## 2 Materials and Methods
### Data and Sources of Information  
Daily climate data (temperature and rainfall) were measured in a nearby field with a weather station. Evapotranspiration was computed using the Thornthwaite equation using observed temperature and rainfall data [23]. Out of 17 hydrologic parameters considered in the study, some drainage system parameters, such as drain depth (B) and drain spacing (L), were obtained from the observed data. The drainage coefficient (DC) computed using the slope and drain area was less than the observed drainage flow. Hence, the maximum observed historical daily subsurface drainage was used as DC in the study. Soil layer profile and respective bottom layer depth were used as that of Drummer, a silty clay loam, from the United States Department of Agriculture (USDA), Natural Resources Conservation Services (NRCS) (Table 1). Corrugated plastic tile drains of diameter 4 inches were installed at 40 ft (12.2 m) spacing at a depth of 3.5 ft (1.07 m) at a slope of 1.2% for CS-3 and 80 ft spacing at a depth of 3.5 ft at the slope of 1.8% for CS-4. The daily drainage flow from the tiles was obtained from the continuously monitored data. Grain corn was planted in both fields on 24 April 2019, harvested on 7 October 2019, and planted on 8 April 2020 and harvested on 7 October 2020, while soybean was planted on 10 April 2021 and harvested on 10 October 2021. All the other coefficients and parameters for evapotranspiration, soil, and crops were initialized based on the past study in the nearby locations [14], which were later calibrated for the observed data.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Meaning** & **Unit** & **Parameter Value** & \\
**Drainage System Parameters** & & & **CS3** & **CS4** \\ \hline H & Depth to Impermeable Layer & cm & 152 & 152 \\ Re * & Effective Radius & cm & 1.1 & 1.1 \\ B & Drain Depth & cm & 107 & 107 \\ L & Drain Spacing & cm & 1220 & 2438 \\ SS * & Maximum surface storage & cm & 1.2 & 0.9 \\ KD * & Kirkham Depth & cm & 1.76 & 2.2 \\ DC & Drainage coefficient & cm/day & 2.09 & 2.36 \\ \hline Soil properties & & & & \\ \multicolumn{4}{c}{ Lateral saturated conductivity} & \\ \multicolumn{4}{c}{ LK5 *} & layer 5 & cm/h & 0.1 & 0.69 \\ \multicolumn{4}{c}{ LK4 *} & layer 4 & cm/h & 3 & 1.5 \\ \multicolumn{4}{c}{ LK3 *} & layer 3 & cm/h & 5.5 & 0.26 \\ \multicolumn{4}{c}{ LK2 *} & layer 2 & cm/h & 2 & 1.09 \\ \multicolumn{4}{c}{ LK1 *} & layer 1 & cm/h & 3 & 1.88 \\ \hline \multicolumn{4}{c}{ Soil type} & & Drummer & Flanagan \\ \multicolumn{4}{c}{ Soil layer bottom depth} & \\ \multicolumn{4}{c}{ layer 5} & cm & 152 & 152 \\ \multicolumn{4}{c}{ layer 4} & cm & 100 & 114 \\ \multicolumn{4}{c}{ layer 3} & cm & 81 & 97 \\ \multicolumn{4}{c}{ layer 2} & cm & 48 & 58 \\ \multicolumn{4}{c}{ layer 1} & cm & 18 & 46 \\ \hline Slope & Surface slope & \% & 1.2 & 1.8 \\ \multicolumn{4}{c}{ Surface length along drain tiles} & cm & 7800 & 8600 \\ \hline \multicolumn{4}{c}{ Soil temperature parameters} & \\ \multicolumn{4}{c}{ ZA *} & ZA coefficient & 3.9 & 7.64 \\ ZB * & ZB coefficient & 1.4 & 1.4 \\ TKA * & Thermal conductivity function (TKA) & 3 & 3.97 \\ TKB * & Thermal conductivity function (TKB) & 1.3 & 0.26 \\ T\_dep & Soil temperature at bottom of soil profile & \({}^{\circ}\)C & 11.5 & 11.5 \\ T\_snow & Avg air temp below which precipitation is snow & \({}^{\circ}\)C & 0 & 0 \\ T\_melt & Average air temp above which snow starts to melt & \({}^{\circ}\)C & 1 & 1 \\ CDEG * & Snow melt coefficient & mm/dd-\({}^{\circ}\)C & 7.6 & 3.58 \\ CICE * & Critical ice content above which infiltration stops & cm\({}^{3}\)/cm\({}^{3}\) & 0.2 & 0.11 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters for DRAINMOD-H with their range and base parameter values for sensitivity analysis.