Analysis of Spectra of Atmospheric Refractive Index Differences

Abstract

When atmospheric refractive index is observed by measuring the index differences between two points, a filtering action is introduced in the fluctuation spectra. A filter function is obtained when the refractive index difference spectra frequency component is divided by the corresponding frequency component of the index spectra for a single‐point data. Test results of this filter function are compared with theoretical models. The measured filter functions for 12 data samples obtained with four refractometers on top of an 85‐m tower, are presented. These 12 cases are arranged in the order of increasing wind variability; that is, of increasing ratio of rms wind‐speed variation to the mean‐wind speed. The measured data are compared with theoretical filter functions derived assuming a “frozen‐atmosphere” model; a statistically homogeneous and isotropic invariant structure being assumed to be carried along at the mean‐wind velocity. A single mean‐wind velocity is assumed for those periods for which the measured wind data indicate a nearly constant flow. For more variable situations an integration over a range of mean‐wind speeds and wind directions is performed. Though there are numerous marked differences between the measured and calculated filter functions (as would be expected whenever a crude model is used to predict results for a truly complex situation), the model assumed does provide satisfactory explanations for many of the observed features. An unexplained anomaly, which appears in the measured filter function for many of the cases, is that at the high‐frequency end, the functions are lower than predicted.