Convective inhibition, subgrid-scale triggering energy, and stratiform instability in a toy tropical wave model

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 m odes, excited by convective (one-signed) and stratiform (two-signed) beatin g processes in tropical deep convection. Separate treatments of deep and sh allow convection ale justified by observations that deep convection is more variable. Deep convection intensity is assumed to be modulated by convecti ve available potential energy (CAPE), while occurence frequency is modulate d by the ratio of convective inhibition (CIN) to "triggering energy" It: a scalar representing the intensity of subgrid-scale fluctuations. Deep conve ctive downdrafts cool and dry the boundary layer but also increase K. Varia tions of Ii make the relationship between convection and thermodynamic vari ables (CAPE, GIN, theta(e)) nonunique and amplify the deep convective respo nse to temperature waves of small (similar to 1 degrees C) amplitude. For a parameter set in which CAPE varions control convection, moist convect ive damping destroys all variability. When CIN/K variations have dominant i mportance (the "inhibition-controlled" regime), a mechanism termed "stratif orm instability" generates large-scale waves. This mechanism involves lower tropospheric cooling by stratiform precipitation, which preferentially occ urs where the already cool lower troposphere favors deep convection, via sm aller CIM. Stratiform instability has two subregimes, based on the relative importance of the two opposite effects of downdrafts: When boundary layer theta(e), reduction (a local negative feedback) is stronger, small-scale wa ves with frequency based on the boundary layer recovery time are preferred. When the K-generation effect (positive feedback) is stronger, very large s cales (low wavenumbers of the domain) develop. A mixture of these scales oc curs for parameter choices based on observations. Model waves resemble obse rved waves, with a phase speed similar to 20 m s(-1) (near the dry wave spe ed of the second internal mode), and a "cold boomerang vertical temperature s structure. Although ii exhibits "quasi-equilibrium'' with other convection variables ( correlations > 0.99), replacing the prognostic K equation with diagnostic e quations based on these relationships can put the model into wildly differe nt regimes, if small time lags indicative of causality are distorted. The r esponse of model convection to climatological spatial anomalies of theta(e) , (proxy For SST) and K (proxy For orographic and coastal triggering) is co nsidered. Higher SST tends broadly to favor convection under either CAPE-co ntrolled or inhibition-controlled regimes, but there: are dynamical embelli shments in the inhibition-controlled regime. The Kelvin wave seems to be th e preferred structure when the model is run on a uniform equatorial beta pl ane.