The Atmospheric Scale Lengths of Turbulence and Its Dependencies Derived from GPS Single Difference with a Common Clock

Abstract

Microwave signals, for example, those from Global Navigation Satellite Systems (GNSS) and very long baseline interferometry, are affected by tropospheric turbulence in such a way that the random fluctuations of the atmospheric index of refraction correlate the phase measurements. These atmospheric correlations are an important error source in space geodetic techniques. For computational reasons, they are neglected in positioning applications, to the detriment of a trustworthy description of the precision, and rigorous test statistics. Fortunately, modelling such correlations is possible by combining concepts from electromagnetic wave propagation in a random medium and the Kolmogorov turbulence theory. In this contribution, we will process single differences GNSS phase observations from a 300 m baseline between two different receivers linked to a common clock. After a preprocessing to filter additional error contributions, such as multipath, we will study the power spectral density of the phase residuals. We will estimate its low and high cutoff frequencies with an adapted unbiased Whittle maximum likelihood estimator. These cutoff frequencies – as predicted by turbulence theory – are related directly to the scale lengths of turbulence, i.e. the size of the eddies that correlate the GNSS observations. The study of their dependencies with the satellite geometry, day of the year, or time of the day provides new insights into the two- and three-dimensional atmospheric turbulence in the atmosphere. In addition, it contributes to improving the stochastic description of random effects impacting GNSS phase observations.