Abstract

The entrainment and detrainment rates are important quantities characterizing airmass exchange between clouds and the environment. One of the challenges in calculating the rates is the need to know the velocity vector of the cloud interface in relation to that of the cloud-free air; however, the interface is not well resolved in most cloud model simulations and so the precise value of the vector is not known. Here a new method is described to approximately calculate mass fluxes across the cloud surface in well-resolved simulations of cumulus convection. The method does away with the need to calculate a cloud interface velocity and instead uses gradients of a defined cloud scalar across the cloud interface. As a result, the entrainment and detrainment rates are expressed as an integration over a small region around the cloud interface. The integrand is composed of the total derivative of the cloud scalar. The new method is applied to large-eddy simulations (LES) of a shallow cumulus case and a deep convection case. Compared to a previous method, the approach described here gives 1.5–2 times smaller exchange rates and shows less noise. The smaller exchange rates are explained as the result of differences in how the two methods correct for the advective contribution to variations of cloud volume. Derived two-dimensional distributions of the exchange rates agree well for both methods. Spatial correlation coefficients are about 0.69–0.88 for entrainment and 0.55–0.78 for detrainment.

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