The evolution characteristics behind the commonly used return stroke engineering model have not been fully understood, which limits the accurate estimation on the lightning damage effect. Therefore, the line charge densities behind the TL, MTLL MTLE, BG, TCS and DU models are discussed under three cases: (a) constant velocity with traditional attenuation function, (b) exponentially decreasing velocity with traditional attenuation function, and (c) exponentially decreasing velocity with improved attenuation function considering time factor. As height increases, the charge density behind the TL, MTLL and MTLE models in case (c) is between that in case (a) and (b). However, owing to the reduction of the inputting charge from the channel base and the gradually prominent deposition effect of the residual charge, the total charge densities in the three cases trend to be consistent with each other in the end. Additionally, the results suggest that the near-region radiated fields yielded by the traditional return stroke model (case (a)) may be smaller than the actual observation. For the BG, TCS and DU models, the connotative charge density is mainly the deposited charge density component. Although the charge density decreases overall with height, the waveform exhibits a "hump" at the height of about 2 km~3 km. The presented results may be of assistance in understanding the commonly used engineering model, as well as in performing more effective protection against lightning hazards.
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