## 3 Results and Discussions
Moreover, more than 90% of the 1182 UCPs showed an agreement between the EIGEN-6C4- and GNSS/leveling-derived geoid heights and between the EGM2008- and GNSS/leveling-derived geoid heights that is better than 30 cm as compared with 84.9% for the GECO GGM. As a result, we concluded that the EGM2008 model is the more suitable GGM from among the three GGMs for determining a suitable gravimetric geoid model for South Korea. In addition, for the assessment of the geoid heights of the KNGeoid models, the three KNGeoid models were interpolated into the GNSS/leveling data locations of the 1182 UCPs, which are shown as red dots in Figure 1. Figure 6 shows the \(1^{\prime}\) gridded residual surface maps between the GNSS/leveling geoid heights \(\left(N_{GSNS/leveling}\right)\) of the 1182 UCPs and the geoid heights \(\left(N_{KNGeoid}\right)\) derived from the three KNGeoid models (KNGeoid13, KNGeoid14, and KNGeoid18). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & \(\leq\)**0.05 m** & \(\leq\)**0.10 m** & \(\leq\)**0.20 m** & \(\leq\)**0.30 m** & \(\leq\)**0.40 m** & \(\leq\)**0.50 m** \\ \hline GECO & 71 (6.0\%) & 158 (13.4\%) & 587 (49.7\%) & 1003 (84.9\%) & 1142 (96.6\%) & 1173 (99.2\%) \\ EIGEN-6C4 & 25 (2.1\%) & 86 (7.3\%) & 673 (56.9\%) & 1108 (93.7\%) & 1150 (97.3\%) & 1168 (98.8\%) \\ EGM2008 & 40 (3.4\%) & 122 (10.3\%) & 733 (62.0\%) & 1086 (91.9\%) & 1152 (97.5\%) & 1172 (99.1\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Percentage of the 1182 UCPs whose absolute values of differences between the geoid heights derived from the GNSS/leveling and those derived from the three GGMs. Figure 5: Histograms of the differences between the geoid heights \(\left(N_{GSNS/leveling}\right)\) derived from GNSS/leveling on the 1182 UCPs and the geoid heights \(\left(N_{GGM}\right)\) derived from the three KNGeoid models. (**a**) GECO; (**b**) EIGEN-6C4; and (**c**) EGM2008. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Min.** & **Max.** & **Mean** & **Std. Dev.** & **RMSE** \\ \hline \(N_{GSNS/leveling}-N_{GECO}\) & \(-\)1.837 & 1.025 & \(-\)0.199 & 0.126 & 0.236 \\ \(N_{GSNS/leveling}-N_{EIGEN-6C4}\) & \(-\)1.817 & 1.010 & \(-\)0.191 & 0.112 & 0.221 \\ \(N_{GSNS/leveling}-N_{EGM2008}\) & \(-\)1.801 & 1.012 & \(-\)0.184 & 0.113 & 0.216 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics of the differences between the geoid heights \(\left(N_{GSNS/leveling}\right)\) derived from the GNSS/leveling on the 1182 UCPs and those \(\left(N_{GGM}\right)\) derived from the three GGMs (unit, m). The statistics of the differences between the geometric geoid heights derived from GNSS/leveling on the 1182 UCPs and the geoid heights derived from the three KNGeoid models are represented as shown in Table 5. The differences between the GNSS/leveling geoid heights and the KNGeoid18 geoid heights represent good agreement with the smallest RMSE (10.3 cm) in Table 5.  
Table 6 presents 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 KNGeoid models. From the histograms of the differences between the GNSS/leveling-derived geoid heights on the 1182 UCPs and the three KNGeoid model-derived geoid heights presented in Figure 7a-c, it is known that 88.6% of the absolute values of differences between the GNSS/leveling-derived geoid heights on the 1182 UCPs and the KNGeoid13-derived geoid heights were below 10.0 cm, whereas 91.3% and 93.7% of the differences between the GNSS/leveling-derived geoid heights on the 1182 UCPs and the KNGeoid14- and KNGeoid18-derived geoid heights, respectively, were less than 10.0 cm. On the basis of the small differences between the GNSS/leveling-derived geoid heights on the 1182 UCPs and the KNGeoid18 model-derived geoid heights, it was concluded that the most recently developed KNGeoid18 model is better than the KNGeoid13 and KNGeoid14 models as a gravimetric geoid model for South Korea.