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 reflectiv ity fields observed by consecutive radar scans are used to find a moving La grangian coordinate on which the reflectivity measurements are as stationar y as possible. After interpolating all the observational data to this optim al moving frame, and assuming the wind field is steady state within several radar scans, one can formulate a cost function which contains the followin g weak constraints: (1) reflectivity is preserved; (2) a geometric relation ship between radial velocity Vr and the Cartesian components u, v, w; (3) m ass 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 circulatio n, it is found that with an appropriate scan strategy, that is, a sufficien t number of radar scans (>2), separated by a short enough period of time (s imilar to 3 minutes), low level circulation can be successfully retrieved u sing data detected by single Doppler radar. This technique is robust in com pensating for observational errors, and, in a qualitative sense, works well when only reflectivity measurements are available.