We examine convective self-aggregation in 15-18 day long cloud-resolving model simulations of radiative convective equilibrium (RCE) using a large domain of 1200 km x 1200 km with 3 km horizontal resolution over a fixed SST of 300 K. In our control simulation, interactive radiative heating and surface turbulent fluxes are used. After five days, convection begins to self-aggregate into coherent fluctuations of wavelength several hundred kilometers in which water vapor path, precipitation, reduced OLR, and enhanced surface fluxes covary. These fluctuations grow with an e-folding timescale of about 5 days. Unlike previous simulations in a smaller channel-shaped domain by Tompkins, the perturbations do not propagate.

We do similar simulations in which we horizontally average the radiative and/or turbulent fluxes before applying them to the model prognostic variables. We find that interactive radiation, but not interactive surface fluxes, are required for the mesoscale self-aggregation to develop. This is also in contrast to Tompkins, who obtained self-aggregation with interactive surface fluxes but fixed radiation.

We propose a simple mathematical model of the self-aggregation instability based on modeling of the moist static energy budget of atmospheric columns of mesoscale horizontal extent. The instability depends strongly on the vertical structure of the convection and in particular the ability of moderately precipitating congestus-dominated convection to import more moist static energy as precipitation increases. As convection intensifies and deepens, the heavily precipitation regions start to develop a more top-heavy profile of convective mass flux that induces horizontal export of moist static energy and provides a brake on the further development of self-aggregation.