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. 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 introduced practices entailing the estimation of scalar average point quantities by the measurement of vector averages over volumes and vice versa. The relationship between vector and scalar averages, and the relationship between volume and point measurements, must therefore both be understood. It is found that their ratio depends upon wind direction variability according to a Bessel function of the standard deviation of the wind direction during the averaging interval. The impact of wind direction variability on power production is also explored. 2) The finite probe length of remote sensing devices incurs a volume averaging bias if wind shear is non-linear. The sensitivity of the devices to signals from a range of heights produces volume averages representing wind speeds within that range. If the wind shear is described by a logarithmic wind profile the apparent height, at which the average wind speed occurs, is found to depend on simple geometrical arguments concerning configuration height and probe length independent of the degree of wind shear. Similar arguments are applied to determine the ideal height across the rotor at which to acquire wind speed data for power curves. 3) The common 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 uniform.
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