Errors in Second Moments Estimated from Monostatic Doppler Sodar Winds. Part I: Theoretical Description

Abstract

We present a theoretical derivation for errors in calculated second moments arising from the temporal and spatial separation between individual wind measurements obtained from three-axis colocated monostatic Doppler sodar systems. The derived relations require as input the sodar monostatic geometric parameters, pulse repetition rate, pulsing sequence, mean wind velocity and an estimate of the turbulence length scale. The model results indicate an optimum monostatic configuration that minimizes the bias due to temporal and spatial separation. A correction for pulse volume averaging is also derived which requires a turbulence length scale and an estimate of the pulse volume diameter. A monostatic technique, based on radar VAD methods, which also minimizes the bias caused by spatial and temporal separations in the sampling volumes, is proposed.