Estimation of Apparent Ionospheric Reflection Height from LEMP Waveforms for the Case of Tilted Lightning Channel

The interaction of lightning electromagnetic pulse with the ionosphere has been often analyzed using the finite-difference time-domain method in the 2-D cylindrical coordinate system or in the 2-D spherical coordinate system. In this article, time-update equations for electric and magnetic fields in the 3-D spherical coordinate system are presented, and vertical electric fields at far distances over the curved surface of the Earth from the base of a vertical or tilted lightning return-stroke channel are computed. The lightning channel is represented by the modified transmission-line model with linear current decay with the distance along the channel. A realistic channel-base current waveform with a risetime of 3 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i>s represented by the Heidler function is used. The ionosphere is simulated by a nonuniform medium whose conductivity increases exponentially with altitude. Apparent ionospheric reflection heights are estimated based on the arrival time difference between the ground wave and the first skywave. When the arrival times of ground wave and skywave are defined as the arrival times of their field peaks, the estimated ionospheric reflection height depends on channel tilt angle and increases with increasing field observation distance. In contrast, when the arrival times of ground wave and skywave are defined as the arrival times of 80% of their field derivative peaks, the estimated ionospheric reflection height is not much influenced by either distance or channel tilt angle.