## 3 Precision Analysis of GNSS-Derived elevations
### Precision Analysis  
For the post-processing of GNSS data, commercial software is allowed in Korea. Thus, Leica Geo Office (LGO) version 8.2 was applied for the processing. The precision of the GNSS-derived elevation at each unknown station was evaluated through comparison with elevation determined by spirit leveling. In the case of regions three and four, the unknown stations were located on islands, and the official elevations given by NGII were computed by referring to the locally determined vertical datum. However, a bridge connecting inland and islands was recently constructed. Thus, the spirit leveling surveying was conducted again, and elevations were re-calculated by fixing them with nearby benchmarks or UCPs; these corrected elevations were applied in this study. The elevations of the unknown stations located in region three were calculated by adding leveling observations to the elevations of the fixed station, U1167. For the stations located in region four, U0531 and TBM were calculated by fixing them to the benchmark 37-25-00. Furthermore, UGN58 and TBM2 were calculated by fixing them to 12-00-30-12. For other unknown stations in regions one, two, and five, the elevations given by NGII were already determined by spirit leveling, so the official elevations were applied without any re-calculations. As all of the elevations of the unknown stations were determined based on spirit leveling (including the re-calculations in regions three and four), the reference elevations are referred to herein as leveling-based elevations regarding precision analysis. As mentioned before, regardless of whether the official values given by NGII or the re-calculated ones were applied, all elevations applied to references values mean normal orthometric heights because real gravity values were not considered. Figure 3 and Table 3 show the differences between GNSS-derived elevations and those obtained from spirit leveling for the 19 unknown stations located in the five test regions for target precisions of 3 and 5 cm. As shown in Figure 3 and Table 3, all GNSS-derived elevations showed differences smaller than 3 cm compared to spirit leveling-based elevations (when GNSS surveying was conducted for 4 h/day for two days). The difference was smaller than 1 cm at ten stations (52.63%), and was smaller than 2 cm at eighteen stations (94.73%). Thus, the mean absolute difference was calculated to be approximately 1 cm. The maximum difference (2.79 cm) was found at Station UHA89, located in region five. Even this did not exceed the target precision of 3 cm, however. Considering that UHA89 had a relatively long baseline compared to the other unknown stations, the GNSS-derived elevation can be said to have sufficiently met the target precision when fixing only two control stations in coastal or island areas. \begin{table}
\begin{tabular}{c c c} \hline Region 1 & Fixed stations & U0354, U0356 \\  & Unknown stations & USS04, USS04B, USS13, USS13B \\ \hline Region 2 & Fixed stations & U0126, U0285 \\  & Unknown stations & UDB05, UDB26, UDB58 \\ \hline Region 3 & Fixed stations & U1140, 14-04-24-06 \\  & Unknown stations & USA03, USA01, U1167, U1168 \\ \hline Region 4 & Fixed stations & UBR22, UBR71 \\  & Unknown stations & U0531, UGN58, TBM1, TBM2 \\ \hline Region 5 & Fixed stations & U0985, U1065 \\  & Unknown stations & UMS76, UMS88, UMS99, UHA89 \\ \hline \end{tabular}
\end{table} 
Table 2: List of surveying stations in the test regions. GNSS-derived elevations computed based on two hours of GNSS data revealed that seven stations (36.84%) showed a difference of less than 1 cm compared to the elevations from spirit leveling. Fourteen (73.68%) and seventeen (89.47%) stations exhibited differences smaller than 2 and 3 cm, respectively. The mean absolute difference was calculated to be approximately 1.5 cm, meaning that elevations with 5 cm precision could be determined based on GNSS and the local geoid model. The maximum difference (3.88 cm) occurred at station UHA89, which also exhibited the largest difference under the 3 cm target precision.