GPT2: Empirical slant delay model for radio space geodetic techniques

A Knowledge-Grounded Task-Oriented Dialogue System with Hierarchical Structure for Enhancing Knowledge Selection

For a task-oriented dialogue system to provide appropriate answers to and services for users' questions, it is necessary for it to be able to utilize knowledge related to the topic of the conversation. Therefore, the system should be able to select the most appropriate knowledge snippet from the knowledge base, where external unstructured knowledge is used to respond to user requests that cannot be solved by the internal knowledge addressed by the database or application programming interface. Therefore, this paper constructs a three-step knowledge-grounded task-oriented dialogue system with knowledge-seeking-turn detection, knowledge selection, and knowledge-grounded generation. In particular, we propose a hierarchical structure of domain-classification, entity-extraction, and snippet-ranking tasks by subdividing the knowledge selection step. Each task is performed through the pre-trained language model with advanced techniques to finally determine the knowledge snippet to be used to generate a response. Furthermore, the domain and entity information obtained because of the previous task is used as knowledge to reduce the search range of candidates, thereby improving the performance and efficiency of knowledge selection and proving it through experiments.

Cross-validated multi-technique geodetic dataset of the Upper Adriatic Sea coastal area of Italy

The geodetic dataset used in the research article entitled “Multi-technique geodetic detection of onshore and offshore subsidence along the Upper Adriatic Sea coasts”[1] is presented here. It consists of the outcomes of three different techniques, i.e. Synthetic Aperture Radar Interferometry (InSAR), Global Navigation Satellite System (GNSS) and topographic Levelling surveys. This dataset has been used for the estimation of onshore and offshore deformation in a mineral concession area located along the Upper Adriatic Sea coastal area (Italy), South-East of Ravenna city. InSAR data covers the period from 2002 to 2018, GNSS data from 1998 to 2018 and levelling data from 2002 to 2017.The different measurements have been cross-validated and referred to a common local reference system fixed in the urban area of Ravenna. This data collection will be very useful for deepening the analysis of any type of deformation in the Ravenna coastal area.

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.

Comprehensive Analysis and Validation of the Atmospheric Weighted Mean Temperature Models in China

Atmospheric weighted mean temperature (Tm) is a key parameter used by the Global Navigation Satellite System (GNSS) for calculating precipitable water vapor (PWV). Some empirical Tm models using meteorological or non-meteorological parameters have been proposed to calculate PWV, but their accuracy and reliability cannot be guaranteed in some regions. To validate and determine the optimal Tm model for PWV retrieval in China, this paper analyzes and evaluates some typical Tm models, namely, the Linear, Global Pressure and Temperature 3 (GPT3), the Tm model for China (CTm), the Global Weighted Mean Temperature-H (GTm-H) and the Global Tropospheric (GTrop) models. The Tm values of these models are first obtained at corresponding radiosonde (RS) stations in China over the period of 2011 to 2020. The corresponding Tm values of 87 RS stations in China are also calculated using the layered meteorological data and regarded as the reference. Comparison results show that the accuracy of these five Tm models in China has an obvious geographical distribution and decreases along with increasing altitude and latitude, respectively. The average root mean square (RMS) and Bias for the Linear, GPT3, CTm, GTm-H and GTrop models are 4.2/3.7/3.4/3.6/3.3 K and 0.7/−1.0/0.7/−0.1/0.3 K, respectively. Among these models, Linear and GPT3 models have lower accuracy in high-altitude regions, whereas CTm, GTm-H and GTrop models show better accuracy and stability throughout the whole China. These models generally have higher accuracy in regions with low latitude and lower accuracy in regions with middle and high latitudes. In addition, Linear and GPT3 models have poor accuracy in general, whereas GTm-H and CTm models are obviously less accurate and stable than GTrop model in regions with high latitude. These models show different accuracies across the four geographical regions of China, with GTrop model demonstrating the relatively better accuracy and stability. Therefore, the GTrop model is recommended to obtain Tm for calculating PWV in China.

Transformer-Based Global Zenith Tropospheric Delay Forecasting Model

Zenith tropospheric delay (ZTD) plays an important role in high-precision global navigation satellite system (GNSS) positioning and meteorology. At present, commonly used ZTD forecasting models comprise empirical, meteorological parameter, and neural network models. The empirical model can only fit approximate periodic variations, and its accuracy is relatively low. The accuracy of the meteorological parameter model depends heavily on the accuracy of the meteorological parameters. The recurrent neural network (RNN) is suitable for short-term series data prediction, but for long-term series, the ZTD prediction accuracy is clearly reduced. Long short-term memory (LSTM) has superior forecasting accuracy for long-term ZTD series; however, the LSTM model is complex, cannot be parallelized, and is time-consuming. In this study, we propose a novel ZTD time-series forecasting utilizing transformer-based machine-learning methods that are popular in natural language processing (NLP) and forecasting global ZTD, the training parameters provided by the global geodetic observing system (GGOS). The proposed transformer model leverages self-attention mechanisms by encoder and decoder modules to learn complex patterns and dynamics from long ZTD time series. The numeric results showed that the root mean square error (RMSE) of the forecasting ZTD results were 1.8 cm and mean bias, STD, MAE, and R 0.0, 1.7, 1.3, and 0.95, respectively, which is superior to that of the LSTM, RNN, convolutional neural network (CNN), and GPT3 series models. We investigated the global distribution of these accuracy indicators, and the results demonstrated that the accuracy in continents was superior to maritime space transformer ZTD forecasting model accuracy at high latitudes superior to that at low latitude. In addition to the overall accuracy improvement, the proposed transformer ZTD forecast model also mitigates the accuracy variations in space and time, thereby guaranteeing high accuracy globally. This study provides a novel method to estimate the ZTD, which could potentially contribute to precise GNSS positioning and meteorology.

Cascading rupture of a megathrust

Understanding variability in the size and location of large earthquakes along subduction margins is crucial for evaluating seismic and tsunami hazards. We present a coseismic slip model for the 2021 M8.2 Chignik earthquake and investigate the relationship of this earthquake to previous major events in the Alaska Peninsula region and to interseismic coupling. Stress changes from the 2020 M7.8 Simeonof event triggered the Chignik event, and together, the earthquakes partially filled an unruptured section along a 3000-km subduction margin that has experienced a series of ruptures along almost its entire length over the past century. Variations in coupling and structural characteristics may make the region more prone to nucleating M7 to M8 events rather than larger M > 8.5 earthquakes. Stress changes and rupture areas suggest that the two recent earthquakes may be part of an 80-year-long rupture cascade and may have advanced seismic hazard in the region.

Forecasting GNSS Zenith Troposphere Delay by Improving GPT3 Model with Machine Learning in Antarctica

Antarctica has a significant impact on global climate change. However, to draw climate change scenarios, there is a need for meteorological data, such as water vapor content, which is scarce in Antarctica. Global navigation satellite system (GNSS) networks can play a major role in overcoming this problem as the tropospheric delay that can be derived from GNSS measurements is an important data source for monitoring the variation of water vapor content. This work intends to be a contribution for improving the estimation of the zenith tropospheric delay (ZTD) obtained with the latest global pressure–temperature (GPT3) model for Antarctica through the use of long short-term-memory (LSTM) and radial basis function (RBF) neural networks for modifying GPT3_ZTD. The forecasting ZTD model is established based on the GNSS_ZTD observations at 71 GNSS stations from 1 January 2018 to 23 October 2021. According to the autocorrelation of the bias series between GNSS_ZTD and GPT3_ZTD, we predict the LSTM_ZTD for each GNSS station for period from October 2020 to October 2021 using the LSTM day by day. Based on the bias between LSTM_ZTD and GPT3_ZTD of the training stations, the RBF is adopted to estimate the LSTM_RBF_ZTD of the verified station, where the LSTM_ZTD represents the temporal forecasting ZTD at a single station, and the LSTM_RBF_ZTD represents the predicted ZTD obtained from space. Both the daily and yearly RMSE are calculated against the reference (GNSS_ZTD), and the improvement of predicted ZTD is compared with GPT3_ZTD. The results show that the single-station LSTM_ZTD series has a good agreement with the GNSS_ZTD, and most daily RMSE values are within 20 mm. The yearly RMSE of the 65 stations ranges from 6.4 mm to 32.8 mm, with an average of 10.9 mm. The overall accuracy of the LSTM_RBF_ZTD is significantly better than that of the GPT3_ZTD, with the daily RMSE of LSTM_RBF_ZTD significantly less than 30 mm, and the yearly RMSE ranging from 5.6 mm to 50.1 mm for the 65 stations. The average yearly RMSE is 15.7 mm, which is 10.2 mm less than that of the GPT3_ZTD. The LSTM_RBF_ZTD of 62 stations is more accurate than GPT3_ZTD, with the maximum improvement reaching 76.3%. The accuracy of LSTM_RBF_ZTD is slightly inferior to GPT3_ZTD at three stations located in East Antarctica with few GNSS stations. The average improvement across the 65 stations is 39.6%.

