Assessment of the three representative empirical models for zenith tropospheric delay(ZTD)using the CMONOC data

The precise correction of atmospheric zenith tropospheric delay(ZTD)is significant for the Global Navigation Satellite System(GNSS)performance regarding positioning accuracy and convergence time.In the past decades,many empirical ZTD models based on whether the gridded or scattered ZTD products have been proposed and widely used in the GNSS positioning applications.But there is no comprehensive evaluation of these models for the whole China region,which features complicated topography and climate.In this study,we completely assess the typical empirical models,the IGGtropSH model(gridded,non-meteorology),the SHAtropE model(scattered,non-meteorology),and the GPT3 model(gridded,meteorology)using the Crustal Movement Observation Network of China(CMONOC)network.In general,the results show that the three models share consistent performance with RMSE/bias of 37.45/1.63,37.13/2.20,and 38.27/1.34 mm for the GPT3,SHAtropE and IGGtropSH model,respectively.However,the models had a distinct performance regarding geographical distribution,elevation,seasonal variations,and daily variation.In the southeastern region of China,RMSE values are around 50 mm,which are much higher than that in the western region,approximately 20 mm.The SHAtropE model exhibits better performance for areas with large variations in elevation.The GPT3 model and the IGGtropSH model are more stable across different months,and the SHAtropE model based on the GNSS data exhibits superior performance across various UTC epochs.

A predictive model for regional zenith tropospheric delay correction

The conventional zenith tropospheric delay(ZTD)model(known as the Saastamoinen model)does not consider seasonal variations affecting the delay,giving it low accuracy and stability.This may be improved with adjustments to account for annual and semi-annual variations.This method uses ZTD data provided by the Global Geodetic Observing System to analyze seasonal variations in the bias of the Saastamoinen model in Asia,and then constructs a model with seasonal variation corrections,denoted as SSA.To overcome the dependence of the model on in-situ meteorological parameters,the SSA+GPT3 model is formed by combining the SSA and GPT3(global pressure-temperature)models.The results show that the introduction of annual and semi-annual variations can substantially improve the Saastamoinen model,yielding small and time-stable variations in bias and root mean square(RMS).In summer and autumn,the bias and RMS are noticeably smaller than those from the Saastamoinen model.In addition,the SSA model performs better in low-latitude and low-altitude areas,and bias and RMS decease with the increase of latitude or altitude.The prediction accuracy of the SSA model is also evaluated for external consistency.The results show that the accuracy of the SSA model(bias:-0.38 cm,RMS:4.43 cm)is better than that of the Saastamoinen model(bias:1.45 cm,RMS:5.16 cm).The proposed method has strong applicability and can therefore be used for predictive ZTD correction across Asia.

A zenith tropospheric delay correction model based on the regional CORS network

Tropospheric delay is a primary error source in earth observations and a variety of radio navigation technologies. In this paper, the relationship between zenith tropospheric delays and the elevation and longitude of stations is analyzed using the zenith tropospheric delay final products of International GNSS Service （IGS） stations from 2011. Two new models are proposed for estimating zenith tropospheric delays from regional CORS data without meteorological data. The proposed models are compared with the direct interpolation method and the remove-restore method using data from Guangxi CORS. The results show that the new models significantly improve the calculated precision. Finally, the root mean square （RMS） errors of the new models were used to estimate the surface precipitable water vapor （PWV） value at CORS station, which was determined to be less than 2 mm.

Impact of Tropospheric Delay Gradients on Total Tropospheric Delay and Precise Point Positioning

