ANALYTIC APPROXIMATIONS FOR MOIST CONVECTIVELY ADJUSTED REGIONS

Solutions are obtained for convective regions in a continuously strati fied, 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 i s constrained to be close to the quasi-equilibrium structure determine d by the convective scheme. This in turn constrains the vertical struc ture of the baroclinic pressure gradients and velocity field. Analytic solutions result for vertical structures, while the horizontal and ti me dependence is governed by equations akin to shallow water equations . These consist of equations linking baroclinic velocities and pressur e gradients, plus a moist static energy equation governing thermodynam ics. This system holds for basic states that are slowly varying in spa ce, for regions where deep convection happens frequently enough to con strain the temperature field. An effective static stability for these convectively constrained motions, the gross moist stability M, is defi ned in terms of thermodynamic variables. In time-dependent solutions, M determines phase speeds in deep convective regions. In solutions for ced by sea surface temperature, M determines the work that must be don e by vertical motion, which must in turn be balanced by surface fluxes . Surface fluxes tend to draw boundary layer temperature and moisture toward values determined by SST, while the convection translates these into deep baroclinic temperature and pressure gradients. The balance between surface fluxes and the effect of the gross moist stability on vertical motion determines how closely boundary layer enthalpy can fol low SST. This picture combines modified versions of mechanisms propose d in simple models by Lindzen and Nigam, and Neelin and Held within a thermodynamically consistent framework. It also helps interpret models with convergence feedback schemes and the Gill model, and allows free parameters in these models to be related to basic thermodynamic quant ities.