*2.5. Model Calibration and Validation*

We applied the SWAT-CUP (SWAT Calibration Uncertainty Program) [59] for model sensitivity analysis, calibration and validation. In SWAT-CUP, parameter uncertainty can be analyzed by using Sequential Uncertainty Fitting version 2 (SUFI2), Generalized Likelihood Uncertainty Estimation (GLUE), Particle Swarm Optimization (PSO), Parameter Solution (ParaSol), or Marko Chain Monte Carlo (MCMC). Each uncertainty analysis method can run multiple simulations and find the ranges of best parameters for the study project. Parameters at any particular sub-basin, land use, soil, slope, and even HRU can be individually calibrated to reflect the unique spatial characteristics.

Among these uncertainty analysis methods, SUFI2, ParaSol and GLUE are easier to calibrate the parameters [59]. It is suggested that 3000, 7500, 10,000, 100,000, and 45,000 times of simulation are needed for SUFI2, ParaSol, GLUE, PSO, and MCMC, respectively, in order to get satisfactory simulation results [59]. SUFI2 method was selected in this study as it requires the least number of simulations. In sensitivity analysis, *p*-value is used to distinguish whether parameters are sensitive or not. Parameters that have *p*-value smaller than or equal to 0.05 are considered as sensitive parameters for further calibration [59]. After sensitivity analysis, the selection of calibrated ranges and fitted values of the parameters are identified based on the statistical criteria (i.e., R2, NSE, PBIAS, and RSR), suggested by [60] with the model performance standards (Table 4).


**Table 4.** Statistical criteria for model performance [60].

R2 is the coefficient of determination, presenting the linear correlation between simulated and observed data. The value of R<sup>2</sup> closer to 1 indicates a higher correlation.

$$\mathbf{R}^2 = \frac{\sum\_{i=1}^n \left(\mathbf{Y}\_i^{sim} - \mathbf{Y}^{mam}\right)^2}{\sum\_{i=1}^n \left(\mathbf{Y}\_i^{obs} - \mathbf{Y}^{mam}\right)^2} \tag{21}$$

where *Ysim* is the simulated data; *Yobs* is observed data; *Ymean* is the average of observation.

Nash–Sutcliffe efficiency (NSE) presents the residuals of measured data [61], and the value ranges from −∞ to 1. NSE value that equals 1, indicates the simulation is same as the observation, while NSE > 0.5 is acceptable for SWAT model performance [60].

$$\text{NSE} = 1 - \left[ \frac{\sum\_{i=1}^{n} \left( \chi\_{i}^{\text{obs}} - \chi\_{i}^{\text{sim}} \right)^{2}}{\sum\_{i}^{n} \left( \chi\_{i}^{\text{obs}} - \chi^{\text{mean}} \right)^{2}} \right] \tag{22}$$

Percent bias (PBIAS) presents whether the simulated data are overestimated or underestimated. When PBIAS is greater than 0, the simulation is underestimated [62].

$$\text{PBIAS}(\%) = \frac{\sum\_{i=1}^{n} \left( Y\_{i}^{\text{obs}} - Y\_{i}^{\text{sim}} \right)}{\sum\_{i=1}^{n} Y\_{i}^{\text{obs}}} \times 100 \tag{23}$$

RMSE-observation standard deviation ratio (RSR) is the ratio between root mean square error and standard deviation. The smaller the RSR is, the better simulation performance is [63].

$$\text{RSR} = \frac{\sqrt{\Sigma\_{i=1}^{n} \left(\chi\_{i}^{obs} - \chi\_{\text{sim}}^{sim}\right)^{2}}}{\sqrt{\Sigma\_{i=1}^{n} \left(\chi\_{i}^{obs} - \chi\_{\text{mm}}^{mm}\right)^{2}}} \tag{24}$$
