Thalia Nikolaidou

and 3 more

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.

Makan A. Karegar

and 3 more

Although reflectometry had not been considered as a primary application of GPS and similar Global Navigation Satellite Systems (GNSS), fast-growing GNSS tracking networks has led to the emergence of GNSS interferometric reflectometry technique for monitoring surface changes such as water level. However, geodetic GNSS instruments are expensive, which is a limiting factor for their prompt and more widespread deployment as a dedicated environmental sensing technique. We present a prototype called Raspberry Pi Reflector (RPR) that includes a low-cost and low-maintenance single-frequency GPS module and a navigation antenna connected to an inexpensive Raspberry Pi microcomputer. A unit has been successfully operating for almost two years since March 2020 in Wesel (Germany) next to the Rhine river. Sub-daily and daily water levels are retrieved using spectral analysis of reflection data. The river level measurements from RPR are compared with a co-located river gauge. We find an RMSE of 7.6 cm in sub-daily estimates and 6 cm in daily means of river level. In August 2021, we changed the antenna orientation from upright to sideways facing the river. The RMSE dropped to 3 cm (sub-daily) and 1.5 cm (daily) with the new orientation. While satellite radar altimetry techniques have been utilized to monitor water levels with global coverage, their measurements are associated with moderate uncertainties and temporal resolution. Therefore, such low-cost and high-precision instruments can be paired with satellite data for calibrating, validating and modeling purposes. These instruments are financially (< US$ 150) and technically accessible worldwide.