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The estimation of the wet refractivity indices is crucial for applications like weather predictions or improving the accuracy of real‐time positioning techniques. Traditionally, solving the inverse tomography problem to estimate these atmospheric parameters has been challenging due to its ill‐posed nature and high computational demands, necessitating additional constraints. To overcome these challenges, the data assimilation method is proposed here to integrate Global Navigation Satellite System (GNSS) observations into a background model. In this study, the Ensemble Kalman Filter (EnKF) was served as the assimilation core to reduce the computational load and to enable the epoch‐wise estimation of wet refractivity indices. The Global Pressure and Temperature 3 (GPT3w) model was utilized as the background, and wet refractivity indices at each epoch were transformed into B‐spline coefficients, representing state vector parameters. Subsequently, GNSS derived zenith wet delay (ZWD) values were integrated into the model using the EnKF method. The study's region encompassed the western parts of Europe and incorporated approximately 893 GNSS stations. Evaluation spanned from 1 January 2017 to 31 December 2017. The estimated wet refractivity indices from the proposed method were compared with observations from 16 existing radiosonde stations, radio occultation data, and ZWD values from the 47 selected GNSS test stations. Additionally, calculated ZWD values, resulting from the integration of wet refractivity indices, were compared to the ZWD values from 47 test stations in the study region. The numerical results demonstrated that the proposed method achieved a root mean square error value of approximately 2.6 ppm, which was nearly 49% and 18% lower than that of the considered empirical and numerical atmospheric models, respectively. Plain Language Summary: Wet refractivity indices measure the amount of water vapor in the atmosphere, which are important for weather forecasting and the accuracy of satellite‐based positioning. Water vapor can affect how signals travel through the atmosphere, influencing weather predictions and positioning systems. Traditional methods to estimate these indices are often slow and complex. In this study, we introduced a data assimilation method to improve the efficiency and accuracy of these estimates. By integrating real‐time satellite observations with a background atmospheric model, we could quickly update the estimates of wet refractivity indices. We tested this method in western Europe using data from 893 Global Navigation Satellite System stations over 1 year. Our new approach significantly reduced errors, showing a major improvement in estimating wet refractivity indices compared to the considered numerical atmospheric model. Key Points: 3D distribution of wet refractivity indices has been estimated using an Ensemble‐based methodThe GPT3w model serves as the background model, and the assimilation of Global Navigation Satellite System zenith wet delay measurements has been conductedThe results show the superior performance of the proposed method compared to the considered empirical and numerical atmospheric models [ABSTRACT FROM AUTHOR]

Abstract The estimation of the wet refractivity indices is crucial for applications like weather predictions or improving the accuracy of real‐time positioning techniques. Traditionally, solving the inverse tomography problem to estimate these atmospheric parameters has been challenging due to its ill‐posed nature and high computational demands, necessitating additional constraints. To overcome these challenges, the data assimilation method is proposed here to integrate Global Navigation Satellite System (GNSS) observations into a background model. In this study, the Ensemble Kalman Filter (EnKF) was served as the assimilation core to reduce the computational load and to enable the epoch‐wise estimation of wet refractivity indices. The Global Pressure and Temperature 3 (GPT3w) model was utilized as the background, and wet refractivity indices at each epoch were transformed into B‐spline coefficients, representing state vector parameters. Subsequently, GNSS derived zenith wet delay (ZWD) values were integrated into the model using the EnKF method. The study's region encompassed the western parts of Europe and incorporated approximately 893 GNSS stations. Evaluation spanned from 1 January 2017 to 31 December 2017. The estimated wet refractivity indices from the proposed method were compared with observations from 16 existing radiosonde stations, radio occultation data, and ZWD values from the 47 selected GNSS test stations. Additionally, calculated ZWD values, resulting from the integration of wet refractivity indices, were compared to the ZWD values from 47 test stations in the study region. The numerical results demonstrated that the proposed method achieved a root mean square error value of approximately 2.6 ppm, which was nearly 49% and 18% lower than that of the considered empirical and numerical atmospheric models, respectively.

Tropospheric delay constitutes a primary source of error in Global Navigation Satellite System (GNSS) navigation positioning. Existing machine learning zenith wet delay (ZWD) models have limitations in their feature extraction capabilities. To address these limitations, we propose a ZWD (CNN_ZWD) model which is built upon observation data collected from 88 radiosonde (RS) stations in China from 2015 to 2017, employing the one-dimensional convolutional neural network (1D-CNN) deep learning method. The accuracy of the CNN_ZWD model is validated using the 2018 RS data and is compared with other models. The results reveal that the root mean square error (RMSE) of the 1D-CNN-based empirical model CNN_ZWD-A is 4.29 cm. This marks a 0.17 cm (3.81 %) improvement over the machine learning empirical models based on the random forest (RF) and back propagation neural network (BPNN) and a 0.70 cm (14.03 %) enhancement over the GPT3 empirical model. Moreover, when meteorological data is available at the station, the meteorological parameterized CNN_ZWD-B model has an RMSE of 2.69 cm. Its precision closely matches that of the RF_ZWD-D model and slightly exceeds the BP_ZWD-F model (RMSE: 2.85 cm). Remarkably, compared to the conventional Saastamoinen (Saa_ZWD) model, our proposed model demonstrates a 32.24 % increase in accuracy. This underscores that incorporating surface meteorological parameters into the functional formulation can significantly enhance the accuracy of regional ZWD prediction in China. Furthermore, compared with the empirical model, the predictive accuracy of the meteorological parameterized ZWD model based on the 1D-CNN exhibits significant improvement, particularly in China's monsoon climate region. [ABSTRACT FROM AUTHOR]

The atmospheric Precipitable water vapor (PWV) is a variable key for weather forecasting and climate change. It is a considerable component of the atmosphere, influencing numerous atmospheric processes, and having physical characteristics. It can be measured directly using radiosonde stations (RS), which are not always accessible and difficult to measure with acceptable spatial and time precision. This study uses the artificial neural network (ANN) application to propose a simple model based on RS data to estimate PWV from surface metrological data. Ten RS stations were used to develop the new model for eight and a half years. In addition, two and a half years of data were used to validate the developed model. The study period is based on the data accessible between 2010 and 2020. The new model needs to collect (vapor pressure, temperature, latitude, longitude, height, day of year, and relative humidity) as input parameters in ANN to predict the PWV. The ANN model validations were based on the root mean square (RMS), correlation coefficient (CC), and T-test. According to the results, the proposed ANN can accurately predict the PWV over Egypt. The results of the new ANN model and eight other empirical models (Saastamoinen, Askne and Nordius, Okulov et al., Maghrabi et al., Phokate., Falaiye et al. (A&B), Qian et al. and ERA 5) are compared in addition, the new PWV model can achieve the best performance with RMS of 0.21 mm. The new model can serve as a will be of practical utility with a high degree of precision in PWV estimation. [ABSTRACT FROM AUTHOR]

The tropospheric delay acquired by the Global Navigation Position System (GPS) Precise Point Positioning (PPP) is continuous and steady, less affected by rainfall. The Water Vapor Radiometer (WVR) can provide real‐time meteorological parameters but is more sensitive to high‐frequency information in troposphere. To explore the use of WVR‐retrieved tropospheric delay and assist other geodetic techniques for atmospheric correction, the tropospheric delay from WVR and co‐located GPS at Shanghai, Beijing, Kunming, and Urumqi stations in China are compared. For the inconsistent values of WVR‐PPP zenith wet delay, the variations of the tropospheric delay from WVR and GPS before and after the rainfall were statistically analyzed. The results suggest that, for the rain rate ranging from 0.1 to 50 mm/hr, the impact of rainfall on WVR could last from 10 min before to 30 min after the rainfall. With filtering WVR data based on meteorological parameters and rain rate, the zenith wet delay between WVR and PPP at Shanghai shows good consistency, the root mean square (RMS) is 6.11 mm, correlation is 0.997, and the RMS in the other three stations ranges from 16.35 to 25.16 mm (correlation ranges in 0.794–0.951). The analysis indicates that the tropospheric delay of WVR is reliable to be applied to space geodetic techniques correction in real‐time with filtering to reduce the effect of rainfall, water vapor, and liquid water variability. Key Points: Comparison of zenith wet delay(ZWD) from water vapor radiometer, co‐located GPS station observations in high temporal resolutionQuantitative analysis of the magnitude and duration of rainfall effects on the zenith wet delay from water vapor radiometer and GPSSuch data analysis and processing might be valuable for assimilating multi‐source data on tropospheric wet delay [ABSTRACT FROM AUTHOR]

In recent years, machine learning techniques, especially artificial neural networks (ANN), have been widely applied for engineering problems since they have proven to be a good predictor, especially in accurate weather forecasting applications. The study aims to evaluate the prediction capability of the novel hybrid ANN-GTO (Gorilla Troops Optimizer), which is not applied for predicting the zenith wet delay (ZWD) in the earlier literature, and the developed ANN-GTO has been compared with two training algorithms, namely Levenberg–Marquardt and Bayesian Regularization, the performance of the ANN-GTO has also been compared with improved ANN methods to illustrate the efficiency of ANN-GTO. The results of all the developed models have been compared via performance criteria. Three inputs, such as pressure, temperature, and water vapour pressure (WVP) have been employed for model training and testing purposes. The analysis outcomes have disclosed that all the ANN enhanced with GTO have overachieved the classic ANN and other hybrid ANN models in predicting ZWD. [ABSTRACT FROM AUTHOR]

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In this study, a tropospheric delay model that integrates tropospheric delays derived from the European Centre for Medium-Range Weather Forecasts fifth-generation global atmospheric reanalysis and the Continuously Operating Reference Station (CORS) network observations in mountainous areas is established, which is then applied to improve GNSS precise point positioning (PPP). Observations of GNSS stations in the Great Dividing Range of eastern Australia are selected for the experiments. The performance of zenith wet delay (ZWD) retrieved from the integrated tropospheric model is evaluated with comparisons to precise point positioning (PPP) estimated ZWD values. Results show that the average root-mean-square value for ZWDs of the integrated tropospheric model is 8.03 mm for the eastern Australian CORS network, showing an improvement of 14.0% compared to that of the CORS interpolation model. Besides, the proposed tropospheric model is applied to regional augmentation precise positioning. Results present that the average positioning accuracy of the tropospheric model-corrected PPP solutions is 1.42 cm, 1.39 cm and 2.90 cm for the east, north and vertical components, respectively, revealing an improvement of 14.5%, 11.5% and 18.6% compared to the PPP solutions with regional CORS corrections. Meanwhile, almost all stations can achieve a faster solution convergence by performing the integrated tropospheric model-corrected PPP. All these results demonstrate the promising potential of the proposed tropospheric model in enhancing precise positioning as well as facilitating applications in the meteorological fields. [ABSTRACT FROM AUTHOR]

The water vapor content in the atmosphere is highly correlated with rainfall events, which can be used as a data source for rainfall prediction or drought monitoring. The GNSS PPP (Precise Point Positioning) technique can be used to estimate the troposphere ZWD (Zenith Wet Delay) parameter which can be converted into precipitable water vapor (PWV). In this study, we first investigate the impacts of the weighting strategies, observation noise settings, and gradient estimation on the accuracy of ZWD and positions. A refined strategy is proposed for the troposphere estimation with uncombined raw PPP model, down-weighting of Galileo/GLONASS/BDS code observation by a factor of 3, using a sine2-type elevation-dependent weighting function and estimating the horizontal gradients. Based on the strategy, the correlation of the estimated tropospheric parameters with the rainfall is analyzed based on the data from the "7.20" rainstorm in Henan Province, China. The PWV is first calculated based on the hourly global pressure and temperature (HGPT) model and compared with the results from ERA5 products. Results show their good consistency during the rainfall period or the normal period with a standard deviation of 3 mm. Then, the high correlation between the PWV and the heavy rain rainfall event is validated. Results show that the accumulated PWV maintains a high level before the rainstorm if a sustainable water supply is available, while it decreased rapidly after the rainfall. In comparison, the horizontal gradients and the satellite residuals are less correlated with the water vapor content. However, the gradients can be used to indicate the horizontal asymmetry of the water vapor in the atmosphere. [ABSTRACT FROM AUTHOR]

