Z-R Relationships Deduced from Forward Scatter Doppler Measurements

Abstract

Measurements were made at 9400 Mc/s of the radio wave scattering from raindrops. The experiment involved forward scattering over a short link and included Doppler frequency measurements which provided data on the vertical velocity of the raindrops. Two methods of analysis were used. The first, an integral analysis, which avoided the assumption of constant rainfall rate between tips of a tipping bucket rain gage, assumed Rayleigh scattering and provided Z-R relationships without measurements of drop size. A special feature of the analysis was that a best estimate of the time required for the rain to fall from the scatter volume to the rain gage was obtained from the data itself for each individual storm. Z-R relationships were obtained for individual storms, for different rain dates, rain types and synoptic conditions. It is shown that the variations noted in Z-R relationships for different synoptic conditions are at least partly explainable in terms of different rainfall rate distributions. The second method of analysis made use of certain features of the first method but was based on an exponential drop-size distribution. Using this distribution, the Gunn and Kinzer drop velocity data and Rayleigh scattering theoretical relationships between scattered power, rainfall rate and Doppler frequency were deduced. These relationships were fitted to the experimental data in such a manner as to eliminate all equipment parameters. The drop-size distribution N(D)dD=0. 103 exp (?45R?0.214D)dD is then deduced without measurement of drop sizes. With this model Rayleigh scattering is shown to fit the data with an error lying between 0.4 and 0.9 decibels. The Z-R relationship best fitting all the data is shown to be Z=244R1.39 in the usual units. Differences in Z-R relationships for different synoptic conditions are shown to be largely the result of the method of analysis and are small when this effect is taken into account. The Z-R relationship for thunderstorms is different and remains so even when the analysis effect is removed.