The Improvement of Time-step method for Ionospheric Delay gradient Estimation

Abstract. We used eight co-located global navigation satellite system (GNSS) stations with different antenna mounts to estimate atmospheric signal propagation delays in the zenith direction and linear horizontal gradients. The gradients are compared with the results from a water vapour radiometer (WVR). The water drops in the atmosphere have a negative influence on the retrieval accuracy of the WVR. Hence, we see better agreement using WVR data with a liquid water content (LWC) less than 0.05 mm compared to when LWC values of up to 0.7 mm are included. We used two different constraints when estimating the linear gradients from the GNSS data. Using a weak constraint enhances the GNSS estimates to track large gradients of short duration at the cost of increased formal errors. To mitigate random noise in the GNSS gradients, we adopted a fusion approach, averaging estimates from the GNSS stations. This resulted in significant improvements for the agreement with the WVR data, a maximum of 17 % increase in the correlation, and a 14 % reduction in the root mean square (RMS) difference for the east gradients. The corresponding values for the north gradients are both 25 %. Overall, no large differences in terms of quality are observed for the eight GNSS stations. However, one station shows slightly poorer agreement for the north gradients compared to the others. This is attributed to the station's proximity to a radio telescope, which causes data loss of observations at low-elevation angles in the south-south-west direction.

Permanent Global Navigation Satellite Systems (GNSS) stations that are operating within the African Geodetic Reference Frame (AFREF) are contributing data to the datum realizations at global, regional and local levels. The infrastructure supports development and administrative functions of African governments, the public and investors throughout the African continent. However, African stations with high quality and continuous data that have been acquired over several decades are limited, which result in a non-uniform network. This means that additional station investment are required in Africa for new stations to contribute to the AFREF project. An assessment of the spatial distribution and densification of GNSS stations that contribute to AFREF ensure future geometrical improvements in the network have the most impact. Established GNSS stations within AFREF network contribute data for the realization of the International Terrestrial Reference Frame (ITRF), International GNSS Service (IGS) products and local AFREF solutions.

CORS station for synergistic monitoring of multivariate surface parameters in expansive soils

Hydrogeodesy is an applied scientific field that uses precise geodetic observations to measure or infer hydrological quantities and their changes over time. Recently, modern geodesy supplies hydrology with a very powerful tools based on the Earth’s artificial satellites, notably GRACE (Gravity Recovery and Climate Experiment) and GNSS (Global Navigation Satellite System). The long-term changes of periods higher than 1 year present in the time series of GNSS station displacements may be due to real geophysical effects, but may also be coupled to effects resulting from the superposition of GNSS systematic errors as well as numerical artefacts. As a result, it is often difficult to use the aforementioned changes to study, for example, long-term changes in the hydrosphere for specific GNSS station locations. Consequently, it is impossible to exploit the main advantage of GNSS over other measurement techniques, in the sense of dense spatial distribution in some parts of the world. In this study, we use wavelet analysis to determine long-term changes from GNSS station displacement time series and displacement time series determined from GRACE data and data from GRACE-assimilating high-resolution hydrological model GLWS v2.0 (Global Land Water Storage) provided by the University of Bonn. Global GNSS time series set was processed by the International GNSS Service (IGS) in the form of the latest reprocessing repro3.We correct the GNSS displacement time series for non-hydrospheric effects, such as non-tidal atmospheric effect, non-tidal oceanic effect, draconic period, post-glacial rebound and ground thermal expansion effects. We use a range of statistical analyses, such as correlation coefficient analysis and dynamic time warping (DTW) distance to assess the similarity of long-term changes between the three data sets. On this basis, we identify GNSS stations for which long-term changes can be analyzed in terms of changes in the terrestrial hydrosphere and those for which the long-term nature of the series is not due to changes in the hydrosphere, but to other effects.

