General Time-Domain Formula for Horizontal Electric Field Excited by Lightning

In this paper, a general domain expression is developed to calculate the horizontal electric field at the ground surface. The expression satisfies stricter conditions than the Cooray-Rubinstein (C-R) and Wait formulae. We proved that the new expression can be reduced into the first approximation of the C-R and Wait formulae. An evaluation that utilized the numerical results obtained by the three formulae was conducted to investigate the error caused by the assumptions made in the C-R and Wait formulae. Finally, the approximate method proposed by Caligaris, Delfino, and Procopio was utilized to evaluate the new formula and the C-R formula through comparison with the results obtained conventionally using the C-R formula.