A Shallow-Water Model for Convective Self-Aggregation

Abstract

Randomly distributed convective storms can self-aggregate in the absence of large-scale forcings. Here we present a 1D shallow-water model to study the convective self-aggregation. This model simulates the dynamics of the planetary boundary layer and represents convection as a triggered process. Once triggered, convection lasts for finite time and occupies finite length. Here we show that the model can successfully simulate self-aggregation, and that the results are robust to a wide range of parameter values. In the simulations, convection excites gravity waves. The gravity waves then form a standing wave pattern, separating the domain into convectively active and inactive regions. We analyze the available potential energy (APE) budget and show that convection generates APE, providing energy for self-aggregation. By performing dimensional analysis, we develop a scaling theory for the size of convective aggregation, which is set by the gravity wave speed, damping time scale, and number density of convective storms. This paper provides a simple modeling framework to further study convective self-aggregation.