First, Helsdon et al. [12] provided the initial development. From initiation at a grid
point, a flash traced the electric-field line outward in both parallel and antiparallel
directions, until the magnitude of the ambient electric field at each end fell below
some certain threshold value. Secondly, if one end of the channel reached ground,
the parameterization terminated at that end, but allowed the other end to continue
developing.
Charge estimation and neutralization were parameterized by applying the
technique proposed by Ziegler and MacGorman [33], except that Ziegler and
MacGorman neutralized charge at all grid points having |p(i, j, k) > Pi (where
p(i, j, k) was the net charge density at the grid point (i, j, k) and pi was the
minimum Ip(i, j, k)| for all grid points to be involved in lightning beyond initial
propagation) throughout the storm, but their parameterization neutralized charge
only at such grid point within a single localized flash.
2.2.2.3 Mansell's Model
Mansell et al [16] proposed a lightning parameterization derived from
the dielectric breakdown model that was developed by Niemeyer et al. [17] and
Wiesmann and Zeller [29] to simulate electric discharges. They extended the
dielectric breakdown model to a three-dimensional domain to represent more
realistic electric field and thunderstorm dynamics.
In their work, the stochastic lightning model (SLM) was an application of
the Wiesmann-Zeller model to simulate bidirectional discharges in the regions
of varying net charge density (e.g., in an electrified thunderstorm). Procedures
for simulating lightning flashes in the thunderstorm model were as follows. A
flash occurred when the magnitude of the electric field exceeded the initiation
threshold E1iit anywhere in the model domain. The lightning initiation point was
chosen randomly from among all the points where the magnitude of the electric
field is greater than 0.9Eint. Both decisions for choosing the initiation threshold