The Use of lce-Liquid Water Potential Temperature as a Thermodynamic Variable In Deep Atmospheric Models

Abstract

Previous studies have shown liquid water potential temperature to be an inappropriate choice for a thermodynamic variable in a deep cumulus convection model. In this study, an alternate form of this variable called ice-liquid water potential temperature (theta-il) is derived. Errors resulting from approximations made are discussed, and an empirical form of the theta-il equation is introduced which eliminates much of this error. Potential temperature lapse rates determined in saturated updrafts and unsaturated downdrafts by various theta-il approximations, an equivalent potential temperature approximation and a conventional irreversible moist thermodynamic approximation are then compared to the potential temperature lapse rate determined from a rigorously derived reversible thermodynamic energy equation. These approximations are then extended to a precipitating system where comparisons are again made. It is found that the errors using the empirical form of the theta-il equation are comparable to those made using conventional irreversible moist thermodynamic approximations. The advantages of using theta-il as an alternative to theta in deep convection and second-order closure models also are discussed.