Effects of Volume Averaging on the Line Spectra of Vertical Velocity from Multiple-Doppler Radar Observations

Abstract

We examine the fidelity of one-dimensional spectra of vertical velocity derived from multiple-Doppler radar observations. For analytical tractability, we use the following assumptions: 1) the turbulent atmosphere has infinite horizontal dimensions and a vanishing vertical velocity at x3 = H (due to elevated inversion or a tropopause) and at the surface; 2) the turbulence is isotropic and has a Kolmogorov spectrum; 3) the combined effect of pulse-volume averaging and objective analysis is to replace point measurements by a volume integral; and 4) for the purpose of estimating the horizontal velocities, multiple non-orthogonal radars may be replaced by two equivalent orthogonal radars. The findings are as follows: a) For equal-resolution radars, the relative response decreases monotonically with wavenumber. Above the cutoff wave-number, the relative response is close to zero, while below ?0.1 of the cutoff wavenumber an asymptotic value less than unity is obtained. This asymptotic value is found to be a function of the vertical resolution. b) Using unequal resolution to resolve some small-scale features should be pursued with caution. Depending on the vertical resolution, the wavenumber and the direction of the line along which the spectrum is taken, some useful small-scale information can be retained, but for some parameter values, unequal resolution can lead to erroneous conclusions. c) Theory and experiment indicate that for flows of finite depth, the attenuation can depend not on the dimensional vertical resolution ?z but on the number of vertical levels that can be resolved by the radars, i.e., on the non-dimensional vertical resolution.