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

Radar data based analysis products such as accumulated rainfall maps dual Doppler wind syntheses and the) modynamic retrievals are prone to substantial error it the temporal sampling interval is too coarse Techniques to mitigate these errors typically make use of advection correction procedures (since 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 in advection correction procedure for the reflectivity field in which the pattern advection component 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 simultaneouslv using a combined analytical and numerical procedure The potential for solution nonuniqueness is explored