## 4 Conclusions  
In this study, the applicability of GNSS-derived height determination for positioning objects located on islands or coastal areas was verified by comparing the GNSS-derived elevations of 19 unknown stations to elevations obtained from spirit leveling. In particular, the basic condition that unknown points should be surrounded by at least three control points in the GNSS-derived height determination could not be easily fulfilled in this coastal and island setting, so the stability obtained when fixing only two fixed points was checked.  
When GNSS-derived elevations on 19 unknown points were determined based on surveying for 4 h/day for two days, all points showed differences smaller than 3 cm compared to the spirit leveling results. Though the maximum difference was 2.97 cm, 18 stations (94.73%) had differences smaller than 2 cm. Thus, the target precision of 3 cm is expected to be fully achievable. When GNSS surveying was conducted for the GNSS-derived height determination, all unknown points met the target precision of 5 cm, and the maximum difference was calculated to be 3.88 cm. Fourteen (73.68%) and 17 (89.47%) stations showed differences of less than 2 cm and 3 cm, respectively. As shown in the test  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Elevation Difference of the Section**} & \multicolumn{3}{c}{**Difference w.r.t. Spirit Leveling**} \\ \cline{2-6}
**unit: m** & **Sea-Crossing Leveling** & **GNSS-Derived** & **Spirit Leveling** & **Sea-Crossing Leveling** & **GNSS-Derived** \\  & **(A)** & **(B)** & **(C)** & **(D = A – C)** & **(E = B – C)** \\ \hline USS04B–USS13B & 0.3201 & 0.3084 & 0.3156 & 0.0045 & \(-\)0.0072 \\ TBM1–TBM2 & \(-\)14.4224 & \(-\)14.412 & \(-\)14.4104 & \(-\)0.012 & \(-\)0.0016 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of elevation differences at two surveying sections among sea-crossing leveling, GNSS-derived height determination, and spirit leveling.  
results, the target precision in GNSS-derived height determination was efficiently met by fixing only two control points. Thus, GNSS-derived elevation can be broadly applied in the surveying field.  
GNSS-derived height determination is an efficient way to connect different vertical datums between inland and island areas, and replace the traditional method of sea-crossing leveling. Here, the possibility of replacing sea-crossing leveling with GNSS-derived height determination was checked in terms of precision and time effectiveness. When applied to two test sections, both surveying methods showed differences smaller than 2.7 cm compared to spirit leveling (this limit was calculated based on surveying guidelines). Furthermore, for one of these sections, the GNSS-derived height determination showed a much smaller difference. The surveying time for GNSS-derived height determination is also shorter than that required for sea-crossing, and the former method also avoids the issue of environmental influences, such as sea fog. However, it should be mentioned that the geoid model should be further improved regarding its relatively low precision in coastal and island areas.  
Conceptualization and methodology, J.L. and J.H.K.; software, J.L. and Y.L.; formal analysis and investigation, J.L., J.H.K. and Y.L.; writing--original draft preparation, J.L. and Y.L.; writing--review and editing, J.L. and J.H.K.; supervision, J.H.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Restrictions apply to the availability of these data. Data was obtained from NGII and are available on request from the NGII.  
The fundamental surveying data including GNSS, spirit leveling as well as sea-crossing leveling for the analysis were obtained by the NGII research project performed in 2016, 2018 and 2020 [21; 22; 23].  
The authors declare no conflict of interest.