Nothing Special   »   [go: up one dir, main page]
Next Article in Journal
Analytical Review of Wind Assessment Tools for Urban Wind Turbine Applications
Previous Article in Journal
Reconstruction of Summer Rainfall over the Last Five Centuries Based on Oak Chronology (Western Pomerania, Poland)
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Atmosphere
Volume 15
Issue 9
10.3390/atmos15091048
atmosphere-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Assessment of BDS-3 PPP-B2b Service and Its Applications for the Determination of Precipitable Water Vapour

by
Xiaoming Wang
1,2,*,
Yufei Chen
1,2,
Jinglei Zhang
1,
Cong Qiu
1,2,
Kai Zhou
1,
Haobo Li
3 and
Qiuying Huang
1,2
1
Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
2
University of Chinese Academy of Sciences, Beijing 100049, China
3
School of Science, Royal Melbourne Institute of Technology (RMIT) University, Melbourne, VIC 3001, Australia
*
Author to whom correspondence should be addressed.
Atmosphere 2024, 15(9), 1048; https://doi.org/10.3390/atmos15091048
Submission received: 17 July 2024 / Revised: 23 August 2024 / Accepted: 25 August 2024 / Published: 29 August 2024
(This article belongs to the Special Issue GNSS Remote Sensing in Atmosphere and Environment (2nd Edition))
Browse Figures
Figure 1
<p>Coverage areas of three BDS GEO satellites. The red, yellow, and purple stars represent subsatellite points of the three GEO satellites located at 80° E, 110.5° E, and 140° E, respectively, and the lines represent their coverage at cut-off angles of (<b>a</b>) 3°, (<b>b</b>) 5°, (<b>c</b>) 7°, and (<b>d</b>) 15°.</p> "> Figure 2
<p>Distribution of the 32 GNSS stations; 11 stations with co-located radiosondes are marked with red triangles, while the location of BJ01 is marked with a green pentagram.</p> "> Figure 3
<p>Daily variation in <span class="html-italic">SISRE</span><sub><span class="html-italic">clk</span>+<span class="html-italic">orb</span></sub> [STD] for (<b>a</b>) GPS and (<b>b</b>) BDS-3 from DOY 069 to 311 in 2022. The results show that the daily <span class="html-italic">SISRE</span><sub><span class="html-italic">clk</span>+<span class="html-italic">orb</span></sub> remains less than 0.1 m for GPS and less than 0.05 m for BDS-3 most of the time.</p> "> Figure 4
<p>ZTD time series derived with different methods (<b>a</b>) and the differences between ZTDs derived with PPP-B2b and GBM (<b>b</b>).</p> "> Figure 5
<p>ZTD error distributions for PPP-B2b solutions. The errors were calculated using the GBM solution as a reference. The results show that the errors are mostly within −30 to 30 mm.</p> "> Figure 6
<p>RMSE (<b>a</b>,<b>b</b>) and bias (<b>c</b>,<b>d</b>) of the ZTD derived with CNES and PPP-B2b using the ZTD provided by IGS as a reference.</p> "> Figure 7
<p>RMSE (<b>a</b>,<b>b</b>) and bias (<b>c</b>,<b>d</b>) of the ZTD derived with CNES and PPP-B2b using the ZTD calculated with GBM satellite/orbit products as a reference.</p> "> Figure 8
<p>RMSE (<b>a</b>–<b>d</b>) and bias (<b>e</b>–<b>h</b>) of the ZTD derived with IGS, GBM, CNES, and PPP-B2b, using the ZTD calculated from ERA5 as a reference.</p> "> Figure 9
<p>RMSE (<b>a</b>–<b>d</b>) and bias (<b>e</b>–<b>h</b>) of the PWV derived with IGS, GBM, CNES, and PPP-B2b using the PWV from ERA5 as a reference.</p> "> Figure 10
<p>PWV variations and the monthly RMSEs of differences between GNSS-derived PWV and ERA5-derived PWV.</p> "> Figure 11
<p>Diurnal anomaly variations in the PWV time series obtained from GNSS and ERA5 in March 2022.</p> "> Figure 12
<p>RMSE (<b>a</b>–<b>d</b>) and bias (<b>e</b>–<b>h</b>) of the ZTD derived with IGS, GBM, CNES, and PPP-B2b using the ZTD from radiosonde as a reference.</p> "> Figure 13
<p>This RMSE (<b>a</b>–<b>d</b>) and bias (<b>e</b>–<b>h</b>) of the PWV derived with IGS, GBM, CNES, and PPP-B2b using the PWV from radiosonde as a reference.</p> "> Figure 14
<p>PWV variations and the monthly RMSs of the differences between GNSS-derived PWV and radiosonde-derived PWV at 11 stations (<b>a</b>–<b>k</b>).</p> "> Figure A1
<p>Frame arrangement structure.</p> ">
Versions Notes

Abstract

:
The precise point positioning (PPP) service via the B2b signal (PPP-B2b) on the BeiDou Navigation Satellite System (BDS) provides high-accuracy orbit and clock data for global navigation satellite systems (GNSSs), enabling real-time atmospheric data acquisition without internet access. In this study, we assessed the quality of orbit, clock, and differential code bias (DCB) products from the PPP-B2b service, comparing them to post-processed products from various analysis centres. The zenith tropospheric delay (ZTD) and precipitable water vapour (PWV) were computed at 32 stations using the PPP technique with PPP-B2b corrections. These results were compared with post-processed ZTD with final orbit/clock products and ZTD/PWV values derived from the European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) and radiosonde data. For stations between 30° N and 48° N, the mean root mean square error (RMSE) of ZTD for the PPP-B2b solution was approximately 15 mm compared to ZTD from the International GNSS Service (IGS). However, accuracy declined at stations between 30° N and 38° S, with a mean RMSE of about 25 mm, performing worse than ZTD estimates using Centre National d’Études Spatiales (CNES) products. The mean RMSEs of PWV derived from PPP-B2b were 3.7 mm and 4.4 mm when compared to PWV from 11 co-located radiosonde stations and ERA5 reanalysis, respectively, and underperformed relative to CNES solutions. Seasonal variability in GNSS-derived PWV was also noted. This reduction in accuracy limits the global applicability of PPP-B2b. Despite these shortcomings, satellite-based PPP services like PPP-B2b remain viable alternatives for real-time positioning and atmospheric applications without requiring internet connectivity.

1. Introduction

Water vapour and temperature are two key variables in the study of the global climate change and the weather nowcasting [1,2,3]. The global navigation satellite systems (GNSSs), which are designed mainly for positioning, navigation, and timing [4], has also been used to remotely sense the Earth’s atmosphere since the 1990s. In 1992, Bevis et al. [5] introduced the concept of ground-based GNSS meteorology for the first time, which has since prompted extensive academic investigation into the precision and reliability of GNSS-derived zenith total delay (ZTD) and precipitable water vapour (PWV). Due to its high accuracy and all-weather operational capability, GNSS-derived ZTD or PWV has become an indispensable dataset for atmospheric and climate studies [6,7,8,9,10,11,12,13] and weather forecasting [14,15,16,17,18]. In addition, GNSS-derived ZTD or PWV have been used in many studies to evaluate data derived with other techniques [19,20] or for tropospheric corrections for remote sensing techniques, e.g., interferometric synthetic aperture radar [21]. In 2013, the International GNSS Service (IGS) formally launched the IGS real-time service (RTS) to provide GNSS orbit and clock correction products to subscribed users via the internet. With the provided real-time satellite orbit and clock corrections [22,23,24], ZTD or PWV can be estimated in real time and with high accuracy using a precise point positioning (PPP) data processing strategy [25]. As demonstrated by Shi et al. [26], the accuracy of real-time ZTD or PWV estimates using PPP highly depends on the quality of the satellite orbit and clock products. Previous studies [27,28,29,30,31,32,33] have demonstrated that the accuracy of real-time tropospheric estimates using PPP with high-accuracy and real-time satellite orbit and clock products can reach 2–3 mm for PWV or approximately 5–10 mm for ZTD. The real-time orbit and clock products adopted in these studies are disseminated through the internet in the state space representation (SSR) format.
Therefore, to estimate the ZTD or PWV in real time with IGS RTS, one must have stable internet access; this limits the use of this technique in areas without reliable internet connections, for example, island, rural, and mountainous areas. With the launch of the last satellite on 23 June 2020, the third generation of the Beidou Navigation Satellite System (BDS-3) began providing timing and navigation services for global coverage [34]. The main feature of BDS-3 is its PPP service via the B2b signal (PPP-B2b), which provides high-accuracy orbit and clock information for BDS-3 and Global Positioning System (GPS) satellites through three geosynchronous equatorial orbit (GEO) satellites [35]. The BDS GEO satellites operate in orbit at altitudes of 35,786 km and are located at 80° E, 110.5° E, and 140° E. Compared with the IGS RTS, the BDS-3 PPP-B2b service is more convenient for users without a reliable internet connection. Figure 1 shows the coverage areas of three BDS GEO satellites on Earth for different elevation cut-off angles. The PPP-B2b service can be accessed by users in most regions of Asia, Europe, Africa, and Oceania, even with the cut-off angle set to 15°.
The quality of orbit and clock information provided by the PPP-B2b service has been assessed in several recent studies [36,37,38]. For example, Tao et al. [38] investigated the accuracy of PPP-B2b orbit and clock products by comparing them with products provided by Wuhan University. The results indicate that the root mean square errors (RMSEs) of the orbits from PPP-B2b were approximately 6 cm and 21 cm in the radial and cross-track directions, respectively, for both GPS and BDS-3. In the along-track direction, the RMSEs were approximately 24 cm and 34 cm for BDS-3 and GPS, respectively. In terms of the clock products, the standard deviations (STDs) of the PPP-B2b clocks were 0.11 ns and 0.13 ns for BDS-3 and GPS, respectively. Recent studies [36,37] also indicate that the average positioning accuracy of static PPP with PPP-B2b corrections is better than 3 cm in the north, east, and upwards directions. This good positioning performance means that tropospheric information could be accurately estimated in real time using the PPP-B2b service, a feature that would be useful in areas without reliable internet connections for weather forecasting and atmospheric studies. The retrieval performance of ZTD in China has been subject to analysis in several studies. Yang et al. [39] reported a RMS difference of 17.4 mm between ZTD values derived using the PPP-B2b service and those estimated by IGS across nine stations from DOY 195 to DOY 200. Xu et al. [40] conducted an analysis of ZTD values derived from PPP-B2b against those provided by the Wuhan University (WHU) analysis centre at eight stations from DOY 187 to DOY 191 in 2021, finding an RMS within 20 mm for stations located in China. However, these investigations are predominantly constrained by their short temporal scope (e.g., one week) and regional focus on China. Given that the effective coverage area of PPP-B2b is not clearly delineated and considering the crucial importance of its temporal stability for operational applications, a more comprehensive study encompassing a broader spatial distribution and extended temporal duration is warranted.
This study conducted a comprehensive investigation into the performance of PPP-B2b corrections, focusing on their application in ZTD/PWV estimation across 32 widely distributed stations over approximately one year. The accuracy of BDS-3, GPS orbit, and clock correction from PPP-B2b was assessed using geodetic benchmark (GBM) products from Deutsches Geo-ForschungsZentrum (GFZ) as a reference. Previous studies have demonstrated centimetre-level agreement between orbit/clock products from different analysis centres, with static positioning results showing only centimetre-level differences between products from the Center for Orbit Determination in Europe and GFZ [41]. Additionally, GFZ’s GBM products have been widely adopted for the evaluation of real-time orbit and clock products [36,42].
The differential code bias (DCB) for BDS-3 from the PPP-B2b service was assessed using data from the German Aerospace Center (DLR) and the Chinese Academy of Sciences (CAS). The ZTD values estimated with the PPP-B2b and Centre National d’Etudes Spatiales (CNES) real-time streams are investigated via comparison with those derived from the final clock and orbit products retrieved from the GBM and ZTD data provided by the IGS. Because it is a well-established method to estimate ZTD/PWV using RTS services, such as CNES RTS, comparing the performance of CNES and PPP-B2b allows us to evaluate the level of accuracy PPP-B2b currently achieves for the real-time applications. As indicated by Yu et al. [43], the orbit accuracy of GNSS products for GPS has been reported to be better than 5 cm in all three directions, with clock errors under 0.1 ns. For BDS, the orbit accuracy is approximately 10 cm, with clock errors around 0.66 ns. The latency of these products is approximately 18 s. The GNSS-derived ZTD and PWV data are compared with those determined from the European Centre for Medium-Range Weather Forecasting (ECMWF) Reanalysis fifth generation (ERA5) and radiosonde observations from the Integrated Global Radiosonde Archive (IGRA). Radiosonde data offer high accuracy through direct atmospheric measurements but are spatially and temporally limited. ERA5, though model-based, provides continuous global coverage and high temporal resolution. Utilizing both datasets allowed us to achieve precise validation where radiosonde data were available, while ensuring broader spatial and temporal analysis with ERA5, offering a more comprehensive assessment of GNSS-derived ZTD and PWV. The investigation, utilizing widely distributed stations and data spanning one year, provides valuable insights into the service’s performance and stability across diverse regions over an extended period.

