Convective self-aggregation as a dual-phase damped gravity wave

We propose a simple, piecewise linear model for self-aggregation based on primitive equations. In this model, each atmospheric column is in one with two possible convective regimes: deep-convective or convectively inhibited, and the thermodynamics in each regime is linearised. The model simulates aggregated and non-aggregated stationary states, reproducing many properties of self-aggregation as simulated by kilometre-resolution models, in particular an hysteresis with multiple equilibria, aggregated and non-aggregated, and a similar sensitivity to convective triggering, domain size, and boundary-layer radiative cooling in the convectively-inhibited region. These results suggest that a self-aggregated state can be considered as a gravity wave with two phases: one convective and one convectively inhibited.