Variance of Radio Frequency Caused by Atmospheric Turbulence in Line-of-Sight Transmissions

The frequency stability of a radio signal propagated over a line-of-sight path is reduced by time variations in phase velocity along the path. This instability caused by the atmosphere will produce errors in frequency measurements made by averaging a standard frequency transmission over a period of time T and also in time interval measurements made by counting the number of cycles of the standard frequency received during a period of time T. Recent measurements of the variations in phase of a received signal at microwave frequencies permit estimation of both types of error as a function of T. These atmosphere-induced errors are compared to the errors inherent in the best currently-available cyrstal oscillators and it appears that the latter source of error is dominant for line-of-sight paths through the atmosphere. The level and slope of the frequency spectra have been observed to vary over wide ranges with time and geographical location. The spectral form W(f)~f^-2/3 expected on the basis of the Obukhov-Kolmogorov theory of atmospheric turbulence has a slope which lies will within the range of observed slopes for the range of fluctuation frequencies from 1 cycle/day to 1 cps.