Predicting the spatial and temporal variation of the electromagnetic fields, currents, and speeds of subsequent return strokes

A mathematical model with a physical basis is introduced to describe the subsequent return strokes in lightning flashes. The input parameters of the model are the channel-base current and the charge distribution along the leader-term-stroke channel. Once these have been specified, the model can be used to describe how the current, speed, and the electromagnetic (EM) fields of the return strokes vary in space and time. It predicts that the current risetime increases with increasing height along the channel while the value of its peak decreases. According to the model simulations, the return-stroke speed reaches its highest value within a few meters of ground level after which it decreases monotonically with increasing height. The EM fields generated by the model reproduce most of the features observed in measured fields and the model predicted return-stroke speed profile agrees with the data obtained in experimental observations. The model predicts that E_p =32I_p/D where I_p is the peak current (in Amperes) and E_p (in V/m) is the peak radiation field observed at distance D (in meters)