Effective earth radius for refraction of radio waves at altitudes above 1 km

Atmospheric refractivity gradients are responsible for the bending of radio and microwave propagation paths such that the electromagnetic line-of-sight deviates from the geometrical line-of-sight. Such refraction effects must be accounted for when the performance of airborne surveillance radar systems is modeled. For propagation paths within 1 km of the earth's surface, the effective earth radius model is normally valid and commonly used. In the present work, a ray trace method for determination of propagation paths in a semi-empirical, stratified atmosphere is described. Results obtained from the ray trace model are employed to show that the effective earth radius method (EERM) can be used for approximate determinations of grazing angle, ground range and slant range for higher altitude paths. Effective earth radius scale factors are given as functions of transmitter altitude for selected values of surface refractivity.