ZPD Retrieval Performances of the First Operational Ship-Based Network of GNSS Receivers over the North-West Mediterranean Sea

This work presents the design and implementation of an operational infrastructure for the monitoring of atmospheric parameters at sea through GNSS meteorology sensors installed on liners operating in the north-west Mediterranean Sea. A measurement system, capable of operationally and continuously providing the values of surface parameters, is implemented together with software procedures based on a float-PPP approach for estimating zenith path delay (ZPD) values. The values continuously registered over a three year period (2020-2022) from this infrastructure are compared with the data from a numerical meteorological reanalysis model (MERRA-2). The results clearly prove the ability of the system to estimate the ZPD from ship-based GNSS-meteo equipment, with the accuracy evaluated in terms of correlation and root mean square error reaching values between 0.94 and 0.65 and between 18.4 and 42.9 mm, these extreme values being from the best and worst performing installations, respectively. This offers a new perspective on the operational exploitation of GNSS signals over sea areas in climate and operational meteorological applications.

Multi-GNSS-Weighted Interpolated Tropospheric Delay to Improve Long-Baseline RTK Positioning

Until now, RTK (real-time kinematic) and NRTK (Network-based RTK) have been the most popular cm-level accurate positioning approaches based on Global Navigation Satellite System (GNSS) signals in real-time. The tropospheric delay is a major source of RTK errors, especially for medium and long baselines. This source of error is difficult to quantify due to its reliance on highly variable atmospheric humidity. In this paper, we use the NRTK approach to estimate double-differenced zenith tropospheric delays alongside ambiguities and positions based on a complete set of multi-GNSS data in a sample 6-station network in Europe. The ZTD files published by IGS were used to validate the estimated ZTDs. The results confirmed a good agreement, with an average Root Mean Squares Error (RMSE) of about 12 mm. Although multiplying the unknowns makes the mathematical model less reliable in correctly fixing integer ambiguities, adding a priori interpolated ZTD as quasi-observations can improve positioning accuracy and Integer Ambiguity Resolution (IAR) performance. In this work, weighted least-squares (WLS) were performed using the interpolation of ZTD values of near reference stations of the IGS network. When using a well-known Kriging interpolation, the weights depend on the semivariogram, and a higher network density is required to obtain the correct covariance function. Hence, we used a simple interpolation strategy, which minimized the impact of altitude variability within the network. Compared to standard RTK where ZTD is assumed to be unknown, this technique improves the positioning accuracy by about 50%. It also increased the success rate for IAR by nearly 1.

Assessment of Contemporary Antarctic GIA Models Using High-Precision GPS Time Series

Past redistributions of the Earth’s mass resulting from the Earth’s viscoelastic response to the cycle of deglaciation and glaciation reflect the process known as glacial isostatic adjustment (GIA). GPS data are effective at constraining GIA velocities, provided that these data are accurate, have adequate spatial coverage, and account for competing geophysical processes, including the elastic loading of ice/snow ablation/accumulation. GPS solutions are significantly affected by common mode errors (CMEs) and the choice of optimal noise model, and they are contaminated by other geophysical signals due primarily to the Earth’s elastic response. Here, independent component analysis is used to remove the CMEs, and the Akaike information criterion is used to determine the optimal noise model for 79 GPS stations in Antarctica, primarily distributed across West Antarctica and the Antarctic Peninsula. Next, a high-resolution surface mass variation model is used to correct for elastic deformation. Finally, we use the improved GPS solution to assess the accuracy of seven contemporary GIA forward models in Antarctica. The results show that the maximal GPS crustal displacement velocity deviations reach 4.0 mm yr−1, and the mean variation is 0.4 mm yr−1 after removing CMEs and implementing the noise analysis. All GIA model-predicted velocities are found to systematically underestimate the GPS-observed velocities in the Amundsen Sea Embayment. Additionally, the GPS vertical velocities on the North Antarctic Peninsula are larger than those on the South Antarctic Peninsula, and most of the forward models underestimate the GIA impact on the Antarctic Peninsula.

