A 3-d self-organized leader propagation model and its engineering approximation for lightning protection analysis

This paper presents a 3-D self-organized model of a downward stepped leader in negative cloud-to-ground lightning. In the model, the characteristic features of stepped leaders are generalized, so that parameters, such as the charge density along with the leader channel, leader corona sheath radius, leader step length, step time interval, and step advance speed, are calculated. Stepwise growth of the 3-D leader channel is developed stochastically. Parameters predicted by the model are qualitatively compatible with observation results, while the engineering approximation of the model for convenient lightning protection analysis is derived thereafter. The model is operated under various conditions at different leader initiation heights and electric potentials. Based on statistics of the simulation results, analytical relationships between the height and potential of leader initiation in the cloud and the charge distribution along the leader channel are approximated. Moreover, the lightning striking distance to flat ground is defined and calculated. Depending on the present model, the striking distance is found to be well associated with the charge density (or electrical potential) of the leader tip near to ground rather than the total charge in the leader channel. Based on appropriate physical understanding, the striking distance is connected to the return stroke peak current.