Efi Foufoula-Georgiou 1; Mohammad Ebtehaj1,2

1 Department of Civil Engineering, Saint Anthony Falls Laboratory and National Center for Earth-Surface Dynamics, University of Minnesota, USA

2 School of Mathematics, University of Minnesota, USA

Abstract The past decades have witnessed a remarkable emergence of new sources of multiscale multi-sensor precipitation data including data from global spaceborne active and passive sensors, regional ground based weather surveillance radars and local rain-gauges. Resolution enhancement of remotely sensed rainfall and optimal integration of multi-sensor data promise a posteriori estimates of precipitation fluxes with increased accuracy and resolution to be used in hydro-meteorological applications. In this context, new frameworks are proposed for resolution enhancement and multiscale multi-sensor precipitation data fusion, which capitalize on two main observations: (1) sparseness of remotely sensed precipitation fields in appropriately chosen transformed domains, (e.g., in wavelet space) which promotes the use of the newly emerged theory of sparse representation and compressive sensing for resolution enhancement; (2) a conditionally Gaussian Scale Mixture (GSM) parameterization in the wavelet domain which allows exploiting the efficient linear estimation methodologies, while capturing the non-Gaussian data structure of rainfall. The proposed methodologies are demonstrated using a data set of coincidental observations of precipitation reflectivity images by the spaceborne precipitation radar (PR) aboard the Tropical Rainfall Measurement Mission (TRMM) satellite and ground-based NEXRAD weather surveillance Doppler radars. Uniqueness and stability of the solution, capturing non-Gaussian singular structure of rainfall, reduced uncertainty of estimation and efficiency of computation are the main advantages of the proposed methodologies over the commonly used standard Gaussian techniques.