Implementing the weak temperature gradient approximation with full vertical structure

A two-column, nonrotating radiative-convective model is formulated in which the free-tropospheric temperature profiles of the two columns are assumed to be identical and steady and the temperature equation is used diagnostically to calculate the vertical velocities [ the weak temperature gradient (WTG) approximation]. These vertical velocities and the continuity equation are then used to calculate the horizontal velocities. No horizontal momentum equation is used. This model differs from other two-column models that have used similar formulations in that here both columns are governed by the same laws rather than different dynamical roles being assigned a priori to the "warm'' and "cold'' columns. The current formulation has the advantage of generalizing trivially to an arbitrary number of columns, a necessity for developing a 3D model under WTG. The two-column solutions compare reasonably well with a reference two-column model that uses a linear, nonrotating horizontal momentum equation and the same underlying radiative-convective code as the WTG model; the reference model is essentially that used earlier by Nilsson and Emanuel, except modified to have significant viscosity only in a boundary layer near the surface. The two solutions compare best in the limit of large horizontal domain size, behavior opposite to what has been found in models that lack an explicit boundary layer and have viscosity throughout the troposphere. The difference is explained in terms of the circulation driven by boundary layer pressure gradients.