In lightning investigations we need simplied get reasonably accurate e
xpressions for the horizontal electric field for an imperfectly conduc
ting ground plant. The Cooray-Rubenstein (CR) prediction model involve
s only the horizontal electric field expression for a perfectly conduc
ting ground, the surface impedance, and the tangential magnetic field
also for a perfectly conducting ground, Here we develop an exact versi
on of this relationship and show analytically how and under what condi
tions it reduces to the CR EXPRESSION.