Zenith Tropospheric Delay Data Research Articles

An optimized BP neural network for modeling zenith tropospheric delay in the Chinese mainland using coupled particle swarm and genetic algorithm

ABSTRACT Tropospheric delay influences high-precision navigation positioning and precipitable water vapor retrieval with the Global Navigation Satellite System (GNSS). Existing Zenith Tropospheric Delay (ZTD) models often struggle to accurately capture the non-linear variations in tropospheric delay. Therefore, this study employs the coupled Particle Swarm Optimization (PSO) algorithm with the Genetic Algorithm Back Propagation (GABP) neural network, combined with ERA5 reanalysis meteorological data, to develop an optimized model (PSO-GABP) for ZTD in the Chinese mainland. Nevertheless, ZTD data at the target point are obtained through four different methods: the integration method, model method, and GPT3 models at varying resolutions (EZTD_P, EZTD_S, GPT3_1, and GPT3_5). The analysis reveals the following: (1) The Root Mean Square (RMS) errors of the ZTD values obtained through these different methods are 1.86 cm, 3.42 cm, 3.99 cm, and 4.09 cm, respectively, when verified against GNSS_ZTD data from 2016. The optimized model yields ZTD values with the RMS error of 0.98 cm, 1.96 cm, 2.34 cm, and 2.36 cm, representing improvements of 47.3%, 42.7%, 41.4%, and 42.3% compared to the pre-optimization results. These improvements are significant; (2) The predictive capability of the constructed ZTD model is evaluated using GNSS_ZTD data from 2019 as a reference. The PSO_EZTD_P model demonstrates excellent accuracy and practicality in the Chinese mainland. As a result, the tropospheric delay optimization model based on the PSO-GABP neural network can provide valuable references for real-time GNSS navigation positioning and precipitable water vapor detection in the Chinese mainland.

GNSS Real-Time ZTD/PWV Retrieval Based on PPP with Broadcast Ephemerides

GNSS precise point positioning (PPP) plays an important role in retrieving atmospheric water vapor values and performing numerical weather prediction. However, traditional PPP relies on real-time orbits and clocks, which require continuous internet or satellite communication. Improved broadcast ephemerides of GNSSs offer new opportunities for PPP with broadcast ephemerides (BE-PPP) instead of using precise ephemeride products. Therefore, we investigated the feasibility of utilizing BE-PPP for retrieving zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) data. We processed the GPS/Galileo observations from 80 IGS stations during a 30-day experiment to retrieve ZTD values using both real-time PPP (RT-PPP) and BE-PPP solutions. Then, we processed observations from 20 EUREF Permanent GNSS Network (EPN) stations to retrieve PWV data. The IGS final tropospheric products were used to validate the ZTD, and radiosonde (RDS) and ERA5 data were used to validate the PWV. The results show that the real-time ZTD from BE-PPP agrees well with that from RT-PPP: the standard deviation (STD) of the ZTD is 1.07 cm when using BE-PPP and 0.6 cm when using RT-PPP. Furthermore, the STD of the PWV is 1.69 mm when using BE-PPP, and 0.96 mm when using RT-PPP, compared to the ERA5-PWV. Compared to the RDS-PWV, the STD is 3.09 mm when using BE-PPP and 1.39 mm when using RT-PPP. In conclusion, the real-time ZTD/PWV products obtained using the BE-PPP solution are consistent with those of RT-PPP and meet the requirements of NWP, so this method can be used as an effective complement to RT-PPP to expand its application potential.