The use of a high-precision a priori zenith wet delay can effectively improve the convergence time and increase the accuracy of precise point positioning (PPP). Considering the limitations of empirical and blind ZWD models, a new lightweight ZWD model was developed based on GNSS observations and ERA5 precipitable water vapor (PWV) and temperature information that can provide reliable ZWD with 0.25° spatial resolution and hourly temporal resolution without relying on massive meteorological parameters. The correlation between the ERA5 PWV/temperature and the GNSS-derived ZWD was first analyzed in 2020 in this study. Subsequently, a functional mapping model based on machine learning was established, considering the effects of spatial and temporal factors, such as time, topography, geographical location. The validation results showed the proposed model's RMSE/STD/Bias were 1.70/1.70/0cm compared with GNSS ZWD, respectively. Furthermore, an independent GNSS and radiosonde ZWD in 2021, was introduced to validate the generalization ability of the proposed model, and the RMSE/STD/Bias values were 1.63/1.49/0.2cm and 2.77/2.63/0.23cm, respectively. The ZWD model developed in this study effectively reduces the dependence on meteorological data from numerical weather models, which is beneficial for broadcasting ZWD data and enhances precise regional positioning and navigation. • A lightweight ZWD model is established without relying massive meteorological data. • Machine learning is used to build a model between GNSS ZWD and multi-source data. • The new model can provide preferable spatiotemporal resolution. • The new model has low RMSE at 1.63 cm. [ABSTRACT FROM AUTHOR]

The motivation of this research is to develop a more accurate global empirical model of zenith wet delay (ZWD) based on a neural network model, which was carried out by introducing a new combined modeling strategy. This strategy was based on two important features about ZWD: the ZWD seasonal variations and ZWD being relevant to site meteorological measurements. The water vapor pressure from GPT2w (e S -GPT2w), the water vapor decrease factor from GPT2w (λ GPT2w), and the weighted mean temperature of GTrop (T m -GTrop) can provide the approximate site seasonal ZWD and then were set as input variables of neural network. With a combination of approximate site seasonal ZWDs and site meteorological measurements, more accurate ZWD estimates can be provided. Based on this new combined modeling strategy, the new ZWD neural network (N-ZWDNN) model was developed. On the other side, the author followed conclusions of the previous studies about zenith tropospheric delay models using neural network, then extended modeling scope to a global scale and developed the traditional ZWD neural network (T-ZWDNN) model. We compared N-ZWDNN with T-ZWDNN on the condition that they were modeled with the same data set. Other two state-of-the-art ZWD models. i.e. the site-augmented GPT2w-ZWD (SAGPT2w-ZWD) model, and the GridZWD model are also included for the comparison. The results show that N-ZWDNN has a global accuracy of 17.8 mm and shows respective 13.6%, 20.7% and 10.9% improvements in accuracy compared with the SAGPT2w-ZWD, GridZWD and T-ZWDNN models for global ZWDs from the earth's surface to 10 km. N-ZWDNN can maintain its superiority in different latitude belts, height ranges and seasons. The new combined modeling strategy and the great non-linearity fitting capability of neural network mostly contributed to the accuracy improvement of N-ZWDNN. In addition, a simplified version of N-ZWDNN (N-ZWDNN-B) was given and site meteorological measurements were not used in this model. [ABSTRACT FROM AUTHOR]

• Improved PPP is used in kinematic model for oscillating displacement monitoring. • The improved PPP has better convergence performance with high cut off angle. • Better accuracy can be achieved by ZWD augmented PPP in kinematic model. This paper developed the tropospheric correction augmented PPP for the purpose of bridge displacement monitoring. ZWD is estimated from undifferenced observations collected by UK CORS, and further applied to augment PPP client for displacement at the bridge surveying points. Coordinate time series obtained by GPS DD are treated as the true bridge displacement, which is used to assess the standard and CORS ZWD augmented PPP solutions obtained by varying cutoff angles. The experimental results reveal that the displacement precision of standard PPP severely depends on the satellite geometry. Meanwhile, the CORS ZWD augmented PPP results are less affected. The RMSE of improved PPP time series in the vertical component drops by 12%, 49% and 66% for the 5°, 10° and 15° cutoff angle cases, respectively. CORS ZWD augmented PPP can improve the monitoring precision and eliminate irregular displacement time series due to poor satellite geometry. [ABSTRACT FROM AUTHOR]

With the development of industrialization, fine particulate matter (PM2.5) severely chills the health of people. Studies have shown that the variation of PM2.5 concentration is related to the Global Navigation Satellite System (GNSS) tropospheric delay. Therefore, it is possible to use the widely distributed continuous operation reference station (CORS) to monitor and predict PM2.5 concentrations with high time resolution. In this paper, the zenith wet delay (ZWD) of five CORS located in Baoding, Hebei Province, China, from Sep 2014 to Feb 2015, is calculated firstly. Then, the correlation between PM2.5 and ZWD is investigated. Finally, the experimental data including PM2.5, ZWD, temperature, air pressure, and relative humidity data sampled in one hour are used to establish PM2.5 concentrations online prediction model based on support vector machine regression (SVMR) model with metabolic method. The experimental results show that in autumn and winter, the correlation coefficient between daily-mean PM2.5 and ZWD is mainly larger than 0.4, and the correlation coefficient between hourly mean PM2.5 and ZWD is mainly larger than 0.3. Meanwhile, in daily cycle analysis, air temperature, air pressure and relative humidity are related to PM2.5 concentration. Finally, Using SVMR model with metabolic method, by combining GNSS and meteorological factors, ideal short-term prediction accuracy is achieved, which shows that the use of GNSS and meteorological factors is potential in predicting PM2.5 concentration.

