Using a low-order model to detect and characterize tornadoes in multiple-Doppler radar data

A new multiple-Doppler radar analysis technique is presented for the objective detection and characterization of tornadoes. The technique consists of fitting radial wind data from two or more radars to a simple analytical model of a tornado and its near-environment. The model combines a uniform flow, linear shear flow, linear divergence flow, and modified combined Rankine vortex (representing the tornado). The latter three fields are allowed to translate. A cost-functional J, designed to account for the discrepancy between model and observations, is defined by projecting the model wind in the direction of the radar(s) to obtain the measured radial wind, which is then compared to actual radial wind. This cost-functional is evaluated over both space and time so that observations can be used at the actual times and locations they were acquired, thus bypassing the need for time interpolation, moving reference frames or other ad-hoc procedures. The parameters in the low order model are determined by minimizing J.

The technique is initially tested using analytically-simulated observations whose wind field and error characteristics are systematically varied. An ARPS (Advanced Regional Predicting System) high-resolution simulation of a tornado is then used as an observation set. The method is tested for a range of sampling strategies and tornado sizes (relative to the spacing of radar observations). The technique shows skill in retrieving key characteristics of the tornado wind field including vortex location, radius and maximum tangential wind speed. The best results are obtained using a multiple-step procedure in which part of the retrieved flow is subtracted from the observations and the retrieval repeated on the residual field.