Assessment of ERA5 derived zenith tropospheric delay data over East African region

The Global Navigation Satellite Systems (GNSS) provide valuable data for computing accurate and reliable Zenith Tropospheric Delay (ZTD) products used in GNSS precise positioning, climate, and meteorological studies. However, inconsistent GNSS data streaming in the East African region, caused by poor internet connectivity, equipment failure, and electrical power outages, results in data gaps that pose an impact on the applications of the ZTD products. To ensure continuous ZTD data availability, alternative approaches are necessary to fill the gaps. This paper evaluates the accuracy and feasibility of computing ZTD over East Africa using the European Centre for Medium-Range Weather Forecasts (ECMWF) 5th Re-Analysis (ERA5) model. The ERA5 ZTD is compared with ZTD data from 13 GNSS stations for the years 2013 to 2020 from the Nevada Geodetic Laboratory (NGL) products. Seven statistical evaluation metrics, including mean bias (MnB), root mean squared error (RMSE), Pearson correlation coefficient (R), coefficient of determination (R2), refined index of agreement (IA), Nash–Sutcliffe coefficient of efficiency (NSE), and Taylor skill score (TSS) were used to determine the agreement between ERA5 and GNSS tropospheric products. The results indicate that ERA5ZTD products match well with GNSS ZTD products, with an average MnB of −0.80 mm, RMSE of 8.94 mm, R of 0.976, R2 of 0.952, IA of 0.986, TSS of 0.975, and NSE of 0.945. The high accuracy and stability of ERA5 data in computing ZTD make it an excellent alternative source of ZTD data to augment GNSS ZTD products for positioning and meteorological applications in the East African region.

A method for calculating real-time ZTD grid data in Chinese regions based on GNSS ZTD modified ERA5 grid products

The low spatial and temporal resolution and poor accuracy of real-time zenith tropospheric delay (ZTD) have always been one of the main constraints during the development of real-time GNSS applications. This paper presents a method to obtain real-time ZTD grid data in Chinese regions utilizing the ZTD-modified ERA5 grid products from GNSS stations. Initially, the original ZTD fitting function for vertical variation is improved. Then, the real-time ZTD grid data for the Chinese region (RZTDG) could be obtained by correcting the 7-day earlier ERA5 data through the real-time ZTD data from the GNSS stations. In this paper, we analyze the performance of the model under various weather conditions, and the results show that it still keeps a high accuracy even under variable weather conditions. ZTD data from 66 radiosonde stations in China in 2022 are used as reference values to evaluate the accuracy of the RZTDG. Experimental results show that the RMSE (2.3 cm) and MAE (1.8 cm) of the RZTDG are comparable to the ERA5 data of the day (RMSE: 2.4 cm, MAE: 1.8 cm) and significantly better than the accuracy of the HGPT2 (RMSE: 5.1 cm, MAE: 4.1 cm). Meanwhile, the Bias of RZTDG (0.1 cm) is much smaller than the Bias of HGPT2 (−0.9 cm) and the Bias of ERA5 (−0.8 cm), proving that the method in this paper has less deviation from the radiosonde ZTD data. Finally, the convergence times of the float PPP with and without tropospheric constraints are counted for 120 GNSS stations for DOY 11–13, DOY 101–103, and DOY 192–194 in 2022. The results show that the convergence time of the float PPP is reduced by 30% after constraining the ZTD using RZTDG.

A global grid model for the estimation of zenith tropospheric delay considering the variations at different altitudes

Abstract. The accuracy of tropospheric delay correction heavily depends on the quality of the tropospheric model, and the zenith tropospheric delay (ZTD) is an important factor affecting the tropospheric delay. Therefore, it is essential to establish a precise ZTD empirical model. The existing ZTD models are constrained by a single fitting function, lack consideration for daily cycle variations, and rely solely on data with one resolution for modeling. To address these limitations, we proposed a global piecewise ZTD empirical grid (GGZTD-P) model. This model considers the daily cycle variation and latitude factor of ZTD, using the sliding window algorithm based on fifth-generation European Centre for Medium-Range Weather Forecasts atmospheric reanalysis data (ERA5). The ZTD data from 545 radiosonde stations and the second Modern-Era Retrospective analysis for Research and Applications (MERRA-2) atmospheric reanalysis data are used to validate the accuracy of the GGZTD-P model. The results indicate that the GGZTD-P model outperforms the global pressure and temperature 3 (GPT3) model, exhibiting 26 % and 53 % lower bias and rms, respectively, when using radiosonde stations as reference values. Furthermore, when evaluated using MERRA-2 atmospheric reanalysis data, the GGZTD-P model consistently exhibits superior performance across various latitude regions. It is expected that the application of this new model will provide improved services for high-precision global navigation satellite system (GNSS) positioning and GNSS meteorology.

