**Vector Retrieval from Coherent Doppler Lidar**In order to understand how wind profiles are obtained by lidar, it is useful to review the difference between the fundamental measured product of the Doppler lidar and secondary retrieved products. Doppler lidars fundamentally measure a Doppler shift along their laser beam propagation path. Therefore, motion of the air orthogonal to the propagation path of the laser beam produces no Doppler shift. Consequently, the basic Doppler lidar output is the *radial velocity*, or the dot product of the velocity vector with the beam direction unit vector. Interpretation and processing of the radial velocity fields can be complex, requiring the resolution of indeterminacy in the basic data through supplementary assumptions or information. Various wind retrieval techniques have been developed to estimate 2D and 3D vector fields from Doppler lidar data. Algorithms range from computationally intensive 4DVAR (four-dimensional variational data assimilation) techniques to simpler and faster methods based on volume velocity processing (VVP) and 2DVAR. Current techniques are generally suitable for many applications such as pollution transport studies and vertical profiling for wind farms assuming that the averaged nature of the products and underlying assumptions are understood. Dual Doppler lidar techniques also provide accurate estimates of the 2D wind field. Advanced vector retrieval algorithms such as the optimal interpolation (OI) algorithm based on data assimilation technique was adapted to work with Doppler lidar data.

*Figure 1. Horizontal velocity vectors from OI technique on a 3.5*^{o} elevation conical scan showing the rotation of winds with height. The scan takes approximately 38 seconds to complete one revolution shown. The colors on the plot represent radial velocity measurements by lidar. Red color (positive values) represent wind moving away from the lidar and blue color (negative values) shows wind moving towards the lidar. Data with low SNR is not shown (white regions).(Krishnamurthy et al. 2011)

^{o}elevation conical scan showing the rotation of winds with height. The scan takes approximately 38 seconds to complete one revolution shown. The colors on the plot represent radial velocity measurements by lidar. Red color (positive values) represent wind moving away from the lidar and blue color (negative values) shows wind moving towards the lidar. Data with low SNR is not shown (white regions).(Krishnamurthy et al. 2011)