A toy model of large-scale deep convection variations is constructed around a radiative-convective equilibrium climate, with an observed mean sounding as its thermodynamic basic state.

Vertical structure is truncated at two modes, excited by convective (one-signed) and stratiform (two-signed) heating processes in tropical deep convection. Separate treatments of deep and shallow convection are justified by observations that deep convection is more variable. Deep convection intensity is assumed to be modulated by CAPE, while occurrence frequency is modulated by the ratio of convective inhibition (CIN) to "triggering energy" K, a scalar representing the intensity of subgridscale fluctuations. Deep convective downdrafts cool and dry the boundary layer, but also increase K. Variations of K make the relationship between convection and thermodynamic variables (CAPE, CIN, qe) nonunique, and amplify the deep convective response to temperature waves of small (~ 1C) amplitude.

For a parameter set in which CAPE variations control convection, moist convective damping destroys all variability. When CIN/K variations have dominant importance (the "inhibition-controlled" regime), a mechanism termed "stratiform instability" generates large-scale waves. This mechanism involves lower-tropospheric cooling by stratiform precipitation, which preferentially occurs where the already-cool lower troposphere favors deep convection, via smaller CIN. Stratiform instability has two sub-regimes, based on the relative importance of the 2 opposite effects of downdrafts: When boundary-layer qe reduction (a local negative feedback) is stronger, small-scale waves with frequency based on the boundary-layer recovery time are preferred. When the K-generation effect (positive feedback) is stronger, very large scales (low wavenumbers of the domain) develop. A mixture of these scales occurs for parameter choices based on observations. Model waves resemble observed waves, with a phase speed ~20 ms-1 (near the dry wave speed of the second internal mode), and a "cold boomerang" vertical temperature structure.

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Convective inhibition, subgridscale triggering energy, and stratiform instability in a toy tropical wave model.

ABSTRACT