Zenith Tropospheric Delay Research Articles

MSE-impact of PPP-RTK ZTD estimation strategies

In PPP-RTK network processing, the wet component of the zenith tropospheric delay (ZTD) cannot be precisely modelled and thus remains unknown in the observation equations. For small networks, the tropospheric mapping functions of different stations to a given satellite are almost equal to each other, thereby causing a near rank-deficiency between the ZTDs and satellite clocks. The stated near rank-deficiency can be solved by estimating the wet ZTD components relatively to that of the reference receiver, while the wet ZTD component of the reference receiver is constrained to zero. However, by increasing network scale and humidity around the reference receiver, enlarged mismodelled effects could bias the network and the user solutions. To consider both the influences of the noise and the biases, the mean-squared errors (MSEs) of different network and user parameters are studied analytically employing both the ZTD estimation strategies. We conclude that for a certain set of parameters, the difference in their MSE structures using both strategies is only driven by the square of the reference wet ZTD component and the formal variance of its solution. Depending on the network scale and the humidity condition around the reference receiver, the ZTD estimation strategy that delivers more accurate solutions might be different. Simulations are performed to illustrate the conclusions made by analytical studies. We find that estimating the ZTDs relatively in large networks and humid regions (for the reference receiver) could significantly degrade the network ambiguity success rates. Using ambiguity-fixed network-derived PPP-RTK corrections, for networks with an inter-station distance within 100 km, the choices of the ZTD estimation strategy is not crucial for single-epoch ambiguity-fixed user positioning. Using ambiguity-float network corrections, for networks with inter-station distances of 100, 300 and 500 km in humid regions (for the reference receiver), the root-mean-squared errors (RMSEs) of the estimated user coordinates using relative ZTD estimation could be higher than those under the absolute case with differences up to millimetres, centimetres and decimetres, respectively.

Developing a global model for the conversion of zenith wet tropospheric delays to integrated water vapour

The tropospheric wet delay is a significant systematic error of GNSS positioning, nevertheless it carries important information to meteorologists. It is closely related to the integrated water vapour that is the upper limit of precipitable water. The zenith wet delay can be converted to the integrated water vapour using a simple conversion factor. This conversion factor can be determined with the empirical formulae derived from radiosonde observations. In the past decades, numerous models were derived for this purpose, but all of these models rely on radiosonde observations stemming from a limited area of the globe. Although these models are valid for the area, where the underlying radiosonde observations were measured, there are several examples that these empirical formulae are used to validate GNSS based integrated water vapour estimations all over the globe. Our aim is to create a global model for the conversion of the zenith tropospheric delay to the integrated water vapour for realtime and nearrealtime applications using globally available Numerical Weather Models (NWM). Thus our model takes into consideration the fact that the model parameters strongly depend on the geographical location. 10 years of monthly mean ECMWF (European Center for Medium-Range Weather Forecast) dataset were used for the derivation of the model parameters in a grid with the resolution of 1° × 1°. The empirical coefficients of the developed models depend on two input parameters, namely the geographical location and the surface temperature measured at the station. Thus, the new models can be used for both realtime and near-realtime GNSS meteorological applications. The developed models were validated using 6 years of independent global ECMWF monthly mean analysis datasets (2011–2016). The results showed, that the application of the original models outside the area of the underlying radiosonde data sets can result in a relative systematic error of 7–8% in the estimation of the conversion factor as well as the estimated IWV values.

Performance Analysis of BDS Medium-Long Baseline RTK Positioning Using an Empirical Troposphere Model.

For GPS medium-long baseline real-time kinematic (RTK) positioning, the troposphere parameter is introduced along with coordinates, and the model is ill-conditioned due to its strong correlation with the height parameter. For BeiDou Navigation Satellite System (BDS), additional difficulties occur due to its special satellite constellation. In fact, relative zenith troposphere delay (RZTD) derived from high-precision empirical zenith troposphere models can be introduced. Thus, the model strength can be improved, which is also called the RZTD-constrained RTK model. In this contribution, we first analyze the factors affecting the precision of BDS medium-long baseline RTK; thereafter, 15 baselines ranging from 38 km to 167 km in different troposphere conditions are processed to assess the performance of RZTD-constrained RTK. Results show that the troposphere parameter is difficult to distinguish from the height component, even with long time filtering for BDS-only RTK. Due to the lack of variation in geometry for the BDS geostationary Earth orbit satellite, the long convergence time of ambiguity parameters may reduce the height precision of GPS/BDS-combined RTK in the initial period. When the RZTD-constrained model was used in BDS and GPS/BDS-combined situations compared with the traditional RTK, the standard deviation of the height component for the fixed solution was reduced by 52.4% and 34.0%, respectively.

