Atmospheric delays are known to cause biases in Global Navigation Satellite System Reflectometry (GNSS-R) altimetry applications, such as for sea-level monitoring. The main quantity of interest is the reflection-minus-direct or interferometric atmospheric delay. Recently, we have presented a rigorous raytracing procedure to account for linear and angular refraction in conjunction with reflection as observed from near-surface platforms. Here, we demonstrate the feasibility of simplifying the ray trajectory by imposing a rectilinear wave propagation model. Two variants were assessed, based on the apparent or refracted satellite direction on the one hand and the geometric or vacuum conditions on the other hand. The former was shown to agree with rigorous results in terms of interferometric radio length while the latter agreed in terms of the interferometric vacuum distance. Upon a judicious combination of the best aspects of the two rectilinear cases, we have defined a mixed variant with excellent agreement with rigorous raytracing in terms of interferometric atmospheric delay. We further showed that mapping functions developed for GNSS positioning cannot be reused for GNSS-R purposes without adaptations. Otherwise, the total atmospheric delay may be underestimated by up to 50% at low elevation angles. The present work facilitates the adaptation of existing atmospheric raytracing software for GNSS-R purposes.
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.
In recent years, numerical weather models have shown the potential to provide a good representation of the electrically neutral atmosphere. This fact has been exploited for the modeling of space geodetic observations. The Vienna Mapping Functions 1 (VMF1) are the NWM-based model recommended by the latest IERS Conventions. The VMF1 are being produced 6 hourly based on the European Centre for Medium-Range Weather Forecasts operational model. UNB-VMF1 provide meteorological parameters aiding neutral atmosphere modeling for VLBI and GNSS, based on the same concept but utilizing the Canadian Meteorological Centre model. This study presents comparisons between the VMF1 and the UNB-VMF1 in both delay and position domains, using global networks of VLBI and GPS stations. It is shown that the zenith delays agree better than 3.5 mm (hydrostatic) and 20 mm (wet) which implies an equivalent predicted height error of less than 2 mm. In the position domain and VLBI analysis, comparison of the weighted root-mean-square error (wrms) of the height component showed a maximum difference of 1.7 mm. For 48% of the stations, the use of VMF1 reduced the height wrms of the stations by 2.6% on average compared to a respective reduction of 1.7% for 41% of the stations employing the UNB-VMF1. For the subset of VLBI stations participating in a large number of sessions, neither mapping function outranked the other. GPS analysis using Precise Point Positioning had a sub-mm respective difference, while the wrms of the individual solutions had a maximum value of 12 mm for the 1-year-long analysis. A clear advantage of one NWM over the other was not shown, and the statistics proved that the two mapping functions yield equal results in geodetic analysis.
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