## 1 Introduction  
The global navigation satellite system (GNSS) is one of the most commonly used techniques for determining the precise positions of various objects, including surveying control stations. Although GNSS generates a precise, three-dimensional (3D) position, the ellipsoidal height determined by GNSS constitutes the geometric distance between the ellipsoidal surface and the object, and does not refer to the vertical datum. Thus, spirit leveling has been continuously used to determine (orthometric) height so as to coincide with the local vertical datum in each case and to ensure precision, despite the widespread use of GNSS in the field of surveying. However, GNSS-derived height determination, which is a modern technique that calculates elevation as the difference between the ellipsoidal and geoidal heights, is now being used, following the development of a precise local geoid [1, 2, 3, 4, 5, 6]. To make it clear, the technique to calculate the elevation based on GNSS and the geoid model is called GNSS-derived height determination, and the calculation result is called elevations in this study. In particular, GNSS-derived height determination is more time- and cost-effective than spirit leveling, so many countries, such as the United States of America (U.S.A.), Australia, Japan, and Korea, draw surveying guidelines and apply them in the surveying field [7, 8, 9, 10]. In GNSS-derived height determination, at least three control stations with published official elevations must be located surrounding the unknown stations, and static GNSS surveying should be performed at the control and unknown stations simultaneously. The observation duration is different for each country, but more than 2 h and two days of surveying are generally used to minimize the error caused by satellite geometry. For reference, the target precision of the GNSS-derived elevation is approximately 2-5 cm, considering 1-3 cm levels of error in GNSS surveying and in the geoid model [7; 8; 9; 10]. In particular, many recent studies have focused on GNSS-derived height determination as an alternative way to unify the vertical datum between inland and island areas. In the case of Korea, control stations located inland were determined through spirit leveling by fixing the origin of the benchmark, which is connected to the Incheon mean sea level. On the other hand, the elevations of stations on the many islands located to the west, south, and east of the Korean peninsula are too far away to perform spirit leveling, so their elevations were determined by fixing the locally determined mean sea level [11]; this led to local biases in islands that are not connected to the mainland via bridges. Sea-crossing leveling was conducted to connect the vertical datum between inland and island areas, but this cannot be a fundamental solution because it is not applicable over long distances. However, GNSS-derived height determination could connect the vertical datum when the geoid is available, covering inland and island areas. Thus, GNSS-derived height determination can be said to be more useful in terms of unifying the vertical datum. For reference, gravity values were not available at control points when the elevations of the control points were determined. Thus, strictly speaking, elevation means normal orthometric heights in Korea. GNSS-derived height determination is considered an efficient way to determine elevations of stations located in the coastal and island areas and connect the separated vertical datum, but its precision has not been evaluated clearly. To evaluate the precision of the GNSS-derived elevations in coastal and island areas, here, GNSS surveying was conducted on control stations with elevations determined by spirit leveling and comparisons were made between the two methods.