2. Data and Methodologies

2.1. PPP-B2b Message and GNSS Observations

Using our custom-developed GNSS receiver and self-developed decoding software, the PPP-B2b corrections were received and decoded in real time at station BJ01 (40.07° N, 116.27° E) in Beijing, China. These corrections were then stored for further study. The receiver is equipped with a K803 GNSS OEM module provided by GomNav Technology Ltd. (ShangHai, China), designed to support the PPP-B2b signal with a centre frequency of 1207.14 MHz and a bandwidth of 20.46 MHz. The PPP-B2b data are acquired and transmitted to an Advanced RISC Machine (ARM) processor via the RS-232 communication standard in binary format. Our in-house developed software on the ARM processor then converts these binary data into ASCII format, enabling the real-time estimation of ZTD and coordinates using the PPP software running on the ARM processor. Furthermore, the software includes functionality for storing PPP-B2b data and transmitting the real-time stream to a Linux server, which broadcasts these corrections to users via the Internet. This capability facilitates broader access to real-time corrections for researchers and practitioners. Additional technical details regarding the structure and processing of PPP-B2b information are provided in the Appendix. Researchers interested in utilizing these corrections can request access by contacting the authors directly via email. The performances of the clock, orbit, and DCB broadcast on the PPP-B2b signal between DOY 069-311 in 2022 were compared with the final clock and orbit products from GBM and DCB from the Multi-GNSS Experiment (MGEX) project. It should be noted that our GNSS receiver could not continuously record the PPP-B2b information in May and June 2022 due to a power supply issue. The GNSS observations were available at 32 stations in RINEX format and were downloaded from the Crustal Dynamics Data Information System (CDDIS) (Noll 2010) or from our own observation network.

2.2. ERA5 Data

The production of the ERA5 dataset was based on the operational use of the Integrated Forecasting System (IFS) Cycle 41r2, with the advanced four-dimensional data assimilation technique and modelling, which provides estimates of atmospheric parameters on an hourly basis from 1950 onwards. More information regarding the ERA5 configuration, how it was produced, and how it fits into the framework of other reanalysis activities in the ECMWF can be found in the study by Hersbach et al. [44].
With the hourly temperature T (in Kelvin), specific humidity q (in kg kg−1), and pressure P (in hPa) at 37 pressure levels provided by ERA5, the ZTD (in meters) was calculated with Equation (1) [45].
Z T D = 10 − 6 k 1 R d ∫ 0 P a n t   1 g ( z ) · d P + 10 − 6 R w   ∫ 0 P a n t   q 1 g z k 2 ′ + k 3 T ·   d P
where R d = 287.053   J · K − 1 · K g − 1 and R w = 461.5   J · K − 1 · K g − 1 are the gas constants for dry air and water vapour, respectively; k 1 = 77.60   K h P a − 1 and k 2 ′ = 22.1   K h P a − 1 [46]; and P a n t (in hPa) is the pressure at the GNSS station height. The first term of the integral in Equation (1) is the zenith hydrostatic delay (ZHD), and the second term is the zenith wet delay (ZWD). g ( z ) is the local gravitational acceleration at geometric height z (in km) [47].
g z = g s ( R s R s + z ) 2
where g s is the local acceleration of gravity at mean sea level at latitude φ and R s is the effective radius of the earth at latitude φ . These parameters can be determined with Equation (3) [48].
g s ≈ 9.80620 · 1 − 0.0026442 · cos ⁡ 2 φ + 5.8 · 10 − 6 · c o s 2 2 φ R s = 6378.137 / ( 1.006803 − 0.006706 · s i n 2 φ )
The PWV (in meters) can be calculated using:
PWV = 1 ρ w ∫ 0 P a n t q g ( z ) d P
where ρ w = 1000   k g m − 3 is the density of water vapour, P is the pressure (in Pa), and q is the specific humidity.
For GNSS stations located above or below the lowest pressure level of ERA5, an interpolation or extrapolation procedure must be performed to determine the pressure, humidity, and temperature at the GNSS station altitude. More details on the extrapolation or interpolation procedures can be found in our previous studies [49,50]. The procedures for converting the GNSS altitude referring to an ellipsoid to an altitude relative to the mean sea level were also described in our previous study [49].

2.3. Radiosonde

The radiosonde data used in this study were provided by IGRA version 2 and consisted of quality-controlled observations of temperature, humidity, and pressure at stations across all continents. The ZTD and PWV are calculated with Equations (1)–(4) using the atmospheric profiles observed by radiosonde data. The specific humidity q is not included in the radiosonde observations and, thus, needs to be calculated with the total pressure P and the vapour pressure P v provided by the IGRA using:
q = 0.622 ⋅ P v P − 0.378 ⋅ P v
As suggested by Haase et al. [45], a quality control procedure was carried out to exclude radiosonde observations that had a large pressure gap (greater than 200 hPa) between two adjacent observation levels.
The maximum altitude reached by a weather balloon varies due to weather conditions and other factors, directly affecting the highest pressure level recorded by the radiosonde [51]. As a result, the ZTD derived from radiosonde data only accounts for the atmospheric contribution up to the recorded level (e.g., 50 hPa), inherently underestimating the total ZTD. To correct for this, Equation (6) [45] was utilized to calculate the contribution of the ZHD from atmospheric layers above the radiosonde’s maximum altitude. This value was then integrated with the ZTD obtained from Equation (1) to provide a more accurate estimation.
∆ Z H D ≈ k 1 R d P 1 g 1 1 + 2 R d T 1 ( R s + z 1 ) g 1 + 2 R d T 1 ( R s + z 1 ) g 1 2
where P 1 , g 1 , T 1 , and z 1 are the pressure, local gravitational acceleration, temperature, and geometric height at the top of the radiosonde observation profile, respectively. Because the water vapour density above the top of the radiosonde profiles is negligible, no contribution is added to the ZWD.
Similar to the determination of ZTD/PWV with ERA5, interpolation or extrapolation was performed to calculate the atmospheric variables at the GNSS station altitude depending on whether the station was above or below the lowest level of the radiosonde profiles. Figure 2 shows the distribution of GNSS stations (blue point) and their co-located radiosonde sites.

2.4. ZTD and PWV Estimation with PPP

The PPP technique is used in this study for estimating the ZTD with PPP-B2b, CNES, and GBM products. PPP is a fast and efficient means of estimating geodetic parameters such as coordinates and tropospheric delay. The accuracy of the PPP solution is highly dependent on the quality of the satellite orbit and clock because this information is introduced into the PPP processing, and the errors in this information are not eliminated or accounted for. With the improvement in the quality of the satellite orbit and the clock from IGS [52], PPP has become a very promising method in many applications, including the estimation of ZTD from a large network with hundreds or thousands of stations. The accuracy of the ZTD estimated with the PPP solution has been assessed in many studies. Thanks to the establishment of a real-time service in 2011 by IGS, the retrieval of the real-time ZTD or PWV using PPP became possible. Several studies [29,30,31,33,53] have demonstrated that the accuracy of the real-time PWV can reach 2~3 mm using PPP with high-accuracy real-time satellite orbit and clock products. A modified version of the RTKLIB software package [54] was utilized in this study for GNSS data processing. This version supports the PPP-B2b stream and incorporates new GNSS processing features, including the GPT3 model, to enhance the accuracy and efficiency of the data analysis.
In PPP processing, the tropospheric delays in the slant direction are usually expressed as [55]:
∆ L = T p r i o r i · m h e + T r e m a i n · m w e + · m w e · c o t ⁡ ( e ) G N cos ⁡ α + G E sin ⁡ α
where T p r i o r i represents the a priori zenith hydrostatic delay derived from an empirical model and m h and m w are the hydrostatic and wet mapping functions, respectively. e and α are the elevation and azimuth, respectively, of the satellites. The remaining tropospheric delay T r e m a i n , along with two gradient parameters G N and G E were estimated during the PPP process.
Thus far, many studies have been conducted with the aim of improving the accuracy of ZTD or PWV using an improved empirical ZHD model [50,56], water vapour-weighted mean temperature calculation methods [49,57,58,59,60,61] advanced ZTD estimation strategies [62,63,64,65,66], and newly developed mapping function and gradient models [61,67,68,69,70,71]. With suggestions from previous studies [64,72,73], a detailed description of the ZTD estimation strategy adopted in this study is presented in Table 1. Zhang et al. [73] suggested that the adoption of a small cut-off elevation can significantly improve the accuracy of the ZTD; thus, the elevation cut-off angle was set to 7° in this study. The Global Pressure and Temperature 3 (GPT3) mapping function [61] and gradient model proposed by Macmillan [74] were adopted for ZTD estimation. The Saastamoinen model with empirical meteorological parameters from GPT3 was used to calculate the a priori value for the ZHD, and the remaining wet delay was estimated as random walk process noise of 5 mm/ √ h [75].
The estimated ZTD was then converted to PWV using Equation (8) [5]:
P W V = ( Z T D − Z H D E R A 5 ) ·   10 6   ρ R w k 3 T m + k 2 ′
with Z H D E R A 5 computed using Equation (9) [5],
Z H D E R A 5 = 2.2779 · P a n t / [ 1 − 0.0026 · cos ⁡ 2 φ − 0.00028 h ]
and T m computed using Equation (10) [5],
T m = 70.2 + 0.72 · T a n t
where P a n t and T a n t are the pressure and temperature at the GNSS station determined with the ERA5 dataset based on the methods described in previous studies [49,50], and h (in km) is the GNSS height above the ellipsoid.