Comprehensive Study on the Tropospheric Wet Delay and Horizontal Gradients during a Severe Weather Event

GNSS meteorology is today one of the most growing technologies to monitor severe weather events. In this paper, we present the usage of 160 GPS reference stations over the period of 14 days to monitor and track Hurricane Harvey, which struck Texas in August 2017. We estimate the Zenith Wet Delay (ZWD) and the tropospheric gradients with 30 s interval using TOMION v2 software and carry out the processing in Precise Point Positioning (PPP) mode. We study the relationship of these parameters with atmospheric variables extracted from Tropical Rainfall Measuring Mission (TRMM) satellite mission and climate reanalysis model ERA5. This research finds that the ZWD shows patterns related to the rainfall rate and to the location of the hurricane. We also find that the tropospheric gradients are correlated with water vapor gradients before and after the hurricane, and with the wind and the pressure gradients only after the hurricane. This study also shows a new finding regarding the spectral distribution of the gradients, with a clear diurnal period present, which is also found on the ZWD itself. This kind of study approaches the GNSS meteorology to the increasing requirements of meteorologist in terms of monitoring severe weather events.

Understanding the Present-Day Spatiotemporal Variability of Precipitable Water Vapor over Ethiopia: A Comparative Study between ERA5 and GPS

Atmospheric water vapor plays a crucial role in atmospheric, climate change, meteorological, and hydrological processes. In a country like Ethiopia, with its complex topography and synoptic-scale spatiotemporal circulation patterns, the analysis of the spatiotemporal variability of precipitable water vapor (PWV) is very challenging, and is hampered by the lack of long observational datasets. In this study, we process the PWV over eight Ethiopian global positioning system (GPS) sites and one close to the Ethiopian eastern border, for the available common period 2013–2020, and compare with the PWV retrieved from the state-of-the-art ERA5 reanalysis. Both PWV datasets agree very well at our sample, with correlation coefficients between 0.96 and 0.99, GPS-PWV show a moderate wet bias compared to ERA5-PWV for the majority of the sites, and an overall root mean square error of 3.4 mm. Seasonal and diurnal cycles are also well captured by these datasets. The seasonal variations of PWV and precipitation at the sites agree very well. Maximum diurnal PWV amplitudes are observed for stations near water bodies or dense vegetation, such as Arbaminch (ARMI) and Bahir Dar (BDMT). At those stations, the PWV behavior at heavy rainfall events has been investigated and an average 25% increase (resp. decrease) from 12 h before (resp. 12 h after) the start of the rainfall event, when the PWV peaks, has been observed.

GPS-Based Multi-Temporal Variation in Precipitable Water over the Territory of Poland

An increase in temperature causes higher evaporation of water from water bodies; consequently, the water content in the atmosphere also increases. The precipitable water (PW), as the water content in the atmospheric air column, is therefore an important parameter to consider when studying climate change. The aim of this study was to analyse multi-annual precipitable water data derived from a dense Global Navigational Satellite Systems (GNSS) network. Twelve years of observations from over a hundred ASG-EUPOS stations were used to estimate changes in precipitation water values over Poland. The data were validated by comparison with the available radio-sounding data. The analysis of the GPS-based PW values showed an upward trend in the PW value of 0.078 mm/year. The spatio-temporal distribution of the mean PW values and their fluctuations over the years were studied and visualised in the form of maps. The results are congruent with the fact that Poland lies on the border of influence of both continental and oceanic climates. Our results are also consistent with other climate research concerning this region.

