4D GPS water vapor tomography: new parameterized approaches

Water vapor is a key variable in numerical weather prediction, as it plays an important role in atmospheric processes. Nonetheless, the distribution of water vapor in the atmosphere is observed with a coarse resolution in time and space compared to the resolution of numerical weather models. GPS water vapor tomography is one of the promising methods to improve the resolution of water vapor measurements. This paper presents new parameterized approaches for the determination of water vapor distribution in the troposphere by GPS. We present the methods and give first results validating the approaches. The parameterization of voxels (volumetric pixels) by trilinear and spline functions in ellipsoidal coordinates are introduced in this study. The evolution in time of the refractivity field is modeled by a Kalman filter with a temporal resolution of 30 s, which corresponds to the available GPS-data rate. The algorithms are tested with simulated and with real data from more than 40 permanent GPS receiver stations in Switzerland and adjoining regions covering alpine areas. The investigations show the potential of the new parameterized approaches to yield superior results compared to the non parametric classical one. The accuracy of the tomographic result is quantified by the inter-quartile range (IQR), which is decreased by 10-20% with the new approaches. Further, parameterized voxel solutions have a substantially smaller maximal error than the non parameterized ones. Simulations show a limited ability to resolve vertical structures above the top station of the network with GPS tomograph

Geometry of GPS dilution of precision : revisited

We revisit the geometric interpretation of GPS Dilution of Precision (DOP) factors giving emphasis on the geometric impact of the receiver clock parameter on conventional GPS positioning solution. The comparison is made between the solutions with and without an estimated receiver clock parameter, i.e., conventional GPS vs pure trilateration solution. The generalized form of the DOP factors is also presented for observation redundancy greater than zero. The DOP factor equations are established as functions of triangle surfaces and tetrahedron volumes formed by the receiver-satellite unit vectors or by these vectors between themselves. To facilitate the comparison of the solutions with and without a receiver clock parameter, the average of receiver-satellite unit vectors is introduced to interpret the DOP factors geometrically. The geometry of satellite outage is also revisited from a geometric point of view. Finally, the geometric interpretation of receiver clock constrains within a positioning solution is also investigated

Characteristics and limitations of GPS L1 observations from submerged antennas

Observations from a submerged GNSS antenna underneath a snowpack need to be analyzed to investigate its potential for snowpack characterization. The magnitude of the main interaction processes involved in the GPS L1 signal propagation through different layers of snow, ice, or freshwater is examined theoretically in the present paper. For this purpose, the GPS signal penetration depth, attenuation, reflection, refraction as well as the excess path length are theoretically investigated. Liquid water exerts the largest influence on GPS signal propagation through a snowpack. An experiment is thus set up with a submerged geodetic GPS antenna to investigate the influence of liquid water on the GPS observations. The experimental results correspond well with theory and show that the GPS signal penetrates the liquid water up to three centimeters. The error in the height component due to the signal propagation delay in water can be corrected with a newly derived model. The water level above the submerged antenna could also be estimated.ISSN:0949-7714ISSN:1432-139

Continuous GPS and broad-scale deformation across the Rhine Graben and the Alps

In order to study the ongoing tectonic deformation in the Rhine Graben area, we reconstruct the local crustal velocity and the strain rate field from GPS array solutions. Following the aim of this work, we compile the velocities of permanent GPS stations belonging to various networks (EUREF, AGNES, REGAL and RGP) in central western Europe. Moreover, the strain rate field is displayed in terms of principal axes and values, while the normal and the shear components of the strain tensor are calculated perpendicular and parallel to the strike of major faults. The results are compared with the fault plane solutions of earthquakes, which have occurred in this area. A broad-scale kinematic deformation model across the Rhine Graben is provided on the basis of tectonics and velocity results of the GPS permanent stations. The area of study is divided into four rigid blocks, between which there might be relative motions. The velocity and the strain rate fields are reconstructed along their borders, by estimating a uniform rotation for each block. The tectonic behaviour is well represented by the four-block model in the Rhine Graben area, while a more detailed model will be needed for a better reconstruction of the strain field in the Alpine regio