Evaluation of Network RTK Positioning Performance Based on BDS-3 New Signal System

The BeiDou navigation satellite system (BDS-3) has been deployed and provides positioning, navigation, and timing (PNT) services for users all over the world. On the basis of BDS-2 system signals, BDS-3 adds B1C, B2a, B2b, and other signals to realize compatibility and interoperability with other global navigation satellite systems (GNSS). Network real-time kinematic (RTK) technology is an important real-time regional high-precision GNSS positioning technology. Combined with the network RTK high-precision service platform software developed by the author’s research group and the measured data of a provincial continuously operating reference station (CORS) in Hubei, this paper preliminarily evaluates the network RTK service performance under the new signal system of BDS-3. The results show that single BDS-3 adopts the new signal combination (B1C+B2a) and transition signal combination (B1I+B3I) when providing virtual reference station (VRS) services, the RTK fixation rate of the terminal is above 95%, and the horizontal and elevation accuracies are within 1cm and 2 cm, respectively, which meets the requirements of providing high-precision network RTK services by a single BDS-3 system. In addition, the positioning accuracy of BDS-2 is relatively poor, while the accuracy of BDS-3 is better than global positioning systems (GPS) and BDS-2. The combined processing effect of the B1I+B3I transition signal of BDS-2/3 is optimal, the accuracy of E and N directions is better than 0.5 cm, and the accuracy of U direction is better than 1.5 cm. It can be seen from the atmosphere correction accuracy, regional error modeling accuracy, and network RTK terminal positioning accuracy that the service effect of the B1C+B2a combination is slightly better than that of the B1I+B3I combination. When a single BDS-3 constellation provides network RTK services, it is recommended to use the B1C+B2a combination as the main frequency solution, and when the BDS-2/3 constellation provides service, it is recommended to use the B1I+B3I combination as the main frequency solution.

Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models

Thanks to the increasing number of permanent GNSS stations in Europe and their long records, we computed position solutions for more than 1000 stations over the last two decades using the REPRO3 orbit and clock products from the IGS CNES-CLS (GRGS) Analysis Center. The velocities, which are mainly due to tectonics and glacial isostatic adjustment (GIA), and the annual solar cycle have been estimated using weighted least squares. The interannual variations have been accounted for in the stochastic model or in the deterministic model. We demonstrated that the velocity and annual cycle, in addition to their uncertainties, depend on the estimation method we used and that the estimation of GPS draconitic oscillations minimises biases in the estimation of annual solar cycle displacements. The annual solar cycle extracted from GPS has been compared with that from loading estimates of several hydrological models. If the annual amplitudes between GPS and hydrological models match, the phases of the loading models were typically in advance of about 1 month compared to GPS. Predictions of displacements modelled from GRACE observations did not show this phase shift. We also found important discrepancies at the interannual frequency band between GNSS, loading estimates derived from GRACE, and hydrological models using principal component analysis (PCA) decomposition. These discrepancies revealed that GNSS position variations in the interannual band cannot be systematically interpreted as a geophysical signal and should instead be interpreted in terms of autocorrelated noise.

A Weighted Mean Temperature Model with Nonlinear Elevation Correction Using China as an Example

The weighted mean temperature (Tm) is a crucial parameter for determining the tropospheric delay in transforming precipitable water vapor. We used the reanalysis data provided by European Centre for Medium-Range Weather Forecasts (ECMWF) to analyze the distribution characteristics of Tm in the vertical direction in China. To address the problem that the precision of the traditional linear function model is limited in fitting the Tm profile, a scheme using the linear and Fourier functions to fit the Tm profile was constructed. Based on the least squares principle (LSQ) to fit the change in its coefficients over time, a Tm model for China with nonlinear elevation correction (CTm-h) was constructed. The experimental results show that, using ECMWF and radiosonde data to evaluate the precision of the CTm-h model, the RMS is 3.43 K and 4.64 K, respectively. Compared to GPT2w, the precision of the CTm-h model in China is increased by about 26.8%. The CTm-h model provides a significant improvement in the correction effect of Tm in the vertical direction, and the Tm profile calculated by the model is closer to the reference value.

A New Approach for the Development of Grid Models Calculating Tropospheric Key Parameters over China

Pressure, water vapor pressure, temperature, and weighted mean temperature (Tm) are tropospheric parameters that play an important role in high-precision global navigation satellite system navigation (GNSS). As accurate tropospheric parameters are obligatory in GNSS navigation and GNSS water vapor detection, high-precision modeling of tropospheric parameters has gained widespread attention in recent years. A new approach is introduced to develop an empirical tropospheric delay model named the China Tropospheric (CTrop) model, providing meteorological parameters based on the sliding window algorithm. The radiosonde data in 2017 are treated as reference values to validate the performance of the CTrop model, which is compared to the canonical Global Pressure and Temperature 3 (GPT3) model. The accuracy of the CTrop model in regards to pressure, water vapor pressure, temperature, and weighted mean temperature are 5.51 hPa, 2.60 hPa, 3.09 K, and 3.35 K, respectively, achieving an improvement of 6%, 9%, 10%, and 13%, respectively, when compared to the GPT3 model. Moreover, three different resolutions of the CTrop model based on the sliding window algorithm are also developed to reduce the amount of gridded data provided to the users, as well as to speed up the troposphere delay computation process, for which users can access model parameters of different resolutions for their requirements. With better accuracy of estimating the tropospheric parameters than that of the GPT3 model, the CTrop model is recommended to improve the performance of GNSS positioning and navigation.

Post-Seismic Deformation Related to the 2016 Central Italy Seismic Sequence From GPS Displacement Time-Series

The 2016-2017 Central Italy earthquake sequence struck the central Apennines between August 2016 and October 2016 with Mw ∈ [5.9; 6.5], plus four earthquakes occurring in January 2017 with Mw ∈ [5.0; 5.5]. We study Global Positioning System time series including near- and far-field domains. We use a variational Bayesian independent component analysis technique to separate the post-seismic deformation from signals caused by variation of the water content in aquifers at hundreds of meters of depth and of the soil moisture. For each independent component, realistic uncertainties and a plausible physical explanation are provided. We focus on the study of afterslip on the main structures surrounding the mainshock, highlighting the role played by faults that were not activated during the co-seismic phase in accommodating the post-seismic deformation. We report aseismic deformation occurring on the Paganica fault, which hosted the Mw 6.1 2009 L'Aquila earthquake, suggesting that static stress transfer and aseismic slip influence the recurrence time of nearby (∼50 km further south of the mainshocks) segments. A ∼2-3 km thick subhorizontal shear-zone, clearly illuminated by seismicity, which bounds at depth the west-dipping normal faults where the mainshocks nucleated, also shows aseismic slip. Since afterslip alone underestimates the displacement in the far-field domain, we consider the possibility that the shear zone marks the brittle-ductile transition, assuming the viscoelastic relaxation of the lower crust as a mechanism contributing to the post-seismic displacement. Our results suggest that multiple deformation processes are active in the first 2 years after the mainshocks.

