A model of coupled oscillators applied to the aerosol-cloud-precipitation system

We simulate the aerosol-cloud-precipitation system as a collection of cloud elements, each coupled through physically based interactions with adjacent clouds. The equations describing the individual clouds follow from the predator-prey model of Koren and Feingold (2011) with the addition of coupling terms that derive from the flow of air between the components resulting from surface divergence or convergence of flows associated with the life cycle of an individual cell. It is shown that some degree of coupling might stabilize clouds that would ordinarily become unstable. Varying the degree of coupling strength has significant influence on the system. For weak coupling, the clouds behave as independent oscillators with little influence on one another. As the local coupling strength increases, a point is reached at which the system becomes highly synchronized, similar to the Sakaguchi et al. (1987) model. Individual cloud oscillators in close proximity to one another can be both in-phase or out-of-phase depending on the choice of the time constant for the delay in communication between components. For the case considered, further increases in coupling strength result in reduced order and eventually unstable growth. Finally it is demonstrated that the set of coupled oscillators mimics qualitatively the spatial structure and synchronized behaviour of both closed and open-cellular cloud fields observed in satellite imagery, and produced by numerically intensive large eddy simulation.