Comparison of ZTD derived from CARRA, ERA5 and ERA5-Land over the Greenland based on GNSS

High-accuracy reanalysis products are beneficial to the retrieval and modeling of zenith tropospheric delay (ZTD) in GNSS positioning and the study of GNSS Meteorology. The performance of meteorological parameters and ZTD derived from Copernicus Arctic Regional ReAnalysis (CARRA), ERA5 and ERA5-Land over the Greenland covering the year of 2020 are comprehensively compared and analyzed in this study. Firstly, the accuracies of the atmospheric pressure, temperature and water vapor pressure retrieved from three reanalysis data are compared with the observations obtained from 6 radiosondes and 30 automatic weather stations. The results show that the accuracy of temperature data from ERA5 pressure-level in the height range of 23–30 km is higher than that of CARRA pressure-level. The atmospheric pressure, temperature and water vapor pressure from CARRA single-level are superior to those of ERA5 single-level and ERA5-Land. Secondly, the ZTD derived from CARRA, ERA5 and ERA5-Land are compared with GNSS final ZTD data from 37 UNAVCO stations. The Root Mean Square error (RMS) values of ERA5 pressure-level ZTD is 6.7 mm, showing slightly better accuracy than CARRA pressure-level ZTD of 10.7 mm. The RMS values of ZTD derived from CARRA single-level, ERA5 single-level and ERA5-Land based on the Saastamoinen model are 11.9 mm, 13.4 mm and 22.7 mm, respectively, which indicates that CARRA single-level ZTD shows best consistency with GNSS ZTD among three single-level reanalysis data. Moreover, the reanalysis-derived ZTD show obviously poorer accuracy in warm-season than that in cold-season.

Regional/Single Station Zenith Tropospheric Delay Combination Prediction Model Based on Radial Basis Function Neural Network and Improved Long Short-Term Memory

Atmospheric water vapor is an essential source of information that predicts global climate change, rainfall, and disaster-natured weather. It is also a vital source of error for Earth observation systems, such as the global navigation satellite system (GNSS). The Zenith Tropospheric Delay (ZTD) plays a crucial role in applications, such as atmospheric water vapor inversion and GNSS precision positioning. ZTD has specific temporal and spatial variation characteristics. Real-time ZTD modeling is widely used in modern society. The conventional back propagation (BP) neural network model has issues, such as local, optimal, and long short-term memory (LSTM) model needs, which help by relying on long historical data. A regional/single station ZTD combination prediction model with high precision, efficiency, and suitability for online modeling was proposed. The model, called K-RBF, is based on the machine learning algorithms of radial basis function (RBF) neural network, assisted by the K-means cluster algorithm (K-RBF) and LSTM of real-time parameter updating (R-LSTM). An online updating mechanism is adopted to improve the modeling efficiency of the traditional LSTM. Taking the ZTD data (5 min sampling interval) of 13 international GNSS service stations in southern California in the United States for 90 consecutive days, K-RBF, R-LSTM, and K-RBF were used for regions, single stations, and a combination of ZTD prediction models regarding research, respectively. Real-time/near real-time prediction results show that the root-mean-square error (RMSE), mean absolute error (MAE), coefficient of determination (R2), and training time consumption (TTC) of the K-RBF model with 13 station data are 8.35 mm, 6.89 mm, 0.61, and 4.78 s, respectively. The accuracy and efficiency of the K-RBF model are improved compared with those of the conventional BP model. The RMSE, MAE, R2, and TTC of the R-LSTM model with WHC1 station data are 6.74 mm, 5.92 mm, 0.98, and 0.18 s, which improved by 67.43%, 66.42%, 63.33%, and 97.70% compared with those of the LSTM model. The comparison experiments of different historical observation data in 24 groups show that the real-time update model has strong applicability and accuracy for the time prediction of small sample data. The RMSE and MAE of K-RBF with 13 station data are 4.37 mm and 3.64 mm, which improved by 47.70% and 47.20% compared to K-RBF and by 28.48% and 31.29% compared to R-LSTM, respectively. The changes in the temporospatial features of ZTD are considered, as well, in the combination model.

