“…(14) when the specific attenuation A hh (expressed in dB km −1 ) is assumed to be related to the horizontally polarized reflectivity Z hh (expressed in mm 6 m −3 ) through a power law A hh =αZ β hh with β assumed constant in range. When the constraint is assumed at the farthest range bin (i.e., the estimated path integrated attenuation at r=r n is used as constraint) the so-called Final Value (FV) (i.e., Meneghini et al, 1983Meneghini et al, , 1992Meneghini and Nakamura, 1990) is obtained Otherwise, if the constraint is applied also to the first range bin (i.e., Z hh m (r 0 )=Z hh (r 0 )) and α is assumed constant in range, the CA solution (Meneghini et al, 1983;Meneghini and Nakamura, 1990) When the differential phase measurements are used to estimate the constraint at the farthest range bin, as proposed in Testud et al (2001), Eq. (16) coincides with the so-called ZPHI algorithm (see Appendix A for more details).…”