Zenith Tropospheric Delay Estimates Research Articles

Real-time retrieval of high-precision ZTD maps using GNSS observation

Zenith Tropospheric Delay (ZTD) is an important factor that restricts the high-precision positioning of global navigation satellite system (GNSS), and it is of great significance in establishing a real-time and high-precision ZTD model. However, existing ZTD models only consider the impact of linear terms on ZTD estimation, whereas the nonlinear factors have rarely been investigated before and thus become the focus of this study. A real-time and high-precision ZTD model for large height difference area is proposed by considering the linear and nonlinear characteristics of ZTD spatiotemporal variations and is called the real-time linear and nonlinearity ZTD (RLNZ) model. This model uses the ZTD estimated from the Global Pressure and Temperature 3 (GPT3) model as the initial value. The linear impacts of periodic term and height on the estimation of ZTD difference between GNSS and GPT3 model is first considered. In addition, nonlinear factors such as geographical location and time are further used to fit the remaining nonlinear ZTD residuals using the general regression neural network method. Finally, the RLNZ-derived ZTD is obtained at an arbitrary location. The western United States, with height difference ranging from −500 to 4000 m, is selected, and the hourly ZTD of 484 GNSS stations provided by the Nevada Geodetic Laboratory (NGL) and the data of 9 radiosonde (RS) stations in the year 2021 are used. Experiment results show that a better performance of ZTD estimation can be retrieved from the proposed RLNZ model when compared with the GPT3 model. Statistical results show the averaged root mean square (RMS), Bias, and mean absolute error (MAE) of ZTD from GPT3 and RLNZ models are 33.7/0.8/25.7 mm and 22.6/0.1/17.4 mm, respectively. The average improvement rate of the RLNZ model is 33 % when compared to the GPT3 model. Finally, the application of the proposed RLNZ model in simulated real-time Precise Point Positioning (PPP) indicates that the accuracy of PPP in N, E and U components is improved by 8 %, 2 %, and 6 % when compared with that from the GPT3-based PPP. Meanwhile, the convergence time in N and U components is improved by 23 % and 7 %, respectively. Such results verify the superiority of the proposed RLNZ model in retrieving real-time ZTD maps for GNSS positioning and navigation applications.

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.

Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations

Multi-Global Navigation Satellite Systems (multi-GNSS) (including GPS, BDS, Galileo, and GLONASS) provide a significant opportunity for high-quality zenith tropospheric delay estimation and its applications in meteorology. However, the performance of zenith total delay (ZTD) retrieval from single- or multi-GNSS observations is not clear, particularly from the new, fully operating BDS-3. In this paper, zenith tropospheric delay is estimated using the single-, dual-, triple-, or four-GNSS Precise Point Positioning (PPP) technique from 55 Multi-GNSS Experiment (MGEX) stations over one year. The performance of GNSS ZTD estimation is evaluated using the International GNSS Service (IGS) standard tropospheric products, radiosonde, and the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5). The results show that the GPS-derived ZTD time series is more consistent and reliable than those derived from BDS-only, Galileo-only, and GLONASS-only solutions. The performance of the single-GNSS ZTD solution can be enhanced with better accuracy and stability by combining multi-GNSS observations. The accuracy of the ZTD from multi-GNSS observations is improved by 13.8%, 43.8%, 27.6%, and 22.9% with respect to IGS products for the single-system solution (GPS, BDS, Galileo, and GLONASS), respectively. The ZTD from multi-GNSS observations presents higher accuracy and a significant improvement with respect to radiosonde and ERA5 data when compared to the single-system solution.

Retrieval of tropospheric delays from multi-GNSS observations in the polar region: effect factors and performance

Precise point positioning (PPP) technique is practical in estimating the zenith tropospheric delay (ZTD). To comprehensively study the factors affecting its accuracy in the polar region, different elevation cutoff angles for each single system and multi-system combination, different tropospheric mapping functions, tropospheric gradients and also seasonal variations are assessed. Meanwhile, European Centre for Medium-Range Weather Forecasts (ECMWF) products are adopted to validate the accuracy of PPP-derived ZTD. The results show that the root mean square (RMS) value of the estimated ZTD and ECMWF products is around 4 mm when the elevation cutoff angle is set to 10 degrees or less. From the view of system combination, it improves the ZTD accuracy in comparison with each individual system. The dual-system combination has 21.8%, 19.0% and 19.1% improvements in its ZTD accuracy compared with the Global navigation satellite system (GLONASS), Beidou navigation satellite system (BDS) and Galileo satellite navigation (GAL) systems. The four-system combination can reach 7.7% further improvement in ZTD estimation than that of the dual-system. For mapping functions, Vienna mapping function 3 (VMF3) function has the best accuracy among the four mapping functions of Niell mapping function (NMF), global mapping function, VMF1 and VMF3, while NMF does not perform as well as others. Considering the tropospheric gradients could get higher accuracy in ZTD estimation than ignoring them. The tropospheric delay estimated in winter is more accurate than that in summer and specifically the RMS value in winter is about 0.9 mm lower than that in summer. Overall, from investigation the estimation of ZTD in the polar region can be optimally handled with a multi-system and VMF3 mapping function at an elevation cutoff angle of 7°, considering the tropospheric gradients.

