Global Navigation Satellite System Research Articles

A Composite Fault Model for the 2024 MW 7.4 Hualien Earthquake Sequence in Eastern Taiwan Inferred From GNSS and InSAR Data

AbstractOn 2 April 2024, an MW 7.4 earthquake struck the northern Longitudinal Valley in eastern Taiwan, about 18 km SSW of Hualien, causing damage and casualties. In this study, we investigated a comprehensive geodetic data set, employing Global Navigation Satellite Systems (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) measurements to assess the rupture geometry associated with earthquake sequence. Although geodetic data can be satisfactorily reproduced by simple single‐fault models (i.e., a high‐angle E‐dipping plane related to the Longitudinal Valley Fault (LVF), or a gentle W‐dipping surface associated with the Central Range Fault, CRF), a composite model involving the rupture of different fault segments (a major CRF‐related W‐dipping fault, a deep segment of the E‐dipping LVF, and the Milun Fault) is able to explain the observations, the distribution of seismicity, and the complex structural arrangement of the northernmost sector of the Longitudinal Valley.

Predicting Athlete Workload in Women's Rugby Sevens Using GNSS Sensor Data, Contact Count and Mass.

The use of session rating of perceived exertion (sRPE) as a measure of workload is a popular athlete load monitoring tool. However, the nature of sRPE means the contribution of salient, sport-specific factors to athlete load in field sports is challenging to isolate and quantify. In rugby sevens, drivers of load include high-speed running and physical contact. In soccer and men's rugby, union acceleration/deceleration also influences load. These metrics are evaluated using data from global navigation satellite system (GNSS) sensors worn by athletes. Research suggests that sensor data methods for identifying load in men's rugby do not accurately quantify female athlete loads. This investigation examined how mass, contact, and accelerations and decelerations at different speeds contribute to load in women's rugby sevens. The study evaluated 99 international matches, using data from 19 full-time athletes. GNSS measures, RPE, athlete mass, and contact count were evaluated using a linear mixed-model regression. The model demonstrated significant effects for low decelerations at low and high speeds, mass, distance, and contact count explaining 48.7% of the global variance of sRPE. The use of acceleration/deceleration and speed from GNSS sensors alongside mass, as well as contact count, presents a novel approach to quantifying load.

The Accuracy of RTK enabled Mobile Phones in RTK denied Areas

Abstract. Surveyors often encounter challenges when tasked with measuring points in regions where buildings disrupt satellite visibility. The precise surveying of points in these areas typically relies on employing total stations. This method effectively extends high precision from unaffected zones (where satellite visibility is assured) to those areas where disruption occurs due to buildings. Total stations achieve this by executing distance and angle measurements from a reference point coordinate to the location where satellite visibility is compromised. The process is notably time-consuming, thereby incurring significant costs. Moreover, the intricate nature of this surveying process necessitates specialized skills and expertise, contributing further to the overall expense. In this study, we investigate an approach based on RTK (Real-Time Kinematic) enabled mobile phones and photogrammetry to achieve the same. In principle, this approach has a similar philosophy. However, instead of working with a few points with good satellite visibility that are obtained by a GNSS (Global Navigation Satellite System) rover, the procedure works with hundreds of observations with varying accuracy. Those accuracies depend on the satellite visibility. Each observation captures an image from the mobile phone together with the GNSS signal and its accuracy. Angle and distance measurements that traditionally are observed by a total station are retrieved by photogrammetry on the total image collection.

CY GNSS significant wave height inversion model based on multivariate machine learning

The Cyclone Global Navigation Satellite System (CYGNSS) provides high-quality Global Navigation Satellite System Reflectometry (GNSS-R) data, which can be reliably used for the inversion of Significant Wave Height (SWH). Due to the high dynamics of CYGNSS, the received signal is easily affected by environmental factors, and the complexity of the sea conditions makes it difficult for simple models to accurately invert SWH. In order to solve the above problems, this paper proposes a multivariate SWH inversion model based on machine learning. According to the formation mechanism of waves and the correlation analysis between CYGNSS parameters and SWH, relevant parameters are selected, and three training schemes of 5 parameters, 9 parameters and 17 parameters are designed. Subsequently, the inversion model was trained and validated using Random Forest (RF) and Convolutional Neural Network (CNN), and the SWH inversion results were compared with the reference values of the European Centre for Medium-range Weather Forecasts (ECMWF). The best inversion model was the 17-parameter CNN inversion model with an RMSE of = 0.1840 m.

