Organization of Precipitation Clusters in a Simple Stochastic Model

Precipitation clusters or contiguous areas of precipitation above a specified threshold are characterized by their size and the enclosed, cumulative precipitation (the cluster power). The probability distributions of the observed precipitation cluster size and power are marked by a long power law range (with slope ~ -3/2) and an exponential cutoff at some large value. This cutoff corresponds to organized, extreme events such as large mesoscale systems or superclusters. A two-dimensional stochastic model of moisture is introduced to generate the statistics of precipitation clusters. The model is minimal but is equipped with distinguishing elements of tropical dynamics including weak temperature gradient (WTG) physics and a Betts-Miller-like precipitation parameterization. The inclusion of stochastically-varying fluxes generates precipitation clusters whose size and power distributions possess a ~ -3/2 power law slope and a large event cutoff, similar to observations. In addition to convective processes, WTG physics amplifying the divergence, temporal autocorrelation in the noise and lateral mixing processes—including by rotational wind advection—are important to the cluster distributions. The cutoff is sensitive to multiple model parameters including the convective adjustment time, evaporation rate, the threshold moisture value that triggers precipitation and the amplitude of the stochastic forcing. This sensitivity is qualitatively captured by the average number of nearest neighbors that a precipitating point can spawn in a given time interval. Analogies between mechanisms of convective organization and stochastic branching processes, which inspired this particular metric, are also posited to explain the robustness of the power law slope (-3/2), seen in models and observations. Implications for climate model diagnostics as well as for the governing behavior of organized tropical convection in present and future climates are discussed.