Deriving Power Spectra from a Three-Component Sonic Anemometer

Abstract

The paper describes the general characteristics of a non-orthogonal sonic anemometer array. The effects of line-averaging and spatial separation (between mid-points of the horizontal paths) are analyzed and spatial transfer functions are derived for power spectra of the longitudinal, lateral and vertical velocity components. While line-averaging always causes spectral attenuation at wavenumbers larger than 1/l (where l is the sonic path length), spatial separation produces cross-contamination between the horizontal velocity spectra at wavenumbers exceeding 1/d (where d is the separation distance). For an array with a 120° angle between the horizontal sonic paths the net effect of this cross-contamination is to overestimate the longitudinal velocity spectrum and underestimate the lateral velocity spectrum. The separation distance which yields maximum flatness in the transfer function for the longitudinal component is found to be 0.6 l. Also discussed are the effects of aliasing and long-term trends on the shape of the computed spectrum and spectral correction for the spatial transfer function in the context of these effects.