Space and time filtering of remotely sensed velocity turbulence

It is well known that the width of a clear-air Doppler radar spectrum can b e used to estimate the small-scale variability of the wind. To do this accu rately requires that all contributions to the spectral width be accounted f or. Recently, an approximate formula for correcting Doppler spectral widths for spatial and temporal filtering effects was proposed. The formula assum es independent additive contributions to the spectral width from the inhere nt volume averaging of the radar-sampling volume and the finite measurement interval. In the present paper the approximate formula is compared to an e xact triple-integral formulation in which the spatial and temporal effects are shown to be coupled in a nonlinear fashion. The required integrations a re evaluated numerically and are carried out over the full range of scales in wavenumber space, in contrast to earlier work, where truncated forms of isotropic, inertial-subrange spectral forms were used to obtain a simple, c losed-form expression. Comparisons show that the approximate formula provid es a good approximation to the integral solution over small to moderate len gth scales, bur that it diverges from the integral solution at larger scale s. Asymptotic limits to the exact integral formulation for large and small scales are presented. Finally, a double-integral solution that can be rapid ly evaluated by any one of a number of commercial mathematics packages has been developed and shown to agree within 2% of the exact solution over all scales.