The Wanshan calibration site (WSCS) is the first in-situ field for calibration and validation (Cal/Val) of HY-2 satellite series in China. It was built in December, 2018 and began business operation in 2020. In order to define an accurate datum for Cal/Val of altimeters, the permanent GNSS station (PGS) data of the WSCS observed on Zhiwan (ZWAN) and Wailingding (WLDD) islands were processed using GAMIT/GLOBK software in a regional solution, combined with 61 GNSS stations distributed nearby, collected from the GNSS Research Center, Wuhan University (GRC). The Hector software was used to analyze the trend of North (N), East (E), and Up (U) directions using six different noise models with criteria of maximum likelihood estimation (MLE), Akaike Information Criteria (AIC), and the Bayesian Information Criteria (BIC). We found that the favorite noise models were white noise plus generalized Gauss–Markov noise (WN + GGM), followed by generalized Gauss–Markov noise (GGM). Then, we compared the PGS velocities of each direction with the Scripps Orbit and Permanent Array Center (SOPAC) output parameters and found that there was good agreement between them. The PGSs in the WSCS had velocities in the N, E, and U directions of −10.20 ± 0.39 mm/year, 31.09 ± 0.36 mm/year, and −2.24 ± 0.66 mm/year for WLDD, and −10.85 ± 0.38 mm/year, 30.67 ± 0.30 mm/year, and −3.81 ± 0.66 mm/year for ZWAN, respectively. The accurate datum was defined for Cal/Val of altimeters for WSCS as a professional in-situ site. Moreover, the zenith wet delay (ZWD) of the coastal PGSs in the regional and sub-regional solutions was calculated and used to validate the microwave radiometers (MWRs) of Jason-3, Haiyang-2B (HY-2B), and Haiyang-2C (HY-2C). A sub-regional PGS solution was processed using 19 continuous operational reference stations (CORS) of Hong Kong Geodetic Survey Services to derive the ZWD and validate the MWRs of the altimeters. The ZWD of the PGSs were compared with the radiosonde-derived data in the regional and sub-regional solutions. The difference between them was −7.72~2.79 mm with an RMS of 14.53~18.62 mm, which showed good consistency between the two. Then, the PGSs’ ZWD was used to validate the MWRs. To reduce the land contamination of the MWR, we determined validation distances of 6~30 km, 16~28 km, and 18~30 km for Jason-3, HY-2B, and HY-2C, respectively. The ZWD differences between PGSs and the Jason-3, HY-2B, and HY-2C altimeters were −2.30 ± 16.13 mm, 9.22 ± 22.73 mm, and −3.02 ± 22.07 mm, respectively.

The water vapor content in the atmosphere is highly correlated with rainfall events, which can be used as a data source for rainfall prediction or drought monitoring. The GNSS PPP (Precise Point Positioning) technique can be used to estimate the troposphere ZWD (Zenith Wet Delay) parameter which can be converted into precipitable water vapor (PWV). In this study, we first investigate the impacts of the weighting strategies, observation noise settings, and gradient estimation on the accuracy of ZWD and positions. A refined strategy is proposed for the troposphere estimation with uncombined raw PPP model, down-weighting of Galileo/GLONASS/BDS code observation by a factor of 3, using a sine2-type elevation-dependent weighting function and estimating the horizontal gradients. Based on the strategy, the correlation of the estimated tropospheric parameters with the rainfall is analyzed based on the data from the “7.20” rainstorm in Henan Province, China. The PWV is first calculated based on the hourly global pressure and temperature (HGPT) model and compared with the results from ERA5 products. Results show their good consistency during the rainfall period or the normal period with a standard deviation of 3 mm. Then, the high correlation between the PWV and the heavy rain rainfall event is validated. Results show that the accumulated PWV maintains a high level before the rainstorm if a sustainable water supply is available, while it decreased rapidly after the rainfall. In comparison, the horizontal gradients and the satellite residuals are less correlated with the water vapor content. However, the gradients can be used to indicate the horizontal asymmetry of the water vapor in the atmosphere.

The zenith wet delay (ZWD) accuracy is one of the most important factors affecting the convergence time and the positioning precision in precise point positioning processing. Taking into account the limitation of the empirical and blind ZWD models, the correlations between the ZWD and temperature and water vapor pressure at each point of the global 1º × 1º grid were analyzed. Based on the global grid of augmentation coefficients derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) data with a temporal resolution of 6 h from 2011 to 2014, a new ZWD augmentation model was established, which is a weighting of differences between the in situ meteorological quantities and those from the GPT3 model. The performance of the proposed model was assessed against three traditional models using different data sources in 2015, i.e., the ECMWF grids and globally distributed International GNSS Service (IGS) sites. The numerical results show that the proposed model outperforms the other three models with the largest RMSE/RRMSE improvement, reaching 1.08 cm/11.37% and 0.99 cm/9.8% when comparing the ECMWF grids and IGS sites, respectively. [ABSTRACT FROM AUTHOR]

The estimation of tropospheric gradients in GNSS data processing is a well-known technique to improve positioning precision. To study the correlation between the tropospheric gradients and the topography, we computed Zenith Wet Delay (ZWD) and tropospheric gradients using the GIPSY-OASIS II SOFTWARE from 2 years of GPS observations recorded at 52 worldwide permanent stations, focusing on regions with significant relief. We observe that gradient directions are stable over time and point towards the relief for most of the considered stations. Based on these results, we discuss the physical meaning of the tropospheric horizontal gradients and we investigate why gradients have this particular direction for stations located nearby high mountains. The GPS stations were selected and classified into four main categories: stations close to a mountain range or an isolated mountain (class 1 and 2), stations surrounded by isolated mountains in several directions or in all directions (class 3 and 4). The correlation between the gradient direction and their magnitude with respect to mountain slopes was analysed. A very clear correlation appears for stations of classes 1 and 2 whereas no correlation is obvious for stations of classes 3 and 4. For 89% of stations in classes 1 and 2, a relevant correlation appears, varying between 0.4 and 1. For 64% of stations in classes 1 and 2, a relevant correlation appears, varying between 0.6 and 1. Horizontal gradients estimation show very significant amplitude and a stable direction all along the year, this main direction is most of the time pointing towards the direction of mountains. This behaviour can be explained by a vertical shift of the tropospheric layer due to the presence of mountains, close to the station and up to the maximum distance of 60 km from the station. This orientation does not seem to depend on seasons because no annual or bimonthly means variations appear for all stations. Moreover diurnal variations do not appear on the spatial distribution of the gradients and results are similar for neighbouring stations, separated by few km, which show that local effects such as multipath propagation have influence. [ABSTRACT FROM AUTHOR]

