## 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, [PERSON] 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 InternationalGNSS 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 [PERSON] 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\({}^{\circ}\) E, 110.5\({}^{\circ}\) E, and 140\({}^{\circ}\) 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\({}^{\circ}\). 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, [PERSON] 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  
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\({}^{\circ}\) E, 110.5\({}^{\circ}\) E, and 140\({}^{\circ}\) E, respectively, and the lines represent their coverage at cut-off angles of (**a**) 3\({}^{\circ}\), (**b**) 5\({}^{\circ}\), (**c**) 7\({}^{\circ}\), and (**d**) 15\({}^{\circ}\).