## 2 Materials and Methods
### BEPS Model Simulation and Evaluation  
#### 2.4.1 BEPS Model Description  
The BEPS model is mainly composed of four parts: energy transmission, carbon cycle, water cycle, and physiological regulation sub-models [68]. It combines ecology, plant physiology, meteorology, and other disciplines to simulate the relationship between the photosynthesis, respiration, carbon distribution, water balance, and energy balance of vegetation [63], which demonstrates the combination of remote sensing data and ecological process models. The main feature of this model is that the instantaneous Farquhar photosynthetic model at the leaf scale is converted into the daily total photosynthetic model through the integration of stomatal conductance to realize the time scale expansion. Then, according to the principle of light transmission in the canopy, the vegetation canopy leaves were divided into shaded and sunlit leaves to simulate the radiation budget of the corresponding leaves. This helps achieve the expansion from the leaf scale to the canopy space scale. Detailed descriptions of the BEPS model can be found in [PERSON] et al. [69] and [PERSON] et al. [65]. The main simulation process of the model is as follows:  
1. The LAI\({}_{\rm sunlit}\) and LAI\({}_{\rm shade}\) are calculated as follows: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Unit** & **Description** & **Value** & **Reference** \\ \hline \(\Omega\) & - & Clumping index & 0.5 & Measurement \\ S\({}_{\rm area}\) & & Specific leaf area & 27 & Measurement \\ V\({}_{\rm m,25}\) & umol m\({}^{-2}\)s\({}^{-1}\) & Maximum carboxylation rate at 25 \({}^{\circ}\)C & 50 & Iteration \\ Q\({}_{10,\rm leaf}\) & - & Q\({}_{10}\) for leaf & 1.4 & Iteration \\ Q\({}_{10,\rm stem}\) & - & Q\({}_{10}\) for stem & 1.3 & Iteration \\ Q\({}_{10,\rm root}\) & - & Q\({}_{10}\) for root & 1.2 & Iteration \\ M\({}_{\rm leaf}\) & kg C m\({}^{-2}\) & Average carbon storage of leaf & 0.15 & [66] \\ M\({}_{\rm stem}\) & kg C m\({}^{-2}\) & Average carbon storage of stem & 1.76 & [66] \\ M\({}_{\rm root}\) & kg C m\({}^{-2}\) & Average carbon storage of root & 1.15 & [66] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Major biological parameters used as inputs into the BEPS model for simulating the CO\({}_{2}\) fluxes of bamboo forests. where \(\rm{LAI}_{\rm{canopy}}\) is the total LAI of the canopy; \(\rm{LAI}_{\rm{sunit}}\) and \(\rm{LAI}_{\rm{shade}}\) are the canopy LAIs of sunit and shaded leaves, respectively; \(\rm{\theta}\) is the daily mean solar zenith angle; and \(\rm{\Omega}\) is the clumping index:  
\[\rm{LAI}_{\rm{sunit}}=2\cos\theta[1-\exp(-0.5\Omega\rm{LAI}/\cos\theta)] \tag{1}\]  
\[\rm{LAI}_{\rm{shade}}{=}\rm{LAI}_{\rm{canopy}}{-}\rm{LAI}_{\rm{sunit}} \tag{2}\]  
(2) The photosynthesis rate is calculated as follows:  
\[\rm{A}=\rm{min}\big{(}W_{\rm{c}},W_{\rm{j}}\big{)}-R_{\rm{d}} \tag{3}\]  
\[\rm{W_{c}}=V_{\rm{m}}\frac{C_{\rm{i}}-\Gamma}{C_{\rm{i}}+K_{\rm{c}}(1+O_{2}/K_ {\rm{o}})} \tag{4}\]  
\[\rm{W_{j}}=J\frac{C_{\rm{i}}-\Gamma}{4(C_{\rm{i}}+2\Gamma)} \tag{5}\]  
\[\rm{R_{d}}=0.015V_{\rm{m}} \tag{6}\]  
where A is the net photosynthesis rate; \(\rm{W_{c}}\) and \(\rm{W_{j}}\) are the Rubisco-limited and RuBPT-limited gross photosynthesis rates, respectively; \(\rm{R_{d}}\) is the daytime leaf dark respiration; \(\rm{V_{m}}\) is the maximum carboxylation rate at 25 \({}^{\circ}\)C; \(\rm{C_{i}}\) and \(\rm{O_{2}}\) are the intercellular \(\rm{CO_{2}}\) and oxygen concentrations in the atmosphere, respectively; \(\rm{\Gamma}\) is the \(\rm{CO_{2}}\) compensation point, without dark respiration; \(\rm{K_{c}}\) and \(\rm{K_{o}}\) are the Michaelis-Menten constants for \(\rm{CO_{2}}\) and \(\rm{O_{2}}\), respectively; and \(\rm{J}\) is the electron transmission rate.