## Appendix A \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Num.** & **Conditional Entropy (I)** & **Cases** & **Method A** & **Num.** & **Conditional Entropy (I)** & **Cases** & **Method D** \\ \hline
1 & 2.455 & 11 & 7 & 1 & 2.779 & 11 & 4 \\
2 & 1.686 & 10 & 7,(11) & 2 & 2.045 & 10 & 4,(7) \\
3 & 0.937 & 9 & 7,11,(1) & 3 & 1.125 & 9 & 4,7,(1) \\
4 & 0.511 & 8 & 7,11,(5,4) & 4 & 0.529 & 8 & 4,7,1,(10,0) \\
5 & 0.260 & 7 & 7,11,15,(4) & 5 & 0.361 & 7 & 4,7,1,10,(8) \\
6 & 0.204 & 6 & 7,11,15,(4,8) & 6 & 0.272 & 6 & 4,7,1,10,8,5,(1) \\
7 & 0.180 & 5 & 7,11,15,(4,8) & 6,(10) & 8 & 0.124 & 4 & 4,7,1,10,8,5,11,(9) \\
8 & 0.127 & 4 & 7,11,15,(4,8) & 6,(10),(2) & 9 & 0.081 & 3 & 4,7,1,10,8,5,11,(9) \\
9 & 0.104 & 3 & 7,11,15,(4,8) & 6,10,(3,2) & 10 & 0.064 & 2 & 4,7,1,10,8,5,11,9,6,(2) \\
10 & 0.088 & 2 & 7,11,15,(4,8) & 6,10,(3,2) & 11 & 0.031 & 1 & 4,7,1,10,8,5,11,9,6,2,(3) \\
11 & 0.051 & 1 & 7,11,15,(4,8) & 6,10,(3,2),(9) & 11 & 0.031 & 1 & 4,7,1,10,8,5,11,9,6,2,(3) \\  & \multicolumn{6}{c}{Computing time 0.88 s} \\ \hline
**Num.** & **Conditional Entropy (Z)** & **Cases** & **Method B** & **Num.** & **Conditional Entropy (Z)** & **Cases** & **Method E** \\ \hline
1 & 2.455 & 11 & 7 & 1 & 2.779 & 11 & 4 \\
2 & 2.097 & 10 & 7,(3) & 2 & 2.164 & 10 & 4,(5) \\
3 & 2.722 & 9 & 7,(3),(1) & 3 & 3.284 & 9 & 4,5,(3) \\
4 & 3.265 & 8 & 7,31,(4) & 4 & 3.671 & 8 & 4,5,3,(8) \\
5 & 3.661 & 7 & 7,31,(4,8) & 5 & 4.127 & 7 & 4,5,3,(8) \\
6 & 3.855 & 6 & 7,31,(4,8) & 6 & 4.347 & 6 & 4,5,3,(9) \\
7 & 4.103 & 5 & 7,31,4,8,5,(9) & 7 & 4.459 & 5 & 4,5,3,8,9,6,(2) \\
8 & 4.196 & 4 & 7,31,4,8,5,9,(10) & 8 & 4.428 & 4 & 4,5,3,8,9,6,2,(7) \\
9 & 4.266 & 3 & 7,31,4,8,5,9,10,6,(1) & 9 & 4.652 & 3 & 4,5,3,8,9,6,2,7,(10) \\
10 & 4.258 & 2 & 7,31,4,8,5,9,10,6,(11) & 10 & 4.759 & 2 & 4,5,3,8,9,6,2,7,10,(11) \\
11 & 4.359 & 1 & 7,31,4,8,5,9,10,6,(11), & 11 & 4.865 & 1 & 4,5,3,8,9,6,2,7,10,(1) \\  & \multicolumn{6}{c}{Computing time 0.6 s} \\ \hline
**Num.** & **Joint Entropy** & **Cases** & **Method C** & **Num.** & **Joint Entropy** & **Cases** & **Method F** \\ \hline
1 & 2.455 & 11 & 7 & 1 & 2.779 & 11 & 4 \\
2 & 0.856 & 55 & 4,11 & 2 & 0.927 & 55 & 4,11 \\
3 & 2.253 & 165 & 26,7 & 3 & 2.531 & 165 & 4,10,11 \\
4 & 3.940 & 300 & 2,5,6,7 & 4 & 4.593 & 330 & 4,7,10,11 \\
5 & 5.724 & 462 & 2,7,9,10,11 & 5 & 6.881 & 462 & 1,4,7,10,11 \\
6 & 7.597 & 462 & 2,6,7,9,10,11 & 6 & 9.147 & 462 & 1,2,4,7,10,11 \\
7 & 9.481 & 330 & 2,5,6,7,9,10,11 & 7 & 11.365 & 330 & 1,2,4,6,7,10,11 \\
8 & 11.374 & 165 & 2,4,5,6,7,9,10,11 & 8 & 13.375 & 165 & 12,4,6,7,9,10,11 \\
9 & 13.008 & 55 & 2,4,5,6,7,9,10,11 & 9 & 15.775 & 55 & 12,4,6,7,9,10,11 \\
10 & 14.722 & 11 & 1,2,4,5,6,7,8,9,10,11 & 10 & 17.934 & 11 & 1,2,4,5,6,7,8,9,10,11 \\
11 & 16.250 & 1 & 1,2,3,4,5,6,7,8,9,10,11 & 11 & 20.031 & 1 & 1,2,3,4,5,6,7,8,9,10,11 \\  & \multicolumn{6}{c}{Computing time 23.17 s} \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Results of a select optimal rain gauge network of methods (mm). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Num.** & **Conditional Entropy (1)** & **Cases** & **Method A** & **Num.** & **Conditional Entropy (1)** & **Cases** & **Method D** \\ \hline
1 & 2.439 & 11 & 7 & 1 & 2.754 & 11 & 4 \\
2 & 1.506 & 10 & 7,(11) & 2 & 1.873 & 10 & 4,7(1) \\
3 & 0.819 & 9 & 7,11,(1) & 3 & 0.948 & 9 & 4,7(1) \\
4 & 0.488 & 8 & 7,11,15,4 & 4 & 0.438 & 8 & 4,7(1,10) \\
5 & 0.216 & 7 & 7,11,15,4,8 & 0, & 0.237 & 6 & 4,7(1,10,8,5,1) \\
6 & 0.153 & 5 & 7,11,15,4,8,6 & 0, & 0.616 & 5 & 4,7(1,10,8,5,1) \\
8 & 0.106 & 4 & 7,11,15,4,8,6 & (10) & 8 & 0.104 & 4 & 4,7(1,10,85,11,9) \\
9 & 0.088 & 3 & 7,11,15,4,8,6 & (10) & 9 & 0.067 & 3 & 4,7(1,10,8,5,11,9) \\
10 & 0.072 & 2 & 7,11,15,4,8,6 & (10,3,2) & 10 & 0.046 & 2 & 4,7(1,10,8,5,11,9,6,2) \\
11 & 0.044 & 1 & 7,11,15,4,8,6 & (10,3,2) & 9 & 11 & 0.022 & 1 & 4,7(1,10,8,5,11,9,6,2) \\ \hline \multicolumn{1}{c}{Computing time: 10.8 s} & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of a select optimal rain gauge network of methods (sg).