Equations (8)-(9) and (12)-(13) are the main prognostic equations for QTCM1.0. Although they need only be solved in x,y and t, the resulting flow solutions are three dimensional. The conceptual point of view implied by these equations differs from the traditional description of diabatic heating driving circulation, which feeds back onto the heating via moisture convergence. In regions in convective quasi-equilibrium, the system (8), (9) and (10) is closed. The moist static energy budget (10) governs the thermodynamics of convective regions, with (12) mainly serving to establish how far the large scale dynamics can push the CAPE out of quasi-equilibrium and how big the heating is. If is large compared to other time scales in the system, (12) is essentially diagnostic for the heating. As one passes from convective to non-convective regions (12) takes over; in between gradually larger departures from quasi-equilibrium occur. Convective heating and precipitation are by-products of a moist dynamics that evolves subject to convective constraints on baroclinic pressure gradients in convective regions. The gross moist stability in (10) thus determines the phase speed of the Madden-Julian oscillation, the magnitude of the circulation response to SST anomalies, and the radius of deformation for motions in deep convective regions. Yu et al (1997) discuss the climatology of the gross moist stability, estimated from radiosonde data and ECMWF analyses.
Over oceans, the net heating into the atmospheric column, in (10), has terms in E, , and longwave fluxes that act as forcing by SST and terms that depend on temperature and moisture that act as a damping to perturbations. Over land, when (14) is near equilibrium, the surface flux vanishes, so the net flux input on the rhs of (10) becomes
Since the outgoing longwave radiation depends on the atmospheric state, the solar input is clearly identified as the forcing of the system, but with important modifications by cloud albedo feedbacks in . Diagnostics based on the moist static energy budget thus have an attractive simplicity, especially over land, in convective regions.
The progression from the simplest QTCM described above to more complex versions consists mainly of adding successive basis functions corresponding to additional physics, particularly shallow convection and boundary layer variations not linked to moist convection. Parameterization of cloud-radiative interactions for these models are under development (Chou and Neelin, CA8.14)
Acknowledgments. Supported under NSF grant ATM-9521389 and NOAA grant NA46GP0244.