Interferometric Synthetic Aperture Radar (InSAR) data stacks offer a means to derive integrated water vapor (IWV) from phase delay observations along the satellite line of sight with high spatial resolution. Since interferometric observations are differential in both space and time, they capture relative IWV changes but lack absolute values, which is the variable integration constant. Existing approaches to obtain absolute IWV from InSAR are typically validated against GNSS observations, weather models, or other remote sensing datasets. However, these validations primarily assess the integration methods rather than the observed interferometric phase delay representing partial wet delay.In this study we investigate the reverse approach by comparing native differential partial wet delay observations from Persistent Scatterer InSAR (PSI), mapped to zenith wet delay (ZWD), with forward-modeled double differential ZWD (DsDt ZWD) derived from GNSS and ERA-5 data. The analysis focuses on a region in Central Europe spanning the France-Germany-Switzerland border from March 2015 to July 2019.The methodology incorporates data from 4.2 million persistent scatterer (PS) points, ERA-5 ZWD interpolated to these locations, and hourly tropospheric wet delay data from 16 GNSS stations. Temporal and spatial differences were computed to generate synthetic DsDt ZWD data stacks, enabling direct comparison of GNSS and ERA-5 ZWD. Analyses were conducted in single differential (temporal) and double differential (temporal and spatial) domains, with evaluations performed at GNSS stations using statistical metrics such as the coefficient of determination (R²) and the Kling-Gupta Efficiency (KGE) index. Seasonal variability was also assessed. Additionally, the study examines how local distances around GNSS stations affect the correlation (R² and KGE) between GNSS-InSAR and GNSS-ERA data, evaluating their impact on measurement consistency.Results reveal valuable insights into the performance of InSAR, GNSS, and ERA-5 ZWD. In the single differential domain, the variance of Dt ZPWD from InSAR aligns closely with GNSS and ERA-5 data. While scatter plots confirm a linear relationship between GNSS and ERA-5, GNSS vs. InSAR trends appear nonlinear. Applying double differences significantly enhances the correlation between GNSS and InSAR, surpassing that of GNSS and ERA-5. The KGE index highlights improved GNSS-InSAR performance, particularly in correlation (R) and variability ratio (Alpha). Seasonal analyses show that GNSS-InSAR excels during summer, with mean R² values twice those of GNSS-ERA, whereas GNSS-ERA performs better in winter. Regional variability is observed, with higher differences in R² and KGE values at stations in the Rhine Valley.In conclusion, this study demonstrates the capability of PS-InSAR to provide high-resolution, accurate differential ZWD estimates, particularly during summer. PS-InSAR shows a stronger correlation with GNSS data in the double differential domain compared to ERA-5, underscoring the value of high-resolution ZWD data. Systematic variations in GNSS-InSAR correlation, identified as potential quality indicators for GNSS ZWD products, further highlight the importance of integrating multi-source geodetic data to enhance ZWD monitoring.

We developed a high-quality global integrated water vapour (IWV) dataset from 12 552 ground-based global positioning system (GPS) stations in 2020. It consists of 5 min GPS IWV estimates with a total number of 1 093 591 492 data points. The completeness rates of the IWV estimates are higher than 95 % at 7253 (58 %) stations. The dataset is an enhanced version of the existing operational GPS IWV dataset provided by the Nevada Geodetic Laboratory (NGL). The enhancement is reached by employing accurate meteorological information from the fifth generation of European ReAnalysis (ERA5) for the GPS IWV retrieval with a significantly higher spatiotemporal resolution. A dedicated data screening algorithm is also implemented. The GPS IWV dataset has a good agreement with in situ radiosonde observations at 182 collocated stations worldwide. The IWV biases are within ±3.0 kg m−2 with a mean absolute bias (MAB) value of 0.69 kg m−2. The standard deviations (SD) of IWV differences are no larger than 3.4 kg m−2. In addition, the enhanced IWV product shows substantial improvements compared to NGL's operational version, and it is thus recommended for high-accuracy applications, such as research of extreme weather events and diurnal variations of IWV and intercomparisons with other IWV retrieval techniques. Taking the radiosonde-derived IWV as reference, the MAB and SD of IWV differences are reduced by 19.5 % and 6.2 % on average, respectively. The number of unrealistic negative GPS IWV estimates is also substantially reduced by 92.4 % owing to the accurate zenith hydrostatic delay (ZHD) derived by ERA5. The dataset is available at https://doi.org/10.5281/zenodo.6973528 (Yuan et al., 2022).

