## 2 Materials and Methods
### Methods  
#### 2.3.1 Trend Analysis  
The Theil-Sen estimator method is a calculation method applicable to trend analysis for long-term series data, which is computationally efficient, insensitive to measurement errors and niche data, and can be combined with the Mann-Kendall trend analysis method to further perform trend significance tests for long-term series data [51]. Its calculation formula is as follows:  
\[\beta=median\ \left(\frac{NPP_{j}-NPP_{i}}{j-i}\right) \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & **Data** & **Year** & **Original Resolution** \\ \hline Net primary productivity data & MOD17A3 HGF v006 & 2000–2019 & 500 m \\ Land use/land cover data & MCD12Q1 v006 & 2001–2019 & 500 m \\ Population data & Population density & 2000, 2005, 2010, 2015, 2019 & 1000 m \\ Gross domestic product data & GDP & 2000, 2005, 2010, 2015, 2019 & 1000 m \\ Digital elevation model data & GDEM v003 & 2019 & 30 m \\ Meteorological data & Temperature, Precipitation, Sunshine & 2000–2019 & 500 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The data sources used in this study. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Category**} & \multicolumn{3}{c}{**Environmental Driving Factors**} & \multicolumn{3}{c}{**Climatic Driving Factors**} & \multicolumn{3}{c}{**Human Activities**} \\ \cline{2-10}  & **DEM/m** & **Slope/\({}^{*}\)** & **Aspect** & **TEM/C** & **PRE/mm** & **TSH/h** & **GDP** & **POP** & **LULC** \\ \hline
1 & –56–66 & 0–0.60 & Flat & 8.90–11.04 & 766–959 & 1450–1598 & 92–63,114 & 45–316 & Forest land \\
2 & 66–182 & 0–6.00 & North & 11.04–28.91 & 959–1102 & 1598–1669 & 63,114–126,137 & 316–984 & Grassland \\
3 & 182–311 & 1.80–32.36 & Northeast & 12.81–14.21 & 1102–1232 & 166–1731 & 126,137–189,159 & 984–920 & Construction Land \\
4 & 311–441 & 3.26–4.71 & East & 14.21–15.24 & 1232–1368 & 1731–1799 & 189,159–252,182 & 2320–4591 & Cultivated land \\
5 & 441–577 & 4.71–6.25 & Southeast & 15.24–15.24 & 1368–1499 & 1799–1873 & 252,182–135,204 & 4591–8198 & Water \\
6 & 577–276 & 6.25–79.79 & South & 15.94–16.51 & 1499–1610 & 1879–1950 & 315,204–382,227 & 3189–132,374 & Other \\
7 & 726–894 & 7.97–9.94 & Southwest & 16.51–17.21 & 1610–1728 & 1950–2024 & 378,227–41,249 & 132,274–18,618 & / \\
8 & 894–1101 & 9.94–12.51 & West & 17.21–18.12 & 1728–1993 & 2024–2098 & 441,429–504,272 & 16,615–23,962 & / \\
9 & 1102–1593 & 12.51–21.84 & Northwest & 18.12–19.39 & 1939–2343 & 2098–2237 & 504,272–567,294 & 23,962–34,115 & / \\ \hline \hline \end{tabular} Notably, “TEM” represents the annual average temperature, “PRE” represents the total annual precipitation, “TSH” represents the total annual sunshine hours, and “POP” represents the number of populations.  
\end{table} 
Table 2: The spatial driving factors of NPP in this study. where: _median ()_ represents taking the median value; \(NPP_{i}\) and \(NPP_{j}\) are the corresponding data (NPP) values in years \(i\) and \(j\), respectively, and \(j>i\); when \(\beta\) = 0, NPP has no change, when \(\beta\) > 0, NPP increases, and vice versa. The Mann-Kendall trend test method is widely used for trend analysis of NPP time series, as it does not require the measurements to obey a normal distribution and is not affected by missing values and outliers when performing trend significance tests [52]. The process is as follows: for the sequence \(X_{t}\) = \(x_{1}\), \(x_{2}\),..., \(x_{n}\), first determine the relationship between the magnitude of \(x_{i}\) and \(x_{j}\) (set to \(S\)) for all pairs of values (\(x_{i}\), \(x_{j}\), \(j>i\)). Hypothesis the data in the \(H_{0}\) series are randomly aligned, i.e., there is no significant trend; there is an upward or downward trend in the \(H_{1}\) series. The test statistic \(S\) is calculated as:  
\[S=\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}sgn\big{(}x_{j}-x_{i}\big{)} \tag{2}\]  
\[sgn\big{(}x_{i}-x_{j}\big{)}=\left\{ \begin{array}{cc}1,&x_{j}-x_{i}>0\\ 0,&x_{j}-x_{i}=0\\ -1,&x_{j}-x_{i}<0\end{array} \right.