Hydrostatic Delay Research Articles

Developments of empirical models for vertical adjustment of precipitable water vapor measured by GNSS

In some applications of Precipitable Water Vapor (PWV) measured by Global Navigation Satellite System (GNSS), we have to consider PWV vertical adjustments (PWVVAs) due to the height differences between the target sites and the GNSS sites. Thus, developments of global empirical models for PWVVAs deserve our attention. In this study, we found that the decrease factor of water vapor (λ) can be also used as the decrease factor of PWV when we use the Smith’s vertical variations of water vapor. Based on this conclusion, PWVVAs can be carried out by using the empirical values of λ and atmospheric total pressure (or zenith hydrostatic delay). Thus, we gave two empirical models for PWVVAs (i.e. PWVVA-Ⅰ and PWVVA-Ⅱ). On the other hand, another aim of this research is to develop an empirical model of PWVVA using neural network (i.e. PWVVANN). Measured PWV of one site, the heights of this site and the target site, and empirical values of λ and zenith hydrostatic delay were considered as the input parameters of the PWVVANN model. The output is the PWV at the target height. Global statistical results verifythat the PWVVANN model has a accuracy of 1.08 mm and its accuracy has increased by respective 30.7 %, 24.4 % and 23.6 % when compared with PWVVA-Ⅰ, PWVVA-Ⅱ and a state of the art model (i.e. the GPWV-H model).

Analysis of Different Height Correction Models for Tropospheric Delay Grid Products over the Yunnan Mountains

Accurate tropospheric delays are of great importance for both Global Navigation Satellite System (GNSS)-based positioning and precipitable water vapor monitoring. The gridded tropospheric delay products, including zenith hydrostatic delays (ZHD) and zenith wet delays (ZWD), are the most ideal method for accessing accurate tropospheric delays. The vertical adjustment method is critical for implementing the gridded tropospheric products. In this work, we consider the different models used for grid products and assess their performance over Yunnan mountains with complex topography. We summarize the main results as follows: (1) The products can provide accurate ZHD with mean biases of −2.6 mm and mean Standard Deviation (STD) of 1.5 mm while the ZWD results from grid products show a performance with biases of −0.4 mm and STD of 1.3 cm over the Yunnan area. (2) The Tv-based model shows a better performance than the T0-based model and IGPZWD in rugged areas with large height differences. The grid products can provide hourly ZHD with biases of 3 mm and wet delay with mean biases of within 2 cm and mean STD of below 3 cm in the Yunnan mountains, which exhibit a large height difference of around 1.5 km. (3) The radiosondes results confirm that the Tv-based model has an obvious advantage in calculating ZHD height corrections for differences within 2 km while the T0-model suffers from a loss in accuracy in the case of large height differences. If the site is located more than 1 km below the reference height, the IGPZWD model can provide a better ZWD with a mean bias of 1.5 cm and a mean STD of 1.7 cm. With vertical reduction models, the grid products can provide accurate ZHD and ZWD in real time, even if in complex area.

The Comparison of Dry Hydrostatic Delay Measurement from GPS Ground-Based and Space- Based Receiver

The Comparison of Dry Hydrostatic Delay Measurement from GPS Ground-Based and Space- Based Receiver

Improving atmospheric pressure vertical correction model using Gaussian function

The Zenith Hydrostatic Delay (ZHD) is essential for high-precision Global Navigation Satellite System (GNSS) and Very Long Baseline Interferometry (VLBI) data processing. Accurate estimation of ZHD relies on in situ atmospheric pressure, which is primarily variable in the vertical direction. Current atmospheric pressure is either site-specific or has limited spatial coverage, necessitating vertical corrections for broader applicability. This study introduces a model that uses a Gaussian function for the vertical correction of atmospheric pressure when in situ meteorological observations are unavailable. Validation with the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5) reveals an average Bias and RMS for the new model of 0.31 hPa and 2.96 hPa, respectively. This corresponds to improvements of 37.5% and 80.3% in terms of RMS compared to two commonly used models (T0 and Tv models) that require in situ meteorological observations, respectively. Additional validation with radiosonde data shows an average Bias and RMS of 1.85 hPa and 4.87 hPa, corresponding to the improvement of 42.8% and 71.1% in RMS compared with T0 and Tv models, respectively. These accuracies are sufficient for calculating ZHD to an accuracy of 1 mm by performing atmospheric pressure vertical correction. The new model can correct atmospheric pressure from meteorological stations or numerical weather forecasts to different heights of the troposphere.

