## 3 Results  
### GPP Estimation by AI Models  
Tables 2 and 3 show the statistics of the daily GPP at the Gwangneung site between 2006 and 2015, including the predictions from SVM, RF, ANN, and DNN as well as the observations from the EC. The mean values of the predicted GPP by the AI models (3.26-3.35 g m\({}^{-2}\) d\({}^{-1}\)) were very similar to those of the EC measurements (3.30 g m\({}^{-2}\) d\({}^{-1}\)). However, the AI models did not well represent very low or very high GPP values, thus the daily GPP under approximately 0.5 g m\({}^{-2}\) d\({}^{-1}\) or over about 8.5 g m\({}^{-2}\) d\({}^{-1}\) was rarely simulated by the AI models. Among the four AI models, the DNN showed the closest predictions in terms of the minimum, maximum, and mean values. Figures 4-7 show the seasonal changes of the predicted daily GPP at the Gwangneung site for the period between 2006 and 2015. The four AI models closely traced the growing season (increasing phase) and the senescence (decreasing phase) of the forest every year. The curve in spring showed an exponential increment, and that of autumn had a relatively longer decreasing period in both AI and EC GPPs. The DNN model followed the GPP peak in May and June better than SVM, RF, and ANN models (Figures 4a, 5a, 6a and 7a). Table 4 shows the validation statistics of the daily GPP in terms of MBE, MAE, RMSE, and CC. The averages of CC had small differences among the four AI models (between 0.90 and 0.93), but the DNN model demonstrated significantly better accuracy in terms of MAE and RMSE. The MAE was approximately 13% ((0.77\(-\)0.68)/0.68) to 25% ((0.85\(-\)0.68)/0.68) better, and the RMSE was about 11% ((1.07\(-\)0.96)/0.96) to 21% ((1.16\(-\)0.96)/0.96) better than the other three models. In the year 2011, South Korea experienced multiple extreme weather events. The four AI models showed the lowest accuracy, with the CC between 0.81 and 0.86 for SVM, RF, and ANN and the CC of 0.90 for the DNN model. A cold wave lasted for almost 40 days from December 2010 to January 2011. Heavy rain for nine consecutive days in June resulted in a large-scale landslide in Seoul. An extraordinarily late heatwave occurred for several days in autumn. Such extreme weather events led to a lower GPP (2.40 g m\({}^{-2}\) d\({}^{-1}\)) than the usual years (3.30 g m\({}^{-2}\) d\({}^{-1}\)), thus the GPP predictions using R\({}_{s}\)\(\downarrow\), T\({}_{\rm air}\), VPD, and EVI did not perform very well due to the unexpected weather conditions. However, the DNN model showed similar predictability to the usual years despite the extreme weather: the MAE of 0.77 g m\({}^{-2}\) d\({}^{-1}\), the RMSE of 1.05 g m\({}^{-2}\) d\({}^{-1}\), and the CC of 0.90. Figures 4c, 5c, 6c and 7c show the time series of 2015 when the predictions of the four models were best among all the years. On the other hand, the predictions in 2011 by SVM, RF, and ANN models did not coincide very well with the EC observations (Figures 4b, 5b and 6b), whereas the DNN predictions in 2011 in Figure 7b had relatively good agreements with the EC values. Additionally, the DNN model could simulate very high GPP values over about 8 g m\({}^{-2}\) d\({}^{-1}\), while the other three models showed an upward stiffness that could not produce such high values. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Min (1) (g m\({}^{-2}\) d\({}^{-1}\))** & **Max (2) (g m\({}^{-2}\) d\({}^{-1}\))** & **Mean (g m\({}^{-2}\) d\({}^{-1}\))** \\ \hline EC & 0.28 & 9.20 & 3.30 \\ SVM & 0.58 & 7.76 & 3.26 \\ RF & 0.74 & 7.83 & 3.35 \\ ANN & 0.85 & 7.49 & 3.35 \\ DNN & 0.55 & 8.49 & 3.29 \\ \hline \hline \end{tabular} \({}^{(1)}\) Minimum value except for lower 2% data; \({}^{(2)}\) maximum value except for upper 2% data.  
\end{table} 
Table 2: Statistics of daily gross primary productivity (GPP) at the Gwangneung site for the period between 2006 and 2015, measured by eddy covariance (EC) and predicted by support vector machine (SVM), random forest (RF), artificial neural network (ANN), and deep neural network (DNN).