*4.2. Statistical Parameters Used for the Calibration and Evaluation of Model*

Several statistical indices were used to evaluate the performance of the model on the field measured data. These include Percentage Error (PE), Root Mean Square Error (RMSE), Model Efficiency (ME) and Coefficient of Determination (R2).

Percentage Error (PE) was determined using the following equation

$$\text{EP} = \frac{(\text{S}\_{\text{i}} - \text{O}\_{\text{i}})}{\text{O}\_{\text{i}}} \times 100\tag{10}$$

where Si and Oi are simulated and observed values, respectively.

The root means square error (RMSE) [37] is presented by the following equation

$$\text{RMSE} = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (\mathbf{S}\_i - \mathbf{O}\_i)^2} \tag{11}$$

with the values of RMSE close to zero indicate the best model fit.

The model efficiency (ME) [38] was applied to assess the effectiveness of the model. The ME indicator compares the variability of prediction errors by the model to those of collected data from the field. If the prediction errors are greater than the data error, then the indicator becomes negative. The upper ME bound is at 1.

$$\text{ME} = \frac{\sum\_{\text{i}=1}^{n} \left(\text{O}\_{\text{i}} - \text{MO}\right)^{2} - \sum\_{\text{i}=1}^{n} \left(\text{S}\_{\text{i}} - \text{O}\_{\text{i}}\right)^{2}}{\sum\_{\text{i}=1}^{n} \left(\text{O}\_{\text{i}} - \text{MO}\right)^{2}} \tag{12}$$

The coefficient of determination (R2), as a result of regression analysis, is the proportion of the variance in the dependent variable (predict value) that is predictable from the independent variable (observed value) and is computed according to [35]

$$\mathbf{R}^2 = \left\{ \frac{\sum\_{i=1}^n \left( \mathbf{O\_i} - \overline{\mathbf{O}} \right) \left( \mathbf{S\_i} - \overline{\mathbf{S}} \right)}{\left[ \sum\_{i=1}^n \left( \mathbf{O\_i} - \overline{\mathbf{O}} \right)^2 \right]^{0.5} \left[ \sum\_{i=1}^n \left( \mathbf{S\_i} - \overline{\mathbf{S}} \right)^2 \right]^{0.5}} \right\}^2 \tag{13}$$

*R*<sup>2</sup> is between 0 and 1.
