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.

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.

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

<p>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.</p>

Evaluation of Visual Functions in Children Using Manifest Refraction: Effect of Age and Refractive Error

It remains unclear whether positive relative accommodation (PRA), negative relative accommodation (NRA), or binocular cross cylinder (BCC) values present differently when manifest refraction (MR) is performed before or after drug-induced mydriasis. This study aimed to compare visual functions in children as measured by refraction and MR after the administration of mydriatics. A total of 483 children (4–18 years old) were categorized into three groups based on MR performed at three visit points: initial MR, refraction after rapid pupil dilation (RRP), and refraction after slow pupil dilation (RSP). The investigated subjects included PRA, NRA, and BCC values. No significant differences in the PRA (P = 0.120), NRA (P = 0.492), and BCC (P = 0.240) values were detected among the MR, RRP, and RSP groups. When the PRA values among different groups were stratified by age, no significant differences were detected. Although there were no statistically significant differences in the NRA values among groups for children aged 4–6 years (P = 0.077) and 7–11 years (P = 0.865), there was a significant difference in the NRA values among groups for children aged 12–18 years (P =0.044). In addition, the BCC values among groups for children aged 7–11 years (P = 0.044) also showed significant differences. Meanwhile, the differences between PRA (P <0.001) and NRA (P = 0.016) among emmetropes, pseudomyopes, myopes, and hyperopes were statistically significant, while the refractive error was not affected by MR assessed with BCC (P = 0.380). Performing MR after pupil dilation could replace MR before mydriasis in children aged 4–6 years, while MR before mydriasis could be omitted for children aged 4–6 years.

Development and Research of a Multi-Medium Motion Capture System for Underwater Intelligent Agents

A multi-medium motion capture system based on markers’ visual detection is developed and experimentally demonstrated for monitoring underwater intelligent agents such as fish biology and bionic robot-fish. Considering the refraction effect between air and water, a three-dimensional (3D) reconstruction model is established, which can be utilized to reconstruct the 3D coordinate of markers underwater from 2D data. Furthermore, the process of markers matching is undertaken through the multi-lens fusion perception prediction combined K-Means clustering algorithm. Subsequently, in order to track the marker of being occluded, according to the kinematics information of fish, an improved Kalman filtering algorithm is proposed. Finally, the feasibility and effectiveness of proposed system are verified through experimental results. The main models and methods in this paper can provide a reference and inspiration for measurement of underwater intelligent agents.

Сombined method of determining vertical refraction correction for electronic tacheometry

This article deals with issue of the vertical refraction effect on the results of trigonometric levelling. The possible affecting the results of EDM levelling by refraction is evaluated. A brief review of methods of correcting the refraction influence is executed. The conclusion is drawn that the accuracy capabilities of refraction correction methods lag behind the level of development of geodetic equipment. As a possible solution of the refraction account problem, a combined method is proposed. This way is based on a geodetic model of the atmosphere and complex gradient meteorological and geodetic measurements. The results of these measurements are the data for calculating the model parameters. The combined use of meteorological and geodetic measurements at several levels enables minimizing the volume of additional measurements, provides the determination of the refraction angle with geodetic accuracy. The results of field experiment are presented. They proved the actuality of the algorithm implementing the combined method of vertical refraction correction calculating, and made an opportunity of working out the proposed way methodically.

Wave–vortex interactions, remote recoil, the Aharonov–Bohm effect and the Craik–Leibovich equation

Three examples of non-dissipative yet cumulative interaction between a single wavetrain and a single vortex are analysed, with a focus on effective recoil forces, local and remote. Local recoil occurs when the wavetrain overlaps the vortex core. All three examples comply with the pseudomomentum rule. The first two examples are two-dimensional and non-rotating (shallow water or gas dynamical). The third is rotating, with deep-water gravity waves inducing an Ursell ‘anti-Stokes flow’. The Froude or Mach number, and the Rossby number in the third example, are assumed small. Remote recoil is all or part of the interaction in all three examples, except in one special limiting case. That case is found only within a severely restricted parameter regime and is the only case in which, exceptionally, the effective recoil force can be regarded as purely local and identifiable with the celebrated Craik–Leibovich vortex force – which corresponds, in the quantum fluids literature, to the Iordanskii force due to a phonon current incident on a vortex. Another peculiarity of that exceptional case is that the only significant wave refraction effect is the Aharonov–Bohm topological phase jump.