The Arakawa-Schubert Parameterization

Abstract

This review paper begins with a brief statement of the cumulus parameterization problem, and a quick summary of the approach of Arakawa and Schubert (AS). This includes a discussion of the large-scale budget equations for dry static energy and water vapor, which include terms representing convective fluxes, and the condensation and evaporation that occur in convective clouds; and a summary of the simple cumulus cloud model proposed by AS, which features multiple ``cloud types.{''} This is followed by a discussion of the interactions between the convective clouds and the planetary boundary layer. We then turn to three important topics on which AS had little or nothing to say, namely the effects of convective downdrafts, a parameterization of convection originating above the PBL top, and a theory of the interactions of convection with stratiform clouds. The quasi-equilibrium closure proposed by AS is briefly summarized here but is discussed in detail in a companion paper in this volume. Finally, we discuss some variants of the AS parameterization which have appeared in recent years.