A Stochastic Lattice Model for Convective Self-aggregation Incorporating Longwave Radiative Effect

Self-aggregation of tropical convection is a universal feature observed in a diverse range of atmospheric environments. Several preceding models conceptualized the self-aggregation of convection as a phase transition driven by collisions between cold pool gust fronts. However, self-aggregation may also be influenced by various physical processes, such as surface fluxes, radiation, and moisture perturbations in the planetary boundary layer, and it remains unclear which process plays a dominant role. In this study, we develop a simple stochastic lattice model for the pattern formation of deep convection, inspired by the two-dimensional Ising model. Here, in addition to the process of cold pool collisions, which have an effect of triggering new convection, we incorporate the process of clear-sky radiative cooling that has an effect of suppressing deep convection as an interaction between clouds. Our results show that by amplifying the intensity of the clear-sky radiative cooling effect, the transition from a quasi-uniform to an inhomogeneous cloud field can be reproduced. The model also successfully explains the dependence of self-aggregation on several model parameters, such as the experimental domain size and the characteristic size of cold pools. Furthermore, by varying the distance over which the subsidence induced by radiative cooling extends, we succeed in capturing a pattern formation that closely resembles the convective clusters observed in the real atmosphere and three-dimensional numerical model simulations.