## 3 Results and Discussion  
Calibration results with the GLM calibration procedure are graphically presented in Figure 2. Results of efficiency measures in the synthetic model with perfect-fit parameter values are given in the second column of Table 4 with the label \"Perfect-fit value.\" The third column in Table 4 shows the results of parameters from the calibration using the GLM algorithm with the use of SVD and Tikhonov regularization. For the GLM procedure, the run time was less than 1 min. Despite the same calculation data, slightly different results were obtained, which can be attributed to the computation noise. This noise was most likely caused by rounding the \(Q_{sim}\) results in the calculation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Benchmark Description** & **Definition 1** & **Value for Perfect-Fit** & **Range** \\ \hline Coefficient of determination (\(\mathrm{R^{2}}\)) & \(\frac{(\sum{(Q_{obs}-\overline{Q_{obs}})}(Q_{sim}-\overline{Q_{sim}}))^{2}}{ \sum{(Q_{obs}-\overline{Q_{obs}})}^{2}}\sum{(Q_{sim}-\overline{Q_{sim}})^{2}}\) & 1 & \(-\infty\) to 1 \\ Nash–Sutcliffe efficiency (NSE) & \(1-\frac{\sum{(Q_{obs}-Q_{sim})}^{2}}{\sum{(Q_{obs}-\overline{Q_{obs}})}^{2}}\) & 1 & \(-\infty\) to 1 \\ Efficiency for log(Q) & \(1-\frac{\sum{(\ln{Q_{obs}}-\ln{Q_{obs}})}^{2}}{\sum{(\ln{Q_{obs}}-\ln{Q_{obs}}) }^{2}}\) & 1 & \(-\infty\) to 1 \\ Flow-weighted efficiency & \(1-\frac{\sum{(Q_{obs}/Q_{obs})}(Q_{obs}-Q_{obs})}{\sum{(Q_{obs}/Q_{obs})}(Q_{ obs}-Q_{obs})}^{2}\) & 1 & \(-\infty\) to 1 \\ Mean difference & \(\frac{\sum{(Q_{obs}-\overline{Q_{obs}})}(Q_{obs}-Q_{obs})}{\sum{(Q_{obs}- \overline{Q_{obs}})}^{2}}\) & 0 & \(-\infty\) to \(\infty\) \\ Efficiency for peak flows & \(1-\frac{\sum{(\ln{Q_{obs}}-\ln{Q_{obs}})^{2}}}{\sum{(\ln{\ln{Q_{obs}}-\ln{Q_{ obs}}})^{2}}}\) & 1 & \(-\infty\) to 1 \\ Volume error & \(1-\frac{\sum{(Q_{obs}-\overline{Q_{sim}})}}{\sum{(Q_{obs}-\overline{Q_{sim}})}}\) & 1 & \(-\infty\) to 1 \\ MARE measure & \(1-\frac{1}{n}\sum{\frac{\sum{(Q_{obs}-\overline{Q_{sim}})}}{Q_{obs}}}\) & 1 & \(-\infty\) to 1 \\ Lindstrom measure & \(NSE-0.1\frac{\sum{(Q_{obs}-Q_{sim})}}{\sum{(Q_{obs}-\overline{Q_{sim}})}}\) & 1 & \(-\infty\) to 1 \\ Spearman rank & \(\frac{\sum{(R_{obs}-\overline{R_{obs}})}^{2}}{\sqrt{\sum{(R_{obs}-\overline{R_{ obs}})}^{2}}}\sum{(S_{sim}-\overline{S_{sim}})^{2}}\) & 1 & \(-\infty\) to 1 \\ The efficiency of low flows & \(1-\frac{\sum{(low_{obs}-low_{obs})}^{2}}{\sum{(low_{obs}-low_{obs})}^{2}}\) & 1 & \(-\infty\) to 1 \\ Low-flow difference & \(\sum{(low_{obs}-low_{obs})}\) & 0 & \(-\infty\) to \(\infty\) \\ \hline \hline \end{tabular}  
* \(Q_{obs}\) is the measured (observed) flow, \(Q_{sim}\) is the modeled (simulated) flow, n is the number of time steps, and \(R_{obs}\) and \(S_{sim}\) are the ranks of \(Q_{obs}\) and \(Q_{sim}\).  
\end{table} 
Table 3: Coefficients for calibration quality assessments, goodness-of-fit measures according to [82]. The NSE of the computation is quite high, as shown in the third column in Table 4. Deviations merely appeared after the tenth decimal place in the NSE (NSE perfect-fit value = 0.9999998607; NSE GLM = 0.9999998605) and after the fifth decimal place in the mean differences benchmark, which can be almost equated with the perfect-fit value. The performance of calibration with CMA-ES, GAP\({}_{13}\), and GAP\({}_{16}\) is shown in columns 4-6 of Table 4. The overall comparison of NSE of all four procedures applied in this study is shown in Figure 3. Based on NSE, one can notice an excellent performance also of CMA-ES and GAP\({}_{13}\), while GAP\({}_{16}\) reached the lowest NSE.