## 4 Results
### Analysis at the State Level  
The analysis at the state level was performed in the same manner as at the county level, except that we did not try to separate irrigated counties. The lower R\({}^{2}\) values of the yields in 2011 (Figure 7) for corn (0.51) and for soybeans (0.58) were partly caused by a large underestimation in Kansas and Nebraska due to the irrigation effects. Because plants in irrigated areas often have higher transpiration rates that help cool their leaves, the MODIS-GPP algorithm, which is sensitive to the environmental factors such as daily temperature or vapor pressure deficit, would tend to underestimate GPP in irrigated areas. Interestingly, the yields were overestimated for the northern states, such as North Dakota and Wisconsin, which may  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**Corn**} & \multicolumn{2}{c}{**Soybean**} \\ \cline{2-7}  & **R\({}^{2}\)** & **RMSE (MT/ha)** & **ME (MT/ha)** & **R\({}^{2}\)** & **RMSE (MT/ha)** & **ME (MT/ha)** \\ \hline
2009 & 0.55 (0.15) & 1.21 (5.52) & \(-\)0.60 (\(-\)5.39) & 0.50 (0.35) & 0.38 (0.86) & \(-\)0.07 (0.77) \\
2010 & 0.54 (0.22) & 1.17 (4.65) & \(-\)0.14 (\(-\)4.38) & 0.73 (0.53) & 0.30 (0.97) & \(-\)0.09 (0.89) \\
2011 & 0.77 (0.46) & 0.89 (4.56) & \(-\)0.18 (\(-\)4.28) & 0.66 (0.53) & 0.38 (1.06) & \(-\)0.02 (0.95) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistics between crop yields estimated from our approach using MODIS data and reported by the NASS for rainfed counties for each year from 2009 to 2011. For comparison, values in parentheses are statistics using the standard MOD17 products.  
Figure 6: Comparisons between crop yields estimated from MODIS data and reported by the NASS for rainfed counties in the Midwestern US. The black line is the 1:1 line. (**A**) Rainfed corn; (**B**) Rainfed soybean.  
have been because crop planting typically starts later in those states than in other regions. It would be more appropriate to use the LAI values from late May rather than mid-May to approximate the LAI of other vegetation during the growing season. Future analysis should incorporate the timing of crop phenology derived from MODIS to improve the yield estimation [59].  
We also estimated the final crop production based on satellite data using the following techniques: (i) the crop yields were estimated from MODIS data; (ii) the harvested areas were derived from the CDL maps by counting pixels within each state, and (iii) the crop production was calculated as the product of crop yields and harvested areas. Compared with the NASS reported data in the Midwestern US, the total crop productions were underestimated (Table 4) due to the underestimated yields in irrigated counties. The errors of estimated total productions were -1.5% for corn and -0.6% for soybeans in 2011 and fall within the acceptable ranges in other years. Note that the crop areas derived from the NASS CDL maps may also contribute errors to our estimation of crop production here.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{3}{c}{**Corn Production**} & \multicolumn{3}{c}{**Soybean Production**} \\ \cline{2-7}  & **Estimated (Tg)** & **Reported (Tg)** & **Error** & **Estimated (Tg)** & **Reported (Tg)** & **Error** \\ \hline
2009 & 253.6 & 291.7 & \(-\)13.04\% & 68.2 & 75.6 & \(-\)9.74\% \\
2010 & 268.1 & 276.3 & \(-\)2.95\% & 73.9 & 77.7 & \(-\)4.79\% \\
2011 & 273.0 & 277.1 & \(-\)1.49\% & 69.8 & 70.2 & \(-\)0.56\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Estimated and reported corn and soybean production for 12 states in the Midwestern US.  
Figure 7: Comparisons between crop yields estimated from MODIS data and reported by the NASS for states in the Midwestern US. The black line is the 1:1 line. (**A**) Corn; (**B**) Soybean.