High-Precision ZTD Model of Altitude-Related Correction

Zenith tropospheric delay (ZTD) is one of the main error sources in space geodesy. The existing regional or global models, such as Global Pressure and Temperature 3 (GPT3), Global Tropospheric model, Global Hopfield, and Shanghai Astronomical observatory tropospheric delay model models, have good performance. However, the precision of these models is relatively low in regions with a large height difference, which becomes the focus of this article. A high-precision ZTD model considering the height effect on tropospheric delay is proposed, and China is selected as study area due to its large height difference, which is called the high-precision ZTD model for China (CHZ). The initial ZTD value is calculated on the basis of the GPT3 model, and the periodic terms of ZTD residual between the global navigation satellite system (GNSS) and GPT3 model, such as annual, semiannual, and seasonal periods, are determined by the Lomb–Scargle periodogram method in different subareas of China. The relationship between the ZTD periodic residual term and the height of the GNSS station is further analyzed at different seasons, and linear ZTD periodic residual models are obtained. A total of 164 GNSS stations derived from the Crustal Movement Observation Network of China and 87 radiosonde stations are selected to validate the proposed CHZ model, and hourly ZTD data derived from GNSS are used to establish the CHZ model. Statistical result shows that the averaged root mean square and Bias of the CHZ model are 21.12 and −2.51 mm, respectively, in the whole of China. In addition, the application of CHZ model in precision point positioning (PPP) show that the convergence time is improved by 34%, 15%, and 35%, respectively, in N, E, and U components when compared to GPT3-based PPP.

Refining the ERA5-based global model for vertical adjustment of zenith tropospheric delay

Tropospheric delay is an important factor affecting high precision Global Navigation Satellite System (GNSS) positioning and also the basic data for GNSS atmospheric research. However, the existing tropospheric delay models have some problems, such as only a single function used for the entire atmosphere. In this paper, an ERA5-based (the fifth generation of European Centre for Medium-Range Weather Forecasts Reanalysis) global model for vertical adjustment of Zenith Tropospheric Delay (ZTD) using a piecewise function is developed. The ZTD data at 611 radiosonde stations and the MERRA-2 (second Modern-Era Retrospective analysis for Research and Applications) atmospheric reanalysis data were used to validate the model reliability. The Global Zenith Tropospheric Delay Piecewise (GZTD-P) model has excellent performance compared with the Global Pressure and Temperature (GPT3) model. Validated at radiosonde stations, the performance of the GZTD-P model was improved by 0.96 cm (23%) relative to the GPT3 model. Validated with MERRA-2 data, the quality of the GZTD-P model is improved by 1.8 cm (50%) compared to the GPT3 model, showing better accuracy and stability. The ZTD vertical adjustment model with different resolutions was established to enrich the model's applicability and speed up the process of tropospheric delay calculation. By providing model parameters with different resolutions, users can choose the appropriate model according to their applications.

Tropical tropopause in Tibet: Insights from ground‐based global navigation satellite system and space‐based radio occultation observations

AbstractChanges in the tropopause can explain regional and global weather and climate. In Tibet, there are few radiosonde stations, and the detection height is not high enough. Radio occultation (RO) data are insufficient because of the small regional scale, which is not conducive to the analysis of tropopause change. Moreover, in some middle and high latitudes, it was more difficult to identify the tropopause height from the temperature profile. In this study, an improved method has been developed for the inversion of the tropical tropopause based on a ground‐based global navigation satellite system (GNSS) network combined with reanalysis data. Using zenith tropospheric delay data from 49 GNSS reference stations in Tibet from January 2017 to December 2019, combined with ERA5 reanalysis, the tropical tropopause (TPH) was successfully inversed, its temporal and spatial distribution is analysed, and compared with ERA5‐derived TPH obtained by the temperature profile of the interpolated co‐site points. In more than 90% of cases, the difference between the two is <2 km. The root mean square of the tropopause difference detected by GNSS‐derived TPH and RO‐derived TPH was ±1.25 km; the accuracies were at the same level. By combining the tropopause obtained from ground‐based GNSS and that from space‐based RO, temporal and spatial changes in the tropopause were analysed. The tropopause in Tibet has a latitude‐zoning distribution with obvious unimodal seasonal changes. Monthly changes excluding seasonal variation indicate a slight downward trend from 2017 to 2019. At the same time, changes in the tropopause are closely related to those in weather and climate. The results of this study confirm that the combination of ground‐based GNSS and space‐based RO can realize long‐term, continuous, and full coverage monitoring of the regional tropopause. This expands the application possibilities of ground‐based GNSS.

