## 3 Results and Discussions  
In this study, the geoid heights in South Korea were first calculated from the three KNGeoid models and three GGMs to evaluate the accuracy of the geoid models on the 1182 GNSS/leveling UCPs installed by NGII, as shown in Figure 1. Figures 2 and 3 show the 1' gridded geoid heights derived from the GGMs (maximum degree 2190) and from the KNGeoid models developed by NGII, respectively. The 1' gridded geoid height maps were computed using the \"surface\" routine, which is a continuous curvature surface gridding algorithm, of Generic Mapping Tools (GMT, [[http://gmt.soest.hawaii.edu](http://gmt.soest.hawaii.edu)]([http://gmt.soest.hawaii.edu](http://gmt.soest.hawaii.edu))) [25]. The geoid heights derived from the three GGMs ranged from 18.0 to 33.4 m, as shown in Figure 2. In Figure 3, the geoid heights derived from the three KNGeoid models are distributed between 17.8 and 33.3 m.  
The three GGMs were interpolated into the GNSS/leveling data locations of the 1182 UCPs, which are shown as red dots in Figure 1, to evaluate the accuracy of the geoid heights derived from the three GGMs. Figure 4 shows the 1' gridded residual surface maps between the geoid heights derived from  
Figure 2: The 1′ gridded geoid height (\(N_{GGM}\)) derived from the three GGMs (max. degree 2190). (a) GECO; (b) EIGEN-6C4; and (c) EGM2008. The attributes listed for this and subsequent maps include the amplitude range (AR = minimum and maximum values), amplitude mean (AM), and amplitude standard deviation (ASD). The red dots represent the locations of the 1182 GNSS/leveling UCPs. the GNSS/leveling on the 1182 UCPs and those derived from the three GGMs (GECO, EIGEN-6C4, and EGM2008). The statistics of the residual surface maps between the geoid heights \(\left(N_{GNSS/leveling}\right)\) derived from the GNSS/leveling on the 1182 UCPs and those \(\left(N_{GGM}\right)\) derived from the three GGMs, shown in Figure 4a-c, respectively, are summarized in Table 3. According to the summarized statistics in Table 3, the geoid heights derived from the three GGMs as compared with those derived from the GNSS/leveling on the 1182 UCPs installed along the western coastal areas of South Korea, shown in Figure 4a-c, respectively, had a maximum difference of \(-1.837\) m (\(126.425^{\circ}\) E, \(37.391^{\circ}\) N), in GECO. The RMSE of the residual surface maps between the geoid heights derived from the GNSS/leveling on the 1182 UCPs and those derived from EGM2008, shown in Table 3, is smaller than that of the residual surface maps between the geoid heights derived from the GNSS/leveling on the 1182 UCPs and those derived from GECO, and between the geoid heights derived from the GNSS/leveling on the 1182 UCPs and those derived from EIGEN-6C4. Figure 4: Residual surface maps between the GNSS/leveling-derived geoid heights \(\left(N_{GNSS/leveling}\right)\) on the 1182 UCPs and those \(\left(N_{GGM}\right)\) derived from the three GGMs. (**a**) GECO; (**b**) EIGEN-6C4; and (**c**) EGM2008. The red dots represent the locations of the 1182 GNSS/leveling UCPs. Figure 3: The \(1^{\prime}\) gridded geoid heights \(\left(N_{KNGoid}\right)\) derived from the three KNGeoid models developed by NGII. (**a**) KNGeoid13; (**b**) KNGeoid14; and (**c**) KNGeoid18. The red dots represent the locations of the 1182 GNSS/leveling UCPs. From the histograms of the differences between the GNSS/leveling-derived geoid heights on the 1182 UCPs and the three GGMs-derived geoid heights presented in Figure 5a-c, the percentage of the absolute values of differences between the GNSS/leveling geoid heights on the 1182 UCPs and the geoid heights derived from the three GGMs was calculated, as shown in Table 4. As can be seen in Table 4, the agreement between the geoid heights derived from the GNSS/leveling on the 1182 UCPs and the EGM2008-derived geoid heights was 62.0% when the absolute values of differences were 20 cm, whereas for the other GGMs, the consistency level was 49.7% and 56.9% for GECO and EIGEN-6C4, respectively.