Assessment of GNSS zenith tropospheric delay responses to atmospheric variables derived from ERA5 data over Nigeria

Tropospheric delay is a major error caused by atmospheric refraction in Global Navigation Satellite System (GNSS) positioning. The study evaluates the potential of the European Centre for Medium-range Weather Forecast (ECMWF) Reanalysis 5 (ERA5) atmospheric variables in estimating the Zenith Tropospheric Delay (ZTD). Linear regression models (LRM) are applied to estimate ZTD with the ERA5 atmospheric variables. The ZTD are also estimated using standard ZTD models based on ERA5 and Global Pressure and Temperature 3 (GPT3) atmospheric variables. These ZTD estimates are evaluated using the data collected from the permanent GNSS continuously operating reference stations in the Nigerian region. The results reveal that the Zenith Hydrostatic Delay (ZHD) from the LRM and the Saastamoinien model using ERA5 surface pressure are of identical accuracy, having a Root Mean Square (RMS) error of 2.3 mm while the GPT3-ZHD has an RMS of 3.4 mm. For the Zenith Wet Delay (ZWD) component, the best estimates are derived using ERA5 Precipitable Water Vapour (PWV). These include the ZWD derived by the LRM having an average RMS of 20.9 mm and Bevis equation having RMS of 21.1 mm and 21.0 mm for global and local weighted mean temperatures, respectively. The evaluation of GPT3-ZWD estimates gives RMS of 45.8 mm. This study has provided a valuable insight into the application of ERA5 data for ZTD estimation. In line with the findings of the study, the ERA5 atmospheric variables are recommended for improving the accuracy in ZTD estimation, required for GNSS positioning.

Refinement of global gridded ray-traced Zenith tropospheric delay over Nigeria based on local GNSS network observations

• Application of deep structured supervised neural network modelling technique. • Data derived from the local GNSS observation within the study area. • A refinement model is developed to predict ZTD parameters at user-defined points. • Improvement in the accuracy of the local refine VMF1-ZTD estimates. Recent studies on the application of Zenith Tropospheric Delay (ZTD) in meteorology and geodesy have shown improved accuracy with the use of locally estimated ZTD compared to Global ZTD. This paper focuses on the refinement of global gridded ray-traced Vienna Mapping Functions 1 (VMF1) ZTD over Nigeria, using ZTD estimates derived from local GNSS Continuously Operating Reference Stations (CORS) observations. Three (3) years of GNSS observations collected at 13 CORS located within the study area were post-processed using GNSS Analysis and Processing Software (GAPS) to derive the local GNSS-ZTD estimates. The global VMF1-ZTD were interpolated at the locations of the local GNSS-CORS. An optimal deep structured supervised Neural Network (NN) was derived by training feedforward networks using the Levenberg-Marquardt backpropagation algorithm, with spatiotemporal variables and VMF1-ZTD as inputs and the GNSS-ZTD as the target. The outputs from the NN model were assessed using internal and external data. Results from internal data evaluations indicated a robust and accurate model output with optimum network performances indicating MSE of ∼7.22 × 10 −6 m and ∼4.56 × 10 −4 m for hydrostatic and wet ZTD networks respectively. The external data evaluations performed using the International GNSS Services (IGS) Zenith Path Delay (ZPD), indicated an RMSE range of ∼0.041 m to 0.095 m for global-VMF1 and ∼0.030 m to 0.037 m for the Local Refine (LR)-VMF1. The results suggest that the application of ZTD estimates derived from local GNSS observations in the refinement of global gridded VMF1-ZTD yields an improved accuracy over Nigeria. Consequently, the LR-VMF1 ZTD estimates are recommended for improved accuracy, required for geodetic and meteorological applications in and around Nigeria :

