LiSBOA (LiDAR Statistical Barnes Objective Analysis) for optimal design of lidar scans and retrieval of wind statistics – Part 1: Theoretical framework

Abstract

Abstract. A LiDAR Statistical Barnes Objective Analysis (LiSBOA) for the optimal design of lidar scans and retrieval of the velocity statistical moments is proposed. LiSBOA represents an adaptation of the classical Barnes scheme for the statistical analysis of unstructured experimental data in N-dimensional space, and it is a suitable technique for the evaluation over a structured Cartesian grid of the statistics of scalar fields sampled through scanning lidars. LiSBOA is validated and characterized via a Monte Carlo approach applied to a synthetic velocity field. This revisited theoretical framework for the Barnes objective analysis enables the formulation of guidelines for the optimal design of lidar experiments and efficient application of LiSBOA for the postprocessing of lidar measurements. The optimal design of lidar scans is formulated as a two-cost-function optimization problem, including the minimization of the percentage of the measurement volume not sampled with adequate spatial resolution and the minimization of the error on the mean of the velocity field. The optimal design of the lidar scans also guides the selection of the smoothing parameter and the total number of iterations to use for the Barnes scheme. LiSBOA is assessed against a numerical data set generated using the virtual lidar technique applied to the data obtained from a large eddy simulation (LES). The optimal sampling parameters for a scanning Doppler pulsed wind lidar are retrieved through LiSBOA, and then the estimated statistics are compared with those of the original LES data set, showing a maximum error of about 4 % for both mean velocity and turbulence intensity.

Validation of near‐shore wind measurements using a dual scanning light detection and ranging system

“…An assumption was made to fit the equation to the dual scanning LiDAR system. Previous studies (e.g., Letizia et al 25 ) have indicated that if small elevation angles are used in dual scanning systems, the right‐side third term in Equation (), which associates the vertical velocity component with a sine of the elevation angle can be deleted from the equation. In this experiment, the maximum elevation angle of 6.0° was configured for the measurements at a height of 180 m for SL 1, and (6.0°) equals 0.105.…”

Effects of the thrust force induced by wind turbine rotors on the incoming wind field: A wind LiDAR experiment

“…The scanning strategy for the scanning LiDAR was optimally designed through the LiDAR Statistical Barnes Objective Analysis (LiSBOA) [17] to quantify the hub-height mean velocity with fundamental half-wavelengths of ∆n x = 1D and ∆n y = 0.5D in the streamwise and spanwise directions, respectively, which are deemed to be adequate to spatially resolve flow features of the induction zone and the near-wake (more details available in [18]). With the logistic constraint of the scanning wind LiDAR located 3D upwind of the wind turbines under investigation for the prevailing WSW wind directions, the optimal scan maximizing the coverage of the target volume (70% of the domain adequately sampled) and the statistical convergence (error on the mean of 0.4 m s −1 ) includes 5 planar position indicator (PPI) scans with a range gate of 50 m, elevation angles of the LiDAR laser beam of [3.42 • , 4.39 • , 6.13 • , 10.13 • , 27.95 • ] spanning the azimuthal range [10 • , 100 • ] with a 2 • angular resolution in the azimuthal direction, resulting in a total sampling time of 112 s.…”

“…Normalized and clustered data should meet the requirement of statistical homogeneity [4,18], which allows using the LiSBOA tool [17] to reconstruct the low-pass filtered mean velocity fields on a Cartesian grid at hub height. To this aim, the pre-conditioned LiDAR data collected within the vertical range z ∈ (H − D/4, H + D/4) are fed to the LiSBOA algorithm using a smoothing parameter of the Barnes scheme σ = 1/3, and the fundamental half-wavelengths provided in Section 2.…”

Identification of the energy contributions associated with wall-attached eddies and very-large-scale motions in the near-neutral atmospheric surface layer through wind LiDAR measurements

“…For instance, LiDAR scans can be optimally designed to probe the atmospheric boundary layer and wakes generated by utility-scale wind turbines (e.g. El-Asha, Zhan & Iungo 2017; Zhan, Letizia & Iungo 2020; Letizia, Zhan & Iungo 2021 a , b ). Regarding atmospheric turbulence, LiDAR measurements were used to detect the inverse-power law (Calaf et al.…”