The Effect of Clustering on the Uncertainty of Differential Reflectivity Measurements

One of the most important avenues of recent meteorological radar research is the application of polarization techniques to improve radar rainfall estimation. A keystone in many of these methods is the so-called differential reflectivity ZDR, the ratio of the reflectivity factor ZH at horizontal polarization backscattered from a horizontally polarized transmission to that corresponding to a vertically polarized transmission ZV. For such quantitative applications, it is important to understand the statistical accuracy of observations of ZDR. The underlying assumption of all past estimations of meteorological radar uncertainties is that the signals obey Rayleigh statistics. It is now evident, however, that as a radar scans, the meteorological conditions no longer always satisfy the requirements for Rayleigh statistics. In this work, ZDR is reconsidered, but this time within the new framework of non-Rayleigh signal statistics. Using Monte Carlo experiments, it is found that clustering of the scatterers multiplies the standard deviation of ZDR beyond what is always calculated assuming Rayleigh statistics. The magnitude of this enhancement depends on the magnitudes of the clustering index and of the cross correlation between ZH and ZV. Also, it does not depend upon the number of independent samples in an ensemble estimate. An example using real radar data in convective showers suggests that non-Rayleigh signal statistics should be taken into account in future implementations of polarization radar rainfall estimation techniques using ZDR. At the very least, it is time to begin to document the prevalence and magnitude of the clustering index in a wide variety of meteorological conditions.