TOA lightning location retrieval on spherical and oblate spheroidal earth geometries

A simple linear algebraic solution is introduced for retrieving the locatio n and time-of-occurrence of lightning ground strikes on a spherical earth f rom a network of four or more time-of-arrival sensors. Since the solution a ccounts for earth curvature, it represents an extension to earlier planar m odel results. A test of the retrieval method is provided using computer-sim ulated datasets. The method is easy to comprehend and completely avoids ref erence to the mathematics of spherical hyperbolas. An extension to the sphe rical earth solution is provided for an oblate spheroidal earth geometry, a nd the importance/relevance of oblate effects are discussed. Future applica tion of these methods in support of the North American National Lightning D etection Network is desirable, but additional theoretical investigations ar e required to incorporate magnetic bearing information into the present sol ution process.