Global, spatially explicit modelling of zenith wet delay with XGBoost

Radio signals transmitted by Global Navigation Satellite System (GNSS) satellites experience tropospheric delays. While the hydrostatic part, referred to as zenith hydrostatic delay (ZHD) when mapped to the zenith direction, can be analytically modelled with sufficient accuracy, the wet part, referred to as zenith wet delay (ZWD), is much more difficult to determine and needs to be estimated. Thus, there exist several ZWD models which are used for various applications such as positioning and climate research. In this study, we present a data-driven, global model of the spatial ZWD field, based on the Extreme Gradient Boosting (XGBoost). The model takes the geographical location, the time, and a number of meteorological variables (in particular, specific humidity at several pressure levels) as input, and can predict ZWD anywhere on Earth as long as the input features are available. It was trained on ZWDs at 10718 GNSS stations and tested on ZWDs at 2684 GNSS stations for the year 2019. Across all test stations and all observations, the trained model achieved a mean absolute error of 6.1 mm, respectively, a root mean squared error of 8.1 mm. Comparisons of the XGBoost-based ZWD predictions with independently computed ZWDs and baseline models underline the good performance of the proposed model. Moreover, we analysed regional and monthly models, as well as the seasonal behaviour of the ZWD predictions in different climate zones, and found that the global model exhibits a high predictive skill in all regions and across all months of the year.

Characterization of Surface Pressure Accuracy and Spatial and Temporal Variations of The GPT3 And HGPT2 Models in The Chinese Region

The accuracy of surface pressure is crucial for obtaining high-precision zenith hydrostatic delay(ZHD). In order to verify the accuracy of the Global Pressure and Temperature model (HGPT2 ) and the Global Pressure and Temperature (GPT3) in obtaining ground air pressure in China, as well as the spatiotemporal variation characteristics of the errors of the two models, this paper uses the ERA5 reanalysis dataset and combines it with actual meteorological data from weather stations to evaluate their performance. The results show that the results show that the HGPT2 model has better accuracy in simulating atmospheric pressure in China than the GPT3 model, with atmospheric pressure bias of -0.54 hPa and -2.09 hPa, and RMS of 4.42 hPa and 4.91 hPa, respectively. This article analyzes the spatial and temporal characteristics of model errors based on China's climate types. The performance of the GPT3 and HGPT2 models varies in different regions, and their accuracy in simulating atmospheric pressure changes is poorer in northern and northwestern China.

Enhancing InSAR accuracy: Unveiling more accurate displacement fields through 3-D troposphere tomography

Interferometric Synthetic Aperture Radar (InSAR) measurements are susceptible to tropospheric delay induced by changes in tropospheric temperature, pressure, and water vapor. While pressure and temperature temporal variations have a limited impact on phase gradients, variations in water vapor, which contribute to the wet component of tropospheric delay, play a significant role. Therefore, obtaining a more accurate estimation of the wet refractivity of the tropospheric layer is crucial for improving InSAR displacement field accuracy. This paper presents the utilization of Global Navigation Satellite Systems (GNSS) tropospheric tomography for reconstructing three-dimensional (3-D) wet refractivity. Various data sources are employed, including GNSS measurements, ERA5 reanalysis data, radiosonde observations, and Sentinel-1A radar acquisitions. ERA5 reanalysis data and radiosonde observations are used to calculate tropospheric hydrostatic delay and to evaluate the wet refractivity obtained from tomography, respectively. The effectiveness of tomography techniques in mitigating the tropospheric signal in unwrapped interferograms is compared with the total tropospheric delay obtained from Generic Atmospheric Correction Online Service (GACOS) products, which is one of the most common approach for tropospheric correction of InSAR measurements. To ensure a comprehensive analysis, the effects of the correction methods are investigated in two different weather conditions. Based on the results, GNSS tropospheric tomography reduces the mean Root Mean Square Error (RMSE) by about 1.2 cm compared to GACOS products. This technique proves to be highly effective in improving the accuracy of InSAR displacement field estimation, particularly under challenging weather conditions.