Machine Learning-Based Soil Moisture Retrieval Using CYGNSS and Interpolated SMAP Data

Abstract. Soil moisture is a crucial component of the global terrestrial ecosystem water vapor cycle, and higher spatial-temporal soil moisture product has significant impacts on research in agriculture, hydrology, and ecology. Spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) is a new remote sensing technology which can be used to retrieve soil moisture. Cyclone Global Navigation Satellite System (CYGNSS), launched by NASA in 2016 to observe ocean surface hurricanes, has also collected a substantial amount of data of GNSS signals reflected over the land. This paper focuses on soil moisture retrieval using CYGNSS and SMAP dataset. In this study, three machine learning methods (GSVM, BP and RF) are used for spatial interpolation of SMAP soil moisture data. Result shows RF interpolation is the best with the RMSE of 0.044 cm3/cm3 and the CC of 0.959 compared with SMAP truly SM. Then soil moisture data after RF interpolation and conventional linear interpolation are respectively used as response variables to train the retrieval model by ELM, BP and RF machine learning methods respectively. Results show that, among the six regression models, the RF-RF regression model performs the best with the RMSE of 0.012 cm3/cm3 and the CC of 0.986. Using this model, we get a global soil moisture product and have higher temporal and spatial resolution.

An Efficient Attentive-GRU Structure for Uncertainty Modelling of Crowdsourced Human Trajectories Under Building-obscured Urban Scenes

Abstract. Uncertainty modelling is regarded as one of the core components in the field of human mobility analysis and urban navigation, that can affect the performance of human behaviour modelling and location information acquisition. Existing uncertainty modelling algorithms towards the human movement trajectory are subjected to random and highly dynamic human motion characteristics and sampling and observation errors of Global Navigation Satellite System (GNSS) signals caused by the occlusion of buildings in urban scenes, which lead to the insufficient spatiotemporal correlation and poor accuracy of uncertainty modelling. To fill in this gap, this paper proposes an efficient attentive-GRU structure for uncertainty modelling of crowdsourced human trajectories under building-obscured urban scenes, that takes into account both temporal correlation and spatial correlation of human-originated GNSS trajectories and related motion features. A period of human motion data is modelled instead of only one or adjacent location points to avoid interference factors caused by the obstruction of urban buildings, and time-varying measurement and sampling errors are further estimated and combined with comprehensive human motion features to improve the accuracy of final uncertainty modelling. Comprehensive experiments indicate that compared with existing uncertainty modelling methods including physical models and deep-learning models, the proposed attentive-GRU structure realizes much better performance under different accuracy indexes.

Unexpected far-field deformation of the 2023 Kahramanmaraş earthquakes revealed by space geodesy.

The spatiotemporal pattern of surface displacements from large earthquakes provides crucial insights about the deformation of Earth's crust at various scales and the interactions among tectonic plates. However, the lack of extensive and large-scale geodetic networks near such seismic events hinders our thorough understanding of the large-scale crustal deformation resulting from earthquakes. Using Türkiye's extensive and continuous global navigation satellite system (GNSS) network during the moment magnitude 7.8 and 7.6 Kahramanmaraş earthquakes on 6 February 2023, we show that large earthquakes can induce far-field crustal deformations (>700 kilometers), exceeding current predictions from elastic dislocation models. They can lead to the mobilization of tectonic plates and the triggering of far-field earthquakes, which carries profound implications for seismic hazard assessments and necessitates a new perspective on crustal deformation and earthquake mechanics.

The Zenith Total Delay Combination of International GNSS Service Repro3 and the Analysis of Its Precision

Currently, ground-based global navigation satellite system (GNSS) techniques have become widely recognized as a reliable and effective tool for atmospheric monitoring, enabling the retrieval of zenith total delay (ZTD) and precipitable water vapor (PWV) for meteorological and climate research. The International GNSS Service analysis centers (ACs) have initiated their third reprocessing campaign, known as IGS Repro3. In this campaign, six ACs conducted a homogeneous reprocessing of the ZTD time series spanning the period from 1994 to 2022. This paper primarily focuses on ZTD products. First, the data processing strategies and station conditions of six ACs were compared and analyzed. Then, formal errors within the data were examined, followed by the implementation of quality control processes. Second, a combination method is proposed and applied to generate the final ZTD products. The resulting combined series was compared with the time series submitted by the six ACs, revealing a mean bias of 0.03 mm and a mean root mean square value of 3.02 mm. Finally, the time series submitted by the six ACs and the combined series were compared with VLBI data, radiosonde data, and ERA5 data. In comparison, the combined solution performs better than most individual analysis centers, demonstrating higher quality. Therefore, the advanced method proposed in this study and the generated high-quality dataset have considerable implications for further advancing GNSS atmospheric sensing and offer valuable insights for climate modeling and prediction.