GPS signals are electromagnetic waves that are affected by the Earth’s atmosphere. The Earth’s atmosphere can be categorized, according to its effect on GPS signals, into the ionosphere (ionospheric delay) and neutral atmosphere (tropospheric delay). The first-order ionospheric delay can be eliminated by linear combination of GPS observables on different frequencies. However, tropospheric delay cannot be eliminated because it is frequency-independent. The total tropospheric delay can be divided into three components. The first is the dry component, the second part is the wet component, and the third part is the horizontal gradients which account for the azimuthal dependence of tropospheric delay. In this paper, the effect of modeling tropospheric gradients on the estimation of the total tropospheric delay and station position is investigated. Long session, one month during January 2015, of GPS data is collected from ten randomly selected globally distributed IGS stations. Two cases are studied: the first case, the coordinates of stations are kept fixed to their actual values and the tropospheric delay is estimated twice, with and without tropospheric gradients. In the second case, the station position is estimated along with the total tropospheric delay with and without tropospheric gradients. It is shown that the average bias of the estimated total tropospheric delay when neglecting tropospheric gradients ranges from ?1.72 mm to 2.14 mm while the average bias when estimating gradients are ?0.898 mm to 1.92 mm which means that the bias is reduced by about 30%. In addition, the average standard deviation of the bias is 4.26 mm compared with 4.52 mm which means that the standard deviation is improved by about 6%.

Empirical model of correction for zenith tropospheric delay

The paper considers the possibility of correction of zenith tropospheric delays, and calculates it with the standard model, which takes into account the values of the refractive index of the troposphere at the time of measurement. Based on the experimental research, this empirical model of correction for zenith tropospheric delays can reduce the measurement er- ror of coordinates to about 30 % and altitude to about 40 %.

An initial investigation of the non-isotropic feature of GNSS tropospheric delay

Tropospheric delay is a significant error source in Global Navigation Satellite Systems(GNSS)positioning.Slant Path Delay(SPD)is commonly derived by multiplying Zenith Tropospheric Delay(ZTD)with a mapping function.However,mapping functions,assuming atmospheric isotropy,restrict the accuracy of derived SPDs.To improve the accuracy,a horizontal gradient correction is introduced to account for azimuth-dependent SPD variations,treating the atmosphere as anisotropic.This study uncovers that,amidst atmospheric dynamics and spatiotemporal changes in moisture content,the SPD deviates from that based on traditional isotropy or anisotropy assumption.It innovatively introduces the concept that SPD exhibits non-isotropy with respect to azimuth angles.Hypothesis validation involves assessing SPD accuracy using three mapping functions at five International GNSS Service(IGS)stations,referencing the SPD with the ray-tracing method.It subsequently evaluates the SPD accuracy with horizontal gradient correction based on Vienna Mapping Function 3(VMF3)estimation.Lastly,the non-isotropic of SPD is analyzed through the ray-tracing method.The results indicate the smallest residual(1.1–82.7 mm)between the SPDs with VMF3 and those with the ray-tracing.However,introducing horizontal gradient correction yields no significant improvement of SPD accuracy.Considering potential decimeter-level differences in SPD due to non-isotropic tropospheric delay across azimuth angles,a precise grasp and summary of these variations is pivotal for accurate tropospheric delay modeling.This finding provides vital support for future high-precision tropospheric delay modeling.

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 fndings of the study,the ERA5 atmospheric variables are recommended for improving the accuracy in ZTD estimation,required for GNSS positioning.

Establishment of a new tropospheric delay correction model over China area

The tropospheric delay is one of the main error sources for radio navigation technologies and other ground-or space-based earth observation systems. In this paper, the spatial and temporal variations of the zenith tropospheric delay (ZTD), especially their dependence on altitude over China region, are analyzed using ECMWF (European Centre for Medium-Range Weather Forecast) pressure-level atmospheric data in 2004 and the ZTD series in 1999-2007 measured at 28 GPS stations from the Crustal Movement Observation Network of China (CMONC). A new tropospheric delay correction model (SHAO) is derived and a regional realization of this model for China region named SHAO-C is established. In SHAO-C model, ZTD is modeled directly by a cosine function together with an initial value and an amplitude at a reference height in each grid, and the variation of ZTD along altitude is fitted with a second-order polynomial. The coefficients of SHAO-C are generated using the meteorology data in China area and given at two degree latitude and longitude interval, featuring regional characteristics in order to facilitate a wide range of navigation and other surveying applications in and around China. Compared with the EGNOS (European Geostationary Navigation Overlay Service) model, which has been used globally and recommended by the European Union Wide Area Augmentation System, the ZTD prediction (in form of spatial and temporal projection) accuracy of the SHAO-C model is significantly improved over China region, especially at stations of higher altitudes. The reasons for the improvement are: (1) the reference altitude of SHAO-C parameters are given at the average height of each grid, and (2) more detailed description of complicated terrain variations in China is incorporated in the model. Therefore, the accumulated error at higher altitude can be reduced considerably. In contrast, the ZTD has to be calculated from the mean sea level with EGNOS and other models. Compared with the direct estimation of ZTD from the 28 GPS stations, the accuracy of the derived ZTD using the SHAO-C model can be improved by 60.5% averagely compared with the EGNOS model. The overall bias and rms are 2.0 and 4.5 cm, respectively, which should be sufficient to satisfy the requirements of most GNSS navigation or positioning applications in terms of the tropospheric delay correction.

