A numerical study of waves reflected from a turbulent ionosphere

Abstract

The phase screen‐diffraction layer method is a powerful tool to study the signal scintillation of a wave propagating in a turbulent, stratified medium. Under the forward scattering approximation, the complex amplitude is shown to satisfy a parabolic equation which describes effects arising from phase changes due to irregularities and diffraction due to phase mixing. Below the turning point, these two effects can be computed sequentially. Stepping in altitude, phase changes are imbeded into each phase screen; diffraction between phase screens is accomplished using FFT techniques. This method is equivalent to the split‐step algorithm known in ocean acoustics but generalized to the case of oblique incidence. Near the turning point, the diffraction effects are assumed negligible due to the small vertical thickness of the considered region. The deterministic part of the wave fields is taken to be proportional to the Airy functions. This allows a more accurate evaluation of the phase change near the turning point than the WKB solutions. The coupling between the ascending and descending wave is discussed. The simulation model is described and, as an example, results for a linearly stratified turbulent ionosphere are given, including statistics of the reflected wave such as power spectrum, scintillation index and spatial correlation.