A Regional Model for Predicting Tropospheric Delay and Weighted Mean Temperature in China Based on GRAPES_MESO Forecasting Products

Accurate tropospheric delay (TD) and weighted mean temperature (Tm) are important for Global Navigation Satellite System (GNSS) positioning and GNSS meteorology. For this purpose, plenty of empirical models have been built to provide estimates of TD and Tm. However, these models cannot resolve TD and Tm variations at synoptic timescales since they only model the average annual, semi-annual, and/or daily variations. As a result, the existed empirical models cannot perform well under extreme weather conditions. To address this limitation, we propose to estimate Zenith Hydrostatic Delay (ZHD), Zenith Wet Delay (ZWD), and Tm directly from the stratified numerical weather forecasting products of the mesoscale version of the Global/Regional Assimilation and PrEdiction System (GRAPES_MESO) of China. The GRAPES_MESO forecasting data has a temporal resolution of 3 h, which provides the opportunity to resolve the synoptic variation. However, it is found that the estimated ZWD and Tm exhibit apparent systematic deviation from in situ observation-based estimates, which is due to the inherent biases in the GRAPES_MESO data. To solve this problem, we propose to correct these biases using a linear model and a spherical cap harmonic model. The estimates after correction are termed as the “CTropGrid” products. When validated by the radiosonde data, the CTropGrid product has biases of 1.5 mm, −0.7 mm, and −0.1 K, and Root Mean Square (RMS) error of 8.9 mm, 20.2 mm, and 1.5 K for ZHD, ZWD, and Tm. Compared to the widely used GPT2w model, the CTropGrid products have improved the accuracies of ZHD, ZWD, and Tm by 11.9%, 55.6%, and 60.5% in terms of RMS. When validating the Zenith Tropospheric Delay (ZTD) products (the sum of ZHD and ZWD) using the IGS ZTD data, the CTropGrid ZTD has a bias of −0.7 mm and an RMS of 35.8 mm, which is 22.7% better than the GPT2w model in terms of RMS. Besides the accuracy improvements, the CTropGrid products well model the synoptic-scale variations of ZHD, ZWD, and Tm. Compared to the existing empirical models that only capture the tidal (seasonal and/or diurnal) variations, the CTropGrid products capture well the non-tidal variations of ZHD, ZWD, and Tm, which enhances the tropospheric delay corrections and GNSS water vapor monitoring at synoptic timescales. Therefore, the CTropGrid product is an important progress in GNSS positioning and GNSS meteorology.

HGPT2: An ERA5-Based Global Model to Estimate Relative Humidity

The neutral atmospheric delay is one of the major error sources in Space Geodesy techniques such as Global Navigation Satellite Systems (GNSS), and its modeling for high accuracy applications can be challenging. Improving the modeling of the atmospheric delays (hydrostatic and non-hydrostatic) also leads to a more accurate and precise precipitable water vapor estimation (PWV), mostly in real-time applications, where models play an important role, since numerical weather prediction models cannot be used for real-time processing or forecasting. This study developed an improved version of the Hourly Global Pressure and Temperature (HGPT) model, the HGPT2. It is based on 20 years of ERA5 reanalysis data at full spatial (0.25° × 0.25°) and temporal resolution (1-h). Apart from surface air temperature, surface pressure, zenith hydrostatic delay, and weighted mean temperature, the updated model also provides information regarding the relative humidity, zenith non-hydrostatic delay, and precipitable water vapor. The HGPT2 is based on the time-segmentation concept and uses the annual, semi-annual, and quarterly periodicities to calculate the relative humidity anywhere on the Earth’s surface. Data from 282 moisture sensors located close to GNSS stations during 1 year (2020) were used to assess the model coefficients. The HGPT2 meteorological parameters were used to process 35 GNSS sites belonging to the International GNSS Service (IGS) using the GAMIT/GLOBK software package. Results show a decreased root-mean-square error (RMSE) and bias values relative to the most used zenith delay models, with a significant impact on the height component. The HGPT2 was developed to be applied in the most diverse areas that can significantly benefit from an ERA5 full-resolution model.

Short-term interaction between silent and devastating earthquakes in Mexico

Either the triggering of large earthquakes on a fault hosting aseismic slip or the triggering of slow slip events (SSE) by passing seismic waves involve seismological questions with important hazard implications. Just a few observations plausibly suggest that such interactions actually happen in nature. In this study we show that three recent devastating earthquakes in Mexico are likely related to SSEs, describing a cascade of events interacting with each other on a regional scale via quasi-static and/or dynamic perturbations across the states of Guerrero and Oaxaca. Such interaction seems to be conditioned by the transient memory of Earth materials subject to the "traumatic" stress produced by seismic waves of the great 2017 (Mw8.2) Tehuantepec earthquake, which strongly disturbed the SSE cycles over a 650 km long segment of the subduction plate interface. Our results imply that seismic hazard in large populated areas is a short-term evolving function of seismotectonic processes that are often observable.

A Comparative Study of BDS Triple-Frequency Ambiguity Fixing Approaches for RTK Positioning

Concerning the triple-frequency ambiguity resolution, in principle there are three different realizations. The first one is to fix all the ambiguities of the original frequencies together. However, it is also believed that fixing the combined integer ambiguities with longer wavelength, such as extra-wide-lane (EWL), wide-lane (WL), should be advantageous. Also, it is demonstrated that fixing sequentially EWL, WL and one type of original ambiguities provides better results, as the previously fixed ambiguities increase parameters’ precision for later fixings. In this paper, we undertake a comparative study of the three fixing approaches by means of experimental validation. In order to realize the three fixing approaches from the same information in terms of adjustment, we developed a processing strategy to provide fully consistent normal equations. We first generate the normal equation with the original undifferentiated carrier phase ambiguities, then map it into that with the combined and double-differenced ambiguities required by the individual approach for fixing. Four baselines of 258 m, 22 km, 47 km and 53 km are selected and processed in both static and kinematic mode using the three ambiguity-fixing approaches. Indicators including time of first fixed solution (TFFS), the correct fixing rate, positioning accuracy and RATIO are used to evaluate and investigate results. We also made a preliminary theoretical explanation of the results by looking into the decorrelation procedure of the ambiguity searching algorithm and the intermediate results. As conclusions, integrated searching of original ambiguities or combined ambiguities has almost the same fixing performance, whereas the sequential fixing of EWL, WL and B1 ambiguities overperforms the integrated searching. By the way, the third-frequency data can shorten the TFFS significantly but can hardly improve the positioning.

Global Assessment of the GNSS Single Point Positioning Biases Produced by the Residual Tropospheric Delay

The tropospheric delay is one of the main error sources that degrades the accuracy of Global Navigation Satellite Systems (GNSS) Single Point Positioning (SPP). Although an empirical model is usually applied for correction and thereby to improve the positioning accuracy, the residual tropospheric delay is still drowned in measurement noise, and cannot be further compensated by parameter estimation. How much this type of residual error would sway the SPP positioning solutions on a global scale are still unclear. In this paper, the biases on SPP solutions introduced by the residual tropospheric delay when using nine conventionally Zenith Tropospheric Delay (ZTD) models are analyzed and discussed, including Saastamoinen+norm/Global Pressure and Temperature (GPT)/GPT2/GPT2w/GPT3, University of New Brunswick (UNB)3/UNB3m, European Geostationary Navigation Overlay System (EGNOS) and Vienna Mapping Functions (VMF)3 models. The accuracies of the nine ZTD models, as well as the SPP biases caused by the residual ZTD (dZTD) after model correction are evaluated using International GNSS Service (IGS)-ZTD products from around 400 globally distributed monitoring stations. The seasonal, latitudinal, and altitudinal discrepancies are analyzed respectively. The results show that the SPP solution biases caused by the dZTD mainly occur on the vertical direction, nearly to decimeter level, and significant discrepancies are observed among different models at different geographical locations. This study provides references for the refinement and applications of the nine ZTD models for SPP users.

Regional Zenith Tropospheric Delay Modeling Based on Least Squares Support Vector Machine Using GNSS and ERA5 Data

The meteorological reanalysis data has been widely applied to derive zenith tropospheric delay (ZTD) with a high spatial and temporal resolution. With the rapid development of artificial intelligence, machine learning also begins as a high-efficiency tool to be employed in modeling and predicting ZTD. In this paper, we develop three new regional ZTD models based on the least squares support vector machine (LSSVM), using both the International GNSS Service (IGS)-ZTD products and European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data over Europe throughout 2018. Among them, the ERA5 data is extended to ERA5S-ZTD and ERA5P-ZTD as the background data by the model method and integral method, respectively. Depending on different background data, three schemes are designed to construct ZTD models based on the LSSVM algorithm, including the without background data, with the ERA5S-ZTD, and with the ERA5P-ZTD. To investigate the advantage and feasibility of the proposed ZTD models, we evaluate the accuracy of two background data and three schemes by segmental comparison with the IGS-ZTD of 85 IGS stations in Europe. The results show that the overall average Root Mean Square Errors (RMSE) value of all sites is 30.1 mm for the ERA5S-ZTD, and 10.7 mm for the ERA5P-ZTD. The overall average RMSE is 25.8 mm, 22.9 mm, and 9 mm for the three schemes, respectively. Moreover, the overall improvement rate is 19.1% and 1.6% for the ZTD model with ERA5S-ZTD and ERA5P-ZTD, respectively. In order to explore the reason of the lower improvement for the ZTD model with ERA5P-ZTD, the loop verification is performed by estimating the ZTD values of each available IGS station. In actuality, the monthly improvement rate of estimated ZTD is positive for most stations, and the biggest improvement rate can even reach about 40%. The negative rate mainly comes from specific stations, these stations are located on the edge of the region, near the coast, as well as the lower similarity between the individual verified station and training stations.

