Search Results (97)

To address the degradation of zenith tropospheric delay (ZTD) prediction accuracy caused by time-varying noise and error accumulation in multi-step forecasting, this study proposes an integrated prediction model, named IBX, which combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), bidirectional long short-term memory (BiLSTM), and extreme gradient boosting (XGBoost). In the proposed framework, ICEEMDAN is first used to decompose the original ZTD series into components at different temporal scales. A three-criterion reconstruction strategy based on the Pearson correlation coefficient, dominant period, and sample entropy is then applied to obtain high-, medium-, and low-frequency subsequences with clearer physical meanings. BiLSTM and XGBoost are used to predict the reconstructed components, and their outputs are fused through a root mean square error (RMS)-based weighting strategy to improve forecasting robustness. Hourly ZTD data from 27 global navigation satellite system (GNSS) stations in China from 2011 to 2020 were used for model validation under 1–12 h rolling forecasting horizons. The results show that IBX achieves the best overall performance among the tested models. Its mean RMS and mean absolute error (MAE) over the 1–12 h horizons are 14.17 mm and 10.24 mm, respectively, which are 22.5% and 21.4% lower than those of the baseline BiLSTM model. Spatial and climate-region-based analyses further indicate that ZTD prediction accuracy is strongly affected by altitude, regional moisture conditions, and climate type. The proposed IBX model shows stable error suppression across heterogeneous station environments, especially in the temperate monsoon region and low-altitude regions with complex water vapor variability. These results demonstrate that IBX provides a reliable and physically interpretable approach for short- to medium-term ZTD forecasting and real-time atmospheric delay correction. Full article

This study evaluates the impact of assimilating the Crustal Movement Observation Network of China (CMONOC) global navigation satellite system (GNSS) tropospheric products on heavy-rainfall simulation over the complex terrain of the Sichuan Basin. Using the Weather Research and Forecasting model with the WRF Data Assimilation (WRF/WRFDA) three-dimensional variational (3DVar) system, we conducted a control (CTRL) experiment and a data-assimilation (DA) experiment for a primary heavy-rainfall event during 10–12 August 2020. The DA experiment applied 6 h cycling assimilation of station-based zenith total delay (ZTD) and precipitable water vapor (PWV). Compared with CTRL, DA improved the placement of the primary rainband and the depiction of peak rainfall. On 10 August, the observed rainfall core (~40 mm) over the northwestern basin was underestimated in CTRL (~15 mm) but was strengthened in DA (~25 mm). Hourly verification at a threshold of 2 mm h⁻¹ showed a higher maximum Threat Score (TS) in DA (0.292) than in CTRL (0.250), and the largest instantaneous gain reached 0.061. For 72 h accumulated precipitation, TS was higher in DA across multiple thresholds (≥10, ≥25, ≥50, and ≥100 mm), with the most pronounced improvement for heavier rainfall categories. Diagnostic analysis indicates that GNSS assimilation introduces dynamically consistent low-level moistening and strengthened convergence at 850 hPa, together with a better-aligned vertical ascent structure during the key stage of the event. An additional heavy-rainfall event during 21–23 August 2021 was further examined as a compact robustness test, and the results showed a generally consistent improvement in precipitation distribution and TS after GNSS assimilation. Overall, the present results suggest that cycling assimilation of CMONOC GNSS ZTD/PWV products can provide effective moisture constraints and improve heavy-rainfall simulation over the Sichuan Basin in the examined cases. Full article