Tropospheric delay accounts for one source of error in global navigation satellite systems (GNSS). To better characterize the tropospheric delays in the temporal and spatial domain and facilitate the safety-critical use of GNSS across China, a method is proposed to generate a grid-based tropospheric product (GTP) using the GNSS network with an empirical tropospheric model, known as IGGtrop. The prototype system generates the GTPs in post-processing and real-time modes and is based on the undifferenced and uncombined precise point positioning (UU-PPP) technique. GTPs are constructed for a grid form ( $$2.0{^{\circ }}\times 2.5{^{\circ }}$$ latitude–longitude) over China with a time resolution of 5 min. The real-time GTP messages are encoded in a self-defined RTCM3 format and broadcast to users using NTRIP (networked transport of RTCM via internet protocol), which enables efficient and safe transmission to real-time users. Our approach for GTP generation consists of three sequential steps. In the first step, GNSS-derived zenith tropospheric delays (ZTDs) for a network of GNSS stations are estimated using UU-PPP. In the second step, vertical adjustments for the GNSS-derived ZTDs are applied to address the height differences between the GNSS stations and grid points. The ZTD height corrections are provided by the IGGtrop model. Finally, an inverse distance weighting method is used to interpolate the GNSS-derived ZTDs from the surrounding GNSS stations to the location of the grid point. A total of 210 global positioning system (GPS) stations from the crustal movement observation network of China are used to generate the GTPs in both post-processing and real-time modes. The accuracies of the GTPs are assessed against with ERA-Interim-derived ZTDs and the GPS-derived ZTDs at 12 test GPS stations, respectively. The results show that the post-processing and real-time GTPs can provide the ZTDs with accuracies of 1.4 and 1.8 cm, respectively. We also apply the GTPs in real-time kinematic GPS PPP, and the results show that the convergence time of the PPP solutions is shortened. These results confirm that the GTPs can act as an efficient information source to augment GNSS positioning over China.

Global Navigation Satellite Systems (GNSSs) offer all-weather and real-time capabilities, enabling the real-time monitoring of precipitable water vapor (PWV). Traditional methods for obtaining high-precision GNSS PWV require meteorological parameters such as pressure and the atmospheric weighted mean temperature, which are inconvenient to obtain at GNSS stations, especially in real-time PWV monitoring. To address these challenges, a deep neural network (DNN)-based model, namely, D-PWV, has been established to directly convert zenith total delay (ZTD) derived from GNSS signals into PWV without relying on meteorological parameters. The performance of the D-PWV model is comprehensively assessed using GNSS PWV, the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5), radiosonde (RS), and data from the 2018 typhoon event Mangkhut in the Guangxi region of China. The results reveal that the D-PWV model exhibits a bias of −0.25, 0.09, and 0.28 mm when compared to GNSS PWV, RS PWV, and ERA5 PWV, respectively. The corresponding RMSE values are 2.00, 3.37, and 2.74 mm. Notably, when compared to the backpropagation neural network (BP), the D-PWV model demonstrates a smaller range of variation in both bias and RMSE across the study area and shows greater stability in the latitudinal direction. Besides, the D-PWV model performs stably during Typhoon Mangkhut, with a correlation coefficient of 0.96 with the RS PWV, and the changes on GNSS stations are also highly consistent with the ERA5 PWV, effectively reflecting the PWV variations in the Guangxi region during the typhoon. It shows that the model constructed in this article can provide real-time PWV values in the absence of measured meteorological parameters.

When compared to the wide range of atmospheric sensing techniques, global navigation satellite system (GNSS) offers the advantage of operating under all weather conditions, is continuous, with high temporal and spatial resolution and high accuracy, and has long-term stability. The utilisation of GNSS ground networks of continuous stations for operational weather and climate services is already in place in many nations in Europe, Asia, and America under different initiatives and organisations. In Africa, the situation appears to be different. The focus of this paper is to assess the conditions of the existing and anticipated GNSS reference network in the African region for meteorological applications. The technical issues related to the implementation of near-real-time (NRT) GNSS meteorology are also discussed, including the data and network requirements for meteorological and climate applications. We conclude from this study that the African GNSS network is sparse in the north and central regions of the continent, with a dense network in the south and fairly dense network in the west and east regions of the continent. Most stations lack collocated meteorological sensors and other geodetic observing systems as called for by the GCOS Reference Upper Air Network (GRUAN) GNSS Precipitable Water Task Team and the World Meteorological Organization (WMO). Preliminary results of calculated zenith tropospheric delay (ZTD) from the African GNSS indicate spatial variability and diurnal dependence of ZTD. To improve the density and geometry of the existing network, countries are urged to contribute more stations to the African Geodetic Reference Frame (AFREF) program and a collaborative scheme between different organisations maintaining different GNSS stations on the continent is recommended. The benefit of using spaced based GNSS radio occultation (RO) data for atmospheric sounding is highlighted and filling of geographical gaps from the station-based observation network with GNSS RO is also proposed.

