Joint distributions of potential vorticity and inert trace constituent in CCM2 and UW θ‐σ model simulations

Abstract

This letter describes an experiment that examines the ability of the University of Wisconsin (UW) hybrid isentropic‐sigma (θ‐σ) and sigma (σ) coordinate models and the NCAR Community Climate Model 2 (CCM2) to transport and conserve the joint distributions of isentropic potential vorticity (Pθ) and a source‐free inert trace constituent related to the initial distribution of Pθ called proxy ozone (O3), during 10‐day isentropic integrations. Under the idealized conditions of this experiment, the governing equations for the atmospheric continuum require that the initial joint distribution of Pθ and O3 be conserved, thereby establishing a test of model accuracy from statistical comparisons of paired values of O3 and Pθ. Any decrease in the initial correlation of unity of Pθ and O3 after integration is an objective measure of a model's skill. Results show that correlation coefficients for the UW θ‐σ model remain higher than those from CCM2 and the UW σ model, demonstrating an inherent advantage in the simulation of trace constituent transport relative to dynamical processes in isentropic versus sigma coordinate models.