## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model Efficiency Benchmark**\({}^{1}\) & **Perfect-Fit Value** & **GLM** & **CMA–ES** & **GAP\({}_{16}\)** & **GAP\({}_{13}\)** \\ \hline Coefficient of determination R2 & \(1\) & \(1\) & 0.999999 & 0.999631 & 0.99999 \\ Model efficiency R\({}_{\rm eff}\) (NSE) & \(1\) & \(1\) & 0.999999 & 0.999628 & 0.999989 \\ [PERSON]–Gupta efficiency KGE & 0.999990 & 0.999990 & 0.999902 & 0.998184 & 0.999003 \\ [PERSON]–Gupta efficiency ”nonparametric” & 0.999844 & 0.999840 & 0.999774 & 0.997672 & 0.999156 \\ Efficiency for log(Q) & \(1\) & \(1\) & 0.999996 & 0.998712 & 0.999946 \\ Flow-weighted efficiency & \(1\) & \(1\) & 0.999999 & 0.999777 & 0.999994 \\ Mean difference & \(0.002825\) & \(0.002860\) & \(0.023888\) & -0.53402 & 0.12956 \\ Efficiency for peak flows & \(1\) & \(1\) & 0.999997 & 0.998706 & 0.999978 \\ Volume error & 0.999990 & 0.999990 & 0.999919 & 0.998193 & 0.999562 \\ MARE measure & \(0.999453\) & 0.999450 & 0.999348 & 0.990692 & 0.996568 \\ Lindstrom measure & \(1\) & \(1\) & 0.999991 & 0.999447 & 0.999946 \\ Spearman rank & \(1\) & \(1\) & 0.999999 & 0.999688 & 0.999987 \\ Efficiency of low flows & \(1\) & \(1\) & 0.999969 & 0.983838 & 0.999292 \\ Low-flow difference & \(0\) & \(0\) & \(0.044\) & \(-1.307\) & \(-1.063\) \\ \hline \hline \end{tabular} \({}^{1}\) Results are rounded to the sixth decimal.  
\end{table} 
Table 4: Calibration results \({}^{1}\) from history matching of the synthetic model over ten years, i.e., 1 October 1981 to 31 December 1991. Figure 2: Observed and simulated discharges with the Gauss–Levenberg–Marquardt method (GLM) calibration procedure for the calibration period from 1 January 1982 to 31 December 1991. PEST_HP calculates parameter sensitivity during the calibration process itself. The normalized sensitivity in the second column of Table 5 shows how the uncertainty in the output of a model can be distributed to different parameters. The TT (temperature threshold) parameter is the most sensitive parameter with normalized sensitivity 1. In contrast, the least sensitive is CFR (refreezing coefficient) and CWH (water-holding capacity) parameters with normalized sensitivities of 0. The results of the calculated parameters with GLM, CMA-ES, and GAP are shown in columns 3-6 of Table 5. The results calibrated by the GLM procedure in the third column of Table 5 give a value close to the perfect-fit parameter value of Table 2. The differences occur only from the fourth to the fifth decimal place as a result of the calibration noise shown in column 3 of Table 5. The parameter values calibrated by the GAP procedure give relatively good results (GAP\  
The advantage of using the GLM with SVD and Tikhonov regularization in the calibration process is evident by comparing the values of individual relative deviations concerning the \"perfect-fit\" of the parameters in Table 6.  
In the regularization process (GLM), almost a perfect match between the true and the calibrated parameters is achieved, deviating by only 0.02% of CFR (refreezing coefficient) shown in the second column in Table 6. This small deviation (noise) is probably a consequence of the computation. Differences occur after the third decimal place. They can be explained by the equation for calculating refreezing meltwater (RM) defined as RM = CFR CFMAX (TT-T (t)) and containing three parameters and one variable [18; 54; 72; 83]. If a parameter such as CFR has independent relationships with other parameters, it cannot be adequately calculated due to over-parameterisation. It is therefore advisable to determine the value of such a parameter based on the expertise of the modeler. As the catchment has no altitude zones, the occurrence of refreezing meltwater was also relatively rare in the observed period. The results of the calibration procedure with GLM are graphically presented in Figures 4 and 5.