Spatially Variable Advection Correction of Radar Data. Part I: Theoretical Considerations

Abstract

Abstract Radar data–based analysis products, such as accumulated rainfall maps, dual-Doppler wind syntheses, and thermodynamic retrievals, are prone to substantial error if the temporal sampling interval is too coarse. Techniques to mitigate these errors typically make use of advection-correction procedures (space-to-time conversions) in which the analyzed radial velocity or reflectivity field is idealized as a pattern of unchanging form that translates horizontally at constant speed. The present study is concerned with an advection-correction procedure for the reflectivity field in which the pattern-advection components vary spatially. The analysis is phrased as a variational problem in which errors in the frozen-turbulence constraint are minimized subject to smoothness constraints. The Euler–Lagrange equations for this problem are derived and a solution is proposed in which the trajectories, pattern-advection fields, and reflectivity field are analyzed simultaneously using a combined analytical and numerical procedure. The potential for solution nonuniqueness is explored.