2.2.3. Model Parameters

The parameters of the numerical model mainly included soil hydraulic parameters and solute transport parameters. The initial values of the soil hydraulic parameters were determined according to the soil medium hydraulic parameter database of the Hydrus-1D software. The initial values of solute transport parameters were based on the measured results of this physical experiment, and the practical value was determined. The inverse solution module of the Hydrus-1D software was used for inversion to obtain the final parameters of the numerical model (Tables 3 and 4).



**Table 4.** Solute transport parameters.


2.2.4. Calibration and Evaluation of the Model

The reliability was verified and analyzed by inputting the solute transport parameters and soil hydraulic parameters through the HYDRUS-1D software, and the simulation's accuracy was evaluated by the coefficient of determination *R*2, and the root mean square error (*RMSE*). The closer the coefficient of determination *R*<sup>2</sup> was to 1, the closer the root mean square error (*RMSE*) was to 0, which means that the model simulation results and the measured results of nitrogen had higher fitting accuracy. The calculation formula is:

$$R^2 = \frac{\sum\_{i=1}^{n} (\stackrel{\frown}{y}\_i - \overline{y})^2}{\sum\_{i=1}^{n} (y\_i - \overline{y})^2} \tag{5}$$

$$RMSE = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} \left( S\_i - M\_i \right)^2} \tag{6}$$

where *Si* and *Mi* are simulated and measured values, respectively; *N* is the number of samples.

According to the simulation results of the numerical model of nitrogen migration and transformation in the water level fluctuation zone, the simulated values of ammonia nitrogen, nitrate nitrogen and nitrite nitrogen are shown in Figures 4–6, and the model fitting results are shown in Table 5. The correlation coefficients are mostly above 0.8. The root mean square error (*RMSE*) is small. Except for the significant simulation error of individual pollutants, the simulation results of the numerical model fit well with the measured results, indicating that the numerical model can better reflect the nitrogen transfer and transformation process under the fluctuation of the groundwater level.

**Figure 4.** The process of nitrogen change in coarse sand ((**a**) nitrate nitrogen; (**b**) nitrite nitrogen; (**c**) ammonium nitrogen).



**Figure 5.** The process of nitrogen change in medium sand ((**a**) nitrate nitrogen; (**b**) nitrite nitrogen; (**c**) ammonium nitrogen).

**Figure 6.** The process of nitrogen change in fine sand ((**a**) nitrate nitrogen; (**b**) nitrite nitrogen; (**c**) ammonium nitrogen).

## **3. Results and Discussion**
