High-Precision Measurements of the Copolar Correlation Coefficient: Non-Gaussian Errors and Retrieval of the Dispersion Parameter μ in Rainfall

The copolar correlation coefficient rho(hv) has many applications, including hydrometeor classification, ground clutter and melting-layer identification, interpretation of ice microphysics, and the retrieval of raindrop size distributions (DSDs). However, the quantitative error estimates that are necessary if these applications are to be fully exploited are currently lacking. Previous error estimates of rho(hv) rely on knowledge of the unknown true rho(hv) and implicitly assume a Gaussian probability distribution function of rho(hv) samples. Frequency distributions of rho(hv) estimates are in fact shown to be highly negatively skewed. A new variable, L = 5 log(10)(1 = rho(hv)), is defined that does have Gaussian error statistics and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of rho(hv). In addition, the manner in which the imperfect collocation of the horizontal and vertical polarization sample volumes may be accounted for is demonstrated. The possibility of using L to estimate the dispersion parameter mu in the gamma drop size distribution is investigated. Including drop oscillations is found to be essential for this application; otherwise, there could be biases in retrieved mu of up to approximately 8. Preliminary results in rainfall are presented. In a convective rain case study, the estimates presented herein show mu to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.