GNSS-assisted optimal alignment method for low-cost SINS motion of vehicle

Abstract To improve the alignment accuracy and environmental applicability of the micro-electromechanical system (MEMS)-based strapdown inertial navigation system (SINS), this study proposes a global navigation satellite system (GNSS)-assisted multi-vector determination of the attitude optimal indirect coarse alignment. Using the inertial information output from the inertial measurement unit and the velocity information from the GNSS, a simplified velocity observation vector is constructed and the velocity lever arm stemming from the mounting position inconsistencies of the GNSS and SINS is fed back into the velocity of the carrier system. When constructing the observation vectors, the integration interval is shortened by reconstructing the two-vector integration formula for reducing the cumulative error of the inertial device. The attitude matrix problem is defined as the Wahba problem, which is solved using the singular value decomposition method. Based on the relationship between gyro zero bias and misalignment angle, the corresponding state and measurement equations are designed. Furthermore, owing to the measurement noise uncertainty, the adaptive traceless Kalman filtering algorithm is introduced to realize the effective adaptation processing of the measurement noise. More accurate attitude matrix estimates are obtained by continuously correcting the carrier system transformation matrix. The running car experiment results show that the proposed method exhibits higher alignment accuracy and environmental applicability than the current MEMS strapdown inertial navigation coarse alignment method and the traditional optimization-based alignment method.

Field-road classification for agricultural vehicles in China based on pre-trained visual model

Field-road classification that automatically identifies the activity (either in-field or on-road) of each point in Global Navigation Satellite System (GNSS) trajectories is a critical process in the behavior analysis of agricultural vehicles. To capture movement patterns specific to agricultural operations, we propose a multi-view field-road classification method, which extracts a physical and a visual feature vector to represent a trajectory point. We propose a task-specific approach using a pre-trained visual model to effectively extract visual features. Firstly, an image is generated based on a point plus its neighboring points to provide the contextual information of the point. Then, an image recognition model, a fine-tuned ResNet model is developed using the pretraining-finetuning paradigm. In such a paradigm, a pre-training process is used to train an image recognition model (ResNet) with natural image datasets (e.g., ImageNet), and a fine-tuning process is applied to update the parameters of the pre-trained model using the trajectory point images, enabling the model to have both general knowledge and task-specific knowledge. Finally, a visual feature is extracted for a point by the fine-tuned model, thereby overcoming the limitations caused by the small-scale generated images. To validate the effectiveness of our multi-view field-road classification, we conducted experiments on four trajectory datasets (Wheat 2021, Paddy, Wheat 2023, and Wheat 2024). The results demonstrated that the proposed method achieves competitive accuracy performance, i.e., 92.56%, 87.91%, 90.31%, and 94.23% on four trajectory datasets, respectively. Extensive experiments demonstrate that our approach can consistently perform better than the existing state-of-the-art method on the four trajectory datasets by 2.99%, 4.42%, 2.88%, and 2.77% in the F1-score, respectively. In addition, we conduct an in-depth analysis to verify the necessity and effectiveness of our method.

Assessing the Adequacy of Earthquake Catalog Sampling for Long-Term Seismicity in Low-to-Moderate Seismic Regions: A Geodetic Perspective

Abstract Seismic hazard assessment in low-to-moderate seismicity regions can benefit from the knowledge of surface deformation rates to better constrain earthquake recurrence models. This, however, amounts to assuming that the known seismicity rate, generally observed over historical times (i.e., up to a few centuries in Europe), provides a representative sample of the underlying long-term activity. We here investigate how this limited sampling can affect the estimated seismic hazard and whether it can explain the disagreement between the seismic moment loading rate as seen by nowadays Global Navigation Satellite Systems (GNSS) measurements and the seismic moment release rate by past earthquakes, as is sometimes observed in regions with limited activity. We approach this issue by running simulations of earthquake time series over very long timescales that account for temporal clustering and the known magnitude–frequency distribution in such regions, and that those are constrained to a seismic moment rate balance between geodetic and seismicity estimates at very long timescales. We show that, in the example of southeastern Switzerland, taken here as a case study, this sampling issue can indeed explain this disagreement, although it is likely that other phenomena, including aseismic deformation and changes in strain rate due to erosional and/or glacial rebound, may also play a significant role in this mismatch.

