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

Radio waves employed 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 radio propagation atmospheric delays are best investigated via raytracing, including reflections, such a procedure is not trivial. We have developed simpler closed formulas to account 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 components, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for the angular component and good for the linear one. For the conditions analyzed, about half of the delay was found to originate above the receiving antenna, for satellites at low 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.