A Cumulus Parameterization Scheme Utilizing a One-Dimensional Cloud Model

Abstract

A method for parameterizing the effects of deep cumulus clouds on the larger scale thermodynamic and moisture fields in numerical models is proposed. Rigorous derivations of the effect of cumulus clouds on their environment are derived for two definitions of the large-scale averaged variables. In the first, the classical Reynolds averaging method is used and the averaged variables vary continuously over the domain. In the second method, which has been popular in the derivation of cumulus parameterization schemes, the averages are defined by dividing an incremental area of the domain (usually the mesh aim) into a region occupied by convection and the remainder of the region which is free of convection. In this method, the large-scale averages assume discrete values over each incremental area. The differences between the large-scale equations that result from these two methods and some possible difficulties that may be encountered when the averaging interval approaches the aim of the convective clo... Abstract A method for parameterizing the effects of deep cumulus clouds on the larger scale thermodynamic and moisture fields in numerical models is proposed. Rigorous derivations of the effect of cumulus clouds on their environment are derived for two definitions of the large-scale averaged variables. In the first, the classical Reynolds averaging method is used and the averaged variables vary continuously over the domain. In the second method, which has been popular in the derivation of cumulus parameterization schemes, the averages are defined by dividing an incremental area of the domain (usually the mesh aim) into a region occupied by convection and the remainder of the region which is free of convection. In this method, the large-scale averages assume discrete values over each incremental area. The differences between the large-scale equations that result from these two methods and some possible difficulties that may be encountered when the averaging interval approaches the aim of the convective clo...