Determination of Air Urban Heat Island Parameters with High-Precision GPS Data

The urban heat island (UHI) effect can contribute to extreme heat exposure. This can be detrimental to human health. In this paper, we propose a method to estimate air temperature to evaluate the spatial distribution and to monitor the intensity of the air urban heat island (AUHI) from existing GPS infrastructure. The proposed algorithm is based on the relationship between the refractivity of the troposphere and environmental variables, as well as the relationships between the zenith tropospheric delay (ZTD), a by-product of the precise point positioning technique, and the refractivity of the troposphere. The advantage of GPS data is its high temporal resolution and the availability of embedded GPS receivers. In this paper, GPS-derived ZTD data from stations in the Hong Kong Special Administrative Region (HKSAR) of China and Tokyo in Japan are processed to estimate the hourly AUHI intensity. The results derived from this technique are validated using meteorological data in the same cities. Mean absolute error values of 0.79 °C in Hong Kong and 0.22 °C in Tokyo are found from data from the summer. Moreover, an overall accuracy of 0.51 °C is found.

Regression models for predicting daily IGS zenith tropospheric delays in West Africa: Implication for GNSS meteorology and positioning applications

AbstractThe ability to precisely and accurately model and predict tropospheric delay is essential for precise global navigation satellite system (GNSS) and meteorological applications. The International GNSS Service (IGS) provides highly accurate and highly reliable daily time series zenith tropospheric delay (ZTD) products for all its member sites using data from each IGS site. Nevertheless, if for reasons such as poor internet connectivity, equipment failure, and power outages the IGS station is inaccessible, gaps are created in the data archive, resulting in degrading the quality of the ZTD estimation, as well as inhibits the quality of precipitable water vapour (PWV) estimation, needed for precise positioning applications, meteorological studies, and weather forecasting. To address this challenge, five regression models are proposed in this study to model and predict daily ZTDs using daily datasets from four IGS stations in West Africa over a period of 5 years (2015–2019). The site‐specific Vienna Mapping Functions 3 (VMF3) products (ZTD, pressure, temperature, water vapour partial pressure) and stations' coordinates (latitudes and longitudes) are used as the predictors, while the IGS final ZTD product as the response variable in fitting the models. Several performance measures are calculated to compare the predictive performance of the models. The results show that the five regression models performed outstandingly and agree very well with the IGS‐ZTD data, and hence provide a useful alternative for ZTD predictions and also in the event the West African IGS stations' ZTD data are unavailable. Nonetheless, the support vector regression model outperformed the remaining four models.

A Comprehensive Evaluation of Key Tropospheric Parameters from ERA5 and MERRA-2 Reanalysis Products Using Radiosonde Data and GNSS Measurements

