Radar Beam Tracing Methods Based on Atmospheric Refractive Index

Simulation of radar beam propagation is an important component of numerous radar applications in meteorology, including height assignment, quality control, and especially the so-called radar forward operator. Although beam propagation in the atmosphere depends on the refractive index and its vertical variation, which themselves depend on the actual state of the atmosphere, the most common method is to apply the 4/3 earth radius model, based on climatological standard conditions. Serious deviations from the climatological value can occur under so-called ducting conditions, where radar beams at low elevations can be trapped or propagate in a waveguide-like fashion, such that this model is unsuitable in this case. To account for the actual atmospheric conditions, sophisticated methods have been developed in literature. However, concerning the practical implementation of these methods, it was determined that the description in the literature is not always complete with respect to possible pitfalls for practical implementations. In this paper, a revised version of an existing method (one example for the above-mentioned “pitfall” statement) is introduced that exploits Snell’s law for spherically stratified media. From Snell’s law, the correct sign of the local elevation is a priori ambiguous, and the revised method explicitly applies (i) a total reflection criterion and (ii) another ad hoc criterion to solve the problem. Additionally, a new method, based on an ordinary differential equation with respect to range, is proposed in this paper that has no ambiguity. Sensitivity experiments are conducted to investigate the properties of these three methods. The results show that both the revised and new methods are robust under nonstandard conditions. But considering the need to catch an elevation sign ambiguity in the revised method (which cannot be excluded to fail in rare instances), the new method is regarded as more robust and unproblematic, for example, for applications in radar forward operators.