## Appendix A
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Num.** & **Conditional Entropy (1)** & **Rank** & **Method A** & **Num.** & **Conditional Entropy (1)** & **Rank** & **Method D** \\ \hline
1 & 1.229 & 7 & 7 & 1 & 1.143 & 7(-) & 7 \\
2 & 0.806 & 3 & 7,11(1) & 2 & 0.897 & 38(-) & 7,1(1) \\
3 & 0.548 & 19 & 7,11(1) & 3 & 0.533 & 17 & 7,1(4) \\
4 & 0.379 & 64 & 7,11(1),5 & 4 & 0.432 & 114(-) & 7,14,4(6) \\
5 & 0.269 & 53(+) & 7,11(5),0(6) & 5 & 0.351 & 172(+) & 7,14,46,11(2) \\
6 & 0.218 & 261(-) & 7,11(5),10(6) & 6 & 0.270 & 216(-) & 7,14,6,11(2) \\
7 & 0.177 & 231(-) & 7,11(5),10(6),4 & 7 & 0.200 & 189(-) & 7,14,6,11,21(0) \\
8 & 0.138 & 9 & 7,11(1),5 & 1,15(6),4 & 8,0 & 0.170 & 132(-) & 7,14,6,11,21(0) \\
9 & 0.121 & 40(-) & 7,11(5),10(6),4 & 8,2(9) & 0 & 0.099 & 40(-) & 7,14,6,11,210,58(3) \\
10 & 0.075 & 11(-) & 7,11(5),10(6),4 & 8,2(9) & 10 & 0.082 & 2(+) & 7,14,6,11,210,58,3(9) \\
11 & 0.061 & 7,11(-) & 7,11(5),10(6),4 & 8,2(9),3 & 11 & 0.037 & 7,1,4,6,11,20,58,3(9) \\ Computing time: 0.53 s & & & & & & & \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c} \hline \hline
**Num.** & **Conditional Entropy (2)** & **Rank** & **Method B** & **Num.** & **Conditional Entropy (3)** & **Rank** & **Method E** \\ \hline
1 & 1.229 & 7 & 7 & 1 & 1.143 & 7(-) & 7 \\
2 & 0.469 & 54(-) & 6.7 & 2 & 0.309 & 54(-) & 6.7 \\
3 & 0.962 & 16(-) & 5,6,7 & 3 & 0.618 & 76(+) & 6,71,1 \\
4 & 1.531 & 330 & 25,6,7 & 4 & 1.071 & 96(+) & 16,71,1 \\
5 & 2.101 & 462(-) & 25,6,7,9 & 5 & 1.568 & 172(+) & 1,4,6,71,11 \\
6 & 2.744 & 462(-) & 25,6,7,9 & 1 & 2.073 & 204(+) & 1,4,6,71,11 \\
7 & 3.488 & 324 & 25,6,7,9,10,11 & 7 & 2.623 & 189 & 1,2,4,6,7,10,11 \\
8 & 4.515 & 162 & 24,55,7,9,10,11 & 8 & 3.141 & 30(+) & 1,23,4,6,7,10,11 \\
9 & 4.712 & 53 & 24,55,7,8,9,10,11 & 9 & 3.646 & 29(+) & 1,23,4,6,7,9,10,11 \\
10 & 5.336 & 11 & 12,45,6,7,8,9,10,11 & 10 & 4.154 & 6(+) & 1,23,4,5,6,7,9,10,11 \\
11 & 5.850 & 13,3,4,5,6,7,8,9,10,11 & 11 & 4.624 & 1,2,3,4,5,6,7,8,9,10,11 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c} \hline \hline
**Num.** & **F**onditional Entropy (2)** & **Rank** & **Method C** & **Num.** & **Joint Entropy** & **Rank** & **Method F** \\ \hline
1 & 1.229 & 7 & 7 & 1 & 1.143 & 7(-) & 7 \\
2 & 0.469 & 54(-) & 6.7 & 2 & 0.309 & 54(-) & 6.7 \\
3 & 0.962 & 16(-) & 5,6,7 & 3 & 0.618 & 76(+) & 6,71,1 \\
4 & 1.531 & 330 & 25,6,7 & 4 & 1.071 & 96(+) & 1,6,71,11 \\
5 & 2.101 & 462(-) & 25,6,7,9 & 5 & 1.568 & 172(+) & 1,4,6,7,11 \\
6 & 2.744 & 462(-) & 25,6,7,9 & 1 & 2.073 & 204(+) & 1,4,6,7,10,11 \\
7 & 3.488 & 324 & 25,6,7,9,10,11 & 7 & 2.623 & 189 & 1,2,4,6,7,10,11 \\
8 & 4.515 & 162 & 24,55,7,9,10,11 & 8 & 3.141 & 30(+) & 1,23,4,6,7,10,11 \\
9 & 4.712 & 53 & 24,55,7,8,9,10,11 & 9 & 3.646 & 29(+) & 1,23,4,6,7,9,10,11 \\
10 & 5.336 & 11 & 12,45,6,7,8,9,10,11 & 10 & 4.154 & 6(+) & 1,23,4,5,6,7,9,10,11 \\
11 & 5.850 & 13,3,4,5,6,7,8,9,10,11 & 11 & 4.624 & 1,2,3,4,5,6,7,8,9,10,11 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c} \hline \hline
**Computing time: 19:20 s** & **Rank** & **Method C** & **Num.** & **Joint Entropy** & **Rank** & **Method F** \\ \hline
1 & 1.229 & 7 & 7 & 1 & 1.143 & 7(-) & 7 \\
2 & 0.469 & 54(-) & 6.7 & 2 & 0.309 & 54(-) & 6.7 \\
3 & 0.962 & 16(-) & 5,6,7 & 3 & 0.618 & 76(+) & 6,71,1 \\
4 & 1.531 & 330 & 25,6,7 & 4 & 1.071 & 96(+) & 1,6,71,11 \\
5 & 2.101 & 462(-) & 25,6,7,9 & 5 & 1.568 & 172(+) & 1,4,6,7,11 \\
6 & 2.744 & 462(-) & 25,6,7,9,10,11 & 6 & 2.073 & 204(+) & 1,4,6,7,10,11 \\
7 & 3.488 & 324 & 25,6,7,9,10,11 & 7 & 2.623 & 189 & 1,2,4,6,7,10,11 \\
8 & 4.515 & 162 & 24,55,7,9,10,11 & 8 & 3.141 & 30(+) & 1,23,4,6,7,10,11 \\
9 & 4.712 & 53 & 24,55,7,8,9,10,11 & 9 & 3.646 & 29(+) & 1,23,4,6,7,9,10,11 \\
10 & 5.336 & 11 & 12,45,6,7,8,9,10,11 & 10 & 4.154 & 6(+) & 1,23,4,5,6,7,9,10,11 \\
11 & 5.850 & 13,3,4,5,6,7,8,9,10,11 & 11 & 4.624 & 1,2,3,4,5,6,7,8,9,10,11 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of a select optimal rain gauge network of methods (weight: monthly average precipitation). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Num.