The alpine Swiss-French airborne gravity survey

In February 1998, a regional-scale, airborne gravity survey was carried out over the French Occidental Alps within the framework of the GéoFrance 3-D research program.The survey consisted of 18 NS and 16 EW oriented lines with a spacing of 10 and 20 km respectively, covering the whole of the Western French Alps (total area: 50 000 km2; total distance of lines flown: 10 000 km). The equipment was mounted in a medium-size aircraft (DeHavilland Twin Otter) flowing at a constant altitude of 5100 m a.s.l, and at a mean ground speed of about 280 km h−1. Gravity was measured using a LaCoste & Romberg relative, air/sea gravimeter (type SA) mounted on a laser gyro stabilized platform. Data from 5 GPS antennae located on fuselage and wings and 7 ground-based GPS reference stations were used to determine position and aircraft induced accelerations.The gravimeter passband was derived by comparing the vertical accelerations provided by the gravimeter with those estimated from the GPS positions. This comparison showed that the gravimeter is not sensitive to very short wavelength aircraft accelerations, and therefore a simplified formulation for computing airborne gravity measurements was developed. The intermediate and short wavelength, non-gravitational accelerations were eliminated by means of digital, exponential low-pass filters (cut-off wavelength: 16 km). An important issue in airborne gravimetry is the reliability of the airborne gravity surveys when compared to ground surveys. In our studied area, the differences between the airborne-acquired Bouguer anomaly and the ground upward-continued Bouguer anomaly of the Alps shows a good agreement: the rms of these differences is equal to 7.68 mGal for a spatial resolution of 8 km. However, in some areas with rugged topography, the amplitudes of those differences have a striking correlation with the topography. We then argue that the choice of an appropriate density (reduction by a factor of 10 per cent) for computing the ground topographic corrections over the highest mountains, results in significantly reducing the differences between airborne and ground upward-continued Bouguer anomalies, which shows that some of the misfit stems from errors in the ground dat

Sensors / The effect of different Global Navigation Satellite System methods on positioning accuracy in elite alpine skiing

In sport science, Global Navigation Satellite Systems (GNSS) are frequently applied to capture athletes' position, velocity and acceleration. Application of GNSS includes a large range of different GNSS technologies and methods. To date no study has comprehensively compared the different GNSS methods applied. Therefore, the aim of the current study was to investigate the effect of differential and non-differential solutions, different satellite systems and different GNSS signal frequencies on position accuracy. Twelve alpine ski racers were equipped with high-end GNSS devices while performing runs on a giant slalom course. The skiers' GNSS antenna positions were calculated in three satellite signal obstruction conditions using five different GNSS methods. The GNSS antenna positions were compared to a video-based photogrammetric reference system over one turn and against the most valid GNSS method over the entire run. Furthermore, the time for acquisitioning differential GNSS solutions was assessed for four differential methods. The only GNSS method that consistently yielded sub-decimetre position accuracy in typical alpine skiing conditions was a differential method using American (GPS) and Russian (GLONASS) satellite systems and the satellite signal frequencies L1 and L2. Under conditions of minimal satellite signal obstruction, valid results were also achieved when either the satellite system GLONASS or the frequency L2 was dropped from the best configuration. All other methods failed to fulfill the accuracy requirements needed to detect relevant differences in the kinematics of alpine skiers, even in conditions favorable for GNSS measurements. The methods with good positioning accuracy had also the shortest times to compute differential solutions. This paper highlights the importance to choose appropriate methods to meet the accuracy requirements for sport applications.(VLID)157451

Tropospheric water vapor: a comprehensive high-resolution data collection for the transnational Upper Rhine Graben region

