A dynamic-physical model for lightning return stroke current and light simulations and its comparison with observations

Abstract

A Lightning flash during a thunderstorm may occur either within the cloud (CC) or between the cloud and ground (CG). A CG usually starts with a leader process followed by a return stroke process. It is this return stroke that produces strong electric current pulses, which may cause damages to various systems on earth. Observation is the most direct and accurate way to understand the property of a lightning return stroke but with limitations and various difficulties in practice. For this sake, various physical and engineering models have been proposed since 1970s to predict the properties of the return stroke parameters with various conditions. A downward lightning flash usually starts with a downward leader and an upward connecting leader followed by an upward return stroke. It is the preceding leader that governs the following return stroke property. Besides, the return stroke property evolves with height and time. These two aspects, however, are not well-addressed in most existing return stroke models. In this study, we present a leader-return stroke consistent model based the time domain electric field integral equation (TD-EFIE), which is a growth and modification of Kumar's macroscopic model. It is a dynamic physical model that could describe the spatial and temporal evolutions of the most important parameters of a lightning return stroke, such as the lightning channel radius and conductance, the lightning current and its propagation in the channel. The model is further extended to simulate the optical and electromagnetic emissions of a return stroke by introducing a set of equations relating the return stroke current and conductance to the optical and electromagnetic emissions. With a presumed leader initiation potential, the model can then simulate the temporal and spatial evolution of the current, charge transfer, channel size and conductance of the return stroke, furthermore the optical and electromagnetic emissions. The model is tested with different leader initiation potentials ranging from -10 to -140 MV, resulting in different return stroke current peaks ranging from 2.6 to 209 kA with different return stroke speed peaks ranging from 0.2 to 0.8 speed of light and different optical power peaks ranging from 4.76 to 248 MW/m. The larger of the leader initiation potential, the larger of the return stroke current and speed. Both the return stroke current and speed attenuate exponentially as it propagates upward. All these results are qualitatively consistent with those reported in the literature.