## 3 Result and Discussion  
### Rain Gauge Network Using Entropy  
The precipitation data were converted to discrete spaces to calculate entropy. Figure 3 compares the entropies for class intervals of 100, 200, 300, and 400. Figure 2(a) shows the entropy of the observed precipitation, and Figure 2(b) shows the entropy of the prediction error. For both cases, the amount of entropy information increased as the class interval increased; however, the pattern of the maximum information amount according to the number of stations was the same. This study was conducted for a fixed class interval of 200.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Locations** & **Period** & **Longitude** & **Latitude** & **Daily Maximum Precipitation** & **Average Annual Precipitation** \\ \hline
1 & UJin & & 36.992 & 129.413 & 279.0 & 1171.1 \\
2 & Andong & & 36.573 & 128.707 & 170.7 & 1047.1 \\
3 & Pohang & & 36.032 & 129.380 & 516.4 & 1194.5 \\
4 & Daegu & & 35.878 & 128.653 & 225.8 & 1077.6 \\
5 & Bonghwa & & 36.944 & 128.914 & 250.0 & 1190.2 \\
6 & Yeonglu & 1988–2016 & 36.872 & 128.517 & 259.5 & 1328.7 \\
7 & Mungyeong & & 36.627 & 128.148 & 161.0 & 1281.5 \\
8 & Yeongdeek & & 36.533 & 129.409 & 296.0 & 1085.2 \\
9 & Ulesong & & 36.356 & 128.688 & 215.5 & 1018.2 \\
10 & Gumi & & 36.130 & 128.320 & 221.0 & 1091.9 \\
11 & Yeongcheon & & 35.977 & 128.951 & 159.0 & 1081.7 \\ \hline \end{tabular}
\end{table}
Table 1: Summary of ASOS.  
Figure 2: Location of rain gauge station in Daegu and Gyeongbuk (ASOS).  
To find the optimal rain gauge stations of the study area using entropy, the first optimal rain gauge station was selected using marginal entropy. First, entropy was calculated using the basic \"emp\" method. The rain gauge station installed in Mungyeong was selected as the first station, as its marginal entropy (2.441) was higher than those of other regions. Daegu (2.766) was selected based on the marginal entropy that used the prediction error.  
Two or more optimal rain gauge stations can be determined using conditional and joint entropies. As conditional entropy (methods A, B, D, and E) sequentially determines the optimal rain gauge stations, it takes a relatively short time compared with the joint entropy methods. Joint entropy (methods C and F) calculates the entropies of all combinations and selects those with the maximum values. Therefore, they require relatively more computing time than conditional entropy. In addition, the combinations of rain gauge stations were selected irregularly. In contrast, the joint entropy of the prediction error that considered the spatiality of stations sequentially selected the optimal rain gauge stations in a manner similar to conditional entropy (Table 2).  
The \"mm\" and \"shrink\" methods showed the same results in all cases as the \"emp\" method (Tables A1 and A2). The calculated entropy values were different, but the selected rainfall network was the same. However, there was a slight difference in the case of the \"sg\" method (Table A3). In the process of selecting two rain gauge stations with conditional entropy using prediction error (method E), the rain gauge network was selected differently. As a result, the estimator differed in terms of the estimation method, but there was no significant difference noted in this study.