Geopositioning time series from offshore platforms in the Adriatic Sea

We provide a dataset of 3D coordinate time series of 37 continuous GNSS stations installed for stability monitoring purposes on onshore and offshore industrial settlements along a NW-SE-oriented and ~100-km-wide belt encompassing the eastern Italian coast and the Adriatic Sea. The dataset results from the analysis performed by using different geodetic software (Bernese, GAMIT/GLOBK and GIPSY) and consists of six raw position time series solutions, referred to IGb08 and IGS14 reference frames. Time series analyses and comparisons evidence that the different solutions are consistent between them, despite the use of different software, models, strategy processing and frame realizations. We observe that the offshore stations are subject to significant seasonal oscillations probably due to seasonal environmental loads, seasonal temperature-induced platform deformation and hydrostatic pressure variations. Many stations are characterized by non-linear time series, suggesting a complex interplay between regional (long-term tectonic stress) and local sources of deformation (e.g. reservoirs depletion, sediment compaction). Computed raw time series, logs files, phasor diagrams and time series comparison plots are distributed via PANGAEA ( https://www.pangaea.de ).

Kriging Interpolation in Modelling Tropospheric Wet Delay

This contribution implements the Kriging interpolation in predicting the tropospheric wet delays using global navigation satellite system networks. The predicted tropospheric delays can be used in strengthening the precise point positioning models and numerical weather prediction models. In order to evaluate the performances of the Kriging interpolation, a sparse network with 8 stations and a dense network with 19 stations from continuously operating reference stations (CORS) of the Netherlands are selected as the reference. In addition, other 15 CORS stations are selected as users, which are divided into three blocks: 5 stations located approximately in the center of the networks, 5 stations on the edge of the networks and 5 stations outside the networks. The zenith tropospheric wet delays are estimated at the network and user stations through the ionosphere-free positioning model; meanwhile, the predicted wet delays at the user stations are generated by the Kriging interpolation in the use of the tropospheric estimations at the network. The root mean square errors (RMSE) are calculated by comparing the predicted wet delays and estimated wet delays at the same user station. The results show that RMSEs of the stations inside the network are at a sub-centimeter level with an average value of 0.74 cm in the sparse network and 0.69 cm in the dense network. The stations on edge and outside the network can also achieve 1-cm level accuracy, which overcomes the limitation that accurate interpolations can only be attained inside the network. This contribution also presents an insignificant improvement of the prediction accuracy from the sparse network to the dense network over 1-year’s data processing and a seasonal effect on the tropospheric wet delay predictions.

High Quality Zenith Tropospheric Delay Estimation Using a Low-Cost Dual-Frequency Receiver and Relative Antenna Calibration

The recent release of consumer-grade dual-frequency receivers sparked scientific interest into use of these cost-efficient devices for high precision positioning and tropospheric delay estimations. Previous analyses with low-cost single-frequency receivers showed promising results for the estimation of Zenith Tropospheric Delays (ZTDs). However, their application is limited by the need to account for the ionospheric delay. In this paper we investigate the potential of a low-cost dual-frequency receiver (U-blox ZED-F9P) in combination with a range of different quality antennas. We show that the receiver itself is very well capable of achieving high-quality ZTD estimations. The limiting factor is the quality of the receiving antenna. To improve the applicability of mass-market antennas, a relative antenna calibration is performed, and new absolute Antenna Exchange Format (ANTEX) entries are created using a geodetic antenna as base. The performance of ZTD estimation with the tested antennas is evaluated, with and without antenna Phase Center Variation (PCV) corrections, using Precise Point Positioning (PPP). Without applying PCVs for the low-cost antennas, the Root Mean Square Errors (RMSE) of the estimated ZTDs are between 15 mm and 24 mm. Using the newly generated PCVs, the RMSE is reduced significantly to about 4 mm, a level that is excellent for meteorological applications. The standard U-blox ANN-MB-00 patch antenna, with a circular ground plane, after correcting the phase pattern yields comparable results (0.47 mm bias and 4.02 mm RMSE) to those from geodetic quality antennas, providing an all-round low-cost solution. The relative antenna calibration method presented in this paper opens the way for wide-spread application of low-cost receiver and antennas.

