# A Method to Improve the Distribution of Observations in GNSS Water Vapor Tomography
## 1 Introduction  
Water vapor accounts for a small percentage of the troposphere, but it is the most active meteorological element, and significantly impacts the atmosphere and plays a key role in various climates and a series of weather phenomena. Measuring and monitoring the water vapor contents and movements, and understanding the temporal-spatial change in water vapor, are important for meteorological research and applications such as precipitation forecasts and extreme weather warnings. The development of Global Navigation Satellite System (GNSS) reference station networks provides rich data sources of high spatiotemporal resolution to monitor water vapor. [PERSON] et al. [1] initially proposed the remote sensing of atmospheric water vapor using GNSS. To achieve spatiotemporal resolution of water vapor information in the research region, a tomographic technique has been widely applied in GNSS meteorology. This method is developed from the medical field [2] in which the density distribution of an object is obtained by X-ray projections. It has been applied to the research of geology [3], earthquakes [4], gas tracing [5], and ionosphere modeling [6]. Since theapplication of troposphere tomography in 4-D wet refractive index first realized by [PERSON] et al. [7], the development of GNSS water vapor tomography has advanced significantly. [PERSON] et al. [8] used a damped least squares method to reveal the spatial and temporal change of refractivity. [PERSON] et al. [9] investigated the impact of tomographic factors such as the number of GNSS stations, elevation cutoff angle, and type of GNSS through simulations. [PERSON] et al. [10] introduced the posterior variance component estimation method to determine the weights of the tomographic equation. [PERSON] and [PERSON] [11] used the Moore-Penrose pseudo-inverse of a variance-covariance matrix in a local tomography troposphere model over a mountainous area. [PERSON] [12] proposed an algebraic reconstruction technique for GNSS tomographic modeling. [PERSON] et al. [13] used a hybrid regularization technique to reconstruct profiles of water vapor without constraint equations. [PERSON] et al. [14] proposed an innovative node parameterization approach in water vapor tomography using a combination of three meshing techniques. The distribution of observations in the above mentioned tomographic approaches is relatively concentrated due to the special structures of GNSS satellite constellations and the unfavorable geometry of GNSS stations in the tomographic region, as well as the specific selection of tomography period (usually 30 min). Unfortunately, some voxels cannot be penetrated by sufficient signal rays [15; 16; 17]. To overcome the ill-posed issue, [PERSON] et al. [18] exploited Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) occultation data for water vapor tomography. [PERSON] et al. [19] introduced the water vapor information of Interferometric Synthetic Aperture Radar (InSAR) into GNSS troposphere tomography. [PERSON] et al. [20] improved the distribution of observations by assimilating the measurements of surface water vapor into GNSS tomography. [PERSON] and [PERSON] [21] assessed the performance of troposphere tomography using multi-source water vapor information, such as radiosonde, GPS, water vapor radiometer (WVR), and numerical weather predictions. Although the combination of various water vapor observation technologies can provide additional observation information, they are still hard to carry out in practice when the cost, spatiotemporal resolution, and other restrictions are considered. COSMIC occultation events occur only at specific times, and the return period of SAR satellites reaches several days, resulting in low temporal resolution of these techniques. The measurements of surface water vapor are unavailable in most tomographic experiments, given that many GNSS receiver stations are not equipped with meteorological equipment.