We studied disastrous heavy rainfall episodes in 2017–2019 summer in SW Japan, especially in the Kyushu region using tropospheric delay data from the Japanese dense global navigation satellite system (GNSS) network GEONET (GNSS Earth Observation Network). This region often suffers from extremely heavy rains associated with stationary fronts during summer. In this study, we first analyze behaviors of water vapor on July 6, 2018, using tropospheric parameters obtained from the database at the University of Nevada, Reno. The data set includes tropospheric delay gradient vectors (G), as well as zenith tropospheric delays (ZTD), estimated every 5 min. At first, we interpolated G to obtain those at grid points and calculated their convergence, similar to the quantity proposed by Shoji (2013) as water vapor concentration (WVC) index. We obtained zenith wet delay (ZWD) from ZTD by removing zenith hydrostatic delay. The raw ZWD values do not really reflect the wetness of the atmosphere above the GNSS station because they largely depend on the station altitudes. To study the dynamics of water vapor before heavy rains, we estimated ZWD converted to the values at sea level. In the inversion scheme, we used G at all GEONET stations and ZWD data at low-altitude (50 mm/h) episodes occurred, that is, July 5, 2017, July 6, 2018, and August 27, 2019. Next, we performed high time resolution analysis (every 5 min) on the days of heavy rain. The results suggest that both WVC and sea-level ZWD go up prior to the onset of the rain, and ZWD decreases rapidly once the heavy rain started. It is a future issue, however, how far these two quantities contribute to forecast heavy rains.

Since millimeter accuracy is required in many GNSS applications such as real-time zenith wet delay (ZWD) estimation, the higher-order ionospheric delays on GNSS signals are no longer negligible. We calculated the second-order ionospheric delays ( I 2 ) and analyzed the impact on the ZWD estimation with GPS-only and combined GPS/BDS observations. The undifferenced PPP model with fixed coordinates was used to estimate the ZWD and horizontal gradients. The method of blockwise sequential least squares was utilized to eliminate the receiver clock biases and compute the I 2 impact on the ZWDs. The I 2 delays on each GNSS satellite observations were calculated with the CODE final TEC map and the 12th generation of the international geomagnetic reference field (IGRF-12) model. The statistical results with the actual observation geometry show that the I 2 delays can reach over 10 mm during the daytime, and the corresponding impact on the estimated ZWD can reach up to several millimeters. At station HKWS, the maximum I 2 impact with GPS only reaches up to 3.1 mm and is still 2.4 mm when both GPS and BDS observations are used. The simulated I 2 impact on the ZWD could reach several millimeters, even though the TEC and geomagnetic values were calculated from relatively moderate background models. Compared with the 5–10 mm precision of real-time ZWD estimation, the I 2 delays must not be ignored, especially during high VTEC periods. [ABSTRACT FROM AUTHOR]

Precise modeling of weighted mean temperature (Tm) is critical for realizing real-time conversion from zenith wet delay (ZWD) to precipitation water vapor (PWV) in Global Navigation Satellite System (GNSS) meteorology applications. The empirical Tm models developed by neural network techniques have been proved to have better performances on the global scale; they also have fewer model parameters and are thus easy to operate. This paper aims to further deepen the research of Tm modeling with the neural network, and expand the application scope of Tm models and provide global users with more solutions for the real-time acquisition of Tm. An enhanced neural network Tm model (ENNTm) has been developed with the radiosonde data distributed globally. Compared with other empirical models, the ENNTm has some advanced features in both model design and model performance, Firstly, the data for modeling cover the whole troposphere rather than just near the Earth’s surface; secondly, the ensemble learning was employed to weaken the impact of sample disturbance on model performance and elaborate data preprocessing, including up-sampling and down-sampling, which was adopted to achieve better model performance on the global scale; furthermore, the ENNTm was designed to meet the requirements of three different application conditions by providing three sets of model parameters, i.e., Tm estimating without measured meteorological elements, Tm estimating with only measured temperature and Tm estimating with both measured temperature and water vapor pressure. The validation work is carried out by using the radiosonde data of global distribution, and results show that the ENNTm has better performance compared with other competing models from different perspectives under the same application conditions, the proposed model expanded the application scope of Tm estimation and provided the global users with more choices in the applications of real-time GNSS-PWV retrival.

The accurate modeling of tropospheric path delay is significant for data processing of radio space-geodetic techniques such as Global Navigation Satellite System (GNSS) and Very-Long-Baseline Interferometry (VLBI). The Vienna Mapping Function 1 (VMF1) model, based on continuous update of Numerical Weather Prediction (NWP) data from the European Centre for Medium-Range Weather Forecasts (ECMWF), is recommended for this purpose in post-processing. The VMF1 coefficients determined from forecast data of the ECMWF are now readily and freely available. However, little or no implementation of this forecast VMF1 (VMF1-FC) model in real-time GNSS or VLBI applications has occurred. This study investigates the performance of the VMF1-FC model in terms of its three components which are critical for the modeling of tropospheric path delay: the Zenith Hydrostatic Delay (ZHD), the Zenith Wet Delay (ZWD) and mapping functions. All three components are assessed in the context of GNSS Precise Point Positioning (PPP) using 28 global stations over a 70-day period. The Zenith Total Delays (ZTD) derived with the VMF1-FC (implemented in real-time PPP) are shown to agree well with the tropospheric delay product from the Center for Orbit Determination Europe (CODE). Root mean square (RMS) errors associated with these ZTD estimates are < 10 mm at all 28 stations. The results also show that the VMF1-FC model performs better than empirical models such as the widely used Global Pressure and Temperature 2 (GPT2) and GPT2 wet (GPT2w), with smaller RMS errors associated with the ZTD estimates. It is recommended that VMF1-FC be applied for future tropospheric delay modeling in real-time GNSS and VLBI applications. [ABSTRACT FROM AUTHOR]

