A simple model of a balanced boundary layer coupled to a large-scale convective circulation

Many simple models of large-scale tropical circulations do not include a frictional boundary layer. A simple model is presented where the convective circulation is coupled to the boundary-layer convergence. In the free troposphere, convection and boundary-layer heating try to relax to a moist adiabat from the local sea surface temperature with a timescale τc -1/3, but other processes act to maintain a weak temperature gradient. There is a mass balance between radiatively-driven subsidence and the large-scale convective mass flux. For a prescribed Gaussian surface temperature, the model predicts a mass flux that varies as and a convective width proportional to its reciprocal. In the boundary layer, there can be significant horizontal temperature gradients and a balance between the pressure gradient and drag is assumed. Coupling between the two layers is mediated by the vertical velocity at the top of the boundary layer. The boundary layer constrains the circulation in three ways. Firstly, it may lengthen the relaxation timescale compared to deep convection. Secondly, the evaporation in the non-convecting region constrains the horizontal moisture advection. Thirdly, it maintains a convective boundary layer where there is a convective mass flux; this condition cannot be satisfied if τc is too small or the drag is too large, thus showing that such values are physically impossible. These results provide testable hypotheses concerning the physics and large-scale dynamics in weather and climate models.