# Node-Based Optimization of GNSS Tomography with a Minimum Bounding Box Algorithm
## 1 Introduction  
Water vapor plays an important role in the Earth's weather and climate systems, the water cycle and the regulation of air temperature. Since the near-Earth surface includes nearly all of the atmosphere's water vapor, remote sensing techniques focus on the area of the lowest layer of Earth's atmosphere, which is the troposphere. Global Navigation Satellite Systems (GNSS) tomography is one of the primary techniques for determining the three-dimensional distribution of water vapor in the tomographic region. The GNSS tomography has proved its capacity to utilize satellite constellation and ground observation stations (i.e., GNSS networks) to build the water vapor field and the meteorological applications. The wet delay of the GNSS signals, caused by atmospheric water vapor, is used to estimate the amount of water vapor between a GNSS satellite and each GNSS station. The total integrated information, which includes spatial information about the water vapor, can be combinedinto a spatially resolved field through tomographic reconstruction techniques. Due to its ability to provide all-weather, high-efficiency, high-resolution vertical and horizontal measurements of water vapor, the GNSS tomography has potential value for severe weather study and short-term weather forecasting in the middle and small scale areas. The size of the areas used in this process depends on the distribution of GNSS signals between the ground-based GNSS network and the GNSS satellite constellation. Today, most tomographic regions used in scientific research are cuboid-shaped in their region. For example, [PERSON] et al. [1] use the Kilauea GNSS network to cover a region of \(20\times 20\) km\({}^{2}\) in the horizontal direction and \(15\) km in altitude. Other examples of the approximate tomographic region dimensions from current research are shown in Table 1. Although the cuboid is the most commonly used tomographic region, there are still some approaches to extend or refine the cuboid-shaped region based on the distribution of the GNSS signals. For example, [PERSON] et al. [2] propose the double models (i.e., inner model and outer model) for the GNSS tomography to extend the tomographic region and increase the information for estimating the results. [PERSON] and [PERSON] [3] compress the height of the tomographic region from \(15\) km to \(8.5\) km to introduce more GNSS signals and then move the tomographic region to the optimal location where the number of the voxels crossed by signals reaches its maximum. [PERSON] et al. [4] propose an adaptive node parameterization approach to adjust the tomographic region at each tomographic epoch dynamically. The methods of using the signals penetrating from the side face of the tomography area [5; 6; 7] and the data of GNSS observations outside the study area are also proposed. [PERSON] et al. [8] optimize the dynamic scope of the tomographic area and propose a height factor model to utilize GNSS rays passing from the side boundary [9]. The tomographic region usually depends on the spatial distribution of the GNSS signal from the ground-based GNSS receivers. However, the most common methods used to determine the dimensions of the tomographic model only consider the GNSS signals' distribution through the top boundary of the model. This is based on the assumption that, for the selected model, any GNSS signals that pierce the top of the model must also be distributed through the lower levels of the model. This assumption is based on the inverted cone-shaped region defined by the GNSS signal distribution from the Earth's surface to the GNSS satellites. The selected rectangular tomographic region is then chosen to include the top-level GNSS signals approximately. This predetermined approximate tomographic region causes some problems. First, the box-shaped region includes several large empty spaces, which have no GNSS signals passing through them.