# Spatial and Temporal Variation of GPP and Its Response to Urban Environmental Changes in Beijing
## Data and Methods
### Methods
#### 2.3.2. \(\mathrm{[PERSON]}-\mathrm{[PERSON]}\) Trend Test  
The Mann-Kendall trend test evaluates time-series data for the presence of monotonic ascends or descends in the Y-axis values [28]. In this research, we employ the M-K test to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data** & \begin{tabular}{c} **Spatial** \\ **Resolution** \\ \end{tabular} & \begin{tabular}{c} **Temporal** \\ **Resolution** \\ \end{tabular} & \
\begin{tabular}{c} **Period** \\ **Period** \\ \end{tabular} &
\begin{tabular}{c} **Data Source** \\ **\end{tabular} \\ \hline AGPP & 500 m & Year & 2000–2020 & 08f51e44 fcf326e8b0f972c34, accessed on \\  & & & 9 February 2024 \\ LST & 1 km & 8-day & 2014–2020 & [[https://ladsweb.modaps.eosdis.nasa.gov/](https://ladsweb.modaps.eosdis.nasa.gov/)]([https://ladsweb.modaps.eosdis.nasa.gov/](https://ladsweb.modaps.eosdis.nasa.gov/)), & accessed on 9 February 2024 \\ LUCC & 30 m & 5-year & 2000–2020 & [[https://www.resdc.cn/DOI/doi.aspx?DOIid=54](https://www.resdc.cn/DOI/doi.aspx?DOIid=54)]([https://www.resdc.cn/DOI/doi.aspx?DOIid=54](https://www.resdc.cn/DOI/doi.aspx?DOIid=54)), & accessed on 7 March 2024 \\ Air & 1 km & Month & 2014–2020 & [[http://loess.geodata.cn](http://loess.geodata.cn)]([http://loess.geodata.cn](http://loess.geodata.cn)), accessed on \\ Temperature & 1 km & Month & 2014–2020 & 11 February 2024 \\ Precipitation & 1 km & Month & 2014–2020 & [[http://loess.geodata.cn](http://loess.geodata.cn)]([http://loess.geodata.cn](http://loess.geodata.cn)), accessed on \\  & & & & 11 February 2024 \\ PM\({}_{2.5}\) & 1 km & Year & 2014–2020 & [[https://weijing-rs.github.io/product.html](https://weijing-rs.github.io/product.html)]([https://weijing-rs.github.io/product.html](https://weijing-rs.github.io/product.html)), & accessed on 11 February 2024 \\ CO & 10 km & Year & 2014–2020 & [[https://weijing-rs.github.io/product.html](https://weijing-rs.github.io/product.html)]([https://weijing-rs.github.io/product.html](https://weijing-rs.github.io/product.html)), & accessed on 11 February 2024 \\ NO\({}_{2}\) & 10 km & Year & 2014–2020 & [[https://weijing-rs.github.io/product.html](https://weijing-rs.github.io/product.html)]([https://weijing-rs.github.io/product.html](https://weijing-rs.github.io/product.html)), & accessed on 11 February 2024 \\ O\({}_{3}\) & 10 km & Year & 2014–2020 & [[https://weijing-rs.github.io/product.html](https://weijing-rs.github.io/product.html)]([https://weijing-rs.github.io/product.html](https://weijing-rs.github.io/product.html)), & accessed on 11 February 2024 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Research data in this study. identify such trends within the AGPP data series. The Mann-Kendall test for a time series is supposed to compute as follows:  
\[\text{sgn}\big{(}\text{x}_{\text{i}}-\text{x}_{\text{j}}\big{)}=\left\{ \begin{array} []{ll}1,&\text{x}_{\text{i}}-\text{x}_{\text{j}}>0\\ 0,&\text{x}_{\text{i}}-\text{x}_{\text{j}}>0\\ -1,&\text{x}_{\text{i}}-\text{x}_{\text{j}}>0\end{array} \right. \tag{2}\]  
\[\text{S}=\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}\text{sgn}\big{(}x_{i}-x_{j}\big{)} \tag{3}\]  
where \(N\) represents the dataset's size, and \(x_{i}\) and \(x_{j}\) are the data values at times \(i\) and \(j\). A negative \(S\) suggests a downward trend, while a positive \(S\) suggests an upward trend. The trend's statistical significance is evaluated using the variance of the MK statistic, applicable when \(N>10\), and is computed as follows:  
\[\text{Var}(\text{s})=\frac{n(n-1)(2n+5)-\sum_{i=1}^{p}q_{i}(q_{i}-1)(2q_{i}+5) }{18} \tag{4}\]  
where \(p\) indicates the number of concurrent groups within the dataset, and qi refers to the count of data points in the \(k\)th group. If the grouping variable is missing, the summation is excluded from the equation. The test statistic's standard \(Z\)-value of the test statistic can be calculated using the subsequent formula:  
\[Z=\left\{ \begin{array}{ll}\frac{\text{S}-1}{\sqrt{\text{var}(\text{S})}}\;S >0\\ 0;S=0\\ \frac{\text{S}-1}{\sqrt{\text{var}(\text{S})}}S<0\end{array} \right.