| Appendix A. Brief review of wave-CISK | [prev] [index] [next] |
In the numerical experiments in this study, there appears a precipitation structure that propagates eastward along the equator coherently, especially in the experiment with Kuo scheme. In this appendix, we will review the theory of equatorial wave-CISK, which may explain preferred conditions of appearance and some characteristics of this eastward propagating precipitation structure.
The concept of "wave-CISK" is developed by Hayashi(1970) as an extension of "CISK" (Conditional Instability of the Second Kind), which is a theory proposed by Charney and Eliassen (1964) to explain the growth of tropical cyclones, i.e., vortical disturbances, to the growth of propagating large-scale wavy disturbances in the equatorial region. The most loose definition of CISK, including wave-CISK, is development of large-scale atmospheric waves or vortices through cooperative interaction with cloud activity. However, it is basically a conceptual model. The definitions of cloud activity and large-scale disturbances, which are the subjects that interact with each other, are not trivial in the first place. There is no definite way of model verification by the use of data from meteorological observations or numerical simulations, either. And hence, meteorologists in recent days do not seem to place great appreciation for this framework. However, we are thinking of CISK or wave-CISK as an effective conceptual model, even nowadays, to obtain a rough picture about the behaviors of precipitation activity. CISK or wave-CISK seems to work as a worthy concept, at least to the extent as shown in this study, for description of the solutions obtained by a simplified GCM In the followings, we will summarize the basics of wave-CISK briefly.
Here, we review the mathematical structure of the propagating instability returning back to the original formulation of Hayashi (1970), in which the heating by cloud activity is assumed to be proportional to the upward motion in the low level atmosphere. We simplify the vertical structure of the atmosphere and adopt a rigid rid top boundary instead of an open boundary at the tropopause. The reason for taking up this particular formulation is that the behavior of Kuo scheme, which is one of the cumulus parameterizations used in this study, can be approximated by this simple formulation, as will be explained shortly. In addition, we suspect that the underlying mathematical structure that results in the appearance of propagating instability might be common in the more sophisticated or generalized versions of wave-CISK, although existence of the rigid rid top boundary might be too favorable for the appearance of growing modes as is critisized by Lindzen (2003).
Behind the term Conditional Instability of the SECOND Kind, there is a concept of CIFK (Conditional Instability of the First Kind). The vertical temperature structure of the earth's atmosphere is usually "conditionally unstable", where the vertical displacement of air parcel without condensation (dry adiabatic process) is stable, while that with condensation (moist adiabatic process) is unstable. The convective instability that develops in this conditionally unstable atmosphere has been simply called "conditional instability", and, after the development of CISK concept, the adjective "first" is added when we prefer to distinct it from CISK.
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