## 4 Results and Discussion
### Experiments under Drought Conditions
With the increase in the number of years for training (i.e., 3, 5, 7, and 9), the validation statistics of the DNN model were gradually improved. The RMSE and correlation coefficient showed a slight sensitivity to the volume of training data. However, the accuracy might not offer a dramatic improvement even if the number of years for training surpasses that of our experiment, which should be examined in future work for big data. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **MBE (1)** & **MAE (2)** & **RMSE (3)** & **MAPE (4)** & **Corr.(5)** \\  & **(ton/ha)** & **(ton/ha)** & **(ton/ha)** & **(\%)** & **Corr.(5)** \\ \hline MARS [6] & 0.168 & 1.153 & 1.643 & 29.2 & 0.810 \\ SVM [7] & 0.019 & 1.123 & 1.423 & 25.0 & 0.875 \\ RF [8] & 0.068 & 1.025 & 1.303 & 23.2 & 0.911 \\ ERT [9] & \(-\)0.056 & 1.012 & 1.248 & 21.6 & 0.922 \\ ANN [10] & 0.171 & 0.975 & 1.304 & 23.7 & 0.912 \\ DNN [11] & \(-\)0.017 & 0.666 & 0.828 & 12.9 & 0.954 \\ \hline \hline \end{tabular} (1) Mean Bias Error; (2) Mean Absolute Error; (3) Root Mean Square Error; (4) Mean Absolute Percentage Error; (5) Correlation Coefficient; (6) Multivariate Adaptive Regression Splines; (7) Support Vector Machine; (8) Random Forest; (9) Extremely Randomized Trees; (10) Artificial Neural Network; (11) Deep Neural Network.  
\end{table} 
Table 4: Summary of validation statistics for prediction of corn yield in 2012 as a drought case. Figure 5: Actual and predicted corn yields for 2006–2015. Red dots, 2012 data under drought conditions; black dots, all other years. (**a**) Multivariate adaptive regression spline (MARS); (**b**) Support vector machine (SVM); (**c**) Random forest (RF); (**d**) Extremely randomized tree (ERT); (**e**) Artificial neural network (ANN); (**f**) Deep neural network (DNN). Figure 6: Maps for (**a**) actual and (**b**) predicted corn yields and the (**c**) prediction errors from the leave-one-year-out blind tests for 2006–2015. The year 2012 for a drought case showed lower corn yields than the other typical years, but the accuracy was similar to that of the other years. In addition to the size of the training dataset, the kinds of input variables can also affect the performance of DNN models. The VHI and the PDSI were used to identify a drought year in our experiment. Here, we incorporated the VHI and the PDSI as an additional input variable for the DNN model. The current model included soil moisture to represent the drought state of cropland. Hence, we examined how the three drought variables (soil moisture, VHI, and PDSI) would influence the performance for prediction. The weights for the three variables connected to the 300-300 hidden units were optimized by the Adaptive Gradient (AdaGrad) algorithm generally used in DNN models. Table 6 shows the validation statistics from the leave-one-year-out blind tests for the year 2012 as a drought case. The model with soil moisture and the model with the addition of VHI and PDSI were compared. The VHI seemed to be appropriate as an additional variable in that the validation statistics showed a slight improvement. On the other hand, the addition of PDSI did not have a critical impact on this experiment. It is partly because the PDSI is an index to represent a climatological drought from the viewpoint of long-term changes, but the VHI is a general indicator of agricultural drought conditions. In addition to the VHI, more input variables that can explain the interactions between climate and vegetation, including evapotranspiration, diurnal temperature change, irrigation capability, and soil properties, will also be necessary for a more reliable prediction of crop yield. Moreover, the appropriate use of drought index will be important for crop yield prediction because a variety of drought indices can represent different aspects of drought conditions.