A unified formulation for the computation of the six-degrees-of-freedom-motion-induced errors in floating Doppler wind LiDARs

Abstract

This work presents an analytical formulation to assess the six-degrees-of-freedom-motion-induced error in floating Doppler wind LiDARs (FDWLs). The error products derive from the horizontal wind speed bias and apparent turbulence intensity. Departing from a geometrical formulation of the FDWL attitude and of the LiDAR retrieval algorithm, the contributions of the rotational and translational motion to the FDWL-measured total error are computed. Central to this process is the interpretation of the velocity–azimuth display retrieval algorithm in terms of a first-order Fourier series. The obtained 6 DoF formulation is validated numerically by means of a floating LiDAR motion simulator and experimentally in nearshore and open-sea scenarios in the framework of the Pont del Petroli and IJmuiden campaigns, respectively. Both measurement campaigns involved a fixed and a floating ZephIRTM 300 LiDAR. The proposed formulation proved capable of estimating the motion-induced FDWL horizontal wind speed bias and returned similar percentiles when comparing the FDWL with the fixed LiDAR. The estimations of the turbulence intensity increment statistically matched the FDWL measurements under all motional and wind scenarios when clustering the data as a function of the buoy’s mean tilt amplitude, mean translational-velocity amplitude, and mean horizontal wind speed.

This research project was part of the project PID2021-126436OB-C21 funded by the Ministerio de Ciencia e Investigación (MCIN)/Agencia Estatal de Investigación (AEI)/10.13039/501100011033 y FEDER “Una manera de hacer Europa”. The work of A. Salcedo-Bosch was supported by grant 2020 FISDU 00455 funded by Generalitat de Catalunya—AGAUR. The work of M.P Araújo da Silva was supported under Grant PRE2018-086054 funded by MCIN/AEI/10.13039/501100011033 and FSE “El FSE invierte en tu futuro”. The European Commission collaborated under projects H2020 ATMO-ACCESS (GA-101008004) and H2020 ACTRIS-IMP (GA-871115).

Peer Reviewed

Postprint (published version)