Mean wind profiles derived from Doppler radar or lidar data using general scanning techniques

A simple variational technique is presented for computing vertical profiles of mean horizontal winds from Doppler radar or lidar data for general scan geometries. Unlike the traditional velocity azimuth display (VAD) method in which the mean field is computed from plan position indicator (PPI) scans at each range gate separately, the current technique assimilates radial velocity information from the entire scan to form a smooth profile of the mean horizontal wind field. It can thus be applied to more general scan geometries, such as volume scans or sequences of range height indicator (RHI) scans at different azimuth angles. In addition, the technique can also be applied to data collected from Doppler systems without motion compensation capabilities, provided the platform attitude is known.

In this study a specific implementation of the technique is presented in which the vertical dependence of the mean horizontal wind components are modeled as expansions of Chebyshev polynomials. Chebyshev polynomials are selected because they form a complete set of basis functions. As such, any arbitrary well-behaved function, within a finite domain, can be represented by an expansion of Chebyshev polynomials. In addition, unlike Fourier series it is possible to impose non-periodic boundary conditions. For practical applications, truncated Chebyshev polynomial expansions provide an efficient and accurate approximation to an arbitrary data series in the least squares sense.

A cost function is defined to be the sum of the squared differences between the measured radial velocity and the radial component of the model at each measurement location within the scan. Minimizing this cost function with respect to the expansion coefficients yields the normal equations, which are inverted to give the expansion coefficients. This technique is applied to several Doppler lidar data-sets in which a variety of scanning techniques are employed. These results are compared to the traditional VAD approach using PPI scans.