3. Evaluation of the Results for Clock, Orbit, and DCB

In this study, the PPP-B2b signal was received and decoded based on the published BDS Signal in Space Interface Control Documents for Open Service Signal PPP-B2b Version 1.0 (BDS-SIS-ICD-PPP-B2b-1.0) provided by the China Satellite Navigation Office [76]. The orbit and clock corrections in the PPP-B2b message were used to correct CNAV1 and LNAV for BDS-3 and GPS, respectively. The precise satellite position can be determined with the orbit correction vector in the PPP-B2b orbit correction message and the broadcast ephemeris. The precise clock offset can be calculated using the clock correction parameter in the PPP-B2b message and the broadcast ephemeris. In this study, the orbit, clock, and DCB performances recovered from PPP-B2b messages were evaluated with products from the MGEX pilot project [77]. Before the comparison between PPP-B2b and GBM products, several inconsistencies between these two sets of products needed to be fixed. For more details on PPP-B2b decoding and the methods used to evaluate the orbit, clock, and DCB, see Appendix A, Appendix B and Appendix C.
Because it takes time to obtain the correction information generated and transmitted from the master control station to users via BDS-3 GEO satellites, latency in the correction message received by the user is inevitable. The results show that the latencies of the PPP-B2b clock offsets received by our receiver at station BJ01 range from 5 s to 9 s for both GPS and BDS-3. These offsets are stable and within the nominal validity of the satellite clock corrections, that is, 12 s. As shown in Table 2, for the GPS satellites, the standard deviation (STD) values ranged from 0.14 ns to 0.20 ns, with a mean value of 0.16 ns; for the BDS-3 medium Earth orbit (MEO) satellites, the STD values ranged between 0.11 ns and 0.17 ns, with a mean value of 0.13 ns. The performances of three inclined geosynchronous orbit (IGSO) satellites, that is, PRN C38-40, were worse than those of the BDS-3 MEO satellites, with a mean STD value of 0.18 ns. The results also indicate that there is an obvious day-to-day variation in the STD values for both GPS and BDS-3. For GPS, the daily STD values vary from 0.05 ns to 0.28 ns, with 83.9% and 35.2% of the values being smaller than 0.2 ns and 0.15 ns, respectively. For BDS-3, the daily mean STD values of the clock errors vary from 0.06 ns to 0.29 ns, with 96.3% and 68.9% of the values being smaller than 0.2 ns and 0.15 ns, respectively.
For the orbit corrections, the latencies were in the range of 21–30 s, which is within the nominal validity of the satellite orbit corrections, that is, 96 s. As shown in Table 2, both GPS and BDS-3 have a higher accuracy in the radial direction than in the along- and cross-track directions. The mean RMSEs for the GPS satellites were 0.08 m, 0.36 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively. For the BDS-3 MEO satellites, the mean RMSEs were 0.10 m, 0.27 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively, which were similar to those of the GPS satellites. For the BDS-3 IGSO satellites, the mean RMSEs in the radial, along-track, and cross-track directions were 0.13 m, 0.37 m, and 0.40 m, respectively, which were worse than those of the BDS-3 MEO and GPS satellites. The results reveal obvious day-to-day variations in the orbit errors for both GPS and BDS-3, especially in the along- and cross-track directions. For GPS, the daily mean RMSEs of the 3D orbit errors vary from 0.22 m to 0.85 m, 57.5% of which are smaller than 0.5 m. For BDS-3, the daily mean RMSEs of the 3D orbit errors vary from 0.19 m to 0.96 m, 71.5% of which are smaller than 0.5 m. The accuracy of ZTD estimation in PPP is heavily dependent on the precision of orbit and clock corrections. Douša [78] reports that tangential orbit errors of 10 cm or radial orbit errors of 1 cm can induce ZTD errors of up to 1.3 cm and 1.0 cm, respectively. However, their study also demonstrated that precise satellite clock corrections can mitigate over 96% of radial orbit errors, aided by the small nadir angle (15°) and ambiguity resolution in PPP. Consequently, even with decimetre-level orbit errors, centimetre-level accuracy for ZTD, and millimetre-level accuracy for PWV, assuming a scale factor of 0.15 between the ZTD and PWV [5], can be achieved, as most orbit errors can be compensated by precise satellite clock corrections and the estimated ambiguity parameter in the PPP approach.
The DCBs that refer to the B3I signal at frequencies of f B 1 I , f B 1 C , and f B 2 a for BDS-3 were compared to those from DLR and CAS provided by the MGEX pilot project, and the mean values of the differences for the study period are shown in Table 3. The systematic bias between each DCB product caused by the zero-assumption adopted in the DCB estimation must be removed before the comparison is conducted. This systematic bias between different DCB products is absorbed by the receiver clock parameter and, thus, does not affect the final positioning or ZTD results. Table 3 shows the STD values of the differences between the different DCB products. We found that the STDs of the differences between the DCBs of DLR and CAS are 0.15 ns, 0.14 ns, and 0.13 ns for frequencies of f B 1 I , f B 1 C , and f B 2 a , respectively. For the frequencies f B 1 C , f B 2 a , and f B 1 I , the STD values of the differences between the DCB from PPP-B2b and the DCB from DLR or CAS were all within 0.4 ns. Although the error in the DCB would lead to a longer convergence time, it could be mostly absorbed by the receiver clock and ambiguity parameter for PPP and, thus, had no effect on the accuracy of the troposphere and coordinate estimates.
The signal-in-space ranging error (SISRE) is a key performance indicator for comparisons of different navigation systems [79]. The instantaneous SISRE, considering that the clock and orbit can be calculated using Equation (11), and the orbit-only SISRE can be calculated using Equation (12):
S I S R E c l k + o r b = ( w R · ∆ r R − ∆ C ) 2 + w A , C 2 · ∆ r A 2 + ∆ r C 2
S I S R E o r b = ( w R · ∆ r R ) 2 + w A , C 2 · ∆ r A 2 + ∆ r C 2
where w R and w A , C 2 are GNSS-dependent SISRE weight factors for the statistical contribution of radial (R), along-track (A), and cross-track (C) errors to the line-of-sight ranging error; ∆ r R , ∆ r A , and ∆ r c are the residuals of the satellite orbit in the R, A, and C directions, respectively; and ∆ C is the clock error. The weight factors w R and w A , C 2 used for different satellite constellations were suggested by Montenbruck, Steigenberger, and Hauschild [79].
With the instantaneous SISREs at different epochs for a specific satellite during the period from DOY 069 to 311 in 2022, the RMSE values of S I S R E c l k + o r b and S I S R E o r b for each satellite type were calculated and are presented in Table 4. The RMSE of S I S R E c l k + o r b varies from 0.60 m to 3.05 m, with a mean value of 1.12 m for GPS, and from 0.36 m to 1.25 m, with a mean value of 0.72 m for BDS-3. It should be noted that GPS satellites with large S I S R E c l k + o r b values mostly belong to the block IIR series. To further investigate the contributions of the orbit and clock errors to S I S R E c l k + o r b , the orbit-only SISRE, that is, S I S R E o r b , was calculated. The mean RMSE values of S I S R E o r b are 0.11 m and 0.13 m for GPS and BDS-3, respectively. These values were much smaller than those of S I S R E c l k + o r b , indicating that clock systematic errors have a much larger contribution to S I S R E c l k + o r b than satellite orbit errors. Therefore, S I S R E c l k + o r b is confirmed to be dominated mainly by clock errors. For tropospheric parameter estimation, we were more concerned about the accuracy of the ZTD estimation than about the convergence time. Therefore, the STD of S I S R E c l k + o r b was investigated in this study. As shown in Table 4, the STD of S I S R E c l k + o r b for BDS-3 (0.03 m) was smaller than that for GPS (0.06 m), which may have benefited from the use of intersatellite laser measurements for the generation of the BDS-3 satellites in the PPP-B2b product.
Figure 3a,b present the variations in the daily S I S R E c l k + o r b [STD] for GPS and BDS-3, respectively, which show obvious fluctuations during the period of DOY 193-216. For GPS, 54.5% and 90.7% of the days have S I S R E c l k + o r b [STD] values smaller than 0.05 m and 0.1 m, respectively. BDS-3 has a much better performance than GPS, with approximately 93.8% of the days having S I S R E c l k + o r b [STD] values less than 0.05 m.

4. PPP-B2b ZTD Estimation and Evaluation of the Results

4.1. Evaluation of Real-Time PPP-B2b ZTD at Station BJ01

Using the PPP-B2b corrections and GNSS observations received in real time at station BJ01, the real-time ZTD was computed and compared to the post-processed ZTD, which was calculated using a combination of GPS and BDS-3 constellations with accurate orbit and clock products from GBM from DOY 117 to the end of DOY 130, 2022. As shown in Figure 4a, the ZTDs derived using the PPP-B2b method with different systems agreed very well with those derived from GBM products. The results in Figure 4b depict that while the differences between PPP-B2b ZTD and GBM ZTD generally fall within the range of ± 3 cm, there is noticeable daily variation in these differences. This variation could be attributed to the daily fluctuations in the accuracy of the PPP-B2b orbit/clock products.
As listed in Table 5, using the post-processed ZTDs derived with the GBM final orbit/clock products as a reference, the ZTD errors stemming from the PPP-B2b corrections were calculated across different satellite systems. Table 5 shows that the ZTDs derived from GPS observations have the smallest bias but the largest RMSE compared to those of the other solutions. The ZTDs derived from the BDS-3 observations have an RMSE of 13.9 mm, which is slightly larger than that of the ZTDs derived from the combination of BDS-3 and GPS observations but smaller than that of the GPS-only solution. As shown in Table 5 and Figure 5, 91% of the errors for the GPS-only solution were in the range of −30 mm to 30 mm, while the percentage for the other solutions reached approximately 98%. For the coordinate accuracy, the RMSEs were 0.9 cm, 0.6 cm, and 4.8 cm in the north, east, and vertical directions, respectively, for the BDS-3/GPS combination solution, which is slightly better than the GPS-only or BDS3-only solution. As suggested by Vey et al. [80], a scaling factor of 4.4 between ZTD and station height is observed for a 10° elevation cutoff angle, meaning that a 4.4 cm error in station height corresponds to a 1 cm error in ZTD. Thus, theoretically, a 4.8 cm error in station height would result in approximately a 1 cm error in the ZTD estimate, which would result in about a 2 mm error in the derived PWV, assuming a scaling factor of 0.15 between ZTD and PWV [5].

4.2. Comparison between ZTD Derived with PPP-B2b/CNES and the Post-Processed Results

As shown in Figure 2, 32 stations were selected for this study to further investigate the performance of the ZTD derived from the PPP-B2b orbit/clock products at different locations. Since the receivers at these stations are not capable of decoding PPP-B2b corrections, the ZTDs at these stations were calculated using the stored PPP-B2b orbit/clock products in SP3 format at station BJ01. As shown in Table 6, the heights of the stations vary from −78.5 m (SGOC, Sri Lanka) to 3646.3 m (LHAZ, Tibetan Plateau). Among these stations, there are four stations with only GPS observations, four stations with GPS observations and some of the BDS-3 satellites, and 24 stations with both GPS and BDS-3 observations.
To simulate the real-time experiment, the GNSS observations and PPP-B2b and CNES orbit/clock products were read and processed epoch by epoch, and the ZTDs were estimated using the strategy listed in Table 1. Using the ZTDs computed with the GBM final products (a combination of GPS and BDS-3) and the ZTD provided by IGS as a reference, the ZTDs computed with the PPP-B2b products were then evaluated over these 32 stations from DOY 069 in 2022 to DOY 054 in 2023.
The results show that the CNES solution outperforms the PPP-B2b solution for all stations, regardless of whether the results are compared with those of the GBM or IGS solution. Using the GBM solution as a reference, the RMSEs of the CNES results range from 5.6 mm to 11.3 mm, with a mean value of 8.0 mm. For the PPP-B2b solution, the RMSEs range from 11.1 mm to 35.3 mm, with a mean value of 21.7 mm. In addition, the ZTDs calculated with the CNES products agree better with the GBM solutions than with the IGS solution in terms of the RMSE at all stations. This could be because both the CNES and GBM solutions were calculated using a combination of GPS and BDS-3 observations, while the IGS solutions were calculated using only GPS observations [81]. The statistical results presented in Table 7 indicate the noticeable dependence of the RMSE of the PPP-B2b ZTD on latitude. Using the GBM ZTD data as a reference, the average RMSE of the PPP-B2b ZTD within the latitudinal band from 30° N to 48° N is 15.7 mm, whereas it is 23.9 mm within the latitudinal band from 0° to 30° N and 25.0 mm between 0° and 38° S. In contrast, the accuracy of the CNES-derived ZTDs does not exhibit a pronounced dependence on latitude. The mean biases of the GNES-derived ZTDs are −0.8 mm and −0.1 mm for the IGS and GBM solutions, respectively, and 0.7 mm and 2.1 mm for the PPP-B2b solution compared to the IGS and GBM solutions, respectively.
The results in Figure 6 and Figure 7 also indicate that the accuracy of the ZTDs derived with PPP-B2b is strongly dependent on the location of the stations. For nine stations (i.e., ULAB, URUM, BIK0, CHAN, TASH, BJ01, BJFS, GAMG, and JFNG) between 30° N and 48° N, the RMSEs of the ZTD range from 11.1 mm to 22.8 mm, with a mean value of 15.7 mm. Among these nine stations, three (CHAN, BIK0, and BJFS) have only GPS observations, and their ZTD results are worse than those of the other stations when a combination of GPS and BDS-3 observations is used. The RMSE of the ZTD results obtained with PPP-B2b at the LHAZ station on the Tibetan Plateau reaches 27.4 mm, which might be due to the lack of BDS-3 observations at this station. For the other stations between 30° N and 38° S, the RMSE ranges from 17.8 mm to 35.3 mm, with a mean value of 24.4 mm, which is obviously larger than that at the stations located between 30° N and 48° N. The results also reveal that the PPP-B2b service for the MOBS station was rarely applicable during most epochs, resulting in no resolution obtained for over 70% of the epochs. This limitation arises from the fact that the PPP-B2b correction information is derived from tracking stations deployed within the territory of China, and its service is primarily designed for China and its surrounding areas. Consequently, the performance of PPP-B2b in regions distant from China, such as southern Australia, could degrade significantly, while in more remote areas like Antarctica, it may even become unavailable, due to a decrease in available satellites and worsening satellite geometry.

4.3. Comparison of the GNSS-Derived ZTD/PWV with That Derived from ERA5

In this study, GNSS-derived ZTD/PWV values are compared with those obtained with ERA5 from DOY 069, 2022 to DOY 059, 2023 at 32 stations. Table 8 shows the comparison results between the GNSS-derived ZTD/PWV (IGS, GBM, CNES, and PPP-B2b) and the ERA5-derived ZTD/PWV. The comparison results reveal that the ZTDs derived from GBM products exhibit the best agreement with the ERA5-derived ZTDs, with a mean RMSE of approximately 18.4 mm across 32 stations. The RMSEs of the IGS and CNES results are 19.0 mm and 19.6 mm, respectively. The PPP-B2b results exhibit the least agreement with the ERA5-derived ZTDs, with a mean RMSE of 27.8 mm. As shown in Table 8 and Figure 8, the RMSE variations for all GNSS solutions exhibit a latitudinal pattern, with higher RMSE values observed between 0° and 30° N than within the latitudinal bands of 30° N to 48° N and 0° to 38° S. In general, the RMSEs of the ZTDs for the IGS, GBM, and CNES solutions are approximately 22 mm between 0° and 30° N, exceeding that between 30° N and 38° S, where the mean value is approximately 17 mm. These spatial variations might be attributed to the fact that the atmospheric parameters in ERA5 are not of the same quality in all regions of the globe. Similarly, GNSS measurements and processing errors can change spatially. For the PPP-B2b ZTDs, the RMSE is 20.9 mm within the latitudinal band from 30° N to 48° N, which is slightly greater than that of the other three GNSS solutions. However, the RMSE of the PPP-B2b ZTDs reaches approximately 30 mm between 30° N and 38° S, which is significantly worse than that of the other solutions. The large errors in the PPP-B2b ZTD results are mainly dominated by the errors in the PPP-B2b orbit/clock products. The mean biases for the IGS, GBM, CNES, and PPP-B2b solutions are −0.9 mm, −1.7 mm, −2.0 mm, and 0.7 mm, respectively.
Figure 9 illustrates the spatial variation in the RMSEs and biases in the GNSS-derived PWV using the ERA5-derived PWV as a reference. As shown in Table 8, the mean RMSE values for the IGS-, GBM-, and CNES-derived PWVs are 3.1 mm, 3.0 mm, and 3.2 mm, respectively. Similar to the spatial variation in the RMSEs of ZTD, the RMSEs of PWV also exhibit a latitude-dependent pattern, with higher values observed between 0° and 30° N than within the latitudinal bands from 30° N to 48° N and 0° to 38° S. The PPP-B2b solutions demonstrate the poorest agreement with the ERA5-derived PWV, with a mean RMSE of 4.4 mm. Generally, the PPP-B2b solution within the latitudinal band from 30° N to 48° N has a smaller RMSE (3.2 mm) than that of the stations within the latitudinal bands from 0° N to 30° N (5.0 mm) and from 0° to 38° S (4.8 mm). The biases of the GNSS-derived PWVs compared to the ERA5-derived PWVs at these 32 stations are mostly within ±1 mm for the IGS, GBM, and CNES solutions and ±2 mm for the PPP-B2b solution.
To further investigate the temporal characteristics of the differences between the GNSS-derived PWV and the ERA-derived PWV, the monthly RMSE of the GNSS-derived PWV was calculated. The results in Figure 10 show that the differences between the GNSS-derived PWV and the ERA-derived PWV strongly depend on the duration at which the PWV has a large seasonal variation. Taking station CHAN as an example (Figure 10c), the RMSE of the IGS-derived PWV increases from 2.44 mm to 5.58 mm when the PWV varies from approximately 1 mm (March 2022) to 60 mm (July 2022). For the COCO station (Figure 10k) located in the equatorial region where the PWV is approximately 40–60 mm throughout the year, the RMSE value remains at approximately 2 mm during the study period and shows no obvious seasonal variation.
In addition to seasonal variations, previous studies have shown that there are strong diurnal variations in PWV time series. In this study, the hourly diurnal anomaly in PWV was calculated by subtracting the daily mean PWV from the corresponding observed hourly PWV. Figure 11 shows the mean diurnal PWV anomaly in March 2022 at six stations, which reveals that the amplitude of the diurnal PWV variation at these stations is approximately 1–2 mm.