GNSS undifferenced signal processing, in which the individual signal of each frequency is treated as independent observable, has drawn increasing interest in GNSS community. However, undifferenced signal processing brings new challenges for cycle slip detection and repair. One important feature is the carrier frequency identification of cycle slips since observations are processed separately. An analysis of real cycle slips in a BDS triple-frequency baseline dataset illustrates the deficiencies in the cycle slip detection process commonly implemented, in the case when cycle slips occur in just one specific carrier frequency. Hence, we propose an improved cycle slip detection and repair approach based on a time-differenced model. Two major advantages characterize this proposed approach. The first one is a significant reduction in false alarms due to carrier frequency identification of cycle slips. Having access to a reliable cycle slip detection method significantly reduces the number of ambiguity parameters to be estimated. The second advantage is the benefit of separating the OSS (Observation at the other frequency of Same Satellite without cycle slip) and OSE (Observation at the Same Epoch from other satellites without cycle slip) from the OCS (Observation with Cycle Slip). The simulation results indicate that separation of the OSS and OSE can significantly improve the model strength of cycle slip estimation, especially OSS. The proposed approach is validated by cycle slip estimation with a real data set. Smaller biases and larger ratio values jointly demonstrate that a much stronger model strength can be achieved. Finally, the cycle slip repair procedure is applied to triple-frequency PPP. The stable and fast convergence, as well as the reduction in standard deviations, proves the efficiency of the proposed approach.

Recent surface movements in the Upper Rhine Graben (URG) area are investigated with geodetic techniques. Line of sight (LOS) displacement rates from SAR interferometry (InSAR), horizontal and vertical rates from coordinate time series of permanent GNSS sites and vertical rates from precise levelling measurements are estimated with high accuracy. We show that the data sets are capable of providing detailed insight into the current movements in the URG area, which is required for a better understanding of geodynamic processes as well as for a reasonable exploitation of geopotentials in the URG. This paper focusses on a comparison of results from InSAR and levelling on a regional and on a local scale. A case study highlights temporal differences in the deformation characteristics of an oil extraction area detected from ERS-1/2 and Envisat data as well as from levelling measurements in multiple epochs. In order to benefit from the advantages of each technique, our work aims on a proper combination to consistently link the different observation methods in a rigorous multi-technique approach.

Remote sensing data have been increasingly used to measure the content of water vapor in the atmosphere and to characterize its temporal and spatial variations. In this paper, we use observations from Global Navigation Satellite System(s) (GNSS) to estimate time series of precipitable water vapor (PWV) by applying the technique of precise point positioning. For an accurate quantification of the absolute PWV, it is necessary to combine the GNSS observations with meteorological data measured directly or inferred at the GNSS site. In addition, measurements of the surface temperature are used to calculate the empirical constant required to convert the GNSS-based delay into water vapor. Our results show strong agreement between the total precipitable water estimated based on GNSS observations and that measured by the sensor MEdium Resolution Imaging Spectrometer with a mean RMS value of 0.98 mm. In a similar way, we compared the GNSS-based total PWV estimates with those produced by the Weather Research and Forecasting (WRF) Modeling System. We found that the WRF model simulations agree well with the GNSS estimates with a mean RMS value of 0.97 mm.

This paper presents the innovative Compressive Sensing (CS) concept for tomographic reconstruction of 3D neutrospheric water vapor fields using data from Global Navigation Satellite Systems (GNSS) and Interferometric Synthetic Aperture Radar (InSAR). The Precipitable Water Vapor (PWV) input data are derived from simulations of the Weather Research and Forecasting modeling system. We apply a Compressive Sensing based approach for tomographic inversion. Using the Cosine transform, a sparse representation of the water vapor field is obtained. The new aspects of this work include both the combination of GNSS and InSAR data for water vapor tomography and the sophisticated CS estimation: The combination of GNSS and InSAR data shows a significant improvement in 3D water vapor reconstruction; and the CS estimation produces better results than a traditional Tikhonov regulari-zation with l 2 norm penalty term.

Over the past 20years, repeat‐pass spaceborne interferometric synthetic aperture radar (InSAR) has been widely used as a geodetic technique to generate maps of the Earth's topography and to measure the Earth's surface deformation. In this paper, we present a new approach to exploit microwave data from InSAR, particularly Persistent Scatterer InSAR (PSI), and Global Navigation Satellite Systems (GNSS) to derive maps of the absolute water vapor content in the Earth's atmosphere. Atmospheric water vapor results in a phase shift in the InSAR interferogram, which if successfully separated from other phase components provides valuable information about its distribution. PSI produces precipitable water vapor (PWV) difference maps of a high spatial density, which can be inverted using the least squares method to retrieve PWV maps at each SAR acquisition time. These maps do not contain the absolute (total) PWV along the signal path but only a part of it. The components eliminated by forming interferograms or phase filtering during PSI data processing are reconstructed using GNSS phase observations. The approach is applied to build maps of absolute PWV by combining data from InSAR and GNSS over the region of Upper Rhine Graben in Germany and France. For validation, we compared the derived PWV maps with PWV maps measured by the optical sensor MEdium‐Resolution Imaging Spectrometer. The results show strong spatial correlation with values of uncertainty of less than 1.5mm. Continuous grids of PWV are then produced by applying the kriging geostatistical interpolation technique that exploits the spatial correlations between the PWV observations.

