Nonlocally coupled moisture model for convective self-aggregation

Abstract

Clouds play a central role in climate physics by interacting with precipitation, radiation, and circulation. Despite being a fundamental issue in convective organization, the self-aggregation of clouds lacks a theoretical explanation due to its complexity. In this study, we introduce an idealized mathematical model where the system's state is represented solely by the vertically integrated water vapor content of atmospheric columns under the weak temperature gradient approximation. By analyzing the nonlinear dynamics of this simplified system, we mathematically elucidate the mechanisms that determine the onset of self-aggregation and the spatial scale of the self-aggregated state. Nonlocal coupling between atmospheric columns induces bistability, leading to dry and moist equilibria. This reflects the circulation effects driven by horizontal differential heating due to convection and radiation. The bistable self-aggregated state realizes when destabilization by nonlocal coupling, triggered by finite-amplitude disturbances in the uniform state, overcomes stabilization by diffusion. For globally coupled systems where all columns are equally coupled, perturbations with the maximum wavelength exhibit the highest growth rate. This results in a solution with an infinitely long wavelength, understood as the dynamical system's heteroclinic trajectories describing the steady state's spatial evolution. Conversely, for nonlocally coupled systems with finite filter lengths, perturbations with wavelengths close to the characteristic length of the coupling are preferred. The results reveal that the balance between nonlocal coupling and diffusion is essential for understanding convective self-aggregation. Moreover, this study suggests a physical similarity between convective self-aggregation and moisture mode.