Review and evaluation of lightning return stroke models including some aspects of their application

Abstract
Four classes of models of the lightning return stroke are reviewed. These four classes are: (1) the gas dynamic models; (2) the electromagnetic models; (3) the distributed-circuit models; and (4) the "engineering" models. Validation of the reviewed models is discussed. For the gas dynamic models, validation is based on observations of the optical power and spectral output from natural lightning. The electromagnetic, distributed-circuit, and "engineering" models are most conveniently validated using measured electric and magnetic fields from natural and triggered lightning. Based on the entirety of the validation results and on mathematical simplicity, we rank the "engineering" models in the following descending order: MTLL, DU, MTLE, BG, and TL. When only the initial peak values of the channel-base current and remote electric or magnetic field are concerned, the TL model is preferred. Additionally discussed are several issues in lightning return-stroke modeling that either have been ignored to keep the modeling straightforward or have not been recognized, such as the treatment of the upper, in-cloud portion of the lightning channel, the boundary conditions at the ground, including the presence of a vertically extended strike object, the return-stroke speed at early times, the initial bi-directional extension of the return stroke channel, and the relation between leader and return stroke models. Various aspects of the calculation of lightning electric and magnetic fields in which return stroke models are used to specify the source are considered, including equations for fields and channel-base current, as well as a discussion of channel tortuosity and branches.

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