The Global Navigation Satellite System (GNSS) plays an important role in retrieving high temporal–spatial resolution precipitable water vapor (PWV) and its applications. The weighted mean temperature (Tm) is a key parameter for the GNSS PWV estimation, which acts as the conversion factor from the zenith wet delay (ZWD) to the PWV. The Tm is determined by the air pressure and water vapor pressure, while it is not available nearby most GNSS stations. The empirical formular is often applied for the GNSS station surface temperature (Ts) but has a lower accuracy. In this paper, the temporal and spatial distribution characteristics of the coefficients of the linear Tm-Ts model are analyzed, and then a piecewise-linear Tm-Ts relationship is established for each GPS station using radiosonde data collected from 2011 to 2019. The Tm accuracy was increased by more than 10% and 20% for 86 and 52 radiosonde stations, respectively. The PWV time series at 377 GNSS stations from the infrastructure construction of national geodetic datum modernization and Crustal Movement Observation Network of China (CMONC) were further obtained from the GPS observations and meteorological data from 2011 to 2019. The PWV accuracy was improved when compared with the Bevis model. Furthermore, the daily and monthly average values, long-term trend, and its change characteristics of the PWV were analyzed using the high-precision inversion model. The results showed that the averaged PWV was higher in Central-Eastern China and Southern China and lower in Northwest China, Northeast China, and North China. The PWV is increasing in most parts of China, while the some PWVs in North China show a downward trend.

Daily displacement time series from Global Navigation Satellite Systems (GNSS) are frequently used to study deformations of the Earth’s surface due to a wide range of different geophysical processes. The recorded deformations result from tectonic activity or non-tectonic processes like volcanism, groundwater fluctuations and atmospheric loading. In addition, local disturbances of the antenna (e.g., snow cover, thermoelastic effects of the monumentation) and artifacts from GNSS processing (e.g., draconitic signals) are sometimes prominently included in coordinate time series. We use a Temporal Convolution Network (TCN) to predict non-tectonic vertical GNSS displacements on a global scale from physics-based non-tidal loading products. We train our model on a global dataset with more than 11,000 GNSS stations from the Nevada Geodetic Laboratory, active from January 2002 until June 2024, and evaluate the performance against independent estimations. Across the hold-out dataset, our TCN derives non-tidal loading GNSS signatures that when compared to the non-tectonic GNSS signal results in a global average reduction in RMSE of 4.7 % with respect to the numerical non-tidal loading models. This approach presents an initial step towards a data-driven complement to physics-based numerical loading models, improving the isolation of non-tectonic signals in GNSS time series and validation of numerical non-tidal loading models.Graphical Supplementary InformationThe online version contains supplementary material available at 10.1186/s40623-026-02385-z.

We compute the vertical displacements in the Amazon Basin using the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) observations, including both the gravity spherical harmonic (SH) solutions from the Center for Space Research (CSR), GeoForschungsZentrum (GFZ) and Jet Propulsion Laboratory (JPL) and mascons from CSR, JPL and Goddard Space Flight Center (GSFC). The correlation coefficients, annual amplitude and root mean squares (RMS) reductions are calculated to assess the agreements between the GRACE/GRACE-FO and Global Navigation Satellite System (GNSS) vertical displacements at 22 selected GNSS stations. For the six GRACE/GRACE-FO products (i.e., CSR SH, GFZ SH, JPL SH, CSR mascon, GSFC mascon and JPL mascon), the mean annual amplitude reductions are 77.6%, 76.4%, 76.3%, 78.6%, 78.5% and 76.6%, respectively, the corresponding mean RMS reductions are 63.2%, 61.7%, 62.3%, 64.9%, 65.3% and 63.8%, respectively, and the mean correlation coefficients are all over 0.93. On the whole, mascon solutions agree slightly better with GNSS solutions than SH solutions do. The CSR SH and the GSFC mascon solutions show the best agreements with the GNSS solution among the 3 SH and 3 mascon products, respectively. We estimate GRACE/GRACE-FO noises using the three-cornered hat (TCH) method and find that the CSR SH and GSFC mascons also have the smallest noise variances among the SH and mascon products, respectively. By analyzing the GNSS stations from the central and southern Amazon Basin, we find that: (1) the RMS reductions when the mascon solutions are removed from GNSS height series are slightly larger than those using the SH solutions in the center, while in south all the RMS reductions are fairly close; (2) for both SH solutions and mascon solutions, the correlation coefficients in the center are slightly larger than those in the south, but conversely, the mean annual amplitude reductions in the center are much smaller than those in the south.