Tropospheric delay is a major error source in the Global Navigation Satellite System (GNSS), and the weighted mean temperature (Tm) is a key parameter in precipitable water vapor (PWV) retrieval. Although reanalysis products like the National Centers for Environmental Prediction (NCEP) and the European Center for Medium-Range Weather Forecasts (ECMWF) Re-Analysis-Interim (ERA-Interim) data have been used to calculate and model the tropospheric delay, Tm, and PWV, the limitations of the temporal and spatial resolutions of the reanalysis data have affected their performance. The release of the fifth-generation accurate global atmospheric reanalysis (ERA5) and the second Modern-Era Retrospective analysis for Research and Applications (MERRA-2) provide the opportunity to overcome these limitations. The performances of the zenith tropospheric delay (ZTD), zenith wet delay (ZWD), Tm, and zenith hydrostatic delay (ZHD) of ERA5 and MERRA-2 data from 2016 to 2017 were evaluated in this work using GNSS ZTD and radiosonde data over the globe. Taking GNSS ZTD as a reference, the ZTD calculated from MERRA-2 and ERA5 pressure-level data were evaluated in temporal and spatial scales, with an annual mean bias and root mean square (RMS) of 2.3 and 10.9 mm for ERA5 and 4.5 and 13.1 mm for MERRA-2, respectively. Compared to radiosonde data, the ZHD, ZWD, and Tm derived from ERA5 and MERRA-2 data were also evaluated on temporal and spatial scales, with annual mean bias values of 1.1, 1.7 mm, and 0.14 K for ERA5 and 0.5, 4.8 mm, and –0.08 K for MERRA-2, respectively. Meanwhile, the annual mean RMS was 4.5, 10.5 mm, and 1.03 K for ERA5 and 4.4, 13.6 mm, and 1.17 K for MERRA-2, respectively. Tropospheric parameters derived from MERRA-2 and ERA5, with improved temporal and spatial resolutions, can provide a reference for GNSS positioning and PWV retrieval.

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

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

Integrated water vapour observations in the Caribbean arc from a network of ground-based GNSS receivers during EUREC<sup>4</sup>A

Abstract. Ground-based Global Navigation Satellite System (GNSS) measurements from nearly 50 stations distributed over the Caribbean arc have been analysed for the period 1 January–29 February 2020 in the framework of the EUREC4A (Elucidate the Couplings Between Clouds, Convection and Circulation) field campaign. The aim of this effort is to deliver high-quality integrated water vapour (IWV) estimates to investigate the moisture environment of mesoscale cloud patterns in the trade winds and their feedback on the large-scale circulation and energy budget. This paper describes the GNSS data processing procedures and assesses the quality of the GNSS IWV retrievals from four operational streams and one reprocessed research stream which is the main data set used for offline scientific applications. The uncertainties associated with each of the data sets, including the zenith tropospheric delay (ZTD)-to-IWV conversion methods and auxiliary data, are quantified and discussed. The IWV estimates from the reprocessed data set are compared to the Vaisala RS41 radiosonde measurements operated from the Barbados Cloud Observatory (BCO) and to the measurements from the operational radiosonde station at Grantley Adams International Airport (GAIA), Bridgetown, Barbados. A significant dry bias is found in the GAIA humidity observations with respect to the BCO sondes (−2.9 kg m−2) and the GNSS results (−1.2 kg m−2). A systematic bias between the BCO sondes and GNSS is also observed (1.7 kg m−2), where the Vaisala RS41 measurements are moister than the GNSS retrievals. The IWV estimates from a collocated microwave radiometer agree with the BCO soundings after an instrumental update on 27 January, while they exhibit a dry bias compared to the soundings and to GNSS before that date. IWV estimates from the ECMWF fifth-generation reanalysis (ERA5) are overall close to the GAIA observations, probably due to the assimilation of these observations in the reanalysis. However, during several events where strong peaks in IWV occurred, ERA5 is shown to significantly underestimate the GNSS-derived IWV peaks. Two successive peaks are observed on 22 January and 23–24 January which were associated with heavy rain and deep moist layers extending from the surface up to altitudes of 3.5 and 5 km, respectively. ERA5 significantly underestimates the moisture content in the upper part of these layers. The origins of the various moisture biases are currently being investigated. We classified the cloud organization for five representative GNSS stations across the Caribbean arc using visible satellite images. A statistically significant link was found between the cloud patterns and the local IWV observations from the GNSS sites as well as the larger-scale IWV patterns from the ECMWF ERA5 reanalysis. The reprocessed ZTD and IWV data sets from 49 GNSS stations used in this study are available from the French data and service centre for atmosphere (AERIS) (https://doi.org/10.25326/79; Bock, 2020b).

