Validity of 2-D electromagnetic approaches to estimate log-amplitude and phase variances due to 3-D ionospheric irregularities

Abstract

To limit the computation time and the computer resource, 2-D numerical approaches such as 2-D parabolic wave equation (2-D PWE) associated with 1-D multiple phase screens (1-D MPS) are classically used to estimate ionospheric scintillation effects on radio wave propagation. However, in the ionosphere, the turbulent fluctuations of the electron density responsible for the scintillation effects are clearly a three-dimensional process. This paper quantitatively assesses the errors potentially induced by the 3-D to 2-D dimensional reduction to predict ionospheric effects in terms of log-amplitude and phase variances. To that purpose, the ionospheric electron density fluctuations are described by an anisotropic turbulent spectrum with three axes of anisotropy. On the one hand, considering four typical configurations (two equatorial and two polar radio links), scintillation effects are evaluated numerically, using 3-D and 2-D PWE-MPS numerical techniques. Some consequences of the dimensional reduction are then qualitatively discussed. On the other hand, an analytical framework that solves the 3-D and 2-D propagation equations in the line-of-sight coordinate system is proposed. Under weak scattering assumption, it allows assessing analytically the consequences of the dimensional reduction whatever the geometry of the transionospheric radio link and, finally, allows 2-D numerical schemes to be used advisedly for the prediction of ionospheric scintillation effects.