4.4. Comparison of the GNSS-Derived ZTD/PWV with That Derived from Radiosonde Data

To further investigate the accuracy of the GNSS-derived ZTD/PWV, the ZTD/PWV data were compared with those derived from co-located radiosonde observations. As shown in Table 9, the RMSEs of the GNSS-derived ZTDs are 13.1 mm, 11.7 mm, 13.4 mm, and 22.4 mm for the IGS, GBM, CNES, and PPP-B2b solutions, respectively, which are much smaller than the RMSEs calculated using ERA5 as a reference for these 11 stations. The mean biases are 0.2 mm, −3.2 mm, −3.8 mm, and 2.9 mm for the IGS, GBM, CNES, and PPP-B2b solutions, respectively. As depicted in Figure 12, the RMSEs for the IGS, GBM, and CNES solutions are generally less than 15 mm at most stations. However, for the PPP-B2b solution, the RMSE of the ZTD exhibits significant variation with latitude. Only three stations, namely, ULAB (47.9° N, 107.1° E), URUM (43.8° N, 87.6° E), and CHAN (43.8° N, 125.4° E), had RMSEs smaller than 20 mm. The largest value was observed at station SEYG (4.7° S, 55.5° E), with a value of 31.6 mm.
Regarding the RMSE of the PWV shown in Table 9, the GBM solutions have the best agreement with the radiosonde-derived PWV, with an RMSE of 2.1 mm, followed by the IGS and CNES solutions, with RMSEs of 2.3 mm and 2.4 mm, respectively. The worst agreement was found between the PPP-B2b solution and the radiosonde results, with an RMSE of 3.7 mm. As shown in Figure 13, for the IGS, GBM, and CNES solutions, the RMSE is smaller than 3 mm at most stations, while the RMSE for the PPP-B2b solution shows an obvious latitude-dependent pattern and is smaller than 3 mm only at stations ULAB, URUM, and CHAN. Like the ZTD comparison results, the GNSS-derived PWVs agree better with the radiosonde-derived PWV than with the ERA5-derived PWV. The biases of the GNSS-derived PWV are mostly within ±2 mm for the four solutions.
Figure 14 shows the variations in the radiosonde-derived PWV (red dots) and the monthly RMSEs of the GNSS-derived PWV. The results also show that the RMSE of the GNSS-derived PWV usually increases with the PWV values when the PWV has a large seasonal variation, which is very evident at stations CHAN, BJFS, and LHAZ.

5. Discussion

Traditionally, real-time estimation of ZTD or PWV requires stable internet access to obtain orbit and clock corrections. The PPP-B2b service, transmitted via BDS-3 satellites, introduces a significant advancement by enabling real-time atmospheric sensing without internet dependence. This capability is particularly beneficial for remote and low-income regions, where access to real-time atmospheric data can mitigate the disastrous impacts of severe weather events.
Our study demonstrates that while the PPP-B2b service achieves acceptable ZTD accuracy in certain regions, such as northern China, with an RMS of approximately 15 mm, comparable to results from previous studies, its performance is notably latitude-dependent. Accuracy decreases to around 25 mm between 30° N and 38° S, and the service becomes nearly unavailable beyond 38° S due to insufficient satellite visibility and poor geometric conditions. This reduction in accuracy significantly limits the global applicability of PPP-B2b, especially for users in the southern hemisphere who require reliable atmospheric data for applications such as real-time weather monitoring, disaster preparedness, and climate research. In regions where accurate weather data are critical for agricultural planning or emergency response, these limitations could lead to less informed decision-making. Previous studies were mostly conducted over very short periods (such as one week). In contrast, our findings, based on a one-year period, reveal that the RMSE of PPP-B2b-derived PWV generally increases with higher PWV values, particularly in regions with significant seasonal variation, when compared with radiosonde-derived PWV.
In contrast, ZTD/PWV accuracy derived from CNES data consistently outperforms PPP-B2b across all stations when compared to post-processed data from ERA-5 and radiosonde observations. According to the World Meteorological Organization (WMO), the threshold and breakthrough accuracy requirements for IWV in nowcasting and real-time monitoring are 5 mm and 2 mm, respectively. While IWV accuracy derived from CNES approaches the “breakthrough” level with a mean RMS of 2.4 mm, the PPP-B2b service currently meets only the “threshold” in China and its surrounding areas. This underscores the need for further refinement of the PPP-B2b service to achieve “breakthrough” accuracy, which is crucial for its operational use in high-accuracy IWV products. Achieving “breakthrough” accuracy is essential because it represents a level of precision that significantly enhances the reliability and utility of atmospheric data in critical applications. While “threshold” accuracy ensures that the data are adequate for basic monitoring purposes, “breakthrough” accuracy enables more precise predictions and timely responses, particularly in nowcasting and very short-range forecasting, where the accuracy and timeliness of data are paramount. Attaining this level of accuracy would make PPP-B2b a more viable tool for operational use, enabling it to compete with or even surpass more established systems in regions where internet access is limited but precise atmospheric data are crucial.
Despite these limitations, satellite-based PPP services like PPP-B2b and Galileo’s High Accuracy Service offer valuable alternatives for real-time positioning and related applications by providing high-accuracy satellite orbit and clock corrections without requiring internet access. To support further research and application development, we have established a server to broadcast these corrections in real-time at stream.champ.org.cn via port 2101. Researchers interested in accessing these corrections can request access by contacting the authors.

6. Conclusions

In this study, the accuracy of the BDS-3 and GPS orbit and clock corrections of PPP-B2b was assessed using GBM products from the GFZ as a reference. The DCB for BDS-3 from the PPP-B2b service was assessed using DLR and CAS data. For the period between DOY 069 and DOY 311 in 2022, the comparison between the PPP-B2b clock and GBM clock yielded STD values of 0.16 ns, 0.13 ns, and 0.18 ns for GPS, BDS-3 MEO satellites, and three BDS-3 IGSO satellites, respectively. Regarding the orbit quality, the mean RMSEs for the GPS satellites were 0.08 m, 0.36 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively. For the BDS-3 MEO satellites, the mean RMSEs were 0.10 m, 0.27 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively, which were similar to those of the GPS satellites. For the BDS-3 IGSO satellites, the mean RMSEs in the radial, along-track, and cross-track directions were 0.13 m, 0.37 m, and 0.40 m, respectively, which were slightly worse than those of the BDS-3 MEO and GPS satellites. The differences between the DCB from PPP-B2b and the DCB from DLR or CAS were within ± 2 ns, and the differences between the DCBs from DLR and CAS were within ± 1 ns. In terms of the SISREs, BDS-3 performed better than the GPS satellites.
The ZTD derived with PPP-B2b and CNES was initially assessed at 32 stations within the region defined by latitude ranging from 38° S to 48° N and longitude from 55° E to 170° E. This evaluation spanned from Day of Year (DOY) 069 in 2022 to DOY 054 in 2023 and involved comparing the derived ZTD with post-processed ZTD obtained using the GBM clock/orbit and ZTD provided by the IGS. The results highlight a strong dependency of the ZTD accuracy derived with PPP-B2b on the latitude of the stations, whether compared to IGS or GBM ZTD results. When utilizing GBM-derived ZTD as a reference, the mean RMSE of PPP-B2b ZTD is 15.7 mm for nine stations situated between 30° N and 48° N. These stations span across diverse locations including northern China (URUM, CHAN, BJ01, and BJFS), Mongolia (ULAB), Uzbekistan (TASH), Japan (USUD), the Republic of Korea (GAMG), and Kyrgyzstan (BIK0). Conversely, for stations positioned between 0° and 30° N, and 0° and 38° S, the mean RMSE increases to 23.9 mm and 25.0 mm, respectively, significantly higher than that observed between 30° N and 48° N. This latitude-dependent pattern of PPP-B2b ZTD remains consistent when compared to the IGS-, ERA5-, and radiosonde-derived ZTD. Additionally, the results indicate that the PPP-B2b service for the MOBS station was rarely applicable at most epochs, with no resolution obtained for more than 70% of the epochs. This limitation arises because the PPP-B2b correction information is derived from tracking stations deployed in China and is intended solely for China and its surrounding areas. Consequently, the performance of PPP-B2b in regions distant from China may degrade due to a reduction in available satellites and a deterioration in satellite geometry. CNES performed much better than PPP-B2b in ZTD estimation, with a mean RMSE of 8.0 mm for 32 stations using GBM-derived ZTD as a reference. The GNSS-derived ZTD/PWV were also compared with those derived from ERA5 and radiosonde. The comparison results reveal that the RMSEs of the GBM-, IGS-, and CNES-derived ZTD and PWV are approximately 20 mm and 3 mm, respectively. For the PPP-B2b solutions, the RMSEs of ZTD and PWV are 27.8 mm and 4.4 mm, respectively, which are worse than those of the IGS, GBM, and CNES solutions. Using the radiosonde-derived ZTD/PWV as a reference, the RMSEs of ZTD and PWV derived with PPP-B2b are 22.4 mm and 3.7 mm, respectively, which are also worse than those of the IGS, GBM, and CNES solutions. The performance of PPP-B2b PWVs also exhibits a strong dependence on location compared to post-processed, ERA-derived, or radiosonde-derived PWVs. In addition, the comparison results also indicate that there are obvious seasonally dependent differences in the GNSS-derived PWV when compared to the PWV computed from ERA5.
The PPP-B2b service represents a significant advancement in GNSS-based atmospheric sensing by enabling real-time orbit and clock corrections without the need for internet access. This capability is particularly beneficial for remote and low-income regions where reliable internet connectivity may be limited, thereby democratizing access to high-accuracy weather and climate data. However, despite these advantages, the current performance of the PPP-B2b service exhibits considerable spatial variability, with diminished accuracy and reliability in regions distant from China. This limitation highlights the need for further enhancements to bring PPP-B2b to the level of robustness and precision found in internet-based real-time services like CNES, which currently outperform PPP-B2b in ZTD and PWV accuracy. Nonetheless, the innovative approach of PPP-B2b provides a strong foundation for expanding real-time GNSS applications, particularly in underserved regions.

Author Contributions

Conceptualization, X.W.; methodology, X.W.; software, K.Z. and J.Z.; validation, Q.H., Y.C. and C.Q.; formal analysis, X.W.; investigation, X.W. and H.L.; resources, X.W.; data curation, X.W.; writing—original draft preparation, X.W.; writing—review and editing, X.W.; visualization, X.W.; supervision, X.W.; project administration, X.W.; funding acquisition, X.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by National Natural Science Foundation of China (42474015) and the funding program from the Aerospace Information Research Institute.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.

