A multipole expansion method for analyzing lightning field changes

Abstract

Abstract. Changes in the surfac• electric field are frequently usexl to infer the 1ocafi•s and magnitudes of lighming-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q model) or a point dipole (the P model). The Q model has four unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P model has six unknown parameters and describes many intracloud (IC) discharges. In this paper we introduce a new analysis method that assumes that the change in the cloud charge can be described by a trun• multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. ff there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a three4imensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been test• on computer-simulated sources and on natural lighming at the NASA Kennedy Space Center and U.S. Air Force Eastern Range.

Analysis of charge transport during lightning using balloon‐borne electric field sensors and Lightning Mapping Array

“…Recently, constraints have been incorporated in the estimation process. In particular, conservation of charge is mentioned by Koshak and Krider [1994] and Koshak et al [1999].…”

Identification of a transient electric dipole over a conducting half space using a simulated annealing algorithm

“…The charges deposited by the flash are often modeled either as a single-point charge or an electric dipole. The electric dipole model can describe well many intracloud discharges [Koshak et al, 1999], isolated thunderstorms [Driscoll et al, 1992], ball lightning lEndeau, 1993], and aircraft-triggered lightning [21//oreau et al, 1992], etc. Therefore the problem of identification of an electric dipole over a conducting half-space by measuring electromagnetic fields at a few ground points is of interest.…”

Explicit full identification of a transient dipole source in the atmosphere from measurement of the electromagnetic fields at several points at ground level

“…The charges deposited by the flash are often modeled as a single point charge or an electric dipole. The electric dipole model can describe well many intracloud discharges [Koshak et al, 1999], isolated thunderstorms [Driscoll et al, 1992], ball-lightning [Endean, 1993], and aircraft-triggered lightning [Moreau et al, 1992], etc. (Note, however, that the model of a single dipole is not applicable, in general, to cloudto-ground lightning, particularly after the first several microseconds, for which a return-stroke channel model is usually applied [see, e.g., Urnan 1985; Thottappillil et al, 1997].)…”

“…The charges deposited by the flash are often modeled as a single point charge or an electric dipole. The electric dipole model can describe well many intracloud discharges [Koshak et al, 1999], isolated thunderstorms [Driscoll et al, 1992] netic fields at two ground points if the dipole orientation does not lie on the plane formed by the dipole and the two measurement points. Explicit identification formulas are given for the simultaneous reconstruction of the location rl -= (Xl, Yl, h), the orientation no, and the transient behavior p(t) of the dipole source.…”