Linear Least-Squares Derivative Gradients of Single-Radar Products and Their Applications for Severe Weather

Linear Least-Squares Derivative (LLSD) gradients of single-radar products, specifically the azimuthal, divergent, and total gradient products derived from the radial velocity, spectrum width, and correlation coefficient products, have shown some utility in aiding in the identification of potentially tornadic storms. To obtain these results, single-radar LLSD gradients of single-radar products from the WSR-88D network were calculated for ~62,500 data points from NCEI Storm Events Database severe weather reports from 2011-2018 (Smith and Elmore 2004, Mahalik et al. 2019). All severe reports that were available within the range of a NEXRAD WSR-88D radar with dual-pol capabilities and that were valid within 90 seconds of a radar scan with available full-sector level II 0.5°-tilt data were used for the analysis. All reports of hail and wind meeting or exceeding the threshold for the National Weather Service (NWS) severe thunderstorm criteria were included, except reports valid within one hour of any tornado in order to distinguish between tornadic and non-tornadic events. Tornado reports were also filtered by only including reports of tornadoes surveyed by the NWS. Median-filtered 0.5°-tilt base radar variables and LLSD derivatives were extracted within a 2.5-km radius of the location of the maximum LLSD azimuthal shear of velocity associated with each storm report. Maxima, minima, and means from the extracted values were computed and analyzed using different populations.

The data analysis includes comparing the data for severe winds, hail, and tornadoes, as well as the intercomparison between weaker and stronger categories of the individual severe threat. The results were evaluated for regional and seasonal differences. In addition, storm mode variations for tornadic data were investigated using a subset of a tornadic dataset from 2013-2016, which totaled ~9,000 data points, hand analyzed by the Storm Prediction Center (SPC).

Tornadic values of several variables were found to have regional differences within the United States, while severe non-tornadic values generally remained within the same range across the continental United States. The LLSD gradient products have potential to aid forecasters in quantifying the strength of velocity couplets or identifying smaller areas within quasi-linear convective systems capable of producing tornadoes, as suggested by results from several case studies provided by NWS forecasters. This study also aims to provide some guidance in identifying values typical for a variety of severe weather.