## 1. Introduction

[2] In the past decades, a considerable research effort has been devoted to developing parsimonious stochastic models of space-time rainfall [e.g., *Lovejoy and Mandelbrot*, 1985; *Gupta and Waymire*, 1990, 1993; *Veneziano et al.*, 1996; *Deidda*, 2000; *Deidda et al.*, 2006; *Lovejoy and Schertzer*, 2006; *Venugopal et al.*, 2006; *Mandapaka et al.*, 2010]. The related theories of multiscale process representation, e.g., in Fourier or wavelet domains, have proven to be useful for quantifying the rainfall variability at multiple scales. A large body of these developments has exploited the way that the second-order statistics of the rainfall process vary across different scales (i.e., 1/*f* spectra). Beyond this, observing non-Gaussian characteristics of precipitation fields and scaling in higher-order statistical moments, the theory of Multifractals and Multiplicative Random Cascades has extensively been used to capture these distinct properties of the rainfall fields [e.g., *Lovejoy and Schertzer*, 1990; *Gupta and Waymire*, 1990, 1993]. Simultaneously, it has been shown that oriented subband encoding of precipitation fields using wavelets can lead to an efficient and rich multiscale representation of spatial rainfall [e.g., *Kumar and Foufoula-Georgiou*, 1993a, 1993b]. Subsequently, an appreciable amount of work has been devoted to extracting the dependency of the parameters of those stochastic models to the underlying physics of the storm [e.g., *Over and Gupta*, 1994; *Perica and Foufoula-Georgiou*, 1996; *Harris et al.*, 1996; *Badas et al.*, 2006; *Nykanen*, 2008; *Parodi et al.*, 2011].

[3] The purpose of this paper is to: (1) demonstrate that precipitation reflectivity images exhibit some remarkably regular multiscale statistical characteristics, mainly related to non-Gaussian (heavy tail) marginals and scale-to-scale dependency, and (2) introduce a new modeling framework based on Gaussian Scale Mixtures (GSM) on wavelet trees which can be explored towards non-Gaussian, multiscale/multisensor data fusion of precipitation fields. In section 2, we present basic statistics from a diverse array of precipitation reflectivity images collected coincidentally from ground-based NEXRAD and the spaceborne Precipitation Radar (PR) abroad the TRMM satellite for two TRMM Ground Validation (GV) sites in Texas and Florida. In section 3, an extensive analysis and comparison of these images in the Fourier domain is undertaken. In section 4, the marginal and joint statistics of these precipitation reflectivity images in the wavelet domain (using an advantageous Undecimated Orthogonal Discrete Wavelet transform) are presented. A novel model based on the GSM on wavelet trees is introduced in section 5, and its potential for reproducing the observed heavy tail and covariance of the rainfall wavelet coefficients at multiple scales is demonstrated. The potential application of this model is also briefly discussed. Finally, section 6 presents conclusions and directions for future research.