## 4 Discussions
### Performance of AI Models  
The results showed a tendency of strong agreement between the GPPs predicted by the AI models and by the EC measurements, explaining approximately 90% of the temporal changes in daily GPP. The phenology of forest vegetation is primarily divided into growth and senescence phases. The predicted GPP at the start of the growing season (increasing phase of each year) and the end of the growing season (decreasing phase of each year) consistently followed the EC measurements. Understanding the seasonal development on daily GPP and environmental factors such as R\({}_{\text{s}}\)\(\downarrow\), T\({}_{\text{air}}\), VPD, and EVI is critical to the applicability of the nonlinear relationships between the input variables and the GPP predictions. Each phase follows a different phenological development, leading to different relationships between the input variables and the GPP. The AI models consistently demonstrated a reasonable correlation in the estimation of daily GPP (Table 4). Indeed, AI techniques in recent years have been considered a viable option for the retrieval of terrestrial carbon fluxes on a spatially continuous grid. Our experiment also showed the possibility of the AI-based GPP prediction, particularly for the local-scale applications for the countries with complex terrains such as South Korea. The integration of AI techniques with satellite images can be an alternative to studies of the interactions between atmosphere and forest ecosystems. Previous studies showed that the AI applications combined with satellite images were effective for estimation of GPP, above-ground biomass, ecosystem respiration, and latent heat flux [24; 25; 48; 49].  
Moreover, a deep learning approach such as DNN in our experiment can be thought of as a better method than the classical AI models such as RF, SVM, and ANN. The DNN presented a superior performance to the other three models in terms of the validation statistics and the representation of seasonal patterns. The overall accuracy decreased in winter because the site is a warm-temperate deciduous forest in which winter photosynthesis is almost inactive. However, the DNN could simulate the winter GPP values much better than the other three AI models. It is because the DNN is a method developed to resolve local minima and overfitting problems of the classical AI models. The DNN model was more optimized in a deep and thick network using the ReLU activation function, the AdaDelta optimizer, and the appropriate outlier management by regularization and dropout techniques. Moreover, we demonstrated that the DNN model performed well despite the multiple extreme weather events such as cold waves, heavy rain, and an autumnal heatwave in 2011 in South Korea. The comparison with MODIS products also showed that our DNN model was locally  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**GPP Data**} & **MBE** & **MAE** & **RMSE** & \\  & **(g m\({}^{-2}\) d\({}^{-1}\))** & **(g m\({}^{-2}\) d\({}^{-1}\))** & **(g m\({}^{-2}\) d\({}^{-1}\))** & **CC** \\ \hline DNN & \(-\)0.014 & 0.405 & 0.537 & 0.975 \\ MODIS (Terra) & 0.224 & 0.998 & 1.278 & 0.916 \\ MODIS (Aqua) & 0.119 & 0.946 & 1.195 & 0.915 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Validation statistics of 8 day gross primary productivity (GPP) at the Gwangenung site from Moderate-resolution Imaging Spectroradiometer (MODIS) products and the deep neural network (DNN) predictions, against the eddy covariance (EC) measurements during 2006–2015.  
optimized for the forests in South Korea on a daily basis, while the parameterization of the MODIS GPP was not specifically suitable for South Korea. Such an outcome of the DNN model was partly because of the spatiotemporally appropriate arrangement of the satellite data. The 16 day albedo and the daily EVI interpolated from 8 day data were also suitable for use in the estimation of daily GPP, which is in accordance with previous studies [50,51].