Horizontal Electric Field Above- and Underground Produced by Lightning Flashes

The horizontal electric field both at points above and below ground in the vicinity of lightning return strokes were evaluated by numerical solution of Sommerfeld's integrals. Results are presented for ground conductivities in the range of 0.01-0.0001 S/m. The results are compared with the following approximate procedures used in the literature to calculate horizontal electric fields: 1) the surface impedance approximation; 2) the quasi-static approximation frequently used in lightning protection standards; and 3) Cooray's simplified formula for the computation of underground electric field. Based on this comparison, the distance range in which these approximations are valid is obtained. The results obtained show that: 1) The surface impedance approximation can generate correct horizontal electric field when the distance to the point of observation is larger than about 50, 200, and 500 m for ground conductivities of 0.01, 0.001, and 0.0001 S/m, respectively. 2) It is necessary to include propagation effects in the magnetic field that is being used as an input in the surface impedance expression when it is being used to calculate the horizontal electric field. 3) Cooray-Rubinstein approximation gives exact results when it is being used to calculate the horizontal electric field aboveground generated by cloud flashes. 4) Cooray's simplified formula connecting the surface horizontal electric field to the underground one gives accurate results, provided that the horizontal electric field at the surface of the ground, which is used as an input, is calculated accurately and the depth of the point of observation is kept much less than the distance to the point of strike.