Uncertainty and bias on velocities determined from an arc-scanning lidar

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Accurate determination of wind speed offshore is important for the progression of offshore wind energy. Arc-scanning lidars offer precise measurements of both wind speed and direction. They can be placed on a fixed footing, such as a transition piece of a fixed-bottom wind turbine, or on the coast. However, the procedure to derive the wind vector relies on the assumption of homogeneous flow, i.e., that the wind vector is constant along the scanning arc. In this study, we derive a theoretical expression for the wind speed bias due to inhomogeneity in the mean flow. We show that inhomogeneity in the flow will mostly affect the wind component tangential to the arc. The dominating term in the bias equation is equal to the range gate distance times the gradient of the wind speed away from the lidar in the direction along the arc, i.e. crudely, how fast the wind component away from the lidar changes with the scan angle. Atmospheric simulations using the Weather Research and Forecast (WRF) model of flow near mountainous coasts (Madeira Island), where the wind gradients are supposed to be largest, are used to estimate the gradient and, thereby, the bias in a real case. Errors in special situations exceed 50%.