The Influence of Different Modelling Factors on Global Temperature and Pressure Models and Their Performance in Different Zenith Hydrostatic Delay (ZHD) Models

Surface temperature and pressure are indispensable variables in Global Navigation Satellite System (GNSS) meteorology. The lack of meteorological observations located at or near the GNSS sites is a big challenge for the calculation of accurate zenith hydrostatic delay (ZHD). Therefore, various empirical models with different model forms were established to provide temperature and pressure values. In this study, the influence of different modelling factors, including model forms, temporal resolution of the data sources, and the spatial resolution of the data sources, is evaluated and the temperature and pressure model with the best performance is developed. On the basis of the meteorological parameters estimated by the above model, we analyzed the global performance of the three most commonly used ZHD models, that is, the Saastamoinen, Hopfield, and Black models. The numerical results show that the model with the idea of time-segmented modelling performs best, of which the global mean root mean square (RMS), mean absolute error (MAE), and standard deviation (SD) are 7.87/6.33/7.17 hPa and 2.95/2.31/2.79 K for pressure and temperature, respectively, using the data sources with temporal resolution of 2 h and spatial resolution of 2.5° × 2° in the reanalysis data comparison. In comparison with the radiosonde data, the mean RMS/MAE/SD are 7.02/5.24/6.46 hPa and 4.05/3.17/3.86 K for pressure and temperature, respectively. The Saastamoinen model with a global mean bias/RMS of 1.01/16.9 mm achieved the best ZHD estimated values compared with the other two ZHD models.

Analysis on the Impacts of Slant Tropospheric Delays on Precise Point Positioning

Tropospheric delay is one main factor affecting the accuracy of precise point positioning (PPP) ambiguity-float and fixed solutions. Investigations mainly focused on evaluating the contributions of tropospheric corrections to the accuracy and reliability of PPP solutions. The tropospheric corrections generally contained the zenith tropospheric delay (ZTD) and the horizontal gradients estimated from relative positioning or PPP. However, the estimated tropospheric delays can be partly absorbed by the carrier phase residuals if the stochastic model is not well-defined. Therefore, along with the ZTD and horizontal gradients, the carrier phase residuals from PPP backward filter are considered to reconstruct slant tropospheric delay (STD). Based on the proposed STD model, its marginal effects on GPS PPP were investigated. Results indicated that the consideration of carrier phase residuals for STD modeling can improve the three-dimensional accuracy to 0.5 cm/1 cm/1.2 cm in the South/North/Up (N/E/U) components. Then, the effects of internal and external STD corrections on PPP float and fixed solutions were analyzed. Compared to the ZTD + gradients augmentation, STD corrections from the same station could improve the PPP accuracy by 51%/51%/60%; the large improvements were because the multipath error and observation noise were eliminated. In comparison, the improvement was 14%/28%/31% using external STD corrections, which indicated the effects of unmodeled tropospheric errors in the phase residuals. The ambiguity-fixing results indicated that the fixing rate of PPP ambiguity was increased by 30% with STD augmentation. As the BeiDou System (BDS) suffered longer convergence than that of GPS, the benefits of STD modeling to the BDS observations were also validated. Overall, the results validated the performance of STD-augmented PPP, which demonstrated the potential application of high-accuracy troposphere products.

GPS Precipitable Water Vapor Estimations over Costa Rica: A Comparison against Atmospheric Sounding and Moderate Resolution Imaging Spectrometer (MODIS)

The quantification of water vapor in tropical regions like Central America is necessary to estimate the influence of climate change on its distribution and the formation of precipitation. This work reports daily estimations of precipitable water vapor (PWV) using Global Positioning System (GPS) delay data over the Pacific region of Costa Rica during 2017. The GPS PWV measurements were compared against atmospheric sounding and Moderate Resolution Imaging Spectrometer (MODIS) data. When GPS PWV was calculated, relatively small biases between the mean atmospheric temperatures (Tm) from atmospheric sounding and the Bevis equation were found. The seasonal PWV fluctuations were controlled by two of the main circulation processes in Central America: the northeast trade winds and the latitudinal migration of the Intertropical Convergence Zone (ITCZ). No significant statistical differences were found for MODIS Terra during the dry season with respect GPS-based calculations (p > 0.05). A multiple linear regression model constructed based on surface meteorological variables can predict the GPS-based measurements with an average relative bias of −0.02 ± 0.19 mm/day (R2 = 0.597). These first results are promising for incorporating GPS-based meteorological applications in Central America where the prevailing climatic conditions offer a unique scenario to study the influence of maritime moisture inputs on the seasonal water vapor distribution.