Acknowledgments

The authors would like to thank the GFZ for providing high-accuracy orbit and clock products, DLR and CAS for providing DCB products, ECMWF for providing ERA5 data, and IGS for providing GNSS observations.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A. Decoding PPP-B2b Corrections

Each PPP-B2b message has a length of 486 bits, with the highest 6 bits indicating the message type, the lowest 24 bits for the cycle redundancy check (CRC), and the remaining 456 bits being the message data. After the 64-ary non-binary low-density parity check (LDPC), encoding and concatenating with 6 symbols of the reserved flags, 6 symbols of the PRN, and 16 symbols of the preamble, the data frame consisted of 1000 symbols. Because the data were broadcast at a rate of 1000 symbols per second, the broadcast time of each data frame was 1 s.
Although 7 message types had been designed, currently only message types 1–4 can be decoded by users; these types include satellite masks (Type 1), satellite orbit corrections and user range accuracy indices (Type 2), DCBs (Type 3), and satellite clock corrections (Type 4). Message type 63 was a null message used to fill in the blank period when there was no information available. As shown in Figure A1 [82], the broadcast time of a complete PPP-B2b message was 48 s. The broadcast times of a complete set of clock correction parameters, orbit correction parameters, and DCBs were 6 s, 7 s, and 4 s, respectively. During a 48-s broadcast period, the type 4 messages were updated eight times, and messages 2 and 3 were updated only once, which means that the update intervals for clock corrections, orbit corrections, and DCBs were 6 s, 48 s, and 48 s, respectively.
Atmosphere 15 01048 g0a1
Figure A1. Frame arrangement structure.
Figure A1. Frame arrangement structure.
Atmosphere 15 01048 g0a1
Table A1 lists the update rate and nominal validity for the different message types.
Table A1. Information update rate and nominal validity.
Table A1. Information update rate and nominal validity.
Information ContentUpdate IntervalNominal Validity
Orbit correction48 s96 s
Clock correction6 s12 s
Differential code bias48 s86,400 s
As shown in Table A2, to ensure the interrelationship among the information content of different message types, the information needed to be matched based on a group of issue of data (IOD), including: IOD of SSR (IOD SSR) for defining the issue number of the SSR; IOD of PRN (IODP) for matching the satellite clock correction and satellite mask; IOD of navigation (IODN); and IOD of correction (IODC) for matching the broadcast navigation message and corrections of the satellite clock and orbit.
Table A2. Message type and IOD type.
Table A2. Message type and IOD type.
Message TypesInformation ContentIOD Type
1Satellite maskIOD SSR, IODP
2Orbit correction and user range accuracy indexIOD SSR, IODN, IODC
3Differential code biasIOD SSR
4Satellite clock correctionIOD SSR, IODP, IODC
5User range accuracy index-
6Clock correction and orbit correction—combination 1-
7Clock correction and orbit correction—combination 2-
8–62Reserved
63Null message

Appendix B. Recovering Precise Orbit Corrections, Clock Offsets, and DCB

The orbit and clock corrections in the PPP-B2b message were used to correct CNAV1 and LNAV for BDS-3 and GPS, respectively. With the orbit correction vector ∂ O in the radial, along-, and cross-track directions provided by the PPP-B2b orbit correction message, the satellite position correction vector ∆ X can be calculated using Equation (A1):
e r = r r e c   = r × r ˙ r × r ˙ e a   = e c ×   e r ∆ X = e r   e a   e c · ∂ O
where e r , e a , and e c are the components of the direction unit vector in the radial, along-, and cross-track directions, respectively, and r and r ˙ represent the satellite position and velocity vectors of the broadcast ephemeris, respectively.
The precise satellite position X o r b can then be calculated using Equation (A2):
X o r b = X b r d − ∆ X
where X b r d is the satellite position calculated based on the broadcast ephemeris.
It should be noted that X o r b calculated using Equation (A2) is the satellite position with the antenna phase centre (APC) as the reference point.
The precise clock offset can be calculated using the clock correction parameter C 0 in the PPP-B2b message via Equation (A3):
d t ¯ B 2 b s y s = d t b r d s y s − C 0 C
where sys [G = GPS, C = BDS-3] denotes the satellite system, d t b r d s y s is the satellite clock offset calculated from the broadcast ephemeris, d t ¯ B 2 b s y s is the precise orbit clock offset, and C is the speed of light.
For GPS, the clock estimations provided in either the broadcast ephemeris or in the PPP-B2b message are estimated using the ionosphere-free linear combination (IFLC) of L 1 / L 2 P(Y) code without considering hardware code bias during the estimation process [79,83]. Therefore, as shown in Equation (A4), the PPP-B2b satellite clock offset d t ¯ B 2 b , I F G contains the actual satellite clock offset and an IFLC of the satellite hardware code bias at frequencies of f 1 and f 2 :
d t ¯ B 2 b , I F G = d t G − B s , I F G = d t G − α B s , 1 G + 1 − α B s , 2 G
where d t G is the actual satellite offset; α = f 1 2 / f 1 2 − f 2 2 , B s , 1 G , and B s , 2 G are the satellite hardware code biases at frequencies of f 1 and f 2 , respectively; and B s , I F G is the IFLC of B s , 1 G and B s , 2 G .
Therefore, when the IFLC of pseudorange observations P 1 and P 2 are adopted in data processing, the satellite hardware code bias can be ignored because it is absorbed in the satellite offset corrections provided by the PPP-B2b message.
For BDS-3, the satellite clock corrections given in PPP-B2b refer to the B3I signal, which means that the recovered satellite clock offset correction, d t ¯ B 2 b , B 3 I C in Equation (A5), contains the actual satellite clock offset and the satellite hardware code bias at the reference frequency f B 3 I .
d t ¯ B 2 b , B 3 I C = d t C − B s , B 3 I C
In Equation (A5), d t C is the actual satellite offset, and B s , B 3 I C is the satellite hardware-code bias for signal B3I.
Therefore, the differences in the satellite code hardware bias between any other signal and the B31 signal must be corrected for dual-frequency data processing with the corresponding DCB parameters. The DCB in the PPP-B2b message is the difference in the satellite hardware code bias between the signal and the reference signal B3I. Thus far, the DCB parameters for BDS-3 at frequencies of f B 1 I , f B 1 C , f B 2 a , f B 2 b − I , and f B 2 b − Q have been broadcast in the PPP-B2b message.

Appendix C. Performance Assessment of Orbit, Clock, and DCB

In this study, the performances of the orbit, clock, and DCB products recovered from PPP-B2b messages were assessed using the final products provided by the Multi-GNSS Experiment (MGEX) pilot project [77], including the orbit/clock products from the GFZ and DCB products from DLR [84] and CAS [85]. Prior to the comparison between the PPP-B2b and GBM products, several inconsistencies existed between these two sets of products that needed to be fixed.
(1) Coordinate and time system: The PPP-B2b orbit products of BDS-3 and GPS use the China Geodetic Coordinate System 2000 (CGCS2000) [86,87] and World Geodetic System 1984 (WGS84) [88] as their reference systems, respectively; they differ from the coordinate system adopted for the GFZ orbit products, that is, IGb14 [89]. Because these three coordinate systems are aligned to the International Terrestrial Reference Frame (ITRF) [90] and agree with each other at the centimetre level, the coordinate system difference between different orbit products was ignored in this study. For the time system, there is a difference of 14 s between the BDS time (BDT) adopted by PPP-B2b BDS-3 products and the GPS time (GPST) adopted by the GBM final products. This difference needed to be corrected prior to clock evaluation.
(2) Satellite orbit evaluation: Because the PPP-B2b satellite orbit and the final orbit from the GBM are referred to APC and the centre-of-mass (CoM), respectively, this reference difference must be corrected using the corresponding phase-centre offset (PCO) values and nominal attitude models using Equation (A6) [91,92] prior to further satellite orbit analysis.
R → C o M = R → A P C + A · P C O s a t
In Equation (A6), A represents the transform matrix from the satellite-fixed coordinate system to the Earth-centered, Earth-fixed (ECEF) coordinate system, R → A P C and R → C o M denote the satellite position vectors in the ECEF coordinate system that are referred to APC and CoM, respectively.
In this study, the PCO values of BDS-3 satellites released by the China Satellite Navigation Office (CSNO) [93] and the PCO values of GPS satellites from the latest IGS antenna information file, that is, igs14.atx, were adopted for this correction. After the PCO correction was made, the RMS of the differences between the PPP-B2b orbit products and the GBM final orbit products could be computed.
(3) Clock offset evaluation: For BDS-3, the PPP-B2b clock offsets are referred to as the APC of the B1I signal, while the GBM final clock offsets are referred to as the CoM of the satellite estimated based on the IFLC of B1I/B3I measurements. Therefore, a correction to this difference was essential for clock offset evaluation. As shown in Equation (A5), the PPP-B2b clock offsets contain a specific satellite hardware code bias of signal B3I. As shown in Equation (A7), the GBM final clock offsets contain a satellite hardware code bias for the IFLC of the measurements at the frequencies of f B 1 I and f B 3 I :
d t ¯ G B M , 13 C = d t C − φ B s , B 1 I C + 1 − φ B s , B 3 I C
where φ = f B 1 I 2 / ( f B 1 I 2 − f B 3 I 2 ) , B s , B 1 I C , and B s , B 3 I C are the satellite hardware code biases at the frequencies of f B 1 I and f B 3 I , respectively.
Therefore, prior to comparing the PPP-B2b clock offsets with the GBM final clock products, the difference in the reference signal caused by the satellite hardware code bias could be calculated using Equation (A8):
∆ D C B = φ B s , B 1 I C + 1 − φ B s , B 3 I C − B s , B 3 I C = f B 1 I 2 f B 1 I 2 − f B 3 I 2 · D C B 1,3 C
where D C B 1,3 C = B s , B 1 I C − B s , B 3 I C is the DCB parameter for the frequency of f B 1 I in the PPP-B2b message.
In addition, the inconsistency caused by the different APC corrections adopted in the generation of PPP-B2b and GBM clock products were also determined with their corresponding PCO values using Equation (A9) [73,94]:
∆ P C O = e B 2 b , 3 − f B 1 I 2 f B 1 I 2 − f B 3 I 2 e G B M , 1 − f B 3 I 2 f B 1 I 2 − f B 3 I 2 e G B M , 3
where e G B M , i represents the Z-components satellite PCO (in metres) adopted in the GBM clock offset generation for measurements at frequencies of f B 1 I (i = 1) and f B 3 I (i = 3), e B 2 b , 3 is the Z-component satellite PCO adopted in the PPP-B2b clock offset generation for measurements at the frequency of f B 3 I .
Finally, we calculated the single-difference (SD) clock difference between the PPP-B2b and GBM clock products using Equation (A10).
∆ C i j = d t ¯ B 2 b , B 3 I C i , j − ∆ D C B + ∆ P C O − d t ¯ G B M , 13 C i , j
where ∆ C i j is the clock difference between the clock offsets from PPP-B2b and the GBM at epoch i for satellite j.
Because of the difference in the underlying realization of the time scale, there was a systematic bias between different clock products. This bias is common to all satellites in the same constellation, but varies from epoch to epoch. This bias was absorbed by the receiver clock parameter and had no effect on the accuracy of the other estimations. Therefore, to eliminate this bias, the Equation (A11) is commonly used to calculate the double-difference (DD) clock time series for the clock performance evaluations.
∇ ∆ C i j = ∆ C i j − ∑ j = 1 N ∆ C i j N
where N is the number of the satellites.
It should be noted that, for PPP-B2b products, only regional satellites can be received at every epoch and, thus, the number of the satellites may vary at different epochs. This may lead to a discontinuity in the DD clock series, severely affecting the STD and RMSE of the DD clock series ∇ ∆ C i j . In clock evaluation, the STD represents PPP positioning accuracy after convergence, and the RMSE usually reflects the PPP convergence time. Therefore, to overcome this problem, Equations (A12) and (A13), proposed by Tao et.al. [33], were used in this study to re-edit the DD series for all satellites:
∇ ∆ C i j = ∇ ∆ C i j − ∆ D D i , i − 1
∆ D D i , i − 1 = 1 N   ∑ j = 1 N ∆ ∇ ∆ C i , i − 1 j     ,   a b s 1 N   ∑ j = 1 N ∆ ∇ ∆ C i , i − 1 j ≥ 0.1   n s         0                                                                     ,   a b s 1 N   ∑ j = 1 N ∆ ∇ ∆ C i , i − 1 j < 0.1   n s
where ∆ ∇ ∆ C i , i − 1 j = ∇ ∆ C i j − ∇ ∆ C i − 1 j is the time difference of the DD clock series.

