Propagation effect of a fractal rough ground boundary on the lightning-radiated vertical electric field

A two-dimension fractional Brown motion (fBm) model is presented for describing the nature rough ground surface. By using an effective surface impedance algorithm derived by Barrick reference, the propagation effects of a fractal rough ground surface on the vertical electric field generated by lightning return strokes are analyzed. The results show that the extra field attenuation increment caused by the roughness decreases with the decrease of the ground conductivity, when the ground conductivity is less than 0.001S/m, the propagation effect of the rough ground surface with a mean square height of less than 10 m is nearly as same as that of the smooth and finitely conducting ground. However, when the ground conductivity is larger than 0.1S/m (wet earth), the frequencies higher than about 2 MHz are attenuated significantly by a rough ground surface with a mean square height of 10 m. For the derivative of the vertical electric field in time domain, the field attenuation caused by a rough ground is significant, while for the peak of the vertical electric field, there is no obvious attenuation.