Polarimetric Spectral Densities for the Analysis of Tornado-Vortex Radar Observations

It is well known that tornadoes pose a great threat to life and property, and that the damage inflicted by them can easily add up to over billions of dollars in costs. Continuous advancements in weather radar technology, such as the polarimetric upgrade to the NEXRAD network, have helped mitigate some of these impacts by offering improved observation capabilities, which could result in increased tornado-warning lead times and near real-time tornado-damage estimation. Studies suggest that tornadic debris show a distinct signature in polarimetric radar observations. The so-called tornadic debris signatures (TDS) can help improve the detection of tornadoes when ground observation is difficult or not possible (e.g., at night or during heavy rainfall). Previous works have catalogued typical values of polarimetric variables corresponding to the TDS, showing high radar reflectivity factor, low differential reflectivity, and low co-polar correlation coefficient. Yet, it is still unknown exactly how the size, shape, and concentration of different debris types affect the polarimetric variables. Additionally, due to the effects of centrifuging, hydrometeors and debris move at slightly different velocities within a tornado vortex, introducing significant biases in the wind velocity as measured by the radar. An accurate measurement of the wind velocity is important to obtain a good estimate of the intensity of tornadoes and to effectively assess the damage. Polarimetric spectral densities (PSD) represent the power-weighted distribution of the polarimetric variables as a function of the Doppler velocity for all the scatterers in a radar resolution volume. Thus, the PSDs have the potential to aid in discriminating targets with distinct polarimetric characteristics that are moving with different Doppler velocities. However, to get accurate estimates of the PSDs a number of independent observations is typically required, which is not practically feasible without degrading the temporal, spatial (range and/or azimuth), or frequency resolution. To overcome this constraint, a bootstrap resampling method of the time-series data is introduced. The method consists of resampling the original I/Q data set while maintaining the temporal coherence of the signal. Although it does not use independent observations of the underlying phenomenon, extensive simulations and performance analyses show that the proposed method has the best performance when compared to conventional methods of PSD estimation. Further, a radar emulator that produces time-series data for tornado-like vortices (including hydrometeors and debris particles) is used to validate the feasibility of the proposed PSD estimator as a means to correct debris centrifuging errors in polarimetric radar measurements of tornadoes. The method proposed in this work is part of a larger framework that is being developed to cross-validate simulations and real-world radar observations of tornadic debris. This framework will help elucidate important scientific questions that remain a challenge in great part due to the extreme difficulty of validating such hypotheses through ground observations and to the uncertainty inherent to radar measurements.