Validation of the Approximate Time-Domain Method for the Lightning-Horizontal Electric Field at the Surface of Two-layer Earth by Using FDTD

Based on the two-dimensional finite-difference time-domain (2-D FDTD) method, we have validated the time-domain method presented by Barbosa (B-P formula) for calculating the lightning-radiated horizontal electric field at the earth surface within distances from 30 to 1000 m from the lightning channel, considering the horizontally stratified earth. The results show that, except for distances in the vicinity of the lightning channel (e.g., 30 m), the B-P approximate formula can approximately predict the field peak value from 50 to 1000 m with a satisfactory accuracy within errors of 10% and its accuracy for subsequent return strokes seems to be more or less the same as that for first return strokes. The rise-time part of the field wave predicted by the B-P approximate formula is similar to that predicted by the 2-D FDTD, however, the tail of the wave predicted by the B-P approximation may be shorter than that by the 2-D FDTD (e.g., 30 and 50 m).