## 2 Materials and Methods
### Model  
CLM4.5 is a state-of-the-art land surface process model in the Community Earth System Model (CESM1.2), which couples terrestrial biogeophysical processes, biogeochemical processes, and hydrological processes. CLM models have been evaluated widely for carbon fluxes and pools, evapotranspiration, leaf area index, land water storage, and soil moisture at different temporal and spatial scales [28; 29; 30; 31; 32; 33; 34]. The CLM4.5 model showed a good performance when simulating GPP at the above four sites [27]. In CLM4.5, photosynthesis in C3 and C4 plants was simulated based on the models of [PERSON] et al. and [PERSON] et al. [35; 36], respectively. Leaf net photosynthesis (A\({}_{n}\)) is defined as follows:  
\[\mathrm{A_{n}=min}\big{(}\mathrm{A_{c}},\mathrm{A_{j}},\mathrm{A_{e}}\big{)}- \mathrm{R_{d}} \tag{1}\]  
where A\({}_{c}\) is the RuBP carboxylase (Rubisco) limited rate of carboxylation (\(\mu\)mol CO\({}_{2}\)m\({}^{-2}\) s\({}^{-1}\)), A\({}_{j}\) is the maximum rate of carboxylation allowed by the capacity to regenerate RuBP (\(\mu\)mol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)), A\({}_{e}\) is the product-limited rate of carboxylation for C3 plants and the PEP carboxylase-limited rate of carboxylation for C4 plants, and R\({}_{d}\) is the leaf dark respiration rate (\(\mu\)mol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)). Photosynthesis is calculated separately for sunlit and shaded leaves to scale up carbon flux from the leaf to canopy levels. \[\mathrm{A_{c}=A_{sun}LAI_{sun}+A_{shade}LAI_{shade}} \tag{2}\]  
where A\({}_{sun}\) and A\({}_{shade}\) are the photosynthesis for sunlit and shaded leaves (CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)), LAI\({}_{shade}\) is the sunlit and shaded leaf area indices, and A\({}_{c}\) is expressed as follows:  
\[\mathrm{A_{c}=\left\{ \begin{array}{cc}\frac{V_{\mathrm{cmax}}(\mathrm{c}- \mathrm{T_{s}})}{\mathrm{c}+\mathrm{K_{c}}(\mathrm{1}+\mathrm{O_{2}}/\mathrm{ K_{0}})}&\mathrm{for\ C3\ plants}\\ \mathrm{V_{cmax}}&\mathrm{for\ C4\ plants}\end{array} \right\} \tag{3}\]  
where V\({}_{cmax}\) is the maximum rate of carboxylation (\(\mu\)mol m\({}^{-2}\) s\({}^{-1}\)); c\({}_{1}\) is the internal leaf CO\({}_{2}\) partial pressure (Pa); o\({}_{1}\) is the O\({}_{2}\) partial pressure (Pa); K\({}_{c}\) and K\({}_{0}\) are the Michaelis-Menten constants (Pa) for CO\({}_{2}\) and O\({}_{2}\), respectively; and \(\mathrm{T_{s}}\) is the CO\({}_{2}\) compensation point (Pa). V\({}_{cmax}\) depends on temperature and is calculated from the value at 25 \({}^{\circ}\)C (V\({}_{cmax25}\)). V\({}_{cmax25}\) varies with foliage nitrogen concentration and specific leaf area. \[\mathrm{V_{cmax25}=N_{a}F_{LNR}F_{NR}a_{R25}} \tag{4}\]  
where N\({}_{a}\) is the area-based leaf nitrogen concentration (g N m\({}^{-2}\) leaf area), F\({}_{LNR}\) is the fraction of leaf nitrogen in Rubisco (g N in Rubisco g\({}^{-1}\) N), F\({}_{NR}\) is the mass ratio of total Rubisco molecular mass to nitrogen in Rubisco (g Rubisco g\({}^{-1}\) N in Rubisco), and a\({}_{R25}\) is the specific activity of Rubisco (\(\mu\)mol CO\({}_{2}\) g\({}^{-1}\) Rubiscos\({}^{-1}\)). N\({}_{a}\) is calculated from the mass-based leaf nitrogen concentration and specific leaf area:  
\[\mathrm{N_{a}=\frac{1}{CN_{L}SLA_{0}}} \tag{5}\]  
where CN\({}_{L}\) is the leaf carbon-to-nitrogen ratio (g C g\({}^{-1}\) N) and SLA\({}_{0}\) is specific leaf area at the canopy top (m\({}^{2}\) leaf area g\({}^{-1}\) C). The vertical variability in SLA within the canopy was simulated by a linear function of SLA and the canopy depth as follows:  
\[\mathrm{SLA(x)=SLA_{0}+mx} \tag{6}\]where SLA\({}_{0}\) is a fixed value of SLA at the top of the canopy (m\({}^{2}\) g\({}^{-1}\)), m is a linear slope coefficient, and x is the canopy depth expressed as overlying leaf area index (m\({}^{2}\) overlying one-sided leaf area m\({}^{2}\) ground area). SLA\({}_{0}\) and m are both assumed to vary with plant functional type. More details of the CLM4.5 model can be found in [PERSON] et al. and [PERSON] et al. (2015); [PERSON] et al. (2016).