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.

Deriving Centimeter-Level Coseismic Deformation and Fault Geometries of Small-To-Moderate Earthquakes From Time-Series Sentinel-1 SAR Images

Small-to-moderate earthquakes (e.g. ≤Mw5.5) occur much more frequently than large ones (e.g. >Mw6.0), yet are difficult to study with InSAR due to their weak surface deformation that are severely contaminated by atmospheric delays. Here we propose a stacking method using time-series SAR images that can effectively suppress atmospheric phase screens and extract weak coseismic deformation in centimeter to sub-centimeter level. Using this method, we successfully derive coseismic surface deformations for three small-to-moderate (Mw∼5) earthquakes in Tibet Plateau and Tienshan region from time-series Sentinel-1 SAR images, with peak line-of-sight deformation ranging from 5–6 mm to 13 mm. We also propose a strategy to downsample interferograms with weak deformation signal based on quadtree mesh obtained from preliminary slip model. With the downsampled datasets, we invert for the centroid locations, fault geometries and slips of these events. Our results demonstrate the potential of using time-series InSAR images to enrich earthquake catalog with geodetic observations for further study of earthquake cycle and active tectonics.

ABSOLUTE LOCALIZATION OF CORNER REFLECTORS WITH TERRASAR-X SPOTLIGHT IMAGES

Synthetic aperture radar, capable of imaging the Earth surface from space in nearly all-weather conditions and high spatial resolution, has shown its outstanding capability for a variety of ground mapping applications. With well-controlled orbits of the new generation SAR satellites, high accuracy absolute localization with multiple SAR images has been demonstrated and become one of the hot spots with increasing attention. In this paper, high-resolution Spotlight-mode TerraSAR-X images acquired from the single orbit track were applied to 3D absolute positioning of three triangular trihedral corner reflectors. In order to overcome the limitation imposed by the acquisitions with very short baselines, a height constraint was introduced and the sub-meter accuracy was derived after carefully compensating for the known error sources, such as atmospheric delays and solid earth tide shifts.

On the multi-technique combination with atmospheric ties

<p align="justify"><span>We explore a new strategy to combine geodetic observations employing the existing and future systems. Imposing atmospheric ties on the combination at either the observation or normal equation level introduces a physical interpretation to the estimated atmospheric delay parameters, </span><span>that is, </span><span>zenith delays and gradients. In essence, besides combining station coordinates via local ties, we combine atmospheric delays via atmospheric ties. The purpose of this work is to assess the advantages and caveats of such a combination approach, on legacy, state-of-the-art, and next generation geodetic systems. We simulate 10 years of observations of all space geodetic techniques that currently contribute to the realization of the international terrestrial reference system; that is, very long baseline interferometry (VLBI), satellite laser ranging (SLR), global navigation satellite systems (GNSS), and Doppler orbitography and radiopositioning integrated by satellite (DORIS). The noise we inject in the simulated observations is technique-specific and - besides a thermal contribution - stems from three-state clock models and ray-traced delays from the latest ECMWF reanalysis, ERA5. To make the simulations more realistic, we estimate the probability of potential observations being successful by utilizing ERA5 fields, for example cloud fields for SLR. To avoid overoptimistic uncertainty estimates, we have accounted for the correlation between observations based on ERA5 fields. In a bias-free setup, we find that the improvement of employing atmospheric ties in addition to local ties to fuse multi-sensor observations, on the combined station coordinates and atmospheric delays is statistically significant for all techniques except for GNSS. We attribute the latter to the relatively good observing geometry. We also find that employing atmospheric ties reveals unaccounted systematic errors stemming from erroneous auxiliary data that are necessary for the reduction of geodetic observations, </span><span>such as </span><span>pressure </span><span>measurements, </span><span>cable </span><span>calibrations, </span><span>and range biases. Performing the observation combination with atmospheric ties improves the combined solution, </span><span>especially </span><span>for sparse observing geometry, and facilitates the detection of unaccounted systematic errors.</span></p>

REDUCTION OF INSAR DEM TROPOSPHERIC NOISE WITH GPS OBSERVATIONS

Satellite Interferometric Synthetic Aperture Radar (InSAR) Signals are often intensively contaminated by atmospheric delays. The atmospheric conditions especially its water vapor content significantly varies in space and with time. Therefore, it is essential to characterize the atmospheric variations in order to mitigate these effects by appropriate means. In the topographic case, for high-resolution DEM generation, the errors may be decreased by choosing interferometric pairs with relatively long baselines, as the error magnitude is inversely dependent on the perpendicular component of the interferometer baseline. For InSAR DEM quality estimation against tropospheric corrected one, we use the GPS measurements to create the reference DEM in the region. The preliminary results show that the corrected DEM by the phase gradient method has the highest correlation with the ground-based observations and the InSAR DEM which is corrected by phase gradient stacking method for water vapor effect in the troposphere has the best accuracy, ranging from 0.07 ~ 5.81 m, while the InSAR original DEM has an accuracy of 0.29 ~ 14.62 m.