Concepts of lightning return stroke models

Return stroke models have been reviewed according to the assumptions they make and their underlying concepts. We have investigated the roots of the modern concepts used to describe return stroke related phenomena and illustrated their developments and deviations from the original idea. We discuss the return stroke models in two categories in accordance with the direction of the charge transfer along the channel. We show that all the models that we have considered can be described by two general sets of mathematical equations. The validation and comparison of models in reproducing measured lightning parameters are discussed. We also show the different methods employed by return stroke models to estimate the return stroke speed and discuss possible improvements that could be introduced into return stroke models in the future.