References

  1. And, I.M.H.; Soden, B.J. Water vapor feedback and global warming. Annu. Rev. Energy Environ. 2000, 25, 441–475. [Google Scholar]
  2. Dessler, A.E.; Zhang, Z.; Yang, P. Water-vapor climate feedback inferred from climate fluctuations, 2003–2008. Geophys. Res. Lett. 2008, 35, 1–4. [Google Scholar] [CrossRef]
  3. Lavers, D.A.; Pappenberger, F.; Zsoter, E. Extending medium-range predictability of extreme hydrological events in Europe. Nat. Commun. 2014, 5, 5382. [Google Scholar] [CrossRef]
  4. Parkinson, B.W.; Enge, P.; Axelrad, P.; Spilker, J.J., Jr. Global Positioning System: Theory and Applications, Volume II; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 1996. [Google Scholar]
  5. Bevis, M.; Businger, S.; Herring, T.A.; Rocken, C.; Anthes, R.A.; Ware, R.H. GPS meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System. J. Geophys. Res. Atmos. 1992, 97, 15787–15801. [Google Scholar] [CrossRef]
  6. Bock, O.; Bosser, P.; Pacione, R.; Nuret, M.; Fourrié, N.; Parracho, A. A high-quality reprocessed ground-based GPS dataset for atmospheric process studies, radiosonde and model evaluation, and reanalysis of HyMeX Special Observing Period. Q. J. R. Meteorol. Soc. 2016, 142, 56–71. [Google Scholar] [CrossRef]
  7. Li, H.; Choy, S.; Wang, X.; Zhang, K.; Jiang, C.; Li, L.; Liu, X.; Hu, A.; Wu, S.; Zhu, D. Estimation of diurnal-provided potential evapotranspiration using GNSS and meteorological products. Atmos. Res. 2022, 280, 106424. [Google Scholar] [CrossRef]
  8. Nilsson, T.; Elgered, G. Long-term trends in the atmospheric water vapor content estimated from ground-based GPS data. J. Geophys. Res. Atmos. 2008, 113, 1–12. [Google Scholar] [CrossRef]
  9. Ning, T.; Elgered, G.; Willén, U.; Johansson, J.M. Evaluation of the atmospheric water vapor content in a regional climate model using ground-based GPS measurements. J. Geophys. Res. Atmos. 2013, 118, 329–339. [Google Scholar] [CrossRef]
  10. Vey, S.; Dietrich, R.; Fritsche, M.; Rülke, A.; Steigenberger, P.; Rothacher, M. On the homogeneity and interpretation of precipitable water time series derived from global GPS observations. J. Geophys. Res. Atmos. 2009, 114, 1–15. [Google Scholar] [CrossRef]
  11. Wang, J.; Zhang, L.; Dai, A.; Van Hove, T.; Van Baelen, J. A near-global, 2-hourly data set of atmospheric precipitable water from ground-based GPS measurements. J. Geophys.Res. Atmos. 2007, 112, 1–17. [Google Scholar] [CrossRef]
  12. Wang, X.; Zhang, K.; Wu, S.; Li, Z.; Cheng, Y.; Li, L.; Yuan, H. The correlation between GNSS-derived precipitable water vapor and sea surface temperature and its responses to El Niño–Southern Oscillation. Remote Sens. Environ. 2018, 216, 1–12. [Google Scholar] [CrossRef]
  13. Zhao, Q.; Yao, Y.; Yao, W. Studies of precipitable water vapour characteristics on a global scale. Int. J. Remote Sens. 2018, 40, 72–88. [Google Scholar] [CrossRef]
  14. Li, H.; Choy, S.; Wang, X.; Liang, H.; Purwar, S.; Zhang, K. Investigating the Optimal Spatial Resolution for Assimilating GNSS PWV into an NWP System to Improve the Accuracy of Humidity Field. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2023, 16, 6876–6887. [Google Scholar] [CrossRef]
  15. Li, H.; Wang, X.; Choy, S.; Jiang, C.; Wu, S.; Zhang, J.; Qiu, C.; Zhou, K.; Li, L.; Fu, E. Detecting heavy rainfall using anomaly-based percentile thresholds of predictors derived from GNSS-PWV. Atmos. Res. 2022, 265, 105912. [Google Scholar] [CrossRef]
  16. Rohm, W.; Guzikowski, J.; Wilgan, K.; Kryza, M. 4DVAR assimilation of GNSS zenith path delays and precipitable water into a numerical weather prediction model WRF. Atmos. Meas. Tech. 2019, 12, 345–361. [Google Scholar] [CrossRef]
  17. Yan, X.; Ducrocq, V.; Poli, P.; Hakam, M.; Jaubert, G.; Walpersdorf, A. Impact of GPS zenith delay assimilation on convective-scale prediction of Mediterranean heavy rainfall. J. Geophys. Res. Atmos. 2009, 114, 1–15. [Google Scholar] [CrossRef]
  18. Yao, Y.B.; Shan, L.L.; Zhao, Q.Z. Establishing a method of short-term rainfall forecasting based on GNSS-derived PWV and its application. Sci. Rep. 2017, 7, 11. [Google Scholar] [CrossRef]
  19. Li, Z.; Muller, J.P.; Cross, P. Comparison of precipitable water vapor derived from radiosonde, GPS, and Moderate-Resolution Imaging Spectroradiometer measurements. J. Geophys. Res. Atmos. 2003, 108, 1–10. [Google Scholar] [CrossRef]
  20. Vaquero-Martínez, J.; Antón, M.; Ortiz de Galisteo, J.P.; Cachorro, V.E.; Álvarez-Zapatero, P.; Román, R.; Loyola, D.; Costa, M.J.; Wang, H.; Abad, G.G.; et al. Inter-comparison of integrated water vapor from satellite instruments using reference GPS data at the Iberian Peninsula. Remote Sens. Enviorn. 2018, 204, 729–740. [Google Scholar] [CrossRef]
  21. Shamshiri, R.; Motagh, M.; Nahavandchi, H.; Haghshenas Haghighi, M.; Hoseini, M. Improving tropospheric corrections on large-scale Sentinel-1 interferograms using a machine learning approach for integration with GNSS-derived zenith total delay (ZTD). Remote Sens. Environ. 2020, 239, 111608. [Google Scholar] [CrossRef]
  22. Caissy, M.; Agrotis, L.; Weber, G.; Hernandez-Pajares, M.; Hugentobler, U. Coming Soon: The International GNSS Real-Time Service. GPS World. 2012. Available online: https://gge.ext.unb.ca/Resources/gpsworld.june12.pdf (accessed on 24 August 2024).
  23. Dousa, J. Precise near Real-Time Gnss Analyses at Geodetic Observatory Pecny—Precise Orbit Determination and Water Vapour Monitoring. Acta Geodyn. Geomater. 2010, 7, 7–17. [Google Scholar]
  24. Dow, J.M.; Neilan, R.E.; Rizos, C. The International GNSS Service in a changing landscape of Global Navigation Satellite Systems. J. Geod. 2009, 83, 191–198. [Google Scholar] [CrossRef]
  25. Zumberge, J.; Heflin, M.; Jefferson, D.; Watkins, M.; Webb, F. Precise point positioning for the efficient and robust analysis of GPS data from large networks. J. Geophys. Res. Solid Earth 1997, 102, 5005–5017. [Google Scholar] [CrossRef]
  26. Shi, J.; Xu, C.; Li, Y.; Gao, Y. Impacts of real-time satellite clock errors on GPS precise point positioning-based troposphere zenith delay estimation. J. Geod. 2015, 89, 747–756. [Google Scholar] [CrossRef]
  27. Danchik, R.J. An overview of transit development. Johns Hopkins APL Tech. Dig. 1998, 19, 19. [Google Scholar]
  28. Dousa, J.; Vaclavovic, P. Real-time zenith tropospheric delays in support of numerical weather prediction applications. Adv. Space Res. 2014, 53, 1347–1358. [Google Scholar] [CrossRef]
  29. Li, X.; Dick, G.; Ge, M.; Heise, S.; Wickert, J.; Bender, M. Real-time GPS sensing of atmospheric water vapor: Precise point positioning with orbit, clock, and phase delay corrections. Geophys. Res. Lett. 2014, 41, 3615–3621. [Google Scholar] [CrossRef]
  30. Yuan, Y.; Zhang, K.; Rohm, W.; Choy, S.; Norman, R.; Wang, C.S. Real-time retrieval of precipitable water vapor from GPS precise point positioning. J. Geophys. Res. Atmos. 2014, 119, 10044–10057. [Google Scholar] [CrossRef]
  31. Lu, C.; Li, X.; Nilsson, T.; Ning, T.; Heinkelmann, R.; Ge, M.; Glaser, S.; Schuh, H. Real-time retrieval of precipitable water vapor from GPS and BeiDou observations. J. Geod. 2015, 89, 843–856. [Google Scholar] [CrossRef]
  32. Guerova, G.; Jones, J.; Dousa, J.; Dick, G.; de Haan, S.; Pottiaux, E.; Bock, O.; Pacione, R.; Elgered, G.; Vedel, H. Review of the state of the art and future prospects of the ground-based GNSS meteorology in Europe. Atmos. Meas. Tech. 2016, 9, 5385. [Google Scholar] [CrossRef]
  33. Yu, C.; Penna, N.T.; Li, Z. Generation of real-time mode high-resolution water vapor fields from GPS observations. J. Geophys. Res. Atmos. 2017, 122, 2008–2025. [Google Scholar] [CrossRef]
  34. Yang, Y.; Mao, Y.; Sun, B. Basic performance and future developments of BeiDou global navigation satellite system. Satell. Navig. 2020, 1, 1. [Google Scholar] [CrossRef]
  35. Yang, Y.; Liu, L.; Li, J.; Yang, Y.; Zhang, T.; Mao, Y.; Sun, B.; Ren, X. Featured services and performance of BDS-3. Sci. Bull. 2021, 66, 2135–2143. [Google Scholar] [CrossRef] [PubMed]
  36. Nie, Z.; Xu, X.; Wang, Z.; Du, J. Initial Assessment of BDS PPP-B2b Service: Precision of Orbit and Clock Corrections, and PPP Performance. Remote Sens. 2021, 13, 2050. [Google Scholar] [CrossRef]
  37. Ren, Z.; Gong, H.; Peng, J.; Tang, C.; Huang, X.; Sun, G. Performance assessment of real-time precise point positioning using BDS PPP-B2b service signal. Adv. Space Res. 2021, 68, 3242–3254. [Google Scholar] [CrossRef]
  38. Tao, J.; Liu, J.; Hu, Z.; Zhao, Q.; Chen, G.; Ju, B. Initial Assessment of the BDS-3 PPP-B2b RTS compared with the CNES RTS. GPS Solut. 2021, 25, 131. [Google Scholar] [CrossRef]
  39. Yang, H.; He, X.; Ferreira, V.; Ji, S.; Xu, Y.; Song, S. Assessment of precipitable water vapor retrieved from precise point positioning with PPP-B2b service. Earth Sci. Inform. 2023, 16, 315–328. [Google Scholar] [CrossRef]
  40. Xu, Y.; Zhao, P.; Wang, J.; Meng, X. Performance Assess of BDS-3 PPP-B2b Signal Service and Its Application in Precipitable Water Vapor Retrieval. In Proceedings of the China Satellite Navigation Conference, Jinan, China, 22–24 May 2024; pp. 118–131. [Google Scholar]
  41. Li, X.; Zhu, Y.; Zheng, K.; Yuan, Y.; Liu, G.; Xiong, Y. Precise Orbit and Clock Products of Galileo, BDS and QZSS from MGEX Since 2018: Comparison and PPP Validation. Remote Sens. 2020, 12, 1415. [Google Scholar] [CrossRef]
  42. Li, B.; Ge, H.; Bu, Y.; Zheng, Y.; Yuan, L. Comprehensive assessment of real-time precise products from IGS analysis centers. Satell. Navig. 2022, 3, 12. [Google Scholar] [CrossRef]
  43. Yu, C.; Zhang, Y.; Chen, J.; Chen, Q.; Xu, K.; Wang, B. Performance Assessment of Multi-GNSS Real-Time Products from Various Analysis Centers. Remote Sens. 2023, 15, 140. [Google Scholar] [CrossRef]
  44. Hersbach, H.; Bell, B.; Berrisford, P.; Hirahara, S.; Horányi, A.; Muñoz-Sabater, J.; Nicolas, J.; Peubey, C.; Radu, R.; Schepers, D.; et al. The ERA5 global reanalysis. Q. J. R. Meteorol. Soc. 2020, 146, 1999–2049. [Google Scholar] [CrossRef]
  45. Haase, J.; Ge, M.; Vedel, H.; Calais, E. Accuracy and variability of GPS tropospheric delay measurements of water vapor in the western Mediterranean. J. Appl. Meteorol. 2003, 42, 1547–1568. [Google Scholar] [CrossRef]
  46. Bevis, M.; Businger, S.; Chiswell, S.; Herring, T.A.; Anthes, R.A.; Rocken, C.; Ware, R.H. GPS meteorology: Mapping zenith wet delays onto precipitable water. J. Appl. Meteorol. 1994, 33, 379–386. [Google Scholar] [CrossRef]
  47. NOAA. US Standard Atmosphere; National Oceanic and Atmospheric Administration: Washington, DC, USA, 1976. Available online: https://ntrs.nasa.gov/citations/19770009539 (accessed on 24 August 2024).
  48. WMO. Guide to Meteorological Instruments and Methods of Observation 2018 Edition (WMO-No. 8); World Meteorological Organisation: Geneva, Switzerland, 2018. [Google Scholar]
