A technique is presented to retrieve relatively small-scale velocity field variations using a sequence of scans of radial velocity measurements from a single-Doppler lidar. This retrieval method is based upon assimilating the observed radial velocity field into a truncated spectral vorticity model. In its present form, the proposed technique retrieves the spatial and temporal variability of two dimensional velocity and vertical vorticity fields in the surface layer under neutrally stable conditions. A least squares variational calculation, implementing the model's adjoint, is performed in order to optimize the agreement between the model and the data. This is accomplished by treating the coefficient of eddy diffusion, mean velocity and the initial conditions of the Fourier amplitudes of the fluctuational velocity field as control parameters. In contrast to space domain methods the spectral approach enables a direct comparison between raw measurements and model output, thereby eliminating the need to interpolate the data to a uniform computational grid.
Retrieval experiments using simulated data are conducted to quantify errors due to aperiodic boundary conditions and measurement noise. The relative root mean squared vector difference between the retrieved and simulated velocity field due to a combination of these factors is generally less than 0.13. In addition, an experiment is performed to retrieve detailed eddy structure using low elevation angle sector scan data obtained from a coherent Doppler lidar. Comparisons between the statistics of the retrieved field with simultaneous surface anemometer data and VAD analysis indicate good qualitative agreement.