Improving GNSS Zenith Wet Delay Interpolation by Utilizing Tropospheric Gradients: Experiments with a Dense Station Network in Central Europe in the Warm Season

The Benchmark data set collected within the European COST Action ES1206 has aimed to support the development and validation of advanced Global Navigation Satellite System (GNSS) tropospheric products, in particular high-resolution zenith delays and tropospheric gradients. In this work we utilize this unique data set to show that the interpolation of GNSS Zenith Wet Delays (ZWDs) can be improved by utilizing tropospheric gradients. To do this we first prove the concept with simulated observations, that is, zenith delays and tropospheric gradients derived from a Numerical Weather Model. We show how tropospheric gradients can be converted to ZWD gradients. Then the ZWD gradients together with the ZWDs at selected reference stations are used in an inverse distance weighting interpolation scheme to estimate the ZWD at some target station. For a station configuration with an average station distance of 50 km in Germany and a period of two months (May and June 2013), we find an improvement of 20% in interpolated ZWDs when tropospheric gradients are taken into account. Next, we replace the simulated by real observations, that is, zenith delays and tropospheric gradients from a Precise Point Positioning (PPP) solution provided with the G-Nut/Tefnut analysis software. Here we find an improvement of 10% in interpolated ZWDs when tropospheric gradients are taken into account.

Estimating the Impact of Global Navigation Satellite System Horizontal Delay Gradients in Variational Data Assimilation

We developed operators to assimilate Global Navigation Satellite System (GNSS) Zenith Total Delays (ZTDs) and horizontal delay gradients into a numerical weather model. In this study we experiment with refractivity fields derived from the Global Forecast System (GFS) available with a horizontal resolution of 0.5°. We begin our investigations with simulated observations. In essence, we extract the tropospheric parameters from the GFS analysis, add noise to mimic observation errors and assimilate the simulated observations into the GFS 24h forecast valid at the same time. We consider three scenarios: (1) the assimilation of ZTDs (2) the assimilation of horizontal delay gradients and (3) the assimilation of both ZTDs and horizontal delay gradients. The impact is measured by utilizing the refractivity fields. We find that the assimilation of the horizontal delay gradients in addition to the ZTDs improves the refractivity field around 800 hPa. When we consider a single station there is a clear improvement when horizontal delay gradients are assimilated in addition to the ZTDs because the horizontal delay gradients contain information that is not contained in the ZTDs. On the other hand, when we consider a dense station network there is not a significant improvement when horizontal delay gradients are assimilated in addition to the ZTDs because the horizontal delay gradients do not contain information that is not already contained in the ZTDs. Finally, we replace simulated by real observations, that is, tropospheric parameters from a Precise Point Positioning solution provided with the G-Nut/Tefnut software, in order to show that the GFS 24h forecast is indeed improved when GNSS horizontal delay gradients are assimilated in addition to GNSS ZTDs; for the considered station (Potsdam, Germany) and period (June and July, 2017) we find an improvement in the retrieved refractivity of up to 4%.

