A study of conditional instability of the second kind /CISK/

The theory of interaction between the cumulus clouds and the large-scale field proposed by Arakawa and Schubert (1974) is used to reexamine the CISK mechanism. After a qualitative discussion, a quantitative study is presented, using a three-level approach. The difference between the cases with conditional and unconditional heating formulations are discussed, and growth rate is treated as an eigenvalue problem. To confirm the results obtained and to extend the study to a case where the basic thermodynamic structure varies in the horizontal direction, the CISK mechanism is analyzed by an initial-value-problem approach. One of the findings is that the cumulus heating formulation of Arakawa and Schubert, through its scale dependence, is an improvement over previous CISK studies.