  49. Wang, X.; Zhang, K.; Wu, S.; Fan, S.; Cheng, Y. Water vapor-weighted mean temperature and its impact on the determination of precipitable water vapor and its linear trend. J. Geophys. Res. Atmos. 2016, 121, 833–852. [Google Scholar] [CrossRef]
  50. Wang, X.; Zhang, K.; Wu, S.; He, C.; Cheng, Y.; Li, X. Determination of zenith hydrostatic delay and its impact on GNSS-derived integrated water vapor. Atmos. Meas. Tech. Discuss 2017, 10, 14. [Google Scholar] [CrossRef]
  51. Pham, C.C.; Nguyen, X.A. Determination of radio wave propagation conditions in the atmosphere of Hanoi using the radiosonde data of balloons. ICT Express 2022, 8, 611–617. [Google Scholar] [CrossRef]
  52. Johnston, G.; Riddell, A.; Hausler, G. The International GNSS Service. In Springer Handbook of Global Navigation Satellite Systems; Teunissen, P.J.G., Montenbruck, O., Eds.; Springer International Publishing: Cham, Switzerland, 2017; pp. 967–982. [Google Scholar]
  53. Junbo, S.; Chaoqian, X.; Jiming, G.; Yang, G. Real-Time GPS Precise Point Positioning-Based Precipitable Water Vapor Estimation for Rainfall Monitoring and Forecasting. Geosci. Remote Sens. IEEE Trans. 2015, 53, 3452–3459. [Google Scholar] [CrossRef]
  54. Takasu, T. RTKLIB: An Open Source Program Package for GNSS Positioning. 2011. Available online: https://www.rtklib.com/ (accessed on 24 August 2024).
  55. Bar-Sever, Y.E.; Kroger, P.M.; Borjesson, J.A. Estimating horizontal gradients of tropospheric path delay with a single GPS receiver. J. Geophys. Res. Solid Earth 1998, 103, 5019–5035. [Google Scholar] [CrossRef]
  56. Tregoning, P.; Herring, T. Impact of a priori zenith hydrostatic delay errors on GPS estimates of station heights and zenith total delays. Geophys. Res. Lett. 2006, 33, 1–5. [Google Scholar] [CrossRef]
  57. Yao, Y.; Zhu, S.; Yue, S. A globally applicable, season-specific model for estimating the weighted mean temperature of the atmosphere. J. Geod. 2012, 86, 1125–1135. [Google Scholar] [CrossRef]
  58. Wang, J.; Zhang, L.; Dai, A. Global estimates of water-vapor-weighted mean temperature of the atmosphere for GPS applications. J. Geophys. Res. Atmos. 2005, 110, 1–17. [Google Scholar] [CrossRef]
  59. Ding, M. A neural network model for predicting weighted mean temperature. J. Geod. 2018, 925, 1187–1198. [Google Scholar] [CrossRef]
  60. Huang, L.; Jiang, W.; Liu, L.; Chen, H.; Ye, S. A new global grid model for the determination of atmospheric weighted mean temperature in GPS precipitable water vapor. J. Geod. 2018, 93, 159–176. [Google Scholar] [CrossRef]
  61. Landskron, D.; Böhm, J. VMF3/GPT3: Refined discrete and empirical troposphere mapping functions. J. Geod. 2018, 92, 349–360. [Google Scholar] [CrossRef] [PubMed]
  62. Li, X.; Dick, G.; Lu, C.; Ge, M.; Nilsson, T.; Ning, T.; Wickert, J.; Schuh, H. Multi-GNSS Meteorology: Real-Time Retrieving of Atmospheric Water Vapor From BeiDou, Galileo, GLONASS, and GPS Observations. Geosci. Remote Sens. IEEE Trans. 2015, 53, 6385–6393. [Google Scholar] [CrossRef]
  63. Lu, C.; Chen, X.; Liu, G.; Dick, G.; Wickert, J.; Jiang, X.; Zheng, K.; Schuh, H. Real-Time Tropospheric Delays Retrieved from Multi-GNSS Observations and IGS Real-Time Product Streams. Remote Sens. 2017, 9, 1317. [Google Scholar] [CrossRef]
  64. Hadas, T.; Hobiger, T.; Hordyniec, P. Considering different recent advancements in GNSS on real-time zenith troposphere estimates. GPS Solut. 2020, 24, 99. [Google Scholar] [CrossRef]
  65. Zhou, F.; Cao, X.; Ge, Y.; Li, W. Assessment of the positioning performance and tropospheric delay retrieval with precise point positioning using products from different analysis centers. GPS Solut. 2020, 24, 12. [Google Scholar] [CrossRef]
  66. Wilgan, K.; Dick, G.; Zus, F.; Wickert, J. Towards operational multi-GNSS tropospheric products at GFZ Potsdam. Atmos. Meas. Tech. 2022, 15, 21–39. [Google Scholar] [CrossRef]
  67. Boehm, J.; Niell, A.; Tregoning, P.; Schuh, H. Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data. Geophys. Res. Lett. 2006, 33, 1–4. [Google Scholar] [CrossRef]
  68. Vey, S.; Dietrich, R.; Fritsche, M.; Rülke, A.; Rothacher, M.; Steigenberger, P. Influence of mapping function parameters on global GPS network analyses: Comparisons between NMF and IMF. Geophys. Res. Lett. 2006, 33, 1–4. [Google Scholar] [CrossRef]
  69. Boehm, J.; Kouba, J.; Schuh, H. Forecast Vienna Mapping Functions 1 for real-time analysis of space geodetic observations. J. Geod. 2009, 83, 397–401. [Google Scholar] [CrossRef]
  70. Yao, Y.; Xu, C.; Zhang, B.; Cao, N. A global empirical model for mapping zenith wet delays onto precipitable water vapor using GGOS Atmosphere data. Sci. China Earth Sci. 2015, 58, 1361–1369. [Google Scholar] [CrossRef]
  71. Qiu, C.; Wang, X.; Li, Z.; Zhang, S.; Li, H.; Zhang, J.; Yuan, H. The Performance of Different Mapping Functions and Gradient Models in the Determination of Slant Tropospheric Delay. Remote Sens. 2020, 12, 130. [Google Scholar] [CrossRef]
  72. Li, X.; Zus, F.; Lu, C.; Dick, G.; Ning, T.; Ge, M.; Wickert, J.; Schuh, H. Retrieving of atmospheric parameters from multi-GNSS in real time: Validation with water vapor radiometer and numerical weather model. J. Geophys. Res. Atmos. 2015, 120, 7189–7204. [Google Scholar] [CrossRef]
  73. Zhang, J.; Wang, X.; Li, Z.; Li, S.; Qiu, C.; Li, H.; Zhang, S.; Li, L. The Impact of Different Ocean Tide Loading Models on GNSS Estimated Zenith Tropospheric Delay Using Precise Point Positioning Technique. Remote Sens. 2020, 12, 3080. [Google Scholar] [CrossRef]
  74. Macmillan, D.S. Atmospheric gradients from very long baseline interferometry observations. Geophys. Res. Lett. 1995, 22, 1041–1044. [Google Scholar] [CrossRef]
  75. Hadas, T.; Teferle, F.N.; Kazmierski, K.; Hordyniec, P.; Bosy, J. Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time. GPS Solut. 2017, 21, 1069–1081. [Google Scholar] [CrossRef]
  76. China Satellite Navigation Office. BeiDou Navigation Satellite System Signal in Space Interface Control Document: Open Service Signal B2b. 2020. Available online: http://www.beidou.gov.cn/xt/gfxz/202008/P020200803362062482940.pdf (accessed on 24 August 2024).
  77. Montenbruck, O.; Steigenberger, P.; Prange, L.; Deng, Z.; Zhao, Q.; Perosanz, F.; Romero, I.; Noll, C.; Stürze, A.; Weber, G. The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS)—Achievements, Prospects and Challenges. Adv. Space Res. 2017, 59, 1671–1697. [Google Scholar] [CrossRef]
  78. Douša, J. The impact of errors in predicted GPS orbits on zenith troposphere delay estimation. GPS Solut. 2010, 14, 229–239. [Google Scholar] [CrossRef]
  79. Montenbruck, O.; Steigenberger, P.; Hauschild, A. Broadcast versus precise ephemerides: A multi-GNSS perspective. GPS Solut. 2015, 19, 321–333. [Google Scholar] [CrossRef]
  80. Vey, S.; Calais, E.; Llubes, M.; Florsch, N.; Woppelmann, G.; Hinderer, J.; Amalvict, M.; Lalancette, M.; Simon, B.; Duquenne, F. GPS measurements of ocean loading and its impact on zenith tropospheric delay estimates: A case study in Brittany, France. J. Geod. 2002, 76, 419–427. [Google Scholar] [CrossRef]
  81. Byram, S.; Hackman, C.; Tracey, J. Computation of a high-precision GPS-based troposphere product by the USNO. In Proceedings of the 24th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, USA, 20–23 September 2011; pp. 572–578. [Google Scholar]
  82. Lu, X.; Chen, L.; Shen, N.; Wang, L.; Jiao, Z.; Chen, R. Decoding PPP Corrections From BDS B2b Signals Using a Software-Defined Receiver: An Initial Performance Evaluation. IEEE Sens. J. 2021, 21, 7871–7883. [Google Scholar] [CrossRef]
  83. Guo, F.; Zhang, X.; Wang, J. Timing group delay and differential code bias corrections for BeiDou positioning. J. Geod. 2015, 89, 427–445. [Google Scholar] [CrossRef]
  84. Montenbruck, O.; Hauschild, A.; Steigenberger, P. Differential code bias estimation using multi-GNSS observations and global ionosphere maps. Navig. J. Inst. Navig. 2014, 61, 191–201. [Google Scholar] [CrossRef]
  85. Wang, N.; Yuan, Y.; Li, Z.; Montenbruck, O.; Tan, B. Determination of differential code biases with multi-GNSS observations. J. Geod. 2016, 90, 209–228. [Google Scholar] [CrossRef]
  86. Cheng, P.; Cheng, Y.; Wang, X.; Xu, Y. Update China geodetic coordinate frame considering plate motion. Satell. Navig. 2021, 2, 2. [Google Scholar] [CrossRef]
  87. Yang, Y. Chinese geodetic coordinate system 2000. Chin. Sci Bull. 2009, 54, 2714–2721. [Google Scholar] [CrossRef]
  88. Merrigan, M.J.; Swift, E.R.; Wong, R.F.; Saffel, J.T. A refinement to the World Geodetic System 1984 reference frame. In Proceedings of the 15th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 2002), Portland, OR, USA, 24–27 September 2002; pp. 1519–1529. [Google Scholar]
  89. Rebischung, P. IGSMAIL-7921: Switch to IGb14 Reference Frame. 2020. Available online: https://lists.igs.org/pipermail/igsmail/2020/007917.html (accessed on 24 August 2024).
  90. Altamimi, Z.; Rebischung, P.; Métivier, L.; Collilieux, X. ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J. Geophys. Res. Solid Earth 2016, 121, 6109–6131. [Google Scholar] [CrossRef]
  91. Yang, C.; Guo, J.; Zhao, Q. Yaw attitudes for BDS-3 IGSO and MEO satellites: Estimation, validation and modeling with inter-satellite link observations. arXiv 2021, arXiv:2112.13252. [Google Scholar] [CrossRef]
  92. Kouba, J.; Héroux, P. Precise Point Positioning Using IGS Orbit and Clock Products. GPS Solut. 2001, 5, 12–28. [Google Scholar] [CrossRef]
  93. China Satellite Navigation Office. Release of the BDS-2/3 Satellite Related Parameters. 2019. Available online: http://www.beidou.gov.cn/yw/gfgg/201912/t20191209_19613.html (accessed on 24 August 2024).
  94. Hauschild, A. Precise GNSS Clock-Estimation for Real-Time Navigation and Precise Point Positioning. Ph.D. Thesis, Technische Universität München, München, Germany, 2010. [Google Scholar]
Atmosphere 15 01048 g001
Figure 1. Coverage areas of three BDS GEO satellites. The red, yellow, and purple stars represent subsatellite points of the three GEO satellites located at 80° E, 110.5° E, and 140° E, respectively, and the lines represent their coverage at cut-off angles of (a) 3°, (b) 5°, (c) 7°, and (d) 15°.
Figure 1. Coverage areas of three BDS GEO satellites. The red, yellow, and purple stars represent subsatellite points of the three GEO satellites located at 80° E, 110.5° E, and 140° E, respectively, and the lines represent their coverage at cut-off angles of (a) 3°, (b) 5°, (c) 7°, and (d) 15°.
Atmosphere 15 01048 g001
Atmosphere 15 01048 g002
Figure 2. Distribution of the 32 GNSS stations; 11 stations with co-located radiosondes are marked with red triangles, while the location of BJ01 is marked with a green pentagram.
Figure 2. Distribution of the 32 GNSS stations; 11 stations with co-located radiosondes are marked with red triangles, while the location of BJ01 is marked with a green pentagram.