Tropospheric water vapor is one of the most important trace gases of the Earth\u27s climate system, and its temporal and spatial distribution is critical for the genesis of clouds and precipitation. Due to the pronounced dynamics of the atmosphere and the nonlinear relation of air temperature and saturated vapor pressure, it is highly variable, which hampers the development of high-resolution and three-dimensional maps of regional extent. With their complementary high temporal and spatial resolutions, Global Navigation Satellite Systems (GNSS) meteorology and Interferometric Synthetic Aperture Radar (InSAR) satellite remote sensing represent a significant alternative to generally sparsely distributed radio sounding observations. In addition, data fusion with collocation and tomographical methods enables the construction of detailed maps in either two or three dimensions. Finally, by assimilation of these observation-derived datasets with dynamical regional atmospheric models, tropospheric water vapor fields can be determined with high spatial and continuous temporal resolution. In the following, a collection of basic and processed datasets, obtained with the above-listed methods, is presented that describes the state and course of atmospheric water vapor for the extent of the GNSS Upper Rhine Graben Network (GURN) region. The dataset contains hourly 2D fields of integrated water vapor (IWV) and 3D fields of water vapor density (WVD) for four multi-week, variable season periods between April 2016 and October 2018 at a spatial resolution of (2.1 km)$^2$. Zenith total delay (ZTD) from GNSS and collocation and refractivities are provided as intermediate products. InSAR (Sentinel-1A/B)-derived double differential slant total delay phases (ddSTDPs) and GNSS-based ZTDs are available for March 2015 to July 2019. The validation of data assimilation with five independent GNSS stations for IWV shows improving Kling–Gupta efficiency (KGE) scores for all seasons, most notably for summer, with collocation data assimilation (KGE = 0.92) versus the open-cycle simulation (KGE = 0.69). The full dataset can be obtained from https://doi.org/10.1594/PANGAEA.936447 (Fersch et al., 2021)

Tropospheric water vapor: a comprehensive high-resolution data collection for the transnational Upper Rhine Graben region

Tropospheric water vapor is one of the most important trace gases of the Earth's climate system, and its temporal and spatial distribution is critical for the genesis of clouds and precipitation. Due to the pronounced dynamics of the atmosphere and the nonlinear relation of air temperature and saturated vapor pressure, it is highly variable, which hampers the development of high-resolution and three-dimensional maps of regional extent. With their complementary high temporal and spatial resolutions, Global Navigation Satellite Systems (GNSS) meteorology and Interferometric Synthetic Aperture Radar (InSAR) satellite remote sensing represent a significant alternative to generally sparsely distributed radio sounding observations. In addition, data fusion with collocation and tomographical methods enables the construction of detailed maps in either two or three dimensions. Finally, by assimilation of these observation-derived datasets with dynamical regional atmospheric models, tropospheric water vapor fields can be determined with high spatial and continuous temporal resolution. In the following, a collection of basic and processed datasets, obtained with the above-listed methods, is presented that describes the state and course of atmospheric water vapor for the extent of the GNSS Upper Rhine Graben Network (GURN) region. The dataset contains hourly 2D fields of integrated water vapor (IWV) and 3D fields of water vapor density (WVD) for four multi-week, variable season periods between April 2016 and October 2018 at a spatial resolution of (2.1 km)2. Zenith total delay (ZTD) from GNSS and collocation and refractivities are provided as intermediate products. InSAR (Sentinel-1A/B)-derived double differential slant total delay phases (ddSTDPs) and GNSS-based ZTDs are available for March 2015 to July 2019. The validation of data assimilation with five independent GNSS stations for IWV shows improving Kling–Gupta efficiency (KGE) scores for all seasons, most notably for summer, with collocation data assimilation (KGE = 0.92) versus the open-cycle simulation (KGE = 0.69). The full dataset can be obtained from https://doi.org/10.1594/PANGAEA.936447 (Fersch et al., 2021)