# A New Method of GPS Water Vapor Tomography for Maximizing the Use of Signal Rays  
[PERSON]  
1 School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China; [EMAIL_ADDRESS] (F.Y.); [EMAIL_ADDRESS] (Y.Z.)  
[PERSON]  
1 School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China; [EMAIL_ADDRESS] (F.Y.); [EMAIL_ADDRESS] (Y.Z.)  
[PERSON]  
1 School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China; [EMAIL_ADDRESS] (F.Y.); [EMAIL_ADDRESS] (Y.Z.)  
[PERSON]  
1 School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China; [EMAIL_ADDRESS] (F.Y.); [EMAIL_ADDRESS] (Y.Z.)  
[PERSON]  
4 Guangxi Key Laboratory for Spatial Information and Geomatics, Guilin University of Technology, Guilin 541004, China; [EMAIL_ADDRESS].  
and natural hazard reduction [3; 4; 5; 6; 7; 8; 9]. Compared with traditional water vapor acquisition methods, such as a radiosonde and microwave radiometer, global positioning system (GPS) tomography has the advantage of a high temporal and spatial resolution, and low construction and maintenance costs [10; 11; 12; 13; 14].  
The concept of water vapor tomography, which refers to the usage of GPS signals as scanning rays in the tomographic grid, was first proposed by [PERSON] et al. and realized by [PERSON] et al. [15; 16]. In GPS water vapor tomography, the research area is covered by ground GPS receivers and discretized into several voxels [17]. The integral equations established by the signal observations are utilized to calculate the wet refractivity or water vapor density within each voxel [18].  
Signal rays penetrate not only from the top boundary of the area, but also from the side face due to the specific distribution of the satellite constellation and receivers and the specific choice of the tomographic area. Traditional methods, which use only the first-mentioned signal rays above, reduce the utilization of GPS observation data and the accuracy of the tomographic result, especially at the bottom of the area. To solve this problem, [PERSON] and [PERSON] estimated the outer part of the signal rays using the UNB3m model based on a ray-tracing method [17], [PERSON] et al. used European center for medium-range weather forecasts (ECMWF) data to calculate the SWV outside the research area [19], and [PERSON] and [PERSON] applied the numerical weather prediction (NWP) profile data to estimate the slant wet delay (SWD) outside the modeling area [20]. [PERSON] et al. proposed a geometric linear method using an empirically exponential negative function to increase the utilization of signal rays [21], whereas [PERSON] et al. introduced a unit scale factor model and reconstructed a sophisticated model for considering the signal rays penetrating from the side face of the study area [22; 23].  
In the above-mentioned methods, their focus is to calculate SWV values of the signal ray generated outside the tomographic grid, which needs external data or models, such as ECMWF, NWP, and UNB3m. This work proposes a new method that does not feature external data and considers and models the troposphere outside the research area as unknown parameters for tomographic modeling to improve the utilization of existing GPS observations and increase the number of voxels crossed by satellite signals. Additionally, contrast methods were conducted to verify the performance of the proposed method.