Abstract
Kelvin wave-CISK (Conditional Instability of the Second Kind) is studied as a possible explanation for the intraseasonal oscillations of the equatorial troposphere. The small-amplitude approximation will be made in part I of this paper. The governing equations of the small-amplitude approximation are nonlinear, however, because of the cumulus parametrization scheme used. It was found that: (1) Kelvin waves when coupled with cumulus healing are never unstable if the cumulus heating rate is smaller than the adiabatic cooling rate; (2) the solution is not equatorially confined if the cumulus heating rate is larger than the adiabatic cooling rate; (3) since a Kelvin wave is not a dispersive wave, the method of characteristics is used to solve the governing equations when the cumulus heating rate is smaller than the adiabatic cooling rate. It was found that the cumulus parametrization scheme often used in theoretical studies of CISK is incompatible with the so called 'jump condition' of the generalized solutions often required by hyperbolic systems of equations.
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