Testing a Cumulus Parameterization With a Cumulus Ensemble Model in Weak Temperature Gradient Mode

This paper prototypes a method for calibrating a cumulus parameterization against a cumulus ensemble model. The key to this technique is to run the cumulus model and the parameterization in identical test cells which provide forcing typical of that seen over tropical oceans. In particular, the mean temperature pro le is relaxed to a reference pro le which is assumed to be characteristic of the environment of the convection. This is done by calculating the mean vertical velocity needed to balance heating due to convection, latent heat release, and radiation with adiabatic cooling. This weak temperature gradient (WTG) vertical velocity pro le is then used to advect moisture vertically and, via mass continuity, through the sides of the test cell, entraining reference pro le air as needed. As an example, a toy cumulus parameterization used previously is altered to reproduce the dependence of rainfall rate on surface wind speed shown by the cumulus ensemble model. This alteration greatly modi es the behavior of simulated large-scale disturbances in an aquaplanet equatorial beta-plane model. In particular, increasing the slope of the rainfall rate-wind speed curve results in the development of much more synoptic-scale variance.