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

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.