Ascending columns, WTG, and convective aggregation

Analytic solutions are derived for a convecting atmosphere with mean ascent using a zero-buoyancy bulk-plume approximation for moist convection. It has been suggested that such solutions should serve as a model for the relationship between humidity, instability, and precipitation in the tropics, but it is shown here that this interpretation is incompatible with the observed weak temperature gradient (WTG). Instead, the solutions can be used to understand the atmospheric state averaged over all tropical convecting regions. Using the analytic solutions in this way, they predict the changes in humidity, instability, and precipitation as a function of the size of the moist patch in a convectively aggregated state.