Assessment of the Impact of GNSS Processing Strategies on the Long-Term Parameters of 20 Years IWV Time Series

Advanced processing of collected global navigation satellite systems (GNSS) observations allows for the estimation of zenith tropospheric delay (ZTD), which in turn can be converted to the integrated water vapour (IWV). The proper estimation of GNSS IWV can be affected by the adopted GNSS processing strategy. To verify which of its elements cause deterioration and which improve the estimated GNSS IWV, we conducted eight reprocessings of 20 years of GPS observations (01.1996–12.2015). In each of them, we applied a different mapping function, the zenith hydrostatic delay (ZHD) a priori value, the cut-off angle, software, and the positioning method. Obtained in such a way, the ZTD time series were converted to the IWV using the meteorological parameters sourced from the ERA-Interim. Then, based on them, the long-term parameters were estimated and compared to those obtained from the IWV derived from the radio sounding (RS) observations. In this paper, we analyzed long-term parameters such as IWV mean values, linear trends, and amplitudes of annual and semiannual oscillations. A comparative analysis showed, inter alia, that in terms of the investigation of the IWV linear trend the precise point positioning (PPP) method is characterized by higher accuracy than the differential one. It was also found that using the GPT2 model and the higher elevation mask brings benefits to the GNSS IWV linear trend estimation.

Real-Time Tropospheric Delay Retrieval from Multi-GNSS PPP Ambiguity Resolution: Validation with Final Troposphere Products and a Numerical Weather Model

The multiple global navigation satellite systems (multi-GNSS) bring great opportunity for the real-time retrieval of high-quality zenith tropospheric delay (ZTD), which is a critical quality for atmospheric science and geodetic applications. In this contribution, a multi-GNSS precise point positioning (PPP) ambiguity resolution (AR) analysis approach is developed for real-time tropospheric delay retrieval. To validate the proposed multi-GNSS ZTD estimates, we collected and processed data from 30 Multi-GNSS Experiment (MGEX) stations; the resulting real-time tropospheric products are evaluated by using standard post-processed troposphere products and European Centre for Medium-Range Weather Forecasts analysis (ECMWF) data. An accuracy of 4.5 mm and 7.1 mm relative to the Center for Orbit Determination in Europe (CODE) and U.S. Naval Observatory (USNO) products is achievable for real-time tropospheric delays from multi-GNSS PPP ambiguity resolution after an initialization process of approximately 5 min. Compared to Global Positioning System (GPS) results, the accuracy of retrieved zenith tropospheric delay from multi-GNSS PPP-AR is improved by 16.7% and 31.7% with respect to USNO and CODE final products. The GNSS-derived ZTD time-series exhibits a great agreement with the ECMWF data for a long period of 30 days. The average root mean square (RMS) of the real-time zenith tropospheric delay retrieved from multi-GNSS PPP-AR is 12.5 mm with respect to ECMWF data while the accuracy of GPS-only results is 13.3 mm. Significant improvement is also achieved in terms of the initialization time of the multi-GNSS tropospheric delays, with an improvement of 50.7% compared to GPS-only fixed solutions. All these improvements demonstrate the promising prospects of the multi-GNSS PPP-AR method for time-critical meteorological applications.

Reduction of ZTD outliers through improved GNSS data processing and screening strategies

Abstract. Though Global Navigation Satellite System (GNSS) data processing has been significantly improved over the years, it is still commonly observed that zenith tropospheric delay (ZTD) estimates contain many outliers which are detrimental to meteorological and climatological applications. In this paper, we show that ZTD outliers in double-difference processing are mostly caused by sub-daily data gaps at reference stations, which cause disconnections of clusters of stations from the reference network and common mode biases due to the strong correlation between stations in short baselines. They can reach a few centimetres in ZTD and usually coincide with a jump in formal errors. The magnitude and sign of these biases are impossible to predict because they depend on different errors in the observations and on the geometry of the baselines. We elaborate and test a new baseline strategy which solves this problem and significantly reduces the number of outliers compared to the standard strategy commonly used for positioning (e.g. determination of national reference frame) in which the pre-defined network is composed of a skeleton of reference stations to which secondary stations are connected in a star-like structure. The new strategy is also shown to perform better than the widely used strategy maximizing the number of observations available in many GNSS programs. The reason is that observations are maximized before processing, whereas the final number of used observations can be dramatically lower because of data rejection (screening) during the processing. The study relies on the analysis of 1 year of GPS (Global Positioning System) data from a regional network of 136 GNSS stations processed using Bernese GNSS Software v.5.2. A post-processing screening procedure is also proposed to detect and remove a few outliers which may still remain due to short data gaps. It is based on a combination of range checks and outlier checks of ZTD and formal errors. The accuracy of the final screened GPS ZTD estimates is assessed by comparison to ERA-Interim reanalysis.