An Optimized Framework for Precipitable Water Vapor Mapping Using TS-InSAR and GNSS

Observations of precipitable water vapor (PWV) in the atmosphere play a crucial role in weather forecasting and global climate change research. Spaceborne Interferometric Synthetic Aperture Radar (InSAR), as a widely used modern geodetic technique, offers several advantages to the mapping of PWV, including all-weather capability, high accuracy, high resolution, and spatial continuity. In the process of PWV retrieval by using InSAR, accurately extracting the tropospheric wet delay phase and obtaining a high-precision tropospheric water vapor conversion factor are critical steps. Furthermore, the observations of InSAR are spatio-temporal differential results and the conversion of differential PWV (InSAR ΔPWV) into non-difference PWV (InSAR PWV) is a difficulty. In this study, the city of Jinan, Shandong Province, China is selected as the experimental area, and Sentinel-1A data in 2020 is used for mapping InSAR ΔPWV. The method of small baseline subset of interferometry (SBAS) is adopted in the data processing for improving the coherence of the interferograms. We extract the atmosphere phase delay from the interferograms by using SRTM-DEM and POD data. In order to evaluate the calculation of hydrostatic delay by using the ERA5 data, we compared it with the hydrostatic delay calculated by the Saastamoinen model. To obtain a more accurate water vapor conversion factor, the value of the weighted average temperature Tm was calculated by the path integral of the ERA5. In addition, GNSS PWV is used to calibrate InSAR PWV. This study demonstrates a robust consistency between InSAR PWV and GNSS PWV, with a correlation coefficient of 0.96 and a root-mean-square error (RMSE) of 1.62 mm. In conclusion, our method ensures the reliability of mapping PWV by using Sentinel-1A interferograms and GNSS observations.

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.

A Precise Zenith Hydrostatic Delay Calibration Model in China Based on the Nonlinear Least Square Method

Abstract Zenith hydrostatic delay (ZHD) is a crucial parameter in Global Navigation Satellite System (GNSS) navigation and positioning and GNSS meteorology. Since the Saastamoinen ZHD model has a larger error in China, it is significant to improve the Saastamoinen ZHD model. This work first estimated the Saastamoinen model using the integrated ZHD as reference values obtained from radiosonde data collected at 73 stations in China from 2012 to 2016. Then, the residuals between the reference values and the Saastamoinen modeled ZHDs were calculated, and the correlations between the residuals and meteorological parameters were explored. The continuous wavelet transform method was used to recognize the annual and semiannual characteristics of the residuals. Because of the nonlinear variation characteristics of residuals, the nonlinear least squares estimation method was introduced to establish an improved ZHD model—China Revised Zenith Hydrostatic Delay (CRZHD)—adapted for China. The accuracy of the CRZHD model was assessed using radiosonde data and International GNSS Service (IGS) data in 2017; the radiosonde data results show that the CRZHD model is superior to the Saastamoinen model with a 69.6% improvement. The three IGS stations with continuous meteorological data present that the BIAS and RMSE are decreased by 2.7 and 1.5 (URUM), 5.9 and 5.3 (BJFS), and 9.6 and 8.8 mm (TCMS), respectively. The performance of the CRZHD model retrieving PWV was discussed using radiosonde data in 2017. It is shown that the CRZHD model retrieving PWV (CRZHD-PWV) outperforms the Saastamoinen model (SAAS-PWV), in which the precision is improved by 44.4%. The BIAS ranged from −1 to 1 mm and RMSE ranged from 0 to 2 mm in CRZHD-PWV account for 89.0% and 95.9%, while SAAS-PWV account for 46.6% and 58.9%. Significance Statement Zenith hydrostatic delay (ZHD) is one of the most important parameters in Global Navigation Satellite System (GNSS) navigation and positioning and GNSS meteorology, which can be derived from a precise ZHD model due to its stability. This research established an improved ZHD model for China to obtain accurate ZHD, which is a prerequisite for pinpoint precipitable water vapor (PWV) retrieval. And the PWV value is beneficial to analyze the change in precipitation in some regions, forecast the short-term rainfall, and monitor the climate.