Evaluation of Zenith Tropospheric Delay Derived from Ray-Traced VMF3 Product over the West African Region Using GNSS Observations

The growing demand for Global Navigation Satellite System (GNSS) technology has necessitated the establishment of a vast and ever-growing network of International GNSS Service (IGS) tracking stations worldwide. The IGS provides highly accurate and highly reliable daily time-series Zenith Tropospheric Delay (ZTD) products using data from the member sites towards the use of GNSS for precise geodetic, climatological, and meteorological applications. However, if for reasons like poor internet connectivity, equipment failure, and power outages, the IGS station is inaccessible or malfunctioning, and gaps are created in the data archive resulting in degrading the quality of the ZTD and precipitable water vapour (PWV) estimation. To address this challenge as a means of providing an alternative data source to improve the continuous availability of ZTD data and as a backup data in the event that the IGS site data are missing or unavailable in West Africa, this paper compares the sitewise operational Vienna Mapping Functions 3 (VMF3) ZTD product with the IGS final ZTD product over five IGS stations in West Africa. Eight different statistical evaluation metrics, such as the mean bias (MB), mean absolute error (MAE), root mean squared error (RMSE), Pearson correlation coefficient (r), coefficient of determination (r2), refined index of agreement (IAr), Nash–Sutcliffe coefficient of efficiency (NSE), and the fraction of prediction within a factor of two (FAC2), are employed to determine the degree of agreement between the VMF3 and IGS tropospheric products. The results show that the VMF3-ZTD product performed excellently and matches very well with the IGS final ZTD product with an average MB, MAE, RMSE, r, r2, NSE, IAr, and FAC2 of 0.38 cm, 0.87 cm, 1.11 cm, 0.988, 0.976, 0.967, 0.992, and 1.00 (100%), respectively. This result is an indication that the VMF3-ZTD product is accurate enough to be used as an alternative source of ZTD data to augment the IGS final ZTD product for positioning and meteorological applications in West Africa.

Зенитная тропосферная задержка по данным GPS наблюдений и измерений радиометром водяного пара в пункте Badg (Бадары, Республика Бурятия)

A comparison was carried out of the values of the total zenith tropospheric delay (ZTD) revealed from the observations of the GPS satellite navigation system and measurements by a microwave radiometer of water vapor (MRWV) at the BADG permanent measurement point located on the territory of the “Badary” Observatory of the Institute of Applied Astronomy of the Russian Academy of Sciences. GPS antenna, MRWV device and meteorological station are located in close proximity to each other. This significantly affected the accuracy of the processed data. The differences in the values of the total zenith tropospheric delay obtained from GPS observations and measurements with a microwave radiometer of water vapor are analyzed in terms of mean and standard deviations and the coefficient of cross-correlation. Comparison of the results for 2020 year showed very good agreement. In summer, the BIAS of the difference between the ZTD data from GPS and MRWV observations is about 0.63% of the average summer ZTD value, the cross-correlation coefficient between the data is K = 0.85. In winter, the BIAS of the difference was about 0.21% of the average winter value of ZTD, the cross-correlation coefficient between the data is about K = 0.93. A high degree of reliability of data on ZTD and tropospheric moisture content obtained by continuous GPS measurements is shown.

Improved Zenith Tropospheric Delay Modeling Using the Piecewise Model of Atmospheric Refractivity

As one of the atmosphere propagation delays, the tropospheric delay is a significant error source that should be properly handled in high-precision global navigation satellite system (GNSS) applications. We propose an improved zenith tropospheric delay (ZTD) modeling method whereby the piecewise model of the atmospheric refractivity is introduced. Compared with using the exponential model to fit ZTD in vertical direction, the ZTD piecewise model has a better performance. Based on ERA5 2.5° × 2.5° reanalysis data produced by the European Centre for Medium-Range Weather Forecasting (ECMWF) from 2013 to 2017, we establish the regional gridded ZTD model (RGZTD) using a trigonometric function for China and the surrounding areas, which ranges from 70° E to 135° E in longitude and from 15° N to 55° N in latitude. To verify the performance of RGZTD model, the ERA5 ZTD data in 2017–2018, the radiosonde ZTD data from 86 radiosonde stations over China in 2017–2018, and the tropospheric delay products on 251 GNSS stations from Crustal Movement Observation Network of China (CMONOC) in 2016–2017 are used as external compliance check data. The results show that the overall accuracy of RGZTD model is better than that of exponential model, UNB3m model, and GPT3 model. Moreover, the accuracy can be improved by about 13.4%, 7.1%, and 6.2% when ERA5 reanalysis data, radiosonde data, and CMONOC data are used as reference values, respectively. High-accuracy ZTD data can be provided because the RGZTD model takes into account the vertical variation of ZTD through the new piecewise model.

