Analytic Approximations for Moist Convectively Adjusted Regions

Solutions are obtained for convective regions in a continuously stratified, linearized primitive equation model using a smoothly posed moist convective adjustment parameterization of cumulus convection. In the approximation in which the convective adjustment time is fast compared to other processes, the vertical structure of the temperature field is constrained to be close to the quasi-equilibrium structure determined by the convective scheme. This in turn constrains the vertical structure of the baroclinic pressure gradients and velocity field. Analytic solutions result for vertical structures, while the horizontal and time dependence is governed by equations akin to shallow water equations. These consist of equations linking baroclinic velocities and pressure gradients, plus a moist static energy equation governing thermodynamics. This system holds for basic states that are slowly varying in space, for regions where deep convection happens frequently enough to constrain the temperature