Tropical cyclones (TCs) are intense rotating storm systems, characterized by strong winds, heavy humidity and storm surges, and usually cause an abnormal increase in regional water vapor during the period of their occurrence. Global navigation satellite system (GNSS) is well-established and initially mainly for positioning, navigation and timing. However, due to their global coverage and 24/7 operability under all weather conditions, GNSS has been widely used in meteorology such as the retrieval of precipitable water vapor (PWV). Since PWV time series obtained from a regional ground GNSS tracking stations network has high temporal and spatial resolutions, in this research, the temporal and spatial variation trends of regional PWVs during several TCs’ periods in Hong Kong were investigated, and a new method using high-resolution GNSS-PWV time series to estimate a TC’s movement was proposed. Test data were from 15 GNSS tracking stations equipped with meteorological sensors, and three GNSS stations without meteorological sensors but using meteorological data interpolated from ERA5 (fifth-generation reanalysis dataset of the European Centre for Medium-range Weather Forecasting) dataset, and six TC events occurred in 2017 were selected for cases studies. Moreover, for a better accuracy of GNSS-PWV, which is converted from the zenith wet delay of the GNSS signal multiplying a conversion factor that uses a weighted mean temperature ( $T_{m}$ ), a seasonal multi-factor $T_{m}$ model was established and tested. Results showed that the new $T_{m}$ model outperformed the previous regional $T_{m}$ model used in Hong Kong. In addition, based on the temporal variation trend and spatial distribution of the regional PWV, one can determine if a TC approaches the region. A geometric approach to estimating a TC’s movement was developed and its test results agreed well with the truth. These results suggest the potential of using GNSS signals to monitor the movements of TCs for short-time TC forecasting due to their high temporal resolution.

SUMMARY On 2023 February 6, a devastating earthquake doublet struck in Türkiye, which caused tremendous damage including about 54 000 fatalities. We use high-rate global navigation satellite system (GNSS) data to study the coseismic static and kinematic displacement, and invert for fault slip distribution of the earthquake doublet. The maximum static coseismic displacements for the Mw7.8 (EQ1) and Mw7.5 earthquake (EQ2) are 0.38 and 4.4 m, respectively. The kinematic displacement recorded by GNSS stations reflect clearly the earthquake rupture process in more detail. We utilize 1-Hz GNSS waveforms, GNSS static displacements and surface rupture measurements to invert for the kinematic rupture model of the earthquake doublet. Our results show a rupture duration of ∼80 s, faulting length ∼350 km and maximum slip ∼7.4 m for EQ1, and a rupture duration of ∼35 s, rupture length ∼190 km and maximum slip ∼9.2 m for EQ2. The slip distributions inverted solely from GNSS coseismic deformation are basically consistent with the results from multisource data. The rupture velocity of EQ1 towards east is about 4.5 km s−1 towards the east and 3.2 km s−1 towards the west. EQ2 nucleates on Çardak fault with bilateral supershear rupture velocity of 5.0∼5.5 km s−1 within the first 0–12 s, subsequently transitioning to subshear rupture at a speed of 1.2 km s−1 towards the east and 3.0 km s−1 towards the west. Our finding of the bilateral supershear ruptures of EQ2 contrasts with the results of unilateral westward supershear rupture of previous studies. We think that this discrepancy could be attributed to the utilization of more geodetic data of the relatively denser GNSS stations in the east flank of EQ2’s epicentre and calculating the mean velocities for individual rupture intervals in this study.