A global empirical model for estimating zenith tropospheric delay

Tropospheric delay acts as a systematic error source in the Global Navigation Satellite Systems(GNSS) positioning. Empirical models UNB3, UNB3 m, UNB4 and EGNOS have been developed for use in Satellite-Based Augmentation Systems(SBAS). Model performance, however, is limited due to the low spatial resolution of the look-up tables for meteorological parameters. A new design has been established in this study for improving performance of the tropospheric delay model by more effectively eliminating the error produced by tropospheric delay. The spatiotemporal characteristics of the Zenith Tropospheric Delay(ZTD) were analyzed with findings that ZTD exhibits different annual variations at different locations and decreases exponentially with height increasing. Spherical harmonics are utilized based on the findings to fit the annual mean and amplitude of the ZTD on a global scale and the exponential function is utilized for height corrections, yielding the ZTrop model. On a global scale, the ZTrop features an average deviation of ?1.0 cm and Root Mean Square(RMS) of 4.7 cm compared with the International GNSS Service(IGS) ZTD products, an average deviation of 0.0 cm and RMS of 4.5 cm compared with the Global Geodetic Observing System(GGOS) ZTD data, and an average deviation of ?1.3 cm and RMS of 5.2 cm compared with the ZTD data from the Constellation Observing System of Meteorology, Ionosphere, and Climate(COSMIC). The RMS of the ZTrop model is 14.5% smaller than that of UNB3, 6.0% smaller than that of UNB3 m, 16% smaller than that of UNB4, 14.5% smaller than that of EGNOS and equivalent to the sophisticated GPT2+Saas model in comparison with the IGS ZTD products. The ZTrop, UNB3 m and GPT2+Saas models are finally evaluated in GPS-based Precise Point Positioning(PPP), as the models act to aid in obtaining PPP position error less than 1.5 cm in north and east components and relative large error(>5 cm) in up component with respect to the random walk approach.

Accuracy Improvement of Zenith Tropospheric Delay Estimation Based on GPS Precise Point Positioning Algorithm

In the precise point positioning(PPP),some impossible accurately simulated systematic errors still remained in the GPS observations and will inevitably degrade the precision of zenith tropospheric delay(ZTD) estimation.The stochastic models used in the GPS PPP mode are compared.In this paper,the research results show that the precision of PPP-derived ZTD can be obviously improved through selecting a suitable stochastic model for GPS measurements.Low-elevation observations can cover more troposphere information that can improve the estimation of ZTD.A new stochastic model based on satellite low elevation cosine square is presented.The results show that the stochastic model using satellite elevation-based cosine square function is better than previous stochastic models.

