Mean K-R Relationships: Practical Results for Typical Weather Radar Wavelengths

Abstract

Total attenuation cross sections of raindrops derived from the Mie theory for wavelengths of 3.2, 5.6, and 10 cm and temperatures of ?10°, 0°, 10°, and 20°C have been calculated and compared to the results of the Rayleigh approximation. The approximation gives (i) unacceptable systematic underestimation of total attenuation cross sections and (ii) a misrepresentation of the temperature influence for the shortest wavelengths. Experimental raindrop-size distributions (RSD) collected during the French ?Cévennes 1986?88? hydrometeorological experiment were subsequently modeled using the classical negative exponential model and a three-parameter gamma model. The exponential model lies between widespread and thunderstorm RSD models proposed elsewhere in the literature, while the gamma model provides a better fit for experimental RSD data for the small diameters. Relationships between the attenuation K (dB km?1) and the rain rate R (mm h?1) are presented for the different wavelengths, temperatures, and RSD. Except for the well-known wavelength dependence of these mean relationships, the combination of errors in the choice of the mean RSD and in the estimation of raindrop temperature may lead to relatively high errors in K. Errors due to the misrepresentation of the RSD shape by an exponential model or to RSD truncation effects are of lesser importance but are not negligible.