Analysis of systematic biases in tropospheric hydrostatic delay models and construction of a correction model

Abstract. In the field of space geodetic techniques, such as global navigation satellite systems (GNSSs), tropospheric zenith hydrostatic delay (ZHD) is chosen as the a priori value of tropospheric total delay. Therefore, the inaccuracy of ZHD will definitely affect parameters like the wet delay and the horizontal gradient of tropospheric delay, accompanied by an indirect influence on the accuracy of geodetic parameters, if not dealt with well at low elevation angles. In fact, however, the most widely used ZHD model currently seems to contain millimeter-level biases from the precise integral method. We explored the bias of traditional ZHD models and analyzed the characteristics in different aspects on a global annual scale. It was found that biases differ significantly with season and geographical location, and the difference between the maximum and minimum values exceeds 30 mm, which should be fully considered in the field of high-precision measurement. Then, we constructed a global grid correction model, which is named ZHD_crct, based on the meteorological data of the year 2020 from the ECMWF (European Centre for Medium-Range Weather Forecasts), and it turned out that the bias of traditional models in the current year could be reduced by ∼ 50 % when the ZHD_crct was added. When we verified the effect of ZHD_crct on the biases in the next year, it worked almost the same as the former year. The mean absolute biases (MABs) of ZHD will be narrowed within ∼ 0.5 mm for most regions, and the SDs (standard deviations) will be within ∼ 0.7 mm. This improvement will be helpful for research on meteorological phenomena as well.

An enhanced integrated water vapour dataset from more than 10 000 global ground-based GPS stations in 2020

Abstract. We developed a high-quality global integrated water vapour (IWV) dataset from 12 552 ground-based global positioning system (GPS) stations in 2020. It consists of 5 min GPS IWV estimates with a total number of 1 093 591 492 data points. The completeness rates of the IWV estimates are higher than 95 % at 7253 (58 %) stations. The dataset is an enhanced version of the existing operational GPS IWV dataset provided by the Nevada Geodetic Laboratory (NGL). The enhancement is reached by employing accurate meteorological information from the fifth generation of European ReAnalysis (ERA5) for the GPS IWV retrieval with a significantly higher spatiotemporal resolution. A dedicated data screening algorithm is also implemented. The GPS IWV dataset has a good agreement with in situ radiosonde observations at 182 collocated stations worldwide. The IWV biases are within ±3.0 kg m−2 with a mean absolute bias (MAB) value of 0.69 kg m−2. The standard deviations (SD) of IWV differences are no larger than 3.4 kg m−2. In addition, the enhanced IWV product shows substantial improvements compared to NGL's operational version, and it is thus recommended for high-accuracy applications, such as research of extreme weather events and diurnal variations of IWV and intercomparisons with other IWV retrieval techniques. Taking the radiosonde-derived IWV as reference, the MAB and SD of IWV differences are reduced by 19.5 % and 6.2 % on average, respectively. The number of unrealistic negative GPS IWV estimates is also substantially reduced by 92.4 % owing to the accurate zenith hydrostatic delay (ZHD) derived by ERA5. The dataset is available at https://doi.org/10.5281/zenodo.6973528 (Yuan et al., 2022).

A Calibrated GPT3 (CGPT3) Model for the Site-Specific Zenith Hydrostatic Delay Estimation in the Chinese Mainland and Its Surrounding Areas

The prior zenith hydrostatic delay (ZHD) is an essential parameter for the Global Navigation Satellite System (GNSS) and very long baseline interferometry (VLBI) high-precision data processing. Meanwhile, the precise ZHD facilitates the separation of the high-precision zenith wet delay (ZWD) to derive precipitable water vapor (PWV). This paper analyzes the temporal variations in the residuals between GPT3 ZHD and reference ZHD from radiosonde (RS) sites, and a calibrated GPT3 (CGPT3) model is proposed for the site-specific ZHD estimation in the Chinese mainland and its surrounding areas based on the annual, semi-annual, and diurnal variations in residuals. Based on the validation using modeling RS data, the mean absolute error (MAE) and root mean square (RMS) of the CGPT3 model are 7.3 and 9.6 mm, respectively. The validation with RS ZHD not involved in the modeling suggests that the MAE and RMS of the CGPT3 model are 7.9 and 10.2 mm, respectively. These results show improvements of 16.8%/16.8% and 14.3%/13.6%, respectively, compared with the MAE and RMS of the GPT3 model and the newly proposed model (GTrop). In addition, the CGPT3 model has excellent spatial and temporal stability in the study area.