Development and evaluation of the refined zenith tropospheric delay(ZTD)models

The tropospheric delay is a significant error source in Global Navigation Satellite System(GNSS)positioning and navigation.It is usually projected into zenith direction by using a mapping function.It is particularly important to establish a model that can provide stable and accurate Zenith Tropospheric Delay(ZTD).Because of the regional accuracy difference and poor stability of the traditional ZTD models,this paper proposed two methods to refine the Hopfield and Saastamoinen ZTD models.One is by adding annual and semi-annual periodic terms and the other is based on Back-Propagation Artificial Neutral Network(BP-ANN).Using 5-year data from 2011 to 2015 collected at 67 GNSS reference stations in China and its surrounding regions,the four refined models were constructed.The tropospheric products at these GNSS stations were derived from the site-wise Vienna Mapping Function 1(VMP1).The spatial analysis,temporal analysis,and residual distribution analysis for all the six models were conducted using the data from 2016 to 2017.The results show that the refined models can effectively improve the accuracy compared with the traditional models.For the Hopfield model,the improvement for the Root Mean Square Error(RMSE)and bias reached 24.5/49.7 and 34.0/52.8 mm,respectively.These values became 8.8/26.7 and 14.7/28.8 mm when the Saastamoinen model was refined using the two methods.This exploration is conducive to GNSS navigation and positioning and GNSS meteorology by providing more accurate tropospheric prior information.

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.

An ERA5 tropospheric parameters-augmented approach for improving GNSS precise point positioning

Precise Point Positioning(PPP) technology has developed into a potent instrument for geodetic positioning, ionospheric modeling, tropospheric atmospheric parameter detection, and seismic monitoring.As atmospheric reanalysis data products’ accuracy and spatiotemporal resolution have improved recently, it has become important to apply these products to obtain high-accuracy tropospheric delay parameters, like zenith tropospheric delay(ZTD) and tropospheric horizontal gradient. These tropospheric delay parameters can be applied to PPP to reduce the convergence time and to increase the accuracy in the vertical direction of the position. The European Centre for Medium-Range Weather Forecasts Reanalysis 5(ERA5) atmospheric reanalysis data is the latest product with a high spatiotemporal resolution released by the European Center for Medium-Range Weather Forecasts(ECMWF). Only a few researches have evaluated the application of ERA5 data to Global Navigation Satellite System(GNSS)PPP. Therefore, this study compared and validated the ZTD products derived from ERA5 data using ZTD values provided by 290 global International GNSS Service(IGS) stations for 2016-2017. The results indicated a stable performance for ZTD, with annual average bias and RMS values of 0.23 cm and 1.09 cm,respectively. Further, GNSS observations for one week in each of the four seasons(spring: DOY 92-98;summer: DOY 199-205;autumn: DOY 275-281;and winter: DOY 22-28) from 34 multi-GNSS experiments(MGEX) stations distributed globally in 2016 were considered to evaluate the performance of ERA5-derived tropospheric delay products in GNSS PPP. The performance of ERA5-enhanced PPP was compared with that of the two standard GNSS PPP schemes(without estimated tropospheric horizontal gradient and with estimated tropospheric horizontal gradient). The results demonstrated that ERA5-enhanced GNSS PPP showed no significant improvement in the convergence times in both the Eastern(E) and Northern(N) directions, while the average convergence time over four weeks in the vertical(U)direction improved by 53.3% and 52.7%, respectively(in the case of pngm station). The average convergence times for each week in the U direction of the northern and southern hemisphere stations indicated a decrease of 16.3%, 12.6%, 9.6%, and 9.1%, and 16.9%, 9.6%, 8.9%, and 14.5%, respectively.Regarding positioning accuracy, ERA5-enhanced PPP showed an improvement of 13.3% and 16.2% over the two standard PPP schemes in the U direction, respectively. No significant improvement in the positioning performance was observed in both the E and N directions. Thus, this study demonstrated the potential application of the ERA5 tropospheric parameters-augmented approach to Beidou navigation and positioning.

Numerical weather modeling-based slant tropospheric delay estimation and its enhancement by GNSS data

Unmitigated tropospheric delay is one of the major error sources in precise point positioning(PPP).Precise Slant Tropospheric Delay(STD)estimation could help to provide cleaner observables for PPP,and improve its convergence,accuracy,and stability.STD is difficult to model accurately due to the rapid spatial and temporal variation of the water vapor in the troposphere.In the traditional approach,the STD is mapped from the zenith direction,which assumes a spherically symmetric local tropospheric profile and has limitations.In this paper,a new approach of directly estimating the STD from high resolution numerical weather modeling(NWM)products is introduced.This approach benefits from the best available meteorological information to improve real time STD estimation,with the RMS residual lower than 3.5 cm above 15°elevation,and 2 cm above 30°.Therefore,the new method can provide sufficient accuracy to improve PPP convergence time.To improve the performance of the new method in highly variable tropospheric conditions,a correction scheme is proposed which combines NWM information with multi-GNSS observations from a network of local continuously operating reference stations.It is demonstrated through a case study that this correction scheme is quite effective in reducing the STD estimation residuals and PPP convergence time.

