# Assessment of Grassland Degradation on the Tibetan Plateau Based on Multi-Source Data
## 2 Materials and Methods
### Methods
#### 2.3.3 Analysis of Changes in Grassland Quality Based on Vegetation Indexes  
Overlaying the grassland fusion product in 2000, 2010 and 2020, the areas where grassland existed in all three years were selected as constant grassland areas. To exclude the interference of grassland area change, constant grassland area in 2000, 2010 and 2020 was used to analyze the quality change. The grassland quality change on the TP was classified into two aspects: vegetation greenness change and carbon sequestration capacity change. In this study, multiple indexes were used to assess the changes in grassland quality on the TP, among which NDVI, EVI and LAI represented vegetation greenness indexes, and SIF, NPP and GPP represented carbon sequestration capacity.  
The Sen Trend and the Mann-Kendall trend significance test were combined to analyze the changing trend of the standard grassland on the TP over a long time series [49]. This method has been applied to drought and hydrological change analysis [50]. The Theil-Sen Median method is computationally efficient and effective in reducing the impact of errors and can be calculated by the following formula:  
\[\beta=Median(\frac{x_{j}-x_{i}}{j-i})\ \ \ \forall\ j\ >\ i \tag{1}\]  
where \(\beta\) is the trend of vegetation indexes, Median 0 represents the median value, \(i\), \(j\) are time series, \(x_{i}\), \(x_{j}\) represent the values of the pixel vegetation index at the time \(i\) and \(j\), respectively, \(\forall\) is a mathematical symbol that represents the \"for all\".  
When \(\beta>0\), it means that the vegetation index in the pixel is on an upward trend; when \(\beta<0\), it means the vegetation index in the pixel is on a downward trend.  
The Mann-Kendall (MK) test is a nonparametric test for time series trendiness that is unaffected by missing values and outliers. The measurements of this method do not need to obey a normal distribution and are suitable for significance testing of long time series. The test statistic \(S\) is calculated using the following formula:  
\[S=\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}sgn(x_{j}-x_{i}) \tag{2}\]  
where \(n\) is the number of data in the series, \(\big{(}x_{j}-x_{i}\big{)}\) is the difference between vegetation indexes of adjacent years, and \(sgn()\) is the sign function, which can be calculated as:  
\[sgn\big{(}x_{j}-x_{i}\big{)}=\begin{cases}+1&x_{j}-x_{i}>0\\ 0&x_{j}-x_{i}=0\\ -1&x_{j}-x_{i}<0\end{cases} \tag{3}\]  
The trend test was performed using the test statistic \(Z\). The \(Z\) value is calculated as:  
\[Z=\left\{\begin{array}{ll}\frac{S}{\sqrt{Var(S)}}\ (S>0)\\ 0&(S=0)\\ \frac{S+1}{\sqrt{Var(S)}}\ (S<0)\end{array}\right. \tag{4}\]where _Var_ is calculated by the following formula:  
\[Var(S)=\frac{n\;(n\;-\;1)\;(2n+5)}{18} \tag{5}\]  
The \(Z\) obeys the standard normal distribution. Under a given significance level (\(\alpha=0.05\)), when \(\mid\!Z\!\mid\!>1.96\), it means that the trend has passed the significance test with a reliability of 95%. The method for judging the significance of the trend is shown in Table 4.