Reconstruction of the spatial distribution of radar reflectivity of precipitation through linear-inversion techniques

The authors present a method aiming to remove the smoothing effect due to the antenna beamwidth in the reconstruction of the rain reflectivity based on radar measurements. The function to be reconstructed is the spatial distribution Z(x, y, h) of the radar reflectivity Z of the precipitation, which is shown to be related by a Fredholm integral equation to the power received by the radar. This integral equation is transformed into a set of linear equations and subsequently solved through a constrained-linear-inversion technique. The method is then applied to the cases of both stratiform and convective rain, leading to an improved estimation of the reflectivity-peak location and intensity, and of the overall reflectivity profile.