The weighted mean temperature (Tm) is a key parameter when converting the zenith wet delay (ZWD) to precipitation water vapor (PWV) in ground-based Global Navigation Satellite System (GNSS) meteorology. Tm can be calculated via numerical integration with the atmospheric profile data measured along the zenith direction, but this method is not practical in most cases because it is not easy for general users to get real-time atmospheric profile data. An alternative method to obtain an accurate Tm value is to establish regional or global models on the basis of its relations with surface meteorological elements as well as the spatiotemporal variation characteristics of Tm. In this study, the complex relations between Tm and some of its essentially associated factors including the geographic position and terrain, surface temperature and surface water vapor pressure were considered to develop Tm models, and then a non-meteorological-factor Tm model (NMFTm), a single-meteorological-factor Tm model (SMFTm) and a multi-meteorological-factor Tm model (MMFTm) applicable to China and adjacent areas were established by adopting the artificial neural network technique. The generalization performance of new models was strengthened with the help of an ensemble learning method, and the model accuracies were compared with several representative published Tm models from different perspectives. The results show that the new models all exhibit consistently better performance than the competing models under the same application conditions tested by the data within the study area. The NMFTm model is superior to the latest non-meteorological model and has the advantages of simplicity and utility. Both the SMFTm model and MMFTm model show higher accuracy than all the published Tm models listed in this study; in particular, the MMFTm model is about 14.5% superior to the first-generation neural network-based Tm (NN-I) model, with the best accuracy so far in terms of the root-mean-square error.

In ground-based GPS meteorology, Tm is a key parameter to calculate the conversion factor that can convert the zenith wet delay (ZWD) to precipitable water vapor (PWV). It is generally acknowledged that Tm is in an approximate linear relationship with surface temperature Ts, and the relationship presents regional variation. This paper employed sliding average method to calculate correlation coefficients and linear regression coefficients between Tm and Ts at every 2° × 2.5° grid point using Ts data from European Centre for Medium-Range Weather Forecasts (ECMWF) and Tm data from “GGOS Atmosphere”, yielding the grid and bilinear interpolation-based TmGrid model. Tested by Tm and Ts grid data, Constellation Observation System of Meteorology, Ionosphere, and Climate (COSMIC) data and radiosonde data, the TmGrid model shows a higher accuracy relative to the Bevis Tm − Ts relationship which is widely used nowadays. The TmGrid model will be of certain practical value in high-precision PWV calculation.

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.

A new concept is proposed for estimating the zenith wet delay (ZWD) and atmospheric weighted average temperature by inputting the temperature, total pressure, and specific humidity from surface weather data. In addition, a new ZWD integral method is described for highly accurate calculation of the ZWD from radiosonde observation. To evaluate the advantages of the new discrete integral formula, we utilized the 8-year radiosonde profiles of 85 stations in China from 2010 to 2017 to validate the accuracy of the radiosonde-derived ZWD. The results showed that the mean accuracy of the ZWD derived from radiosonde data was 4.28 mm. Next, the new ZWD model was assessed using two sets of reference values derived from radiosonde data and GNSS precise point positioning in China. The results confirm that the new development improved the accuracy of the estimation of the tropospheric wet delay from the surface meteorological data. The performance of this new model can be seen as an important step toward accurately correcting the tropospheric delay in Global Navigation Satellite System (GNSS) real-time navigation and positioning. It can also be used in GNSS meteorology for weather forecasting and climate research.

In this paper, the method of estimating the variation of Zenith Path Delay (ZPD) estimation method will be illustrate and evaluate using Real Time Kinematic Differential Global Positioning System (RTK-DGPS). The GPS provides a relative method to remotely sense atmospheric water vapor in any weather condition. The GPS signal delay in the atmosphere can be expressed as ZPD. In order to evaluate the results, four points had been chosen in the university of Baghdad campus to be rover ones, with a fixed Base point. For each rover position a 155 day of coordinates measurements was collected to overcome the results. Many models and mathematic calculations were used to extract the ZPD using the Matlab environment. The result shows that the ZPD values in mm depend on the water vapor intensity in the atmosphere and the mean temperatures. Also, the mean temperature model can be generated to calculate the Water Vapor Intensity( WVI ( for 20 km highest. [ABSTRACT FROM AUTHOR]

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

We calculated the key parameters of ground-based GPS water vapor inversion in each grid point and got the time series of the conversion factor Π-1by using the global zenith wet delay (ZWD) grid data with a spatial resolution of 2.5°×2°(longitude × latitude) provided by global geodetic observing system (GGOS) Atmosphere and precipitable water vapor (PWV) products with a same spatial resolution provided by European Centre for Medium-Range Weather Forecasts (ECMWF) from 2005 to 2011, followed by the analysis of temporal and spatial characteristic. We establish a global empirical model of Π which is related to the site's latitude, longitude, altitude and the day of year (doy) without meteorological data. Then we used the GGOS Atmosphere and ECMWF grid data that not involved in modeling in 2012, 661 radiosonde stations' data in 2012 to test accuracy of the model. The results show that the mean deviation (Bias) is -0.179 mm and root mean square error (Root Mean Square Error, RMS) is 1.806 mm from the grid data; the Bias is 0.465 mm, RMS is 0.789 mm from radiosonde data. Both of them indicate the accuracy and stability of the model is high with a small systematic bias on a global scale. [ABSTRACT FROM AUTHOR]

