# Monitoring Vegetation Change and Its Potential Drivers in Inner Mongolia from 2000 to 2019
## 2 Materials and methods
### Methods  
#### 2.3.1 Spatial Trend Analysis Methods  
The combination of the Theil-Sen trend analysis and the Mann-Kendall test does not require the data to follow a certain distribution when analyzing trends over a time series. Furthermore, the combination is more resistant to data errors and the results from the significance level test are more scientifically reliable than other research methods [29]. Theil-Sen trend analysis is a very reliable non-parametric statistical calculation method that is computationally efficient, insensitive to measurement errors and outlier data, and is often used in the trend analysis of long time series. This is calculated as follows:  
\[\beta=Median\left(\frac{NDVI_{j}-NDVI_{i}}{j-i}\right), \tag{1}\]  
where \(NDVIj\) and \(NDVIi\) are the NDVI values of a certain pixel in years \(j\) and \(i\), respectively. In this study, \(2019\geq j\geq i\geq 2000\). Additionally, the median represented here is the median \begin{table}
\begin{tabular}{c c c c} \hline
**Dataset** & **Time Scale** & **Spatial Scale** & **Source of Data** \\ \hline NDVI & 2000–2019 & 1 km & \
\begin{tabular}{c} MOD13A3 \\ ([[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 date: 23 December 2020 \\ Inner Mongolia Statistical Yearbook \\ (2000–2019) \\ accessed date: 23 December 2020 \\ SRTM3 \\ ([[https://earthexplorer.usgs.gov/](https://earthexplorer.usgs.gov/)]([https://earthexplorer.usgs.gov/](https://earthexplorer.usgs.gov/))) \\ accessed date: 24 December 2020 \\ (Centralized extraction of elevation data \\ accessed date: 23 December 2020 \\ (1:1 million soil map of the People’s Republic of China \\ accessed date: 23 December 2020 \\ [[https://www.resdc.cn](https://www.resdc.cn)]([https://www.resdc.cn](https://www.resdc.cn)) \\ accessed date: 24 December 2020 \\ Number of livestock \\ (2010) \\ (Cong domestic product (GDP) \\ (1:1 km \\ (1:1 km \\ (1:1 km \\ (1:1 km \\ (1:1 km \\ \end{tabular} &
\begin{tabular}{c} 1 km \\ ([[https://www.resdc.cn](https://www.resdc.cn)]([https://www.resdc.cn](https://www.resdc.cn)) \\ accessed date: 24 December 2020 \\ [[https://www.resdc.cn/edical](https://www.resdc.cn/edical)]([https://www.resdc.cn/edical](https://www.resdc.cn/edical)) date: 24 December 2020 \\ [[https://www.resdc.cn/DOI](https://www.resdc.cn/DOI)]([https://www.resdc.cn/DOI](https://www.resdc.cn/DOI)) [60] \\ accessed date: 25 December 2020 \\ [[https://www.worldpop.org/project](https://www.worldpop.org/project)]([https://www.worldpop.org/project](https://www.worldpop.org/project)) \\ accessed date: 25 December 2020 \\ [[https://www.worldpop.org/project](https://www.worldpop.org/project)]([https://www.worldpop.org/project](https://www.worldpop.org/project)) \\ accessed date: 25 December 2020 \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 1: Sources of dataset. of the requested series. When \(\beta\) is greater than 0, an increasing trend is observed in the NDVI and when \(\beta\) is less than 0, the NDVI presents a decreasing trend. When \(\beta\) is equal to 0, the NDVI is stable. The Mann-Kendall method is a non-parametric statistical test that was originally proposed by [PERSON] in 1945 and further refined by [PERSON] and [PERSON]. It is advantageous as it does not require normally distributed measurements or a linear trend and remains unaffected by missing values or outliers. It is widely used for the trend significance testing of long-series data [61]. The Mann-Kendall statistic \(S\) is calculated for the time series {_NDVIi_} as follows:  
\[S=\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}sgn\big{(}NDVI_{j}-NDVI_{i}\big{)} \tag{2}\]  
Figure 2: NDVI drivers and spatial distribution in Inner Mongolia. where \(n\) is the length of the time series, and \(sgn\) is the sign function, defined as:  
\[sgn\big{(}NDVI_{j}-NDVI_{i}\big{)}=\left\{