Abstract
Weather radar signals fluctuate because of relative motions among the scatterers; these fluctuations must be accounted for in quantitative reflectivity measurements. The standard theory of weather signal fluctuations assumes targets of fixed reflectivity. In actual measurements, signals from a volume in space and over a short period of time are combined to yield an overall reflectivity measurement. Within this measurement region the reflectivity may not be constant, in which case the standardβfluctuation theory will not strictly apply.
It is shown that the theory can readily be extended to include reflectivity variations. Models of the reflectivity structure are introduced to assess the effects of these variations on reflectivity measurements. If the measurement is made by averaging the signal and applying the standard theory, it will tend to underestimate the actual target reflectivity whenever variations are present except for the special case of a radar with a quadratic receiver response. If reflectivity is measured by selecting the maximum intensity level from a sample of size N and applying standard theory, it will tend to overestimate the actual target reflectivity when variations are present. The variance of the measurement is increased by reflectivity variations, whether averaging or peakβdetecting is employed. These effects are expected to introduce only small errors (less than 5 dB) in all but extreme cases of reflectivity variations, but such errors can be significant in applications of radar to problems in hydrology or communications, where high accuracy of measurements is required.