An approximate formula for the calculation of the horizontal electric field from lightning at close, intermediate, and long range

TLDR

The authors propose an approximate formula to compute the horizontal electric field from lightning at various distances and heights. The formula is analytically simple, easily implemented in frequency and time domains, and validated against Sommerfeld integral approximations across a broad distance range. The formula proves useful for lightning‑induced voltage calculations, matches well with Sommerfeld integral approximations over a broad range of distances, and predicts a sharp initial pulse followed by a slower opposite‑polarity change for negative ground lightning at close range.

Abstract

We present an approximate formula to calculate the horizontal electric field from lightning that is applicable for close, intermediate, and long distances to the lightning, at ground level and at a height above ground. The formula is analytically simple and can be readily implemented for numerical calculations in the frequency and in the time domains. The formula can be particularly useful for lightning induced voltage calculations. A test of the formula by comparison with the results obtained using good approximations to Sommerfeld's integrals is presented. The results compare favorably for a wide range of distances. Theoretical waveforms obtained with a return stroke model and the formula predict that, for negative ground lightning, the horizontal component of the electric field at close range and at a height of a few meters above the ground starts with a sharp pulse directed toward the lightning channel and is followed by a slower field change of opposite polarity.