Studying Scale Invariance in Remotely Sensed Rainfall

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Rainfall is produced by atmospheric processes which are highly nonlinear and operate and interact at a wide range of scales. One of the main challenges to hydrologists, meteorologists and climatologists is to measure, model and predict the nature of the extreme variability exhibited by rainfall at different scales. Recent research has indicated the exciting possibility that rainfall may exhibit scaling/multiscaling characteristics, i.e., small scale fluctuations are statistically similar to large scale fluctuations except for one or more factors related to scale. The presence of such a hidden structure in the highly irregular patterns of rainfall at different scales will improve our understanding of the rainfall process and will significantly influence our approach to rainfall modeling, measurement and prediction. The goal of the proposed research is to develop a new theoretical framework for identifying and studying the presence of scale invariant relationships in remotely sensed rainfall. Our approach, based on multiresolution wavelet analysis, is different from contemporary approaches. It is more general and has the major advantage of being able to handle non-stationarity/inhomogeneity and anisotropy efficiently, all of which are important characteristics of space-time rainfall fields. Preliminary implementation of our approach to spatial rainfall has given very promising results and has pointed out new directions for data analysis which have the potential of unraveling simple structures from the complex non-homogenous anisotropic spatial rainfall fields. Also, as part of this research, the possibility of using scaling concepts for subgrid scale parametrization and resolution- independent rainfall estimation, will be explored.