## 2 Materials and Methods
### Statistical Analysis  
To explore the interannual changes of winter wheat cropping areas and grain production from 2008-2018, we calculated the anomaly of each variable as the difference between the value in a specific year and the multi-year average from 2008-2018, and then normalized it by the multi-year average. We used linear regression models to quantify the relationships between grain production and cropping areas, and between GPP\({}_{\text{VPM}}\) and grain production at national and county scales. The performance of models was assessed using the coefficient of determination (R\({}^{2}\)), bias, and root mean square error (RMSE) between the modeled grain production estimates and the NASS grain production statistics. The regression slope between grain production and GPP\({}_{\text{VPM}}\), representing the conversion coefficient from GPP\({}_{\text{VPM}}\) to grain production, was also termed as the GPP-based harvest index (HI\({}_{\text{GFP}}\)).  
\[R^{2}=\left(\frac{\sum_{i=1}^{n}\left(GP_{sim}(i)-\overline{GP_{sim}}\right) \times\left(\left(GP_{NASS}(i)-\overline{GP_{NASS}}\right)\right)}{\sqrt{ \sum_{i=1}^{n}\left(GP_{sim}(i)-\overline{GP_{sim}}\right)^{2}}\sqrt{\sum_{i= 1}^{n}\left(GP_{NASS}(i)-\overline{GP_{NASS}}\right)^{2}}}\right)^{2} \tag{5}\]  
\[RMSE=\sqrt{\sum_{i=1}^{n}\left(GP_{sim}(i)-GP_{NASS}(i)\right)^{2}/n} \tag{6}\]  
\[bias=GP_{sim}-GP_{NASS} \tag{7}\]where \(GP_{sim}\) is the simulated grain production at a county scale based on linear models, \(\overline{GP_{sim}}\) is the mean \(GP_{sim}\) across counties in the CONUS, \(i\) is the county number, and n is the total number of counties. As there are missing NASS statistics data for some counties over the years, we only kept those counties with continuous data from 2008-2018. The total number is 795. \(GP_{NASS}\) is the NASS grain production, \(\overline{GP_{NASS}}\) is the mean \(GP_{NASS}\) across counties in the CONUS.  
In-Sensor Forecasting of Winter Wheat Grain Production Using Cumulated GPP\({}_{\text{VPM}}\) Data  
Accurate and timely prediction of grain production and yield is one requirement in crop production monitoring programs. To explore the in-season prediction skill from GPP\({}_{\text{VPM}}\), linear regression models were applied between cumulated GPP (GPP\({}_{\text{cum}}\)) over time and grain production at the county scale (see Equation (1)).  
\[Grain\ Production=a\times\sum_{1}^{t}(GPP_{t}\times k)+b\ \ \ t=1,2,3,\ldots,46 \tag{8}\]  
where \(t\) is the time intervals in a year (ranging from 1 to 46), as GPP\({}_{\text{VPM}}\) data are at an 8-day temporal resolution and have 46 estimates within each year; \(k\) is the number of days within a time interval, being 8 days for \(t=1\) to 45, and 5 or 6 days (non-leap year, leap year) for \(t=46\). In this study, we used a calendar year schedule to run the statistical models for all counties, though winter wheat is usually planted in late fall of the previous year (e.g., late September to October). The GPP\({}_{\text{cum}}\) in the previous fall season is usually low and was not included in Equation (1), as we tried to make the task simple, without delineating the exact planting dates of winter wheat in the fall season of the previous year. We also assumed that it has a negligible effect on the modeling skills.