An equilibrium model for marine shallow cumulus convection

A new variant of the w* closure for the shallow cumulus mass flux is presented which retains the fractional area of the active updrafts in its formulation. Accordingly, the mass flux becomes dependent on humidity conditions, which represents a stabilizing feedback mechanism. As a consequence, the simplified budget equation for boundary layer humidity is analytically solvable. This simple equilibrium model explains the robustness of the mass flux of shallow cumulus fields, as typically observed in large-eddy simulations, observations and general circulation models. The model impacts on climatology are further evaluated by embedding it in an intermediate-complexity tropical climate model.