A Regional Zenith Tropospheric Delay (ZTD) Model Based on GPT3 and ANN

The delays of radio signals transmitted by global navigation satellite system (GNSS) satellites and induced by neutral atmosphere, which are usually represented by zenith tropospheric delay (ZTD), are required as critical information both for GNSS positioning and navigation and GNSS meteorology. Establishing a stable and reliable ZTD model is one of the interests in GNSS research. In this study, we proposed a regional ZTD model that makes full use of the ZTD calculated from regional GNSS data and the corresponding ZTD estimated by global pressure and temperature 3 (GPT3) model, adopting the artificial neutral network (ANN) to construct the correlation between ZTD derived from GPT3 and GNSS observations. The experiments in Hong Kong using Satellite Positioning Reference Station Network (SatRet) were conducted and three statistical values, i.e., bias, root mean square error (RMSE), and compound relative error (CRE) were adopted for our comparisons. Numerical results showed that the proposed model outperformed the parameter ZTD model (Saastamoinen model) and the empirical ZTD model (GPT3 model), with an approximately 56%/52% and 52%/37% RMSE improvement in the internal and external accuracy verification, respectively. Moreover, the proposed method effectively improved the systematic deviation of GPT3 model and achieved better ZTD estimation in both rainy and rainless conditions.

Evaluation of the ZWD/ZTD Values Derived from MERRA-2 Global Reanalysis Products Using GNSS Observations and Radiosonde Data

Tropospheric delay is one of the main errors affecting high-precision positioning and navigation and is a key parameter of water vapor detection in the Global Navigation Satellite System (GNSS). The second Modern-Era Retrospective analysis for Research and Applications (MERRA-2) is the latest generation of reanalysis data collected by the National Aeronautics and Space Administration (NASA), which can be used to calculate tropospheric delay products with high spatial and temporal resolution. However, there is no report analyzing the accuracy of the zenith tropospheric delay (ZTD) and zenith wet delay (ZWD) calculated from MERRA-2 data. This paper evaluates the performance of the ZTD and ZWD values derived from global MERRA-2 data using global radiosonde data and International GNSS Service (IGS) precise ZTD products. The results are as follows: (1) Taking the precision ZTD products of 316 IGS stations from around the world from 2015 to 2017 as the reference, the average root mean square (RMS) of the ZTD values calculated from the MERRA-2 data is better than 1.35 cm, and the accuracy difference between different years is small. The bias and RMS of the ZTD values show certain seasonal variations, with a higher accuracy in winter and a lower accuracy in summer, and the RMS decreases from the equator to the poles. However, those of the ZTD values do not show obvious variations according to elevation. (2) Relative to the radiosonde data, the RMS of the ZWD and ZTD values calculated from the MERRA-2 data are better than 1.37 cm and 1.45 cm, respectively. Furthermore, the bias and RMS of the ZWD and ZTD values also show some temporal and spatial characteristics, which are similar to the test results of the IGS stations. It is suggested that MERRA-2 data can be used for global tropospheric vertical profile model construction because of their high accuracy and good stability in the global calculation of the ZWD and ZTD.

Precipitable Water Vapor Retrieval from Shipborne GNSS Observations on the Korean Research Vessel ISABU

We estimate precipitable water vapor (PWV) from data collected by the low-cost Global Navigation Satellite System (GNSS) receiver at a vessel. The dual-frequency GNSS receiver that the vessel ISABU is equipped with that is operated by the Korea Institute of Ocean Science and Technology. The ISABU served in the Pacific Ocean for scientific research during a period from August 30 to September 21, 2018. It also performs radiosonde observations to obtain a vertical profile of troposphere on the vessel’s path. The GNSS-derived PWV is compared to radiosonde observations and the Atmospheric Infrared Sounder (AIRS) on NASA’s Aqua satellite output. A bias and root-mean-square (RMS) error between shipborne GNSS-PWV and radiosonde-PWV were −1.48 and 5.22 mm, respectively. When compared to the ground GNSS-PWV, shipborne GNSS-PWV has a relatively large RMS error in comparison with radiosonde-PWV. However, the GNSS observations on the vessel are still in good agreement with radiosonde observations. On the other hand, the GNSS-PWV is not well linearly correlated with AIRS-PWV. The RMS error between the two observations was approximately 8.97 mm. In addition, we showed that the vessel on the sea surface has significantly larger carrier phase multipath error compared to the ground-based GNSS observations. This also can result in reducing the accuracy of shipborne GNSS-PWV. However, we suggest that the shipborne GNSS has sufficient potential to derive PWV with the kinematic precise point positioning (PPP) solution on the vessel.

Assessment of Empirical Troposphere Model GPT3 Based on NGL's Global Troposphere Products

Tropospheric delay is one of the major error sources in GNSS (Global Navigation Satellite Systems) positioning. Over the years, many approaches have been devised which aim at accurately modeling tropospheric delays, so-called troposphere models. Using the troposphere data of over 16,000 global stations in the last 10 years, as calculated by the Nevada Geodetic Laboratory (NGL), this paper evaluates the performance of the empirical troposphere model GPT3, which is the latest version of the GPT (Global Pressure and Temperature) series model. Owing to the large station number, long time-span and diverse station distribution, the spatiotemporal properties of the empirical model were analyzed using the average deviation (BIAS) and root mean square (RMS) error as indicators. The experimental results demonstrate that: (1) the troposphere products of NGL have the same accuracy as the IGS (International GNSS Service) products and can be used as a reference for evaluating general troposphere models. (2) The global average BIAS of the ZTD (zenith total delay) estimated by GPT3 is −0.99 cm and the global average RMS is 4.41 cm. The accuracy of the model is strongly correlated with latitude and ellipsoidal height, showing obviously seasonal variations. (3) The global average RMS of the north gradient and east gradient estimated by GPT3 is 0.77 mm and 0.73 mm, respectively, which are strongly correlated with each other, with values increasing from the equator to lower latitudes and decreasing from lower to higher latitudes.

VMF3o: the Vienna Mapping Functions for optical frequencies

The troposphere is considered as one of the major error sources in space geodetic techniques. Thus, accurate troposphere delay models are essential to provide high-quality products, such as reference frames, satellite orbits, or Earth rotation parameters. In this paper, a new troposphere delay model for satellite laser ranging, the Vienna Mapping Functions 3 for optical frequencies (VMF3o), is introduced. The model parameters are derived from ray-traced delays generated by an in-house ray-tracing software. VMF3o comprises not only zenith delays and mapping functions, but also linear horizontal gradients, which are not part of the standard SLR analysis yet. The model parameters are dedicated to a signal wavelength of 532 nm. Since some SLR stations operate also with other wavelengths, VMF3o provides a correction formula to transform the model parameters to any requested wavelength between 350 and 1064 nm. A test demonstrates that the correction formula approximates slant delays calculated at different wavelengths very accurately. The remaining error for slant delays at a wavelength of 1064 nm adds up to only a few millimetres at 10 ∘ elevation angle. A comparison study of the modelled delays that are derived from VMF3o and ray-traced delays was carried out to examine the quality of the model approach. The remaining differences of modelled and ray-traced delays are expressed as mean absolute error. At 5 ∘ elevation angle, the mean absolute error is only a few millimetres. At 10 ∘ elevation angle, it is at the 1 mm level. The results of the comparison also reveal that introducing linear horizontal gradients reduces the mean absolute error by more than 80% for low elevation angles.

