## 1 Introduction  
Global Navigation Satellite System (GNSS) technology has become an efficient atmospheric water vapor detection tool for studying rainstorm events and the El Nino-Southern Oscillation (ENSO) phenomenon [1; 2; 3; 4]. Highly accurate integrated water vapor (IWV) can be inverted through GNSS observation signals, which has been used for global meteorological assessment and analysis [5; 6]. Furthermore, to obtain water vapor with a high spatial resolution, medical chromatography has been introduced to retrieve the three-dimensional water vapor fields over a study area [7]. Due to several significant advantages, including observation data accessibility, all-weather availability, wide-coverage,and a high spatiotemporal resolution, GNSS tomography has been favored by many researchers and has developed rapidly over the past 20 years [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. The GNSS tomographic model based on voxel discretization (i.e., the survey area is divided into many cubes) is the most mature and primary tomographic model, requiring a dense network of GNSS stations with a homogeneous spatial distribution. However, due to the GNSS acquisition geometry and satellite constellations, satellite signals resemble an inverted cone, and many voxels are not intersected by any GNSS signals, especially for voxels closer to the horizon [19; 20]. Several methods have been developed to solve this problem. [PERSON] et al. [7] added the spatial positional relationship between the voxels as constraints to the tomographic observation system, and the horizontal constraint was optimized by [PERSON] et al. [21] with a Gaussian weighted function. Alternatively, the water vapor information (e.g., wet refractivity (WR) or water vapor density (WVD) profile) from radiosonde data and ground meteorological data was considered a priori constraint for improving the tomographic equations [9; 22]. With the rapid development of the BeiDou Navigation Satellite System (BDS) and GLObal NAvigation Satellite System (GLONASS), a new tomography method based on multi-GNSS observation signals has been proposed [23; 24; 25]. The multi-GNSS observations optimize the geometric distribution of rays and reduce the number of empty voxels in the tomography model, which greatly improves the performance of tomography solutions. In addition to GNSS data, remote sensing data are also used to help retrieve the three-dimensional water vapor field. The studies of [PERSON] et al. [13], [PERSON] et al. [15], and [PERSON] et al. [26] combined GNSS data and Interferometric Synthetic Aperture Radar (InSAR) data as input observation information for the tomographic system, which avoids the issue of an overabundance of empty voxels. The wet refractivity profiles from the Atmospheric Infrared Sounder (AIRS) were introduced into the tomographic model as an initial condition in the work of [PERSON] et al. [16]. However, only GNSS signals passing from the top boundary were selected as effective rays for the tomography system in the foregoing studies. A number of rays penetrating from the side of the tomography area were eliminated, which has attracted the attention of researchers. The main challenge for side signals is the estimation of the sectional slant wet delay (SWD) of inside signals. [PERSON] and [PERSON] [14] first introduced a scale factor model to determine the water vapor content of inside signals. Compared with the radiosonde data, the average root mean square error (RMSE) of tomography solutions decreased from 1.60 g/m\({}^{3}\) in the traditional method to 1.23 g/m\({}^{3}\) in the optimized approach. Accordingly, [PERSON] et al. [27] proposed an analogous truncation factor model to calculate the sectional SWD of side rays for GNSS stations located outside of the research region, which improved the mean RMSE of results from 1.44 to 1.17 g/m\({}^{3}\). A two-step method was performed in both works. First, they calculated the water vapor content of GNSS signals using the initial water vapor field retrieved by the traditional tomography algorithm.