## 2 Materials and Methods
### Methods
#### 2.3.2 Sen + MK Trends Analysis  
The combination of Theil-Sen median trend analysis and the Mann-Kendall test provides a robust and reliable method for detecting trends in long-term time series data [47]. The approach effectively captures the spatiotemporal variation patterns of cropland CWUE, GPP, NPP, and ET in Henan Province during 2001-2019. The Theil-Sen median trend is calculated by the formula:  
\[\text{Sen}=Median(\frac{X_{\text{a}}-X_{b}}{a-b}),\ 2001\leq\text{b}\leq a\leq 2019 \tag{4}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Unit** & **Time Period** & **Temporal Resolutions** & **Spatial Resolutions** & **Data Source** \\ \hline GPP & gCm\({}^{-2}\)y\({}^{-1}\) & 2001–2019 & 500 m & 8 days & [[https://ladsweb.modaps.eosdis.nasa.gov/](https://ladsweb.modaps.eosdis.nasa.gov/)]([https://ladsweb.modaps.eosdis.nasa.gov/](https://ladsweb.modaps.eosdis.nasa.gov/)) \\ NPP & gCm\({}^{-2}\)y\({}^{-1}\) & 2001–2019 & 500 m & 8 days & [[https://ladsweb.modaps.eosdis.nasa.gov/](https://ladsweb.modaps.eosdis.nasa.gov/)]([https://ladsweb.modaps.eosdis.nasa.gov/](https://ladsweb.modaps.eosdis.nasa.gov/)) \\ ET & mmy\({}^{-1}\) & 2001–2019 & 500 m & 8 days & [[https://glass-product.bru.edu.cn/introduction/](https://glass-product.bru.edu.cn/introduction/)]([https://glass-product.bru.edu.cn/introduction/](https://glass-product.bru.edu.cn/introduction/)) \\  & & & & & ET.html (accessed on 5 April 2024) \\ LAI & N/A & 2001–2019 & 500 m & 8 days & [[https://glass-product.bru.edu.cn/type.html](https://glass-product.bru.edu.cn/type.html)]([https://glass-product.bru.edu.cn/type.html](https://glass-product.bru.edu.cn/type.html)) \\  & & & & & & (accessed on 5 May 2024) \\ Land use & N/A & 2001–2019 & 500 m & annual scale & [[https://doi.org/10.5067/MODIS/MED12Q1.006](https://doi.org/10.5067/MODIS/MED12Q1.006)]([https://doi.org/10.5067/MODIS/MED12Q1.006](https://doi.org/10.5067/MODIS/MED12Q1.006)) \\ Temperature & \({}^{\circ}\)C & 2001–2019 & 1 km & monthly scale & [[https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)]([https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)) \\ Precipitation & mm & 2001–2019 & 1 km & monthly scale & [[https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)]([https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)) \\ Rad & N/A & 2001–2019 & 1 km & 8 days & [[https://www.geodata.cn/](https://www.geodata.cn/)]([https://www.geodata.cn/](https://www.geodata.cn/)) \\ Sun & h & 2001–2019 & 1 km & annual scale & [[https://www.geodata.cn/](https://www.geodata.cn/)]([https://www.geodata.cn/](https://www.geodata.cn/)) \\ GDP & million USD/km\({}^{2}\) & 2001–2019 & 1 km & annual scale & [[https://doi.org/10.6084/m9.figshare.17004523.v1](https://doi.org/10.6084/m9.figshare.17004523.v1)]([https://doi.org/10.6084/m9.figshare.17004523.v1](https://doi.org/10.6084/m9.figshare.17004523.v1)) \\  & & & & & (accessed on 10 November 2024) \\ Irrigation & N/A & 2001–2019 & 500 m & annual scale & [[https://www.nessdc.org.cn/](https://www.nessdc.org.cn/)]([https://www.nessdc.org.cn/](https://www.nessdc.org.cn/)) \\ DEM & m & 2000 & 30 m & N/A & [[https://www.gscloud.cn/](https://www.gscloud.cn/)]([https://www.gscloud.cn/](https://www.gscloud.cn/)) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of data used in this study. X represents one of the CWUE, GPP, NPP, or ET metrics. A positive Sen slope (Sen > 0) indicates an increasing trend in X, while a negative Sen slope (Sen < 0) reflects a declining trend. The Mann-Kendall test is calculated as follows:  
Let \(\{X_{\text{b}}\},\text{b}=2001,2002,\ldots,2019\), define the \(Z\) statistic as  
\[Z= \begin{cases}\frac{S-1}{\sqrt{s(S)}},S>0\\ 0,S=0\quad\text{of which, }S=\sum_{a=1}^{n-1}\sum_{b=a+1}^{n}\text{sgn}(X_{ \text{a}}-X_{b})\\ \frac{S+1}{\sqrt{s(S)}},S<0\end{cases}  \tag{5}\]  
\[\text{sgn}(X_{\text{a}}-X_{b})= \begin{cases}1,X_{a}-X_{b}>0\\ 0,X_{a}-X_{b}=0\\ -1,X_{a}-X_{b}<0\end{cases}