## 4 Materials and Methods
### BEPS Model  
The BEPS model was developed from the FOREST-BGC ecological process model [10; 40] to simulate vegetation processes, such as photosynthesis, respiration, carbon partitioning, and water and energy balance [13]. Therefore, the model includes several relevant modules, such as for photosynthesis, energy and water balance, and soil. During the simulation of vegetation productivity, the classic Farquhar photosynthesis model was adopted in BEPS to mimic the photosynthesis process of green plants [10]. However, the disadvantage of  
Figure 6: Flowchart of tree rings analysis. this simulation is that it only simulates the instantaneous photosynthesis of a single leaf; therefore, expansions on both the temporal and the spatial scales are required. The model realizes the conversion from the instantaneous scale to the daily scale using daily integration. As the various parts and tissues of the vegetation receive different quantities and quality of light, their photosynthesis intensities are also different. Therefore, treating the entire canopy as a large leaf will introduce substantial errors. Therefore, the BEPS model divides the canopy into sun leaves and shade leaves and introduces the leaf aggregation index to characterize the aggregation degree of the leaves [41]. This is intended to reduce the influence of the shape and structure of the plant canopy on radiation absorption, light received by the leaf's surface, and mutual shading. By calculating the photosynthesis processes of sun and shade leaves separately, the BEPS model realizes the expansion of the canopy on the spatial scale, which eventually leads to the derivation of the gross primary production (\(GPP\)) of vegetation on a daily scale. The vegetation NPP is subsequently calculated by subtracting the autotrophic respiration of the vegetation from the \(GPP\). The model introduces the leaf aggregation index to calculate the leaf area index of the sun and shade leaves \(LAI_{sun}\) and \(LAI_{shade}\), respectively:  
\[ \begin{array}{l}LAI_{sun}=2\cos\theta(1-\exp(-0.5\Omega LAI/\cos\theta)),\\ LAI_{shade}=LAI-LAI_{sun}\end{array}  \tag{1}\]  
where \(LAI\) is the leaf area index of the plant canopy; \(\theta\) is the sun zenith angle; \(\Omega\) is the leaf aggregation index, which was defined based on different vegetation types. The model subsequently calculates the solar radiation received by the sun and shade leaves, i.e., \(S_{sun}\) and \(S_{shade}\):  
\[ \begin{array}{l}S_{sun}=S_{dir}\cos\alpha/\cos\theta+S_{shade}\\ S_{shade}=(S_{diff}-S_{diff,under})/LAI+C\\ C=0.07\Omega S_{dir}(1.1-0.1 LAI)\exp(-\cos\theta),\\ S_{diff,under}=S_{diff}\exp(-0.5\Omega LAI/\cos\theta)\\ \cos\theta_{mean}=0.537+0.025 LAI\end{array}  \tag{2}\]  
where \(S_{dir}\) and \(S_{diff}\) are the direct and scattered radiation received on the canopy, \(S_{diff,under}\) is the scattered radiation received under the canopy, \(\alpha\) is the average leaf solar radiation distribution angle, \(C\) is the multiple scattered radiation of the direct radiation, and \(\theta_{mean}\) is the mean sun zenith angle of the scattered radiation. The model subsequently calculates the total photosynthesis of the vegetation canopy:  
\[A_{conopy}=A_{sun}LAI_{sun}+A_{shade}LAI_{shade}, \tag{3}\]  
where \(A_{sun}\) and \(A_{shade}\) are the photosynthesis levels of the sun and shade leaves, respectively. Lastly, the model calculates the NPP:  
\[ \begin{array}{l}GPP=A_{conopy}L_{dap}F_{GPP},\\ R_{a}=R_{m}+R_{g}=\sum{(R_{m,i}+R_{g,i})}\end{array}  \tag{4}\]  
where \(GPP\) is the gross primary productivity; \(L_{day}\) is the length of the day; \(F_{GPP}\) is the proportional coefficient when converting from photosynthesis to \(GPP\); \(R_{a}\), \(R_{m}\), and \(R_{g}\) represent autotrophic respiration, maintenance respiration, and growth respiration, respectively; \(i\) represents the different parts of the vegetation (with 1, 2, and 3 representing the leaves, stems, and roots, respectively).