## 2 Study Area and Datasets
### Data Processing  
We first extracted the cropland pixels from the CDL recorded as corn (ID = 1) and soybean (ID = 5). Then, we carried out spatial re-arrangement to distribute the input variables (NDVI, EVI, LAI, FPAR, GPP, PPT, TMAX, TMIN, TMEAN, and SM) on the CDL grid, using the nearest neighbor method. By referring to the quality index of the MODIS products, only the best-quality pixels were extracted for NDVI, EVI, LAI, FPAR, and GPP. For comparison with county-level yield statistics, all the gridded variables were aggregated in accordance with the polygon zone of each county using a zonal mean operation. Finally, two databases were built for corn- and soybean-sown areas (Figure 2).  
For the 10 candidate explanatory variables, we conducted a multi-collinearity test using the variation inflation factor (VIF). The VIF of the \(j\)-th explanatory variable \(x_{j}\) is expressed as:  
\[\text{VIF}\Big{(}x_{j}\Big{)}=\frac{1}{1-R_{j}^{2}}, \tag{3}\]  
where \(R_{j}^{2}\) is the R-squared value of the regression equation, with \(x_{j}\) as a response variable and the other \(x\) variables as regressors. It indicates the degree to which an explanatory variable is correlated with the other explanatory variables. The actual input variables for our crop yield models were selected through the multi-collinearity test. The variables with VIF \(>\) 10 were generally excluded from the input data, because they could respond erratically to small changes in the model or the data [(39)]. Six variables were selected as valid explanatory variables: EVI, LAI, GPP, PPT, SM, and either TMAX (for corn) or TMIN (for soybean). The optimal temperature for soybean growth is between 20 and 26 \({}^{\circ}\)C; germination, flowering, and pod development can be delayed with lower temperatures [(40)]. Temperatures of 25-33 \({}^{\circ}\)C are appropriate for the growth of corn, which originated from tropical regions; temperature \(>\) 35 \({}^{\circ}\)C without sufficient rainfall can decrease growth [(41)]. Table 2 shows the correlation coefficients between the selected explanatory variables and the yields for corn and soybean.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Data**} & \multicolumn{1}{c}{**Spatial Resolution**} & \multicolumn{1}{c}{**Temporal Resolution**} & \multicolumn{1}{c}{**Source**} \\ \hline Cropland & CDL\({}^{(1)}\) & 56 m (2006–2009) & & \\  & & 30 m (2010–2015) & Yearly & USDA\({}^{(12)}\) \\ \hline Satellite Images & NDTN\({}^{(2)}\) & 250 m & 16 days & \\  & EVI\({}^{(3)}\) & 250 m & 16 days & \\  & LAI\({}^{(4)}\) & & & \\  & FPAR\({}^{(5)}\) & 500 m & 8 days & \\  & GPP\({}^{(6)}\) & & & \\ \hline \multirow{3}{*}{Meteorological Data} & PPT\({}^{(7)}\) & & & \\  & TMAX\({}^{(8)}\) & 4 km & Monthly & PRISM\({}^{(14)}\) Climate Group \\ \cline{1-1}  & TMIN\({}^{(10)}\) & & & \\ \hline Hydrological Data & SM\({}^{(11)}\) & 0.25\({}^{\circ}\) & Monthly & NASA GES DISC\({}^{(15)}\) \\ \hline Crop Yield Statistics & Corn Soybean & County & Yearly & USDA\({}^{(12)}\) \\ \hline \multicolumn{5}{l}{(1) Cropland Data Layer; (2) Normalized Difference Vegetation Index; (3) Enhanced Vegetation Index; (4) Leaf Area Index; (5) Fraction of Photosynthetically Activate Radiance; (6) Gross Primary Production; (7) Precipitation; (8) Maximum air temperature; (9) Minimum air temperature; (10) Mean air temperature; (11) Soil Moisture; (12) United States Department of Agriculture; (13) National Aeronautics and Space Administration’s Earth Observing System Data and Information System; (14) Parameter-elevation Regression on Independent Slopes Model; (15) NASA’s Goddard Earth Sciences Data and Information Services Center.} \\ \end{tabular}
\end{table}
Table 1: Summary of the dataset used in this study.