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

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 C·km, 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.