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.

Cubic Phase Distortion and Irregular Degradation on SAR Imaging Due to the Ionosphere

“…If the initial complex amplitude is u(x, z 0 , ω) = 1, then the received complex amplitude on the ground or next screen can be obtained by repeating the aforementioned process of (13)- (15).…”

“…However, the single-layer model is applicable in the weak scintillation limit [11]. Aiming at this issue, a model called multiple phase screen (MPS) technique is used in this paper, which can accommodate cases in both weak and strong scattering [11]- [15]. Under the conditions of oblique incidence and anisotropic irregularities, we apply it to study the random effects of scintillation on azimuthal resolution.…”

Pseudoreciprocity in a disturbed nonisotropic medium and its application to radio wave propagation

“…These equations can take account of perturbations in the medium and hence are suitable for investigating the effect of ionospheric disturbances such as TIDs. The equations incorporate both diffractive and refractive effects and so offer an alternative to phase screen type approaches [ Nickisch , 1992; Wagen and Yeh , 1986]. The equations have been developed into a form that is amenable to FFT techniques and so can form the basis of efficient propagation algorithms.…”

“…These new equations allow the perturbed field to be calculated without resorting to the Rytov approximation. The techniques provide an alternative to the phase screen methods [ Nickisch , 1992; Wagen and Yeh , 1986] that have be also been used to study the radio wave propagation through a disturbed isotropic ionospheric medium. Additionally, however, the new approach incorporates nonisotropic effects.…”

Modelling the ionospheric effects in HF radar long term integration

“…From their results, we will integrate a disturbing ionosphere profile inside the path of the HF radar signal. To do so, the electron density distribution [8] should be disturbed according to (3):…”