A Regional NWP Tropospheric Delay Inversion Method Based on a General Regression Neural Network Model

Tropospheric delay is a major error source that affects the initialization and re-initialization speed of the Global Navigation Satellite System’s (GNSS) medium-/long-range baseline in Network Real-Time Kinematic (NRTK) positioning. Fusing the meteorological data from the Numerical Weather Prediction (NWP) model to estimate the zenith tropospheric delay (ZTD) is one of the current research hotspots. However, research has shown that the ZTD derived from NWP models is still not accurate enough for high-precision GNSS positioning applications without the estimation of the residual tropospheric delay. To date, General Regression Neural Network (GRNN) has been applied in many fields. It has a high learning speed and simple structure, and can approximate any function with arbitrary precision. In this study, we developed a regional NWP tropospheric delay inversion method based on a GRNN model to improve the accuracy of the tropospheric delay derived from the NWP model. The accuracy of the tropospheric delays derived from reanalysis data of the European Center for Medium-Range Weather Forecasts (ECMWF) and the US National Centers for Environmental Prediction (NCEP) was assessed through comparisons with the results of the International GPS Service (IGS). The variation characteristics of the residual of the ZTD inverted by NWP data were analyzed considering the factors of temperature, humidity, latitude, and season. To evaluate the performance of this new method, the National Center Atmospheric Research (NCAR) troposphere data of 650 stations in Japan in 2005 were collected as a reference to compare the accuracy of the ZTD before and after using the new method. The experimental results showed that the GRNN model has obvious advantages in fitting the NWP ZTD residual. The mean residual and the root mean square deviation (RMSD) of the ZTD inverted using the method of this study were 9.5 mm and 12.7 mm, respectively, showing reductions of 20.8% and 19.1%, respectively, as compared to the standard NWP model. For long-range baseline (155 km and 207 km), the corrected NWP-constrained RTK showed a reduction of over 43% in the initialization time compared with the standard RTK, and showed a reduction of over 24% in the initialization time compared with the standard NWP-constrained RTK.

A Refined Regional Model for Estimating Pressure, Temperature, and Water Vapor Pressure for Geodetic Applications in China

Pressure, temperature, and water vapor pressure are basic meteorological parameters that are frequently required in Global Navigation Satellite System (GNSS) positioning/navigation and GNSS meteorology. Although models like Global Pressure and Temperature (GPT) and Global Pressure and Temperature 2 wet (GPT2w) were developed for these demands, their spatial resolutions are lower than 0.75° and temporal resolutions are below 6 h, which limits their achievement. The publication of European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 hourly 0.25° × 0.25° data offers the opportunity to lift this limitation. In this work, the ERA5 surface data are used to evaluate the temporal variabilities of pressure, temperature, and water vapor pressure in the area of China. We characterize their diurnal variations using hourly data and take into account their geographical variations by 0.25° × 0.25° grids. In addition, we improve the height corrections for the three parameters employing the ERA5 pressure level data. Through these efforts, we build a new regional model named Chinese pressure, temperature, and water vapor pressure (CPTw), which has the advanced resolution of 0.25° × 0.25° and temporal resolution of 1 h. We evaluate the performance using ERA5 data and radiosonde data compared with the approved GPT2w model. Results demonstrate that the accuracies of the new model are superior to the GPT2w model in all meteorological parameters. The validation with the radiosonde data shows RMS for pressure, temperature, and water vapor pressure of the CPTw model is reduced by 14.1%, 25.8%, and 4.8%, compared with that of the GPT2w model. The new model catches especially well the diurnal changes in pressure, temperature, and water vapor pressure, which have never been realized before. Since the CPTw model can provide accurate empirical pressure, temperature, and water vapor pressure for any time and location in China and its surrounding areas, it can not only meet the need of empirical meteorological parameters in real-time geodetic applications like GNSS positioning and navigation, but it is also useful for GNSS meteorology.

Modeling and Forecasting the GPS Zenith Troposphere Delay in West Antarctica Based on Different Blind Source Separation Methods and Deep Learning

Tropospheric delay is an important error source in global positioning systems (GPS), and the water vapor retrieved from the tropospheric delay is widely used in meteorological research such as climate analysis and weather forecasting. Most zenith tropospheric delay (ZTD) models are presently used as positioning corrections, and few models are used for the estimation of water vapor, especially in Antarctica. Through two blind source separation algorithms (principal component analysis (PCA) and independent component analysis (ICA)), a back-propagation (BP) neural network and a deep learning technique (long short-term memory (LSTM) network), we establish an hourly high-accuracy ZTD model for GPS meteorology using the GPS-ZTD from 52 GPS stations in West Antarctica. Our results show that under the condition in which the principal components (PCs) and independent components (ICs) remain fixed after decomposition, the mean accuracy of the models for West Antarctica using PCA or ICA are better than 10 mm. Compared with the ZTDs from the nonmodeling stations, the mean root mean square (RMS) of the PCA and ICA models are 9.3 and 8.9 mm, respectively, and the correlation coefficients between the GPS-ZTD and model-ZTDs all exceed 90%. The accuracy of the ICA model is slightly higher than that of the PCA model, and the ICs of the ICA model show more consistent spatial responses. The six-hour forecast is the best among the forecast results, with a mean correlation coefficient of 90.6% and a mean RMS of 7.2 mm using GPS-ZTD. The long-term forecast result is significantly inaccurate, as the correlation coefficient between the 24-h forecast and GPS-ZTD is only 63.2%. Generally modest results have been achieved (HSS ≤ 0.38). Furthermore, the forecast accuracy in coastal areas is lower than that in inland areas. Our study confirms that the combined use of ICA and deep learning in ZTD modeling can effectively restore the original signals, and short-term forecasting can be effectively used in GPS meteorology. However, further development of the technology is necessary.

An ERA5-Based Hourly Global Pressure and Temperature (HGPT) Model

The Global Navigation Satellite System (GNSS) meteorology contribution to the comprehension of the Earth’s atmosphere’s global and regional variations is essential. In GNSS processing, the zenith wet delay is obtained using the difference between the zenith total delay and the zenith hydrostatic delay. The zenith wet delay can also be converted into precipitable water vapor by knowing the atmospheric weighted mean temperature profiles. Improving the accuracy of the zenith hydrostatic delay and the weighted mean temperature, normally obtained using modeled surface meteorological parameters at coarse scales, leads to a more accurate and precise zenith wet delay estimation, and consequently, to a better precipitable water vapor estimation. In this study, we developed an hourly global pressure and temperature (HGPT) model based on the full spatial and temporal resolution of the new ERA5 reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). The HGPT model provides information regarding the surface pressure, surface air temperature, zenith hydrostatic delay, and weighted mean temperature. It is based on the time-segmentation concept and uses the annual and semi-annual periodicities for surface pressure, and annual, semi-annual, and quarterly periodicities for surface air temperature. The amplitudes and initial phase variations are estimated as a periodic function. The weighted mean temperature is determined using a 20-year time series of monthly data to understand its seasonality and geographic variability. We also introduced a linear trend to account for a global climate change scenario. Data from the year 2018 acquired from 510 radiosonde stations downloaded from the National Oceanic and Atmospheric Administration (NOAA) Integrated Global Radiosonde Archive were used to assess the model coefficients. Results show that the GNSS meteorology, hydrological models, Interferometric Synthetic Aperture Radar (InSAR) meteorology, climate studies, and other topics can significantly benefit from an ERA5 full-resolution model.

Precise Point Positioning on the Reliable Detection of Tropospheric Model Errors

Precise point positioning (PPP) is one of the well-known applications of Global Navigation Satellite System (GNSS) and provides precise positioning solutions using accurate satellite orbit and clock products. The tropospheric delay due to the neutral atmosphere for microwave signals is one of the main sources of measurement error in PPP. As one component of this delay, the hydrostatic delay is usually compensated by using an empirical correction model. However, how to eliminate the effects of the wet delay during a weather event is a challenge because current troposphere models are not capable of considering the complex atmosphere around the receiver during situations such as typhoons, storms, heavy rainfall, et cetera. Thus, how positioning results can be improved if the residual wet delays are taken into account needs to be investigated . In this contribution, a real-time procedure of recursive detection, identification and adaptation (DIA) is applied to detect the model errors which have the same effects on both phase and code observables; e.g., the model error caused by the tropospheric delay. Once the model errors are identified, additional parameters are added to the functional model to account for the measurement residuals. This approach is evaluated with Global Positioning System (GPS) data during two rainfall events in Darwin, Australia, proving the usefulness of compensated residual slant wet delay for positioning results. Comparisons with the standard approach show that the precision of the up component is improved significantly during the periods of the weather events; for the two case studies, 72.46% and 64.41% improvements of root mean squared error (RMS) resulted, and the precision of the horizontal component obtained by the proposed approach is also improved more than 30% compared to the standard approach. The results also show that the identified model errors are concentrated at the beginning of both heavy rainfall processes when the front causes significant spatial and temporal gradients of the integrated water vapor above the receiver.