Multipath effects caused by reflections in the near-field and far-field of a GNSS antenna represent a major error source in static and kinematic GNSS positioning applications. Since these effects are strongly site-specific, a generally valid and practicable analytical multipath model is still lacking. In contrast, using GNSS carrier phase observation residuals, the multipath stacking (MPS) methods are able to take site-specific conditions into account. We propose an advanced approach to performing residual-based MPS in the space domain. Being superior to most conventional attempts in which stacking cells have a fixed azimuthal resolution, our suggested method makes use of congruent cells and rigorous statistical assessments in terms of outlier detection and significance evaluation of the stacked values. The advanced stacking approach is applied to representative phase residuals from static precise point positioning. The results show that the use of congruent cells allows for MPS at high elevation angles and with a fine spatial resolution. Applying the resulting MPS maps at the residual level, both near-field and far-field effects at high and low elevation angles, respectively, can be significantly mitigated. In comparison with the conventional approach, the advanced one enables a larger reduction of about 20 % in the SD of residuals.

Observation weighting is an essential component of GPS stochastic modeling and plays a key role in reliable outlier detection and parameter estimation. Nowadays, satellite elevation angle and SNR are used as quality indicators for GPS phase measurements in high-accuracy geodetic applications. In comparison with elevation-dependent models, SNR-based weighting schemes represent the reality better, but usually require greater implementation efforts. Relying upon a representative analysis of empirical SNR-based weights, this paper proposes the elevation-dependent exponential weighting function EXPZ, which benefits from realistic SNR-based weights and enables easy software implementation. To process GPS data from a regional network, this advanced weighting scheme is implemented in the Bernese GPS Software 5.0 and is compared with the conventional elevation-dependent COSZ model in terms of phase ambiguity resolution, troposphere parameter (TRP) estimation, and site coordinate determination. The results show that the proposed EXPZ model significantly attenuates the downweighting effects on low-elevation observations and improves the success rates of ambiguity resolution by about 10%, the standard deviations of site-specific TRPs by about 40%, and the repeatability of daily coordinate estimates by up to 2.3 mm (50%).

Datasets of the GNSS Upper Rhine Graben Network (GURN) and the national levelling networks in Germany, France and Switzerland are investigated with respect to current surface displacements in the Upper Rhine Graben (URG) area. GURN consists of about 80 permanent GNSS (Global Navigation Satellite Systems) stations. The terrestrial levelling network comprises 1st and 2nd order levelling lines that have been remeasured at intervals of roughly 25 years, starting in 1922. Compared to earlier studies national institutions and private companies made available raw data, allowing for consistent solutions for the URG region. We focussed on the southern and eastern parts of the investigation area. Our preliminary results show that the levelling and GNSS datasets are sensitive to resolve small surface displacement rates down to an order of magnitude of 0.2 mm/a and 0.4 mm/a, respectively. The observed horizontal velocity components for a test region south of Strasbourg, obtained from GNSS coordinate time series, vary around 0.5 mm/a. The results are in general agreement with interseismic strain built-up in a sinistral strike–slip regime. Since the accuracy of the GNSS derived vertical component is insufficient, data of precise levelling networks is used to determine vertical displacement rates. More than 75% of the vertical rates obtained from a kinematic adjustment of 1st order levelling lines in the eastern part of URG vary between − 0.2 mm/a and + 0.2 mm/a, indicating that this region behaves stable. Higher rates up to 0.5 mm/a in a limited region south of Freiburg are in general agreement with active faulting. We conclude that both networks deliver stable results that reflect real surface movements in the URG area. We note, however, that geodetically observed surface displacements generally result from a superposition of different effects, and that a separation in tectonic and non-tectonic processes needs additional information and expertise.

