The Bootstrap Dual Polarimetric Spectral Density Estimator

Polarimetric weather radar variables provide useful information about the characteristics and motion of hydrometeors in the radar resolution volume. However, the information in these variables may be masked when the meteorological signal of interest is contaminated by clutter. The dual-polarimetric spectral densities (DPSD) may unveil additional information about the polarimetric characteristics of groups of scatterers moving at different Doppler velocities in a given radar resolution volume. However, to get accurate estimates, conventional DPSD estimation methods require averaging a number of spectra (typically obtained from different range gates, radials, or scans) or averaging in frequency. In general, any kind of averaging would degrade either the spatial, temporal, or frequency resolution of the spectra and could mask important features of the meteorological phenomenon. In an attempt to overcome these limitations, in this work we introduce the Bootstrap DPSD estimator, which allows the estimation of DPSDs from a single dwell with minimal resolution loss. Briefly, the proposed estimator generates a number of I/Q time-series pseudo-realizations through bootstrap resampling of pre-conditioned original time-series samples. The co-polar and cross-polar power spectral densities obtained from these pseudo-realizations are then averaged, and the resulting spectra are combined to obtain the polarimetric spectra. As a final step, a bias correction is applied to obtain DPSDs with good quality and the best spatial, temporal, and frequency resolutions. The statistical performance of the Bootstrap DPSD estimator is compared to that of conventional methods, and the advantages of the Bootstrap DPSD estimator are demonstrated in the context of identifying different types of scatterers moving with different radial velocities in the radar volume. Finally, the Bootstrap DPSD estimator is used to illustrate the benefits of polarimetric spectral analysis with radar data from recent tornadic events.