The random amplitude and phase fluctuations observed in trans-ionospheric radio signals are caused by the presence of electron density irregularities in the ionosphere. Ground-based measurements of radio wave signals provide information about the medium through which these signals propagate. The Canadian High Arctic Ionospheric Network (CHAIN) Global Position System (GPS) receivers record radio signals emitted by the GPS satellites, enabling the study of their spectral characteristics.This study presents examples of phase spectra with two power-law components. These components exhibit steeper spectral slopes at higher frequencies and shallower ones at lower frequencies. In most cases, the breaking frequency point is statistically larger than the frequency associated with the Fresnel scale under the Taylor hypothesis. To be more specific, we conducted a spectral characterization of sixty (60) events recorded by the CHAIN Churchill GPS receiver, which is located in the auroral oval. When fluctuations above the background level are only observed in the phase, the spectra tend to be systematically steeper. Conversely, the power increase in higher frequency fluctuations accompanying amplitude scintillation tends to result in shallower spectra. A basic yet powerful model of radio wave propagation through a turbulent ionosphere, characterized by a power law electron density spectrum, can help to explain the two power laws observed in the scintillation events presented in this study by identifying the role played by small-scale ionospheric irregularities in diffraction.

Ground-based amplitude measurements of GNSS signal during ionospheric scintillation are analyzed using prevalent data analysis tools developed in the fields of fluid and plasma turbulence. One such tool is the structure function of order $q$, with $q = 1$ to $q = 6$, which reduces to the computation of the second order difference in the GPS signal amplitude at various time lags, and allows for the exploration of dominant length scales in the propagation medium. We report the existence of a range where the structure function is linear with respect to time lag. This linear time-segment could be considered as an analog to the inertial range in the context of neutral and plasma turbulence theory. Below the linear range, the structure function increases nonlinearly with time lag, again in good concordance with the intermittent character of the signal, given that a parallel is drawn with turbulence theory. Quantitatively, the slope of the structure function in the linear range is in good agreement with the scaling exponent determined from in-situ measurements of the electrostatic potential at low altitude (E-region) and the electron density at the topside ionosphere (F-Region). This in turn suggests the conjecture that scintillation could be considered a proxy for ionospheric turbulence. Furthermore, we have found that the probability distribution function of the second order difference in the signal amplitude has non-Gaussian features at large time-lags; a result that seems inconsistent with equilibrium statistical physics which suggests a Gaussian distribution for the conventional random walk processes.