## 4 Modeling of C and Water Dynamics in Terrestrial Ecosystems
### Modeling Coupled C, N and Water Dynamics--An Ecohydrological Approach  
C and N dynamics and hydrological processes are closely linked. The stomatal conductance (g\({}_{\rm s}\)) is the key linkage between C assimilation (photosynthesis) and transpiration. An empirical equation is used in the second-generation LSMs to calculate g\({}_{\rm s}\), which is hypothesized to be controlled by the environmental conditions [31]. While field and laboratory studies have documented that leaf photosynthesis also affects g\({}_{\rm s}\). Therefore, [PERSON] _et al._[24] proposed a semi-empirical stomatal conductance formulation (Ball-Woodrow-Berry model), in which g\({}_{\rm s}\) is controlled by both photosynthesis and the environmental conditions. Most of third-generation LSMs (Ecological models, e.g., SiB2 [139,150]; CN-CLASS [28]; _Ecosys_[183-184; and EASS [143]]) fully couple photosynthesis and transpiration processes by employing the Ball-Woodrow-Berry stomatal conductance formulation.  
In addition to the coupling of hydrological condition and C assimilation through the linkage of g\({}_{\rm s}\), C assimilation is also coupling with N dynamics through another biochemical parameter, \(V_{c\,\max}^{\,25}\)--maximum carboxylation rate at 25 \({}^{\circ}\)C. In the photosynthesis model proposed by [PERSON] _et al._[174], the net photosynthetic rate \(A_{net}\) at leaf level is a function of two tightly-correlated parameters \(V_{c\,\max}^{\,25}\) and \(J_{c\,\max}^{\,25}\)(the maximum electron transport rate at 25 \({}^{\circ}\)C), and is calculated as:  
\[A_{net}=\min(\,A_{c},A_{j})-R_{d} \tag{1}\]  
where \(A_{c}\) and \(A_{j}\) are Rubiso-limited and light-limited gross photosynthesis rates, respectively, and \(R_{d}\) is the daytime leaf dark respiration and computed as \(R_{d}=0.015\)\(V_{c\,\max}\). \(A_{c}\) and \(A_{j}\) are expressed as:  
\[A_{c}=V_{c\,\max}\,\frac{C_{c}-\Gamma^{*}}{C_{c}+K_{c}(1+O_{c}\,/\,K_{o})}\] (2a) and:\[A_{j}=J_{\max}\frac{C_{c}-\Gamma^{*}}{4(C_{c}+2\Gamma^{*})} \tag{2b}\]  
where \(C_{c}\) and \(O_{c}\) are the intercellular CO\({}_{2}\) and O\({}_{2}\) mole fractions (mol mol\({}^{-1}\)), respectively; \(\Gamma^{*}\) is the CO\({}_{2}\) compensation point without dark respiration (mol mol\({}^{-1}\)); \(K_{c}\) and \(K_{o}\) are Michaelis-Menten constants for CO\({}_{2}\) and O\({}_{2}\) (mol mol\({}^{-1}\)), respectively. In the nutrient-limited stands, \(A_{net}\) is generally limited by \(A_{c}\), while \(A_{c}\) is dominantly controlled by a parameter \(V_{c\max}\) (see Eqn. 2a). Many research results showed \(V_{c\max}^{25}\) is very sensitive to leaf N status (more specifically leaf Rubisco-N) [134,185-187]. As a result in some ecosystem models (i.e., C&N-CLASS [23]), \(V_{c\max}^{25}\) is calculated as a nonlinear function of Rubisco-N following observations made by [PERSON] and [PERSON] [134]:  
\[V_{c\max}^{25}(N)=\alpha\big{[}1-\exp(-1.8N_{r0}\big{]} \tag{3}\]  
where \(\alpha\) is the maximum value of \(V_{c\max}^{25}\) and \(N_{r0}\) is the leaf Rubisco-N (g N m\({}^{-2}\) leaf area) in the top canopy.  
The coupled C, N and water processes have been carefully considered in most of the third-generation LSMs (e.g., SiB2 [139,140,150]); CN-CLASS [28] and _Ecosys_[183,184]), the models' grids, however, are isolated from their neighboring grids mainly due to the availability of input data. Vertical soil hydrological processes are hard to be realistically simulated if the lateral flows are ignored by assuming that the Earth is \"flat\". However, simulations of the topographically-driven lateral water flows are important components in most of spatially-distributed models, while the detailed ecophisiological processes are weakly represented [188]. Much effort to bridge these two different models has been increasingly made [33,35,188-194]. However, a model coupling approach--a full combination of ecosystem model and hydrological model, i.e., ecohydrological modeling, is still lacking.