Mathematical Constraints on the Use of Transmission Line Models for Simulating Initial Breakdown Pulses in Lightning Discharges

Abstract:

A significant portion of the in-cloud lightning development is observed as a series of initial breakdown pulses (IBPs) that are characterized by an abrupt change in the electric field at a remote sensor. Recent experimental and theoretical studies have attributed this process to the stepwise elongation of an initial lightning leader inside the thunderstorm [da Silva and Pasko, JGR, 120, 4989–5009, 2015, and references therein]. Attempts to visually observe these events are hampered due to the fact that clouds are opaque to optical radiation. Due to this reason, throughout the last decade, a number of researchers have used the so-called transmission line models (also commonly referred to as engineering models), widely employed for return stroke simulations, to simulate the waveshapes of IBPs, and also of narrow bipolar events. The transmission line (TL) model approach is to prescribe the source current dynamics in a certain manner to match the measured E-field change waveform, with the purpose of retrieving key information about the source, such as its height, peak current, size, speed of charge motion, etc. Although the TL matching method is not necessarily physics-driven, the estimated source characteristics can give insights on the dominant length- and time-scales, as well as, on the energetics of the source. This contributes to better understanding of the environment where the onset and early stages of lightning development takes place.

In the present work, we use numerical modeling to constrain the number of source parameters that can be confidently inferred from the observed far-field IBP waveforms. We compare different modified TL models (i.e., with different attenuation behaviors) to show that they tend to produce similar waveforms in conditions where the channel is short. We also demonstrate that it is impossible to simultaneously retrieve the speed of source current propagation and channel length from an observed IBP waveform, in contrast to what has been previously done in the literature. Finally, we demonstrate that the simulated field-to-current conversion factor in IBP sources can vary by more than one order of magnitude, making peak current estimates for intracloud lightning processes a challenging task.