Abstract
Abstract. Probability distribution functions of shallow cumulus cloud core entrainment and detrainment rates are calculated using 4362 individual cumulus clouds isolated from LES (large eddy simulation) using a cloud tracking algorithm. Calculation of the mutual information between fractional entrainment/detrainment and a variety of mean cloud core properties suggests that fractional entrainment rate is best predicted by the mean cloud buoyancy B and the environmental buoyancy lapse rate dθρ/dz at that level, while fractional detrainment is best predicted by the mean vertical velocity w and the critical mixing fraction χc. Fractional entrainment and detrainment rates are relatively insensitive to cloud core horizontal area, and the perimeter of horizontal cloud core sections display an a0.73 dependence. This implies that cloud core mass entrainment flux E is proportional to cloud core cross-sectional area instead of cloud core surface area, as is generally assumed. Empirical best-fit relations for ε(B, dθρ/dz and δ(w, χc) are found for both individual shallow cumulus clouds and cloud ensembles. It is found that clouds with high buoyancy in strong stratification experience low entrainment rates, while clouds with high vertical velocities and critical mixing fractions experience low detrainment rates.
Highlights
Introduction condensed liquidwateOr.ieTnheceentrainment and detrainment rates of a cloud at a given height can be formally defined as (Siebesma, 1998)Shallow cumulus clouds, sometimes referred to as tradewind cumulus, occur in the tropics as a transitional state between stratus decks, which occur in strongly stratified downwelling regions, and deep cumulus clouds, which occur in weakly stratified upwelling regions
Using measures of the mutual information shared between cloud properties and the fractional entrainment and detrainment rates, we develop a parameterization to predict the mean fractional entrainment and detrainment rates of individual shallow cumulus clouds, and extend this to the prediction of the bulk entrainment and detrainment rates of the cloud ensemble
65 303 samples remain for the Barbados Oceanographic and Meteorological Experiment (BOMEX) output and 87 327 samples remain for the Atmospheric Radiation Measurement study (ARM) output
Summary
All LES calculations in this paper were made using the System for Atmospheric Modelling (SAM version 6.8.2; Khairoutdinov and Randall, 2003). The direct entrainment/detrainment estimation method of Dawe and Austin (2011a) was used to calculate vertical profiles of and δ These calculations were done by horizontally summing the instantaneous mass entrainment E and detrainment D over a region including the cloud core plus all points immediately outside the cloud core. The summed E and D values are divided by the cloud core vertical mass flux M calculated using horizontal cloud core areas calculated by the tetrahedral surface interpolation algorithm to generate self-consistent and δ values (Fig. 1) This results in 147 060 samples of cloud core properties at various heights and times for the BOMEX output, and 134 949 samples for the ARM output. 65 303 samples remain for the BOMEX output and 87 327 samples remain for the ARM output
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