## 4 Discussion
### Issues with Yield Estimation across Different Years  
The goal of this study was to establish a crop yield estimation model applicable across different years for regions with mixed crops using MODIS vegetation indices. The long-term crop yield increasing trend has not been considered in some of the similar yield estimation models [1; 21; 42]. Using a regression tree approach, [PERSON] estimated corn and soybean yields from MODIS NDVI and the daytime land surface temperature (LST) in the United States corn belt region [1]. The estimation error for the years 2006-2011 was 0.38-0.47 t/ha for soybean and 0.96-1.26 t/ha for corn. Taking into consideration the yield trends, we obtained an estimation error of 0.29-0.32 t/ha for soybean and 0.74-0.87 for corn using peak growing stage EVI2 only. Using a simple linear regression and phenologically adjusted MODIS EVI2, [PERSON] and [PERSON] estimated crop yields in Central United States [42], and obtained a relative estimation error of 8%-14% for soybean and 9%-12% for corn in the years 2004-2009. In our study, the estimation error using crop-specific masks was 9.7% for soybean and 7.3% for corn. This shows the effectiveness of our model for crop yield estimation. Although the established multiple linear regression models performed well for yield estimation of the three crops across different years, large estimation error can happen in some years. Figure 9 shows the comparison of MRAE for yield estimation, obtained using the all-year multiple linear regression models and using the year-specific strongest linear regression models based on time-series EVI2 only. Each sample represents estimation error for one year. The samples reside mostly below the 1:1 lines, showing a lower estimation accuracy using the all-year model. For winter wheat, the difference between the all-year model and the year-specific model was relatively small. The largest difference was in 2016 for the models using the general cropland mask, with MRAE of 16% for the all-year model and 10% for the year-specific model, and respective MRAE of 11% and 13% for the models using crop-specific mask (Figure 9a). For corn, the largest difference was observed in 2004, with MRAE of 14% using crop specific mask, 12% using the general cropland mask for the all-year model, and 4% for the year-specific model (Figure 9b). For soybean, the largest difference was observed in 2004 (15% and 16% using the all-year model, and 6% and 7% using year-specific model, for general cropland mask and crop-specific mask, respectively) and 2007 (24% and 20% using the all-year model, and 7% and 11% using the year-specific model, for general cropland mask and crop-specific mask, respectively) (Figure 9c). This large difference in estimation errors between  
Figure 8: Relationships of county level areal proportions of corn and soybean combined with (**a**) EVI2 at day-of-year (DOY) 153 and (**b**) corn yield. the all-year model and the year-specific model might have been induced by a lower than normal precipitation in the maturity stage of the two crops (in September). Figure 10 shows the monthly precipitation during July-September versus the long term monthly precipitation normal, as obtained from the weather station in London, Ontario. The monthly precipitation in September of 2004 (18.4 mm) and 2007 (44.6 mm) was much lower than normal (98.9 mm), which may have impacted crop growth after the peak stage in August, which had not been captured by peak growing stage EVI2. It was considered that the year-specific model captured the spatial variability of yields, whereas the all-year model captured both spatial and temporal variability. It then seems that spatial variability of corn and soybean yields were captured by EVI2 better than that of winter wheat, as demonstrated by a generally lower MRAE using the year-specific model. In contrast, the all-year models showed an inefficiency in capturing inter-annual variability of corn and soybean yields for some years (Figure 9b,c).