A New Scene Sensing Model Based on Multi-Source Data from Smartphones

Smartphones with integrated sensors play an important role in people’s lives, and in advanced multi-sensor fusion navigation systems, the use of individual sensor information is crucial. Because of the different environments, the weights of the sensors will be different, which will also affect the method and results of multi-source fusion positioning. Based on the multi-source data from smartphone sensors, this study explores five types of information—Global Navigation Satellite System (GNSS), Inertial Measurement Units (IMUs), cellular networks, optical sensors, and Wi-Fi sensors—characterizing the temporal, spatial, and mathematical statistical features of the data, and it constructs a multi-scale, multi-window, and context-connected scene sensing model to accurately detect the environmental scene in indoor, semi-indoor, outdoor, and semi-outdoor spaces, thus providing a good basis for multi-sensor positioning in a multi-sensor navigation system. Detecting environmental scenes provides an environmental positioning basis for multi-sensor fusion localization. This model is divided into four main parts: multi-sensor-based data mining, a multi-scale convolutional neural network (CNN), a bidirectional long short-term memory (BiLSTM) network combined with contextual information, and a meta-heuristic optimization algorithm.

Construction of global IGS-3D electron density (Ne) model by deep learning

In this study, we construct a global IGS-3D Ne model that generates global 3-D electron density (Ne) from International Global Navigation Satellite Systems (GNSS) Service (IGS) total electron content (TEC) data through deep learning. As a first step towards this, we make a model to generate a vertical electron density profile from a TEC value using Multi-Layer Perceptron (MLP). In this process, we use the vertical electron density profiles and the corresponding TEC values of the IRI-2016 model from 2001 to 2008 for training, 2009 and 2014 for validation, and 2010 to 2013 for a test. The next step is to generate global IGS electron density profiles using the global IGS TECs as input data for the model, which is called the global IGS-3D Ne model. We evaluate the IGS-3D Ne model by comparing the electron density profiles from the incoherent scatter radars (ISRs) at three stations with the IGS-3D Ne model from 2010 to 2013. The evaluation shows that the electron density profiles from the IGS-3D Ne model are closer to the ISR data than those of the IRI model, especially at high latitudes. The IGS-3D Ne model shows that the averaged root mean square error (RMSE) values between IGS and ISR electron density profiles are 0.37 log(m−3), 0.22 log(m−3), and 0.34 log(m−3) for all test datasets at Jicamarca, Millstone Hill, and EISCAT stations, respectively. These results suggest that our method has sufficient potential to enhance the ability to predict global electron density profiles.

Evaluation of GOCE/GRACE and combined global geopotential models using GNSS/levelling data over Nigeria

AbstractGlobal Geopotential Models (GGMs) provide valuable information about Earth’s gravity field functionals, such as geoid heights and gravity anomalies. However, ground-based datasets are required to validate these GGMs at the regional and local scales. In this study, we validated the accuracy of GGMs by comparing them with ground-based Global Navigation Satellite System (GNSS)/levelling data for the first time in Nigeria. We employed two validation scenarios: with and without considering spectral consistency using the spectral enhancement method (SEM) to incorporate high and very high frequencies of the gravity field spectrum from the combined global gravity field model (XGM2019e_2159) and the residual terrain model (RTM) derived from the Shuttle Radar Topography Mission (SRTM) data, respectively. The results of this evaluation confirmed that the application of SEM improved the assessment of the GGM solutions in an unbiased manner. Integrating XGM2019e_2159 and SRTM data to constrain the high-frequency component of geoid heights in Gravity Field and Steady-State Ocean Circulation Explorer (GOCE)-based GGMs led to an improvement of approximately 10% in reducing the standard deviation (STD) relative to when SEM was not applied. GO_CONS_GCF_2_TIM_R6 at spherical harmonics (SH) of up to degree and order 260 demonstrated the lowest STD when compared to GO_CONS_GCF_2_DIR_R6 and GO_CONS_GCF_2_SPW_R5, with a reduction from 0.380 m without SEM application to 0.342 m with SEM implementation. In addition, four transformation models, namely, linear, four-parameter, five-parameter, and seven-parameter models, were evaluated. The objective is to mitigate the reference system offsets between the GNSS/levelling data and the GGMs and to identify the particular parametric model with the smallest STD across all GGMs. This effort reduced the GGMs misfits to GNSS/levelling to 0.30 m, representing a 15.3% decrease in STD. Notably, the XGM2019e_2159 model provides this improvement.

