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.
Highlights
Reliable measurements of the wind velocity vector field are essential for understanding the complex nature of atmospheric turbulence and providing valuable data sets for the validation of theoretical and numerical models
A revisited Barnes objective analysis for sparse, nonuniform distributed, and stationary lidar data has been formulated to calculate mean, variance, and higher-order statistics of the wind velocity field over a structured N -dimensional Cartesian grid. This LiDAR Statistical Barnes Objective Analysis (LiSBOA) provides a theoretical framework to quantify the response in the reconstruction of the velocity statistics as a function of the spatial wavelengths of the velocity field under the investigation and quantification of the sampling error
The LiSBOA framework provides guidelines for the optimal design of scans performed with a scanning Doppler pulsed wind lidar and the calculation of wind velocity statistics
Summary
Reliable measurements of the wind velocity vector field are essential for understanding the complex nature of atmospheric turbulence and providing valuable data sets for the validation of theoretical and numerical models. The scope of this work is to define a methodology to postprocess scattered data of a turbulent velocity field measured through a scanning Doppler wind lidar (or eventually other remote sensing instruments) to calculate mean, standard deviation and even higher-order statistical moments on a Cartesian grid. The adoption of a directional smoothing parameter, σp, where p is a generic direction, allows maximizing the utilization of the data retrieved through inherently anisotropic measurements, such as the line-of-sight fields detected by remote sensing instruments (Askelson et al, 2000; Trapp and Doswell, 2000) With this in mind, we propose a linear scaling of the physical coordinates before the application of LiSBOA to recover a pseudo-isotropic velocity field. Violation of the inequality (Eq 8) will lead to local aliasing, with the energy content of the undersampled wavelengths being added to the low-frequency part of the spectrum
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