# Effect of the Partitioning of Diffuse and Direct APAR on GPP Estimation
## 2 Materials and Methods
### Diffuse and Direct APAR (DDA)-Based Method for Half-Hourly GPP Estimation  
The diffuse and direct APAR (DDA)-based model was originally derived from the concept of radiation conversion efficiency [6; 52], which further partitions diffuse and direct APAR in the half-hourly GPP estimation:  
\[GPP_{DDA}=LUE\times APAR_{direct}+LUE\times\alpha\times APAR_{diffuse} \tag{11}\]  
where \(APAR_{direct}\) and \(APAR_{diffuse}\) are the absorbed photosynthetically active radiation (APAR) under direct and diffuse sky conditions. \(\alpha\) is an enhancement factor for correcting the increase of LUE due to the clouds under diffuse sky conditions. [PERSON] et al. [10] found that \(\alpha\) slightly varied, ranging from 1.01 (crop) to 1.29 (wetland) across various vegetation types (Table 3). If the influence of diffuse light on LUE is not considered, half-hourly GPP can be determined using the EC-LUE model directly [53]:  
\[GPP_{TA}=LUE\times APAR_{total}=LUE\times(APAR_{direct}+APAR_{diffuse}) \tag{12}\]  
where \(GPP_{TA}\) is the half-hourly GPP calculated which do not considered the diffuse lights, \(APAR_{total}\) is the total APAR which concludes the diffuse and direct APAR. \(APAR_{direct}\) and \(APAR_{diffuse}\) are partitioned using the EBR FAPAR product [39]:  
\[APAR_{direct}=PAR_{direct}\times FAPAR_{direct}^{t_{i}} \tag{13}\]  
\[APAR_{diffuse}=PAR_{diffuse}\times FAPAR_{diffuse} \tag{14}\]  
\[PAR_{direct}=PAR\times(1-K_{d}) \tag{15}\]  
\[PAR_{diffuse}=PAR\times K_{d} \tag{16}\]  
\[K_{d}=\frac{PAR_{diffuse}}{PAR}=\frac{SW\_{DIF}\times 0.48}{SW\_IN}\times 0.48 \tag{17}\]  
where \(K_{d}\) is the diffuse fraction derived from the ratio of FLUXNET2015 half-hourly observations of diffuse incoming shortwave radiation (SW_DIF, \(W/\mathrm{m^{2}}\)) and incoming shortwave radiation (SW_IN, \(W/\mathrm{m^{2}}\)), 0.48 is a constant used for transforming the incoming shortwave radiation to PAR [31], \(PAPAR_{direct}^{t_{i}}\) is the FAPAR value under direct sky conditions per 30 min within a day, which is calculated from the EBR FAPAR product:  
\[PAPAR_{direct}^{t_{i}}=\frac{1-\tau_{t_{i}}}{1-\tau_{t_{0}}}\times FAPAR_{ direct}^{t_{0}} \tag{18}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Vegetation Type 1** & **DBF** & **ENF** & **EBF** & **GRA** & **CRO** & **SAV** \\ \hline \(\epsilon_{\text{max}}\) (g C/M)) & 2.02 & 3.16 & 3.92 & 3.32 & 2.85 & 1.54 \\ \(\varphi\) (ppm) & 60 & 20.69 & 30 & 75 & 64 & 41 \\ VPD\({}_{0}\) (k Pa) & 0.54 & 0.69 & 0.29 & 1.21 & 0.89 & 1.04 \\ \hline \hline \end{tabular}  
* DBF: deciduous broadleaf forest; ENF: evergreen needleleaf forest; EBF: evergreen broadleaf forest; GRA: grass; CRO: crop; WET: wetland; SAV: savannas; SHR: shrubland.  
\end{table} 
Table 2: Model parameters used in EC-LUE for different vegetation types [51]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Vegetation Type 1** & **DBF** & **ENF** & **EBF** & **GRA** & **CRO** & **SAV** \\ \hline \(\alpha\) & 1.26 & 1.21 & 1.16 & 1.25 & 1.01 & 1.16 \\ \hline \hline \end{tabular}  
* DBF: deciduous broadleaf forest; ENF: evergreen needleleaf forest; EBF: evergreen broadleaf forest; GRA: grass; CRO: crop; WET: wetland; SAV: savannas; SHR: shrubland.  
\end{table} 
Table 3: The enhancement factor of the LUE under diffuse radiation conditions. where \(FAPAR_{direct}^{l_{0}}\) denotes the instantaneous FAPAR value at 10:30 a.m. with a temporal resolution of one day. A non-linear method of spline interpolation was used for interpolating the eight-day EBR FAPAR [39] to daily scales in order to match the FLUXNET meteorological data at half-hourly scale.