Monitoring terrestrial water storage changes using GNSS vertical coordinate time series in Amazon River basin

Aiming at the Terrestrial Water Storage(TWS) changes in the Amazon River basin, this article uses the coordinate time series data of the Global Navigation Satellite System (GNSS), adopts the Variational Mode Decomposition and Bidirectional Long and Short Term Memory(VMD-BiLSTM) method to extract the vertical crustal deformation series, and then adopts the Principal Component Analysis(PCA) method to invert the changes of terrestrial water storage in the Amazon Basin from July 15, 2012 to July 25, 2018. Then, the GNSS inversion results were compared with the equivalent water height retrieved from Gravity Recovery and Climate Experiment (GRACE) data. The results show that (1) the extraction method proposed in this article has better denoising effect than the traditional method; (2) the surface hydrological load deformation can be well calculated using GNSS coordinate vertical time series, and then the regional TWS changes can be inverted, which has a good consistency with the result of GRACE inversion of water storage, and has almost the same seasonal variation characteristics; (3) There is a strong correlation between TWS changes retrieved by GNSS based on surface deformation characteristics and water mass changes calculated by GRACE based on gravitational field changes, but GNSS satellite’s all-weather measurement results in a finer time scale compared with GRACE inversion results. In summary, GNSS can be used as a supplementary technology for monitoring terrestrial water storage changes, and can complement the advantages of GRACE technology.

Low-degree gravity field coefficients based on inverse GNSS method: insights into hydrological and ice mass change studies

The relative displacements of stations from a global network of Global Navigation Satellite System (GNSS) sites provide information on global mass transport. In this study, we use 19 years of global GNSS station displacements from the 3rd International GNSS Service reprocessing campaign to estimate the coefficients of the spherical harmonics of the Earth’s gravity field up to degree and order 8 using the inverse GNSS method based on elastic loading theory. The results indicate that the C30 coefficient can be derived based on GNSS station displacements as an alternative to solutions provided by Satellite Laser Ranging (SLR) and Gravity Recovery and Climate Experiment (GRACE). GNSS may support GRACE solutions that face the problems of deriving C30, which has fundamental meaning in estimating ice mass changes in polar regions. The recovery of Antarctic ice sheet mass change from January 2007 to December 2020 based on coefficients replaced by GNSS estimates results in a linear trend of − 152 ± 4 Gt/year, in comparison to − 149 ± 2 Gt/year for the replacement based on SLR from GRACE Technical Note #14. The results indicate that the spatial and seasonal patterns of terrestrial water storage changes derived from GNSS are consistent with those estimated using GRACE/GRACE Follow-On and SLR at a few-millimeter level in the Amazon and Brahmaputra River basin regions.

Power or speed: Which metric is more accurate for modelling endurance running performance on track?

This study aimed to compare the accuracy of the power output, measured by a power meter, with respect to the speed, measured by an inertial measurement unit (IMU) and a global navigation satellite system (GNSS) sport watch to determine the critical power (CP) and speed (CS), work over CP (W') and CS (D'), and long-duration performance (i.e., 60 min). Fifteen highly trained athletes randomly performed seven time trials on a 400m track. The CP/CS and W'/D' were defined through the inverse of time model using the 3, 4, 5, 10, and 20 min trials. The 60 min performance was estimated through the power law model using the 1, 3, and 10 min trials and compared with the actual performance. A lower standard error of the estimate was obtained when using the power meter (CP: 2.7 [2.1-3.3] % and W': 13.8 [10.4-17.3] %) compared to the speed reported by the IMU (CS: 3.4 [2.5-4.3] %) and D': 20.7 [16.6-24.7] %) and GNSS sport watch (CS: 3.4 [2.5-4.3] % and D': 20.6 [16.7-24.7] %). A lower coefficient of variation was also observed for the power meter (4.9 [3.7-6.1] %) Regarding the speed reported by the IMU (10.9 [7.1-14.8] %) and GNSS sport watch (10.9 [7.0-14.7] %) in the 60 min performance estimation, the power meter offered lower errors than the IMU and GNSS sport watch for modelling endurance performance on the track.