Analysing the Zenith Tropospheric Delay Estimates in On-line Precise Point Positioning (PPP) Services and PPP Software Packages.

As Global Navigation Satellite System (GNSS) signals travel through the troposphere, a tropospheric delay occurs due to a change in the refractive index of the medium. The Precise Point Positioning (PPP) technique can achieve centimeter/millimeter positioning accuracy with only one GNSS receiver. The Zenith Tropospheric Delay (ZTD) is estimated alongside with the position unknowns in PPP. Estimated ZTD can be very useful for meteorological applications, an example is the estimation of water vapor content in the atmosphere from the estimated ZTD. PPP is implemented with different algorithms and models in online services and software packages. In this study, a performance assessment with analysis of ZTD estimates from three PPP online services and three software packages is presented. The main contribution of this paper is to show the accuracy of ZTD estimation achievable in PPP. The analysis also provides the GNSS users and researchers the insight of the processing algorithm dependence and impact on PPP ZTD estimation. Observation data of eight whole days from a total of nine International GNSS Service (IGS) tracking stations spread in the northern hemisphere, the equatorial region and the southern hemisphere is used in this analysis. The PPP ZTD estimates are compared with the ZTD obtained from the IGS tropospheric product of the same days. The estimates of two of the three online PPP services show good agreement (<1 cm) with the IGS ZTD values at the northern and southern hemisphere stations. The results also show that the online PPP services perform better than the selected PPP software packages at all stations.

Assessment of local GNSS baselines at co-location sites

As one of the major contributors to the realisation of the International Terrestrial Reference System (ITRS), the Global Navigation Satellite Systems (GNSS) are prone to suffer from irregularities and discontinuities in time series. While often associated with hardware/software changes and the influence of the local environment, these discrepancies constitute a major threat for ITRS realisations. Co-located GNSS at fundamental sites, with two or more available instruments, provide the opportunity to mitigate their influence while improving the accuracy of estimated positions by examining data breaks, local biases, deformations, time-dependent variations and the comparison of GNSS baselines with existing local tie measurements. With the use of co-located GNSS data from a subset sites of the International GNSS Service network, this paper discusses a global multi-year analysis with the aim of delivering homogeneous time series of coordinates to analyse system-specific error sources in the local baselines. Results based on the comparison of different GNSS-based solutions with the local survey ties show discrepancies of up to 10 mm despite GNSS coordinate repeatabilities at the sub-mm level. The discrepancies are especially large for the solutions using the ionosphere-free linear combination and estimating tropospheric zenith delays, thus corresponding to the processing strategy used for global solutions. Snow on the antennas causes further problems and seasonal variations of the station coordinates. These demonstrate the need for a permanent high-quality monitoring of the effects present in the short GNSS baselines at fundamental sites.

Erratum and addendum to the paper ‘A new ZTD model based on permanent ground-based GNSS-ZTD data’, Survey Review, 2016, 48(351), 385–391

We correct some errors and give some more research for our paper published in Survey Review, 2016, 48(351), 385–391. This note is a correction owing to the use of the questionable surface meteorological measurements of the International GNSS Service (IGS) and also gives more sufficient studies to validate our method due to our inadequate study. Numerical weather model values of surface meteorological data were used to check the IGS surface meteorological measurements and long-time zenith tropospheric delay values at 76 radiosonde stations in Russia and near Russia were added as test data. Revised, updated and additional results were shown and analysed, which provide more evidence to show that the new proposed ISAAS model has a better accuracy than the Saastamoinen in Russia.

