A Preliminary Study of Retrieving Vortex Circulation Using A Lagrangian Coordinate and Single Doppler Radar Data


A moving frame of reference technique is proposed so that the retrieval of cross-beam wind components is feasible from observations by single Doppler Radar without sacrificing data resolution. In this algorithm, the reflectivity fields observed by consecutive radar scans are used to find a moving Lagrangian coordinate on which the reflectivity measurements are as stationary as possible. After interpolating all the observational data to this optimal moving frame, and assuming the wind field is steady state within several radar scans, one can formulate a cost function which contains the following weak constraints: (1) reflectivity is preserved; (2) a geometric relationship between radial velocity Vr and the Cartesian components u, v, w; (3) mass conservation; and (4) weak vertical vorticity. By minimizing this cost function, the unobserved cross-beam wind component can be recovered.

Applying this algorithm to a simulated, idealized Rankine vortex circulation, it is found that with an appropriate scan strategy, that is, a sufficient number of radar scans (>2), separated by a short enough period of time (~3 minutes), low level circulation can be successfully retrieved using data detected by single Doppler radar. This technique is robust in compensating for observational errors, and, in a qualitative sense, works well when only reflectivity measurements are available.

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