Fractal geometry in precipitation

Abstract

Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, represented by a set of physical equations such as the Navier-Stokes equations, energy balances and hydrological cycle among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal dimensions, which are non-integer values that represent the complexity of variables like the precipitation. However, observed precipitation is measured as an aggregate variable over time, thus physical analysis of the observed fluxes is very limited. Therefore, this review aims to go through the different approaches used in the identification and analysis of the complexity of the observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for classification of climatic features, including monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy and time scaling in intensity-duration-frequency curves.