## 3 Results
### Inter-Annual Variability of the Linear Relationships  
Linear regression was conducted for each year between county level yields and time-series EVI2 extracted using the two types of cropland masks. The results for the strongest correlations are shown in Figure 5, which include relative root mean square error (RRMSE, %), coefficient of determination  
Figure 4: Correlation coefficient between crop yield and EVI2 obtained through the multiple linear regression model, using data for all years (2003–2016). EVI2 was extracted using general cropland mask (GM) and crop-specific masks (SM). \(R^{2}\), and mean relative absolute error (MRAE) (%). Annual averages of county level yields and the coefficient of variation (CV) (%) are also shown in Figure 5.  
For winter wheat (Figure 5a,d), county level annual yield variability--represented by CV--was between 10% and 21% during the 14 year period. Except for 2011 using the general cropland mask and 2012 using crop specific mask, the strongest linear correlation between yields and EVI2 was significant at the 5% level (\(n=27\)). The correlations between yields and EVI2 showed a strong inter-annual variation, as represented by both MRAE and DOY, at which the strongest correlation was observed. DOY of the strongest positive correlation ranged between 193 (mid-July) and 241 (end of August) when the general cropland mask was used, and ranged between DOY 121 (early May) and 169 (mid-June) when crop-specific mask was used. MRAE was larger than 10% for a few years and in most cases ranged between 7% and 9%. Figure 5: Annual variation of the strongest correlation between crop yields and time-series EVI2, extracted using a general cropland mask (GM) and crop-specific masks (SM) for winter wheat (**a,d**), corn (**b,e**), and soybean (**c,f**). Yield: average county level yield; \(R^{2}\): coefficient of determiation; CV: coefficient of variation of yields; RRMSE: root mean square error relative to average yield; MRAE: mean relative absolute error. Samples from the three agricultural regions were analyzed together. For corn (Figure 5b,e), CV of county level yields ranged between 7% and 17%. Correlation between yields and EVI2 was significant (\(n=26\)) for all cases. DOY of the largest \(R^{2}\) was between 193 (mid-July) and 257 (mid-September), but mostly in late July and early August. DOY for the two crop masks was about the same for most years but had large differences for some of the years. For instance, the best DOY was 241 using the general cropland mask and 201 using the crop-specific mask in 2006. MRAE was below 8% in most cases, and for some cases was as low as 3%, for example, in 2003 and 2011. MRAE was comparable using the two crop masks, although there was a slight tendency of a smaller MRAE using the general cropland mask. For soybean (Figure 5c,f), CV of county level yields showed a larger inter-annual variation than the other two crops, ranging between 6% (in 2013) and 25% (in 2007). Correlation was significant at the 5% level (\(n=25\)) for all years except for 2014 using the crop-specific mask (\(R^{2}=0.07\)). Similar to that for corn, the time window best for soybean yield estimation was between mid-July and late August. Although estimation error remained relatively low in most cases (MRAE \(<7\%\)), a large difference in the best DOY within a time window of about 40 days after late July (DOY = 193) was also observed. To illustrate the inter-annual variation of the relationships between crop yields and EVI2, scatter-plots between reported crop yields and EVI2 were shown in Figure 6 for 3 years (2006, 2011, and 2016) as examples. EVI2 was extracted using the crop-specific masks from the time with strongest correlation for winter wheat, corn, and soybean, respectively. Inter-annual variability of the relationships between crop yields and EVI2 was remarkable, both in terms of best time for the prediction and the regression models. For winter wheat, the range of yields was much wider in 2011 and 2016 than in 2006, with CV of 21%, 18%, and 13%, respectively.