Catastrophe-Concept-Based Cumulus Parameterization: Correction of Systematic Errors in the Precipitation Diurnal Cycle over Land in a GCM

Abstract

Abstract The onset of cumulus convection in a grid column is a catastrophe, also known as a subcritical instability. Accordingly, in designing a cumulus parameterization scheme the onset of cumulus convection requires that a parameter crosses a critical value and the termination of cumulus convection requires that the same or a different parameter crosses a different critical value. Once begun, cumulus convection continues to exist, regardless of whether the onset criterion is still met, until the termination criterion is met. Also, the intensity of cumulus precipitation is related to how far the state is from the termination, not the onset, criterion. The cumulus parameterization schemes currently in use in GCMs, however, treat the onset of cumulus convection as a supercritical instability; namely, convection is turned on when a parameter exceeds a critical value and is turned off when the same parameter falls below the same critical value. Also, the intensity of cumulus precipitation is related to how far this critical value has been exceeded. Among the adverse consequences of the supercritical-instability-concept-based cumulus parameterization schemes are that over relatively flat land the precipitation peak occurs around noon—4–6 h too soon—and that the amplitude of the precipitation diurnal cycle is too weak. Based on the above-mentioned concept, a new cumulus parameterization scheme was designed by taking advantage of the existing infrastructure of the relaxed Arakawa–Schubert scheme (RAS), but replacing RAS's guiding principle with the catastrophe concept. Test results using NASA's Goddard Earth Observing System GCM, version 5 (GEOS-5), show dramatic improvement in the phase and amplitude of the precipitation diurnal cycle over relatively flat land.