A new formulation of advection-correction for radar data

It has long been recognized that radar-data-based analysis products such as wind retrievals, thermodynamic retrievals, and accumulated rainfall maps are prone to substantial error if the temporal resolution of the data is not sufficient to resolve the flow unsteadiness. Techniques to mitigate such errors typically use "advection-corrections" based on Taylor's frozen turbulence hypothesis or, equivalently, radar data are redefined in a moving reference frame. In these approaches, spatial patterns are considered to be of permanent form and to translate horizontally with constant pattern-translation components U, V. The present investigation is concerned with a new variational-based procedure of advection-correction in which provision is made for spatially-variable pattern-translation fields. We envision these pattern-translation fields as characterizing a flow of larger-scale than the small-scale features we want to resolve in the analysis, and so demand that the spatial variations of U, V be gradual. Spatially-variable pattern-translation fields may be particularly relevant in the analysis of tornados and other small scale vortices in which the most intense feature (tornado) may be embedded within a mesocyclone or other non-uniform larger-scale mesoscale feature. The new method is Lagrangian in nature, and trajectories are determined as part of the solution. Following a derivation of the procedure, the method is tested with analytical data from a virtual radar and with real radar data of a tornadic supercell thunderstorm over central Oklahoma.