Concerning the horizontal electric field of lightning

In lightning investigations we need simple yet reasonably accurate expressions for the horizontal electric field for an imperfectly conducting ground plant. The Cooray-Rubenstein (see Radio Sci., vol.27, no.4, p.529-38, 1992, and IEEE Trans. Electromag. Compat., vol.38, no.8, p.531-535, 1996) prediction model involves only the horizontal electric field expression for a perfectly conducting ground, the surface impedance, and the tangential magnetic field also for a perfectly conducting ground. We develop an exact version of this relationship and show analytically how and under what conditions it reduces to the CR expression.