The New Improved ZHD and Weighted Mean Temperature Models Based on GNSS and Radiosonde Data Using GPT3 and Fourier Function

Compared to the zenith hydrostatic delay (ZHD) obtained from the Saastamonien model based on in-situ measured meteorological (IMM) data and radiosonde-derived weighted mean temperature (Tm), the ZHD and Tm deviations of the GPT3 model have shown obvious periodic trends. This article analyzed the seasonal variations of GPT3-ZHD and GPT3-Tm during the 2016–2020 period in the Yangtze River Delta region, and the new improved ZHD and Tm models were established by the multi-order Fourier function. The precision of the improved-ZHD model was verified using IMM-ZHD products from 7 GNSS stations during the 2016–2020 period. Furthermore, the precisions of improved Tm and precipitable water vapor (PWV) were verified by radiosonde-derived Tm and PWV in the 2016–2019 period. Compared with the IMM-ZHD and GNSS-PWV products, the mean Bias and RMS of GPT3-ZHD are −0.5 mm and 2.1 mm, while those of GPT3-PWV are 2.7 mm and 11.1 mm. Compared to the radiosonde-derived Tm, the mean Bias and RMS of GPT3-Tm are −0.8 K and 3.2 K. The mean Bias and RMS of the improved-ZHD model from 2019 to 2020 are −0.1 mm and 0.5 mm, respectively, decreasing by 0.4 mm and 1.6 mm compared to the GPT3-ZHD, while those of the improved-Tm are −0.6 K and 2.7 K, respectively, decreasing by 0.2 K and 0.5 K compared to GPT3-Tm. The mean Bias and RMS of PWV calculated by GNSS-ZTD, improved-ZHD, and improved-Tm are 0.5 mm and 0.6 mm, respectively, compared to the GNSS-PWV, decreasing by 2.2 mm and 10.5 mm compared to the GPT3-PWV. It indicates that the improved ZHD and Tm models can be used to obtain the high-precision PWV. It can be applied effectively in the retrieval of high-precision PWV in real-time in the Yangtze River Delta region.

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.

Data and documents used in ZHD_crct model (Analysis of Systematic Biases in Tropospheric Hydrostatic Delay Models and Construction of Correction Model)

Data and documents used in ZHD_crct model (Analysis of Systematic Biases in Tropospheric Hydrostatic Delay Models and Construction of Correction Model)

Modeling of precipitable water vapor from GPS observations using machine learning and tomography methods

This paper studies the application of two machine learning methods to model precipitable water vapor (PWV) using observations of 23 GPS stations from the local GPS network of north-west of Iran in 2011. In a first step, the zenith tropospheric delay (ZTD) and zenith hydrostatic delay (ZHD) is calculated with the Bernese GNSS software and Saastamoinen model as revised by Davis, respectively. Then, by subtracting the ZHD from the ZTD, the zenith wet delay (ZWD) is obtained at each GPS station, for all times. In a second step, ZWD is modeled by two different machine learning methods, based on the latitude, longitude, DOY, time, relative humidity, temperature and pressure. After training a Support Vector Machine (SVM) and an Artificial Neural Network (ANN), ZWD temporal and spatial variations are estimated. Using the formula by Bevis, the ZWD can be converted to PWV at any time and space, for each machine learning method. The accuracy of the two new models is evaluated using control stations, exterior and radiosonde station, whose observations were not used in the training step. Also, all the results of the SVM and ANN are compared with a voxel-based tomography (VBT) model. In the control and exterior stations, ZWD estimated by the SVM (ZWDSVM) and ANN (ZWDANN) is compared with the ZWD obtained from the GPS (ZWDGPS). Also, in the control and exterior stations, precise point positioning (PPP) is used to evaluate the accuracy of the new models. In the radiosonde station, the PWV of the new models (PWVSVM, PWVANN) is compared with the radiosonde PWV (PWVradiosonde) and voxel-based PWV (PWVVBT). The averaged relative error of the SVM, ANN and VBT models in the control stations is 10.50%, 12.71% and 12.91%, respectively. For SVM, ANN and VBT models, the averaged RMSE at the control stations is 1.87 (mm), 2.22 (mm) and 2.29 (mm), respectively. Analysis of the results of PWV estimated by the SVM, ANN and VBT, as well as the surface precipitation obtained from meteorological stations, indicate the high accuracy of the SVM in comparison with the ANN and VBT model. In the results shown in this paper, the SVM has the best ability to accurately estimate ZWD and PWV, using local GPS network observations.