Space-based observations of crustal deflections for drought characterization in Brazil

Widespread environmental impacts of frequent drought episodes in Brazil have resulted in several drought-related diagnostics studies. However, the potential of many "opportunistic sensors", such as the Global Positioning System (GPS), has not yet been considered in hydrological hazard monitoring in Brazil. In this study, the response of the Earth's crust to Brazil's 2012-2015 drought event in different structural provinces is analyzed by comparing GPS-observed vertical crustal deformations (VCDs) with the terrestrial water storage (TWS) derived from the Gravity Recovery and Climate Experiment (GRACE). The results indicate that there is no spatial correlation between annual amplitudes of the TWS and VCDs in different structural provinces apart from the purely elastic response of the crust to TWS dynamics, at almost all the 39 GPS stations that were analyzed. However, approximately 15% of the monitoring stations show that VCD leads TWS with a phase lag of 2-4 months. Errors associated with VCD and TWS are within the accepted range for space geodetic techniques (i.e., GPS and GRACE) and despite the need for further investigation, the phase lead seems to be associated with rainfall, which impacts the TWS through the hydrographs. Overall, the GPS-based drought index (DI_VCD) reflects the water depletion in many regions of Brazil, which agrees with the GRACE-based DI_TWS in terms of the Spearman correlation coefficient (ranging from 0.4 to 0.9) in the Amazon, Tocantins, La Plata, and São Francisco river basins. This agreement confirms the drought persistence during the study period and that DI_VCD can be used to monitor hydrological droughts. In regions in which DI_TWS sufficiently agrees with DI_VCD (48% of the sites), near real-time drought monitoring is feasible. This could be useful in the optimization of models for the forward prediction of drought events in other regions worldwide, where GPS vertical displacements strongly correlate with hydrological GRACE signals.

A Method to Improve the Distribution of Observations in GNSS Water Vapor Tomography

Water vapor is an important driving factor in the related weather processes in the troposphere, and its temporal-spatial distribution and change are crucial to the formation of cloud and rainfall. Global Navigation Satellite System (GNSS) water vapor tomography, which can reconstruct the water vapor distribution using GNSS observation data, plays an increasingly important role in GNSS meteorology. In this paper, a method to improve the distribution of observations in GNSS water vapor tomography is proposed to overcome the problem of the relatively concentrated distribution of observations, enable satellite signal rays to penetrate more tomographic voxels, and improve the issue of overabundance of zero elements in a tomographic matrix. Numerical results indicate that the accuracy of the water vapor tomography is improved by the proposed method when the slant water vapor calculated by GAMIT is used as a reference. Comparative results of precipitable water vapor (PWV) and water vapor density (WVD) profiles from radiosonde station data indicate that the proposed method is superior to the conventional method in terms of the mean absolute error (MAE), standard deviations (STD), and root-mean-square error (RMS). Further discussion shows that the ill-condition of tomographic equation and the richness of data in the tomographic model need to be discussed separately.

Near-source high-rate GPS, strong motion and InSAR observations to image the 2015 Lefkada (Greece) Earthquake rupture history

The 2015/11/17 Lefkada (Greece) earthquake ruptured a segment of the Cephalonia Transform Fault (CTF) where probably the penultimate major event was in 1948. Using near-source strong motion and high sampling rate GPS data and Sentinel-1A SAR images on two tracks, we performed the inversion for the geometry, slip distribution and rupture history of the causative fault with a three-step self-consistent procedure, in which every step provided input parameters for the next one. Our preferred model results in a ~70° ESE-dipping and ~13° N-striking fault plane, with a strike-slip mechanism (rake ~169°) in agreement with the CTF tectonic regime. This model shows a bilateral propagation spanning ~9 s with the activation of three main slip patches, characterized by rise time and peak slip velocity in the ranges 2.5-3.5 s and 1.4-2.4 m/s, respectively, corresponding to 1.2-1.8 m of slip which is mainly concentrated in the shallower (<10 km) southern half of the causative fault. The inferred slip distribution and the resulting seismic moment (M₀ = 1.05 × 10¹⁹ N m) suggest a magnitude of M _w 6.6. Our best solution suggests that the occurrence of large (M _w  > 6) earthquakes to the northern and to the southern boundaries of the 2015 causative fault cannot be excluded.