Precise Positioning in Alpine Areas with Troposphere and Multipath Estimation

Real-time kinematic (RTK) positioning with Global Navigation Satellite System (GNSS) signals is widely used, e.g., for surveying, agriculture, and potentially for autonomous vehicles and unmanned air vehicles in the future. In this paper, an extended RTK positioning for significant height differences between two low-cost GNSS receivers with patch antennas is presented. In this case, the classical model for double difference measurements needs to be extended, i.e., a differential tropospheric zenith delay and pseudorange multipath errors need to be estimated besides the baseline and carrier phase integer ambiguities. The increased number of unknowns results in an ill-conditioned system of observation equations and a substantial correlation between the state estimates. We introduce prior information on the differential tropospheric zenith delay based on the differential air pressure and exploit the temporal correlation of pseudorange multipath errors. Moreover, a criterion for the integer ambiguity candidate vector selection is provided, which is robust over phase multipath and unavoidable errors in the float ambiguity covariance matrix. The proposed method is validated with two low-cost GNSS modules that were placed at the Zugspitzplatt (2601 m a.s.l.) and Eibsee (1018 m a.s.l.). The obtained estimates for the baseline and differential tropospheric zenith delay show a high repeatability over several independent ambiguity fixings. The residuals of the fixed carrier phase measurements are within 2 cm for almost all satellites, which confirms both the measurement model and the ambiguity fixing.

A New Zenith Tropospheric Delay Grid Product for Real-Time PPP Applications over China.

Tropospheric delay is one of the major factors affecting the accuracy of electromagnetic distance measurements. To provide wide-area real-time high precision zenith tropospheric delay (ZTD), the temporal and spatial variations of ZTD with altitude were analyzed on the bases of the latest meteorological reanalysis product (ERA-Interim) provided by the European Center for Medium-Range Weather Forecasts (ECMWF). An inverse scale height model at given locations taking latitude, longitude and day of year as inputs was then developed and used to convert real-time ZTD at GPS stations in Crustal Movement Observation Network of China (CMONOC) from station height to mean sea level (MSL). The real-time ZTD grid product (RtZTD) over China was then generated with a time interval of 5 min. Compared with ZTD estimated in post-processing mode, the bias and error RMS of ZTD at test GPS stations derived from RtZTD are 0.39 and 1.56 cm, which is significantly more accurate than commonly used empirical models. In addition, simulated real-time kinematic Precise Point Positioning (PPP) tests show that using RtZTD could accelerate the BDS-PPP convergence time by up to 32% and 65% in the horizontal and vertical components (set coordinate error thresholds to 0.4 m), respectively. For GPS-PPP, the convergence time using RtZTD can be accelerated by up to 29% in the vertical component (0.2 m).

A grid-based tropospheric product for China using a GNSS network

Tropospheric delay accounts for one source of error in global navigation satellite systems (GNSS). To better characterize the tropospheric delays in the temporal and spatial domain and facilitate the safety-critical use of GNSS across China, a method is proposed to generate a grid-based tropospheric product (GTP) using the GNSS network with an empirical tropospheric model, known as IGGtrop. The prototype system generates the GTPs in post-processing and real-time modes and is based on the undifferenced and uncombined precise point positioning (UU-PPP) technique. GTPs are constructed for a grid form ( $$2.0{^{\circ }}\times 2.5{^{\circ }}$$ latitude–longitude) over China with a time resolution of 5 min. The real-time GTP messages are encoded in a self-defined RTCM3 format and broadcast to users using NTRIP (networked transport of RTCM via internet protocol), which enables efficient and safe transmission to real-time users. Our approach for GTP generation consists of three sequential steps. In the first step, GNSS-derived zenith tropospheric delays (ZTDs) for a network of GNSS stations are estimated using UU-PPP. In the second step, vertical adjustments for the GNSS-derived ZTDs are applied to address the height differences between the GNSS stations and grid points. The ZTD height corrections are provided by the IGGtrop model. Finally, an inverse distance weighting method is used to interpolate the GNSS-derived ZTDs from the surrounding GNSS stations to the location of the grid point. A total of 210 global positioning system (GPS) stations from the crustal movement observation network of China are used to generate the GTPs in both post-processing and real-time modes. The accuracies of the GTPs are assessed against with ERA-Interim-derived ZTDs and the GPS-derived ZTDs at 12 test GPS stations, respectively. The results show that the post-processing and real-time GTPs can provide the ZTDs with accuracies of 1.4 and 1.8 cm, respectively. We also apply the GTPs in real-time kinematic GPS PPP, and the results show that the convergence time of the PPP solutions is shortened. These results confirm that the GTPs can act as an efficient information source to augment GNSS positioning over China.