Precipitable water (PW) is considered as one of the most important weather parameters in meteorology. Moreover, moisture affects the propagation of the Global Positioning System’s (GPS) signals. Using four different models, the current paper tries to identify the best relationship between the atmospheric error known as zenith wet delay (ZWD) and PW. For that matter, based on 54,330 radiosonde profiles from 11 stations, two different models i.e. linear and quadratic have been derived for Iran. For analyzing the accuracy of these models, ZWDs of three permanent GPS stations located in the cities of Tehran, Ahvaz and Tabriz have been used. Applying the aforementioned models as well as those already developed for Europe and the U.S., PWs are derived at the position of these stations in Iran. Further, in this research, root mean square error (RMSE) and bias are the measures for selecting the optimal model. Here, the bias and the RMSE (between GPS and radiosonde derived PWs) for the proposed linear model for Iran is 1.44 mm and 4.42 mm, and for quadratic model 2.18 mm and 4.74 mm respectively while, the bias and the RMSE for Bevis’ linear model is 2.63 mm and 4.98 mm and for Emardson and Derk’s quadratic models are 2.80 mm and 5.08 mm respectively. As such, it is observed that the bias of the proposed linear model for Iran is 1.19 mm and 1.36 mm less than the Bevis’ and Emardson and Derk’s models. In addition, the RMSE of the proposed linear model is 0.56 and 0.66 mm less than the RMSE of the later ones. This emphasizes that the estimation of the model coefficients must be based on regional meteorological measurements.

The importance of water vapor in research of global climate change and weather forecast cannot be over emphasized; therefore substantial efforts have been made in exploring the optimal methods to measure water vapor. It is well-established that with a conversion factor, zenith wet delays can be mapped onto precipitable water vapor (PWV). However, the determination of the exact conversion factor depends heavily on the accurate calculation of a key variable, weighted mean temperature of the troposphere ( T). As a critical parameter in Global Positioning System (GPS) meteorology, T has recently been modeled into a global grid known as GWMT. The GWMT model only requires the location and the day of year to calculate T. Despite the advantages that the GWMT model offers, anomalies still exist in oceanic areas due to low sampling resolution. In this study, we refine the GWMT model by incorporating the global T grid from Global Geodetic Observing System (GGOS) and obtain an improved model, GWMT-G. The results indicate that the GWMT-G model successfully addresses the anomaly in oceanic areas in the GWMT model and significantly improves the accuracy of T in other regions. [ABSTRACT FROM AUTHOR]

In this study, the correlation between T, a key variable in GNSS water vapor inversion, and surface temperature ( T) was calculated on a global scale based on the global geodetic observing system (GGOS) atmosphere T data and European centre for medium-range weather forecasts (ECMWF) surface temperature data. The results show that their correlation is mainly affected by latitudes, and the correlation is stronger at high latitudes and weaker at low latitudes. Although the correlation is relatively weak in the tropic areas, the temperature changes so little in a year in these areas that we can still achieve good T results by linear regression model. Based on these facts, 'GGOS atmosphere' T data and ECMWF T data from 2005 to 2011 were used to establish the global latitude-related linear regression model. The new model has root mean square error (RMSE) of 3.2, 3.3, and 4.4 K, respectively, compared with respect to the 'GGOS atmosphere' data, COSMIC data, and radiosonde data and is more accurate than the Bevis T- T relationship. [ABSTRACT FROM AUTHOR]

Taiwan is located at the land-sea interface in a subtropical region. Because the climate is warm and moist year round, there is a large and highly variable amount of water vapor in the atmosphere. In this study, we calculated the Zenith Wet Delay (ZWD) of the troposphere using the ground-based Global Positioning System (GPS). The ZWD measured by two Water Vapor Radiometers (WVRs) was then used to verify the ZWD that had been calculated using GPS. We also analyzed the correlation between the ZWD and the precipitation data of these two types of station. Moreover, we used the observational data from 14 GPS and rainfall stations to evaluate three cases. The offset between the GPS-ZWD and the WVR-ZWD ranged from 1.31 to 2.57 cm. The correlation coefficient ranged from 0.89 to 0.93. The results calculated from GPS and those measured using the WVR were very similar. Moreover, when there was no rain, light rain, moderate rain, or heavy rain, the flatland station ZWD was 0.31, 0.36, 0.38, or 0.40 m, respectively. The mountain station ZWD exhibited the same trend. Therefore, these results have demonstrated that the potential and strength of precipitation in a region can be estimated according to its ZWD values. Now that the precision of GPS-ZWD has been confirmed, this method can eventually be expanded to the more than 400 GPS stations in Taiwan and its surrounding islands. The near real-time ZWD data with improved spatial and temporal resolution can be provided to the city and countryside weather-forecasting system that is currently under development. Such an exchange would fundamentally improve the resources used to generate weather forecasts. [ABSTRACT FROM AUTHOR]

In ground-based GPS meteorology, weighted mean temperature is the key parameter to calculate the conversion factor which will be used to map zenith wet delay to precipitable water vapor. In practical applications, we can hardly obtain the vertical profiles of meteorological parameters over the site, thus cannot use the integration method to calculate weighted mean temperature. In order to exactly calculate weighted mean temperature from a few meteorological parameters, this paper studied the relation between weighted mean temperature and surface temperature, surface water vapor pressure and surface pressure, and determined the relationship between, on the one hand, the weighted mean temperature, and, on the other hand, the surface temperature and surface water vapor pressure. Considering the seasonal and geographic variations in the relationship, we employed the trigonometry functions with an annual cycle and a semi-annual cycle to fit the residuals (seasonal and geographic variations are reflected in the residuals). Through the above work, we finally established the GTm-I model and the PTm-I model with a $$2^{\circ }\times 2.5^{\circ }(\mathrm{lat}\times \mathrm{lon})$$ resolution. Test results show that the two models both show a consistent high accuracy around the globe, which is about 1.0 K superior to the widely used Bevis weighted mean temperature-surface temperature relationship in terms of root mean square error. [ABSTRACT FROM AUTHOR]

