## 3 Data Analysis  
1. Trend Analysis  
Trend analysis takes each pixel as the research unit. Analyzing the pixel changes in different periods reflects the vegetation dynamics of the whole study area under a certain time series [30], which can eliminate the influence of abnormal factors so as to more accurately reflect the trend of vegetation evolution. \[Slope=\frac{n\times\sum_{k=1}^{n}k\times x_{k}-\sum_{k=1}^{n}k\times\sum_{k=1 }^{n}x_{k}}{n\times\sum_{k=1}^{n}k^{2}-\left(\sum_{k=1}^{n}k\right)^{2}} \tag{1}\]  
where \(Slope\) is the changing trend of NDVI; \(n\) is the length of time series, which is 21 in this study; \(x_{k}\) is the \(k\)-year NDVI value, \(k=1,\ 2,\ 3\cdots 21\); when \(Slope\) is positive, it indicates that the vegetation index increases with time; otherwise, it shows a degradation trend. The significance test was carried out by using the \(F\) test method, and the \(p\)-value was taken as 0.01 and 0.05. Figure 1: Geographical location of Ordos City. (2) Sustainability Analysis  
The Hurst index, based on (R/S) analysis, can predict the future development trend by judging the dependence of time series [4; 31; 32]. The principle is as follows:  
Define the NDVI of time series within the research years as \(x(i)\)\((i=1,\ 2,\dots,\ 19)\) for any number of years \(t\), then:  
The mean value is:  
\[\overline{x}(i)=\frac{\sum_{i=1}^{t}x_{i}}{t},t=1,2,3\dots,19 \tag{2}\]  
The cumulative deviation is:  
\[X(i,t)=\sum_{u=1}^{i}(x(u)-\overline{x}(i)),1\leq i\leq t \tag{3}\]  
The extreme difference is defined as:  
\[R(t)=\underset{1\leq t\leq i}{\max}X(i,t)-\underset{1\leq t\leq i}{\min}X(i,t) \tag{4}\]  
The standard deviation is:  
\[(t)=\left[\left(\frac{\sum_{i}^{t}(x(i)-\overline{x}(t))}{t}\right)^{2} \right]^{\frac{1}{2}},t=1,\ 2,\ 3\dots,\ 19 \tag{5}\]  
Taking \(\ln(t/2)\) as the horizontal axis and \(\ln(R(t)/S(t))\) as the vertical axis, a double logarithmic coordinate system was built. The data of 19 points were linearly fitted by the least square method, and the slope obtained was the Hurst index (\(H\)). \[ln\frac{R(t)}{S(t)}=H\cdot ln\frac{t}{2}+lnC,\ t=1,\ 2,\ 3\dots,\ 19 \tag{6}\]  
The Hurst index has the characteristic that the change trend of the future is similar to that of the past when the index value is greater than 0.5, and the change trend is contrary to the past when the index value is between 0 and 0.5 (Table 1). Therefore, the Hurst index was used to forecast and analyze the future change of the vegetation NDVI in Ordos City. (3) Path Analysis  
Path analysis is a multivariate statistical technique to study the direct and indirect relationship between independent variables and dependent variables through the decomposition of the surface direct correlation between independent variables and dependent variables [33]. The principle is as follows:  
If the correlation coefficient between independent variables and independent variables is \(r_{x_{i}x_{j}}\), the correlation coefficient between independent variables and dependent variables is \(R_{x_{i}y}\)  
\[ \begin{bmatrix}1&r_{x_{1}x_{1}}&\cdots&r_{x_{2}x_{n}}\\ r_{x_{2}x_{1}}&1&\cdots&r_{x_{2}x_{n}}\\ \vdots&\vdots&\ddots&\vdots\\ r_{x_{n}x_{1}}&r_{x_{n}x_{2}}&\cdots&1\end{bmatrix}\begin{bmatrix}A_{1y}\\ A_{2y}\\ \vdots\\ A_{ny}\end{bmatrix} = \begin{bmatrix}R_{x_{1}y}\\ R_{x_{2}y}\\ \vdots\\ R_{x_{n}y}\end{bmatrix}  \tag{7}\]