Three‐dimensional fractal modeling of intracloud lightning discharge in a New Mexico thunderstorm and comparison with lightning mapping observations

Abstract

[1] The direct comparison of lightning mapping observations by the New Mexico Tech Lightning Mapping Array (LMA) with realistic models of thundercloud electrical structures and lightning discharges represents a useful tool for studies of electrification mechanisms in thunderstorms, initiation and propagation mechanisms of different types of lightning discharges as well as for understanding of electrical and energetic effects of tropospheric thunderstorms on the upper regions of the Earth's atmosphere. This paper presents the formulation of a new three-dimensional probabilistic model for investigating the structure and development of bidirectional positive and negative lightning leaders. The results closely resemble structures observed by the LMA during intracloud discharges. The model represents a synthesis of the original dielectric breakdown model based on fractal approach proposed by Niemeyer et al. (1984) and the equipotential lightning channel hypothesis advanced by Kasemir (1960) and places special emphasis on obtaining self-consistent solutions preserving complete charge neutrality of the discharge trees at any stage of the simulation. A representative simulation run is compared to a typical intracloud discharge measured by LMA in a New Mexico thunderstorm on 31 July 1999. Following the conclusions from Coleman et al. (2003), the comparison of the model and observed discharges reveals that an adequate choice of the electrical structure of the model thundercloud permits the development of a model intracloud discharge reproducing principal features of the observed event including the initial vertical extension of the discharge between the main negative and upper positive charge regions of the thundercloud, and the subsequent horizontal propagations in these regions. Also consistent with observations (e.g., Coleman et al., 2003), negative and positive leaders mainly develop in the upper positive and main negative charge regions, respectively. For the particular model case presented in this paper, the total charge transfer, the vertical dipole moment and the average linear charge density associated with the development of bidirectional structure of leader channels are estimated to be 37.5 C, 122 CÁkm, and 0.5 mC/m, respectively, in good agreement with related data reported in the refereed literature. The model results also demonstrate that the bulk charge carried by the integral action of positive and negative leaders leads to a significant (up to 80%) reduction of the electric field values inside the thundercloud, significantly below the lightning initiation threshold.

Asymmetries in bidirectional leader development of lightning flashes

“…Both sides of the bidirectional tree are treated identically. As Riousset et al [2007] show, the modeled discharges share many similarities with real discharges. Recently, bidirectional leader models have been used by Krehbiel et al [2008] and Riousset et al [2010] to explain how lightning discharges can grow out of the cloud and strike Earth, or instead escape out of the cloud top as a blue jet or gigantic jet.…”

“…The model of Mansell et al [2002] may temporarily put one end of the tree on hold in case any deviation from neutrality arises. The models of Mazur and Ruhnke [1998], Bazelyan and Raizer [2000], Behnke et al [2005], and Riousset et al [2007] shift the potential of the leader such that its net induced charge is zero. The potential of the leader is the average ambient potential over the leader length [Bazelyan and Raizer, 2000].…”

“…[50] One physical element missing from the bidirectional leader concept [Kasemir, 1960] and lightning simulation models like those of Riousset et al [2007] and Mansell et al [2002] is the widely observed difference in leader propagation speed. In such models, charge is induced along a conducting leader channel as the leader ends propagate into opposite polarity charge regions (potential wells).…”

“…Recent models [Mansell et al, 2002;Riousset et al, 2007Riousset et al, , 2010 extend branched lightning channels stochastically to a new grid point in its vicinity when the potential difference between lightning channel and surrounding grid points with cloud charge exceeds a threshold. The potential on the channel and surroundings is then recalculated and the procedure is repeated until no more new nodes can be found that surpass the threshold.…”

CELLS v1.0: updated and parallelized version of an electrical scheme to simulate multiple electrified clouds and flashes over large domains

“…Solomon and Baker (1996) developed a complete electrical scheme with individual lightning flash treatment, but in a simplified 1.5-dimension kinematic cloud model which prevented real case studies. On the other side, Mazur and Ruhnke (1998) and Riousset et al (2007) discussed on the propagation of cloud discharges, but with an idealized charge distribution, and did not integrate their lightning scheme in a cloud model.…”