Compensation of vector and volume averaging bias in lidar wind speed measurements

Abstract

A number of vector and volume averaging considerations arise in relation to remote sensing, and in particular, Lidar. 1) Remote sensing devices obtain vector averages. These values are often compared to the scalar averages associated with cup anemometry. The magnitude of a vector average is less than or equal to the scalar average obtained over the same period. The use of Lidars in wind power applications has entailed the estimation of scalar averages by vector averages and vice versa. The relationship between the two kinds of average must therefore be understood. It is found that the ratio of the averages depends upon wind direction variability according to a Bessel function of the standard deviation of the wind direction during the averaging interval. 2) The finite probe length of remote sensing devices also incurs a volume averaging bias when wind shear is non-linear. The sensitivity of the devices to signals from a range of heights produces volume averages which will be representative of wind speeds at heights within that range. One can distinguish between the effective or apparent height the measured wind speeds represent as a result of volume averaging bias, and the configuration height at which the device has been set to measure wind speeds. If the wind shear is described by a logarithmic wind profile the apparent height is found to depend mainly on simple geometrical arguments concerning configuration height and probe length and is largely independent of the degree of wind shear. 3) The restriction of the locus of points at which radial velocity measurements are made to the circumference of a horizontally oriented disc at a particular height is seen to introduce ambiguity into results when dealing with wind vector fields which are not irrotational.