Simulation of GPS radio occultation signals through Sporadic-E using the multiple phase screen method
Graphical abstract
Introduction
The ionosphere is a key source of signal distortion and propagation path alteration for radio frequency (RF) intra- or trans-terrestrial wireless communication and sensing at frequencies in the L-band and below (Basler et al., 1988). Although considerable progress has been made since signals were first reflected from the bottom of the E-layer (Joly, 1902), we still lack the observational capabilities and theoretical understanding to predict ionospheric conditions with enough granularity for applications such as HF geolocation (Mitchell et al., 2017).
Global Navigational Satellite Systems (GNSS) have become the ideal transmitters of opportunity to measured the state of the ionosphere, either by a proliferation of ground-based receivers (Maeda and Heki, 2014, 2015; Maeda et al., 2016) or through use of the specially designed low Earth orbit (LEO) satellites such as the Constellation Observing Satellite for Meteorology, Ionosphere, and Climate (COSMIC) system. This satellite constellation and its recently launched followon of six additional satellites designated COSMIC II, provide a receive system to pair with GNSS transmitters able to characterize vertical electron density gradients in the ionosphere through radio occultation (RO) measurements. RO provides a measure of distortion as a known signal passes through varying indices of refraction in the ionosphere (Hajj and Romans, 1998; Carrano et al., 2011) and neutral atmosphere (Kursinski et al., 1997; Melbourne, 2004; Schreiner et al., 2007).
Previous research has demonstrated the effectiveness of using GPS-RO to identify sporadic-E (Es) layers through particular amplitude and phase signatures in the received signal (Hocke et al., 2001; Wu et al., 2005; Zeng and Sokolovskiy, 2010; Yue et al., 2015; Niu et al., 2015; Arras and Wickert, 2018). Specifically, a linear relationship between the S2 scintillation index and the blanketing frequency of the sporadic-E layer (fbEs) has recently been proposed by Arras and Wickert (2018) and Resende Chagas et al. (2018) (n.b., here we used S2 instead of S4 following the Briggs and Parkin (1963) terminology). Gooch et al. (2020) applied the linear mapping technique to a larger RO data set and compared the results against ionosonde measurements across the globe. Their results indicate that the relationship between S2 and fbEs may depend on additional sporadic-E characteristics and may not necessarily be linear with respect to fbEs. The simulations of Zeng and Sokolovskiy (2010) also support this claim with a strong dependence of the RO signal amplitude profiles in the measurement plane on sporadic-E width, length, and orientation.
This work expands on the Gooch et al. (2020) study by simulating signal propagation through idealized layers using the multiple phase screen (MPS) method (Knepp, 1982; Wu et al., 2005; Zeng and Sokolovskiy, 2010) in order to determine the relationship between S2 and sporadic-E parameters. Additionally, a new metric to estimate fbEs from a spatial Fourier transform of the signal intensity is presented as an alternative approach for extracting sporadic-E characteristics from GPS-RO measurements.
Throughout this document, we use fbEs to characterize the Es intensity following the comparisons between GPS-RO and ionosonde measurements presented in Arras and Wickert (2018); Resende Chagas et al. (2018); Gooch et al. (2020). The fbEs parameter is the maximum blanketing frequency of the Es layer as measured by ionosondes and is related to the electron density through where is the maximum electron density of the blanketing layer. This conversion does not account for the background E-layer density as calculated by the metallic ion fbμEs parameter (Haldoupis, 2019), but is used as a stand-in approximation for the sporadic-E intensity to analyze trends.
Section snippets
Parabolic wave equation
The MPS method is an iterative numerical approach for solving the parabolic wave equation. Originally described in Leontovich and Fock (1946), the simplifications applied to wave propagation allow for a substantial reduction in computational time and resources compared to full-wave processes (e.g. Finite Difference Time Domain, FDTD, or Method of Moments, MoM). The phase screen parabolic approach can thus be applied to problem sets that would be prohibitively large for FDTD or MoM methods,
S2 simulations
Amplitude scintillation caused by lensing from sporadic-E layers is commonly used to locate Es from GPS-RO measurements (Wu et al., 2005; Arras et al., 2008). One metric commonly used is the S2 scintillation index, which is the standard deviation of the signal amplitude divided by the mean (Briggs and Parkin, 1963):where the electric field amplitude, , is used as the signal amplitude in these simulations through the reduced wave construct . Here we adopt the Briggs and Parkin (1963)
Spectral method
In an attempt to find an additional metric capable of extracting fbEs values from intense sporadic-E layers, a spatial Fourier transform is taken of the final output screen of the phase screen simulation with a sampling frequency of (1/38 cm−1). Fig. 6 reveals the spatial spectrum of the diffracted plane wave through a sporadic-E layer with an effective length of 65 km, a vertical thickness of 1.75 km, and a fbEs of 10 MHz. There are several structural components that can be observed in
Conclusions
The multiple phase screen method was used for simulations of GPS L1 radio occultation signals through various idealized sporadic-E layers to analyze changes in signal amplitude profiles at the measurement plane. An investigation of the S2 scintillation index found a strong dependence on fbEs and Es size (length, width, and vertical thickness). A linear regime between S2 and fbEs was found for lower fbEs values before the S2 plateaued. The fbEs value of the plateau point depends on the effective
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We would like to thank L. J. Nickisch from NorthWest Research Associates for several helpful discussion on the multiple phase screen method and sporadic-E profiles.
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