## 2 Materials and Methods  
### Model Description  
The boreal ecosystem productivity simulator (BEPS) is a process-based ecosystem model with half-hourly time steps developed by [PERSON] and [PERSON] [44]. The two-leaf enzyme kinetic terrestrial ecosystem model is the core module for calculating GPP in the BEPS model. It can calculate the instantaneous stomatal conductance of vegetation and photosynthesis, and through multiple iterations, it enables the convergence of photosynthesis and stomatal conductance [45; 46]. In BEPS, the canopy-level GPP is simulated as follows:  
\[GPP=A_{sun}LAI_{sun}+A_{sh}LAI_{sh} \tag{1}\]  
The net photosynthetic rate (\(\mu\) mol/m\({}^{2}\) s) of the leaves is denoted by \(A\). In Equation (1), both the photosynthetic rate and the leaf area index were divided into two parts: \"sunlit\" and \"shaded\". LAI is the leaf area index; the sunlit LAI (\(LAI_{sun}\)) and shaded LAI (\(LAI_{sh}\)) are calculated as follows. The leaf area index (LAI) is divided into two parts in the model: the sunlit leaves and the shaded leaves. The sunlit leaves are represented by (\(LAI_{sun}\)), and the shaded leaves by (\(LAI_{sh}\)). The splitting method of the sunlit and shaded leaves is as follows: [44]:  
\[LAI_{sun}=2 cos\theta\left(1-e^{-0.5\Omega L/cos\theta}\right) \tag{2}\]  
\[LAI_{sh}=L-LAI_{sun} \tag{3}\]  
The leaf area index (I, m\({}^{2}\) m\({}^{-2}\)) was split into the areas of the sunlit and shaded leaves based on the diurnal variation in the solar zenith angle (\(\theta\)). Following [47], the net carboxylation rate at the leaf level is calculated as the minimum of  
\[A_{c,i}=V_{c\ max}\frac{C_{c,i}-\Gamma_{i}^{*}}{C_{c,i}+K_{c}(1+O_{c,i}/K_{o})} \tag{4}\]  
and  
\[A_{j,i}=J\frac{C_{c,i}-\Gamma_{i}^{*}}{4\left(C_{c,i}+2\Gamma_{i}^{*}\right)} \tag{5}\]  
where \(A_{c,i}\) and \(A_{j,i}\) are Rubiso-limited and RuBP-limited gross photosynthesis rates (\(\mu\) mol/m\({}^{2}\) s), respectively. \(V_{max}\) is the maximum carboxylation rate (\(\mu\) mol/m\({}^{2}\) s); \(J\) is the electron transport rate (\(\mu\) mol/m\({}^{2}\) s); \(C_{c,i}\) and \(O_{c,i}\) are the intercellular CO\({}_{2}\) and O\({}_{2}\) mole fractions (mol/mol, respectively); \(\Gamma_{i}^{*}\) is the CO\({}_{2}\) compensation point without dark respiration (mol/mol; \(K_{c}\) and Ko are Michaelis-Menten constants for CO\({}_{2}\) and O\({}_{2}\) (mol/mol), respectively. This research drew on the previous research ideas and improved the model by modifying the module for calculating photosynthesis [48; 49; 50; 51]. \[A=A_{p}F \tag{6}\]  
In this study, the impact of ozone on photosynthesis is re-examined. The product of the original assimilation rate \(A_{p}\) of the BEPS model and the influence coefficient \(F\) of ozone on photosynthetic rate is recorded as the new photosynthetic rate \(A\) of the BEPS model output. \(F\) can be expressed as follows:  
\[F=1-\alpha\big{(}POD_{y}\big{)} \tag{7}\]  
where \(POD_{y}\) is the instantaneous leaf uptake of O\({}_{3}\) over a vegetation-specific threshold, y, in nmol/m\({}^{2}\) s. \"\(\alpha\)\" is the coefficient by which the photosynthesis of vegetation decreases after absorbing ozone. And PODy can be expressed as follows  
\[POD_{y}=\frac{O_{3}}{R+\frac{K_{c\alpha}}{g}} \tag{8}\]  
where \(R\) is the aerodynamic and boundary layer resistance between the leaf surface and reference level (s/m), \(g\) is the leaf conductance for H\({}_{2}\)O (m/s). The resistance ratio of the blade to ozone and water vapor is set as a constant \(kO_{3}=1.67\). After taking into account the effect of ozone, Equation (5) can be rewritten as:  
\[A_{j,i}=J\frac{C_{c,i}-\Gamma_{i}^{*}}{4\big{(}C_{c,i}+2\Gamma_{i}^{*}\big{)}}\times F \tag{9}\]  
By multiple iterations, the change in stomatal conductance caused by ozone concentration leads to a change in the intercellular CO\({}_{2}\)(C\({}_{c,i}\)), resulting in a change in \(J_{max}\). \(J_{max}\) and C\({}_{c,i}\) affect the change in stomatal conductance during the next iteration, thereby reducing the absorption of O\({}_{3}\).