Cumulus Parameterization and CISK

Abstract

Arakawa's recent parameterization of the effects of a cumulus ensemble on the large-scale environment is applied to the problem of conditional instability of the second kind (CISK). In particular, Charney's linear, two-level, line-symmetry CISK model of the ITCZ is re-examined using a simplified non-entraining cloud version of the Arakawa scheme. It is found that the growth rate is maximum, in fact infinite, at some reasonable mesoscale rather than at cumulus scale as is characteristic of Charney's solution. A more accurate semi-analytic model of CISK is considered and it is found that a separable, line-symmetric CISK solution is always possible under very general conditions. In both the two-level and semi-analytic models of CISK, it is proved that a necessary condition for the existence of a growing solution is that the mass flux into the clouds exceeds the Ekman pumping out of the boundary layer, or equivalently, that the air between the clouds must subside and therefore heat the environment by adiabatic compression.