Modeling tropical precipitation in a single column

A modified formulation of the traditional single column model for represent ing 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 on e of the columns becomes very large compared to the other. Only a single co lumn is explicitly modeled, but its free tropospheric temperature, rather t han its mean vertical velocity, is prescribed. This allows the precipitatio n and vertical velocity to be true prognostic variables, as in prior analyt ical theories of tropical precipitation. Two models developed by other auth ors are modified according to the proposed formulation. The first is the in termediate atmospheric model of J. D. Neelin and N. Zeng, but with the hori zontal connections between columns broken, rendering it a set of disconnect ed column models. The second is the column model of N. O. Renno, K. A. Eman uel, and P. H. Stone. In the first model, the set of disconnected column mo dels is run with a fixed temperature that is uniform in the Tropics, and in solation, SST, and surface wind speed taken from a control run of the origi nal model. The column models produce a climatological precipitation field t hat is grossly similar to that of the control run, despite that the circula tion implied by the column models is not required to conserve mass. The add ition of horizontal moisture advection by the wind from the control run sub stantially improves the simulation in dry regions. In the second model the sensitivity of the modeled steady-state precipitation and relative humidity to varying SST and wind speed is examined. The transition from shallow to deep convection is simulated in a "Lagrangian" calculation in which the col umn 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 stead y-state case, due to the effect of horizontal moisture advection (viewed in a Lagrangian reference frame). In both of the models, the steady-state moi sture convergence is a nearly unique function of the surface evaporation wh en horizontal moisture advection is neglected, a result that is explained i n terms of the moisture and moist static energy budgets. The proposed formu lation can also be applied to limited-area three-dimensional models, such a s cloud-resolving models. Additionally, with further development, it may be possible to use the fixed-temperature constraint as the basis for a trunca ted atmospheric dynamics appropriate for the study of tropical climate.