Extension of the Diendorfer‐Uman lightning return stroke model to the case of a variable upward return stroke speed and a variable downward discharge current speed

Abstract

A new lightning return stroke model has recently been proposed by Diendorfer and Uman (1990). In this model, if one specifies a current at the channel base (ground), a constant return stroke speed, and a channel discharge time constant, one can derive analytically the current and charge as a function of time and height associated with the channel above ground. Here we present a more general and more straightforward derivation of the Diendorfer‐Uman model. In the new formulation we allow a variable return stroke speed that can be any arbitrary function of height. The influence of a decrease in speed with height, as occurs in nature, on the channel current and charge distributions and on the radiated electric and magnetic fields is determined and compared with the constant speed case. For a given channel base current, a decreasing speed with height does not change the initial peak electric and magnetic fields appreciably from the values found for a constant speed having the same value as the variable speed at the channel base, but a decreasing speed can cause considerable changes in field waveshapes for both the distant radiation fields and the near electrostatic fields. In addition to allowing an arbitrary return stroke speed, the new formulation of the Diendorfer‐Uman model allows the downward propagating current waves released by the return stroke front also to have an arbitrary variable speed, whereas the original model assumed that speed to be constant at the speed of light.