## 2 Materials and Methods
### Methods
#### 2.2.1 Flow Calibration
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Description** \\ \hline SUFI-2 & In SUFI 2, it is considered that the uncertainty in the simulations is observed in a uniform way. The sources of uncertainties are the driving variables, the conceptual model, parameters, and measured data. \\ \hline GLUE & In this method, once the general probability has been defined, all the parameters are randomly sampled from the previous distribution. The parameters are thus grouped either into a behavioral set or into a non-behavioral set by comparing them to a given threshold probability. The parameters are then weighted according to their behavior. Finally, the uncertainty is predicted. \\ \hline PSO & Here, the uncertainty prediction method is based on stochastic population optimization. The optimization is performed from a random sampling of parameters. \\ \hline PARASOL & During the PARASOL method, a global optimization criterion (GOC) is first fixed. The method seeks to minimize the objective functions (OF) or GOC from the Shuffle Complex algorithm (SCE-UA). \\ \hline MCMC & MCMC proceeds with a random sampling, which adapts to the posterior distribution. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SWAT-CUP methods. Latin Hypercube sampling is the sampling method used in this study. It makes it possible to calculate the global sensitivity by calculating a multiple regression system of the parameters considered [43]:  
\[g=\alpha+\sum_{i=1}^{m}\betaibi \tag{4}\]  
where \(\alpha=\frac{\sigma_{\mathrm{s}}}{\sigma_{\mathrm{m}}}\), \(\beta=\frac{\mu_{\mathrm{s}}}{\mu_{\mathrm{m}}}\). \(\sigma_{\mathrm{s}}\) and \(\sigma_{\mathrm{m}}\) are considered to be the respective standard deviations of the simulated and observed data; \(\mu_{\mathrm{s}}\) and \(\mu_{\mathrm{m}}\) are the averages of the simulated and observed data. The relative impact of each parameter on the flow is identified from a statistical test. This impact is noted bi. The global sensitivity is related to the variation of the objective function, which depends on the observed variation of the parameter considered when all parameters change. * Uncertainty analysis P-factor and R-factor are used to calculate the uncertainties at 2.5% (XI) and 97.5% (Xu) percentiles of the cumulative distribution at each point. P-factor indicates the percentage of observed data bracketed using 95 PPU. R-factor is the average thickness of the 95 PPU band obtained from the standard deviation of the observed data [44]. * Calibration analysis We chose NSE, R\({}^{2}\), and PBIAS as objective functions to analyze the performance and accuracy of the simulations. The PBIAS measures the percentage of bias. When PBIAS is 0, the simulation is said to be accurate. A positive PBIAS shows an underestimation of the model, while negative values indicate an overestimation of the model bias [45]. Its use makes it possible to refine and make more precise predictions of the model [46] in [47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58]. NSE (Equation (5)) varies from \(-\infty\) to 1 (for a strong link between observed and simulated values). Equation (6) is used to calculate PBIAS. [PERSON] et al. [50] made the classification of model performance:  
PBIAS < \(\pm\)10: very good performance model;  
\(\pm\)10 < PBIAS < \(\pm\)15: good performance model;  
\(\pm\)15 < PBIAS < \(\pm\)25: satisfactory performance;  
PBIAS > \(\pm\)25: unsatisfactory performance. R\({}^{2}\) is calculated according to Equation (7); it varies from 0 to 1, 1 representing a perfect simulation [59]. A value greater than 0.5 is often accepted because it expresses a good restitution of the observed data [36].