## 2 Materials and Methods
### Calibration and Validation  
The DRAINMOD model was run from January 2017 to December 2022 with a warmup period from January 2017 to November 2018. The calibration of DRAINMOD parameters was conducted for daily and annual subsurface flow for the period of November 2018 to December 2020 for continuous corn production, and the validation was carried out for the period of January 2021 to May 2022. The model was initialized using known data as well as available literature for unknown parameters. First, a range of parameters was selected based on the literature and judgment based on the field conditions (Table 1). The flow parameters were divided into an array for the step interval of approximately 5%. The Monte Carlo simulation was performed by running DRAINMOD 2000 times each to obtain the best set of parameters using integrated Python codes and DRAINMOD. The parameter range was updated by sensitivity analysis and graphical plots of the Monte Carlo simulation results. The process was repeated till the model outputs well represented the observed flow. Some manual adjustments were made for the final calibration of the model on the lateral hydraulic conductivity and maximum surface storage following both the graphical and statistical approaches.  
Absolute values of Nash-Sutcliffe model efficiency coefficient (NSE), coefficient of determination (RSQ), root mean square efficiency (RMSE), and percentage bias (PBIAS) for the daily subsurface drainage flow and total cumulative flow were the objective functions considered for calibration of the model. RSQ ranges from 0 to 1 and indicates the correlation between observed and simulated data series of daily drainage flow, with 1 being the best correlation [26]. NSE ranges from \(-\infty\) to 1 and represents the closeness between the data series [27]. RMSE quantifies the average magnitude of differences between simulated and observed values, while PBIAS denotes whether the simulated outputs are overestimated or underestimated [28]. Calibration was considered satisfactory when the objective functions for NSE and RSQ were greater than 0.4 for the daily hydrological data, and the difference between cumulative flow was less than 10%. The graphical plot of daily hydrology data and cumulative flow was used to assess the anomalies between the simulated and observed values, for instance, in peak flow and slope of cumulative flow data.  
\[NSE=1-\frac{\sum_{i=1}^{n}(O_{i}-S_{i})^{2}}{\sum_{i=1}^{n}(O_{i}-\overline{ O})^{2}}\]  
\[R^{2}=\frac{\sum_{i=1}^{n}(O_{i}-\overline{O})*\left(S_{i}-\overline{S} \right)}{\sqrt{\sum_{i=1}^{n}(O_{i}-\overline{O})^{2}}\;*\sqrt{\sum_{i=1}^{n} (S_{i}-\overline{S})^{2}}}\]  
\[PBIAS=\frac{\sum_{i=1}^{n}(O_{i}-S_{i})}{\sum_{i=1}^{n}O_{i}}\times 100\]  
\[RMSE=\sqrt{\sum_{i=1}^{n}(O_{i}-S_{i})^{2}/n}\]  
\begin{table}
\begin{tabular}{l r r r} \hline \hline
**Parameters** & **Meaning** & **Unit** & **Parameter Value** & \\
**Drainage System Parameters** & & & **CS3** & **CS4** \\ \hline Objective functions & CS-3 & & CS-4 & \\  & Calibration & Validation & Calibration & Validation \\ NSE & 0.5 & 0.58 & 0.49 & 0.46 \\ RSQ & 0.5 & 0.645 & 0.53 & 0.52 \\ RMSE & 0.206 & 0.161 & 0.196 & 0.192 \\ PBIAS & \(-5.70\%\) & \(-28\%\) & 1.86\% & \(-25\%\) \\ \hline \hline \end{tabular}  
* *  
where \(O_{i}\) is the observed value, \(S_{i}\) is the simulated value and \(\overline{O}\) is the mean of observed values, \(\overline{S}\) is the mean simulated values and n is the number of data.