On the Equivalence of Dual-Wavelength and Dual-Polarization Equations for Estimation of the Raindrop Size Distribution

Abstract

For air- and spaceborne weather radars, which typically operate at frequencies of 10 GHz and above, attenuation correction is usually an essential part of any rain estimation procedure. For ground-based radars, where the maximum range within the precipitation is usually much greater than that from air- or spaceborne radars, attenuation correction becomes increasingly important at frequencies above about 5 GHz. Although dual-polarization radar algorithms rely on the correlation between raindrop shape and size, while dual-wavelength weather radar algorithms rely primarily on non-Rayleigh scattering at the shorter wavelength, the equations for estimating parameters of the drop size distribution (DSD) are nearly identical in the presence of attenuation. Many of the attenuation correction methods that have been proposed can be classified as one of two types: those that employ a kZ (specific attenuation?radar reflectivity factor) relation, and those that use an integral equation formalism where the attenuation is obtained from the DSD parameters at prior gates, either stepping outward from the radar or inward toward the radar from some final range gate. The similarity is shown between the dual-polarization and dual-wavelength equations when either the kZ or the integral equation formulation is used. Differences between the two attenuation correction procedures are illustrated for simulated measurements from an X-band dual-polarization radar.