We can map zenith wet delays onto precipitable water with a conversion factor, but in order to calculate the exact conversion factor, we must precisely calculate its key variable $$T_\mathrm{m}$$. Yao et al. (J Geod 86:1125-1135, . doi:) established the first generation of global $$T_\mathrm{m}$$ model (GTm-I) with ground-based radiosonde data, but due to the lack of radiosonde data at sea, the model appears to be abnormal in some areas. Given that sea surface temperature varies less than that on land, and the GPT model and the Bevis $$T_\mathrm{m}$$- $$T_\mathrm{s}$$ relationship are accurate enough to describe the surface temperature and $$T_\mathrm{m}$$, this paper capitalizes on the GPT model and the Bevis $$T_\mathrm{m}$$- $$T_\mathrm{s}$$ relationship to provide simulated $$T_\mathrm{m}$$ at sea, as a compensation for the lack of data. Combined with the $$T_\mathrm{m}$$ from radiosonde data, we recalculated the GTm model coefficients. The results show that this method not only improves the accuracy of the GTm model significantly at sea but also improves that on land, making the GTm model more stable and practically applicable. [ABSTRACT FROM AUTHOR]

We present comparisons of 10-year-long time series of the atmospheric zenith wet delay (ZWD), estimated using the global positioning system (GPS), geodetic very long baseline interferometry (VLBI), a water vapour radiometer (WVR), radiosonde (RS) observations, and the reanalysis product of the European Centre for Medium-Range Weather Forecasts (ECMWF). To compare the data sets with each other, a Gaussian filter is applied. The results from 10 GPS-RS comparisons using sites in Sweden and Finland show that the full width at half maximum at which the standard deviation (SD) is a minimum increases with the distance between each pair. Comparisons between three co-located techniques (GPS, VLBI, and WVR) result in mean values of the ZWD differences at a level of a few millimetres and SD of less than 7 mm. The best agreement is seen in the GPS-VLBI comparison with a mean difference of −3.4 mm and an SD of 5.1 mm over the 10-year period. With respect to the ZWD derived from other techniques, a positive bias of up to ~7 mm is obtained for the ECMWF reanalysis product. Performing the comparisons on a monthly basis, we find that the SD including RS or ECMWF varies with the season, between 3 and 15 mm. The monthly SD between GPS and WVR does not have a seasonal signature and varies from 3 to 7 mm. [ABSTRACT FROM AUTHOR]

Abstract: As a preliminary step for assessing the impact of global positioning system (GPS) refractive delay data in numerical weather prediction (NWP) models, the GPS zenith tropospheric delays (ZTD) are analyzed from 28 permanent GPS sites in the Chinese mainland. The objectives are to estimate the GPS ZTD and their variability in this area. The differences between radiosonde precipitable water vapor (PWV) and GPS PWV have a standard deviation of 4mm in delay, a bias of 0.24mm in delay, and a correlation coefficient of 0.94. The correlation between GPS ZTD and radiosonde PWV amounts to 0.89, indicating that the variety of tropospheric zenith delay can reflect the change of precipitable water vapor. The good agreement also guarantees that the information provided by GPS will benefit the NWP models. The time series of GPS ZTD, which were derived continuously from 2002 to 2004, are used to analyze the change of precipitable water vapor in Chinese mainland. It shows that the general trend of GPS ZTD is diminishing from the south-east coastland to the north-west inland, which is in accordance with the distribution of Chinese annual amount of rainfall. The temporal distribution of GPS ZTD in the Chinese mainland is that the GPS ZTD reaches maximum in summer, and it reaches minimum in winter. The long term differences between the observational data sources require further study before GPS derived data become useful for climate studies. [Copyright &y& Elsevier]

The feasibility of GPS precipitable water vapor (PWV) is discussed based on the comparison of Radiosonde and GPS PWV where the correlation coefficient is 0.94 and the RMS is 4.0 mm. PWV change in the Chinese mainland in 2004 is graphed with the gridding method of splines in tension, according to the GPS data of the crust monitor observation network in China, combined with relevant meteorology information. According to the distribution of the annual amount of rainfall in the country, it can be concluded that the total trend of the PWV is diminishing from the south-east coastland to the north-west inland. The PWV reaches its maximum during July and August, and the minimum is reached during January and February. According to the PWV, from high to low, all districts can be ranked as south-east coastland, the inland and the tableland. [ABSTRACT FROM AUTHOR]

The accuracy and drift of atmospheric path delay due to water vapor as derived from satellite microwave radiometers (MWR) is vital to altimetric measures of sea-level change. In this study a continuous time series of dual frequency GPS data from a number of offshore sites is used to examine the long term stability of the TOPEX/Poseidon radiometer and investigate initial performance of that of Jason-1. The location offshore eliminates the problems associated with land based/coastal locations where extrapolation of the GPS tropospheric correction to subsatellite points offshore are required to avoid background surface heat emissions contaminating the MWR delay measurement. [ABSTRACT FROM AUTHOR]

The modernized GLONASS (GLObal NAvigation Satellite System) provides new opportunities for estimating ZWD (zenith wet delay) and PWV (precipitable water vapor) for meteorology and climate related studies. In this study, ZWD/PWV retrieval from GLONASS and GPS (Global Positioning System) observations are assessed by comparing the results with radiosonde observations from nearly co-located GNSS (Global Navigation Satellite Systems) stations. The current consistency between GPS and GLONASS data for ZWD/PWV retrieving is investigated for the first time in the region after the access mode change of the GLONASS. The GPS and GLONASS observations for one month of each season for 8 regionally distributed stations from the CORS-TR (Continuously Operating Reference Stations - Turkey) network are processed. The results show that the GPS ZWD agrees well with the GLONASS ZWD, the RMS (root mean square) of ZWD differences is about 4.1–11.84 mm that is about 0.6–1.78 mm in PWV. ZWD differences are ranged from −20 mm to 20 mm on average for all stations. Correlation coefficients of ZWD differences for GNSS stations exceeds 84%, which means that the results obtained from GLONASS consistent with GPS. Also, PWV estimated from GLONASS observations have almost same RMS values at inland stations, while the combined solution having smallest for most of the stations. • After GLONASS implemented the CDMA, this is the first study about GLONASS in Turkey. • GLONASS ZWD and PWV estimation accuracy is as high as GPS estimated ones. • PWV estimated from Combined GNSS solution gives the most accurate results compared to other strategies. [ABSTRACT FROM AUTHOR]