<p>A devastating earthquake (Mw 6.2) occurred on December 29, 2020,  near the town of Petrinja, in Croatia, a few kilometers north of the Bosnian border with Croatia. The earthquake affected Bosnia and Herzegovina as well, and many buildings in northwestern Bosnia and Herzegovina were severely damaged. The main earthquake impact was preceded by two strong for-shocks, which shows a great resemblance to the Banja Luka earthquake of 1969. Seismic activity at the end of December 2020 and January 2021 was manifested through the occurrence of a large number of seismic events, namely: one earthquake of magnitude 6.2, two earthquakes of magnitude between 5.0 and 6.0, twenty-two earthquakes of magnitude between 4.0 and 5.0, sixty-six earthquakes of magnitude 3.0 and 4.0 and two hundred and seventy-seven earthquakes of magnitude between 2.0 and 3.0. This earthquake is a consequence of the movement of the Adriatic microplate and its interaction with the Eurasian tectonic plate. Its movement results in the creation of current seismicity in Croatia, Bosnia and Herzegovina, Italy, Montenegro, Serbia, Slovenia.</p><p>Today, analysis of the deformations of the Earth's crust plays an important role in research related to the entire seismic cycle. The phases of seismic cycles can be reliably estimated using time series of daily coordinates from continuously operating stations of the Global Navigation Satellite System (GNSS).</p><p>In this study, we used five time-series GNSS positions (Sarajevo, Poreč, Ljubljana, Požega, and Zadar), daily resolutions (24 hours) in the IGS14 reference frame, taken from Nevada Geodetic Laboratory through the website. We determined the coseismic displacement field of the Mw 6.2 Petrinja mainshock using downloaded the GNSS time-series as well as coseismic displacement field for all earthquakes of magnitude over 4. We processed data for the GNSS time series for the period from January 2016 to December 2020. GNSS stations are located at distances ~100 km to the ~250 km distances the epicenter of the Petrinja earthquake, of which the Poreč station is the closest. JavaScript Object Notation (JSON) text format was used for processing all earthquakes in our study. JSON offset file is created based on the data downloaded from USGS (U.S. Geological Survey).</p><p>This paper, apply interactive processing in tectonics and seismology, presented offset in time series as a consequence of earthquakes. We have concluded that the cumulative movement of the Earth's crust is not only a consequence of large earthquakes but also the cause of many smaller accumulated movements caused by smaller earthquakes. The paper presents the contribution in the field of application of satellite positioning methods in geodynamic research and defines an approach that enables objective quantification of deformations of the Earth's crust in cases of seismic events. The earthquake occurred in a fault that extends approximately in the northwest-southeast direction and passes through Pokuplje near Petrinja and Glina. This fault is the boundary between two very different tectonic blocks, the Dinarides and the Pannonian Basin. Therefore, it can be said that the different stresses and displacements in these blocks are compensated through these blocks.</p>

We study vertical ground displacement time series from Global Navigation Satellite System (GNSS) stations to measure deformation associated with hydrological drought in the Po river basin. Focusing on interannual trend changes, rather than seasonal (annual) components, we found a clear spatially correlated deformation signal that is temporally (anti)correlated with changes in the Po river level and the SPEI‐12 drought index, with stations moving upward during periods of river/index level decrease and vice versa. In the 2021–2022 time span, which culminated in the most severe drought of the last two centuries, we estimate the amount and spatial distribution of water loss in the basin and its surroundings. Excluding the seasonal signals, between January 2021 and August 2022, the GNSS stations underwent uplift, up to 7 mm, which corresponds to ∼70 Gtons of water loss. Compared to Global Land Data Assimilation System and Gravity Recovery and Climate Experiment estimates, GNSS results show a similar temporal evolution of water content but a more heterogeneous distribution of values. We show that continuous GNSS networks provide an effective way to monitor multiannual trend changes in water storage even in small water basins and serve as a reliable indicator of drought severity.

Analysis of precipitable water vapour characteristics from GNSS measurements during the snow season in Liaoning Province, China