Direct entrainment and detrainment rate distributions of individual shallow cumulus clouds in an LES

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 dθ_ρ/dz at that level, while fractional detrainment is best predicted by the mean vertical velocity w and the critical mixing fraction χ_c. Fractional entrainment and detrainment rates are relatively insensitive to cloud core horizontal area, and the perimeter of horizontal cloud core sections display an a^0.73 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, dθ_ρ/dz and δ(w, χ_c) 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.