It is well recognized that there exists a need for accurate prediction of precipitation, whether it is for improvement of flood warning systems, water system management, or groundwater recharge assessment (Krajewski and Smith, 2002) . Weather radar has enabled us to improve our quantitative observations of precipitation in the field of radar hydrology. However, radar-based estimates of rainfall accumulation and/or rate are subject to numerous uncertainties. Some errors may arise due to the

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... ent complexity of the mechanical and electronic system of detection while others may be due to the complexity of the terrain. As a result, the relation between measured radar reflectivity and surface rainfall is highly complex and can be influenced by many factors (Austin, 1987) . Even though it has been the subject of many studies, no satisfactory method has been developed to date for accurately estimating rainfall when high spatial and temporal resolution is required (Anagnostou and Krajewski, 1997) . We propose to develop an approach to calibrate radar by applying a mathematical method originally proposed by Carasso et al. (1978) for image processing. The method of the Marching-Jury Backward Beam Equation (Atmadja and Bagtzoglou, 2001a; Bagtzoglou and Atmadja, 2003) is studied and then coupled to discrete Fourier image processing techniques to solve a two-dimensional (2D) problem with homogeneous diffusion coefficient backwards. The difficulties associated with this ill posed, backwards diffusion problem are well recognized (Atmadja and Bagtzoglou,