## 3 Results
### Spatiotemporal Dynamics of GPPVPM and Grain Production from NASS Dataset from 2008-2018  
At the national scale, winter wheat grain production showed a decreasing trend from 2008-2018 (Figure 6), which is largely determined by the decrease in planted and harvested area (Figure 1). GPPVPM showed a similar decreasing trend as grain production from 2008 to 2018, but with strong response in some drought years, such as 2011 and 2014. At the county scale, we quantified the interannual trends of GPPVPM and grain production from 2008-2018 (Figure 7). Out of 291 counties with continuous NASS grain production data during the 11 years, winter wheat grain production showed increasing trends in 90 counties and decreasing trends in 201 counties (Figure 7a,c). The interannual trend of NASS grain production had a strong linear relationship with the that of GPPVPM (Figure 7e). Out of 2609 counties in the CONUS, GPPVPM data show 821 counties with a substantial increase in the number of 2008-2018 (Figure 7f). Figure 5: The relationships between county-level winter wheat grain production and cropping areas in the CONUS from 2008 to 2018 from the CDL and NASS datasets (plt_CDL, plt_NASS, harv_NASS). (**a**) Grain production versus CDL planted area, (**b**) grain production versus NASS planted area, and (**c**) grain production versus NASS harvested area. The black solid line is the linear regression result for all the counties from 2008 to 2018. Figure 6: Interannual changes of (**a**) NASS winter wheat grain production (prod_NASS) and total GPP estimated from VPM (GPPVPM), (**b**) anomalies of prod_NASS and GPPVPM for the mean of 2008–2018. ing trend and 1788 counties with a decreasing trend (Figure 7b,d). Many counties with a decrease in \(\mathrm{GPP_{VPM}}\) were located in the Great Plains (South Dakota, Kansas, Oklahoma) and the states along the Mississippi River (Figure 7b,d). Many counties in the northwestern states and the western edge of the Southern Great Plains showed an increasing trend of \(\mathrm{GPP_{VPM}}\) (Figure 7b,d). The probability distributions of the interannual trends of NASS grain production and \(\mathrm{GPP_{VPM}}\) were similar, with narrow ranges of normal distribution (Figure 7f). Figure 7: Interannual trends of NASS winter wheat grain production (prod\(\_\)NASS) and \(\mathrm{GPP_{VPM}}\) from 2008–2018 in the CONUS at a county scale. (**a**) Changing trend for NASS grain production from 2008–2018; (**b**) changing trend for \(\mathrm{GPP_{VPM}}\) from 2008–2018; (**c**) \(p\)-value of the linear regression model for calculation of NASS grain production trends, S means significant trend with \(p<0.05\), and NS means not significant trend with \(p>0.05\); (**d**) similar to (**c**), but for the trend of \(\mathrm{GPP_{VPM}}\); (**e**) linear regression between the trend of NASS grain production and of \(\mathrm{GPP_{VPM}}\) for those counties with continuous NASS grain production and \(\mathrm{GPP_{VPM}}\) data from 2008–2018; (**f**) histograms for the trend of NASS grain production and of \(\mathrm{GPP_{VPM}}\). The Relationships between County-Level GPP\({}_{\text{VPM}}\) and Winter Wheat Grain Production from 2008 to 2018  
At the county scale, the relationships between GPP\({}_{\text{VPM}}\) and winter wheat grain production from 2008 to 2018 varied from one year to another (Figure 8a), with R\({}^{2}\) values ranging from 0.59 (2008) to 0.75 (2016) (Table 3). The slope values in the models with no intercept (GP = HI\({}_{\text{GPP}}\times\) GPP\({}_{\text{VPM}}\)) varied from 0.25 (2012) to 0.33 (2011) (Table 3). When all the county-year data in the CONUS were used in the linear regression model for GPP\({}_{\text{VPM}}\) and grain production (GP), GPP\({}_{\text{VPM}}\) could explain 68% of the variance in winter wheat grain production (Figure 8a). The relationships (Figure 8b) were also affected by the differences between the planted area calculated from CDL and harvested area from NASS statistics, which varied according to county and year (Figure 3).