Statistical scaling, Shannon entropy, and Generalized space-time q-entropy of rainfall fields in tropical South America

We study diverse scaling and information theory characteristics of Mesoscale Convective Systems (MCSs) as seen by the Tropical Rainfall Measuring Mission (TRMM) over continental and oceanic regions of tropical South America, and 2/D radar rainfall fields from Amazonia. The bi-dimensional Fourier spectra of MCSs exhibit inverse power laws with respect to the spatial scale, whose scaling exponents, beta, capture the type of spatial correlation of rainfall among the study regions, including those over the Andes of Colombia as well as over oceanic and Amazonian regions. The moment-scaling analysis evidences that the structure function deviates from simple scaling at order q > 1.0, thus signaling the multi-scaling nature of rainfall fields within MCSs in tropical South America, with departures from simple scaling associated with the physical characteristics of MCSs over the different study regions. Entropy is estimated for a large set of radar rainfall fields during the distinctive atmospheric regimes (Easterly and Westerly events) in this part of Amazonia. Results evidence that there are significant differences in the dynamics of rainfall among regimes. No clear-cut relationship is found between entropy and the first two statistical moments, but power fits in space and time, S(gamma) similar to gamma(-eta) for skewness and, S(kappa) similar to kappa(-c) for kurtosis. The exponents eta and epsilon are statistically different between Easterly and Westerly events, although the significance of fits is less when L-moments are used to estimate skewness and kurtosis. Interesting differences are identified between the time and space generalized q-entropy functions of Amazonian rainfall fields. In both cases, the functions are a continuous set of power laws (analogous to the structure function in turbulence), S(T, q) similar to T-beta, and, S(lambda, q) similar to lambda(beta), covering a broad range of temporal and spatial scales. Both time and space generalized q-entropy functions exhibit linear growth in the range -1.0 < q < -0.5, and saturation of the exponent beta for q >= 1.0. In the case of the spatial analysis, the exponent saturates at similar to 1. 0, whereas at = 0.5 for the temporal case. Results are similar for time series extracted from the S-POL radar and time series of rainfall in tropical Andes. Additionally, differences in values of for q >= 1.0 between Easterly and Westerly events are not statistically significant. (C) 2015 AIP Publishing LLC.