Electronic Theses and Dissertations

Date of Award


Document Type


Degree Name

Ph.D. in Physics


Physics and Astronomy

First Advisor

Thomas C. Marshall

Second Advisor

Atef Z. Elsherbeni

Third Advisor

Luca Bombelli

Relational Format



Initial breakdown pulses (IBPs) observed at the beginning of cloud-to-ground (CG) lightning flashes and stepped leaders that followed IBPs were modeled using multi-sensor electric field change (E-change) measurements. This study uses data collected with a network of ten E-change sensors located at Kennedy Space Center. Locations (x,y,z,t) of IBPs were found using a time-of-arrival technique called PBFA. Location errors were determined from Monte Carlo simulations and were usually less than 100 m for horizontal coordinates and several hundreds of meters for altitude. Comparison of PBFA source locations to locations from a VHF lightning mapping system shows that PBFA locates most of the `classic' IBPs while the VHF system locates only a few percent of them. As the flash develops during the IB stage, PBFA and the VHF system obtain similar locations when they detect the same IBPs. PBFA also can reliably locate the IBPs of intra-cloud flashes and return stroke (RS) locations. PBFA locations were used as constraints to model six 'classic' IBPs using three modified transmission line (MTL) models (MTLL--linearly decaying current, MTLE—exponentially decaying current, MTLEI—exponentially increasing current) from the literature and a new model, MTLK, with the current following the Kumaraswami distribution. All four models did a good job of modeling all six IBPs; the MTLE model was most often the best fit. It is important to note that for a given pulse, there is good agreement between the different models on a number of parameters: current risetime, current falltime, two current shape factors, current propagation speed, and the IBP charge moment change. Ranges and mean values of physical quantities found are: current risetime [4.8–25, (13±6)] microseconds, current falltime [15–37, (25±6)] microseconds, current speed [0.78–1.8, (1.3±0.3)]×10 8 m/s (excluding one extreme case of MTLEI), channel length [0.20–1.6, (0.6±0.3)] km, charge moment [0.015–0.30, (0.12±0.10)] C km, peak current [16–404, (80±80)] kA , and absolute average line charge density [0.11–4.7, (0.90±0.90)] mC/m. Currents in the MTLL and MTLE models deposit negative charge along their paths and the mean total charges deposited (Qtot) were -0.35 and -0.71 C. MTLEI currents effectively deposited positive charge along their paths with Qtot = 1.3 C. MTLK is more special regarding how it handles the charges. Initially, along the lower current path, negative charge is deposited and positive charge is deposited onto its upper path making the overall charge transfer almost zero, (Qtot = 3.8×10 -5). Because of this the MTLK model apparently obeys conservation of charge (without making that a model constraint). Two stepped leaders were modeled to match multiple E-change measurements. Time evolution and 2-D locations of stepped leaders were obtained from data collected with a high-speed video camera operated at 50,000 frames/s. The Lu et al. 2011 TDMD (time dependent multidipole) model was used with some modifications. Negative charges were deposited at stepped leader tips based on measured light intensity, and positive charges were deposited at PBFA/LDAR2 locations of IBPs where the stepped leaders probably started. The method has unique advantage of obtaining locations of CG stepped leaders including its branches, unlike previous studies that used simpler paths. Some physical quantities calculated for both stepped leaders: average line charge density = -1.49 and -0.813 mC/m, average current = 0.39 and 0.38 kA, average 2-D stepped leader speed 2.67 and 4.8×105 m/s. These quantities are in excellent agreement with previous studies.



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