## 2 Materials and Methods
### Analysis  
According to the definition of autumn crop, the final production is most related to the summer season. The satellite-derived data from June to August 2015 and 2016 were extracted while using the following processes. Firstly, we extracted \"SIF 757 nm\" and \"SIF 771 nm\" values (henceforth denoted as SIF757 and SIF771), where the land cover type was cropland with an IGBP index of 12 and removed the negative values, which may affect the results. The SIF data were created as a grid map and resampled to 500 m spatial resolution. Subsequently, the VIs data were also resampled to the same spatial resolution and masked with the cropland data to obtain the cropland VIs data. The cropland data of 2015 and 2016 were obtained from the MCD12Q1 product, respectively. These satellite-derived data were used zonal statistics for 31 China provinces at monthly and seasonal scales by means of ArcGIS10.1 (ESRI, Redlands, CA, USA) to obtain the mean pixel value and the cropland pixels for each province. The converted value was the mean pixel value, multiplied by the cropland pixels. These converted values were henceforth denoted as SIF757', SIF771', EVI', and NDVI'. The relationships of these converted values with autumn crop production statistics were evaluated at monthly and seasonal timescales while using the following equation:  
\[Value_{i}^{\prime}\ =\ \overline{Value_{i}}\times n_{i} \tag{3}\]  
where \(Value_{i}^{\prime}\) and \(\overline{Value_{i}}\) represented the converted satellite-derived product value and the mean satellite-derived product pixel value for each province, respectively; \(n_{i}\) represented the cropland pixels for each province; and, \(i\), which ranged from 1 to 31, represented the province where the statistical data were available when the SIF data passed by. To compare the potential of OCO-2 SIF and MODIS VIs in estimating autumn crop production, the correlations between the converted OCO-2 SIF products (SIF757, SIF771), MODIS VIs (EVI, NDVI), and the government's autumn crop production statistics were evaluated at monthly and seasonal scales. The SIF data were spatially discrete points, because the viewing modes alternate from orbit to orbit. We calculated the value at a monthly scale while using the points that passed by in June, July, and August, respectively. Subsequently, the values at a seasonal scale using the total points of summer (June, July, and August) were calculated. We obtained the monthly scale value directly and calculated the value at seasonal scale while using the average of June, July, and August data since VIs were monthly raster data. The correlations between SIF757', SIF771', EVI', NDVI', and autumn crop production were evaluated while using the coefficient of determination (R\({}^{2}\)). Root mean square error (RMSE) and mean absolute error (MAE) [6; 40] were used to evaluate the performance of crop production estimation. The indicators were calculated while using the following equations:  
\[R^{2}=1-\frac{\sum_{1}^{n}(y_{i}-\hat{y_{i}})^{2}}{\sum_{1}^{n}y_{i}^{2}} \tag{4}\]  
\[RMSE=\sqrt{\frac{\sum_{1}^{n}(y_{i}-\hat{y_{i}})^{2}}{n}} \tag{5}\]  
\[MAE=\frac{\sum_{1}^{n}\abs{y_{i}-\hat{y_{i}}}}{n} \tag{6}\]  
where \(n\) was the number of provinces used for validation. \(\hat{y_{i}}\) was the SIF757', SIF771', EVI', NDVI' (Equation (4)), and estimated autumn crop production (Equations (5) and (6)). Additionally, \(y_{i}\) was the government's autumn crop production statistics (ten kilotons). All of the statistical analyzes were performed while using SPSS Statistics 22 (IBM, Chicago, IL, USA), Origin2017 (OriginLab, Northampton, MA, USA), and MATLAB R2017b (MathWorks, Nadick, MA, USA). Generally, the optimal result is judged by a maximum R\({}^{2}\) value, minimum RMSE, and MAE values. In addition, the relationships between SIF757', SIF771', EVI', NDVI', and the autumn crop production statistics were modeled based on the most relevant month or season data in 2015.