Accuracy assessment of reanalysis datasets for GPS-PWV estimation using Indian IGS stations observations

GPS PWV (Precipitable Water Vapour) is estimated using three years ECMWF, JRA55, MERRA2, and NCEP datasets for two IGS stations HYDE and IISC in India to assess their accuracies over the Indian region. The NWP derived temperature, pressure, zenith hydrostatic delay (ZHD), zenith wet delay (ZWD), and PWV values are validated using AWS observations and derived products. The obtained PWV values are also compared with the total column water product from ECMWF. The results show absolute mean temperature differences of 1–2 °K and pressure differences of 1–4 hPa for HYDE and IISC. NWP models' pressure and temperature values strongly correlate with AWS values with R2 close to 0.9 in most of the cases. The estimated zenith tropospheric delay (ZTD) shows an average difference between 4 mm and 9 mm with respect to IGS ZTD. The mean differences between NWP and reference PWV values are observed from 1 mm to 3 mm. All the derived products obtained using NWP datasets are close to the reference AWS products. However, PWV derived using ECMWF, JRA55 and NCEP is very much close to AWS PWV and can be used for precise PWV computation in this region.

A global grid model for calibration of zenith hydrostatic delay

The determination of zenith hydrostatic delay (ZHD) is a key step to obtain water vapor information using GNSS technique, and it can be used to separate zenith wet delay (ZWD) with high accuracy from GNSS measurements. Estimates of ZHD are generally of higher accuracy when obtained from accurate pressure information and using the Saastamoinen model rather than when obtained from climatology. To improve this model, we analyzed the differences between the integrated ZHD and the Saastamoinen modeled ZHD, explored the relationship between the ZHD differences and meteorological parameters, and proposed a calibration model based on a global 2.5°×2° grid using the 5 years of pressure levels from the ERA5 reanalysis data provided by European Center for Medium-Range Weather Forecasts (ECMWF). The performance of the calibration model was assessed against the Saastamoinen model using different data sources in 2016, i.e., the ERA5 data and globally distributed radiosonde data. The numerical results show that the calibration model outperforms the Saastamoinen model with a global 59%/89% improvement of RMSE and bias in the ECMWF comparison. In comparison with the radiosonde data, the mean bias/RMSE of the calibration model improves by 5.14/3.24, 1.73/1.47 and 3.15/2.84 mm against the Saastamoinen model in the latitude zones of <30°, 30–60°, and >60°, respectively.

Impact of Tropospheric Mismodelling in GNSS Precise Point Positioning: A Simulation Study Utilizing Ray-Traced Tropospheric Delays from a High-Resolution NWM

In GNSS analysis, the tropospheric delay is parameterized by applying mapping functions (MFs), zenith delays, and tropospheric gradients. Thereby, the wet and hydrostatic MF are derived under the assumption of a spherically layered atmosphere. The coefficients of the closed-form expression are computed utilizing a climatology or numerical weather model (NWM) data. In this study, we analyze the impact of tropospheric mismodelling on estimated parameters in precise point positioning (PPP). To do so, we mimic PPP in an artificial environment, i.e., we make use of a linearized observation equation, where the observed minus modelled term equals ray-traced tropospheric delays from a high-resolution NWM. The estimated parameters (station coordinates, clocks, zenith delays, and tropospheric gradients) are then compared with the known values. The simulation study utilized a cut-off elevation angle of 3° and the standard downweighting of low elevation angle observations. The results are representative of a station located in central Europe and the warm season. In essence, when climatology is utilized in GNSS analysis, the root mean square error (RMSE) of the estimated zenith delay and station up-component equal about 2.9 mm and 5.7 mm, respectively. The error of the GNSS estimates can be reduced significantly if the correct zenith hydrostatic delay and the correct hydrostatic MF are utilized in the GNSS analysis. In this case, the RMSE of the estimated zenith delay and station up-component is reduced to about 2.0 mm and 2.9 mm, respectively. The simulation study revealed that the choice of wet MF, when calculated under the assumption of a spherically layered troposphere, does not matter too much. In essence, when the ‘correct’ wet MF is utilized in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component remain at about 1.8 mm and 2.4 mm, respectively. Finally, as a by-product of the simulation study, we developed a modified wet MF, which is no longer based on the assumption of a spherically layered atmosphere. We show that with this modified wet MF in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component can be reduced to about 0.5 mm and 1.0 mm, respectively. In practice, its success depends on the ability of current (future) NWM to predict the fourth coefficient of the developed closed-form expression. We provide some evidence that current NWMs are able to do so.