## 3 Result and Discussion
### Optimal Number of Rain Gauge Stations  
For comparing the six methods, the errors generated by predicting the average daily precipitation of the unselected stations based on the selected stations were evaluated through MAE, RMSE, bias, and Corr (Figure 5). Figure 4: The performances of all combination gauge networks. Figure 5: Result of MAE, RMSE, bias, and correlation coefficient (Corr) variation according to the numbers of stations for the rain gauge network calculated by different methods. Conditional entropy methods (methods A, B, D, and E) generally exhibited similar results. For joint entropy methods (methods C and F), the results were similar until the number of stations was three; different results were observed for a higher number of stations. The conditional entropy methods exhibited better results than joint entropy because MAE and RMSE for these were lower, and Corr was higher. With regard to the bias, methods A and B showed a tendency to predict lower values than the observed values, while methods C, D, E, and F predicted higher values. For the RMSE, methods A and D exhibited similar results; however, they started to show different results when the number of stations reached nine. The RMSE of method A became lower and exhibited excellent performance, with Pohang being the location of the added station. For method D, Pohang was the last station added. This was because it exhibited the highest daily maximum precipitation of 516.4 mm based on the research data mentioned above. In method B, the rain gauge stations installed in coastal areas were first selected. As for the RMSE values of methods A and B, method A exhibited better results when the number of stations was less than six, and method B when the number of stations was six or more. In other words, methods A and B exhibited relatively good performance. Table 5 and Figure 6 show the RMSE results for determining the optimal number of stations. S shows the actually decreasing amount under the assumption that RMSE decreases at equal intervals as the number of rain gauge stations increases. In other words, it is meaningful to find the values of S higher than one and higher than the average value. For method A, the numbers of stations where S was higher than one were 2, 3, 9, and 10. The number of stations that exhibited the highest value was two (4.436), followed by nine (1.334), three (1.173), and 10 (1.162). For method B, the numbers of stations where S was higher than one were 2, 4, 6, and 9. The number of stations that showed the highest value was two (4.119), followed by six (1.912), four (1.300), and nine (1.106). R is the predictive power of i rain gauge stations by comparing the total RMSE reduction with the RMSE reduction when i stations are used. For method A, R was 83.45% and represented more than 80% when the number of stations was nine or higher. For method B, R was 81.26% and represented more than 80% when the number of stations was six or higher. Subsequently, R did not significantly increase \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Method A**} & \multicolumn{2}{c}{**Method B**} \\ \hline
**No.** & **S** & **R** & **No.** & **S** & **R** \\ \hline
2 & 4.436 & 49.28\% & 2 & 4.119 & 45.77\% \\
3 & 1.173 & 62.32\% & 3 & 0.652 & 53.02\% \\
4 & 0.337 & 66.05\% & 4 & 1.300 & 67.46\% \\
5 & 0.220 & 68.50\% & 5 & \(-\)0.670 & 60.01\% \\
6 & 0.386 & 72.79\% & 6 & 1.912 & 81.26\% \\
7 & \(-\)0.613 & 65.98\% & 7 & 0.627 & 88.23\% \\
8 & 0.238 & 68.62\% & 8 & \(-\)0.206 & 85.94\% \\
9 & 1.334 & 83.45\% & 9 & 1.106 & 98.23\% \\
10 & 1.162 & 96.37\% & 10 & 0.159 & 100.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: RMSE result to determine the optimal number of stations for the rain gauge network. Figure 6: Optimal number of rain gauge networks using RMSE: (**a**) reduction of RMSE (S); (**b**) ratio of RMSE (R). even with an increase in the number of stations. Hence, six stations were judged to be appropriate.