A coarsening model for self-organization of tropical convection

If the influence of humidity on cumulus convection causes moist regions of the tropical troposphere to become moister and dry regions to become drier, and if horizontal mixing of moisture is not rapid enough to overcome this tendency, then the atmosphere will tend to separate into increasingly large moist and dry regions through a process of coarsening. We present a simple model for the moisture budget of the free troposphere, including subsidence drying, convective moistening, and horizontal mixing, and a constraint on total precipitation representing radiative-convective equilibrium. When initialized with a spatially uncorrelated moisture distribution, the model shows self-organization of precipitation with two main stages: A coarsening stage where the correlation length grows proportional to time to the power 1/2 and a droplet stage where precipitation is confined to a decreasing number of circular moist regions. A potential function is introduced to characterize the tendency for self-organization, which could be a useful diagnostic for analyzing cloud-resolving model simulations.