On the Accuracy of Wait's Formula Along a Mixed Propagation Path Within 1 km from the Lightning Channel

We have examined the accuracy of Wait's formula for evaluating lightning vertical electric field and azimuthal magnetic field over a mixed propagation path (vertically stratified) by using the finite-difference time-domain (FDTD) technique at near (200 m) and intermediate (1000 m) distance range from the lightning channel. For the first return stroke, Wait's formula has a reasonable accuracy for predicting lightning electromagnetic fields within distances of 1000 m. However, for the subsequent return stroke, although Wait's formula predicts the nearly same field peaks as that by FDTD no matter how the ground conductivity is vertically stratified, some waveform differences can be observed at the early-time response within a few microseconds. Therefore, Wait's formula may cause some errors for predicting the field derivates within tens or hundreds of meters.