This paper prototypes a method for calibrating a cumulus parametrization against a cumulus ensemble model. The key to this technique is to run the cumulus model and the parametrization in identical ‘test cells’ that provide forcing typical of that seen over tropical oceans. In particular, the mean temperature profile is relaxed to a reference profile that 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’ vertical-velocity profile is then used to advect moisture vertically and, via mass continuity, through the sides of the test cell, entraining reference-profile air as needed.
As an example, a toy cumulus parametrization used previously is altered to reproduce the dependence of rainfall rate on surface wind speed shown by the cumulus ensemble model. This alteration greatly changes the behaviour of simulated large-scale disturbances in an aquaplanet equatorial beta-plane model. In particular, increasing the slope of the curve of rainfall rate against wind speed results in the development of much greater synoptic-scale variance. Copyright © 2007 Royal Meteorological Society