## 3 Results  
### Relationships of OCO-2 SIF and MODIS VIs with Autumn Crop Production at Monthly and Seasonal Scales  
We compared the relationship between the SIF757', SIF771', EVI', NDVI', and the government's autumn crop production statistics at monthly and seasonal scales. The results for the 2015 summer show that the converted OCO-2 SIF data, MODIS VIs, and the government's autumn crop production statistics were strongly correlated (Figure 2). In general, SIF771' (R2 = 0.548-0.716, \(p\) < 0.01) was more strongly correlated with the government's autumn crop production statistics than SIF757' (R2 = 0.526-0.692, \(p\) < 0.01). In addition, EVI' (R2 = 0.628-0.664, \(p\) < 0.01) and NDVI' (R2 = 0.666-0.672, \(p\) < 0.01) had equally strong correlations with the government's autumn crop production statistics. The strongest relationship of SIF757' (R2 = 0.692, \(p\) < 0.01), SIF771' (R2 = 0.716, \(p\) < 0.01), EVI' (R2 = 0.664, \(p\) < 0.01), and NDVI' (R2 = 0.672, \(p\) < 0.01) was observed in July (Figure 2b). The mean R2 of SIF757' and SIF771' were 0.643 and 0.662. Additionally, the mean R2 of EVI' and NDVI' were 0.650 and 0.668. Moreover, the correlation between SIF' and autumn crop production was higher than VIs' for both monthly and seasonal scales, except in June, during the summer of 2015 (Table 1). In addition, the correlation between VIs' (EVI' and NDVI') and autumn crop production do not greatly vary among months. By contrast, the correlation between SIF' (SIF757' and SIF771') and autumn crop production among the months exhibited great variation. Figure 2: The correlations between the SIF757’, SIF771’, EVI’, NDVI’, and the government’s autumn crop production statistics (ten kilotons) in China during June to August 2015 at the monthly and seasonal scales. The parameter’ represent SIF757’ (W m\({}^{-2}\) sr\({}^{-1}\) μm\({}^{-1}\)), SIF771’ (W m\({}^{-2}\) sr\({}^{-1}\) μm\({}^{-1}\)), EVI’, and NDVI’, respectively. Performance Evaluation of the Autumn Crop Production Estimated by the Converted OCO-2 SIF and MODIS VIs  
The SIF\({}^{\prime}\) and VIs\({}^{\prime}\) in July had the strongest correlation with the autumn crop production statistics according to the relationship between the SIF\(757^{\prime}\), SIF\(771^{\prime}\), EVI\({}^{\prime}\), NDVI\({}^{\prime}\), and the government's autumn crop production statistics in the summer of 2015 (Figure 2 and Table 1). 4 models con be chosen to estimate autumn crop production (Table 2). The fitted models with \(p\)-values that were lower than 0.01 indicated a significant relationship between the SIF\(757^{\prime}\), SIF\(771^{\prime}\), EVI\({}^{\prime}\), NDVI\({}^{\prime}\), and the government's autumn crop production statistics, and confirmed the reliable predictive capability of these models. Growing evidence suggested that the relationship between vegetation photosynthesis (gross primary productivity, GPP) and SIF is linearly related [41; 42; 43; 44; 45]. Moreover, terrestrial GPP drives the terrestrial food chain [46]. Therefore, we assumed that SIF and production are related linearly and selected the linear model to predict the autumn crop production. The linear models in July (Table 2) were utilized to estimate autumn crop production in each province in 2016 (Figure 3). 2016 was the only one year in which OCO-2 SIF product, MODIS VIs products, and the government's autumn crop production statistics data could be matched, except for 2015. The robustness of the coefficients derived from these production estimation models for each province in 2016 was evaluated while using RMSE and MAE. The scatterplots between the production statistics and estimated productions demonstrated satisfactory results (Figure 3). The estimated autumn crop productions of each model were close to the government's autumn crop production statistics in 2016 (Table 3). Moreover, the performances of SIF\(757^{\prime}\), SIF\(771^{\prime}\), EVI\({}^{\prime}\), and NDVI\({}^{\prime}\) are comparable.