Retrieval of the Change of Precipitable Water Vapor by GPS Technique

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

Research on Error Analysis and Correction Technique of Atmospheric Refraction for InSAR Measurement with Distributed Satellites

SAR interferometry with distributed satellites is a technique based on the exploitation of the interference pattern of two SAR images acquired synchronously. The interferogram contains geometric, atmospheric, topographic and land defomation. This paper focuses on atmospheric effects on SAR interferometry, which shows theoretically that the relationship among ionosphere TEC and troposphere parameters such as temperature, relative humitdity and pressure with respect to slant rang changes. An atmospheric correction method is given in the end.

GSTAR:an innovative software platform for processing space geodetic data at the observation level

To meet the demands for the data combination with multiple space geodetic techniques at the observation level,we developed a new software platform with high extensibility and computation efficiency,named space Geodetic SpatioTemporal data Analysis and Research software(GSTAR).Most of the modules in the GSTAR are coded in C++with object-oriented programming.The layered modular theory is adopted for the design of the software,and the antenna-based data architecture is proposed for users to construct personalized geodetic application scenarios easily.The initial performance of the GSTAR software is evaluated by processing the Global Navigation Satellite System(GNSS)data collected from 315 globally distributed stations over two and a half years.The accuracy of GNSS-based geodetic products is evaluated by comparing them with those released by International GNSS Service(IGS)Analysis Centers(AC).Taking the products released by European Space Agency(ESA)as reference,the Three-Dimension(3D)Root-Mean-Squares(RMS)of the orbit differences are 2.7/6.7/3.3/7.7/21.0 cm and the STandard Deviations(STD)of the clock differences are 19/48/16/32/25 ps for Global Positioning System(GPS),GLObal NAvigation Satellite System(GLONASS),Galileo navigation satellite system(Galileo),BeiDou Navigation Satellite System(BDS),Medium Earth Orbit(MEO),and BDS Inclined Geo-Synchronous Orbit(IGSO)satellites,respectively.The mean values of the X and Y components of the polar coordinate and the Length of Day(LOD)with respect to the International Earth Rotation and Reference Systems Service(IERS)14 C04 products are-17.6 microarc-second(μas),9.2μas,and 14.0μs/d.Compared to the IGS daily solution,the RMSs of the site position differences in the north/east/up direction are 1.6/1.5/3.9,3.8/2.4/7.6,2.5/2.4/7.9 and 2.7/2.3/7.4 mm for GPS-only,GLONASS-only,Galileo-only,and BDS-only solution,respectively.The RMSs of the differences of the tropospheric Zenith Path Delay(ZPD),the north gradients,and the east gradients are 5.8,0.9,and 0.9 mm with respect to the IGS products.The X and Y components of the geocenter motion estimated from GPS-only,Galileo-only,and BDS-only observations well agree with IGS products,while the Z component values are much nosier where anomalous harmonics in GNSS draconitic year can be found.The accuracies of the above products calculated by the GSTAR are comparable with those from different IGS ACs.Compared to the precise scientific orbit products,the 3D RMS of the orbit differences for the two Gravity Recovery and Climate Experiment Follow-on(GRACE-FO)satellites is below 1.5 cm by conducting Precise Point Positioning with Ambiguity Resolution(PPP-AR).In addition,a series of rapid data processing algorithms are developed,and the operation speed of the GSTAR software is 5.6 times faster than that of the Positioning and Navigation Data Analyst(PANDA)software for the quad-system precise orbit determination procedure.