an overall jump Richardson number, utilizing as scaling velocity the standard deviation of vertical velocity existing at the top of the mixed layer (near the center of the capping inversion). This velocity is found to be a fraction of the generalized convective velocity for the mixed layer as a whole which is greater for cloud-capped mixed layers than for clear mixed layers.

Outlook for Research on Subtropical Marine Stratification Clouds

“…Randall (1980a) derived a stability criterion for this entrainment instability and discussed its possible role in determining the distribution of cloudiness over the subtropical oceans. Deardorff (1980b) presented results from a highresolution three-dimensional numerical model, which indicate that the onset of the instability is accompanied by rapid entrainment, a significant reduction in cloudiness, and a decrease in the effectiveness of turbulent mixing in maintaining well-mixed in-cloud conditions. Moeng and Arakawa (1980) and Chen and Cotton (1983) obtained similar results using higher-order-closure models.…”

“…Numerical simulations of stratus and stratocumulus systems have been performed with simple mixed-layer models (Lilly, 1968), higher-order closure models (Moeng and Arakawa, 1980;Chen and Cotton, 1983), large-eddy models (Deardorff, 1980a;Sommeria, 1976), and general circulation models (Suarez et al, 1983;Randall, 1983). As a result of these studies, several key theoretical issues have emerged, and a carefully designed observational program is needed to resolve them.…”

“…The potential importance of the thickness of the layer of cloud-top radiative cooling for the dynamics of the marine layer, and particularly for determining the entrainment rate, has been discussed by Deardorff (1976), Kahn and Businger (1979), Schubert et al (1979), Randall (1980b), Lilly and Schubert (1980), and Fravalo et al (1980). The finite area-averaged thickness of the cooling layer arises from the finite transmissivity of the cloud, and also from the presence of small-scale fluctuations of the cloud-top height due to turreting and waves.…”

“…Beginning with the classic paper by Lilly (1968), researchers have used one-dimensional (Schubert, 1976;Chai and Telford, 1983), two-dimensional (Moeng and Arakawa, 1982;Kraus and Leslie, 1982), and three-dimensional (Deardorff, 1980a) models to study the evolution and dynamics of these systems. Suarez et al (1983) have simulated the global distribution of low stratiform clouds with a general circulation model.…”

Pollutant transport in a Convective Boundary Layer with LES

“…(1)- (5) are related to the resolved-scale field through the eddy diffusivity coefficients. In this LES version, these coefficients are parameterized using the modified nonlinear eddy viscosity formulation proposed by Sullivan et al (1994) and the Turbulent Kinetic Energy (TKE) in the subgrid-scale is estimated from the prognostic equation proposed by Deardorff (1980).…”