The column-averaged heat budget. Main problem is how to write fluxes as function of gradients of surface temperature or some other mean model quantity. Representation of energy transport by a diffusion. Limitations of the diffusive approximation: (a) The problem of determining diffusivity. (b) The problem of representing latent heat transport (i.e. the hydrological cycle) (c) The problem of representing tropical heat transport. (d) Problems of representing lapse rate, water vapor and cloud effects.
Brief mention: Alternate approach to formulation of a vertically integrated model: Form equations for vertically integrated entropy (amounts to diffusing potential temperature). In this case, heating terms show up as an entropy source and don't integrate out in terms of the T.O.A. budget.
Models based on diffusion of moist static energy. (Energy flux proportional to gradient of MSE instead of proportional to gradient of surface temp).
Representing the hydrological cycle: Is diffusing moisture a good idea? Distinction between moisture as a radiative agent and moisture as a means of energy transport and source of precip.
Representing the tropics. Does diffusion of MSE represent the Hadley cell?
Representation of Top-of-Atmosphere and surface fluxes. If atmosphere is in equilibrium, net surface flux equals tent TOA flux, as described in seasonal cycle chapter. TOA flux just given using the OLR(T) fit. Brief mention of variant: Models which track surface and atmospheric temperature separately.
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