Development of Global Tropospheric Empirical Correction Model with High Temporal Resolution

The accuracy of global tropospheric empirical models depends on the model expression and the modeling data sources. Although the current temporal resolution of available models is usually one day, it is anticipated that this will be improved in the future. To achieve compatibility with future high temporal-resolution data sources, this study develops a new global tropospheric correction model, the Wuhan-University Global Tropospheric Empirical Model (WGTEM). Evaluation of WGTEM model expression determines that it has better precision than other models, and this is attributed to its ability to consider diurnal variations in meteorological parameters and the double-peak daily variation in air pressure, which are not concerned in other models. The external accuracy of the WGTEM was evaluated after modeling with the European Centre for Medium-range Weather Forecasts (ECMWF) ERA-Interim products, and results show its accuracy exceeds that of the current ITG model and its Zenith Tropospheric Delay (ZTD) performance is also superior.

Evaluation of Zenith Tropospheric Delay Derived from ERA5 Data over China Using GNSS Observations

The latest reanalysis of the European Center for Medium-Range Weather Forecasts (ECMWF), ERA5, can provide atmospheric data for calculating Zenith Tropospheric Delay (ZTD) with hourly temporal resolution, which is a key factor in Global Navigation Satellite System (GNSS) high-precision application. This paper is aimed at evaluating the performance of ZTD derived from ERA5 reanalysis data over China using 219 GNSS stations of the Crustal Movement Observation Network of China (CMONOC) covering the period from 2015 to 2016. The site-specific hourly ZTD at these stations is obtained by integration method and Saastamoinen model method on ERA5 pressure-level and surface-level reanalysis data with the temporal resolution of 1 h and the spatial resolution of 0.25° × 0.25°. Firstly, the atmospheric temperature and pressure that derived from ERA5 are compared with temperature and pressure obtained from meteorological sensors available at 193 GNSS stations. The biases are 2.31 °C and 1.26 mbar implying the accuracy and feasibility of ERA5 pressure and temperature for calculating ZTD over China. Secondly, the performance of ERA5 ZTD is systematically evaluated using ZTD from 219 GNSS sites. The average bias and Root Mean Square (RMS) of ERA5 pressure-level ZTD at all test stations in integration method are approximately 2.97 mm and 11.49 mm respectively, and those of ERA5 surface-level ZTD in model method are 7.97 mm, 39.25 mm, which indicates that ERA5 pressure-level ZTD has a higher accuracy over China. Further analysis indicates that the accuracies of ZTD derived from ERA5 pressure-level and surface-level data are approximately 13.8% and 10.9% higher than those from of ERA-Interim pressure-level and surface-level data. Moreover, ERA5 is able to accurately capture the short-term (hourly) variation of ZTD, which further indicates the better performance of ERA5. Thirdly, the temporal and spatial variation characteristics of ERA5 ZTD accuracy are further analyzed over China. The results show that the ZTD in the southern region has the lower accuracy compared with that in the northern region over China due to the influence of latitude and altitude. Furthermore, it is found that the ERA5 ZTD over China has obvious seasonality, with higher accuracy in winter and lower accuracy in summer.

SHAtropE—A Regional Gridded ZTD Model for China and the Surrounding Areas

A regional zenith tropospheric delay (ZTD) empirical model, referred to as SHAtropE (SHanghai Astronomical observatory tropospheric delay model—Extended), is developed and provides tropospheric propagation delay corrections for users in China and the surrounding areas with improved accuracy. The SHAtropE model was developed based on the ZTD time series of the continuous GNSS sites from the Crustal Movement Observation Network of China (CMONOC) and GNSS sites of surrounding areas. It combines the exponential and periodical functions and is provided as regional grids with a resolution of 2.5° × 2.0° in longitude and latitude. At each grid point, the exponential function converts the ZTD from the site height to the ellipsoid, and the periodical terms, including both annual and semi-annual periods, describe ZTD’s temporal variation. Moreover, SHAtropE also provides the predicted ZTD uncertainty, which is valuable in Precise Point Positioning (PPP) with ZTD being constrained for faster convergence. The data of 310 GNSS sites over 7 years were used to validate the new model. Results show that the SHAtropE ZTD has an accuracy of 3.5 cm in root mean square (RMS) quantity, which has a mean improvement of 35.2% and 5.4% over the UNB3m (5.4 cm) and GPT3 (3.7 cm) models, respectively. The predicted uncertainty of SHAtropE ZTD shows seasonal variations, where the values are larger in summer than in winter. By applying the SHAtropE model in the static PPP, the convergence time of GPS-only and BDS-only solutions are reduced by 8.1% and 14.5% respectively compared to the UNB3m model, and the reductions are 6.9% and 11.2% respectively for the GPT3 model. As no meteorological data are required for the implementation of the model, the SHAtropE could thus be a refined tropospheric model for GNSS users in mainland China and the surrounding areas. The method of modeling the ZTD uncertainty can also be used in further global tropospheric delay modeling.

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.

Modelling the Altitude Dependence of the Wet Path Delay for Coastal Altimetry Using 3-D Fields from ERA5

Wet path delay (WPD) for satellite altimetry has been provided from external sources, raising the need of converting this value between different altitudes. The only expression available for this purpose considers the same altitude reduction, irrespective of geographic location and time. The focus of this study is the modelling of the WPD altitude dependence, aiming at developing improved expressions. Using ERA5 pressure level fields (2010–2013), WPD vertical profiles were computed globally. At each location and for each vertical profile, an exponential function was fitted using least squares, determining the corresponding decay coefficient. The time evolution of these coefficients reveals regions where they are highly variable, making this modelling more difficult, and regions where an annual signal exists. The output of this modelling consists of a set of so-called University of Porto (UP) coefficients, dependent on geographic location and time. An assessment with ERA5 data (2014) shows that for the location where the Kouba coefficient results in a maximum Root Mean Square (RMS) error of 3.2 cm, using UP coefficients this value is 1.2 cm. Independent comparisons with WPD derived from Global Navigation Satellite Systems and radiosondes show that the use of UP coefficients instead of Kouba’s leads to a decrease in the RMS error larger than 1 cm.

PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS

Precise point positioning (PPP) has been used for decades not only for general positioning needs but also for geodetic and other scientific applications. The CNES-CLS Analysis Centre (AC) of the International GNSS Service (IGS) is performing PPP with phase ambiguity resolution (PPP-AR) using the zero-difference ambiguity fixing approach also known as “Integer PPP” (IPPP). In this paper we examine the postprocessed kinematic PPP and PPP-AR using Galileo-only, GPS-only and Multi-GNSS (GPS + Galileo) constellations. The interest is to examine the accuracy for each GNSS system individually but also of their combination to measure the current benefits of using Galileo within a Multi-GNSS PPP and PPP-AR. Results show that Galileo-only positioning is nearly at the same level as GPS-only; around 2–4 mm horizontal and aound 10 mm vertical repeatability (example station of BRUX). In addition, the use of Galileo system—even uncompleted—improves the performance of the positioning when combined with GPS giving mm level repeatability (improvement of around 30% in East, North and Up components). Repeatabilities observed for Multi-GNSS (GPS + GAL) PPP-AR, taking into account the global network statistics, are a little larger, with 8 mm in horizontal and 17 mm in vertical directions. This result shows that including Galileo ameliorates the best positioning accuracy achieved until today with GPS PPP-AR.

A Global Model for Estimating Tropospheric Delay and Weighted Mean Temperature Developed with Atmospheric Reanalysis Data from 1979 to 2017

Precise modeling of tropospheric delay and weighted mean temperature (Tm) is critical for Global Navigation Satellite System (GNSS) positioning and meteorology. However, the model data in previous models cover a limited time span, which limits the accuracy of these models. Besides, the vertical variations of tropospheric delay and Tm are not perfectly modeled in previous studies, which affects the performance of height corrections. In this study, we used the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis from 1979 to 2017 to build a new empirical model. We first carefully modeled the lapse rates of tropospheric delay and Tm. Then we considered the temporal variations by linear trends, annual, and semi-annual variations and the spatial variations by grids. This new model can provide zenith hydrostatic delay (ZHD), zenith wet delay (ZWD), and Tm worldwide with a spatial resolution of 1° × 1°. We used the ECMWF ERA-Interim data and the radiosonde data in 2018 to validate this new model in comparison with the canonical GPT2w model. The results show that the new model has higher accuracies than the GPT2w model in all parameters. Particularly, this new model largely improves the accuracy in estimating ZHD and Tm at high-altitude (relative to the grid point height) regions.

