North Alabama Lightning Mapping Array (LMA): VHF Source Retrieval Algorithm
and Error Analyses

W. J. KOSHAK,* R. J. SOLAKIEWICZ,⁺ R. J. BLAKESLEE,* S. J. GOODMAN,* H. J. CHRISTIAN,* J. M. HALL,^#
J. C. BAILEY,^@ E. P. KRIDER,^& M. G. BATEMAN,** D. J. BOCCIPPIO,* D. M. MACH,⁺⁺ E. W. MCCAUL,**
M. F. STEWART,⁺⁺ D. E. BUECHLER,⁺⁺ W. A. PETERSEN,⁺⁺ D. J. CECIL⁺⁺

*Earth Science Department, NASA Marshall Space Flight Center, Huntsville, Alabama
⁺Chicago State University, Chicago, Illinois
^#Computer Sciences Corporation, Huntsville, Alabama
^@Raytheon ITSS, Huntsville, Alabama
^&The University of Arizona, Tucson, Arizona
**Universities Space Research Association, Huntsville, Alabama
⁺⁺University of Alabama in Huntsville, Huntsville, Alabama

ABSTRACT

Two approaches are used to characterize how accurately the north Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA Marshall Space Flight Center (MSFC) and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix Theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50 ns, but all other possible errors (e.g., anomalous VHF noise sources) are neglected. The detailed spatial distributions of retrieval errors are provided. Even though the two methods are independent of one another, they nevertheless provide remarkably similar results. However, altitude error estimates derived from the two methods differ (the Monte Carlo result being taken as more accurate). Additionally, this study clarifies the mathematical retrieval process. In particular, the mathematical difference between the first-guess linear solution and the Marquardt-iterated solution is rigorously established thereby explaining why Marquardt iterations improve upon the linear solution.