A cellular automaton model of tropical oceanic rain clusters with criticality

Abstract

The distributions of the cluster area, A , and total rain rate, R , for tropical oceanic rain clusters from a cellular automaton (CA) are analysed for their scaling exponent ζ A , ζ R , and β where f ( s ) ∼ s-ζS; S∈{A,R}; f ( s ) the probability distribution of S ; β is that for rain rate conditioned by rain area. The CA only includes a few simple rules representing a small set of dynamics thought to be important for convective organization. These rules represent large-scale destabilization of the atmosphere under the moisture static energy framework with a slow driving timescale, as well as convective cells interaction through propagating gravity waves with a fast relaxation timescale. The CA exhibits percolation-like criticality, and the ζ A is estimated to be near the theoretical 2-dimensional percolation value of 187/91. This agrees well with the ζ A estimates over the Indian Ocean warm pool and the tropical Atlantic reported in previous modelling study, implying numerical models behave like percolation. Although other critical exponents of the rain cluster distributions from the CA, namely the η S (scaling exponent of the characteristic scale) and D S (cluster fractal dimension), S∈A,R, depend on the adjustable parameter of the CA, the ζ A is robust to the adjustable parameter. Although the CA cannot account for the observation-based ζ A ∼ 5/3 reported elsewhere that is quite universal over all oceans, further tuning of it such as through the convective cells interaction strength or how they interact may allow the CA to produce the observed exponent. Whether such behaviour can arise from a genuinely self-organized mechanism, rather than through parameter tuning, remains a question for future investigation.