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<br />propagation process. Such instruments as the
<br />Lightning Mapping Array (LMA), developed by P.
<br />Krehbiel and colleagues at the New Mexico
<br />Institute of Mining and Technology, are revealing
<br />more about these processes. What the LMA has
<br />revealed is that there is a definite difference in the
<br />breakdown process associated with positive and
<br />negative leaders, which attend the in-cloud portion
<br />of both cloud~to-ground and intracloud flashes.
<br />Also, we have little understanding of the branching
<br />process. This is another area where modeling,
<br />coupled with new observations can increase our
<br />knowledge. The new lightning scheme that we
<br />have developed attempts to model the breakdown
<br />process at the leader tip by considering random
<br />free electrons. The situation at the tip of positive
<br />and negative leaders is different. To this point all
<br />leader processes have been treated the same.
<br />We are now at the point where we can use the
<br />scheme to investigate different breakdown
<br />processes for oppositely charged leaders to see
<br />how channel formation and propagation differs.
<br />Channel behavior can be compared with data
<br />obtained by the LMA for verification purposes.
<br />The lightning scheme offers a method of coming to
<br />understand the formation of lightning channels
<br />more completely than ever before.
<br />
<br />Models have advanced significantly with
<br />respect to complexity since 1970, just as our
<br />observing capabilities have increased. Modeling
<br />work, coupled with field observations and
<br />laboratory investigations have helped advance our
<br />understanding of the electrification of
<br />thunderstorms. In the process, as the
<br />sophistication of each component has increased,
<br />more detailed investigations have become
<br />possible. In truth, the more we have come to
<br />know, the more we realize how much there is left
<br />to understand. Modeling is an essential tool to
<br />help us continue to increase our understanding of
<br />thunderstorms and there place in the atmosphere.
<br />
<br />6. FINAL COMMENTS
<br />
<br />Although Dr. Orville is less recognized for his
<br />contributions in the area of thunderstorm electrical
<br />modeling than he is in the areas of cloud and
<br />precipitation physics, dynamics, and weather
<br />modification, nonetheless his contributions have
<br />been seminal. He established the protocol for
<br />inclusion of electrical effects in multidimensional
<br />models and was an advisor to those carrying out
<br />the first such modeling efforts. He was also a co-
<br />author of the first published work involving coupled
<br />thundercloud modeling. As important as this
<br />
<br />research was, perhaps his most important
<br />contribution has been as a mentor and inspiration
<br />to those of us who have continued the work that
<br />he began, which has brought us to where we are
<br />today - where electrical models are providing
<br />insight into some of the oldest and most vexing
<br />questions associated with thunderstorms and
<br />opening up new avenues of investigation not
<br />thought possible only a few years ago. While he
<br />may best be remembered for his work in other
<br />areas, he stands as a pioneer in thunderstorm
<br />electrical modeling, and it is my privilege to
<br />recognize his legacy in this area.
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<br />7. REFERENCES
<br />
<br />Baker, M. B., H. J. Christian, and J. Latham, 1995:
<br />A computational study of the relationships
<br />linking lightning frequency and other
<br />thundercloud parameters. Quart. J. Roy.
<br />Meteor. Soc., 121,1525-1548.
<br />
<br />Beard, K. V. K., and H. T. Ochs, 1986: Charging
<br />mechanisms in clouds and thunderstorms. In
<br />The Earth's Electrical Environment, National
<br />Acad. Press, Washington, DC, 114-130.
<br />
<br />Borucki, W. J., and W. L. Chameides, 1984:
<br />Lightning: Estimates of the rates of energy
<br />dissipation and nitrogen fixation. Rev.
<br />Geophys., 22, 363-372.
<br />
<br />Chiu, C. 5., 1974: Convective electrification of
<br />clouds. Ph.D. dissertation, New Mexico
<br />Institute of Mining and Technology, Socorro,
<br />199 pp.
<br />
<br />Chiu, C. 5., 1978: Numerical study of cloud
<br />electrification in an axisymmetric, time-
<br />dependent cloud model. J. Geophys. Res.,
<br />83,5025-5049.
<br />
<br />Chiu, C. 5., and J. D. Klett, 1976: Convective
<br />electrification of clouds. J. Geophys. Res., 81,
<br />1111-1124.
<br />
<br />Chiu, C. 5., and H. D. Orville, 1978: Numerical
<br />modeling of hailstorm electrification.
<br />Preprints, Conf. on Cloud Phys. and
<br />Atmospheric Electricity, Issaquah, WA, Amer.
<br />Meteor. Soc., 631-634.
<br />
<br />Davis, M. H., 1964: Two charged spherical
<br />conductors in a uniform electric field: forces
<br />and field strength. Quart. J. Mech. Appl.
<br />Math., 17, 499-511.
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