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A LiDAR Statistical Barnes Objective Analysis (LiSBOA) for optimal design ofLiDAR scans and retrieval of the velocity statistical moments is proposed. TheLiSBOA represents an adaptation of the classical Barnes scheme for thestatistical analysis of unstructured experimental data in N-dimensional spacesand it is a suitable technique for the evaluation over a structured Cartesiangrid of the statistics of scalar fields sampled through scanning LiDARs. TheLiSBOA is validated and characterized via a Monte Carlo approach applied to asynthetic velocity field. This revisited theoretical framework for the Barnesobjective analysis enables the formulation of guidelines for optimal design ofLiDAR experiments and efficient application of the LiSBOA for thepost-processing of LiDAR measurements. The optimal design of LiDAR scans isformulated as a two cost-function optimization problem including theminimization of the percentage of the measurement volume not sampled withadequate spatial resolution and the minimization of the error on the mean ofthe velocity field. The optimal design of the LiDAR scans also guides theselection of the smoothing parameter and the total number of iterations to usefor the Barnes scheme.

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