Zenith Tropospheric Delay (ZTD) and its associated atmospheric water vapor information constitute essential environmental variables for Earth observation (EO)-based atmospheric monitoring and environmental variable retrieval. High-quality ZTD products are therefore of great importance for the post-processing, refinement, and reconstruction of atmospheric environmental variables at regional scales. Among existing observation techniques, Global Navigation Satellite System (GNSS) measurements provide high-precision ZTD estimates and have become an important means for retrieving tropospheric delay and water vapor. However, the sparse and uneven spatial distribution of GNSS stations limits their direct applicability for continuous environmental monitoring. Reanalysis-based products, such as ERA5 provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), offer EO big data with excellent spatiotemporal continuity but suffer from pronounced systematic biases compared to precision GNSS retrievals, restricting their direct use in high-accuracy regional applications. To address these limitations, this study proposes a Residual Correction Kriging method for ZTD (RK ZTD) that integrates GNSS ZTD and ERA5 ZTD grids through a multi-source data fusion framework. High-precision GNSS ZTD is treated as reference data, and the differences between GNSS ZTD and ERA5 ZTD at modeling stations are defined as residuals to characterize the systematic bias in ERA5 ZTD grids. A Kriging interpolation algorithm is then employed to model the spatial distribution of these residuals and generate residual correction grids. By superimposing the interpolated residual grids onto the ERA5 ZTD grids, a refined and high-precision regional ZTD product is reconstructed. Experiments were conducted using observations collected in 2023 from 36 GNSS stations in the Netherlands, including 10 modeling stations and 26 independent validation stations, together with concurrent ERA5-derived ZTD grids. The results demonstrate that the proposed RK ZTD model provides spatially robust and high-precision ZTD products across the study region. The RK ZTD achieves a Root Mean Square Error (RMSE) of 5.70 mm, representing improvements of 58.4% and 35.4% compared with the original ERA5 ZTD (13.69 mm) and the GNSS-Kriging ZTD (8.82 mm), respectively. Moreover, the absolute bias is reduced to 0.41 mm, in contrast to 5.15 mm for the ERA5 ZTD, indicating that systematic biases are effectively mitigated. Spatial and seasonal analyses further confirm that the proposed method maintains stable performance across all seasons and significantly alleviates interpolation inaccuracies caused by sparse GNSS stations, even under extreme weather conditions such as Storm Ciarán, proving its value for advanced Earth environmental science applications. Full article

This study assesses how satellite clock products affect Precise Point Positioning (PPP) for GPS, Galileo, and GPS+Galileo. Multi-GNSS data at 30 s were processed for 12 global IGS stations over one week in 2025, with each day split into eight independent three-hour sessions. SP3 clocks (ORB, 5 min) were compared with dedicated CLKs (CLO, 5 s, 30 s, 5 min) across final (FIN), rapid (RAP), and ultra-rapid (ULT; observed/predicted) product lines from multiple analysis centers. Two timing strategies were tested: nearest-epoch sampling (CLOCK0) and linear interpolation (CLOCK1). CLO consistently delivered the lowest 2D/3D errors and the fastest convergence. ORB degraded accuracy by a few millimeters and extended convergence by ~5–10 min, most notably for GPS. With 5 min clocks, CLOCK1 yielded small gains for Galileo but often hurt GPS; with 30 s clocks, interpolation was immaterial; 5 s clocks offered no measurable benefit. FIN outperformed RAP; OPS slightly outperformed MGEX; ESA/GFZ ranked highest. ULT solutions were weaker, especially in the predicted half. Zenith tropospheric delay (ZTD) biases were negligible; variance was smallest for GPS+Galileo with CLO (~7–10 mm), increased by ~1–2 mm with ORB, and was largest in ULT. Dense, high-quality clock products remain essential for reliable PPP. Full article

Precipitable water vapor (PWV) is an important component of atmospheric spatial parameters and plays a vital role in meteorological studies. In this study, PWV retrieval by real-time precise point positioning (PPP) technique is validated by using global navigation satellite system (GNSS) observations and four real-time products from different analysis centers, which are Centre National d’Etudes Spatiales (CNES), Internation GNSS Service (IGS), Japan Aerospace Exploration Agency (JAXA), and Wuhan University (WHU). To comparatively analyze the performance of each scenario, the single-system (GPS/Galileo/BDS3), and multi-system (GPS + Galileo + BDS) PPP techniques are applied for zenith tropospheric delay (ZTD) and PWV retrieval. Then, the ZTD and PWV are evaluated by comparison with the IGS final ZTD product, the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) data, and radiosondes observations provided by the University of Wyoming. Experimental results demonstrate that the root mean squares error (RMS) of ZTD differences from multi-system solutions are below 11 mm with respect to the four-product series and the RMS of PWV differences are below 3.5 mm. As for single-system solution, the IGS real-time products lead to the worst accuracy compared with the other products. Besides the scenario of BDS3 observations with IGS real-time products, the RMS of ZTD differences from the GPS-only and Galileo-only solutions are all less than 15 mm compared to the four-product series, as well as the RMS of PWV differences is under 5 mm, which meets the accuracy requirement for GNSS atmosphere sounding. Full article

