A wavelet-based spectral method for extracting self-similarity measures in time-varying two-dimensional rainfall maps

Abstract

Many environmental time-evolving spatial phenomena are characterized by a large number of energetic modes, the occurrence of irregularities, and self-organization over a wide range of space or time scales. Precipitation is a classical example characterized by both strong intermittency and multiscale dynamics, and these features generate persistence, long-range dependence, and extremes (whether be it droughts or extreme floods). Over the last two decades, time-frequency or time-scale transforms have become indispensable tools in the analysis of such phenomena and, as a consequence, a number of wavelet-based spectral methods are now routinely employed to estimate Hurst exponents and other measures of regularity and scaling. In this article, an ensemble of new wavelet-based spectral tools for analysis of 2-D images is proposed. The new scale-mixing wavelet spectrum is applied to the analysis of time sequences of two-dimensional spatial rainfall radar images characterized by either convective or frontal systems. Intermittent spatial patterns connected to the precipitation-formation mechanisms were encoded in low-dimensional informative descriptors appropriate for classification, discrimination analyses and possible integration with climate models. We found that convective rainfall spatial patterns compared to frontal patterns produce spectral signatures consistent with their generation mechanism.