## 2 Materials and Methods
### Data
#### 2.2.3 Input Data Processing  
MODIS is a satellite sensor that has been developed to monitor Earth's atmosphere, land, and ocean environment with the launch of Terra and Aqua satellites in 1999 and 2002, respectively [30]. The input data for the AI models (R\({}_{\rm s}\)\(\downarrow\), T\({}_{\rm air}\), VPD, and EVI) were derived from multiple MODIS products (Table 1). Most of the data have a spatial resolution of 1 to 5 km, which is suitable for the area size (2.2 km\({}^{2}\)) of the forest stand at the Gwangneung site. R\({}_{\rm s}\)\(\downarrow\), a key component for the land surface energy budget, is primarily used as a meteorological input variable for the retrieval of GPP [31]. To calculate R\({}_{\rm s}\)\(\downarrow\), we used a 16 day composite of the black- and the white-sky albedos for shortwave radiation extracted from the MCD43B3 product. For the parameterization of R\({}_{\rm s}\)\(\downarrow\), we employed the Bird Model [32] that considers both diffuse and direct radiation. The R\({}_{\rm s}\)\(\downarrow\) is then expressed as:  
\[\mbox{R${}_{\rm s}$}\)\(\downarrow\)= \(\mbox{$I_{dir}$}+\mbox{$I_{diff}$})/\left(1-a_{g}\)-\(a_{g}\right) \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**MODIS Product** & **Data Extracted** & **Spatial Resolution** & \begin{tabular}{c} **Temporal** \\ **Compositing** \\ \end{tabular} & \
\begin{tabular}{c} **Related Input Variable** \\ **for This Study** \\ \end{tabular} \\ \hline \multirow{2}{*}{MCD43B3} & Black- and white-sky albedo for & 1 km & 16 days \({}^{(1)}\) & R\({}_{\rm s}\)\(\downarrow\)\({}^{(3)}\) \\ \cline{1-1}  & shortwave radiation & & & \\ \hline MYD04\_L2 & Aerosol optical depth & 10 km & 1 day & R\({}_{\rm s}\)\(\downarrow\) \\ \hline MYD05\_L2 & Total column precipitable water & 5 km & 1 day & R\({}_{\rm s}\)\(\downarrow\) \\ \hline MYD07\_L2 &
\begin{tabular}{c} Air and dew-point temperatures, \\ total ozone, and surface pressure \\ \end{tabular} & 5 km & 1 day & R\({}_{\rm s}\)\(\downarrow\), T\({}_{\rm air}\)\({}^{(4)}\), and VPD \({}^{(5)}\) \\ \hline MOD13A2 (Terra) & Enhanced vegetation index & 1 km & 8 days \({}^{(2)}\) & EVI \({}^{(6)}\) \\ \hline \end{tabular} \({}^{(1)}\) 16 day composite was assigned to each of the 16 days; \({}^{(2)}\) 8 day composite was interpolated to daily values; \({}^{(3)}\) downward shortwave radiation; \({}^{(4)}\) air temperature; \({}^{(5)}\) vapor pressure deficit; \({}^{(6)}\) enhanced vegetation index.  
\end{table} 
Table 1: Moderate-resolution Imaging Spectroradiometer (MODIS) products used in the calculation of input data for the estimation of daily gross primary productivity (GPP) in the forest of South Korea. where \(I_{dir}\) is the direct radiation; \(I_{diff}\) is the diffuse radiation; \(a_{g}\) is the ground albedo; \(a_{s}\) is the atmospheric albedo. The 16 day albedo was assigned to each of the 16 days because the forest albedo does not significantly vary during a 16 day period [30; 33]. From the daily black- and white-sky albedos, the actual albedo was calculated using the MODIS lookup table for a fraction of the diffuse radiation regarding a given solar zenith angle and a 550 nm aerosol optical depth (AOD) [33]. For the parameterization of AOD, we rearranged the daily AOD images using a statistical gap-filling method [34; 35]. Total column precipitable water (TPW), total ozone, and surface pressure were also parameterized according to the Bird Model [33]. The daily R\({}_{s}\)\(\downarrow\) calculated by this process showed high accuracy with the correlation coefficient (CC) over 0.9 against the Automated Surface Observing System (ASOS) in South Korea [35]. The air and dew-point temperatures from the lowest atmospheric layer (surface layer) were used in the calculation of VPD by subtracting the actual vapor pressure (\(e_{a}\)) from the saturated vapor pressure (\(e_{s}\)) [36]. The \(e_{s}\) is a function of air temperature, and the \(e_{a}\) can be derived from the \(e_{s}\) and the relative humidity calculated by air and dew-point temperatures.