Scale, Scaling and Multifractals in Geophysics: Twenty Years on

Abstract

We consider three developments in high number of degrees of freedom approaches to nonlinear geophysics: a) the transition from fractal geometry to multifractal processes, b) the self-organized critical (SOC) generation of extremes via multifractal phase transitions c) the generalization from isotropic scale invariance (self-similar fractals, multifractals) to (anisotropic) generalized scale invariance. We argue that these innovations are generally necessary for geophysical applications. We illustrate these ideas with data analyses from both the atmosphere and the earth's surface, as well as with multifractal simulations.