In this paper, we have extended the Cooray-Rubinstein (C-R) approximate formula into the fractal rough ground surface and then validate its accuracy by using three-dimensional (3-D) finite-difference time-domain (FDTD) method at distances of 50 m and 100 m from the lightning channel. The results show that the extended C-R formula has an accepted accuracy for predicting the lightning-radiated horizontal electric field above the fractal rough and conducting ground, and its accuracy increases a little better with the higher of the earth conductivity. For instance, when the conductivity of the rough ground is 0.1 S/m, the error of the peak value predicted by the extended C-R formula is less than about 2.3%, while its error is less than about 6.7% for the conductivity of 0.01 S/m. The rough ground has much effect on the lightning horizontal field, and the initial peak value of the horizontal field obviously decreases with the increase of the root-mean-square height of the rough ground at early times (within several microseconds of the beginning of return stroke).
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