The PPP-B2b service of BeiDou-3 enables real-time precise point positioning (RT-PPP) through correction information contained in B2b signals, circumventing the reliance on ground-based network infrastructures. This study comprehensively evaluates the accuracy of PPP-B2b correction parameters and their impact on positioning and tropospheric zenith total delay (ZTD) estimation. The PPP-B2b DCB products exhibit good consistency with the Chinese Academy of Sciences (CAS) reference, with average differences below 1.2 ns and standard deviations within 0.11 ns, indicating comparable performance to CAS products. For BDS-3 satellites, PPP-B2b achieves a radial orbit accuracy of 0.07 m and a clock standard deviation of 0.17 ns, outperforming the Centre National d’Études Spatiales (CNES) real-time products in both aspects. For GPS satellites, the corresponding accuracies are 0.06 m and 0.20 ns. Kinematic PPP experiments using combined GPS and BDS-3 observations yield horizontal and vertical accuracies of 4.3 cm and 2.8 cm, respectively, comparable to CNES results, while the BDS-3-only solution performs better than CNES but is still slightly inferior to the CODE. The ZTD estimation accuracy reaches 1.8 cm for GPS+BDS-3 combinations and 2.3 cm for BDS-3-only cases. Overall, PPP-B2b delivers centimeter-level performance in real-time positioning and ZTD estimation, demonstrating strong potential as an independent, space-based precise service, though further improvement is required for GPS-only applications. Full article

The Zenith Tropospheric Delay (ZTD) is a significant atmospheric error affecting the accuracy of the Global Navigation Satellite System (GNSS). Accurate estimation of the ZTD is essential for enhancing GNSS positioning precision and plays a critical role in meteorological and climate-related applications. To address the limitations of current deep learning models in capturing long-term dependencies in ZTD sequences and overcoming computational inefficiencies, this study proposes SSMB-ZTD—an efficient deep learning model based on an improved selective State Space Model (SSM) architecture. To address the challenge of modeling long-term dependencies, we introduce a joint time and position embedding mechanism, which enhances the model’s ability to learn complex temporal patterns in ZTD data. For improving efficiency, we adopt a lightweight selective SSM structure that enables linear-time modeling and fast inference for long input sequences. To assess the effectiveness of the proposed SSMB-ZTD model, this study employs high-precision Zenith Tropospheric Delay (ZTD) products obtained from 27 IGS stations as reference data. Each model is provided with 72 h of historical ZTD inputs to forecast ZTD values at lead times of 3, 6, 12, 24, 36, and 48 h. The predictive performance of the SSMB-ZTD model is evaluated against several baseline models, including RNN, LSTM, GPT-3, Transformer, and Informer. The results show that SSMB-ZTD consistently outperforms RNN, LSTM, and GPT-3 in all prediction scenarios, with average improvements in RMSE reaching 31.2%, 37.6%, and 48.9%, respectively. In addition, compared with the Transformer and Informer models based on the attention mechanism, the SSMB-ZTD model saves 47.6% and 21.2% of the training time and 38.6% and 30.0% of the prediction time on average. At the same time, the accuracy is better than the two. The experimental results demonstrate that the proposed model achieves high prediction accuracy while maintaining computational efficiency in long-term ZTD forecasting tasks. This work provides a novel and effective solution for high-precision ZTD prediction, contributing significantly to the advancement of GNSS high-precision positioning and the utilization of GNSS-based meteorological information. Full article