Establishment of a Real-Time Local Tropospheric Fusion Model

The tropospheric delay is one major error source affecting the precise positioning provided by the global navigation satellite system (GNSS). This error occurs because the GNSS signals are refracted while travelling through the troposphere layer. Nowadays, various types of model can produce the tropospheric delay. Among them, the globally distributed GNSS permanent stations can resolve the tropospheric delay with the highest accuracy and the best continuity. Meteorological models, such as the Saastamoinen model, provide formulae to calculate temperature, pressure, water vapor pressure and subsequently the tropospheric delay. Some grid-based empirical tropospheric delay models directly provide tropospheric parameters at a global scale and in real time without any auxiliary information. However, the spatial resolution of the GNSS tropospheric delay is not sufficient, and the accuracy of the meteorological and empirical models is relatively poor. With the rapid development of satellite navigation systems around the globe, the demand for real-time high-precision GNSS positioning services has been growing dramatically, requiring real-time and high-accuracy troposphere models as a critical prerequisite. Therefore, this paper proposes a multi-source real-time local tropospheric delay model that uses polynomial fitting of ground-based GNSS observations, meteorological data, and empirical GPT2w models. The results show that the accuracy in the zenith tropospheric delay (ZTD) of the proposed tropospheric delay model has been verified with a RMS (root mean square) of 1.48 cm in active troposphere conditions, and 1.45 cm in stable troposphere conditions, which is significantly better than the conventional tropospheric GPT2w and Saastamoinen models.

Crustal Deformation Prior to the 2017 Jiuzhaigou, Northeastern Tibetan Plateau (China), Ms 7.0 Earthquake Derived from GPS Observations

The 2017 Jiuzhaigou Ms 7.0 earthquake occurred on the northeastern margin of the Tibetan Plateau, with no noticeable rupture surface recognized. We characterized the pre-seismic deformation of the earthquake from GPS (Global Positioning System) data at eight continuous and 73 campaign sites acquired over the 2009–2017 period. With respect to the Eurasian plate, the velocity field showed a noticeable decrease, from west of the epicenter of the Jiuzhaigou earthquake to the western edge of the Longmenshan fault, in the southeast direction. The total northwest west–southeast east shortening rate in the vicinity of the epicentral area was in the range of 1.5 mm/y to 3.1 mm/y. With a GPS velocity transect across the Huya fault (HYF), where the epicenter was located, we estimated the activity of the HYF, showing a dominant left-lateral slip rate of 3.3 ± 0.2 mm/y. We calculated strain rates using a spherical wavelet-based multiscale approach that solved for the surface GPS velocity according to multiscale wavelet basis functions while accounting for spatially variable spacing of observations. Multiscale components of the two-dimensional strain rate tensor showed a complex crustal deformation pattern. Our estimates of strain rate components at the scale of seven and eight revealed extensional strain rate on the northern extension of the HYF. The Jiuzhaigou earthquake occurred at the buffer zone between extensional and compressional deformation, and with significant maximum shear rates being 100–140 nanostrain/y. In addition, a maximum shear strain rate of 60–120 nanostrain/y appeared around the epicenter of the 2013 Ms 6.6 Minxian–Zhangxian earthquake. These findings imply that inherent multiscale strain rates could be separated to identify strain accumulation related to medium- and large-sized earthquakes.

Real-time tropospheric delay retrieval with GPS, GLONASS, Galileo and BDS data

The precise point positioning (PPP) is a promising technology for the real-time retrieval of atmospheric parameters with a single receiver in anywhere, all-weather and any time. The real-time atmospheric parameters can be applied to the time-critical meteorology, such as the severe weather nowcasting. The PPP is a satellite-based technology. Multi-constellation integration can enhance satellite geometry and increase measurement redundancy so that the solutions of atmospheric parameters are expected to be improved. Currently, the Global Navigation Satellite System (GNSS) family includes recovered GLONASS and modernized GPS as well as the emerging Galileo and BDS. A week of GNSS observations from 160 stations are processed to retrieve the tropospheric zenith total delay (ZTD) in real time. The four-constellation mixed real-time precise products including satellite orbit and clock corrections are adopted, and their quality is evaluated. The performance of ZTD estimates is assessed in terms of accuracy and convergence time by comparing with final tropospheric ZTD products provided by two analysis centers. The ZTDs retrieved from different constellation combinations (i.e., GPS/GLONASS/Galileo/BDS, GPS/GLONASS, and GPS-only), different processing models for ionospheric delays (i.e., ionospheric-free (IF) combined PPP, and uncombined (UC) PPP), and different modes (i.e., real-time mode, and post-processing mode) are compared.

Establishment and Evaluation of a New Meteorological Observation-Based Grid Model for Estimating Zenith Wet Delay in Ground-Based Global Navigation Satellite System (GNSS)

With the availability to high-accuracy a priori zenith wet delay (ZWD) data, the positioning efficiency of the precise point positioning (PPP) processing can be effectively improved, including accelerating the convergence time and improving the positioning precision, in ground-based Global Navigation Satellite System (GNSS) technology. Considering the limitations existing in the state-of-the-art ZWD models, this paper established and evaluated a new in-situ meteorological observation-based grid model for estimating ZWD named GridZWD using the radiosonde data and the European Centre for Medium-Range Weather Forecasts (ECWMF) data. The results show that ZWD has a strong correlation with the meteorological parameter water vapor pressure in continental and high-latitude regions. The root of mean square error (RMS) of 24.6 mm and 36.0 mm are achievable by the GridZWD model when evaluated with the ECWMF data and the radiosonde data, respectively. An accuracy improvement of approximately 10%~30% compared with the state-of-the-art models (e.g., the Saastamoinen, Hopfield and GPT2w models) can be found for the new built model.

New Geodetic and Gravimetric Maps to Infer Geodynamics of Antarctica with Insights on Victoria Land

In order to make inferences on the geodynamics of Antarctica, geodetic and gravimetric maps derived from past and new observations can be used. This paper provides new insights into the geodynamics of Antarctica by integrating data at regional and continental scales. In particular, signatures of geodynamic activity at a regional extent have been investigated in Victoria Land (VL, Antarctica) by means of Global Navigation Satellite System (GNSS) permanent station observations, data from the VLNDEF (Victoria Land Network for Deformation control) discontinuous network, and gravity station measurements. At the continental scale, episodic GNSS observations on VLNDEF sites collected for 20 years, together with continuous data from the International GNSS Service (IGS) and Polar Earth Observing Network (POLENET) sites, were processed, and the Euler pole position assessed with the angular velocity of the Antarctic plate. Both the Bouguer and the free-air gravity anomaly maps were obtained by integrating the available open-access geophysics dataset, and a compilation of 180 gravity measurements collected in the VL within the Italian National Program for Antarctic Research (PNRA) activities. As a result, new evidence has been detected at regional and continental scale. The main absolute motion of VL is towards SE (Ve 9.9 ± 0.26 mm/yr, Vn −11.9 ± 0.27 mm/yr) with a pattern similar to the transforms of the Tasman and Balleny fracture zones produced as consequence of Southern Ocean spreading. Residual velocities of the GNSS stations located in VL confirm the active role of the two main tectonic lineaments of the region, the Rennick–Aviator and the Lillie–Tucker faults with right-lateral sense of shear. The resulting VL gravity anomalies show a NW region characterized by small sized Bouguer anomaly with high uplift rates associated and a SE region with low values of Bouguer anomaly and general subsidence phenomena. The East and West Antarctica are characterized by a different thickness of the Earth’s crust, and the relative velocities obtained by the observed GNSS data confirm that movements between the two regions are negligible. In East Antarctica, the roots of the main subglacial highlands, Gamburtsev Mts and Dronning Maud Land, are present. The Northern Victoria Land (NVL) is characterized by more scattered anomalies. These confirm the differences between the Glacial Isostatic Adjustment (GIA) modeled and observed uplift rates that could be related to deep-seated, regional scale structures.

