Instrumental errors in spectral-width turbulence measurements by radars

Abstract

Measurements of turbulent energy dissipation rates by radar spectral-width procedures require differencing two numbers to produce a difference that is small relative to the two initial numbers. In particular, the square of the so-called “beam-broadening” component must be subtracted from the square of a measured spectral width. Because the difference is relatively small, it is very sensitive to statistical fluctuations in each of the initial measured parameters. The method by which the measured spectral width is determined can impact the accuracy of the measurements, and, in addition, the beam-broadened component is affected by errors in the measured wind, variability in the mean wind, wind-shear, and aspect-sensitivity of the scatterers. All these effects can impact the measurements of turbulence, and in some cases can even produce physically unrealistic “negative” values of turbulence strength. In this paper, we investigate the relative importance of (i) variability of the mean wind within the averaging period, (ii) digitization errors and the accuracy of determination of the spectral width, (iii) the particular beam-broadening model employed, and (iv) anisotropy of the scatterers. Although these terms are often discussed in the literature, we have quantified their relative importance. The accuracy of determination of the spectral width is the most important source of error, followed by variability of the mean wind in the averaging period. In addition to these studies, we also develop a new formula for accurate determination of the beam-broadened spectral width. This includes a new term that was missing from earlier formulations.