It has been observed that rainfall may be estimated from the attenuation of microwave links. In this paper, we propose a new approach to this problem (for a single microwave link), which is based on a dynamical model of the attenuation without rain. This dry-air model combines local smoothing with quasi-periodicity over 24 hours. Rainfall causes large deviations of the attenuation from this dry-air model, and the rainfall can be estimated from these deviations.