## 4 Conclusions  
In this paper, the enhanced Gauss-Levenberg-Marquardt (GLM) procedure in combination with the singular value decomposition (SVD) and Tikhonov regularization is presented and applied to calibrate the conceptual hydrological model. The procedure was evaluated and compared with two other global calibration techniques (GAP and CMA-ES). Based on the results of this study, the following conclusions can be drawn regarding the presented combined used of GLM, SVD, and Tikhonov regularization:  
* The combined GLM procedure enabled an almost perfect match between true and calculated parameters. Only one parameter out of 16 showed a deviation of only 0.02%. * By knowing the true model parameters, various calibration parameter settings can be tested. With the appropriate parameter settings of calibration, the calibration noise was reduced, and the calibration efficiency was improved. * Only with the GLM procedure, the precise values of parameters on the HBV-Land model for both peak and low flows were obtained. In other words, only the combined GLM process was able to eliminate the calibration noise in the case of simulations based on the synthetic model runoff. * The run time of the combined GLM procedure was significantly shorter than those of the compared procedures. For the same case study, the combined GLM calibration procedure was approximately 60 and 200-times shorter than of CMA-ES and GAP, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline
**Model Efficiency Benchmark** & **Perfect-Fit Value** & **GLM** & **CMA-ES** & **GAP\({}_{16}\)** & **GAP\({}_{13}\)** \\ \hline Coefficient of determination R2 & \(1\) & \(1\) & \(0.999995\) & \(0.998259\) & \(0.999989\) \\ Model efficiency NSE & \(1\) & \(1\) & \(0.999994\) & \(0.998092\) & \(0.999987\) \\ Kling-Gupta efficiency KGE & \(0.999987\) & \(0.99998\) & \(0.999924\) & \(0.984518\) & \(0.998326\) \\ Kling-Gupta efficiency “non-parametric” NPE & \(0.999811\) & \(0.99981\) & \(0.999562\) & \(0.984741\) & \(0.998312\) \\ Efficiency for log(Q) LogR\({}_{\text{eff}}\) & \(1\) & \(1\) & \(0.99992\) & \(0.993776\) & \(0.999872\) \\ Flow-weighted efficiency FlowWeightedNSE & \(1\) & \(1\) & \(0.99995\) & \(0.998288\) & \(0.999996\) \\ Mean difference & \(-0.001665\) & \(-0.0035\) & \(0.02267\) & \(-2.79455\) & \(0.31087\) \\ Efficiency for peak flows & \(1\) & \(1\) & \(0.99982\) & \(0.995366\) & \(0.999985\) \\ Volume error & \(0.999993\) & \(0.99999\) & \(0.999879\) & \(0.988476\) & \(0.998718\) \\ MARE measure & \(0.999205\) & \(0.99921\) & \(0.998851\) & \(0.970793\) & \(0.994208\) \\ Lindstrom measure & \(1\) & \(1\) & \(0.999982\) & \(0.99694\) & \(0.999859\) \\ Spearman rank & \(1\) & \(1\) & \(0.99996\) & \(0.998679\) & \(0.999981\) \\ Efficiency for low flows & \(1\) & \(1\) & \(0.999977\) & \(0.980824\) & \(0.999784\) \\ Low-flow difference & \(0.001\) & \(-0.007\) & \(0.232\) & \(-11.999\) & \(-2.27\) \\ \hline \end{tabular} \({}^{1}\) Results are rounded to the sixth decimal.  
\end{table} 
Table 7: Validation results \({}^{1}\) of the HBV-Land model for the period 1 October 2001 to 31 December 2011. Figure 7: Validation period 1 January 2002 to 31 December 2011, validated with GLM. * The GLM calibration process in all cases calculated the same NSE value, and values of calibrated parameters remained the same, regardless of the number of repetitions of the calibration process. The same repeating results can be attributed to the nonstochastic behavior in GLM calibration procedures [84], in contrast to stochastic evolutionary procedures (CMA-ES and GAP in this study). The minimum error variance in the objective function was obtained with the GLM procedure in all cases. * The noise in the calculation results with the GLM method was practically the same in either calibrating or validating the procedure. In the modeling, therefore, only computational noise remained in the results. * The result of calibration with the GLM procedure, which would be stuck at the local minimum, was not detected in this study.