## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**IDW***} & \multicolumn{2}{c}{**OIDW**} & \multicolumn{2}{c}{**KG**} \\ \hline
**Station** & \(\beta\) & **MSE** & **Time (s)** & \(\beta\) **(std.dev)** & **SE** &
\begin{tabular}{c} **Time (s)** \\ **(std.dev)** \\ \end{tabular} & **MSE** \\ \hline Agigea & & 26.8233 & & 26.8233 & & 23.92 \\ Albesti & 39.1014 & & 39.1016 & & 21.38 \\ Altan Tepe & 26.3154 & & 26.3154 & & 23.51 \\ Amaceae & 25.5319 & & 25.5319 & & 23.47 \\ Baia & 24.9642 & & 24.9642 & & 32.85 \\ Baltagesti & 31.246 & & 31.2461 & & 24.62 \\ Birunta & 40.4631 & & 40.4633 & & 26.39 \\ Casian & 28.3496 & & 28.3496 & & 18.97 \\ Casimcea & 27.3955 & & 27.3956 & & 32.10 \\ Ceamurlia & 25.3455 & & 25.3455 & & 19.54 \\ Cerna & 28.2859 & & 28.2859 & & 39.45 \\ Cheia & 19.4690 & & 19.4690 & & 46.48 \\ Cobadin & 30.3138 & & 30.3138 & & 38.22 \\ Corbu & 25.2591 & & 25.2591 & & 21.94 \\ Crucea & 30.8561 & & 30.8562 & & 26.21 \\ Cuza Voda & 23.8778 & & 23.8777 & & 25.27 \\ Daieni & 47.0681 & & 47.0681 & & 24.30 \\ Dobromir & 29.2771 & & 29.2771 & & 22.91 \\ Dorobantu & 35.8369 & & 35.8369 & & 34.72 \\ Grec & 26.8270 & 190 & 1.59207 & 26.8271 & 4.846 & 25.23 \\ Hamcearca & 29.0369 & & (\(1.1813\times 10^{-4}\)) & 29.0370 & (\(1.0498\)) & 22.56 \\ Independenta & 35.639 & & 35.6389 & & 18.11 \\ Lipinta & 27.4559 & & 27.4559 & & 33.12 \\ Lumina & 31.1541 & & 31.1540 & & 36.45 \\ Mihai Viteazu & 30.7684 & & 30.7684 & & 74.91 \\ Negru Voda & 40.186 & & 40.1860 & & 43.82 \\ Negureni & 73.7331 & & 73.7331 & & 2.69 \\ Niculiet & 45.067 & & 45.067 & & 48.99 \\ Nuntasi & 21.0675 & & 21.0675 & & 29.32 \\ Pantelimon & 49.9444 & & 49.9444 & & 21.09 \\ Peceneaga & 22.1274 & & 22.1275 & & 38.29 \\ Pecineaga & 31.8819 & & 31.8821 & & 33.92 \\ Pestera & 35.9176 & & 35.9176 & & 26.19 \\ Pietreni & 31.7759 & & 31.7759 & & 22.79 \\ Posta & 24.7646 & & 24.7646 & & 21.12 \\ Sacele & 20.8606 & & 20.8606 & & 27.64 \\ Saraiu & 25.9453 & & 25.9453 & & 23.21 \\ Satu Nou & 23.8919 & & 23.8919 & & 47.47 \\ Silistea & 22.8196 & & 22.8195 & & 33.66 \\ Topolog & 30.4321 & & 30.4321 & & 24.51 \\ Zebil & 26.6736 & & 26.6736 & & 29.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter \(\beta\) values obtained in experiments performed using the series recorded at all (51) meteorological stations, in the scenario A2. For OIDW, the values in the parentheses are the standard deviation of the parameter identified, computed over the 50 independent runs. Comparison with KG. Therefore the time to run the experiments in scenario B1 is smaller than in A1 (1.31 times in for IDW* and 1.66 times for OIDW). Tables 3-6 contain the results obtained in experiments performed using the 51 meteorological stations, in scenario A2 and B2, respectively. Results in Table 3 prove that PSO converges to the optimal \(\beta\), as it was identified by grid search (standard deviation of \(1.1813\times 10^{-4}\)). For the main stations, the standard deviations are equal up to the third decimal for almost all the series. The computational effort, reported as run time, was significantly smaller (40 times) in the case of the OIDW algorithm (190 s for IDW* and 4.846 s for OIDW). The average MSE computed in A2 experiments were the following: 30.64324 (IDW*), 30.64315 (OIDW) and 30.876 (KG)--computed using the MSE for the main series; 31.0671 (IDW*), 31.0671(OIDW) and 29.5480 (KG)--computed using the MSE for the 41 secondary series and 30.9840 (IDW*), 30.9840 (OIDW) and 29.7924 (KG)--computed using all series. We found that the average MSE was smaller in all situations in scenario A2 for the main series, by comparison to scenario A1. The smallest average MSE in scenarios A1 and A2 corresponded to KG, when extracting only the secondary series (followed by the case when using all the series) for the MSE computation. The results from Table 5 reveal little to no difference between the \(\beta\)'s identified by grid search and those identified by PSO search. Therefore, the MSE's associated to the computed IDW approximations were identical.