To accurately estimate Zenith Tropospheric Delay (ZTD) for high-precision positioning of the Global Navigation Satellite System (GNSS), this study proposes a modeling method of ZTD based on the UNB3m model and Kriging spatial interpolation, in which the optimal spatial interpolation parameters are determined based on the errors corresponding to different combinations of the interpolation parameters, and the spatial distribution of the GNSS modeling stations is determined by the interpolation errors of the randomly selected GNSS stations for several times. To verify the accuracy and reliability of the proposed model, the ZTD estimates of 132,685 epochs with 1 h or 2 h temporal resolution for 28 years from 1997 to 2025 of the global network of continuously operating GNSS tracking stations are used as inputs; the ZTD results at any position and the corresponding observation moment can be obtained with the proposed model. The experimental results show that the model error is less than 30 mm in more than 85% of the observation epochs, the ZTD estimation results are less affected by the horizontal position and height of the GNSS stations than traditional models, and the ZTD interpolation error is improved by 10–40 mm compared to the GPT3 and UNB3m models at the four GNSS checking stations. Therefore, this technology can provide ZTD estimation results for single- and dual-frequency hybrid deformation monitoring, as well as dense ZTD data for Precipitable Water Vapor (PWV) inversion. Since the proposed method has the advantages of simple implementation, high accuracy, high reliability, and ease of promotion, it is expected to be fully applied in other high-precision positioning applications. Full article

BeiDou navigation satellite system (BDS) precise point positioning (PPP)-B2b has significant potential for application in meteorological fields, such as standalone water vapor monitoring in depopulated area without Internet. In this study, the practical ability of water vapor monitoring using the BDS PPP-B2b service is illustrated through a continuously operated water vapor monitoring system in Wuhan, China, with a 25-day experiment in 2025. Original observations from the Global Positioning System (GPS) and BDS are collected and processed in the near real-time (NRT) mode using ephemeris from the PPP-B2b service. Precipitable water vapor PWV monitored with B2b ephemeris are evaluated with radiosonde and ERA5 reanalysis, respectively. Taking PWV from radiosonde observations as the reference, RMS of PWV based on B2b ephemeris varies from 3.71 to 4.66 mm for different satellite combinations. While those values are with a range from 3.95 to 4.55 mm when compared with ERA5 reanalysis. These values are similar to those processed with the real-time ephemeris from the China Academy of Science (CAS). In general, this study demonstrates that the practical accuracy of water vapor monitored based on the BDS PPP-B2b service can meet the basic demand for operational meteorology for the first time. This will provide a scientific reference for its wide promotion to meteorological applications in the near future. Full article

Water vapor plays a crucial role in maintaining global energy balance and water cycle, and it is closely linked to various meteorological disasters. Precipitable water vapor (PWV), as an indicator of variations in atmospheric water vapor content, has become a key parameter for meteorological and climate monitoring. However, due to limitations in observation costs and technology, traditional atmospheric monitoring techniques often struggle to accurately capture the distribution and variations in space–time water vapor. With the continuous advancement of Global Navigation Satellite System (GNSS) technology, ground-based GNSS monitoring technology has shown rapid development momentum in the field of meteorology and is considered an emerging monitoring tool with great potential. Hence, based on the GNSS observation data from July 2023, this study retrieves PWV using the Global Pressure and Temperature 3 (GPT3) model and evaluates its application performance in the “7·31” extremely torrential rain event in Beijing in 2023. Research has found the following: (1) Tropospheric parameters, including the PWV, zenith tropospheric delay (ZTD), and zenith wet delay (ZWD), exhibit high consistency and are significantly affected by weather conditions, particularly exhibiting an increasing-then-decreasing trend during rainfall events. (2) Through comparisons with the PWV values through the integration based on fifth-generation European Centre for Medium-Range Weather Forecasts (ERA-5) reanalysis data, it was found that results obtained using the GPT3 model exhibit high accuracy, with GNSS PWV achieving a standard deviation (STD) of 0.795 mm and a root mean square error (RMSE) of 3.886 mm. (3) During the rainfall period, GNSS PWV remains at a high level (>50 mm), and a strong correlation exists between GNSS PWV and peak hourly precipitation. Furthermore, PWV demonstrates the highest relative contribution in predicting extreme precipitation, highlighting its potential value for monitoring and predicting rainfall events. Full article

