Based on this catastrophe concept, two different criteria--one for the initiation and the other for the termination of cumulus convection--are introduced into cumulus parameterization. This cumulus parameterization approach differs fundamentally from those approaches based on the Arakawa-Schubert quasi-equilibrium assumption and its relaxed forms in the sense that the former treats the onset of convection as a catastrophe and the latter as a non-catastrophe, also known as supercritical instability. A catastrophe has two separate criteria for transition between quasi-equilibrium states; whereas a non-catastrophe has only one.
Since a catastrophe is a rapid transition, it cannot be modeled by any scheme based on a quasi-equilibrium assumption, which filters out any rapid transient processes. The transient processes of a cloud ensemble, which are filtered out by the Arakawa-Schubert quasi-equilibrium assumption, are preserved in our approach. These transient processes include some of the diurnal cycle of cumulus convection and most of the ability of one cloud cluster to excite inertial gravity waves to trigger another cloud cluster. The Arakawa-Schubert scheme and its relaxed forms allow a good amount of precipitation diurnal cycle but yield a large phase shift due to their non-catastrophe design.
Our approach has been implemented in the NASA/Goddard GCM, taking advantage of the infrastructure of the relaxed Arakawa-Schubert scheme (RAS) but replacing RAS's guiding principle with the catastrophe concept outlined above. Some preliminary results will be shown.