A New Global Tropospheric Delay Model Considering the Spatiotemporal Variation Characteristics of ZTD With Altitude Coefficient

AbstractTropospheric delay error is independent of the signal's frequency and has strong spatiotemporal variation. It is one of the most severe error sources of satellite navigation and spatial measurement. In view of the limitation of global zenith tropospheric delay (GZTD) model considering the altitude coefficient β as a constant and ignoring its spatiotemporal variation, this paper analyzes the spatiotemporal distribution of zenith tropospheric delay (ZTD) with altitude variation coefficient β based on the meteorological reanalysis data provided by the European Centre for Medium‐Range Weather Forecasting from 2011 to 2015. The global altitude coefficient β model is established by using the trigonometric function and seventh‐order spherical harmonics function model, and then the global tropospheric delay model R_GZTD (reconstruction GZTD) is reconstructed by using Gbeta (Global beta β) model. The R_GZTD model gives high‐accuracy global distribution of tropospheric delays without meteorological parameters. The results show that the internal accuracy of the R_GZTD model is 3.22 cm, which has a good fitting effect. This paper uses the tropospheric delay products in 2016–2017 provided by the International GNSS Service, the tropospheric delay calculated by the European Centre for Medium‐Range Weather Forecasting reanalysis data, and the radiosonde ZTD data in 2016–2017 as external compliance check data. The results show that the accuracy of the R_GZTD model is better than that of the GZTD model, UNB3m model, and the global pressure and temperature 2 wet model in the global and regional scope. Especially in areas with a higher altitude, the correction effect of the R_GZTD model is more significant. The root‐mean‐square error is 8.5% smaller than that of the GZTD model in the range of 0–500 m, 14.6% smaller in the range of 500–1,000 m, 12.5% smaller in the range of 1,000–2,000 m, and 16.8% smaller in the range above 2,000 m. The accuracy with the increasement of height is due to the fact that the R_GZTD model takes account of the spatiotemporal variation of β.

Assessing the Impact of GNSS ZTD Data Assimilation into the WRF Modeling System during High-Impact Rainfall Events over Greece

The derivation of global navigation satellite systems (GNSSs) tropospheric products is nowadays a state-of-the-art technique that serves both research and operational needs in a broad range of applications in meteorology. In particular, GNSS zenith tropospheric delay (ZTD) data assimilation is widely applied in Europe to enhance numerical weather predictions (NWPs). The current study presents the first attempt at introducing assimilation of ZTDs, derived from more than 48 stations of the Hellenic GNSS network, into the operational NWP system of the National Observatory of Athens (NOA) in Greece, which is based on the mesoscale Weather Research and Forecasting (WRF) model. WRF was applied during seven high-impact precipitation events covering the dry and wet season of 2018. The simulation employing the ZTD data assimilation reproduces more accurately, compared to the control experiment, the observed heavy rainfall (especially for high precipitation events, exceeding 20 mm in 24h) during both dry and wet periods. Assimilating ZTDs also improves the simulation of intense (>20 mm) convective precipitation during the time window of its occurrence in the dry season, and provides a beneficial influence during synoptic-scale events in the wet period. The above results, which are statistically significant, highlight an important positive impact of ZTD assimilation on the model’s precipitation forecast skill over Greece. Overall, the modelling system’s configuration, including the assimilation of ZTD observations, satisfactorily captures the spatial and temporal distribution of the observed rainfall and can therefore be used as the basis for examining further improvements in the future.