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Convective Self-Aggregation as a Cold-Pool Driven Critical Phenomenon

Convective self-aggregation is when thunderstorm clouds cluster over a constant temperature surface in radiative convective equilibrium. Self-aggregation was implicated in the Madden-Julian Oscillation and hurricanes. Yet, numerical simulations succeed or fail at producing self-aggregation, depending on modeling choices. Common explanations for self-aggregation invoke radiative effects, acting to concentrate moisture in a sub-domain. Interaction between cold pools, caused by rain evaporation, drives reorganization of boundary layer moisture and triggers new updrafts. We propose a simple model for aggregation by cold pool interaction, assuming a local number density $ρ(\mathbf{r})$ of precipitation cells, and that interaction scales quadratically with $ρ(\mathbf{r})$. Our model mimics global energy constraints by limiting further cell production when many cells are present. The phase diagram shows a continuous phase transition between a continuum and an aggregated state. Strong cold pool-cold pool interaction gives a uniform convective phase, while weak interaction yields few and independent cells. Segregation results for intermediate interaction strength.