subtracted positive charge equally from all charged particles in the positive region;
and similarly, subtracted negative charge equally from all charged particles in the
negative region.
Ziegler and MacGorman [33] also applied a simple parameterization, but used
a three-dimensional model to treat the bulk effect of lightning on storm charge in
a time step. They neutralized a fraction of the net charge at all grid points where
the magnitude of the net charge density exceeded 0.5 nC/m3 to imitate the effect of
lightning releasing the charge from its channels. The above bulk-flash schemes are
relatively easy to implement but lack realism.
2.2.2 Lightning Model with Explicit Lightning Channels
Most lightning discharge models with explicit channel treat only a one-
dimensional or unbranched channel. The branching of lightning channels would
be very difficult to treat analytically because of the lack of symmetry and the
incomplete understanding of the processes.
2.2.2.1 The Model of Helsdon et al.
Helsdon et al. [9, 10, 11, 12] estimated both the geometry and charge distri-
bution of an intercloud lightning flash in a two-dimensional Storm Electrification
Model (SEM). Since then, their parameterization has been extended to a three-
dimensional numerical cloud model. They applied the concept of bidirectional
leader [13]: The parameterized lightning propagated bidirectionally (initially
parallel and antiparallel to the electric field) from the point of initial breakdown.
Their parameterization produced a single, unbranched channel that traced
the electric-field line from an initial point. Initiation, propagation direction, and
termination of the discharge were computed using the magnitude and direction
of the electric field vector as the determining criteria. The charge redistribution
associated with lightning was approximated by assuming that the channel remained
electrically neutral over its total length.