Simple models of the tropical atmosphere (Gill 1980, Webster 1981, Zebiak 1986, Lindzen and Nigam 1987, Neelin and Held 1987, Wang and Li 1993) have proven useful for a number of problems, especially those where it is sufficient to obtain low-level wind from a given latent heating or sea surface temperature (SST). These models make different assumptions about convection, and there is an unresolved debate about the relative importance of competing mechanisms by which the SST pattern can potentially influence the circulation. However, the models behave similarly (Neelin 1989) and have a number of tunable parameters that are sufficiently ill-constrained that the models can be fit to the low-level wind field (e.g., Allen and Davey 1993). To resolve such ambiguities, and to approach problems involving radiative transfer, surface heat exchange, cloud effects and the stability of the tropical climatology, it becomes more important to have models intermediate between these and general circulation models (GCMs). Seager and Zebiak (1995) take a numerical approach to this problem, using a linear primitive equation model with the Betts-Miller (1986) scheme.
We outline here a very different approach in which we parlay theoretical results into a numerical scheme. We have analytical results for vertical structure that hold under certain approximations in convective regions (Neelin and Yu 1994; Yu and Neelin 1994). These result from using the constraints on temperature that occur in quasi-equilibrium convective closures. By using these as the leading basis functions in a Galerkin representation of vertical structure, we get a model that gives back the theoretical results in simple cases, but is valid more generally. Because the main benefits depend on the use of quasi-equilibrium constraints, we refer to these models as ``quasi-equilibrium tropical circulation models'' (QTCMs).
We present here the simplest model version, along with a summary of the general approach to deriving these models.