## 2 Materials and Methods
### AEM Model  
The process-based ecosystem model used in this study, AEM, couples the biogeochemical (carbon and water processes) and biophysical processes (energy balance) and is a spatially explicit ecosystem model [2; 35]. Based on the field studies, the vertical root distribution and the plant structure  
Figure 1: Study area (**a**) and the plant functional type distribution (**b**). TNF: temperate needle-leaf forest; TBF: temperate broadleaf forest; GRS: grass; NPS: non-pheratophyte shrub; PS: phreatophyte shrub; CRP: crop; NVG: No vegetation; STL: settlement; SPT: Summer pasture.  
of the xeric vegetation are well addressed in AEM. It uses a detailed mechanistic submodel to describe the water movement along the groundwater-soil-root-leaf continuum. The Farquhar biochemical model was coupled to AEM to calculate the gross primary production (GPP) [45]. For a single plant, the daily NPP is estimated as the balance of the GPP and the autotrophic respiration (Ra) shown in Equation (1):  
\[\text{NPP}=\text{GPP}-\text{Ra} \tag{1}\]  
where NPP (g C/(plant day)) is the net primary productivity, GPP (g C/(plant day)) is the gross primary production and Ra (g C/(plant day)) is the auto respiration that can be calculated by Equation (2):  
\[\text{Ra}=\text{Rm}+\text{Rg} \tag{2}\]  
where Rm (g C/(plant day)) is the daily maintenance respiration and Rg (g C/(plant day)) is the growth respiration. The Rm is calculated by the ambient temperature while the Rg is calculated by a constant ratio of 25% of the residual between GPP and Rm [35; 46].  
The ET in AEM was calculated from the plant transpiration, soil evaporation and canopy interception evaporation as shown in Equation (3):  
\[\text{ET}=\text{Tran}+\text{Es}+\text{Ec} \tag{3}\]  
where Tran (mm/(plant day)) is the plant's daily transpiration that is controlled by the water availability from the soil and the potential transpiration determined by the weather conditions [35]. Es (mm/(plant day)) is the soil evaporation that is assumed to only take place in the top 5 cm soil layer. Ec (mm/(plant day)) is the canopy interception evaporation. More details about AEM can be found in the literature [35].  
The WUE is defined as a ratio of photosynthetic carbon taken up to water consumed [47], and it is a very important parameter to measure the health of the ecosystem and check the influence of the environmental changes on the ecosystem, since it is more sensitive to the ambient changes than NPP or ET [25; 48]. Here we calculate the WUE as the ratio of GPP to ET as shown in Equation (4):  
\[\text{WUE}=\text{GPP}/\text{ET}. \tag{4}\]  
The AEM model has been validated by field observations for daily ET, NPP, vegetation, and soil carbon storage in Central Asia [2; 35; 3]. Recently, [PERSON] et al. [17] validated the performance of AEM in predicting NPP dynamics under manipulated climate and CO\({}_{2}\) concentration by using 28 experimental sites. These validation results show that AEM could correctly simulate the carbon and water fluxes and pools of the arid ecosystem in Central Asia. Therefore, AEM has been widely used to study the biogeochemical processes of the arid ecosystem in Central Asia and China, including the vegetation and soil carbon storage dynamics, and NPP, GPP, and ET responses to climate change and CO\({}_{2}\) fertilization effects for different vegetation types, such as GRS, xeric shrubs, and forests [3; 4; 14; 17; 18; 37].