## 2 Materials and Methods
### RHESSys Model--Two-Way Ecohydrological Model  
The RHESSys model is a two-way coupled ecohydrological model designed to simulate the dynamic cycling of materials, such as water, carbon, and nitrogen, through complex interactions between the atmosphere, soil, and vegetation [43]. Unlike traditional ecohydrological models that commonly utilize basin-grid or basin-subbasin-grid structures, RHESSys organizes the spatial domain into hierarchical, homogeneous units at multiple scales. This approach integrates both horizontal and vertical connectivity in ecohydrological processes by coupling water and carbon fluxes, enabling a more comprehensive simulation of ecosystem dynamics. Due to these advanced modeling frameworks, RHESSys has been successfully applied across diverse spatial scales, from small basins of approximately 0.1 km\({}^{2}\) to large basins covering up to 60,000 km\({}^{2}\)[44]. The precise description of the dynamic interaction between ecological and hydrological processes has made this model more widely used in various studies such as vegetation variations, climate change impact and vegetation water demand [45; 46]. The model performances of the model were assessed by using evaluation metrics such as Nash-Sutcliffe Efficiency (NSE), LogNSE and Percent bias (Pbias) (Equations (1)-(3)) to evaluate runoff, evapotranspiration and GPP in the study area. The widely used Soil and Water Assessment Tool (SWAT) [47] model was used to compare the performance of the simulation with the RHESSys model in the study area. \[NSE=1\quad\frac{\sum\limits_{i=1}^{n}{(Q_{i,obs}\quad Q_{i,sim})^{2}}}{\sum \limits_{i}^{n}}\]turbed watershed, the existing flow regime represents the ecological water requirements (EWRs) that ecosystems have adapted to over centuries. Our focus is on evaluating this assumption rather than examining the specific water needs and seasonal dynamics of individual plant and animal communities in streams and floodplains. Therefore, this study calculates instream EWRs based on a long-term runoff series. Previous studies have suggested that river ecosystems and aquatic species have adapted to the natural hydrological fluctuations of the watershed, including seasonal and interannual variations in water availability (such as precipitation, runoff and evaporation). As a result, many studies have used characteristic indicators, such as the long-term minimum runoff, to represent the minimum flow required to sustain the ecosystem and its basic functions [20; 49]. However, these methods do not capture the seasonal variation of minimum runoff. To address this, our study introduces the \"ratio\" approach, which uses the mean value over a consistent time period to derive the monthly ecological water requirements (EWRs) for the river system. It determines the ratio between the multi-year average monthly runoff and the minimum monthly average runoff as two key indicators, using this ratio to estimate instream EWRs based on observed runoff. Nevertheless, this method can result in lower EWRs in wet years compared to dry years. To address this, the study further compares the minimum multi-year monthly average runoff with the EWRs derived from the ratio, taking the higher value as the actual instream EWRs. The equations are as follows:  
\[\overline{\mathcal{O}}=\frac{1}{12}{\sum\limits_{i=1}^{12}{\overline{q}_{i}}}, \ \overline{q}_{i}=\frac{1}{n}{\sum\limits_{j=1}^{n}{q_{ij}}} \tag{4}\]  
\[\overline{\mathcal{O}}_{\min}=\frac{1}{12}{\sum\limits_{i=1}^{12}{\overline{q}_ {\min(i)}}},\ \overline{q}_{\min(i)}=\min(q_{ij}),j=1,2,\ldots,n \tag{5}\]  
\[\eta=\overline{\mathcal{O}}_{\min}\ /\ \overline{\mathcal{O}} \tag{6}\]  
\[\mathcal{O}_{l}= \begin{pmatrix}\overline{q}_{i}&\eta,if\ (\overline{q}_{i}&\eta> \overline{q}_{\min(i)})\\ \overline{q}_{\min(i)},if\ (\overline{q}_{i}&\eta<\overline{q}_{\min(i)}) \end{pmatrix}