The Curvature of TEC as a Proxy for Ionospheric Amplitude Scintillation

Fluctuations in the ionospheric electron density cause distortions in the Global Navigation Satellite Systems (GNSS) signals recorded on the ground. The examination of these distortions reveal some of the physical conditions under which the electron density fluctuations develop as well as their physical characteristics. Several studies have investigated the correlation between the rate of change of the total electron content $\left(ROTI\right)$ and amplitude and phase scintillation indices $S_4$ and ${\sigma }_{\Phi }$, respectively. These studies stipulate that $ROTI$ could be used as a proxy for scintillation indices. The link between the scintillation indices and the variations in $TEC$ is investigated both theoretically and empirically. Our study shows that the second derivative (the Laplacian) of the $TEC$ provides a better diagnosis of the nature of the interaction of trans-ionospheric radio signals with ionospheric irregularities. In the refractive case, the second derivative of $TEC$ fluctuations vanishes. In the diffractive limit, we show that the amplitude scintillation index and the standard deviation of the second derivative of $TEC$ are linearly dependent. The theoretical results are empirically validated with measurements of GNSS radio signals propagating through the auroral ionospheric region and recorded by ground receivers of the Canadian High Arctic Ionospheric Network (CHAIN). The present study suggests that the use of $ROTI$ as a proxy for scintillation occurring in the polar and auroral regions must be taken with caution.