On the validity of the Cooray formula for the evaluation of the underground horizontal electric fields of lightning

Using a parallel implementation of the finite difference time domain (FDTD) technique, we test the accuracy of the Cooray formula in which the underground horizontal electric field is evaluated using its counterpart at the air-soil interface. This latter can be calculated using either (i) the original Cooray-Rubinstein (CR) formula in which the magnetic field at ground level is evaluated assuming the ground as a perfect conductor, (ii) taking into account propagation effects in the computation of the magnetic field. We show that, by taking into account propagation effects in the computation of the magnetic fields used in the CR formula and for ground conductivities of 0.001 S/m and higher, the underground horizontal electric field can be evaluated using the Cooray formula with acceptable accuracy.