## 3 Precision Analysis of GNSS-Derived elevations
### Possibility of Substituting GNSS-Derived Height Determination for Sea-Crossing Leveling  
GNSS-derived height determination is a useful surveying technique to connect islands, which refers to a local vertical datum, to inland unified vertical datum. The unification of various vertical datums is required in the field of surveying or construction, for example, when constructing bridges, to ensure safety. Furthermore, GNSS-derived height determination is meaningful because it could help to realize global unified vertical datum, which would be especially useful for monitoring, warning, and restoration of disasters across countries [24; 25; 26]. Before the introduction of GNSS and the construction of the precision geoid model, the elevations of stations located in islands were determined by sea-crossing leveling. The details of the surveying techniques and instruments used differ depending on the observation distance between the control and unknown stations, but the principle remains unchanged: both the distance and angle are measured and then converted to vertical elevation. When the leveling network is disconnected due to rivers or seas, the distance between the control and unknown stations generally exceeds a few kilometers. Thus, surveying instruments are set to both sides where the control and unknown stations are located and observations are collected at the same time to minimize errors (i.e., collimation and atmospheric refraction errors). In addition, the required number of observation repetitions increases as the distance between stations increases. For reference, Korean surveying guidelines state that observations should be performed for three days with a total of 280 repetitions at a distance of 3 km [27]. In this study, sea-crossing leveling was conducted in two regions to check the possibility of substituting GNSS-derived height determination for sea-cross leveling. USS04B-USS13B, located in region one, and TBM1-TBM2, located in region four, were the selected surveying sections. The distances for both sections are approximately 3.33 km. In the case of USS04B-USS13B, sea-crossing leveling was conducted following Korean surveying guidelines; 280 repetitions (140 repetitions per side) of observation data were collected for seven days in 2016 [21]. When analyzing the dataset, it was found that 80 repetitions per side were sufficient to determine the elevation difference of the section [21]. Thus, for section TBM1-TBM2, 120 repetitions per side were observed for six days. The final elevation differences of each section were then determined by averaging all observations [23]. Table 4 shows the elevation differences determined by sea-crossing leveling, GNSS-derived height determination, and spirit leveling. In the case of GNSS-derived height determination and spirit leveling, the elevation differences were computed based on the elevation of each station. The GNSS-derived elevation in each case refers to the elevation obtained from the 3 cm target precision. The elevation difference for section USSS04B-USS13B was determined to be 0.3156 m; differences of 0.3201 and 0.3084 m were calculated for sea-crossing leveling and GNSS-derived height determination, respectively. Compared to the elevation difference calculated from spirit leveling, both surveying techniques showed a difference of less than 1 cm. When surveying is performed again, the elevation  
difference between stations should not exceed 15 mm \(\sqrt{S}\) (where \(S\) is the distance in km) according to the Korean surveying guidelines [27]. This means that the results from sea-crossing leveling and GNSS-derived height determination should coincide with a level of approximately 2.7 cm; in both cases, these techniques met this limit. In the case of section TBM1-TBM2, the sea-crossing leveling and GNSS-derived elevations were both smaller than the above limit. However, GNSS-derived elevation did not exceed the limit of surveying and showed better consistency than sea-crossing at the approximately 1 cm level.