The Impact of Estimating High-Resolution Tropospheric Gradients on Multi-GNSS Precise Positioning

Benefits from the modernized US Global Positioning System (GPS), the revitalized Russian GLObal NAvigation Satellite System (GLONASS), and the newly-developed Chinese BeiDou Navigation Satellite System (BDS) and European Galileo, multi-constellation Global Navigation Satellite System (GNSS) has emerged as a powerful tool not only in positioning, navigation, and timing (PNT), but also in remote sensing of the atmosphere and ionosphere. Both precise positioning and the derivation of atmospheric parameters can benefit from multi-GNSS observations. In this contribution, extensive evaluations are conducted with multi-GNSS datasets collected from 134 globally-distributed ground stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) network in July 2016. The datasets are processed in six different constellation combinations, i.e., GPS-, GLONASS-, BDS-only, GPS + GLONASS, GPS + BDS, and GPS + GLONASS + BDS + Galileo precise point positioning (PPP). Tropospheric gradients are estimated with eight different temporal resolutions, from 1 h to 24 h, to investigate the impact of estimating high-resolution gradients on position estimates. The standard deviation (STD) is used as an indicator of positioning repeatability. The results show that estimating tropospheric gradients with high temporal resolution can achieve better positioning performance than the traditional strategy in which tropospheric gradients are estimated on a daily basis. Moreover, the impact of estimating tropospheric gradients with different temporal resolutions at various elevation cutoff angles (from 3° to 20°) is investigated. It can be observed that with increasing elevation cutoff angles, the improvement in positioning repeatability is decreased.

A Theoretical and Empirical Integrated Method to Select the Optimal Combined Signals for Geometry-Free and Geometry-Based Three-Carrier Ambiguity Resolution

Twelve GPS Block IIF satellites, out of the current constellation, can transmit on three-frequency signals (L1, L2, L5). Taking advantages of these signals, Three-Carrier Ambiguity Resolution (TCAR) is expected to bring much benefit for ambiguity resolution. One of the research areas is to find the optimal combined signals for a better ambiguity resolution in geometry-free (GF) and geometry-based (GB) mode. However, the existing researches select the signals through either pure theoretical analysis or testing with simulated data, which might be biased as the real observation condition could be different from theoretical prediction or simulation. In this paper, we propose a theoretical and empirical integrated method, which first selects the possible optimal combined signals in theory and then refines these signals with real triple-frequency GPS data, observed at eleven baselines of different lengths. An interpolation technique is also adopted in order to show changes of the AR performance with the increase in baseline length. The results show that the AR success rate can be improved by 3% in GF mode and 8% in GB mode at certain intervals of the baseline length. Therefore, the TCAR can perform better by adopting the combined signals proposed in this paper when the baseline meets the length condition.

Physical applications of GPS geodesy: a review

Geodesy, the oldest science, has become an important discipline in the geosciences, in large part by enhancing Global Positioning System (GPS) capabilities over the last 35 years well beyond the satellite constellation's original design. The ability of GPS geodesy to estimate 3D positions with millimeter-level precision with respect to a global terrestrial reference frame has contributed to significant advances in geophysics, seismology, atmospheric science, hydrology, and natural hazard science. Monitoring the changes in the positions or trajectories of GPS instruments on the Earth's land and water surfaces, in the atmosphere, or in space, is important for both theory and applications, from an improved understanding of tectonic and magmatic processes to developing systems for mitigating the impact of natural hazards on society and the environment. Besides accurate positioning, all disturbances in the propagation of the transmitted GPS radio signals from satellite to receiver are mined for information, from troposphere and ionosphere delays for weather, climate, and natural hazard applications, to disturbances in the signals due to multipath reflections from the solid ground, water, and ice for environmental applications. We review the relevant concepts of geodetic theory, data analysis, and physical modeling for a myriad of processes at multiple spatial and temporal scales, and discuss the extensive global infrastructure that has been built to support GPS geodesy consisting of thousands of continuously operating stations. We also discuss the integration of heterogeneous and complementary data sets from geodesy, seismology, and geology, focusing on crustal deformation applications and early warning systems for natural hazards.

