Analytic Approximations for Moist Convectively Adjusted Regions

Jia-Yuh Yu and J. David Neelin
J. Atmos. Sci., 54, 1054-1063, 1997.

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© Copyright 1997 by the American Meteorological Society.

Abstract. Solutions are obtained for convective regions in a continuously stratified, linearized primitive equation model using a smoothly posed moist convective adjustment (MCA) parameterization of cumulus convection. In the approximation that 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 (QE) 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 field.

An effective static stability for these convectively constrained motions---the gross moist stability, M---is defined in terms of thermodynamic variables. In time dependent solutions, M determines phase speeds in deep convective regions. In solutions forced by sea surface temperature (SST), M determines the work that must be done 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 follow SST. This picture combines modified versions of mechanisms proposed in simple models by Lindzen and Nigam (1987) and Neelin and Held (1987) within a thermodynamically consistent framework. It also helps interpret models with convergence feedback schemes and the Gill (1980) model, and allows free parameters in these models to be related to basic thermodynamic quantities.

Citation. Yu, J.-Y., and J. D. Neelin, 1997: Analytic approximations for moist convectively adjusted regions. J. Atmos. Sci., 54, 1054-1063.

Acknowledgments. This work was supported jointly by NSF grant ATM-9521389 and NOAA grant NA46GP0244 and also by National Sciences Council in Taiwan under grants NSC85-2111-M-034-002 and NSC85-2111-M-034-003.

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