A two-column radiative-convective model of the tropical atmosphere is formulated which uses the Weak Temperature Gradient (WTG) approximation to determine the flow field. Traditional two-column models use momentum equations to compute the velocities. WTG allows this model to use the temperature equation to compute the velocities. WTG is used to assume that the temperature profiles of the two columns are identical in the free troposphere. As a result, the temperature equation can then be used to calculate the vertical velocities. These vertical velocities and the continuity equation can then be used to calculate the horizontal velocities.

This model is compared to the `traditional' two-column model of Nilsson and Emanuel, which uses a momentum equation and the same single column radiative-convective code as the WTG model. This comparison shows how well the WTG model captures the essential physics of the traditional model in the inviscid limit. Runs are made with fixed sea surface temperature (SST) for a range of SSTs. The vertical velocity and precipitation fields simulated in the two models are very similar. The temperature field is not as similar, which can be shown to be the result of the scheme used in the WTG model to match the temperature of the free troposphere to the temperature at the top of the planetary boundary layer.