Expressions for far electric fields produced at an arbitrary altitude by lightning return strokes

[1] Electromagnetic fields produced at high altitudes by return strokes in cloud-to-ground lightning are needed in studies of transient luminous events in the mesosphere. Such calculations require the use of a lightning return stroke model. Two of the widely used return stroke models are (1) the modified transmission line model with exponential decay (MTLE) of current with height and (2) the modified transmission line model with linear decay (MTLL) of current with height. In this paper, simplified expressions based on the MTLE and MTLL models are derived for calculating far (radiation) electric fields produced at an arbitrary elevation angle by lightning return strokes. It is shown that different (for example, containing either spatial or time integral), but equivalent equations can be derived for each of the models. Predictions of simplified expressions are compared with electric fields computed using exact expressions, including all the field components, and the validity of simplified expressions for distances that are much greater than the radiating channel length is confirmed.