Analysis of a Warm Cloud-Precipitation Competition Model and Implications for Cloud Aggregation

Shallow cumulus evolution and self-organization into different cloud patterns is a complicated process, with many not well understood elements. To shed more light on the physical processes involved we study the dynamical behavior of a simple predator-prey type model of warm cloud evolution, consisting of four nonlinear coupled differential equations for vertical motion, cloud water concentration, cloud droplet concentration, and rain water concentration. Each evolution equation consists of simple parameterizations of the physical processes that control cloud growth and decay. Adjacent clouds are then coupled together in a 2D grid through convergence and divergence of vertical winds between grid cells, which moves air and moisture about the domain and influences the growth and decay of neighboring clouds. This model produces stable, oscillatory behavior with individual cloud lifetimes averaging around 30 minutes, as well as exhibiting self-organization into relatively synchronized clusters. By further adjusting the strength of instability and vertical wind shear within the system, two of the proposed drivers of shallow cumulus structure, we explore the impact on different cloud structures as seen in nature and compared to observations.