Applying Malawi Continuously Operating Reference Stations (CORS) in GNSS Meteorology

Global Navigation Satellite System (GNSS) signals in the L-band are affected by the non-dispersive neutral atmosphere. Regardless of their center frequency, the L-band code and phase observations are affected by the same measure of delay. GNSS receivers play a significant role in quantifying the zenith tropospheric delay (ZTD) from satellite signals. Malawi has a Continuously Operating Reference Stations (CORS) network which was established to support research in geophysical geodesy and geodynamics. However, the quality of the observations tracked by the CORS has never been tested in terms of its meteorological application. In this paper, the ZTD estimation approach and the evaluation of results from the Global Positioning System (GPS) measurements are presented. The optimal approach of precise point positioning (PPP) was used to estimate ZTD from one-week datasets which were collected from six CORS monuments distributed in the northern and southern regions of Malawi. In addition, the zenith wet delay (ZWD) and zenith hydrostatic delay (ZHD) were also estimated to determine their respective contributions to the total delay in all the stations. Alongside the meteorological parameters, the positioning repeatabilities were also established for all stations. Results indicate that the averaged ZTD, ZWD and ZHD can reach as high as 247mm, 47 mm, and 199 mm, respectively. The minimum ZTD, ZWD, and ZHD for the stations can drop to as low as 220 mm, 24 mm, and 181 mm, respectively. This indicates that the ZHD contributes to more than 90% of the total delay at the stations. For the positioning performance, there was no obvious disparity in the latitude (less than 0.5 cm), longitude (less than 1 cm), and ellipsoidal height repeatabilities (less than 1.5 cm). Thus, the results clearly demonstrate that the Malawi CORS network may be used for GNSS-based meteorological applications using the available geodetic receivers. However, for high precision meteorological applications, Malawi may consider densifying the available network with geodetic grade receivers.
  

Assessment of tropospheric modeling on PPP-AR performances under brazilian atmospheric condition

In the Global Navigation Satellite System (GNSS), ambiguity resolution (AR) can shorten observation time and increase the positioning quality. The correct tropospheric modeling is intrinsically related to the ability to perform AR. Here, we assessed the influence of different tropospheric correction alternatives on AR for static Precise Point Positioning (PPP) in Brazilian territory. Our goal was to provide directions to users when choosing a suitable tropospheric model for application in PPP-AR under Brazilian atmospheric conditions. Thus, this study was carried out using well-known models such as the Saastamoinen model and the Zenith Tropospheric Delay (ZTD) Estimation and Numerical Weather Prediction (NWP) model from CPTEC/INPE. Six GNSS stations from the Brazilian Network for Continuous Monitoring (RBMC) (BRAZ, UFPR, RNNA, POVE, SMAR, and SAGA) were selected. Different GNSS processing setups were considered for GNSS data registered at selected stations during summer and winter. The assessment was based on a statistical analysis of positioning accuracy during one-hour sessions. The results indicated that such as the ZTD Estimation, the NWP model provides an accuracy of a few centimeters. On the other hand, the Saastamoinen model provided decimeter level accuracy, thus it is not the recommended choice for PPP-AR in the experimental conditions.

Comparative analysis of real-time precise point positioning method in terms of positioning and zenith tropospheric delay estimation

The positioning performance of widely used real-time precise point positioning (RT-PPP) software packages BNC, RTKLIB, and PPP-WIZARD were tested in terms of convergence time and accuracy. The convergence time of PPP-WIZARD solutions is reduced by ambiguity resolution (AR). The GPS + GLONASS + GALILEO (GRE) mode improved the convergence time of GPS + GALILEO (GE) mode by 22.0%, 15.5%, 17.1%, and 11.4% for the BNC, RTKLIB, PPP-WIZARD (AR) and PPP-WIZARD, respectively. For the GRE mode, RMSEs of the BNC, RTKLIB, PPP-WIZARD (AR), and PPP-WIZARD software packages in the horizontal/vertical component are 3.8/5.6, 2.6/6.2, 3.3/6.5, 4.3/7.0 cm, respectively. In comparison with the IGS-ZTD (International GNSS Service ZTD), BNC, RTKLIB, PPP-WIZARD (AR), and PPP-WIZARD solutions show a mean bias of 0.28, −0.72, 2.80, and 2.83 cm, respectively in GE mode. The GRE mode reduced the RMSEs of the ZTD estimations of BNC, RTKLIB, PPP-WIZARD (AR) and PPP-WIZARD by 2.9%, 5.1%, 0.6%, and 0.4% respectively.

