## 3 Results
### Relationships of OCO-2 SIF and MODIS VIs with Autumn Crop Production at Monthly and Seasonal Scales
The best performance was observed in the autumn crop productions that were estimated using SIF\(757^{\prime}\) in July (R\({}^{2}\) = 0.678, \(p\) < 0.01; RMSE = 748.901 ten kilotons; MAE = 567.629 ten kilotons). The OCO-2 SIF products performed better than MODIS VIs products when estimating the autumn crop production and SIF\(757^{\prime}\) performed best. We conducted a detailed analysis of the estimation of SIF\(757^{\prime}\) in order to identify the constraints that affect the estimation accuracy of SIF (Figure 4). We calculated the deviation percentage of the autumn crop production estimated while using SIF\(757^{\prime}\) in 2016, and the percentage of cropland that was covered by SIF data in each province. Meanwhile, the minimum percentage of cropland covered by SIF data is up to 3.762% (Anhui) and the maximum percentage of cropland covered by SIF data is up to 4.524% (Heilongjiang). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**June**} & \multicolumn{4}{c}{**July**} \\ \hline  & SIF\(757^{\prime}\) & SIF\(771^{\prime}\) & EVI\({}^{\prime}\) & NDVI\({}^{\prime}\) & SIF\(757^{\prime}\) & SIF\(771^{\prime}\) & EVI\({}^{\prime}\) & NDVI\({}^{\prime}\) \\
**R\({}^{2}\)** & 0.526 & 0.548 & 0.628 & 0.667 & 0.692 & 0.716 & 0.664 & 0.672 \\ \(p\)**-value** & & \multicolumn{4}{c}{\(<\)0.01} & & \multicolumn{4}{c}{\(<\)0.01} & \\ \hline  & \multicolumn{4}{c}{**August**} & \multicolumn{4}{c}{**Summer**} \\ \hline  & SIF\(757^{\prime}\) & SIF\(771^{\prime}\) & EVI\({}^{\prime}\) & NDVI\({}^{\prime}\) & SIF\(757^{\prime}\) & SIF\(771^{\prime}\) & EVI\({}^{\prime}\) & NDVI\({}^{\prime}\) \\
**R\({}^{2}\)** & 0.669 & 0.683 & 0.652 & 0.666 & 0.686 & 0.702 & 0.656 & 0.666 \\ \(p\)**-value** & & \multicolumn{4}{c}{\(<\)0.01} & & \multicolumn{4}{c}{\(<\)0.01} & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The correlations between the SIF\(757^{\prime}\), SIF\(771^{\prime}\), EVI\({}^{\prime}\), NDVI\({}^{\prime}\), and the government’s autumn crop production statistics in China during June to August 2015 at monthly and seasonal scales. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Time** & **Parameter\({}^{\prime}\)** & **Model** & **N** & **R\({}^{2}\)** & \(p\)**-Value** \\ \hline \multirow{4}{*}{July} & SIF\(757^{\prime}\) & \(\hat{y}_{i}=0.01338\times x_{i}+604.01428\) & 30 & 0.692 & \textless{}0.01 \\  & SIF\(771^{\prime}\) & \(\hat{y}_{i}=0.02050\times x_{i}+608.13718\) & 30 & 0.716 & \textless{}0.01 \\  & EVI\({}^{\prime}\) & \(\hat{y}_{i}=0.01280\times x_{i}+547.13583\) & 30 & 0.664 & \textless{}0.01 \\  & NDVI\({}^{\prime}\) & \(\hat{y}_{i}=0.00869\times x_{i}+540.97517\) & 30 & 0.672 & \textless{}0.01 \\ \hline \hline \end{tabular} Note: \(\hat{y}_{i}\) represents the estimated autumn crop production; \(x_{i}\) represents SIF\(757^{\prime}\), SIF\(771^{\prime}\), EVI\({}^{\prime}\) and NDVI\({}^{\prime}\), respectively.  
\end{table} 
Table 2: Best-fit models for each parameter\({}^{\prime}\), which was used to estimate the autumn crop production in China. The lower the percentage of cropland covered by SIF data, the higher the deviation percentage of autumn crop production estimated while using the SIF757\({}^{\prime}\). Meanwhile, in Beijing, Hainan, Qinghai, Tianjin, Ningxia, and Xinjiang, where the autumn crop production is approximately less than five million tons and the elevation is higher than 1000 m, the deviation percentage of autumn crop production estimated using the SIF757\({}^{\prime}\) exceeded 100% (Figure 4a). Besides, in Sichuan, Chongqing, Hunan, Shaanxi, and other provinces with large undulating terrain and broken cropland, the autumn crop production that was estimated using the SIF757\({}^{\prime}\) was also not very accurate (Figure 4).