A simplification of rigorous atmospheric raytracing based on judicious rectilinear paths for near-surface GNSS reflectometry

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

Modeling neutral-atmospheric electromagnetic delays in a “big data” world

If left unmodeled, the delay suffered by electromagnetic waves while crossing the neutral atmosphere negatively affects Global Navigation Satellite System positioning. The modeling of the delay has been carried out by means of empirical models formulated based on climatological information or using information extracted from numerical weather prediction (NWP) models. This paper explores the potential use of meteorological information of several types that will become available with the increasing number of sensors (e.g. a cell phone, or the thermometer of a nearby smart home) in cyberspace. How can we make use of these potentially huge data-sets, which may help to provide the best possible representation of the neutral atmosphere at any given time, as readily and as accurately as possible? This situation falls in the realm of Big Data. A few potential scenarios, a sequential improvement of Marini mapping function coefficients, a self-feeding NWP, and near real-time empirical model updates, are discussed in this paper. The pros and cons of each approach are discussed in comparison with what is done today. Experiments indicate that they have potential for a positive contribution

Impact of different NWM-derived mapping functions on VLBI and GPS analysis

Abstract 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

Validation of closed-form expressions for the atmospheric altimetry correction in ground-based GNSS reflectometry based on rigorous ray-tracing

GNSS reflectometry (GNSS-R) ability to remote sense the Earth’s surface is affected by an atmospheric bias, as pointed out by several recent studies. In particular, sea level altimetry retrievals are biased in proportion to the reflector height, while by-products, such as tidal amplitudes, are underestimated. Previously, we developed an atmospheric ray-tracing procedure to solve rigorously the three-point boundary value problem of ground-based GNSS-R observations. We defined the reflection-minus-direct or interferometric delay in terms of vacuum distance and radio length. We clarified the roles of linear and angular refraction in splitting the total delay in two components, along-path and geometric. We introduced for the first time two subcomponents of the atmospheric geometric delay, the geometry shift and geometric excess. Finally, we defined atmospheric altimetry corrections necessary for unbiased altimetry retrievals based on half of the rate of change of the atmospheric delays with respect to sine of elevation angle. Later, for users without access to ray-tracing software, we developed closed-form expressions for the atmospheric delay and altimetry correction. The first expression accounts for the angular component of refraction (bending), leading to a displaced specular reflection point. The second one accounts for the linear component (speed retardation) in a homogeneous atmosphere. The expressions are parametrized in terms of refractivity and elevation bending, which can be obtained from empirical models, such as the GPT2 or Bennet’s, or fine-tuned based on in situ pressure and temperature. We also provide a correction for the satellite elevation angle such that the refraction effect is nullified. We validated these expressions against rigorous ray-tracing results and showed that the discrepancy is caused by assumptions in the derivation of the closed formulas. We found the corrections to be beneficial even for small reflector heights, as approximated half of the atmospheric effect originates above the receiving antenna at low satellite elevation angles

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

Radio wave propagation involved in global navigation satellite system reflectometry (GNSS-R) is subject to atmospheric refraction. Even for ground-based tracking stations, in applications such as coastal sea-level altimetry, the interferometric or reflection-minus-direct effect might be significant. Although atmospheric propagation delays are best investigated numerically 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, validated against independent raytracing. We provide specific expressions for the two 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 both components. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites