Effective earth radius

From Glossary of Meteorology

effective earth radius

In radar and radio propagation studies, a value for the radius of the earth that may be used in place of the actual radius to correct for refraction by the atmosphere.

The effective earth radius is a convenient fiction that makes straight the actual curved path of a radio ray in the atmosphere by presenting it relative to an imaginary earth with a radius larger than the radius of the real earth, thus maintaining the relative curvature between earth and radio ray. The effective earth radius Re is approximately
where R is the radius of the earth and dn/dz is the refractive index gradient of its atmosphere. The effective earth radius is well defined only to the extent that dn/dz is constant. Moreover, because n varies with frequency, so does the effective earth radius. The index of refraction of the atmosphere ordinarily decreases with altitude so that radar or radio waves that are transmitted horizontally are refracted downward. The radius of curvature of the propagating rays depends on the vertical gradient of the refractive index. For standard refraction conditions, the effective earth radius is 4/3 times the geometric radius.