## 2 Methods
### The Improved Water-Carbon Coupling DTVGM Ecohydrological Model  
The Distributed Time Variant Gain Model (DTVGM) has been developed and successfully applied to many basins in China [34; 35; 36]. So far, it has been extended to simulating land-surface processes including water, energy and carbon fluxes by coupling with the CASACNP model [37]. The physically based coupled model could capture the mechanism of the interactions between vegetation dynamics and the water cycle quite well and could be used to investigate the responses of ecohydrological processes to changing climate and vegetation, and consequently the attributions of ET and GPP.  
In this study, the DTVGM is further improved based on the coupled model by solving the ecohydrological processes iteratively according to the following equations to ensure water balance. At each daily time step, the water balance equation can be expressed as:  
\[P_{i}+AW_{i}=AW_{i+1}+RS_{i}+ET_{i}+RI_{i}+RG_{i} \tag{1}\]  
The above equation could be solved using the Newton iteration method as follows:  
\[\begin{split} f(AW)&=2 AW-P-AW_{i}+RS_{i}+RI_{i}+RG_ {i}+ET_{i}\\ AW^{j+1}&=AW^{j}-\frac{f(AW^{j})}{f^{\prime}(AW)} \end{split} \tag{2}\]  
where \(P\) is the daily effective rainfall arriving at the ground surface, \(AW\) is the daily mean soil water content, \(ET\) is the daily actual evapotranspiration, \(RS\), \(RI\) and \(RG\) are the daily  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Catchment**} & \multicolumn{3}{c}{**Dominant Land Cover**} & \multirow{2}{*}{**Area (km\({}^{2}\))**} \\ \cline{2-2} \cline{4-5}  & **Forest** & **Grassland** & **Cropland** & \\ \hline Baigouhe & 83\% & 9\% & 2\% & 641.17 \\ Jumahe & 64\% & 22\% & 10\% & 4801.27 \\ Baishahe & 36\% & 49\% & 10\% & 493.67 \\ Tanghe & 22\% & 50\% & 21\% & 4257.41 \\ Dashahe & 32\% & 55\% & 7\% & 3688.61 \\ Cine & 47\% & 38\% & 8\% & 483.51 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The area and dominant land cover of the six catchments in the study area.  
surface runoff, interflow runoff and groundwater runoff, respectively. The subscripts \(i\) and \(i\)+1 represent the time steps. The superscript \(j\) is the iteration number. The evapotranspiration was calculated with three components including canopy-intercepted water evaporation in the wet leaves, transpiration in the dry leaves and soil evaporation based on the two-source method [37].  
For gross primary production, the daily canopy photosynthesis model [38] is selected. The photosynthesis rate are calculated as follows:  
\[A=\min\bigl{(}A_{c}-A_{j}\bigr{)}-R_{d} \tag{3}\]  
where \(A_{c}\) and \(A_{j}\) are the Rubiso-limited and light-limited gross photosynthesis, \(R_{d}\) is the daytime leaf dark respiration. Details can be found in [38].  
The major calculation procedure to iteratively solve of the ecohydrological processes are shown in Figure 2. Firstly, the initial mean soil water content was set to calculate the soil resistance. The stomatal conductance, photosynthesis and the canopy resistance were calculated, and were affected by soil moisture. Then, the ET with its three components and runoff could be estimated. After that, ET, effective rainfall and runoff were input to Equation (1) to solve the mean soil water content by comparing it with the initial mean soil water content until it converges using the Newton iteration. With these calculation steps, the mean soil moisture was iteratively calculated, and then the ET, GPP and other fluxes were estimated.  
Figure 2: The major calculation procedure of the simulation.