Dynamics of glacier calving at the ungrounded margin of Helheim Glacier, southeast Greenland

During summer 2013 we installed a network of 19 GPS nodes at the ungrounded margin of Helheim Glacier in southeast Greenland together with three cameras to study iceberg calving mechanisms. The network collected data at rates up to every 7 s and was designed to be robust to loss of nodes as the glacier calved. Data collection covered 55 days, and many nodes survived in locations right at the glacier front to the time of iceberg calving. The observations included a number of significant calving events, and as a consequence the glacier retreated ~1.5 km. The data provide real-time, high-frequency observations in unprecedented proximity to the calving front. The glacier calved by a process of buoyancy-force-induced crevassing in which the ice downglacier of flexion zones rotates upward because it is out of buoyant equilibrium. Calving then occurs back to the flexion zone. This calving process provides a compelling and complete explanation for the data. Tracking of oblique camera images allows identification and characterisation of the flexion zones and their propagation downglacier. Interpretation of the GPS data and camera data in combination allows us to place constraints on the height of the basal cavity that forms beneath the rotating ice downglacier of the flexion zone before calving. The flexion zones are probably formed by the exploitation of basal crevasses, and theoretical considerations suggest that their propagation is strongly enhanced when the glacier base is deeper than buoyant equilibrium. Thus, this calving mechanism is likely to dominate whenever such geometry occurs and is of increasing importance in Greenland.

Estimating zenith tropospheric delays from BeiDou navigation satellite system observations

The GNSS derived Zenith Tropospheric Delay (ZTD) plays today a very critical role in meteorological study and weather forecasts, as ZTDs of thousands of GNSS stations are operationally assimilated into numerical weather prediction models. Recently, the Chinese BeiDou Navigation Satellite System (BDS) was officially announced to provide operational services around China and its neighborhood and it was demonstrated to be very promising for precise navigation and positioning. In this contribution, we concentrate on estimating ZTD using BDS observations to assess its capacity for troposphere remote sensing. A local network which is about 250 km from Beijing and comprised of six stations equipped with GPS- and BDS-capable receivers is utilized. Data from 5 to 8 November 2012 collected on the network is processed in network mode using precise orbits and in Precise Point Positioning mode using precise orbits and clocks. The precise orbits and clocks are generated from a tracking network with most of the stations in China and several stations around the world. The derived ZTDs are compared with that estimated from GPS data using the final products of the International GNSS Service (IGS). The comparison shows that the bias and the standard deviation of the ZTD differences are about 2 mm and 5 mm, respectively, which are very close to the differences of GPS ZTD estimated using different software packages.

Long-term comparisons between two-way satellite and geodetic time transfer systems

Global Positioning System (GPS) observations recorded in the United States and Europe were used to evaluate time transfer capabilities of GETT (geodetic time transfer). Timing estimates were compared with two-way satellite time and frequency transfer (TWSTFT) systems. A comparison of calibrated links at the U.S. Naval Observatory, Washington, D.C., and Colorado Springs, CO, yielded agreement of 2.17 ns over 6 months with a standard deviation of 0.73 ns. An uncalibrated link between the National Institute of Standards and Technology (NIST) and Physikalisch-Technische Bundesanstalt, Braunschweig, Germany, has a standard deviation of 0.79 ns over the same time period.

Carrier-phase time transfer

We have conducted several time-transfer experiments using the phase of the GPS carrier rather than the code, as is done in current GPS-based time-transfer systems. Atomic clocks were connected to geodetic GPS receivers; we then used the GPS carrier-phase observations to estimate relative clock behavior at 6-minute intervals. GPS carrier-phase time transfer is more than an order of magnitude more precise than GPS common view time transfer and agrees, within the experimental uncertainty, with two-way satellite time-transfer measurements for a 2400 km baseline. GPS carrier-phase time transfer has a stability of 100 ps, which translates into a frequency uncertainty of about two parts in 10(-15) for an average time of 1 day.