LiSBOA: LiDAR Statistical Barnes Objective Analysis for optimal design of LiDAR scans and retrieval of wind statistics. Part I: Theoretical framework

A LiDAR Statistical Barnes Objective Analysis (LiSBOA) for optimal design of LiDAR scans and retrieval of the velocity statistical moments is proposed. The LiSBOA represents an adaptation of the classical Barnes scheme for the statistical analysis of unstructured experimental data in N-dimensional spaces and it is a suitable technique for the evaluation over a structured Cartesian grid of the statistics of scalar fields sampled through scanning LiDARs. The 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 optimal design of LiDAR experiments and efficient application of the LiSBOA for the post-processing 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.