## 2 Materials and Methods
### Methods
#### 2.4.2 The Dominant Factors Driving Extreme Changes in WUE  
To analyze the differing sensitivities of GPP and ET to climate change across regions, we adopted the method proposed by the United States Drought Monitor (USDM), which identifies abnormal climatic conditions based on threshold percentiles of key hydroclimatic variables. This method defines abnormal climatic events as those occurring near the 33.3 rd percentile probability [56]. On this basis, we defined the extreme ranges for the components of WUE, namely GPP and ET.  
Annual GPP and ET time series are divided into extreme ranges, with values before the 33.3 rd percentile and after the 66.7 th percentile defined as extremes. By examining whether the annual GPP and ET values corresponding to the annual extremes of WUE fall within these defined extreme ranges, the dominant factors influencing WUE changes can be effectively identified. This method can be involved in two extreme cases: annual minimum WUE and annual maximum WUE. The following describes the judgment details for the case when WUE is the annual minimum:  
\[\mathrm{WUE_{t}}=\mathrm{min}(\mathrm{WUE})=\frac{\mathrm{GPP_{t}}}{\mathrm{ ET_{t}}} \tag{3}\]  
\[\mathrm{I:GPP_{t}}\in\mathrm{GPP_{<33.3\%}}\cap\mathrm{ET_{t}}\in\mathrm{ ET_{>66.7\%}}\]  
\[\mathrm{II:GPP_{t}}\in\mathrm{GPP_{<33.3\%}}\cap\mathrm{ET_{t}}\
otin \mathrm{ET_{>66.7\%}}\]  
\[\mathrm{III:GPP_{t}}\
otin\mathrm{GPP_{<33.3\%}}\cap\mathrm{ET_{t}}\in \mathrm{ET_{>66.7\%}}\]  
\[\mathrm{IV:GPP_{t}}\
otin\mathrm{GPP_{<33.3\%}}\cap\mathrm{ET_{t}}\
otin \mathrm{ET_{>66.7\%}}\]  
where \(\mathrm{WUE_{t}}\), \(\mathrm{GPP_{t}}\), and \(\mathrm{ET_{t}}\) represent the annual values of GPP and ET corresponding to the annual minimum WUE. \(\mathrm{GPP_{<33.3\%}}\) refers to the sequence before the 33.3 rd percentile of the annual GPP series and \(\mathrm{ET_{>66.7\%}}\) refers to the sequence after the 66.7 th percentile of the annual ET series.  
Case I is considered as WUE interannual variations being collectively dominated by both GPP and ET, Case II and Case III as being dominated by the single factors GPP and ET, respectively, and Case IV as having no dominant factors for WUE interannual variations.  
The same approach can be applied to determine the dominant factors influencing the variation when WUE reaches its maximum value. The following describes the judgment details for the case when WUE is the annual maximum:  
\[\mathrm{WUE_{t}}=\mathrm{max}(\mathrm{WUE})=\frac{\mathrm{GPP_{t}}}{\mathrm{ ET_{t}}} \tag{4}\]  
\[\mathrm{V:GPP_{t}}\in\mathrm{GPP_{>66.7\%}}\cap\mathrm{ET_{t}}\in\mathrm{ ET_{<33.3\%}}\]  
\[\mathrm{VI:GPP_{t}}\in\mathrm{GPP_{>66.7\%}}\cap\mathrm{ET_{t}}\
otin \mathrm{ET_{<33.3\%}}\]  
\[\mathrm{VII:GPP_{t}}\
otin\mathrm{GPP_{>66.7\%}}\cap\mathrm{ET_{t}}\in \mathrm{ET_{<33.3\%}}\]  
\[\mathrm{VIII:GPP_{t}}\
otin\mathrm{GPP_{>66.7\%}}\cap\mathrm{ET_{t}}\
otin \mathrm{ET_{<33.3\%}}\]  
where \(\mathrm{WUE_{t}}\), \(\mathrm{GPP_{t}}\), and \(\mathrm{ET_{t}}\) represent the annual values of GPP and ET corresponding to the annual maximum WUE. \(\mathrm{GPP_{>66.7\%}}\) refers to the sequence after the 66.7 th percentile of the annual GPP series and \(\mathrm{ET_{<33.3\%}}\) refers to the sequence before the 33.3 th percentile of the annual ET series.  
Case V is considered as WUE interannual variations being jointly dominated by both GPP and ET, Case VI and Case VII as being dominated by the single factors GPP and ET, respectively, and Case VIII as having no dominant factors for WUE interannual variations.