Probabilistic approach to constrained techniques for path attenuation compensation: A numerical study for C- and X-band radars

It is well established that weather radar systems operating at frequencies approximately equal to 5 GHz or greater can suffer from rain attenuation. Rain rate estimates at these attenuated wavelengths can be accomplished through the Hitschfeld-Bordan (HB) algorithm (Hitschfeld and Bordan, 1954). It has been widely demonstrated that the forward implementation of the HB alghoritm can lead to unstable solutions when the path attenuation becomes large. The divergence associated with the HB method can be prevented by restricting its use for light rain rates. In case of moderate to high rain rates, the attenuation correction is typically based on constrained methods, such as the surface reference techniques (SRT), especially developed for single frequency, incoherent and non-polarimetric airborne weather radars (Iguchi and Meneghini, 1994). These methods uses the path integrated attenuation (PIA) as a constraint in a manner to find a stable solution through a backward implementation of the HB algorithm. PIA measurements are generally extracted from the echo that arise from reference surfaces, such as mountains (for ground-base radars) or the sea (for airborn radars). For polarimetric weather radars, PIA estimate is directly related to ΦDP .