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 (?u) is derived. Errors resulting from approximations made are discussed, and an empirical form of the ?u equation is introduced which eliminates much of this error. Potential temperature lapse rates determined in saturated updrafts and unsaturated downdrafts by various ?u 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 ?u equation are comparable to those made using conventional irreversible moist thermodynamic approximations. The advantages of using ?u as an alternative to ? in deep convection and second-order closure models also are discussed.