## 2 GNSS-Derived Height Determination  
GNSS-derived height determination is a modern surveying technique that determines the elevation as the difference between the ellipsoidal height from GNSS surveying and the geoidal height from the local geoid model. For reference, the gravimetric geoid is determined by referring to the global mean sea level, so that the hybrid geoid, which is adjusted to be identical to the local vertical datum by fitting the gravimetric geoid to the local GNSS/Leveling data, is applied. However, the modeled geoid surface is not identical to the true geoid surface. Thus, the elevation, computed by directly subtracting the geoidal height from the ellipsoidal height determined by GNSS surveying, does not coincide with the elevation as determined by spirit leveling. Therefore, removing the bias between the geoid surfaces is key to determining the GNSS-derived elevation. However, it is impossible to determine the bias between these geoid surfaces. Thus, it is assumed that the geoid surface is the same, and the adjusted ellipsoidal height is calculated as the sum of the official elevation determined by leveling and geoidal height. This value is used instead of the ellipsoidal height from GNSS surveying to remove the bias. A more detailed description of the procedure for determining GNSS-derived elevation is provided in Figure 1. Here, P is a fixed station where the precise position and height (ellipsoidal height and elevation) are already known, and A is an unknown station. First, the adjusted ellipsoidal height at P is calculated as a sum of the elevation determined by leveling and geoidal height, as shown in the following equation. \[h_{P,Adjusted}=H_{P}+N_{P,Geoid\ model} \tag{1}\]where \(h_{P,Adjusted}\) and \(H_{P}\) are the adjusted ellipsoidal height and official elevation, respectively, for \(P\). \(N_{P,Goid\ model}\) is the geoidal height calculated from the local geoid model at \(P\). Second, the ellipsoidal height at \(A\) is determined via GNSS post-processing. As the adjusted ellipsoidal height is used at \(P\), the adjusted ellipsoidal height is computed at \(A\). During this processing, in principle, the latitude, longitude, and adjusted ellipsoidal height of the fixed station should be fixed. However, only the adjusted ellipsoidal height is fixed when the latitude and longitude are fixed at other fixed stations. Finally, the elevation at \(A\) is calculated by subtracting the geoidal height from the ellipsoidal height determined in step 2, following the equation below:  
\[H_{A}=h_{A,Adjusted}-N_{A,Goid\ model} \tag{2}\]  
where \(H_{A}\) is the GNSS-derived elevation, \(h_{A,Adjusted}\) is the adjusted ellipsoidal height determined by GNSS processing, and \(N_{A,Goid\ model}\) is the geoidal height calculated from the local geoid model at \(A\). The guidelines for GNSS-derived height determination in Korea was introduced in 2014, following the above principle [12; 13]. This approach assumes that the static differential GNSS surveying is conducted to obtain GNSS data. In detail, it is applicable when the target precision of the GNSS-derived elevation is 3 cm and 5 cm, respectively. The required observation duration differs according to the desired target precision. To obtain a target precision of 3 cm, it is necessary to survey for 4 h/day for two days. The observation time for each day should be set considering satellite geometry. Only 2 h of GNSS surveying is sufficient for a target precision of 5 cm, however. The logging time intervals shorter than 30 s and 15 s, respectively, is necessary. To guarantee the stability of the geometric distribution, all unknown stations should be surrounded by at least three fixed stations. This is a common approach in countries applying the GNSS-derived height determination technique. However, it is not possible to apply this method in all scenarios. In the case of coastal regions or islands, control stations are not always located in the required locations, and there are fewer available stations than requirements.