## 4 Results and Discussion
### Experiments under Heatwave Conditions  
Next, we evaluated the accuracy of the AI models for predicting crop yield under heatwave conditions by performing sensitivity analyses for heatwaves of different durations during the study period. We extracted cases in which the counties experienced a heatwave for longer than a given period of days (\(\geq\)3 to \(\geq\)15 days). Then, we calculated validation statistics for these heatwave cases according to the duration of the heatwave using the six AI models for corn yield. As shown in Figure 7, prediction errors tended to increase as the duration of the heatwave increased. However, the accuracy of the DNN model remained significantly stable despite the increase of the heatwave days. In contrast, the errors of the other five models increased somewhat sharply over time. It is interpreted that the DNN model was very robust to unexpected heatwave disasters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **MBE (1)** & **MAE (2)** & **RMSE (3)** & **MAPE (4)** & **Corr.(5)** \\  & **(ton/ha)** & **(ton/ha)** & **(ton/ha)** & **(\%)** & **Corr.(5)** \\ \hline Current model (w/ SM (6)) & \(-\)0.017 & 0.666 & 0.828 & 12.9 & 0.954 \\ Current model (w/ SM) + VHI (7) & \(-\)0.038 & 0.618 & 0.791 & 11.4 & 0.954 \\ Current model (w/ SM) + PDSI (8) & \(-\)0.021 & 0.704 & 0.914 & 12.5 & 0.937 \\ Current model (w/ SM) + VHI + PDSI & 0.013 & 0.632 & 0.818 & 11.4 & 0.950 \\ \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) Soil Moisture; (7) Vegetation Health Index; (8) Palmer Drought Severity Index.  
\end{table} 
Table 6: Summary of validation statistics according to the addition of drought-related variables for prediction of corn yield in 2012 as a drought case. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No. of Years** & **No. of** & **MBE (2)** & **MAE (3)** & **RMSE (4)** & **MAPE (5)** & **Corr.(6)** \\
**for Training** & **Experiments (1)** & **(ton/ha)** & **(ton/ha)** & **(ton/ha)** & **(\%)** & **Corr.(6)** \\ \hline
3 years & 20 out of \(\mathrm{\SIUnitSymbolMicro C}_{3}\) & 0.070 & 0.920 & 1.154 & 19.0 & 0.919 \\
5 years & 20 out of \(\mathrm{\SIUnitSymbolMicro C}_{5}\) & \(-\)0.091 & 0.915 & 1.153 & 19.1 & 0.926 \\
7 years & 20 out of \(\mathrm{\SIUnitSymbolMicro C}_{7}\) & 0.007 & 0.874 & 1.090 & 18.2 & 0.931 \\
9 years & 1 (\(\mathrm{\SIUnitSymbolMicro C}_{9}\)) & \(-\)0.017 & 0.666 & 0.828 & 12.9 & 0.954 \\ \hline \hline \end{tabular} (1) Randomly chosen from the whole combinations; (2) Mean Bias Error; (3) Mean Absolute Error; (4) Root Mean Square Error; (5) Mean Absolute Percentage Error; (6) Correlation Coefficient.  
\end{table} 
Table 5: Summary of validation statistics according to the number of years used in training for prediction of corn yield in 2012 as a drought case. For the heatwaves longer than five and seven days, the average corn yields were 6.628 and 5.938 ton/ha, respectively. Considering that the average corn yield of all the cases was 9.606 ton/ha during the 10 years, it looks like the heatwave significantly damaged the corn yields. Despite the unexpected heatwave disasters, the DNN model showed much lower prediction errors, with the MAE of 0.781 ton/ha for heatwaves exceeding five days, than the other five models having MAE values between 1.068 and 1.352 ton/ha (Table 7). The RMSE of the DNN model was 1.033 ton/ha while the RMSE of the other five models ranged from 1.345 to 1.776 ton/ha, which corresponded to 30% (i.e., \([1.345-1.033]\)/1.033) to 72% (i.e., \([1.776-1.033]\)/1.033) higher accuracy than the other five models in terms of RMSE. Similarly, for heatwaves longer than seven days, the DNN model outperformed the other five models by approximately 31% to 77% in terms of RMSE (Table 7). Figure 7: Validation statistics for prediction of corn yield during heatwave obtained from leave-one-year-out experiments for 2006–2015.