INVESTIGATION OF THE AIR QUALITY CHANGE EFFECT ON GNSS SIGNALS

Abstract. Air pollution is the most important environmental problem in Zonguldak city center. Since bituminous coal is used for domestic heating in houses and generating electricity in thermal power plants, particulate matter (PM10) is the leading air pollutant. Previous studies have shown that the water vapor in the troposphere is responsible for the tropospheric zenith delay in Global Navigation Satellite System (GNSS) measurements. In this study, data obtained from the ZONG GNSS station from Türkiye Ulusal Sabit GNSS Ağı (TUSAGA-Active network) in the central district of Zonguldak province, processed with GIPSY-OASIS II and GAMIT/GlobK software using the VMF1 mapping function, which is developed previously and considered to be the most accurate model. The resulting values were examined separately in terms of software. The meteorological parameters obtained from the Turkish State Meteorological Service and the air pollution values obtained from the Ministry of Environment and Urban Planning were analyzed and the zenith delay values were compared. When wet zenith delays of different days with different amounts of PM10 concentrations were examined in succession and under the same meteorological conditions, differences in the range of 20–40 mm on ZTD were observed.

Precipitable water comparisons over Ghana using PPP Techniques and reanalysis data

Atmospheric Water vapor is an important greenhouse gas and contributes greatly in maintaining the Earth’senergy balance. This critical meteorological parameter is not being sensed by any of the 22 synoptic weatherstations in Ghana. This study presents a highly precise tool for water vapor sensing based on the concept GlobalNavigation Satellite Systems (GNSS) meteorology and tests the computed results against global reanalysis data.Conventional approaches used to sense the atmospheric water vapor or precipitable water (PW) such as such asradiosondes, hygrometers, microwave radiometers or sun photometers are affected by meteorological conditionsand expensive. Whereas GNSS meteorological concept offers an easier, inexpensive and all-weather technique toretrieve Precipitable Water (PW) or Integrated water vapor (IWV) from zenith tropospheric delays (ZTD) overa reference station. This study employed precise point positioning (PPP) techniques to quantify the extendof delays on the signal due to the troposphere and stratosphere where the atmospheric water vapor resides.Stringent processing criteria were set using an elevation cut-off of 5 degrees, precise orbital and clock products,nominal tropospheric correction and mapping functions. The delays which are originally slanted are mappedunto the zenith direction and integrated with surface meteorological parameters to retrieve PW or IWV. ThegLAB software, Canadian Spatial Reference System (CSRS) and Automatic Precise Positioning Service (APPS)online PPP services were the approaches used to compute ZTD. PW values obtained were compared with JRA,ERA-interim and NCEP global reanalysis data. Correlation analysis were run on the logged station data usingthe three approaches and global reanalysis data. The obtained results show stronger correlation between theretrieved PW values and those provided by the ERA-interim. Finally, the study results indicate that with amore densified network of GNSS base stations the retrieved PW or IWV will greatly improve numerical weatherpredictions in Ghana.

Comparison of shipborne GNSS-derived precipitable water vapor with radiosonde in the western North Pacific and in the seas adjacent to Japan

We installed two global navigation satellite system (GNSS) antennas on a research vessel, the RYOFU MARU of the Japan Meteorological Agency, and conducted experimental observations to assess the GNSS-derived precipitable water vapor (PWV) from October 19, 2016, to August 6, 2017. One antenna was set on the mast (MAST), while another antenna was set on the upper deck (DECK). The GNSS analysis was conducted using the precise point positioning procedure with a real-time GNSS orbit. A quality control (QC) procedure based on the amount of zenith tropospheric delay (ZTD) time variation was proposed. After the QC was applied, the retrieved PWVs were compared to 77 radiosonde observations. The PWVs of MAST agreed with the radiosonde observations with a 1.7 mm root mean square (RMS) difference, a − 0.7-mm bias, and 3.6% rejection rate, while that of DECK showed a 3.2, − 0.8 mm, and 15.7%. The larger RMS and higher rejection rate of DECK imply a stronger multi-path effect on the deck. The differences in the GNSS PWV versus radiosonde observations were compared to the atmospheric delay, the estimated altitude of the GNSS antenna, the vessel’s moving speed, the wind speed, and the wave height. The atmospheric delay and GNSS antenna altitude showed moderate correlation with the differences. The results suggest the kinematic PPP’s potential for practical water vapor monitoring over oceans worldwide. At the same time, from the growing negative biases with the PWV value and with estimated antenna altitude, it could be inferred that the difficulty grows in separating the signal delay from the vertical coordinate under high-humidity conditions.

Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning

During past decades, precise point positioning (PPP) has been proven to be a well-known positioning technique for centimeter or decimeter level accuracy. However, it needs long convergence time to get high-accuracy positioning, which limits the prospects of PPP, especially in real-time applications. It is expected that the PPP convergence time can be reduced by introducing high-quality external information, such as ionospheric or tropospheric corrections. In this study, several methods for tropospheric wet delays modeling over wide areas are investigated. A new, improved model is developed, applicable in real-time applications in China. Based on the GPT2w model, a modified parameter of zenith wet delay exponential decay wrt. height is introduced in the modeling of the real-time tropospheric delay. The accuracy of this tropospheric model and GPT2w model in different seasons is evaluated with cross-validation, the root mean square of the zenith troposphere delay (ZTD) is 1.2 and 3.6 cm on average, respectively. On the other hand, this new model proves to be better than the tropospheric modeling based on water-vapor scale height; it can accurately express tropospheric delays up to 10 km altitude, which potentially has benefits in many real-time applications. With the high-accuracy ZTD model, the augmented PPP convergence performance for BeiDou navigation satellite system (BDS) and GPS is evaluated. It shows that the contribution of the high-quality ZTD model on PPP convergence performance has relation with the constellation geometry. As BDS constellation geometry is poorer than GPS, the improvement for BDS PPP is more significant than that for GPS PPP. Compared with standard real-time PPP, the convergence time is reduced by 2–7 and 20–50% for the augmented BDS PPP, while GPS PPP only improves about 6 and 18% (on average), in horizontal and vertical directions, respectively. When GPS and BDS are combined, the geometry is greatly improved, which is good enough to get a reliable PPP solution, the augmentation PPP improves insignificantly comparing with standard PPP.

Tropospheric products of the second GOP European GNSS reprocessing (1996–2014)

Abstract. In this paper, we present results of the second reprocessing of all data from 1996 to 2014 from all stations in International Association of Geodesy (IAG) Reference Frame Sub-Commission for Europe (EUREF) Permanent Network (EPN) as performed at the Geodetic Observatory Pecný (GOP). While the original goal of this research was to ultimately contribute to the realization of a new European Terrestrial Reference System (ETRS), we also aim to provide a new set of GNSS (Global Navigation Satellite System) tropospheric parameter time series with possible applications to climate research. To achieve these goals, we improved a strategy to guarantee the continuity of these tropospheric parameters and we prepared several variants of troposphere modelling. We then assessed all solutions in terms of the repeatability of coordinates as an internal evaluation of applied models and strategies and in terms of zenith tropospheric delays (ZTDs) and horizontal gradients with those of the ERA-Interim numerical weather model (NWM) reanalysis. When compared to the GOP Repro1 (first EUREF reprocessing) solution, the results of the GOP Repro2 (second EUREF reprocessing) yielded improvements of approximately 50 and 25 % in the repeatability of the horizontal and vertical components, respectively, and of approximately 9 % in tropospheric parameters. Vertical repeatability was reduced from 4.14 to 3.73 mm when using the VMF1 mapping function, a priori ZHD (zenith hydrostatic delay), and non-tidal atmospheric loading corrections from actual weather data. Raising the elevation cut-off angle from 3 to 7° and then to 10° increased RMS from coordinates' repeatability, which was then confirmed by independently comparing GNSS tropospheric parameters with the NWM reanalysis. The assessment of tropospheric horizontal gradients with respect to the ERA-Interim revealed a strong sensitivity of estimated gradients to the quality of GNSS antenna tracking performance. This impact was demonstrated at the Mallorca station, where gradients systematically grew up to 5 mm during the period between 2003 and 2008, before this behaviour disappeared when the antenna at the station was changed. The impact of processing variants on long-term ZTD trend estimates was assessed at 172 EUREF stations with time series longer than 10 years. The most significant site-specific impact was due to the non-tidal atmospheric loading followed by the impact of changing the elevation cut-off angle from 3 to 10°. The other processing strategy had a very small or negligible impact on estimated trends.