Real-time precise point positioning-based zenith tropospheric delay for precipitation forecasting

GPS-based Zenith Tropospheric Delay (ZTD) estimation should be easily obtained in a cost-effective way, however, the most previous studies focus on post-processed ZTD estimates using satellite orbit and clock products with at least 3–9 hours latency provided by International GNSS Service (IGS), which limits the GNSS meteorological application for nowcasting. With the development of IGS’s real-time pilot project (RTPP), this limitation was removed by April, 2013 as real-time satellite orbit and clock products can be obtained on-line. In this paper, on the one hand, the GPS-derived ZTD estimation was evaluated using the IGS final and real-time satellite products based on independently developed PPP software. On the other hand, the analysis of the time series of GPS-derived ZTD by least-square fitting of a broken line tendency for a full year of observations, and a forecasting method for precipitation is proposed based on the ZTD slope in the ascending period. The agreement between ZTD slope and the ground rainfall records suggested that the proposed method is useful for the assisted forecasting, especially for short-term alarms.

Combined orbits and clocks from IGS second reprocessing

The Analysis Centers (ACs) of the International GNSS Service (IGS) have reprocessed a large global network of GPS tracking data from 1994.0 until 2014.0 or later. Each AC product time series was extended uniformly till early 2015 using their weekly operational IGS contributions so that the complete combined product set covers GPS weeks 730 through 1831. Three ACs also included GLONASS data from as early as 2002 but that was insufficient to permit combined GLONASS products. The reprocessed terrestrial frame combination procedures and results have been reported already, and those were incorporated into the ITRF2014 multi-technique global frame released in 2016. This paper describes the orbit and clock submissions and their multi-AC combinations and assessments. These were released to users in early 2017 in time for the adoption of IGS14 for generating the operational IGS products. While the reprocessing goal was to enable homogeneous modeling, consistent with the current operational procedures, to be applied retrospectively to the full history of observation data in order to achieve a more suitable reference for geophysical studies, that objective has only been partially achieved. Ongoing AC analysis changes and a lack of full participation limit the consistency and precision of the finished IG2 products. Quantitative internal measures indicate that the reprocessed orbits are somewhat less precise than current operational orbits or even the later orbits from the first IGS reprocessing campaign. That is even more apparent for the clocks where a lack of robust AC participation means that it was only possible to form combined 5-min clocks but not the 30-s satellite clocks published operationally. Therefore, retrospective precise point positioning solutions by users are not recommended using the orbits and clocks. Nevertheless, the orbits do support long-term stable user solutions when used with network processing with either double differencing or explicit clock estimation. Among the main benefits of the reprocessing effort is a more consistent long product set to analyze for sources of systematic error and accuracy. Work to do that is underway but the reprocessing experience already points to a number of ways future IGS performance and reprocessing campaigns can be improved.

Performance Analysis of BDS Medium-Long Baseline RTK Positioning Using an Empirical Troposphere Model

For GPS medium-long baseline real-time kinematic (RTK) positioning, the troposphere parameter is introduced along with coordinates, and the model is ill-conditioned due to its strong correlation with the height parameter. For BeiDou Navigation Satellite System (BDS), additional difficulties occur due to its special satellite constellation. In fact, relative zenith troposphere delay (RZTD) derived from high-precision empirical zenith troposphere models can be introduced. Thus, the model strength can be improved, which is also called the RZTD-constrained RTK model. In this contribution, we first analyze the factors affecting the precision of BDS medium-long baseline RTK; thereafter, 15 baselines ranging from 38 km to 167 km in different troposphere conditions are processed to assess the performance of RZTD-constrained RTK. Results show that the troposphere parameter is difficult to distinguish from the height component, even with long time filtering for BDS-only RTK. Due to the lack of variation in geometry for the BDS geostationary Earth orbit satellite, the long convergence time of ambiguity parameters may reduce the height precision of GPS/BDS-combined RTK in the initial period. When the RZTD-constrained model was used in BDS and GPS/BDS-combined situations compared with the traditional RTK, the standard deviation of the height component for the fixed solution was reduced by 52.4% and 34.0%, respectively.

Refined discrete and empirical horizontal gradients in VLBI analysis

Missing or incorrect consideration of azimuthal asymmetry of troposphere delays is a considerable error source in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). So-called horizontal troposphere gradients are generally utilized for modeling such azimuthal variations and are particularly required for observations at low elevation angles. Apart from estimating the gradients within the data analysis, which has become common practice in space geodetic techniques, there is also the possibility to determine the gradients beforehand from different data sources than the actual observations. Using ray-tracing through Numerical Weather Models (NWMs), we determined discrete gradient values referred to as GRAD for VLBI observations, based on the standard gradient model by Chen and Herring (J Geophys Res 102(B9):20489-20502, 1997. 10.1029/97JB01739) and also for new, higher-order gradient models. These gradients are produced on the same data basis as the Vienna Mapping Functions 3 (VMF3) (Landskron and Böhm in J Geod, 2017. 10.1007/s00190-017-1066-2), so they can also be regarded as the VMF3 gradients as they are fully consistent with each other. From VLBI analyses of the Vienna VLBI and Satellite Software (VieVS), it becomes evident that baseline length repeatabilities (BLRs) are improved on average by 5% when using a priori gradients GRAD instead of estimating the gradients. The reason for this improvement is that the gradient estimation yields poor results for VLBI sessions with a small number of observations, while the GRAD a priori gradients are unaffected from this. We also developed a new empirical gradient model applicable for any time and location on Earth, which is included in the Global Pressure and Temperature 3 (GPT3) model. Although being able to describe only the systematic component of azimuthal asymmetry and no short-term variations at all, even these empirical a priori gradients slightly reduce (improve) the BLRs with respect to the estimation of gradients. In general, this paper addresses that a priori horizontal gradients are actually more important for VLBI analysis than previously assumed, as particularly the discrete model GRAD as well as the empirical model GPT3 are indeed able to refine and improve the results.

A New Zenith Tropospheric Delay Grid Product for Real-Time PPP Applications over China

Tropospheric delay is one of the major factors affecting the accuracy of electromagnetic distance measurements. To provide wide-area real-time high precision zenith tropospheric delay (ZTD), the temporal and spatial variations of ZTD with altitude were analyzed on the bases of the latest meteorological reanalysis product (ERA-Interim) provided by the European Center for Medium-Range Weather Forecasts (ECMWF). An inverse scale height model at given locations taking latitude, longitude and day of year as inputs was then developed and used to convert real-time ZTD at GPS stations in Crustal Movement Observation Network of China (CMONOC) from station height to mean sea level (MSL). The real-time ZTD grid product (RtZTD) over China was then generated with a time interval of 5 min. Compared with ZTD estimated in post-processing mode, the bias and error RMS of ZTD at test GPS stations derived from RtZTD are 0.39 and 1.56 cm, which is significantly more accurate than commonly used empirical models. In addition, simulated real-time kinematic Precise Point Positioning (PPP) tests show that using RtZTD could accelerate the BDS-PPP convergence time by up to 32% and 65% in the horizontal and vertical components (set coordinate error thresholds to 0.4 m), respectively. For GPS-PPP, the convergence time using RtZTD can be accelerated by up to 29% in the vertical component (0.2 m).

VMF3/GPT3: refined discrete and empirical troposphere mapping functions

Incorrect modeling of troposphere delays is one of the major error sources for space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). Over the years, many approaches have been devised which aim at mapping the delay of radio waves from zenith direction down to the observed elevation angle, so-called mapping functions. This paper contains a new approach intended to refine the currently most important discrete mapping function, the Vienna Mapping Functions 1 (VMF1), which is successively referred to as Vienna Mapping Functions 3 (VMF3). It is designed in such a way as to eliminate shortcomings in the empirical coefficients b and c and in the tuning for the specific elevation angle of 3 ∘ . Ray-traced delays of the ray-tracer RADIATE serve as the basis for the calculation of new mapping function coefficients. Comparisons of modeled slant delays demonstrate the ability of VMF3 to approximate the underlying ray-traced delays more accurately than VMF1 does, in particular at low elevation angles. In other words, when requiring highest precision, VMF3 is to be preferable to VMF1. Aside from revising the discrete form of mapping functions, we also present a new empirical model named Global Pressure and Temperature 3 (GPT3) on a5 ∘ × 5 ∘ as well as a1 ∘ × 1 ∘ global grid, which is generally based on the same data. Its main components are hydrostatic and wet empirical mapping function coefficients derived from special averaging techniques of the respective (discrete) VMF3 data. In addition, GPT3 also contains a set of meteorological quantities which are adopted as they stand from their predecessor, Global Pressure and Temperature 2 wet. Thus, GPT3 represents a very comprehensive troposphere model which can be used for a series of geodetic as well as meteorological and climatological purposes and is fully consistent with VMF3.