Mean field theory for tropical precipitation

A modified formulation of the traditional single column model for representing a limited area near the equator is proposed. This formulation can also be considered a two-column model in the limit as the area represented by one of the columns becomes very large compared to the other. Only a single column is explicitly modeled, but its free tropospheric temperature, rather than its mean vertical velocity, is prescribed. This allows the precipitation and vertical velocity to be true prognostic variables, as in prior analytical theories of tropical precipitation. Two models developed by other investigators are modified according to the proposed formulation. The first is an intermediate atmospheric model with two vertical modes, but with the horizontal connections between columns broken, rendering it a set of disconnected column models. The second is a true single colum model with 50 hPa vertical resolution. In the first model, the set of disconnected column models is run with a fixed temperature that is uniform in the tropics, and insolation, SST, and surface wind speed taken from a control run of the original model. The column models produce a climatological precipitation field which is grossly similar to that of the control run, despite that the circulation implied by the column models is not required to conserve mass. The addition of horizontal moisture advection by the wind from the control run substantially improves the simulation in dry regions. In the second model the sensitivity of the modeled steady-state precipitation and relative humidity to varying sea surface temperature (SST) and wind speed is examined. The transition from shallow to deep convection is simulated in a ``Lagrangian'' calculation in which the column model is subjected to an SST that increases in time. In this simulation, the onset of deep convection is delayed to a higher SST than in the steady-state case, due to the effect of horizontal moisture advection (viewed in a Lagrangian reference frame). In both of the models, the steady-state moisture convergence is a nearly unique function of the surface evaporation when horizontal moisture advection is neglected, a result which is explained in terms of the moisture and moist static energy budgets. The proposed formulation can also be applied to limited area three-dimensional models, such as cloud resolving models.