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.

Kinematic Zenith Tropospheric Delay Estimation with GNSS PPP in Mountainous Areas

The use of global navigation satellite systems (GNSS) precise point positioning (PPP) to estimate zenith tropospheric delay (ZTD) profiles in kinematic vehicular mode in mountainous areas is investigated. Car-mounted multi-constellation GNSS receivers are employed. The Natural Resources Canada Canadian Spatial Reference System PPP (CSRS-PPP) online service that currently processes dual-frequency global positioning system (GPS) and Global’naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) measurements and is now capable of GPS integer ambiguity resolution is used. An offline version that can process the above and Galileo measurements simultaneously, including Galileo integer ambiguity resolution is also tested to evaluate the advantage of three constellations. A multi-day static data set observed under open sky is first tested to determine performance under ideal conditions. Two long road profile tests conducted in kinematic mode are then analyzed to assess the capability of the approach. The challenges of ZTD kinematic profiling are numerous, namely shorter data sets, signal shading due to topography and forests of conifers along roads, and frequent losses of phase lock requiring numerous but not always successful integer ambiguity re-initialization. ZTD profiles are therefore often only available with float ambiguities, reducing system observability. Occasional total interruption of measurement availability results in profile discontinuities. CSRS-PPP outputs separately the zenith hydrostatic or dry delay (ZHD) and water vapour content or zenith wet delay (ZWD). The two delays are analyzed separately, with emphasis on the more unpredictable and highly variable ZWD, especially in mountainous areas. The estimated delays are compared with the Vienna Mapping Function 1 (VMF1), which proves to be highly effective to model the large-scale profile variations in the Canadian Rockies, the main contribution of GNSS PPP being the estimation of higher frequency ZWD components. Of the many conclusions drawn from the field experiments, it is estimated that kinematic profiles are generally determined with accuracy of 10 to 20 mm, depending on the signal harshness of the environment.

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.

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

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

Assessment of GNSS PPP-Based Zenith Tropospheric Delay

Abstract This study assesses the precision of zenith tropospheric delay (ZTD) obtained through triple-constellation global navigation satellite system (GNSS) precise point positioning (PPP). Various ZTD estimates are obtained as by-products from GPS-only, GPS/Galileo, GPS/BeiDou, and triple-constellation GPS/Galileo/BeiDou PPP solutions. Triple-constellation GNSS observations from a number of globally distributed reference stations are processed over a period of seven days in order to investigate the daily performance of the ZTD estimates. The estimated ZTDs are then validated by comparing them with the International GNSS Service (IGS) tropospheric products and the University of New Brunswick (UNB3m) model counterparts. It is shown that the ZTD estimates agree with the IGS counterparts with a maximum standard deviation (STD) of 2.4 cm. It is also shown that the precision of estimated ZTD from the GPS/Galileo and GPS/Galileo/BeiDou PPP solutions is improved by about 4.5 and 14%, respectively, with respect to the GPS-only PPP solution. Moreover, it is found that the estimated ZTD agrees with the UNB3m model with a maximum STD of 3.1 cm. Furthermore, the GPS/Galileo and GPS/Galileo/BeiDou PPP enhance the precision of the ZTD estimates by about 6.5 and 10%, respectively, in comparison with the GPS-only PPP solution.

The Impact of Different Ocean Tide Loading Models on GNSS Estimated Zenith Tropospheric Delay Using Precise Point Positioning Technique

Global navigation satellite systems (GNSSs) have become an important tool to derive atmospheric products, such as the total zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) for weather and climate studies. The ocean tide loading (OTL) effect is one of the primary errors that affects the accuracy of GNSS-derived ZTD/PWV, which means the study and choice of the OTL model is an important issue for high-accuracy ZTD estimation. In this study, GNSS data from 1 January 2019 to 31 January 2019 are processed using precise point positioning (PPP) at globally distributed stations. The performance of seven widely used global OTL models is assessed and their impact on the GNSS-derived ZTD is investigated by comparing them against the ZTD calculated from co-located radiosonde observations. The results indicate that the inclusion or exclusion of the OTL effect will lead to a difference in ZTD of up to 3–15 mm for island stations, and up to 1–2 mm for inland stations. The difference of the ZTD determined with different OTL models is quite small, with a root-mean-square (RMS) value below 1.5 mm at most stations. The comparison between the GNSS-derived ZTD and the radiosonde-derived ZTD indicates that the adoption of OTL models can improve the accuracy of GNSS-derived ZTD. The results also indicate that the adoption of a smaller cutoff elevation, e.g., 3° or 7°, can significantly reduce the difference between the ZTDs determined by GNSS and radiosonde, when compared against a 15° cutoff elevation. Compared to the radiosonde-derived ZTD, the RMS error of GNSS-derived ZTD is approximately 25–35 mm at a cutoff elevation of 15°, and 15–25 mm when the cutoff elevation is set to 3°.

