## 2 Materials and Methods
### GPP Modeling Approach  
The cloud-adjusted light use efficiency model (LUEc) [13] is an adaptation of the simple light use efficiency model of [PERSON] [21] based on earlier progressive work [3; 7] to incorporate scalars to estimate daily GPP as:  
\[\text{daily GPP}=\varepsilon_{0}\times\text{C}_{\text{scalar}}\times\text{T }_{\text{scalar}}\times\text{W}_{\text{scalar}}\times\text{P}_{\text{scalar}} \times\text{APAR} \tag{8}\]  
\(\varepsilon_{0}\) is the daily light use efficiency during clear sky conditions, APAR is the daily photosynthetically active photon flux absorbed by the green portion of the canopy (Equation (10)); the scalars account for the impact of diffuse light (\(\text{C}_{\text{scalar}}\)), air temperature (\(\text{T}_{\text{scalar}}\)), water stress (\(\text{W}_{\text{scalar}}\)), and phenology (\(\text{P}_{\text{scalar}}\)). \(\varepsilon_{0}\) and the four scalars combined represent the well-known daily light use efficiency term, \(\varepsilon\)[21]:  
\[\text{daily GPP}=\varepsilon\times\text{APAR} \tag{9}\]  
where  
\[\text{APAR}=\text{PAR}_{\text{in}}\times[1-\exp(-\text{k}\times\text{gLA})] \tag{10}\]  
Canopy extinction coefficients are the same as those used in the previous study [13] and are the average value of k for each crop when gLAI is greater than 1.5 m\({}^{2}\) m\({}^{-2}\) and dead LAI is less than 0.5 m\({}^{2}\) m\({}^{-2}\). Calculations of the scalars follow those previously mentioned using gridded Daymet and MODIS-derived LAI values instead of AmeriFlux on-site meteorological and biophysical observations as model input. This was done to meet our objective of evaluating the LUEc applicability in using input data derived from remotely sensed satellite data and gridded weather datasets to evaluate the potential to provide regional GPP estimates. A summary of each scalar is provided here but the reader is directed to [PERSON] et al. [13] for details. \(\text{C}_{\text{scalar}}\). \(\text{C}_{\text{scalar}}\) accounts for the effects of diffuse lighting on photosynthesis [3]. Plants tend to use diffuse light more efficiently than direct sunlight. \(\varepsilon\) will increase on overcast days, where lighting is more diffuse than on clear days. \(\text{C}_{\text{scalar}}\) is calculated as:  
\[\text{C}_{\text{scalar}}=\text{a}+\beta\times[(\text{PAR}_{\text{d}}/\text{ PAR}_{\text{in}})-0.17] \tag{11}\]  
The term \(\beta\) is the sensitivity of daily light use efficiency to diffuse light and \(\text{PAR}_{\text{d}}\) is the diffuse PAR flux. As \(\text{PAR}_{\text{d}}\) is not commonly measured, the ratio \(\text{PAR}_{\text{d}}/\text{PAR}_{\text{in}}\) can be approximated using a cloudiness coefficient (CC) term [13]:  
\[\text{PAR}_{\text{d}}/\text{PAR}_{\text{in}}=1.08\text{CC}+0.21 \tag{12}\]  
which is determined from \(\text{PAR}_{\text{in}}\) and PAR potential (\(\text{PAR}_{\text{pot}}\)):  
\[\text{CC}=1-(\text{PAR}_{\text{in}}/\text{PAR}_{\text{pot}}) \tag{13}\]PAR\({}_{\rm pot}\) refers to the estimated potential amount of incoming PAR flux, accounting for influences such as time of year, latitude, atmospheric pressure, and elevation as calculated by [PERSON] and [PERSON] [17] with corrections reported in [PERSON] et al. [13]. T\({}_{\rm scalar}\). Initially developed by [PERSON] et al. [22] in regions excluding croplands, T\({}_{\rm scalar}\) takes into account temperature effects on photosynthesis. The scalar is calculated using mean daily temperature, T\({}_{\rm avg}\), calculated as the average of Daymet minimum and maximum temperatures. The constants for minimum temperature, maximum temperature, and optimal temperature (10, 48, and 28 \({}^{\circ}\)C, respectively) of [PERSON] et al. [23] designed specifically with maize were used to define T\({}_{\rm scalar}\) as:  
\[\rm T_{scalar}=[(T_{avg}-10)\times(T_{avg}-48)]/[(T_{avg}-10)\times(T_{avg}-48 )]-(T_{avg}-28)^{2}\} \tag{14}\]  
while croplands were not examined in [PERSON] et al. [22], values for ecoregions were consistent.