GNSS/IMU integrated navigation heading angle enhancement algorithm based on dual-antenna TDCP

In the integrated navigation system of Global Navigation Satellite System (GNSS) and Inertial Measurement Unit (IMU), attitude estimation, especially accurate estimation of heading angle, is particularly important for real-time monitoring of vehicle driving status. However, since IMU is divergent in the altitude channel, its error will gradually accumulate if it is not accurately constrained. Therefore, the estimation accuracy of heading angle is insufficient in vehicle-mounted applications where the heading angle changes frequently. In order to solve the problem of poor navigation attitude estimation accuracy in the loose combination of traditional GNSS and IMU, this paper proposes a GNSS/IMU integrated navigation heading angle enhancement algorithm based on dual-antenna epoch carrier phase difference (TDCP). This method solves the vehicle heading angle through dual-antenna TDCP to increase the input dimension of the integrated navigation filter fusion observation value, and uses Hatch filtering and anti-error adaptive filtering to improve the observation domain pseudorange accuracy and GNSS/IMU integrated navigation positioning and attitude determination performance respectively. Experimental results show that compared with the traditional GNSS/IMU integrated navigation method, the proposed algorithm improves the positioning and speed measurement accuracy in the three-dimensional direction by and respectively 22.12%, 41.27%and the vehicle heading angle accuracy is improved 46.29%.

Assessment of FY-3E GNOS II Radio Occultation Data Using an Improved Three-Cornered Hat Method

The spatial–temporal sampling errors arising from the differences in geographical locations and measurement times between co-located Global Navigation Satellite System (GNSS) radio occultation (RO) and radiosonde (RS) data represent systematic errors in the three-cornered hat (3CH) method. In this study, we propose a novel spatial–temporal sampling correction method to mitigate the sampling errors associated with both RO–RS and RS–model pairs. We analyze the 3CH processing chain with this new correction method in comparison to traditional approaches, utilizing Fengyun-3E (FY-3E) GNSS Occultation Sounder II (GNOS II) RO data, atmospheric models, and RS datasets from the Hailar and Xisha stations. Overall, the results demonstrate that the improved 3CH method performs better in terms of spatial–temporal sampling errors and the variances of atmospheric parameters, including refractivity, temperature, and specific humidity. Subsequently, we assess the error variances of the FY-3E GNOS II RO, RS and model atmospheric parameters in China, in particular the northern China and southern China regions, based on large ensemble datasets using the improved 3CH data processing chain. The results indicate that the FY-3E GNOS II BeiDou navigation satellite system (BDS) RO and Global Positioning System (GPS) RO show good consistency, with the average error variances of refractivity, temperature, and specific humidity being less than 1.12%2, 0.13%2, and 700%2, respectively. A comparison of the datasets from northern and southern China reveals that the error variances for refractivity are smaller in northern China, while temperature and specific humidity exhibit smaller error variances in southern China, which is attributable to the differing climatic conditions.

Assessment and Validation of Small-Scale Tropospheric Delay Estimations Based on NWP Data

This paper investigates the applicability of the Numerical Weather Prediction (NWP) data for characterizing the gradient of zenith wet delay in horizontal direction observed on short baselines over larger territories. A three-year period of data for an area covering Scandinavia and Finland is analyzed, and maximum gradients during the considered period are identified. To assess the quality of the NWP-based estimates, results for a smaller region are compared with the estimates obtained using Global Navigation Satellite System (GNSS) measurements processed by the GipsyX/RTGx software package (version 2.1) from a cluster of GNSS reference stations. Additionally, the NWP data from 7 to 9 August 2023 covering a period that includes a storm with high rain intensities over Southern Norway leading to sustained flooding are processed and analyzed to assess if the gradient of zenith wet delay in the horizontal direction increases significantly during such events. The results show that maximum gradients in the range of 40–50 mm/km are detected. When comparing NWP-based estimates to GNSS-based estimates, the tropospheric delays show a very strong correlation. The tropospheric gradients, however, show a weak correlation, probably due to the uncertainty in the NWP data exceeding the gradient values. The data captured during the storm show that while the tropospheric delay increases significantly it is difficult to see increases in the gradient of zenith wet delay in the horizontal direction using this data source and resolution.