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The interaction between tropical convective heating and thermally forced circulation is investigated using a global dry primitive-equation model with the parameterization of wave-conditional instability of the second kind (CISK). It is demonstrated that deep convective heating can hardly sustain itself through the moisture convergence at low levels regardless of the fraction of immediate consumption of converged moisture. In contrast, when the fraction is large, shallow convective heating and its forced circulation exhibit preferred growth of small scales. As the “CISK catastrophe” mainly comes from the instantaneous characters of moisture–convection feedback in the conventional wave-CISK, a noninstantaneous wave-CISK is proposed, which highlights the accumulation–consumption (AC) time scale for the convective heating accumulation and/or the converged moisture consumption. In the new wave-CISK, once moisture is converged, the release of latent heat takes place gradually within an AC time scale. In this sense, convective heating is not only related to the instantaneous moisture convergence at the current time, but also to that which occurred in the past period of the AC time scale. The noninstantaneous wave-CISK could guarantee the occurrence of convective heating and/or moisture convergence at larger scales, and then favor the growth of long waves, and thus solve the problem of CISK catastrophe. With the new wave-CISK and AC time scale of 2 days, the simulated convective heating-driven system bears a large similarity to that of the observed convectively coupled Kelvin wave.

Noninstantaneous Wave-CISK for the Interaction between Convective Heating and Low-Level Moisture Convergence in the Tropics