Nonlocally coupled moisture model for convective self-aggregation

Clouds play a central role in climate physics by interacting with precipitation, radiation, and circulation. Although the self-aggregation of clouds is a fundamental problem in convective organization, a theoretical explanation of how it occurs has not been established owing to its complexity. Here, we introduce an idealized mathematical model of the phenomenon in which the state of the system is represented solely by the atmospheric columns' vertically integrated water vapor content. By analyzing the nonlinear dynamics of this simplified system, we mathematically elucidated the mechanisms that determine the onset of self-aggregation and the spatial scale of the self-aggregated state. Nonlocal coupling between atmospheric columns makes the system bistable with dry and moist equilibria, reflecting the effect of circulation driven by horizontal differential heating due to convection and radiation. The bistable self-aggregated state is realized when destabilization by nonlocal coupling triggered by finite-amplitude disturbances in the uniform state overwhelms the stabilization by diffusion. For globally coupled systems in which all the columns are equally coupled, the perturbation of the maximum wavelength has the maximum growth rate. A solution with an infinitely long wavelength exists, which can be understood as the dynamical system's heteroclinic trajectories describing the steady state's spatial evolution. In contrast, for nonlocally coupled systems with finite filter lengths, perturbation of the wavelength close to the characteristic length of the coupling is preferred. The results revealed that the balance between nonlocal coupling and diffusion is essential for understanding convective self-aggregation.