Statistical quality of spectral polarimetric variables for weather radar

Spectral polarimetry for weather radar capitalizes on both Doppler and polarimetric measurements to reveal polarimetric variables as a function of radial velocity through spectral analysis. For example, spectral differential reflectivity at a given velocity represents the differential reflectivity from all the scatterers that have the same radial velocity within the radar resolution volume. The commonly used differential reflectivity and co-polar correlation coefficient can be represented as the weighted sum of their spectral components. Spectral polarimetry has been used in several applications such as suppression of both ground and biological clutter, retrieval of individual drop size distributions from a mixture of different types hydrometeors, and retrieval of turbulence intensity. Although spectral polarimetry has shown promising advantages, the quality of these spectral polarimetric estimators has not been studied comprehensively. In this work, the statistical quality of spectral differential reflectivity and spectral co-polar correlation coefficient were derived using perturbation method. The results show that the bias and standard deviation (SD) of the two estimators depend on the spectral signal-to-noise ratio, spectral co-polar correlation coefficient, the number of spectrum average, and spectral differential reflectivity. These derived statistical errors were further verified using simulations, where the time series signals from both H and V channels were generated based on modeled spectral polarimetric variables and signal-to-noise-ratio. Three cases with different values of spectral co-polar correlation coefficient and different variations of spectral differential reflectivities were simulated for 100 realizations each. The results demonstrate that not only the model spectral differential reflectivity and spectral co-polar correlation coefficient can be reconstructed, but also the bias and SD obtained from simulations are consistent with the theoretical derivations.