## 2 Materials and Methods
### Extreme Climate Indices  
This study utilizes the definitions of 27 Extreme Climate Indices (ECIs) established by the Expert Team on Climate Change Detection and Indices (ETCCDI) ([[http://etccdi.pacificclimate.org/list_27_indices.shtml](http://etccdi.pacificclimate.org/list_27_indices.shtml)]([http://etccdi.pacificclimate.org/list_27_indices.shtml](http://etccdi.pacificclimate.org/list_27_indices.shtml)), accessed on 22 July 2024), to analyze extreme climate events in the NFYS region between 2001 and 2023, based on daily meteorological data processed from ERA5 hourly meteorological data of ERA5 Climate and Forecast (CF) Metadata Convention v1.7 ([[https://cds.climate.copernicus.eu/](https://cds.climate.copernicus.eu/)]([https://cds.climate.copernicus.eu/](https://cds.climate.copernicus.eu/)), accessed on 22 July 2024). These ECIs are systematically classified into three distinct categories: intensity indices, duration indices, and frequency indices [36]. The specific classification criteria are detailed in Tables S1 and S2 of the supplementary document. To analyze trends in ECI and GPP, this study employs the Mann-Kendall test and Theil-Sen Median trend analysis, both of which are non-parametric statistical methods [37]. The trends are quantified by the \(\beta\) and \(Z\) values, where \(\beta\) represents the magnitude of the trend and \(Z\) indicates the statistical significance. Specifically, a positive \(\beta\) value (\(\beta>0\)) signifies an increasing trend, while a negative \(\beta\) value (\(\beta<0\)) indicates a decreasing trend. Since \(\beta\) values are rarely exactly zero, trends with \(\beta\) values between \(-0.001\) and \(0.001\) are classified as stable [38]. At the 0.05 significance level, trends are categorized as statistically significant if \(|\,Z|\,\geq\,1.96\) and non-significant if \(|\,Z|\,<\,1.96\)[39]. Based on the combination of \(Z\) and \(\beta\) values, trends are further classified into five distinct levels: significant decrease, decrease, stable (less change), increase, and significant increase. The Pearson correlation coefficient was utilized to quantify the lag effect of GPP in response to climate variability. The calculation is formulated as follows: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Data** & **Variables** & **Abb** & **SR** & **TS** & **Source** \\ \hline \multirow{4}{*}{Meteorological Data} & Maximum temperature & \multirow{2}{*}{T\({}_{\text{max}}\)} & \multirow{2}{*}{0.1 \(\times\) 0.1\({}^{\circ}\)} & \multirow{2}{*}{2001–2023} & ERA5 Climate and Forecast (CF) & \\  & & & & & Metadata Convention v1.7 \\ \cline{1-1} \cline{4-6}  & Maximum temperature & & & & [[https://cds.climate.copernicus.eu/](https://cds.climate.copernicus.eu/)]([https://cds.climate.copernicus.eu/](https://cds.climate.copernicus.eu/)), & \\ \cline{1-1} \cline{4-6}  & Minimum temperature & \multirow{2}{*}{T\({}_{\text{min}}\)} & \multirow{2}{*}{0.25 \(\times\) 0.25\({}^{\circ}\)} & \multirow{2}{*}{2025–2035} & CMIP6 [[https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)]([https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)), & \\ \cline{1-1}  & Precipitation & & & & accessed on 22 July 2024 \\ \hline \multirow{4}{*}{GPP Data} & GOSIF-GPP & GPP & 0.05 \(\times\) 0.05\({}^{\circ}\) & \multirow{2}{*}{2001–2023} & [[https://globalecology.unh.edu/](https://globalecology.unh.edu/)]([https://globalecology.unh.edu/](https://globalecology.unh.edu/)) & \\ \cline{1-1}  & & & & & /data/GOSIF-GPP.html, accessed on 22 July 2024 \\ \cline{1-1} \cline{4-6}  & \multirow{2}{*}{CO\({}_{2}\) flux} & GPP & 2.3 m & 2015–2018 & [[http://www.csdata.org/p/837/](http://www.csdata.org/p/837/)]([http://www.csdata.org/p/837/](http://www.csdata.org/p/837/)), & \\ \cline{1-1} \cline{4-6}  & & & & & accessed on 22 July 2024 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detailed information on the data acquired in the study (Abb: abbreviation; SR: spatial resolution; TS: Time Span). \[