*3.3. Calibration of SPARROW Models and Uncertainty Analysis*

#### *3.2. Calibration of SPARROW Models and Uncertainty Analysis*  3.3.1. Calibration of SPARROW Models

3.2.1. Calibration of SPARROW Models NWLS calibration of SPARROW models in 2017 was executed, based on 58 and 144 water quality stations in PLB and HRB, respectively. The correlation coefficient (*R*2), the mean square error (MSE), the root mean square error (RMSE), and the NSE (see Table 1) NWLS calibration of SPARROW models in 2017 was executed, based on 58 and 144 water quality stations in PLB and HRB, respectively. The correlation coefficient (*R* 2 ), the mean square error (MSE), the root mean square error (RMSE), and the NSE (see Table 2) were assessed to evaluate the performances of the models.

were assessed to evaluate the performances of the models. **Table 2.** Results of SPARROW models.


PLB 58 0.89 0.25 0.50 0.88 HRB 144 0.53 1.91 1.38 0.52 For the results of SPARROW models for PLB and HRB, the values of *R*2 were 0.89 and 0.53, respectively, which verified the acceptability of SPARROW models. MSE were 0.25 and 1.91, respectively. The RMSE for the models were around 0.50 and 1.38, respec-For the results of SPARROW models for PLB and HRB, the values of *R* <sup>2</sup> were 0.89 and 0.53, respectively, which verified the acceptability of SPARROW models. MSE were 0.25 and 1.91, respectively. The RMSE for the models were around 0.50 and 1.38, respectively. Although the RMSE of HRB was significantly higher, similar values have been reported by other studies (RMSE = 1.40 [54], RMSE = 0.96 [16]). In addition, the NSE values were similar to the *R* <sup>2</sup> values, which indicated the robustness of the models. Figures 5a and 6a are scatterplots of predicted values versus observed values, in which the majority of the points are located in the vicinity of bisection. The scatterplots of residuals illustrated homoscedasticity (Figures 5b and 6b). The aforementioned analysis implied rational performance of the SPARROW models.

tively. Although the RMSE of HRB was significantly higher, similar values have been reported by other studies (RMSE = 1.40 [54], RMSE = 0.96 [16]). In addition, the NSE values were similar to the *R*2 values, which indicated the robustness of the models. Figures 5a and 6a are scatterplots of predicted values versus observed values, in which the majority of the points are located in the vicinity of bisection. The scatterplots of residuals illustrated homoscedasticity (Figures 5b and 6b). The aforementioned analysis implied rational per-

tively. Although the RMSE of HRB was significantly higher, similar values have been reported by other studies (RMSE = 1.40 [54], RMSE = 0.96 [16]). In addition, the NSE values were similar to the *R*2 values, which indicated the robustness of the models. Figures 5a and 6a are scatterplots of predicted values versus observed values, in which the majority of the points are located in the vicinity of bisection. The scatterplots of residuals illustrated homoscedasticity (Figures 5b and 6b). The aforementioned analysis implied rational per-

*Water* **2022**, *14*, x FOR PEER REVIEW 9 of 19

**Figure 5.** Scatterplots of (**a**) predicted values versus observed values and (**b**) residuals in PLB. **Figure 5.** Scatterplots of (**a**) predicted values versus observed values and (**b**) residuals in PLB. **Figure 5.** Scatterplots of (**a**) predicted values versus observed values and (**b**) residuals in PLB.

**Figure 6.** Scatterplots of (**a**) predicted values versus observed values and (**b**) residuals in HRB. **Figure 6.** Scatterplots of (**a**) predicted values versus observed values and (**b**) residuals in HRB.

**Figure 6.** Scatterplots of (**a**) predicted values versus observed values and (**b**) residuals in HRB. 3.3.2. Parameters and Uncertainty Analysis

formance of the SPARROW models.

formance of the SPARROW models.

3.2.2. Parameters and Uncertainty Analysis The bootstrap method was used to perform uncertainty analysis of SPARROW model parameters. Point sources, farmland, woodland and grassland, and residential land were considered as the main NH4+-N sources. Tables 2 and 3 show the evaluation of PLB and HRB, respectively. The coefficients of these sources all fell into the 90% confidence interval. The coefficients of farmland, woodland and grassland, and residential land were larger than 1, similar to the coefficients reported in other studies [55,56]. The coefficients 3.2.2. Parameters and Uncertainty Analysis The bootstrap method was used to perform uncertainty analysis of SPARROW model parameters. Point sources, farmland, woodland and grassland, and residential land were considered as the main NH4+-N sources. Tables 2 and 3 show the evaluation of PLB and HRB, respectively. The coefficients of these sources all fell into the 90% confidence interval. The coefficients of farmland, woodland and grassland, and residential land were larger than 1, similar to the coefficients reported in other studies [55,56]. The coefficients The bootstrap method was used to perform uncertainty analysis of SPARROW model parameters. Point sources, farmland, woodland and grassland, and residential land were considered as the main NH<sup>4</sup> + -N sources. Tables 3 and 4 show the evaluation of PLB and HRB, respectively. The coefficients of these sources all fell into the 90% confidence interval. The coefficients of farmland, woodland and grassland, and residential land were larger than 1, similar to the coefficients reported in other studies [55,56]. The coefficients of point sources were lower than 1, which suggested overestimates in the data of point sources.

of point sources were lower than 1, which suggested overestimates in the data of point sources. of point sources were lower than 1, which suggested overestimates in the data of point sources. Slope, average precipitation, and temperature were chosen as the land-to-water delivery variables for the SPARROW models. The coefficients of these sources all fell into the 90% confidence interval. Point sources and average precipitation showed statistical significance (*p* < 0.05) for PLB, while only average temperature showed statistical significance (*p* < 0.05) for HRB. Both stream decay variables lay in the 90% confidence intervals for PLB and HRB. Meanwhile, only the reach decay factor of a small river showed statistical significance (*p* < 0.05) for HRB.


**Table 3.** Evaluation of parameters in PLB.

**Table 4.** Evaluation of parameters in HRB.

