Analytical formulas for refraction of radiowaves from exoatmospheric sources

Abstract

We present new analytical formulas for the atmospheric refraction of radiowaves from exoatmospheric sources, such as the Sun. The refraction formulas are derived from the so‐called Effective Earth's Radius Model (k‐Model) or 4/3‐Model which is widely used for atmospheric radars. The new formulas for the refraction angle as a function of elevation are compared to numerical results from the atmospheric refraction routines of the Starlink positional astronomy library and to refraction observations of operational weather radars in the Netherlands and Finland. It is concluded that the refraction formulas from the k‐Model are in good agreement (within 0.02°) with the reference calculations and radar observations. As the k‐Model is used in numerous radar applications, it is expected that these easy‐to‐use refraction formulas, which are consistent with this physical model, can be of wide use.