Atmosphere 15 01048 g002
Atmosphere 15 01048 g003
Figure 3. Daily variation in SISREclk+orb [STD] for (a) GPS and (b) BDS-3 from DOY 069 to 311 in 2022. The results show that the daily SISREclk+orb remains less than 0.1 m for GPS and less than 0.05 m for BDS-3 most of the time.
Figure 3. Daily variation in SISREclk+orb [STD] for (a) GPS and (b) BDS-3 from DOY 069 to 311 in 2022. The results show that the daily SISREclk+orb remains less than 0.1 m for GPS and less than 0.05 m for BDS-3 most of the time.
Atmosphere 15 01048 g003
Atmosphere 15 01048 g004
Figure 4. ZTD time series derived with different methods (a) and the differences between ZTDs derived with PPP-B2b and GBM (b).
Figure 4. ZTD time series derived with different methods (a) and the differences between ZTDs derived with PPP-B2b and GBM (b).
Atmosphere 15 01048 g004
Atmosphere 15 01048 g005
Figure 5. ZTD error distributions for PPP-B2b solutions. The errors were calculated using the GBM solution as a reference. The results show that the errors are mostly within −30 to 30 mm.
Figure 5. ZTD error distributions for PPP-B2b solutions. The errors were calculated using the GBM solution as a reference. The results show that the errors are mostly within −30 to 30 mm.
Atmosphere 15 01048 g005
Atmosphere 15 01048 g006
Figure 6. RMSE (a,b) and bias (c,d) of the ZTD derived with CNES and PPP-B2b using the ZTD provided by IGS as a reference.
Figure 6. RMSE (a,b) and bias (c,d) of the ZTD derived with CNES and PPP-B2b using the ZTD provided by IGS as a reference.
Atmosphere 15 01048 g006
Atmosphere 15 01048 g007
Figure 7. RMSE (a,b) and bias (c,d) of the ZTD derived with CNES and PPP-B2b using the ZTD calculated with GBM satellite/orbit products as a reference.
Figure 7. RMSE (a,b) and bias (c,d) of the ZTD derived with CNES and PPP-B2b using the ZTD calculated with GBM satellite/orbit products as a reference.
Atmosphere 15 01048 g007
Atmosphere 15 01048 g008
Figure 8. RMSE (a–d) and bias (e–h) of the ZTD derived with IGS, GBM, CNES, and PPP-B2b, using the ZTD calculated from ERA5 as a reference.
Figure 8. RMSE (a–d) and bias (e–h) of the ZTD derived with IGS, GBM, CNES, and PPP-B2b, using the ZTD calculated from ERA5 as a reference.
Atmosphere 15 01048 g008
Atmosphere 15 01048 g009
Figure 9. RMSE (a–d) and bias (e–h) of the PWV derived with IGS, GBM, CNES, and PPP-B2b using the PWV from ERA5 as a reference.
Figure 9. RMSE (a–d) and bias (e–h) of the PWV derived with IGS, GBM, CNES, and PPP-B2b using the PWV from ERA5 as a reference.
Atmosphere 15 01048 g009
Atmosphere 15 01048 g010
Figure 10. PWV variations and the monthly RMSEs of differences between GNSS-derived PWV and ERA5-derived PWV.
Figure 10. PWV variations and the monthly RMSEs of differences between GNSS-derived PWV and ERA5-derived PWV.
Atmosphere 15 01048 g010
Atmosphere 15 01048 g011
Figure 11. Diurnal anomaly variations in the PWV time series obtained from GNSS and ERA5 in March 2022.
Figure 11. Diurnal anomaly variations in the PWV time series obtained from GNSS and ERA5 in March 2022.
Atmosphere 15 01048 g011
Atmosphere 15 01048 g012
Figure 12. RMSE (a–d) and bias (e–h) of the ZTD derived with IGS, GBM, CNES, and PPP-B2b using the ZTD from radiosonde as a reference.
Figure 12. RMSE (a–d) and bias (e–h) of the ZTD derived with IGS, GBM, CNES, and PPP-B2b using the ZTD from radiosonde as a reference.
Atmosphere 15 01048 g012
Atmosphere 15 01048 g013
Figure 13. This RMSE (a–d) and bias (e–h) of the PWV derived with IGS, GBM, CNES, and PPP-B2b using the PWV from radiosonde as a reference.
Figure 13. This RMSE (a–d) and bias (e–h) of the PWV derived with IGS, GBM, CNES, and PPP-B2b using the PWV from radiosonde as a reference.
Atmosphere 15 01048 g013
Atmosphere 15 01048 g014
Figure 14. PWV variations and the monthly RMSs of the differences between GNSS-derived PWV and radiosonde-derived PWV at 11 stations (a–k).
Figure 14. PWV variations and the monthly RMSs of the differences between GNSS-derived PWV and radiosonde-derived PWV at 11 stations (a–k).
Atmosphere 15 01048 g014
Table 1. ZTD estimation strategy with PPP-B2b.
Table 1. ZTD estimation strategy with PPP-B2b.
ItemsStrategies
ObservablesIFLC of the pseudorange and carrier phase
FrequenciesGPS L1/L2 and BDS-3 B1I/B3I (B1C/B2a)
Elevation cut-off angle 7 °
ZTD estimationThe a priori value for the hydrostatic delay was calculated using the Saastamoinen model with pressure and temperature from GPT3; the wet delay was estimated as a random walk process noise of 5   mm / √ h
Mapping functionGPT3
Gradient parametersNorth and east components of the tropospheric gradient parameters were estimated
Receiver clockThe receiver clock was estimated for GPS and BDS-3 separately
Solution typeStatic with float ambiguities
Corrections modelsPhase wind-up, relativistic delays, and the effects of the solid Earth pole tide and ocean pole tide were modelled according to IERS Conventions 2010
Table 2. Evaluation of the PPP-B2b orbit and clock.
Table 2. Evaluation of the PPP-B2b orbit and clock.
SystemSTD of Clock Errors
(ns)		RMSE of Orbit Errors (m)
RadialAlong-TrackCross-Track
GPS0.160.080.360.28
BDS-3 MEO0.130.100.270.28
BDS-3 IGSO0.180.130.370.40
Table 3. STD values of the differences between different DCB products (unit: ns).
Table 3. STD values of the differences between different DCB products (unit: ns).
D C B D L R - D C B P P P − B 2 b D C B C A S - D C B P P P − B 2 b D C B D L R - D C B C A S
FrequencyB1IB1C(P)B2a(P)B1IB1C(P)B2a(P)B1IB1C(P)B2a(P)
STD0.360.370.220.350.370.270.150.140.13
Table 4. Statistical results for the SISREs (unit: m).
Table 4. Statistical results for the SISREs (unit: m).
SystemSatellite Type S I S R E o r b
[RMSE]		 S I S R E c l k + o r b
[RMSE]		 S I S R E c l k + o r b
[STD]
GPSIIR0.111.940.07
IIR-M0.100.940.06
IIF0.110.960.06
III0.120.630.04
Mean0.111.120.06
BDS-3MEO0.120.580.03
IGSO0.140.870.04
Mean0.130.720.03
Table 5. Comparison between the real-time ZTDs derived with PPP-B2b corrections and post-processed ZTDs derived with the GBM final orbit/clock products.
Table 5. Comparison between the real-time ZTDs derived with PPP-B2b corrections and post-processed ZTDs derived with the GBM final orbit/clock products.
StrategyError Range
[Min, Max]		Percentage in the Range
[−30 mm, 30 mm] (%)		Bias (mm)RMSE (mm)
GPS-only[−57.7, 67.5]91.1−0.317.8
BDS-only[−41.9, 32.2]98.5−6.413.9
BDS + GPS[−44.6, 40.3]98.2−2.513.4
Table 6. Information on the GNSS stations and co-located radiosonde stations.
Table 6. Information on the GNSS stations and co-located radiosonde stations.
GNSSCo-Located Radiosonde
Station
Name		Latitude (°)Longitude (°)Height (m)Observation SystemStation
Name		Horizontal Distance (km)Height Difference (m)
ULAB47.9107.11575.6G + CMGM0004429214.98−117.4
URUM43.887.6858.9G + CCHM000514633.092.4
CHAN43.8125.4271.5GPS onlyCHM0005416121.8920.1
BIK042.974.5744.9GPS onlyN/AN/AN/A
TASH41.369.3439.7G + CN/AN/AN/A
BJ0140.1116.385.5G + CN/AN/AN/A
BJFS39.6115.987.4GPS onlyCHM0005451149.1964.6
USUD36.1138.41508.6G + CN/AN/AN/A
GAMG35.6127.9925.9G + CN/AN/AN/A
JFNG30.5114.571.3G + CN/AN/AN/A
LHAZ29.791.13646.3GPS onlyCHM000555913.001.0
LCK426.981.064.2G + CINM0004236919.437.2
SHLG25.791.91007.2G + CN/AN/AN/A
TWTF25.0121.2201.5G + C (C19-37)N/AN/AN/A
NCKU23.0120.298.2G + C (C19-30)N/AN/AN/A
HKFN22.5114.141.2G + C (C19-30)N/AN/AN/A
HKQT22.3114.25.2G + C (C19-30)HKM000450046.10−17.2
PTGG14.5121.084.9G + CN/AN/AN/A
CUSV13.7100.576.1G + CN/AN/AN/A
GUAM13.6144.9201.9G + CGQM0009121214.8670.3
IISC13.077.6843.7G + CN/AN/AN/A
SGOC6.979.9−78.5G + CN/AN/AN/A
SEYG−4.755.5−37.6G + CSEM000639851.62−1.0
CIBG−6.5106.8169.1G + CN/AN/AN/A
DGAR−7.372.4−64.9G + CN/AN/AN/A
COCO−12.296.8−35.3G + CCKM000969960.10−0.2
KAT1−14.4132.2184.3G + CN/AN/AN/A
PTVL−17.7168.386.4G + CN/AN/AN/A
VACS−20.357.5421.2G + CN/AN/AN/A
MCHL−26.4148.1534.6G + CN/AN/AN/A
YARR−29.0115.3241.4G + CASM0009440368.58229.45
MOBS−37.8145.040.6G + CN/AN/AN/A
Table 7. Comparison between the ZTD derived with PPP-B2b/CNES corrections and the GBM/IGS final orbit/clock products (unit: mm).
Table 7. Comparison between the ZTD derived with PPP-B2b/CNES corrections and the GBM/IGS final orbit/clock products (unit: mm).
SolutionsLatitude RangeIGS Results as ReferenceGBM Results as Reference
RMSEBiasRMSEBias
CNES30~48° N10.0−1.38.0−0.4
0~30° N11.20.18.0−0.4
0~38° S10.3−0.97.90.3
Mean10.4−0.88.0−0.1
PPP-B2b30~48° N16.21.515.72.7
0~30° N25.72.523.92.6
0~38° S24.8−1.025.01.1
Mean22.20.721.72.1
Table 8. Comparison between ZTD/PWV derived from GNSS and ERA5 (unit: mm).
Table 8. Comparison between ZTD/PWV derived from GNSS and ERA5 (unit: mm).
SolutionsLatitude RangeZTDPWV
RMSEBiasRMSEBias
IGS30~48° N18.3−3.02.9−0.5
0~30° N22.40.83.60.1
0~38° S16.4−0.62.7−0.1
Mean19.0−0.93.1−0.1
GBM30~48° N15.7−3.52.5−0.6
0~30° N21.2−0.93.4−0.3
0~38° S16.8−1.02.7−0.3
Mean18.4−1.73.0−0.4
CNES30~48° N17.8−4.12.8−0.7
0~30° N22.3−1.43.6−0.4
0~38° S17.3−0.72.8−0.2
Mean19.6−2.03.2−0.4
PPP-B2b30~48° N20.9−0.73.2−0.2
0~30° N31.21.35.00.1
0~38° S29.90.94.80.0
Mean27.80.74.40.0
Table 9. Comparison between the ZTD/PWV derived from GNSS and radiosonde (unit: mm).
Table 9. Comparison between the ZTD/PWV derived from GNSS and radiosonde (unit: mm).
SolutionsLatitude RangeZTDPWV
RMSBiasRMSBias
IGS30~48° N12.72.32.1−0.1
0~30° N15.3−1.42.5−0.5
0~38° S11.6−0.92.2−0.8
Mean13.10.22.3−0.4
GBM30~48° N10.2−1.71.9−0.8
0~30° N12.2−3.42.2−1.0
0~38° S13.1−5.22.4−1.4
Mean11.7−3.22.1−1.0
CNES30~48° N13.5−1.92.4−0.9
0~30° N12.9−3.92.4−1.1
0~38° S13.9−6.42.6−1.7
Mean13.4−3.82.4−1.2
PPP-B2b30~48° N17.0−0.42.8−0.9
0~30° N25.14.64.1−1.3
0~38° S26.15.04.4−0.1
Mean22.42.93.7−0.8
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Wang, X.; Chen, Y.; Zhang, J.; Qiu, C.; Zhou, K.; Li, H.; Huang, Q. Assessment of BDS-3 PPP-B2b Service and Its Applications for the Determination of Precipitable Water Vapour. Atmosphere 2024, 15, 1048. https://doi.org/10.3390/atmos15091048

AMA Style

Wang X, Chen Y, Zhang J, Qiu C, Zhou K, Li H, Huang Q. Assessment of BDS-3 PPP-B2b Service and Its Applications for the Determination of Precipitable Water Vapour. Atmosphere. 2024; 15(9):1048. https://doi.org/10.3390/atmos15091048

Chicago/Turabian Style

Wang, Xiaoming, Yufei Chen, Jinglei Zhang, Cong Qiu, Kai Zhou, Haobo Li, and Qiuying Huang. 2024. "Assessment of BDS-3 PPP-B2b Service and Its Applications for the Determination of Precipitable Water Vapour" Atmosphere 15, no. 9: 1048. https://doi.org/10.3390/atmos15091048

APA Style

Wang, X., Chen, Y., Zhang, J., Qiu, C., Zhou, K., Li, H., & Huang, Q. (2024). Assessment of BDS-3 PPP-B2b Service and Its Applications for the Determination of Precipitable Water Vapour. Atmosphere, 15(9), 1048. https://doi.org/10.3390/atmos15091048

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop