A Dimensionless Parameter for Predicting Convective Self‐Aggregation Onset in a Stochastic Reaction‐Diffusion Model of Tropical Radiative‐Convective Equilibrium

We introduce a minimal stochastic lattice model for the column relative humidity (R) in the tropics, which incorporates convective moistening, horizontal transport and subsidence drying. The probability of convection occurring in a location increases with R, based on Tropical Rainfall Measuring Mission observations, providing a positive feedback that could lead to aggregation. We show that the simple model reproduces many aspects of full-physics cloud resolving model experiments. Depending on model parameter settings and domain size and resolution choices, it can produce both random and aggregated equilibrium states. Clustering occurs more readily with larger domains and coarser resolutions, in agreement with full-physics models. Using dimensional arguments and fits from empirical data, we derive a dimensionless parameter which we call the aggregation number, Nag, that predicts whether a specific model and experiment setup will result in an aggregated or random state. The parameter includes the moistening feedback strength, the horizontal moisture transport efficiency, the subsidence timescale, the domain size and spatial resolution. Using large ensembles of experiments, we show that the transition between random and aggregated states occurs at a critical value of Nag. We argue that Nag could help to understand the differences in aggregation states between full-physics, cloud resolving models, which show little consensus about the robustness of self-organized patterns, whose emergence appears to be sensitive to the model setup, physics and parameterizations.