## 3 Results
### Performances of DNNs for Corn and Soybean Yield Prediction  
County-level yields of corn and soybean, monthly means of climate (T, P, and VPD) and maxima of EVI and SIF from May to September were used to train DNN models. Table 1 shows the performances of DNN models with different combinations of inputs. Models with inputs of SIF, EVI, SIF plus EVI, and Climate have moderate to high coefficients of determination, indicating the usefulness of satellite and climate information in predicting corn and soybean yields. Among models only with EVI, SIF, and climate as inputs, the models with climate predictors performed the best, explaining 76% and 82% variations of county-level corn and soybean yields, respectively. Models only with monthly maximum SIF as inputs performed the poorest. The integration of SIF and EVI could improve the performance of yield estimating models that only used either SIF or EVI data as predictors. In addition, the combination of satellite and climate data significantly improved model performances. Specifically, models with both EVI and climate as inputs outperformed the climate-based models, increasing R\({}^{2}\) from 0.76 to 0.86 for corn and from 0.82 to 0.87 for soybean. The combination of climate information with SIF also improved the estimates of the yields, with R\({}^{2}\) increased from 0.76 to 0.80 for corn and from 0.82 to 0.83 for soybean. These results suggest that OCO-2 SIF could make some contributions to the yield estimate, but less than MODIS EVI. The models with all SIF, EVI, and climate variables as inputs performed similar to the models with EVI and climate as inputs, implying that OCO-2 SIF provided less useful information for capturing the spatial variations of corn and soybean yields in the study area than EVI. Figure 3: Correlation coefficients of county-level corn (**a**) and soybean (**b**) yields with individual variables in different months. The \(SIF_{mom}\), \(EVI_{mom}\) and climate variables are monthly mean values. The \(SIF_{max}\) and \(EVI_{max}\) are monthly maximum values (P = precipitation; T= temperature; VPD = vapor pressure deficit). The analysis of variance (ANOVA) and the Tukey Honest Significant Difference (HSD) tests [84] were conducted to investigate whether the differences among model performances in the 100 repeated experiments are significant (Tables S2 and S3). The ANOVA tests for both corn and soybean showed significant differences among performances of different models (\(p<0.001\)). Additionally, the Tukey HSD tests demonstrated that most of the performance differences between paired models were significant, except for the differences between 'EVI + Climate' and 'SIF + EVI + Climate' models for both corn and soybean, and between 'Climate' and 'SIF + EVI' for corn. These results further confirmed that the addition of SIF data into the 'EVI + Climate' models did not improve the estimates of both corn and soybean yields. However, there are significant differences between the 'EVI' and the 'SIF + EVI' models, and between the 'Climate' and the 'SIF + Climate' models. This indicated that the inclusion of SIF could improve the 'Climate' model and 'EVI' model for estimating yields of corn and soybean. The performances and stability of DNNs were compared by summarizing the repeated CV results. As shown in Figure 4, the 'Climate' model had lower minimum and first quantile values of R\({}^{2}\) than those of the 'SIF + Climate' and 'EVI + Climate' models for both corn and soybean. This means that, even for the worst cases, the models with both satellite and climate predictors outperformed the models with only climate data as inputs. A similar finding was also observed between the 'SIF + EVI' and 'EVI' models for soybean, and the former performed better than the latter under the worst and other conditions.