## 2 Materials and Methods
### Calibration and Validation  
Four basic steps were followed in this study:  
1. **Field Year Selection**. For statistical purposes, 75% of field years were chosen randomly without replacement (i.e., 47 out of the 65 total field years) to calibrate the model (Table 2), to ensure at least one field year was reserved for each crop type for validation purposes for a total of 18 field years (Table 3). * **LUEc Calibration**. The iterative training process using an R script as described in [PERSON] et al. (2013) was used to determine \(\varepsilon_{0}\), \(\beta\), \(\sigma_{\text{Wscalar}}\), and \(\sigma_{\text{Pscalar}}\) values for irrigated and nonirrigated maize and soybean crops. The training utilized input values from the selected calibration field year flux data, Daymet derived \(\text{T}_{\text{avg}}\), VPD, APAR, and \(\text{T}_{\text{scalar}}\), and remotely-derived gLAI. The iterative process trained the parameters using a step-by-step method in which each scalar was estimated one at a time. During the iteration in which a parameter is calculated, assumptions are made about the other parameters to mimic optimal field conditions. Once the parameters are calculated, the iterations are repeated using the entire calibration dataset to produce \(\varepsilon_{0}\), \(\beta\), \(\sigma_{\text{Wscalar}}\), and \(\sigma_{\text{Pscalar}}\) values with corresponding standard deviations. The calibrated dataset includes AmeriFlux-derived GPP, Daymet-derived \(\text{T}_{\text{avg}}\), VPD, CC, APAR, and \(\text{T}_{\text{scalar}}\), and remotely derived gLAI data. Additionally, gLAI\({}_{\text{max}}\) values for irrigated and rainfed soybean and maize were estimated from MODIS-derived gLAI data (Equations (5) and (6)). From these outputs, scalars were calculated (Equations (8)-(15)). * **Daily GPP Estimation**. Data from validation field year datasets (Table 3) and parameters derived from the iterative process along with specified constants (Table 4), were used to calculate daily values of the scalars, \(\text{C}_{\text{scalar}}\), \(\text{W}_{\text{scalar}}\), and \(\text{P}_{\text{scalar}}\) (Equations (11), (14), and (15)) and APAR (Equation (10)), from which daily GPP values were estimated (Equation (8)). \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Calibration Years**} \\ \hline
**Site** & **Maize** & **Soybean** \\ \hline US-Ne1 (NE—irrigated) & 2002–2005, 2007, 2009–2012 & – \\ US-Ne2 (NE—irrigated) & 2003, 2005, 2007, 2009, 2010, 2013 & 2002, 2004, 2008 \\ US-Ne3 (NE) & 2003, 2005, 2011, 2013 & 2006, 2008, 2010, 2012 \\ US-Br1 (IA) & 2005, 2007, 2009 & 2006,2008 \\ US-Br3 (IA) & 2006, 2010 & 2007, 2009, 2011 \\ US-Bo1 (IL) & 2001, 2005, 2007 & 2002, 2004 \\ US-Ro1 (MN) & 2005, 2009, 2011 & 2006, 2010, 2012 \\ \hline
**Field Years** & **30** & **17** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: AmeriFlux calibration field years. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Validation Years**} \\ \hline
**Site** & **Maize** & **Soybean** \\ \hline US-Ne1 (NE—irrigated) & 2006, 2008, 2013 & N/A \\ US-Ne2 (NE—irrigated) & 2011, 2012 & 2006 \\ US-Ne3 (NE) & 2007, 2009 & 2002, 2004 \\ US-Br1 (IA) & 2011 & 2010 \\ US-Br3 (IA) & 2008 & 2005 \\ US-Bo1 (IL) & 2003 & 2006 \\ US-Ro1 (MN) & 2007 & 2008 \\ \hline
**Field Years** & **11** & **7** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: AmeriFlux validation field years.