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A Spherical Earth Solution for TOA Lightning Location RetrievalWith the advent of high-speed digital computers, the method of chi square minimization is a highly practical means for analyzing a wide variety of (otherwise intractable) nonlinear inversion problems in applied mathematical physics. Little thought or effort is required to apply the chi square method to obtain quick and reasonable estimates of a solution, and the method offers a means to assess retrieval errors. Because the method is simple and practical it is sometimes hastily applied to problems that can be solved by formal analytic or quasi-analytic means. Presently, Global Atmospherics Inc. (GAI) finds the minimum of a chi square function to analyze time-of-arrival (TOA) and magnetic bearing data derived from the National Lightning Detection Network (NLDN); ellipsoidal Earth geometry is assumed. An analytic solution to this problem has not yet been attained, but the consideration and solving of less general problem statements might eventually lead to a final solution. In the present study, the problem of retrieving lightning ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered. It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (such as the chi square method mentioned above). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A quasi-analytic extension of the spherical Earth solution for an oblate spheroidal Earth geometry is considered in a related study. The incorporation of magnetic bearing information into these analytic solutions would lead to a general and elegant analytic retrieval scheme that would most likely replace the chi square estimation theory currently employed by Global Atmospherics Inc. (GAI).
Document ID
19990078593
Acquisition Source
Marshall Space Flight Center
Document Type
Reprint (Version printed in journal)
Authors
Koshak, William J,
(Global Hydrology and Climate Center Huntsville, AL United States)
Date Acquired
August 19, 2013
Publication Date
January 1, 1999
Subject Category
Meteorology And Climatology
Meeting Information
Meeting: Atmospheric Electricity
Location: Guntersville, AL
Country: United States
Start Date: June 7, 1999
End Date: June 11, 1999
Distribution Limits
Public
Copyright
Other

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