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 modelled. For propagation paths within 1 kilometer of the Earth's surface, the effective Earth radius model, which accounts for bending of rays by rescaling the Earth's radius, 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 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 a function of transmitter altitude for selected values or surface refractivity. However, it must be emphasized that very accurate propagation prediction still requires detailed ray trace calculations in the context of accurate atmospheric models.