Spectral correction of turbulent energy damping on wind lidar measurements due to spatial averaging

Abstract

Continuous advancements in pulsed wind lidar technology have enabled compelling wind turbulence measurements within the atmospheric boundary layer with probe lengths shorter than 20 m and sampling frequency on the order of 10 Hz. However, estimates of the radial velocity from the back-scattered lidar signal are inevitably affected by an averaging process within each probe volume, generally modeled as a convolution between the true velocity projected along the lidar line-of-sight and an unknown weighting function representing the energy distribution of the laser pulse along the probe length. As a result, the spectral energy of the turbulent velocity fluctuations is damped within the inertial subrange, thus not allowing one to take advantage of the achieved spatio-temporal resolution of the lidar technology. We propose to correct the turbulent energy damping on the lidar measurements by reversing the effect of a low-pass filter, which can be estimated directly from the power spectral density of the along-beam velocity component. Lidar data acquired from three different field campaigns are analyzed to describe the proposed technique, investigate the variability of the filter parameters and, for one dataset, assess the corrected velocity variance against sonic anemometer data. It is found that the order of the low-pass filter used for modeling the energy damping on the lidar velocity measurements has negligible effects on the correction of the second-order statistics of the wind velocity. In contrast, the cutoff wavenumber plays a significant role in spectral correction encompassing the smoothing effects connected with the lidar probe length. Furthermore, the variability of the spatial averaging on wind lidar measurements is investigated for different wind speed, turbulence intensity, and sampling height. The results confirm that the effects of spatial averaging are enhanced with decreasing wind speed, smaller integral length scale and, thus, for smaller sampling height. The method proposed for the correction of the second-order turbulent statistics of wind-velocity lidar data is a compelling alternative to existing methods because it does not require any input related to the technical specifications of the used lidar system, such as the energy distribution over the laser pulse and lidar probe length. On the other hand, the proposed method assumes that surface-layer similarity holds..