Attenuation is one of major problems in the quantitative estimation of rainfall from radars measuring at wavelengths smaller than 10 cm. However, most of radars out of the USA are C-band radars and, therefore, significantly affected by attenuation effects. This makes necessary the correction of radar measurements for attenuation, which is nowadays not usually done. The main reason for it is that the analytical solution (derived by Hitschfeld and Bordan in 1954) is very unstable with small errors in radar measurements or in the estimation of the parameters of the Z-k relationship.

In this work, a variational method is proposed for attenuation correction. It consists on the minimization of a cost function that is composed of two terms: the first one imposes the solution to be close to the analytical solution of the attenuation problem, while the second term constrains the ?model? to observations. In this case, estimations of Path Integrated Attenuation (PIA) from the mountain returns are used as observations.

The behavior of this methodology is evaluated in the case of C-band radars under some simplifying assumptions.