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 velocity represents the differential reflectivity from all the scatterers that have the same radial velocity of interest within the radar resolution volume. Spectral polarimetry has been applied to suppress both ground and biological clutter, retrieve individual drop size distributions from a mixture of different types of hydrometeors, and estimate turbulence intensity, for example. Although spectral polarimetry has gained increasing attention, statistical quality of the estimation of spectral polarimetric variables has not been investigated. In this work, the bias and standard deviation (SD) of spectral differential reflectivity and spectral copolar correlation coefficient estimated from averaged spectra were derived using perturbation method. The results show that the bias and SD of the two estimators depend on the spectral signal-to-noise ratio, spectral copolar correlation coefficient, the number of spectrum average, and spectral differential reflectivity. A simulation to generate time series signals for spectral polarimetry was developed and used to verify the theoretical bias and SD of the two estimators.