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 ζA, ζR, and β where f(s)~s-ζS; S∈{A,R}; f(s) the probability distribution of S. 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 ζA­ is estimated to be near the 2-dimensional percolation value of 187/91. This agrees well with the ζA estimates over the Indian Ocean warm pool and the tropical Atlantic reported in previous modelling study. Although other critical exponents of the rain cluster distributions from the CA, namely the ηS (scaling exponent of characteristic scale with driving force) and DS (cluster fractal dimension), S∈(A, R}, depend on the adjustable parameter of the CA, the ζA is robust to the adjustable parameter. Although the CA cannot account for the observed ζA ~ 5/3 reported elsewhere based on observations, further tuning of it such as through the convective cells interaction strength or manner may make it approach the state of self-organized criticality.