Variational analysis methods for retrieval of wind field from single-Doppler radar data

The variational analysis methods are applied to retrieve the steady state wind field from single-Doppler radar data. The wind field is retrieved by fitting, in the least-squares sense, constraining model equations to observations measured during a short assimilation period (2 or 3 time sequences). The weak and strong constraint formalisms are reviewed and examined using the one-dimensional linear advection equation as a constraint. It is shown that the retrieval is not unique, but the problem can be controlled by a smoothness constraint. Variational two-dimensional and three-dimensional wind retrieval algorithms are developed and tested using actual dual-Doppler radar data. The conservation of reflectivity and the radial momentum equation are used as weak constraints in both algorithms. The anelastic form of the continuity equation is also included as a strong constraint in the three-dimensional algorithm. The two-dimensional algorithm is tested and compared to echo tracking methods using Doppler radar observations in the clear-air planetary boundary layer. The resolution at which the methods can effectively retrieve the horizontal wind field is examined in detail. The variational algorithm can properly retrieve wind structures greater than 10 km wavelength. The three-dimensional algorithm is tested using observations of a precipitating microburst. It is demonstrated that the three-dimensional wind field can be retrieved, but the method fails near the ground level. In addition, the retrieval is sensitive to the radar position relative to the observational domain due to systematic model errors. The computational efficiency of the three-dimensional wind retrieval algorithm allows its semi-operational implementation at the J. S. Marshall Radar Observatory of McGill University.