# Regional Crop Gross Primary Productivity and Yield Estimation Using Fused Landsat-MODIS Data
## 3 Results
### Crop Yield Monitoring in Montana
These results showed moderate correspondence between Yield\({}_{\text{M}}\) and Yield\({}_{\text{F}}\) values for winter wheat (\(r\) = 0.57) and barley (\(r\) = 0.68), but much lower correlations for spring wheat and peas (\(r\) < 0.10), including large negative model biases (\(-\)12.0\(--\)71.4%) and degraded RMSE (32.9-75.3%) relative to the available observations. The small number of field-scale yield observations makes it difficult to draw conclusions about the performance of the algorithm to retrieve field-scale yields. For instance, the Yield\({}_{\text{F}}\) observations for peas only represented one year of data from a single farm, generating the largest relative model bias (\(-\)71.4%) and RMSE (75.3%) among the four crop types represented; whereas, there were only three site-years of data for spring wheat from three different farms, inducing large relative model bias (\(-\)40.1%) and RMSE (50.5%). When all of the field-scale crop yield data were combined, the Yield\({}_{\text{M}}\) performance showed improved correspondence (\(r\) = 0.44, \(p\) < 0.05), relative bias (\(-\)36.1%) and RMSE (48.8%). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Crop Type**} & **Mean of P\({}_{\text{N}}\)** & **Mean of P\({}_{\text{N}}\)** & \multirow{2}{*}{\(r\)} & **Bias** & **Relative** & **RMSE** & **Relative** \\  & **(10\({}^{3}\) Ton)** & **(10\({}^{3}\) Ton)** & **(10\({}^{3}\) Ton)** & **(10\({}^{3}\) Ton)** & **Bias** & **(10\({}^{3}\) Ton)** & **RMSE** \\ \hline Alfalfa & 67.22 \(\pm\) 48.97 & 59.81 \(\pm\) 50.25 & 0.85 & \(-\)7.41 & \(-\)11.0\% & 28.44 & 42.3\% \\ Barley & 33.19 \(\pm\) 44.81 & 31.50 \(\pm\) 42.77 & 0.96 & \(-\)1.69 & \(-\)5.1\% & 12.22 & 36.8\% \\ Maize & 102.07 \(\pm\) 8.19 & 9.91 \(\pm\) 7.84 & 0.91 & \(-\)0.36 & \(-\)3.5\% & 3.46 & 33.6\% \\ Peas & 10.70 \(\pm\) 13.87 & 10.44 \(\pm\) 14.39 & 0.98 & 0.24 & 2.2\% & 3.10 & 29.0\% \\ Durum Wheat & 39.55 \(\pm\) 68.91 & 35.50 \(\pm\) 72.21 & 1.00 & \(-\)4.05 & \(-\)10.2\% & 8.67 & 21.9\% \\ Spring Wheat & 59.41 \(\pm\) 70.94 & 52.49 \(\pm\) 70.45 & 0.97 & \(-\)6.91 & \(-\)11.6\% & 19.05 & 32.1\% \\ Winter Wheat & 70.84 \(\pm\) 10.11 & 69.87 \(\pm\) 107.93 & 0.99 & \(-\)0.97 & \(-\)14.4\% & 14.87 & 21.0\% \\ All Crops & 51.08 \(\pm\) 69.22 & 47.10 \(\pm\) 68.20 & 0.96 & \(-\)3.98 & \(-\)7.8\% & 18.89 & 37.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparisons between mean county-level crop production from the USDA NASS survey (P\({}_{\text{N}}\)) and mean modeled crop production (P\({}_{\text{M}}\)) for each county in Montana from 2008 to 2015 (all of the correlations are significant with \(p<0.05\)). Figure 6: Example spatial distribution of estimated crop yield for winter wheat across MT and Liberty County in 2015; grey areas denote other CDL-defined crop types represented in this study, while white areas denote other land cover types excluded from the analysis. Although inconclusive, these results indicate meaningful, but lower model accuracy in delineating field level variations in crop yields relative to the county-level results. The spatial distribution of the model uncertainties for alfalfa, barley, spring wheat and winter wheat at the county level are presented in Figure 7 because these crops were grown in most counties during 2008 to 2015 in Montana and permit the evaluation of the spatial variability of estimation errors. Estimation errors for alfalfa production (Figure 7a) tended to be larger in the more mountainous western portion of MT and in the eastern end of the state near the border with North Dakota. In these two regions, irrigated agriculture has increased significantly in the last few decades, and the mix of dryland and irrigated farming has the potential to increase the variance in production in these counties. Additionally, western Montana's complex terrain produces highly variable climatic conditions, which also translates into high production variability. Variability in farming practices (dryland versus irrigated) also applies to spring and winter wheat (Figure 7b,d).