Statistics of Precipitation Reflectivity Images and Cascade of Gaussian-scale Mixtures in the Wavelet Domain: A Formalism for Reproducing Extremes and Coherent Multi-scale Structures

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Journal of Geophysical Research







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To estimate precipitation intensity in a Bayesian framework, given multiple sources of noisy measurements, a priori information about the multiscale statistics of precipitation is essential. In this paper, statistics of remotely sensed precipitation reflectivity imageries are studied using two different data sets of randomly selected storms for which coincident ground-based and spaceborne precipitation radar data were available. Two hundred reflectivity images of independent storm events were collected over two ground validation sites of the Tropical Rainfall Measurement Mission (TRMM) in the United States. Comparing ground-based and spaceborne images, second-order statistics of the measurement error is characterized. The average spectral signature and second-order scaling properties of those images are documented at different orientations in the Fourier domain. Decomposition of images using band-pass multiscale oriented filters reveals remarkable non-Gaussian marginal statistics and scale-to-scale dependence. Our results show that despite different physical storm structures, there are some inherent statistical properties which can be robustly parametrized and exploited as a priori information for parsimonious multiscale estimation of precipitation fields. A particular mixture of Gaussian random variables in the wavelet domain was found to be a suitable probability model that can reproduce the non-Gaussian marginal distribution as well as the scale-to-scale joint statistics of precipitation reflectivity data, important for properly capturing extremes and the coherent multiscale features of rainfall fields.

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