In this paper, a method for the estimation of the spatial rainfall distribution over a specified service area from a limited number of path-averaged rainfall measurements is proposed. The aforementioned problem is formulated as a nonnegativity constrained convex optimization problem with priors that influence both sparsity and clustering properties of the spatial rainfall distribution. The spatial covariance matrix is derived from the climatological variogram model and used to construct a basis for the spatial rainfall vector. A proper selection of the representation basis and the priors that directly relate to the spatial properties of the rainfall guarantee an efficient reconstruction with a low compression rate (fewer measurements).