Establishment of a Site-Specific Tropospheric Model Based on Ground Meteorological Parameters over the China Region.

China is a country of vast territory with complicated geographical environment and climate conditions. With the rapid progress of the Chinese BeiDou satellite navigation system (BDS); more accurate tropospheric models must be applied to improve the accuracy of navigation and positioning. Based on the formula of the Saastamoinen and Callahan models; this study develops two single-site tropospheric models (named SAAS_S and CH_S models) for the Chinese region using radiosonde data from 2005 to 2012. We assess the two single-site tropospheric models with radiosonde data for 2013 and zenith tropospheric delay (ZTD) data from four International GNSS Service (IGS) stations and compare them to the results of the Saastamoinen and Callahan models. The experimental results show that: the mean accuracy of the SAAS_S model (bias: 0.19 cm; RMS: 3.19 cm) at all radiosonde stations is superior to those of the Saastamoinen (bias: 0.62 cm; RMS: 3.62 cm) and CH_S (bias: −0.05 cm; RMS: 3.38 cm) models. In most Chinese regions; the RMS values of the SAAS_S and CH_S models are about 0.51~2.12 cm smaller than those of their corresponding source models. The SAAS_S model exhibits a clear improvement in the accuracy over the Saastamoinen model in low latitude regions. When the SAAS_S model is replaced by the SAAS model in the positioning of GNSS; the mean accuracy of vertical direction in the China region can be improved by 1.12~1.55 cm and the accuracy of vertical direction in low latitude areas can be improved by 1.33~7.63 cm. The residuals of the SAAS_S model are closer to a normal distribution compared to those of the Saastamoinen model. Single-site tropospheric models based on the short period of the most recent data (for example 2 years) can also achieve a satisfactory accuracy. The average performance of the SAAS_S model (bias: 0.83 cm; RMS: 3.24 cm) at four IGS stations is superior to that of the Saastamoinen (bias: −0.86 cm; RMS: 3.59 cm) and CH_S (bias: 0.45 cm; RMS: 3.38 cm) models.

A simplified GNSS tropospheric delay model based on the nonlinear hypothesis

We have derived a global zenith tropospheric delay simplified model (GZTDS), assuming that the troposphere is a nonlinear system and can be handled as a black box. The GZTDS and its variation in time can be expressed as a series of cosine components, which represent various periods of tropospheric delay changes. Undetermined coefficients are extracted by data fitting from the mean sea level historical data of the global geodetic observing system atmosphere on a 2° × 2.5° grid. A combination of our model and the Vienna Mapping Function 1 can predict slant delays for global navigation satellite system sites using the zenith angle and nearest grid coordinates as the input and generate a global slant tropospheric delay simplified model (GSTDS) and its extension. Comparisons with the zenith delays provided by the International GNSS Service at 358 sites show that the biases are between −3.36 and 2.41 cm, and the mean standard deviation is 3.46 cm for the year 2014. This result is at the same level of accuracy as the global pressure and temperature 2 wet model (GPT2w), with the GZTDS requiring no local meteorological parameters. The accuracy of GSTDS depends on the zenith angle and shows nonlinear characteristics. Several statistics of biases and standard deviations illustrate model adaptation with respect to latitude or altitude.

A new voxel-based model for the determination of atmospheric weighted mean temperature in GPS atmospheric sounding

Abstract. The Global Positioning System (GPS) is a powerful atmospheric observing system for determining precipitable water vapour (PWV). In the detection of PWV using GPS, the atmospheric weighted mean temperature (Tm) is a crucial parameter for the conversion of zenith tropospheric delay (ZTD) to PWV since the quality of PWV is affected by the accuracy of Tm. In this study, an improved voxel-based Tm model, named GWMT-D, was developed using global reanalysis data over a 4-year period from 2010 to 2013 provided by the United States National Centers for Environmental Prediction (NCEP). The performance of GWMT-D was assessed against three existing empirical Tm models – GTm-III, GWMT-IV, and GTm_N – using different data sources in 2014 – the NCEP reanalysis data, surface Tm data provided by Global Geodetic Observing System and radiosonde measurements. The results show that the new GWMT-D model outperforms all the other three models with a root-mean-square error of less than 5.0 K at different altitudes over the globe. The new GWMT-D model can provide a practical alternative Tm determination method in real-time GPS-PWV remote sensing systems.