A Variational Method for Filling in Missing Data in Doppler Velocity Fields

Single-Doppler radar data are often missing in important regions of a severe storm due to low return power, low signal-to-noise ratio, ground clutter associated with normal and anomalous propagation, and missing radials associated with partial or total beam blockage. Missing data impact the ability of WSR-88D algorithms to detect severe weather. To aid the algorithms, we develop a variational technique that fills in Doppler velocity data voids smoothly by minimizing Doppler velocity gradients while not modifying good data. This method provides estimates of the analyzed variable in data voids without creating extrema. Actual single-Doppler radar data of four tornadoes are used to demonstrate the variational algorithm. In two cases, data are missing in the original data, and in the other two, data are voided artificially. The filled-in data match the voided data well in smoothly varying Doppler velocity fields. Near singularities such as tornadic vortex signatures, the match is poor as anticipated. The algorithm does not create any velocity peaks in the former data voids, thus preventing false triggering of tornado warnings. Doppler circulation is used herein as a far-field tornado detection and advance-warning parameter. In almost all cases, the measured circulation is quite insensitive to the data that have been voided and then filled. The tornado threat is still apparent.