## 4 Results and Discussion
### Model Validation with Statistical Yield and Production at the County Level  
We used the above-calibrated RF models to estimate the yields of maize and sunflower, and then compared the estimated yield and production with the official statistical data at the county level in the irrigation district in 6 years (from 2010 to 2015) to further validate the model. Figures 4 and 5 showed the inter-annual variations of the accuracy of RF models driven by different predictors for maize and sunflower in the irrigation district, respectively. For maize, models 1, 2 and 5 had higher estimation accuracy in different years, with the RMSE ranging from 0.57 to 1.29 t/ha, from 0.48 to 0.93 t/ha, and from 0.69 to 0.91 t/ha, and the RE ranging from 4.5% to 11.7%, from 4.3% to 8.5%, and from 5.1% to 8.1%, respectively. These three models also performed better in model calibration. Among these 3 models, model 5 has the highest accuracy with the multi-year average values of RMSE and RE of 0.75 t/ha and 6.1%, respectively. Figure 4: The RMSE (**a**) and RE (**b**) of RF models for maize yield estimation from 2010 to 2015. Figure 3: The RMSE (t/ha), coefficient of determination (\(R^{2}\)), and adjusted \(R^{2}\) of RF models driven by different predictors for maize (**a**) and sunflower (**b**). For sunflower, models 5, 6 and 8 had higher estimation accuracy in different years, with the ranges of RMSE of 0.22-0.77, 0.21-0.64, and 0.28-0.58 t/ha, and corresponding RE of 5.3-16.8%, 4.1-15.8%, and 6.4-17.1%, respectively. Among these models, model 8 has the highest accuracy with the multi-year average values of RMSE and RE of 0.40 t/ha and 10.1%, respectively. As a result, models 1, 2 and 5 were chosen as the three better models for maize, while models 5, 6 and 8 as the better models for sunflower. The model 5 was among the three better models for both maize and sunflower, which indicates that the yields of maize and sunflower can be estimated fairly well with NDVI series 50 days before crop harvest and implicates the possibility of crop yield forecast before harvest. If we could estimate the NDVI series 50 days before crop harvest without NDVI data of the final growth period using appropriate interpolation or curve fitting methods, then the crop yield can be forecasted before crop harvest. The possibility of crop yield forecast before harvest will be considered in further studies. Furthermore, we calculated the total production of maize and sunflower in four counties (Dengkou, Linhe, Hangjinhouqi and Wuyuan) using the above eight models by adding up the total production of all maize or sunflower pixels in each county. As a result, we obtained 24 (4 counties in 6 years) estimated total production for maize and sunflower, respectively, which were compared with the official statistical productions during 2010 to 2015 (Table 4). From Table 4, the \(R^{2}\) and the adjusted \(R^{2}\) were mostly over 0.45 for maize and over 0.60 for sunflower. The RE were mostly less than 30% for maize and 35% for sunflower. It can also be found that \(R^{2}\) and the adjusted \(R^{2}\) for model validation using total production are smaller than that for model calibration using crop yield per unit area, which is reasonable because errors in the estimated total production include errors in both yield estimation and crop classification. Compared with previous crop yield estimation studies using machine learning methods [7; 11; 43] with the \(R^{2}\) ranging from 0.2 to 0. The scatter plots for the three better model estimated and statistical productions in four counties during 2010 to 2015 are shown in Figures 6 and 7. For maize, the model 5 has close \(R^{2}\) values to the other two models and the smallest RMSE and RE values. For sunflower, the model 8 has close RMSE and RE values to the other two models and the highest \(R^{2}\) value. Consequently, we selected the model 5 to estimate the maize yields, and the model 8 to estimate the sunflower yields.