# Regional Crop Gross Primary Productivity and Yield Estimation Using Fused Landsat-MODIS Data
## 3 Results
### Crop Yield Monitoring in Montana  
Using the calibrated HI\({}_{\rm GPP}\) values for each crop type (Table 3), crop yield (Yield\({}_{\rm M}\)) was estimated for each MT crop type over the 2008 to 2015 study period. Crop production was then calculated as crop yield multiplied by the total planted area each year for each crop type across MT. The comparisons of the estimated crop production (P\({}_{\rm M}\)) with reported annual county-level NASS crop production (P\({}_{\rm N}\)) values for the 2008 to 2015 record and MT domain are summarized in Table 5 and Figure 5; these results indicated strong correspondence between P\({}_{\rm M}\) and P\({}_{\rm N}\) at the MT county level (\(r\geq 0.85\), \(p<0.05\)). The P\({}_{\rm M}\) results also showed large spatial and annual variability in MT crop yields, which were generally consistent with the NASS crop production survey record. The P\({}_{\rm M}\) results showed the strongest correlation with P\({}_{\rm N}\) for durum wheat (\(r\approx 1.00\), \(p<0.05\)), with moderate model bias (\(-10.2\%\)) and low relative RMSE (\(21.9\%\)). The P\({}_{\rm M}\) relationship with P\({}_{\rm N}\) for alfalfa had the lowest correlation (\(r=0.85\)), the second largest relative bias (\(-11.0\%\)) and the largest relative RMSE (\(42.3\%\)) difference due to larger annual fluctuations in model estimated production than the county survey record. Alfafa for hay production is mixed with grasses and occurs on both irrigated and non-irrigated lands across nearly all MT counties, which may explain the relatively larger estimation errors for this crop. The P\({}_{\rm M}\) and P\({}_{\rm N}\) relationship for winter wheat showed the strongest correspondence (\(r=0.99\), \(p<0.05\)), with relatively low bias (\(-1.5\%\)) and RMSE (\(21.0\%\)). Crops that are mostly rainfed in MT (barley, peas, durum wheat, winter wheat) showed overall lower average estimation uncertainties (Table 5; Figure 5). The model crop production results showed strong correlation (\(r=0.96\)) and low relative bias (\(-7.8\%\)) with the reported NASS county-level data when the model results were combined for all major MT crops during the 2008 to 2015 study period. However, the model results showed a lower RMSE (\(37.0\%\)) performance, mainly due to the relatively large difference between P\({}_{\rm M}\) and P\({}_{\rm N}\) for alfalfa. The spatial pattern of estimated 30-m resolution Yield\({}_{\rm M}\) results is illustrated in Figure 6 for winter wheat in 2015. The 30-m results reveal the heterogeneous distribution of field dimensions and crops within the region, as well as the large variation of Yield\({}_{\rm M}\) levels for winter wheat driven largely by spatial and temporal variations in NDVI. Winter wheat accounted for approximately 52.2% of the total cropland area in Liberty County and 24.1% of the total cropland area across MT in 2015. However, this crop type is distributed with other crops (shown in grey) in a complex spatial mosaic that is effectively delineated by the 30-m results. Figure 5: The comparisons between modeled annual crop production and USDA NASS reported county-level crop production data during the study period of 2008 to 2015 for the major crop types across Montana, including alfalfa, barley, maize, peas, durum wheat, spring wheat and winter wheat. The red dotted line is the 1:1 line, while the black dashed line is the linear regression relationship. Despite the enhanced delineation of field characteristics, the 30-m resolution Yield\({}_{\text{M}}\) results showed relatively low correspondence with the field-scale crop yield data (Yield\({}_{\text{F}}\)) obtained at four farms representing barley, peas, spring wheat and winter wheat.