An advanced residual error model for tropospheric delay estimation

Global navigation satellite systems (GNSS) are widely used for safety-of-life positioning applications. Such applications require high integrity, availability, and continuity of the positioning service. Integrity is assessed by the definition of a protection level, which is an estimation of the maximum positioning error at extremely low probability levels. The emergence of multi-frequency civilian signals and the availability of satellite-based augmentation systems improve the modeling of ionospheric disturbances considerably. As a result, in many applications the tropospheric delay tends to become one of the limiting factors of positioning—especially at low elevation angles. The currently adopted integrity concepts employ a global constant to model the variance of the residual tropospheric delay error. We introduce a new approach to derive residual tropospheric delay error models using the extreme value analysis technique. Seventeen years of global numerical weather model fields are analyzed, and new residual error models are derived for some recently developed tropospheric delay models. Our approach provides models that consider both the geographical location and the seasonal variation of meteorological parameters. Our models are validated with a 17-year-long time series of zenith tropospheric delay estimates as provided by the International GNSS Service. The results show that the developed models are still conservative, while the maximal residual error of the tropospheric delay is still improved by 39–55%. This improvement yields higher service availability and continuity in safety-of-life applications of GNSS.

High Quality Zenith Tropospheric Delay Estimation Using a Low-Cost Dual-Frequency Receiver and Relative Antenna Calibration

The recent release of consumer-grade dual-frequency receivers sparked scientific interest into use of these cost-efficient devices for high precision positioning and tropospheric delay estimations. Previous analyses with low-cost single-frequency receivers showed promising results for the estimation of Zenith Tropospheric Delays (ZTDs). However, their application is limited by the need to account for the ionospheric delay. In this paper we investigate the potential of a low-cost dual-frequency receiver (U-blox ZED-F9P) in combination with a range of different quality antennas. We show that the receiver itself is very well capable of achieving high-quality ZTD estimations. The limiting factor is the quality of the receiving antenna. To improve the applicability of mass-market antennas, a relative antenna calibration is performed, and new absolute Antenna Exchange Format (ANTEX) entries are created using a geodetic antenna as base. The performance of ZTD estimation with the tested antennas is evaluated, with and without antenna Phase Center Variation (PCV) corrections, using Precise Point Positioning (PPP). Without applying PCVs for the low-cost antennas, the Root Mean Square Errors (RMSE) of the estimated ZTDs are between 15 mm and 24 mm. Using the newly generated PCVs, the RMSE is reduced significantly to about 4 mm, a level that is excellent for meteorological applications. The standard U-blox ANN-MB-00 patch antenna, with a circular ground plane, after correcting the phase pattern yields comparable results (0.47 mm bias and 4.02 mm RMSE) to those from geodetic quality antennas, providing an all-round low-cost solution. The relative antenna calibration method presented in this paper opens the way for wide-spread application of low-cost receiver and antennas.

Improved GPT2w (IGPT2w) model for site specific zenith tropospheric delay estimation in China

Despite being a systematic error source in global navigation satellite system (GNSS) positioning and navigation, tropospheric delay is a key parameter in GNSS meteorology. Therefore, deriving a zenith tropospheric delay (ZTD) value as accurately as possible from an empirical model without using auxiliary data is a prerequisite for the high-precision application of GNSS positioning and navigation. To reach the goal above, this paper proposes an improved model to estimate the ZTD based on the Global Pressure and Temperature 2 wet (GPT2w) model, which is called the improved GPT2w (IGPT2w) model. The GPT2w-derived ZTD is first calculated as the initial value of the IGPT2w model, and the time series of ZTD residual can thus be obtained between the GNSS- and GPT2w-derived ZTDs over GNSS stations. Analysis of the long time series variation of ZTD residuals using the multichannel singular spectrum analysis method reveals evident periodic signals. The Lomb–Scargle method is then used to determine the specific values of these periodic signals, and different periods are identified at various GNSS stations. Therefore, a ZTD residual model that considers annual, semi-annual, and seasonal periods is established. The IGPT2w model, in which the ZTD value is obtained by combining the estimated ZTD residual and the GPT2w-derived ZTD, can be acquired. A total of 188 GNSS stations in China throughout 2015 to 2017 are selected to validate the IGPT2w model. In the model, the GNSS-derived ZTD is obtained using the GAMIT/GLOBK software, and the accuracy is validated using radiosonde data with root mean square and bias of 1.9 and 0.1 cm, respectively, at 33 collocated stations in China. Statistical results reveal that the accuracy of the IGPT2w-derived ZTD is improved by 13.7% compared with that of the GPT2w-derived ZTD when the GNSS-derived ZTD is regarded as the reference. Such result indicates that the proposed IGPT2w model outperforms the GPT2w model in China.