The performance of Precise Point Positioning (PPP) using different Global Navigation Satellite System (GNSS) product sets, including broadcast ephemerides, International GNSS Service Real-Time Service (IGS-RTS) corrections, Galileo High Accuracy Service (HAS) corrections, and precise products from the Center for Orbit Determination in Europe (CODE) Multi-GNSS Experiment (MGEX), has been evaluated. The availability of solutions, convergence time, position accuracy and Zenith Tropospheric Delay (ZTD) estimation across these products were analyzed using simulated real-time and postprocessing static modes, using data from globally distributed stations with a 1 s observation interval. The results indicate that precise products from the MGEX provide the highest accuracy, achieving centimeter-level precision in post-processed mode. Real-time simulated solutions, such as HAS and IGS-RTS, deliver promising results, with Galileo HAS meeting its target accuracy of 20 cm horizontally and 40 cm vertically and a convergence time under 5 min. However, Global Positioning System (GPS) performance within HAS is limited by a significantly lower correction availability—around 67% on average compared to over 95% for Galileo—which negatively impacts PPP performance. ZTD estimation results show that real-time services (HAS, IGS-RTS) achieved errors within 1–3 cm, sufficient for meteorological applications. This study highlights the growing importance of HAS in real-time positioning applications and suggests further improvements in GPS for enhanced performance. Full article

Tropospheric delay is the main error source that affects the further improvement of the accuracy of space geodesy. High-precision zenith tropospheric delay (ZTD) can be used as a prior value for precise point positioning (PPP) in global navigation satellite systems (GNSSs) to enhance the speed and accuracy of real-time PPP solutions. Using the Saastamoinen ZTD model, we computed ZTDs using different meteorological elements. One ZTD was termed MZTD and was obtained from 80 reference sites in the China Mainland Crustal Movement Observation Network (CMONOC), the other was termed HZTD and was obtained from elements acquired from the improved version of the hourly global pressure and temperature atmospheric model (HGPT2). The results indicate that the accuracy of the MZTD was 12.94% higher than that of the HZTD, with the ZTDs estimated by post-processing GNSS values as the reference values. Additionally, the MZTD and HZTD were both applied as constraints to the PPP solution. The application of the MZTD constraints to the PPP floating-point solution resulted in a 28.9% improvement in accuracy and a 36.4% decrease in convergence time in the U-direction as a maximum, compared with the application of the HZTD constraints. Full article

Zenith Tropospheric Delay (ZTD) is a significant source of atmospheric error in the Global Navigation Satellite System (GNSS). Developing a high-accuracy ZTD prediction model is essential for both GNSS positioning and GNSS meteorology. To address the challenges of incomplete information extraction and gradient explosion present in current single and combined neural network models that utilize serial ensemble learning, this study proposes a VMD-Informer-BiLSTM-EAA hybrid model based on a parallel ensemble learning strategy. Additionally, it takes into account the non-stationarity of the ZTD sequence. The model employs the Variational Mode Decomposition (VMD) method to address the non-stationarity of ZTD. It utilizes both the informer and Bidirectional Long Short-Term Memory (BiLSTM) architectures to learn ZTD data in parallel, effectively capturing both long-term trends and short-term dynamic changes. The features are then fused using the Efficient Additive Attention (EAA) mechanism, which assigns weights to create a more comprehensive representation of the ZTD data. This enhanced representation ultimately leads to improved predictions of ZTD values. We fill in the missing parts of the GNSS-derived ZTD using the ZTD data from ERA5, sourced from the IGS stations in the Australian region, specifically at 12 IGS stations. These interpolated data are then used to develop a VMD-Informer-BiLSTM-EAA hybrid model for ZTD predictions with a one-year forecast horizon. We applied this model to predict the ZTD for each IGS station in our study area for the year 2021. The numerical results indicate that our model outperforms several comparative models, such as VMD–Informer, Transformer, BiLSTM and GPT3, based on the following key metrics: a Root Mean Square Error (RMSE) of 1.43 cm, a Mean Absolute Error (MAE) of 1.15 cm, a Standard Deviation (STD) of 1.33 cm and a correlation coefficient (R) of 0.96. Furthermore, our model reduces the training time by 8.2% compared to the Transformer model, demonstrating superior prediction performance and robustness in long-term ZTD forecasting. This study introduces a novel approach for high-accuracy ZTD modeling, which is significantly beneficial for precise GNSS positioning and the detection of water vapor content. Full article

