A Cellular Automata Model of Tropical Oceanic Rain Clusters with Self-organized Criticality

Tropical oceanic rain clusters exhibit complex organization patterns that can reveal fundamental principles governing convective systems. In this study, we develop a simple cellular automaton (CA) model that captures essential dynamics of tropical convection, using only a minimal set of physical rules. The model focuses on how local destabilization and stabilizing feedbacks, mediated by gravity waves, shape the spatial structure of rain clusters. Specifically, the distributions of the cluster area, A, and total rain rate, R, for tropical oceanic rain clusters from the CA model are analyzed for their scaling exponent ζ_A, ζ_R, and β where ; f(s) the probability distribution of S, E(R¦a) ~ a^β, E(R¦a) the conditional expectation of R given A = a.

We find that the CA naturally exhibits critical behavior, resembling patterns seen in percolation theory. Specifically, the size distribution of rain clusters follows a scaling law whose exponent is remarkably robust and closely matches the theoretical value for 2D percolation. This suggests that rain clusters in certain tropical regions may organize in a “percolation-like” manner, where large, connected clusters emerge in a critical state. Comparisons with regional climate model simulations over the tropics (Teo et al. 2021) show that rain clusters over the Indian Ocean and tropical Atlantic behave similarly to the critical clusters in our CA, while deviations over the Pacific may result from stronger large-scale destabilization over the western Pacific warm pool and the eastern Pacific ITCZ. Although our CA reproduces key scaling relationships between cluster area and rain rate, it does not fully account for the observed ζ_A ~ 5/3 reported in observational studies (Teo et al. 2017). We propose a simplified version of the CA that may reconcile this difference through tunable criticality.

References:

Teo, C.-K., H.-N. Nuynh, T.-Y. Koh, K. K. W. Cheung, B. Legras, L.-Y. Chew, and L. Norford, 2017: The universal scaling characteristics of tropical oceanic rain clusters. J. Geophys. Res. Atmos., 122, 5582–5599, https://doi.org/10.1002/2016JD025921.

Teo, C.-K., T.-Y. Koh, K. K. W. Cheung, B. Legras, H. Nguyen, L.-Y. Chew, and L. Norford, 2021: Scaling characteristics of modeled tropical oceanic rain clusters. Quart. J. Roy. Meteorol. Soc., 147, 1055–1069, https://doi.org/10.1002/qj.3959.