Variability and accuracy of Zenith Total Delay over the East African tropical region

The Global Navigation Satellite System (GNSS) can be used to derive accurately the Zenith Tropospheric Delay (ZTD) under all-weather conditions. The derived ZTDs play a vital role in climate studies, weather forecasting and are operationally assimilated into numerical weather prediction models. In this study, variations and statistical analysis of GNSS-derived ZTD over the East African tropical region are analysed. The data is collected from 13 geodetic permanent stations for the period of 4 years from 2013 to 2016. The 13 stations consist of 5 International GNSS Service (IGS) stations plus 8 stations as follows: 4 Africa Array stations and 4 Malawi Rifting stations from Uganda, Kenya, Tanzania and Rwanda. The ZTD time series were processed using goGPS software version 1.0 beta1, a MATLAB based GNSS processing software, originally developed for kinematic applications but recently re-engineered for quasi static applications. The annual variation of the ZTD time series was investigated using Lomb Scargle periodograms. The semi-annual frequency has the dominant power in subregion 1 (latitudes 4 °S and 4 °N) and the annual frequency has the dominant power in subregion 2 (latitudes 12 °S to 4 °S). The highest ZTD estimates occur during the rainy seasons, at all stations, and the lowest estimates occur during the dry seasons. The results also show that the ZTD estimates are largest at stations located at low elevation (regions close to the Indian Ocean). The derived ZTDs are compared to the values derived from the GIPSY-OASIS via Jet Propulsion Laboratory (JPL) online Automatic Precise Positioning Service (APPS) and the Unified Environmental Modelling System (UEMS) numerical weather prediction (NWP) model. The comparison of goGPS and APPS ZTD at the 13 stations shows an overall average bias, Root Mean Square (RMS) and standard deviation (stdev) of −0.9 mm, 3.2 mm and 3.0 mm respectively, with correlation coefficients ranging from 0.974 to 0.999. The comparison of goGPS ZTD against UEMS NWP ZTD at 8 selected stations shows average bias, RMS and stdev of −12.4 mm, 22.0 mm and 17.6 mm respectively, with correlation coefficients ranging from 0.802 to 0.974. The agreement between the GPS ZTD and the NWP ZTD indicates that goGPS ZTD can be assimilated into NWP models in the East African region.

Potential of Cost-Efficient Single Frequency GNSS Receivers for Water Vapor Monitoring

Dual-frequency Global Navigation Satellite Systems (GNSSs) enable the estimation of Zenith Tropospheric Delay (ZTD) which can be converted to Precipitable Water Vapor (PWV). The density of existing GNSS monitoring networks is insufficient to capture small-scale water vapor variations that are especially important for extreme weather forecasting. A densification with geodetic-grade dual-frequency receivers is not economically feasible. Cost-efficient single-frequency receivers offer a possible alternative. This paper studies the feasibility of using low-cost receivers to increase the density of GNSS networks for retrieval of PWV. We processed one year of GNSS data from an IGS station and two co-located single-frequency stations. Additionally, in another experiment, the Radio Frequency (RF) signal from a geodetic-grade dual-frequency antenna was split to a geodetic receiver and two low-cost receivers. To process the single-frequency observations in Precise Point Positioning (PPP) mode, we apply the Satellite-specific Epoch-differenced Ionospheric Delay (SEID) model using two different reference network configurations of 50–80 km and 200–300 km mean station distances, respectively. Our research setup can distinguish between the antenna, ionospheric interpolation, and software-related impacts on the quality of PWV retrievals. The study shows that single-frequency GNSS receivers can achieve a quality similar to that of geodetic receivers in terms of RMSE for ZTD estimations. We demonstrate that modeling of the ionosphere and the antenna type are the main sources influencing the ZTD precision.