Estimations of Mass Fluxes for Cumulus Parameterizations from High-Resolution Spatial Data

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Abstract
The core of the mass flux formulation, on which the majority of the current cumulus parameterizations are based, is to transport physical variables by the so-called mass flux for individual physical components, such as convective updrafts, downdrafts, and environment. These parameterizations use horizontal means over the subdomains occupied by these physical components to define the mass fluxes and transported variables. However, evaluations of the mass flux formulation against high-resolution spatial data obtained from explicit numerical models reveal that it substantially underestimates vertical transport of heat, moisture, and momentum by deep convection. The present paper proposes an alternative approach, in which the effective values weighted toward extreme values are used both for the mass flux and the transported variable to obtain an accurate estimate of vertical transport. Statistically, the distribution of convective variables is so widely distributed within individual subdomains that t...