Scaling statistics in a critical, nonlinear physical model of tropical oceanic rainfall

Over the last two decades, concepts of scale invariance have come to the fore in both modeling and data analysis in hydrological precipitation research. With the advent of the use of the multiplicative random cascade model, these concepts have become increasingly more important. However, unifying this statistical view of the phenomenon with the physics of rainfall has proven to be a rather nontrivial task. In this paper, we present a simple model, developed entirely from qualitative physical arguments, without invoking any statistical assumptions, to represent tropical atmospheric convection over the ocean. The model is analyzed numerically. It shows that the data from the model rainfall look very spiky, as if generated from a random field model. They look qualitatively similar to real rainfall data sets from Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE). A critical point is found in a model parameter corresponding to the Convective Inhibition (CIN), at which rainfall changes abruptly from non-zero to a uniform zero value over the entire domain. Near the critical value of this parameter, the model rainfall field exhibits multifractal scaling determined from a fractional wetted area analysis and a moment scaling analysis. It therefore must exhibit long-range spatial correlations at this point, a situation qualitatively similar to that shown by multiplicative random cascade models and GATE rainfall data sets analyzed previously (Over and Gupta, 1994; Over, 1995). However, the scaling exponents associated with the model data are different from those estimated with real data. This comparison identifies a new theoretical framework for testing diverse physical hypotheses governing rainfall based in empirically observed scaling statistics.