## 4 Results and Discussion
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & \multicolumn{3}{c}{**IDW\({}^{\star}\)**} & \multicolumn{3}{c}{**OIDW**} & \multicolumn{2}{c}{**KG**} \\ \hline
**Station** & \(\beta\) & **MSE** & **Time (s)** & \(\beta\) **(std.dev)** & **MSE** & **Time (s)** & **MSE** \\ \hline Adamclisi & & 29.1151 & & & 29.1151 & & 31.78 \\ Cernavoda & & 22.166 & & & 22.166 & & 25.78 \\ Constanta & & 29.2801 & & & 29.28 & & 36.47 \\ Corugea & & 17.9985 & & & 17.9984 & & 29.95 \\ Harsova & & 36.2216 & & 1.59207 & 36.2214 & 4.846 & 31.51 \\ Jurilovca & & 32.2055 & & (1.1813 \(\times 10^{-4}\)) & 32.2054 & (1.0498) & 37.43 \\ Mangalia & & 39.0367 & & & 39.0366 & & 27.38 \\ Medgidia & & 29.2706 & & & 29.2702 & & 31.47 \\ Sulina & & 46.5612 & & & 46.5612 & & 28.05 \\ Tulcea & & 24.5771 & & & 24.5772 & & 28.94 \\ \hline \end{tabular}
\end{table} 
Table 3: 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. \begin{table}
\begin{tabular}{l c c c c c c c} \hline  & \multicolumn{3}{c}{**IDW\({}^{\star}\)**} & \multicolumn{3}{c}{**OIDW**} & \multicolumn{2}{c}{**KG**} \\ \hline
**Station** & \(\beta\) & **MSE** & **Time (s)** & \(\beta\) **(std.dev)** & **MSE** & **Time (s)** & **MSE** \\ \hline Adamclisi & & 29.1151 & & & 29.1151 & & 31.78 \\ Cernavoda & & 22.166 & & & 22.166 & & 25.78 \\ Constanta & & 29.2801 & & & 29.28 & & 36.47 \\ Corugea & & 17.9985 & & & 17.9984 & & 29.95 \\ Harsova & & 36.2216 & & 1.59207 & 36.2214 & 4.846 & 31.51 \\ Jurilovca & & 32.2055 & & (1.1813 \(\times 10^{-4}\)) & 32.2054 & (1.0498) & 37.43 \\ Mangalia & & 39.0367 & & & 39.0366 & & 27.38 \\ Medgidia & & 29.2706 & & & 29.2702 & & 31.47 \\ Sulina & & 46.5612 & & & 46.5612 & & 28.05 \\ Tulcea & & 24.5771 & & & 24.5772 & & 28.94 \\ \hline \end{tabular}
\end{table} 
Table 2: The values of the \(\beta\) parameter obtained in experiments performed using the series recorded at the 10 main meteorological stations, in the scenario B1. Comparison with KG. In both scenarios (A1 and B1), OIDW found the optimum, as it was exhaustively identified by IDW. Moreover, the differences between the mean squared errors of the approximations computed with IDW using the \(\beta\) values identified with grid search (IDW*) and OIDW were not statistically significant. Additionally, the MSEs associated to the IDW algorithms are almost identical; in some cases, these are better than those obtained by KG. The standard deviations of \(\beta\) are very small in both scenarios. This signifies that the PSO search for \(\beta\) is stable--PSO converged in all the 50 runs to very similar values. The average MSE are 30.9327 for IDW* and OIDW in scenario A1; 30.3704 for IDW* and 30.3718 for OIDW in scenario B1 and 31.022 for KG, respectively (Tables 1 and 2). It was expected that OIDW in the scenario A1 (Table 1) would yield larger prediction errors than the individual OIDW's in the scenario B1 (Table 2), since in B1 the algorithm tries to fit a much smaller number of data points. Nevertheless, the differences with respect to KG are significant only in one case (e.g., Adamclisi). OIDW is run for each station in scenario B1, hence the computational times in Table 2 add up, for a fair comparison; OIDW is run only once for the entire set in A1, with the time as reported in Table 1.