Journal of Geoscience and Environment Protection, 2016, 4, 125-135 Published Online April 2016 in SciRes. http://www.scirp.org/journal/gep http://dx.doi.org/10.4236/gep.2016.44016 How to cite this paper: Lozbin, A., Shpadi, Y. and Inchin, A. (2016) Triangles Technique for Time and Location Finding of the Lightning Discharge in Spherical Model of the Earth. Journal of Geoscience and Environment Protection, 4, 125-135. http://dx.doi.org/10.4236/gep.2016.44016 Triangles Technique for Time and Location Finding of the Lightning Discharge in Spherical Model of the Earth Anatoliy Lozbin, Yuriy Shpadi, Alexander Inchin Scientific Space Systems Laboratory, Institute of Space Techniques and Technologies, Almaty, Kazakhstan Received 15 February 2016; accepted 25 April 2016; published 28 April 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract The spherical model of time and location calculation of the lightning discharge is given. The calcu- lations are made by means of radio signals detection by sensors of the distributed network. The full solution of a problem of lightning discharge cloud-ground type location for three sensors is given. Based on this task the lightning location method for a network of sensors was developed. By means of computational experiments, the analysis of accuracy of the model depending on radio signals detection accuracy at observing stations was done. Keywords Lightning, Time of Arrival Technique (TOA), Atmospheric, Spherical Trigonometry 1. Introduction Let ( ) , i i i P ϕθ be 3 different points on the Earth’s surface with longitude i ϕ and latitude i θ , 1, 2, 3 i = . In these points, we have sensors receiving a radio signal from lightning discharge. Let there was a lightning dis- charge in the time moment s t in some point ( ) , s s s P ϕ θ of the Earth’s surface. Radio signals from this dis- charge were detected by the sensors in the i t , 1, 2, 3 i = time points. Assuming that the radio signal (low fre- quency) reaches each sensor on the shortest way along an Earth’s surface, we will receive system of three equa- tions for lightning discharge time and location determination.  ( ) , 1, 2, 3, i s s i s PP c t t i = − = (1) where,  i s PP —length of a smaller arch of a big circle of the terrestrial sphere connecting points i P and s P , s c —the speed of radio wave.