Fast Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray–Rubinstein Formula

Cooray–Rubinstein formula has been extensively used for the evaluation of the horizontal component of the electric field generated by a lightning return stroke over a lossy ground. Considering the good characteristics of the formulation in terms of “step response” kernel $K_{\varepsilon }(t)$ corresponding to the ground surface impedance, proposed by Andreotti et al . recently, a new method for evaluating the Cooray–Rubinstein formula in the time domain is proposed in this paper. In this method, $K_{\varepsilon }(t)$ is first expressed by an integral of exponential function based on the integral formula of the modified Bessel function of the first kind, and then approximated by a piecewise exponential function using the Gauss numerical integration. Finally, taking advantage of the piecewise recursive convolution, the time-domain Cooray–Rubinstein formula for evaluating the lightning horizontal electric field can be calculated accurately and efficiently. The validity and efficiency of the proposed method are demonstrated by the comparisons with the methods in other literature.