## 3 Methodology
### CEVSA Model  
The CEVSA model is the vegetation submodel estimating vegetation distribution and calculating net primary production (NPP) [25], carbon allocation and litter production, which simulates synthesis of the biophysical and biogeochemical processes between vegetation, soil and the atmosphere.  
The model consists of three sub-modules, biophysical module, plant physiological growth module, and soil carbon reservoir module. Biophysical module is primarily used to calculate the hydrothermal exchanges between atmosphere and land, and the dynamics of soil moisture. Plant physiological growth module is mainly used to calculate the accumulation and distribution of carbon and nitrogen between various organs of plants, as well as the plant photosynthesis and respiration. Soil carbon reservoir module is used to estimate the decomposition and transformation of soil organic matter.  
\[\mathrm{A_{b}}=\mathrm{min}\big{(}\mathrm{W_{c}},\mathrm{W_{j}},\mathrm{W_{P}} \big{)}\left(1-\frac{0.5\mathrm{P_{0}}}{\mathrm{\tau P_{c}}}\right)-\mathrm{R_ {d}} \tag{5}\]  
\[\mathrm{A_{d}}=\frac{\mathrm{g_{s}}}{160}(\mathrm{P_{a}}-\mathrm{P_{c}}) \tag{6}\]  
\[\mathrm{g_{s}}=\left(\mathrm{g_{0}(T)}+\mathrm{g_{1}(T)}\frac{\mathrm{AR_{h} }}{\mathrm{P_{a}}}\right)\mathrm{K_{g}(w_{s})} \tag{7}\]  
\[\mathrm{ET}=\frac{\mathrm{sR_{n}}+\mathrm{c_{p}}\mathrm{\rho g_{a}D}}{\sigma( \mathrm{s}+\gamma(1+\mathrm{g_{a}}/\mathrm{g_{n}}))} \tag{8}\]  
\[\frac{\mathrm{dw_{s}}}{\mathrm{dt}}=\mathrm{Rain}-\mathrm{ET}-\mathrm{Runoff} \tag{9}\]  
where \(\mathrm{A_{b}}\) and \(\mathrm{A_{d}}\) are the assimilation rate determined by enzyme system and stomatal conductance; \(\mathrm{g_{s}}\) is stomatal conductance to water vapor; \(\mathrm{W_{c}}\) is the carboxylation rate; \(\mathrm{W_{j}}\) is the carboxylation rate depended on the rate of electron transport; \(\mathrm{W_{p}}\) is the carboxylation rate; \(\mathrm{P_{0}}\) and \(\mathrm{P_{c}}\) are the internal partial pressures of \(\mathrm{O_{2}}\) and \(\mathrm{CO_{2}}\), respectively; \(\mathrm{\tau}\) is the specificity factor for \(\mathrm{CO_{2}}\); \(\mathrm{R_{d}}\) is the rate of respiration in light; \(\mathrm{Pa}\) is the partial pressure of \(\mathrm{CO_{2}}\) in the leaf surface; \(\mathrm{R_{h}}\) is relative humidity of the air surrounding the leaf; \(\mathrm{K_{g}(w_{s})}\) is a hyperbolic response function which describes the influence of soilwater content \(\mathrm{w_{s}}\) on stomatal conductance \(\mathrm{g_{s}}\); \(\mathrm{c_{p}}\) is the heat of air; \(\mathrm{g_{n}}\) is the stomatal conductance; \(\mathrm{g_{a}}\) is the boundary layer conductance; \(\mathrm{R_{n}}\) is the net radiation; \(\gamma\) is the psychometric constant; \(\sigma\) is the heat of vaporization; \(\rho\) is the mean air density; D is vapor pressure deficit; s is the slope of saturation vapour pressure; \(\mathrm{w_{s}}\) is the soil water content; and Rain, ET and Runoff are the rainfall reaching the ground, evapotranspiration and runoff, respectively.  
Plant must have sufficient woody biomass to support the mass of leaves, and the structure needs to be maintained by the proper allocation of carbon among stem (\(\mathrm{a_{s}}\)), root (\(\mathrm{a_{R}}\)), and leaf (\(\mathrm{a_{L}}\)); the allocation of assimilated product is calculated using Equations (10)-(12):  
\[\mathrm{a_{s}}=\frac{\epsilon_{\mathrm{s}}+\omega(1-\mathrm{L})}{1+\omega(2- \mathrm{L}-\mathrm{W})} \tag{10}\]  
\[\mathrm{a_{R}}=\frac{\epsilon_{\mathrm{R}}+\omega(1-\mathrm{W})}{1+\omega(2- \mathrm{L}-\mathrm{W})} \tag{11}\]  
\[\mathrm{a_{L}}=\frac{\epsilon_{\mathrm{L}}}{1+\omega(2-\mathrm{L}-\mathrm{W}) }=1-\mathrm{a_{s}}-\mathrm{a_{R}} \tag{12}\]  
where \(\epsilon_{\mathrm{s}}\), \(\epsilon_{\mathrm{R}}\), \(\epsilon_{\mathrm{L}}\) and \(\omega\) are plant function type (PET) dependent parameters following the rule of \(\epsilon_{\mathrm{s}}+\epsilon_{\mathrm{R}}+\epsilon_{\mathrm{L}}=1\). L and W represent light and water availability, respectively.