Modeling Initial Breakdown Pulses of Lightning Flashes Using a Matrix Inversion Method

Karunarathne, Nilmini; Karunarathne, Sumedhe; Marshall, T. C.; Stolzenburg, Maribeth

doi:10.1029/2018rs006695

Cited by 6 publications

(11 citation statements)

References 25 publications

(86 reference statements)

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“…The third technique we apply to obtain I ( t ) is the matrix inversion method (Karunarathne et al, ). For far‐field observations, equation can be expressed as

E_{z} ()(, D, t) ~ E_{r} ()(, D, t) = E ()(, t) = \int_{H_{1}}^{H_{2}} g ()(, z) \frac{\partial I ()(, τ)}{\partial t} normald z true]

where

τ = t - \frac{z - H_{1}}{v} - \frac{\sqrt{D^{2} + z^{2}}}{c}

is the retarded time and

g ()(, z) = \frac{- 1}{2 normalπ ε_{0}} \frac{D^{2}}{c^{2} {(D^{2} + z^{2})}^{\frac{3}{2}}} ()(, \frac{H_{2} - z}{H_{2} - H_{1}})

.…”

Section: Overview Of Ibp Modelingmentioning

confidence: 99%

“…As described in Karunarathne et al (), if e n is ignored, equation can be written as

E_{n} = \sum_{m = 1}^{M} g_{m} normalΔ z {\dot{I}}_{k} m = 1, 2, \dots, M

where

{\dot{I}}_{k}

is an element in a matrix representing d I /d t . Then, d I /d t is determined by inverting equation , and I ( t ) is determined by integration (see Karunarathne et al () for details).…”

Section: Overview Of Ibp Modelingmentioning

confidence: 99%

“…However, the modeling of each IBP uses E‐change data from all available sensors and uses all terms in equation . Karunarathne et al () found that this method of determining IBP currents worked well even for modeling IBP waveforms having substantial electrostatic and induction contributions (i.e., for IBP waveforms recorded at sensor sites located within 10 km of the IBP). All of the IBP currents modeled herein used data from four sensor sites located at >20 km from the IBPs (from a total of four to six sensor sites).…”

Section: Overview Of Ibp Modelingmentioning

confidence: 99%

“…In the present work, we study IBPs by first extracting the IBP current waveform from the E‐change data using the matrix inversion method (Karunarathne et al, ) and two other methods, Hilbert transform (e.g., Shao et al, ) and Hertzian dipole approximation (e.g., Nag & Rakov, ). Rather than modeling a single pulse from several different flashes, for the first time we model a series of classic IBPs from the IB stage of three CG flashes.…”

Section: Introductionmentioning

confidence: 99%

“…In Karunarathne et al (2014) the three models searched for six to eight unknown parameters to fit each of the six measured IBPs. Recently, Karunarathne et al (2019) developed a "matrix inversion" method of modeling classic IBPs and applied it to the same six IBPs studied by Karunarathne et al (2014). By extracting the IBP current from E-change measurements at multiple sensor sites, the matrix inversion method reduced the number of unknown parameters to only two while providing better fits to the measured IBPs.…”

Section: Introductionmentioning

confidence: 99%

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Studying Sequences of Initial Breakdown Pulses in Cloud‐to‐Ground Lightning Flashes

et al. 2020

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The properties of the first 5–12 classic initial breakdown pulses (IBPs) of three cloud‐to‐ground (CG) lightning flashes were determined using a modified transmission line model. As part of the modeling, the current with respect to time of each IBP was determined from the measured electric field changes at multiple sites using three theoretical methods called Hilbert transform, Hertzian dipole, and matrix inversion. In the transmission line modeling the length of each IBP was estimated from high‐speed video data of the IBPs. The modeling provided the following properties of the larger classic IBPs in each flash: peak current, velocity, total charge, charge moment, radiated power, and total energy dissipated for successive IB pulses in three developing lightning flashes. For the main initial leader channel in the three CG flashes (and for one long branch), IBP peak current was largest for the first or second classic IBP and declined mostly monotonically with successive IBPs. For the same channels, IBP current velocity was smallest for the first classic IBP and increased mostly monotonically with successive IBPs. The smallest velocities were (2.0, 2.5, 2.5, 3.0) × 107 m/s, respectively, while the largest velocities were (9.2, 12.2, 11.5, 12.0) × 107 m/s, respectively. These data support earlier hypotheses that it is the classic IB pulses during initial leader of normal negative CG flashes that change the nonconductive air into an ionized path that is sufficiently long and conductive to start the stepped leader.

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“…The third technique we apply to obtain I ( t ) is the matrix inversion method (Karunarathne et al, ). For far‐field observations, equation can be expressed as

E_{z} ()(, D, t) ~ E_{r} ()(, D, t) = E ()(, t) = \int_{H_{1}}^{H_{2}} g ()(, z) \frac{\partial I ()(, τ)}{\partial t} normald z true]

where

τ = t - \frac{z - H_{1}}{v} - \frac{\sqrt{D^{2} + z^{2}}}{c}

is the retarded time and

g ()(, z) = \frac{- 1}{2 normalπ ε_{0}} \frac{D^{2}}{c^{2} {(D^{2} + z^{2})}^{\frac{3}{2}}} ()(, \frac{H_{2} - z}{H_{2} - H_{1}})

.…”

Section: Overview Of Ibp Modelingmentioning

confidence: 99%

“…As described in Karunarathne et al (), if e n is ignored, equation can be written as

E_{n} = \sum_{m = 1}^{M} g_{m} normalΔ z {\dot{I}}_{k} m = 1, 2, \dots, M

where

{\dot{I}}_{k}

is an element in a matrix representing d I /d t . Then, d I /d t is determined by inverting equation , and I ( t ) is determined by integration (see Karunarathne et al () for details).…”

Section: Overview Of Ibp Modelingmentioning

confidence: 99%

Section: Overview Of Ibp Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%