Full‐wave reflection of lightning long‐wave radio pulses from the ionospheric D region: Numerical model

Abstract

[1] A model is developed for calculating ionospheric reflection of electromagnetic pulses emitted by lightning, with most energy in the long-wave spectral region (f $ 3-100 kHz). The building block of the calculation is a differential equation full-wave solution of Maxwell's equations for the complex reflection of individual plane waves incident from below, by the anisotropic, dissipative, diffuse dielectric profile of the lower ionosphere. This full-wave solution is then put into a summation over plane waves in an angular direct Fourier transform to obtain the reflection properties of curved wavefronts. This step models also the diffraction effects of long-wave ionospheric reflections observed at short or medium range ($200-500 km). The calculation can be done with any arbitrary but smooth dielectric profile versus altitude. For an initial test, this article uses the classic D region exponential profiles of electron density and collision rate given by Volland. With even these simple profiles, our model of full-wave reflection of curved wavefronts captures some of the basic attributes of observed reflected waveforms recorded with the Los Alamos Sferic Array. A follow-on article will present a detailed comparison with data in order to retrieve ionospheric parameters.

Lightning-generated whistler waves observed by probes on the Communication/Navigation Outage Forecast System satellite at low latitudes

“…The fact that the magnetic field is basically horizontal at these low latitudes would suggest that the whistler mode waves might follow a more complicated path to arrive at the satellite within the low-latitude ionosphere environment. Indeed, the lower-frequency ranges of the spectrum we covered have wavelengths which can be thousands of km, and therefore ray tracing studies may be insufficient, and a full wave analysis such as employed by Jacobson et al [2009] may be required to fully analyze the details of the propagation paths.…”

An improved ray theory and transfer matrix method‐based model for lightning electromagnetic pulses propagating in Earth‐ionosphere waveguide and its applications

“…Although the FDTD model [ Hu and Cummer , ; Marshall , ] is a powerful tool with great precision, burdensome computing makes it almost impossible to solve the inversion problem especially under situations that the parameter library is huge. The Jacobson's full‐wave model [ Jacobson et al ., ; Shao et al ., ; Lay et al ., ] is also an efficient tool to probe the ionosphere, but their technique retrieving the ionosphere electron density profile could be further improved. They retrieved the ionosphere electron density profile by matching the time delay and amplitude of the inversed sky wave peak modeled with that observed [ Shao et al ., ; Lay et al ., ], which may cause ambiguity when applying to the double‐peaked sky wave in nighttime.…”

“…In the air below the ionosphere, we adopt the Ray Theory with the same incident angle finding technique used by Jacobson et al . [] and a modified transfer function to treat the LEMP propagation. The whole simulation is realized with the Matlab codes.…”

“…Once d G , ‖ R ‖ , and ω of E 0 are determined, θ i can be retrieved by a phase unwrapping process suggested by Jacobson et al . []. The phase swapping process is to find the angle that has the maximum phase integration among all incident angles, which is also known as the quasi‐specular incident angle or the concentrated incident angle in this study.…”

FDTD Modeling of LEMP Propagation in the Earth‐Ionosphere Waveguide With Emphasis on Realistic Representation of Lightning Source

“…A ray‐theory‐based frequency domain model for studying VLF/LF signal propagation was developed by Jacobson, Shao, and Holzworth (), who also reviewed previously proposed models of this type (see also Jacobson, Shao, & Lay, , and Shao & Jacobson, ). Using this model and LEMPs recorded by the Los Alamos Sferic Array, Shao, Lay, and Jacobson () and Lay, Shao, and Jacobson () inferred the reduction of electron density in the lower ionosphere caused by thunderstorms.…”