In September 2008, the Institut de Physique du Globe de Strasbourg (Ecole et Observatoire des Sciences de la Terre) and the Geodetic Institute of Karlsruhe University (now: Karlsruhe Institute of Technology) established the transnational cooperation GURN (GNSS Upper Rhine Graben Network). Within the GURN initiative, these institutions are cooperating in order to carry out geo-scientific research in the framework of the transnational project TOPO-WECEP (Western and Central European Platform; link: http://www.topo-wecep.eu/), which succeeded the former project URGENT (Upper Rhine Graben Evolution and NeoTectonics; link: http://comp1.geol.unibas.ch) of the EUCOR universities (European Confederation of Upper Rhine Universities).

High spatially and temporally variable atmospheric water vapour causes an unknown delay in microwave signals transmitted by space-borne sensors. This delay is considered as a major limitation in Interferometric Synthetic Aperture Radar (InSAR) applications as well as high-precision applications of Global Navigation Satellite Systems (GNSS). On the other hand, the delay could be quantified to derive atmospheric parameters such as water vapour. Temporal variability of water vapour is well estimated from ongoing GNSS measurements, while InSAR provides information about the spatial variations of water vapour. This project aims at assimilating InSAR phase observations and spatially-sparse GNSS measurements for the determination of atmospheric water vapour. In this contribution GNSS-based water vapour calculations and assessment of different strategies are presented. Work in progress is also reported including some preliminary results.

The dominant error source for short wavelength spaceborne radar signals is due to water vapor present in the neutral atmosphere (neutrosphere). This distortion signal is characterized by high variations in time and space, and can be exploited as a valuable source for quantifying the water vapor content of the Earth's atmosphere. Available water vapor measurements provided by Envisat Medium Resolution Imaging Spectrometer (MERIS) and simulations from numerical weather prediction models are still limited in observing rapid fluctuations of water vapor. Therefore, we are investigating Interferometric Synthetic Aperture Radar (InSAR) for water vapor mapping. In this paper, water vapor maps derived from Persistent Scatterer InSAR (PSI), MERIS, and the Weather Research and Forecasting (WRF) model are presented with comparative analyses.

This paper verifies the performance of the automated ARMA identification using the toolbox ARMASA. For this purpose, a representative data base is generated by means of ARMA simulation with respect to sample size, correlation level, and model complexity. The model error defined as a transform of the prediction error is used as measure for the deviation between the true and the estimated model. The results of the study show that the recognition rates of underlying true processes increase with increasing sample sizes and decrease with rising model complexity. Considering large sample sizes, the true underlying processes can be correctly recognised for nearly 80% of the analysed data sets. Additionally, the model errors of first-order AR resp. MA processes converge clearly more rapidly to the corresponding asymptotical values than those of high-order ARMA processes.

When processing observational data from global navigation satellite systems (GNSS), the carrier phase measurements are generally assumed to follow a normal distribution. Although full knowledge of the probability distribution of the observables is not required for parameter estimation, for example when using the least-squares method, the distributional properties of GNSS observations play a key role in quality control procedures, such as outlier and cycle-slip detection, in ambiguity resolution, as well as in the reliability assessment of estimation results. In addition, when applying GNSS positioning under critical observation conditions with respect to multipath and atmospheric effects, the validity of the normal distribution assumption of GNSS observables certainly comes into doubt. This paper illustrates the discrepancies between the normal distribution assumption and reality, based on a large and representative data set of GPS phase measurements covering a range of factors, including multipath impact, baseline length, and atmospheric conditions. The statistical inferences are made using the first through fourth sample moments, hypothesis tests, and graphical tools such as histograms and quantile–quantile plots. The results show clearly that multipath effects, in particular the near-field component, produce the dominant influence on the distributional characteristics of GNSS observables. Additionally, using surface meteorological data, considerable correlations between distributional deviations from normality on the one hand and atmospheric relative humidity on the other are detected.

SUMMARY In order to improve the education of young researchers (master degree, PhD, PostDocs) a cooperation between the Department of Geomatics (DGEOM), Federal University of Paraná (UFPR), Curitiba (Brazil) and the Geodetic Institute (GIK), University Karlsruhe (TH), Karlsruhe (Germany) was established which now exists since more than five years. The joint venture is actually called "PROBRAL: Precise positioning and height determination by means of GPS: Modeling of errors and transformation into physical heights" and focuses on research and education within the field of satellite geodesy. PROBRAL is funded by the Brazilian academic exchange service CAPES and the German academic exchange service DAAD. The geodetic aim of this research project is to validate and improve the quality of 3d positions derived from observations related to navigation satellite systems like GPS. In order to fulfill this ambitious goal sustainably, research has to be carried out in close cooperation. At the same time, e.g. to guarantee continuous success, a coordinated education has to be ensured. Besides technical education aspects key competencies (e.g. language, capacity for teamwork, project management skills) are trained. Within the paper especially the lessons which were learned from this project are discussed in detail.