## 3 Results
### Importance of Different Variables  
The feature importance (FI) scores of predictors in the 'EVI + SIF + Climate' models were calculated for examining the importance of individual predictors in estimating corn and soybean yields. The 'EVI + SIF + Climate' models were used because they included the most comprehensive inputs relative to other models using only satellite or climate predictors. Figure 7 shows the importance of the variables in predicting corn and soybean yields, with a higher FI value indicating a greater contribution to the  
Figure 6: Spatial distribution of percentage error (PE) of county-level corn and soybean yields estimated by models using either satellite or climate predictors. Left panels are the maps for the corn, and right are for the soybean. The figure includes results from models that only input SIF (**a,b**), only input EVI (**c,d**), input both SIF and EVI (**e,f**), and only input climate data (**g,h**). In each plot, the density plot in the upright corner presents the overall distribution of PE of all the available counties. The red dashed lines and ‘M’ in the density plots represent the mean values of PE, and the black ones are the referenced lines located at zero. Positive values mean that estimated yields were lower than census data, vice versa.  
model performances. It should also be noted that the FI analysis is model-specific because different variables might have dissimilar functions in different DNNs, and the FI results for other models were presented in Figures S4-S6.  
In the 'EVI + SIF + Climate' model, both satellite and climate predictors in the peak growing months (from June to August), which is corresponding with the grain filling and reproductive periods in the Midwestern U.S. [85], were essential in estimating crop yields. Specifically, EVI in July was the most important variable determining yields of both corn and soybean. In this month, corn and soybean here started the reproductive stage [45; 86], and EVI effectively captures the growing status of the crop. EVI in August is the second important factor for predicting soybean yield and the third important remote sensing factor for predicting corn yield in the Midwest states, which was also confirmed by a previous study [46]. They declared that the inclusion of EVI in August noticeably reduced the uncertainty of yield prediction. As for climate variables, VPD in July and temperature in June acted as the important determinants for yields of corn and soybean, respectively. VPD has a strong impact on the stomatal conductance of crops, which affects carbon assimilation [7; 87; 88]. As shown in Figure 3, VPD in July had a significant negative correlation with the corn yield. Temperature determines VPD and influences photosynthetic activities, and thus constrains biomass production and influences crop yield [89; 90; 91]. In the study region, the temperature in June played an important role in determining the yield of soybean, just following EVI in July and August (Figures 3 and 7). SIF was generally less important for estimating corn and soybean yields in comparison with EVI and climate variables. The information carried by SIF into the model might be overshadowed by EVI. As shown in Table 1, 'EVI + SIF + Climate' and 'EVI + Climate' models performed very similarly.