Correlation patterns and information flows in rainfall fields

We present an analysis of nonlinear correlation patterns and symmetries within ‘measured’ rain fields. Various methods borrowed from Information Theory and their skills in untangling the mechanisms underlying the wild space–time variability of the rainfall process are reviewed. The second order information cumulant, namely mutual information, is used to describe the global (linear and non-linear) correlation features of observed rainfall fields and its performances are compared with more traditional correlation measures. In particular, we focus on the scaling properties of information exchanges, based on the analysis of a broad data-set of rainfall measurements performed at fine resolution in time, at about 100 meteorological stations in North–West Italy, during a period of 2 years. We further discuss the influence of the finite-size effect on inferring information statistics from relatively ‘short’ hydrological time series and the problem of robustness in estimating their scaling properties under these conditions. The results of this study indicate the key role of estimation techniques in unravelling global correlation features and their dependence on aggregation scales in space and time. Interesting results are also achieved by performing global correlation analysis on the binary signal (rain/no-rain) extracted from rain records, since the high resolution binary structure of rainfall seems to incorporate the core correlation features of the process.