# Exploring the Spatiotemporal Alterations in China's GPP Based on the DTEC Model
## 2 Materials and Methods
### Methods  
#### 2.3.1 DTEC Model  
DTEC is a two-leaf light-use efficiency model based on the diffusion fraction. The model considers the effects of scattered radiation, diffuse fraction and soil water stress on GPP [11]. The main structure of the model is as follows:  
\[\text{GPP}=(\varepsilon_{\text{msu}}\times\text{APAR}_{\text{sun}}\ + \varepsilon_{\text{msh}}\times\text{APAR}_{\text{shd}}\ )\times W_{\varepsilon}\times T_{\varepsilon} \tag{1}\]  
\[\text{APAR}_{\text{sun}}=\left[\text{PAR}_{\text{dir}}\times\frac{\cos( \beta)}{\cos(\theta)}+\frac{\text{PAR}_{\text{diff}}-\text{PAR}_{\text{diff,u}} }{\text{LAI}}+\text{C}\right]\times\text{LAI}_{\text{sun}} \tag{2}\]  
\[\text{APAR}_{\text{shd}}\ =\left[\frac{\text{PAR}_{\text{diff}}-\text{PAR}_{\text{ diff, u}}}{\text{LAI}}+\text{C}\right]\times\text{LAI}_{\text{shd}} \tag{3}\]  
\[\text{LAI}_{\text{sum}}=2\times\cos(\theta)\times\left[1-\exp\left(-0.5\times \Omega\times\frac{LAI}{\cos(\theta)}\right)\right] \tag{4}\]  
\[\text{LAI}_{\text{shd}}\ =\text{LAI}-\text{LAI}_{\text{sum}} \tag{5}\]  
\[\text{PAR}_{\text{diff}}=\text{PAR}\times D_{f} \tag{6}\]  
\[D_{f}=0.7527+3.8453 SI-16.316 SI^{2}+18.962 SI^{3}-7.0802 SI^{4} \tag{7}\]\[SI=\frac{PAR}{\left[0.48S_{0}\cos(\theta)\right]} \tag{8}\]  
\[W_{\epsilon}=E/E_{PT} \tag{9}\]  
\[T_{\epsilon}=\frac{(T_{\mathrm{a}}-T_{\mathrm{min}})(T_{\mathrm{a}}-T_{\mathrm{ max}})}{(T_{\mathrm{a}}-T_{\mathrm{min}})(T_{\mathrm{a}}-T_{\mathrm{max}})-\left(T_{ \mathrm{a}}-T_{\mathrm{opt}}\right)^{2}} \tag{10}\]  
where \(\epsilon_{\mathrm{msu}}\) and \(\epsilon_{\mathrm{msh}}\) are the maximum LUEs of the sun and shade leaves, respectively. For C3 plants: \(\epsilon_{\mathrm{msh}}=3.78\times\mathrm{D}_{\mathrm{f}}^{1.8}\), \(\epsilon_{\mathrm{msu}}=1.67\) g C/MJ, and for C4 plants: \(\epsilon_{\mathrm{msh}}=5.78\times\mathrm{D}_{\mathrm{f}}^{1.8}\), \(\epsilon_{\mathrm{msu}}=2.56\) g C/MJ. APAR\({}_{\mathrm{Sun}}\) and APAR\({}_{\mathrm{shd}}\) are the photosynthetically active radiation absorbed by the sun and shade leaves, respectively. \(W_{\epsilon}\) is the water stress factor, in which E is the actual evapotranspiration and E\({}_{\mathrm{PT}}\) is the potential evapotranspiration. T\({}_{\epsilon}\) is the temperature stress factor, in which T\({}_{\mathrm{a}}\) is the air temperature and T\({}_{\mathrm{min}}\), T\({}_{\mathrm{max}}\), and T\({}_{\mathrm{opt}}\) are the minimum, maximum, and optimal temperatures for photosynthesis in biomes, respectively. C is the contribution of direct radiation to the scattered radiation after multiple scattering, and the formula is \(0.07\Omega\times\mathrm{PAR}_{\mathrm{dir}}\times(1.1-0.1\mathrm{LAI})\times \mathrm{e}^{(-\cos(\theta))}\). \(\Omega\) is the vegetation type index. \(\beta\) is the mean leaf solar angle, which is \(60^{\circ}\), and \(\theta\) is the solar zenith angle. PAR\({}_{\mathrm{dir}}\), \(\mathrm{PAR}_{\mathrm{dir}}\) and PAR\({}_{\mathrm{dir,u}}\) are the direct photosynthetically active radiation, scattered photosynthetically active radiation and scattered radiation under the canopy, respectively, in which PAR\({}_{\mathrm{dir}}=\mathrm{PAR}-\mathrm{PAR}_{\mathrm{dir}}\) and PAR\({}_{\mathrm{dir,u}}=\mathrm{PAR}_{\mathrm{dir}}\times\mathrm{e}^{(-0.5\times\Omega \times\mathrm{LAI})/(0.537+0.025\mathrm{LAI})}\). LAI\({}_{\mathrm{sun}}\) and LAI\({}_{\mathrm{shd}}\) are the LAIs for sunny and shady leaves, respectively, which were obtained by separating the LAI products. PAR is the photosynthetically active radiation, calculated as \(0.48\mathrm{R}_{\mathrm{g}}\), where \(\mathrm{R}_{\mathrm{g}}\) is the solar radiation. \(\mathrm{D}_{\mathrm{f}}\) is the scattering ratio, SI is the clear sky index, and \(S_{0}\) is the solar constant (\(1367\) W/m\({}^{-2}\)).