## 2 Methods
### Quantification of the Effects on ET and GPP  
For a given catchment, the changes of certain ecohydrological indicator \(Y\) (ET or GPP) can be affected by meteorological variables (\(M\)), elevated atmospheric carbon dioxide (eCO\({}_{2}\), \(C\)), land cover change (\(L\)) and the interactive effects (\(I\)) between climate, eCO\({}_{2}\) and land cover. \[Y=f(M,C,L) \tag{4}\]  
According to [39], the changes in \(Y\) (\(\Delta Y\)) at a catchment scale under changing environment can be expressed using [PERSON] approximation as follows:  
\[ \begin{array}{l}\frac{\Delta Y}{\Delta t}\approx\frac{\Delta Y_{M}}{\Delta t }+\frac{\Delta Y_{C}}{\Delta t}+\frac{\Delta Y_{i}}{\Delta t}+\frac{\Delta Y_{ i}}{\Delta t}\\ \\ \Delta Y_{M}=\frac{\partial f}{\partial M}\Delta M+\frac{1}{2t}\frac{\partial^{2 }f}{\partial M^{2}}\Delta M^{2}+\cdot\cdot\cdot+\frac{1}{n!}\frac{\partial^{n} f}{\partial M^{2}}\Delta M^{n}\\ \\ \Delta Y_{C}=\frac{\partial f}{\partial C}\Delta C+\frac{1}{2t}\frac{\partial ^{2}f}{\partial C^{2}}\Delta C^{2}+\cdot\cdot\cdot+\frac{1}{n!}\frac{\partial^ {n}f}{\partial C^{n}}\Delta C^{n}\\ \\ \Delta Y_{L}=\frac{\partial f}{\partial L}\Delta L+\frac{1}{2t}\frac{\partial ^{2}f}{\partial L^{2}}\Delta L^{2}+\cdot\cdot\cdot+\frac{1}{n!}\frac{\partial ^{n}f}{\partial L^{2}}\Delta L^{n}\end{array}  \tag{5}\]  
where \(\Delta M\), \(\Delta C\), \(\Delta L\) are the changes of climate variables, eCO\({}_{2}\) and land cover, \(\Delta Y_{M}\), \(\Delta Y_{C}\), \(\Delta Y_{L}\), \(\Delta Y_{I}\) represent the changes in \(Y\) caused by climate change, eCO\({}_{2}\), land cover changes and the interactive effects between the above three factors. In order to quantify the contributions of climate change, eCO\({}_{2}\) and land-use and cover change on GPP and ET in the six catchments from 2000 to 2019, ten experimental scenarios were designed, including the baseline (S0), climate variables detrend including atmospheric pressure-detrend (S1), temperature-detrend (S2), humidity-detrend (S3), precipitation-detrend (S4), windspeed-detrend (S5), solar radiation-detrend (S6), carbon dioxide-detrend (S7), land-use and cover changes (S8) and all factor changes scenario (S9). The details of the scenarios are shown in Table 2. The detrend of climate variables is based on the removal of the long-term linear trend during 2000 to 2019 as follows:  
\[X^{\prime}_{Y_{i,d}}=\left[\frac{X_{Y_{i}}-a\times(Y_{i}-Y_{0})}{X_{Y_{i}}} \right]\times X_{Y_{i,d}} \tag{6}\]  
where \(X_{Y_{i,d}}\) and \(X^{\prime}_{Y_{i,d}}\) denote the daily original and detrended climate variable at the \(d\) day in the year \(Y_{i}\); \(X_{Y_{i}}\) is the average values of the climate variable; \(a\) represents the linear trend of the values of the climate variable; \(Y_{i}\) refers to the year from 2000 to 2019 and \(Y_{0}\) is the base year. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenarios** & **Scenario Name** & **Descriptions** \\ \hline S0 & Baseline & All the driving factors including historical meteorological variables, CO\({}_{2}\) and land coverage are used to drive the model. \\ S1 & Atmospheric pressure-detrend & The atmospheric pressure is detrended using historical records. \\ S2 & Temperature-detrend & The temperature is detrended using historical records. \\ S3 & Humidity-detrend & The relative humidity is detrended using historical records. \\ S4 & Precipitation-detrend & The precipitation is detrended using historical records. \\ S5 & Windspeed-detrend & The windspeed is detrended using historical records. \\ S6 & Solar radiation-detrend & The sunshine duration is detrended using historical records. \\ S7 & Carbon dioxide-detrend & The carbon dioxide is detrended using historical records. \\ S8 & Land use and cover changes & The land use is set at 2000 using historical records. \\ S9 & All-detrend and no land use change & All the meteorological variables and CO\({}_{2}\) are detrended and the land use is set at 2000. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of the ten experimental scenarios settings.