Development and validation of comprehensive closed formulas for atmospheric delay and altimetry correction in ground-based GNSS-R

Radio waves used in Global Navigation Satellite System Reflectometry (GNSS-R) are subject to atmospheric refraction, even for ground-based tracking stations in applications such as coastal sea-level altimetry. Although atmospheric delays are best investigated via ray-tracing, its modification for reflections is not trivial. We have developed closed-form expressions for atmospheric refraction in ground-based GNSS-R and validated them against raytracing. We provide specific expressions for the linear and angular components of the atmospheric interferometric delay and corresponding altimetry correction, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for the angular component and good for the linear one. About half of the delay was found to originate above the receiving antenna at low satellite elevation angles. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites. We also provide an equivalent correction for the effective satellite elevation angle such that the refraction effect is nullified. Lastly, we present the limiting conditions for negligible atmospheric altimetry correction (sub-cm), over domain of satellite elevation angle and reflector height. For example, for 5-meter reflector height, observations below 20° elevation angle have more than 1-centimeter atmospheric altimetry error.