Zenith tropospheric delay (ZTD) is a significant atmospheric error that impacts the Global Navigation Satellite System (GNSS). Developing a high-precision, long-term forecasting model for ZTD can provide valuable insights into the overall trends of predicted ZTD, which is essential for improving GNSS positioning and analyzing changes in regional climate and water vapor. To address the challenges of incomplete information extraction and gradient explosion in a single neural network when forecasting ZTD long-term, this study introduces an Informer–LSTM Hybrid Prediction Model. This model employs a parallel ensemble learning strategy that combines the strengths of both the Informer and LSTM networks to extract features from ZTD data. The Informer model is effective at capturing the periodicity and long-term trends within the ZTD data, while the LSTM model excels at understanding short-term dependencies and dynamic changes. By merging the features extracted by both models, the prediction capabilities of each can complement one another, allowing for a more comprehensive analysis of the characteristics present in ZTD data. In our research, we utilized ERA5-derived ZTD data from 11 International GNSS Service (IGS) stations in Europe to interpolate the missing portions of GNSS-derived ZTD. We then employed this interpolated data from 2016 to 2020, along with an Informer–LSTM Hybrid Prediction Model, to develop a long-term prediction model for ZTD with a prediction duration of one year. Our numerical results demonstrate that the proposed model outperforms several comparative models, including the LSTM–Informer based on a serial ensemble learning model, as well as the Informer, Transformer, LSTM, and GPT3 empirical ZTD models. The performance metrics indicate a root mean square error (RMSE) of 1.91 cm, a mean absolute error (MAE) of 1.45 cm, a mean absolute percentage error (MAPE) of 0.60, and a correlation coefficient (R) of 0.916. Spatial distribution analysis of the accuracy metrics showed that predictive accuracy was higher in high-latitude regions compared to low-latitude areas, with inland regions demonstrating better performance than those near the ocean. This study introduced a novel methodology for high-precision ZTD modeling, which is significant for improving accurate GNSS positioning and detecting water vapor content. Full article

Utilizing real-time precise point positioning (PPP) technology is an effective approach for obtaining high-precision zenith tropospheric delay (ZTD). Without relying on the terrestrial internet, Galileo high accuracy service (HAS) can provide precise orbit and precise clock products for the world. A thorough assessment of the ZTD accuracy of real-time PPP calculations based on Galileo HAS products in global regions is necessary to promote its application in the field of global navigation satellite system (GNSS) meteorology. The observation data of HAS from 1 to 7 September 2023 were selected for the experiment. Firstly, the accuracy of satellite orbit and clock products of the HAS GPS and HAS Galileo system are evaluated. Then, real-time PPP positioning accuracy within and outside the HAS service area is analyzed. Finally, 104 IGS stations in the world are selected to analyze the ZTD accuracy of real-time PPP calculations based on Galileo HAS products. The experimental results show that during the test period, the RMSE values of the satellite orbit products of the HAS GPS in the radial, along, and cross directions were 4.57 cm, 10.62 cm, and 7.56 cm, respectively. The HAS Galileo RMSE values were 2.81 cm, 8.02 cm, and 7.47 cm, respectively. The RMSE values of the clock products were 0.38 ns and 0.15 ns, respectively. At the selected stations, the real-time PPP positioning accuracies outside the HAS service area and within the service area were similar, and the correlation coefficient between HAS ZTD and IGS ZTD was above 0.90. In the global region, the average bias and RMSE values of the real-time PPP ZTD of the HAS GPS were −0.31 mm and 16.78 mm. Those of the HAS Galileo were 2.30 mm and 15.89 mm, and those of the HAS GPS/Galileo were −0.25 mm and 16.11 mm, respectively. Moreover, each system showed that the accuracy of the HAS ZTD inside the service area was better than that outside the service area. Compared with the single system, the real-time PPP ZTD continuity and stability of the dual system were better. Full article