## 2 Materials and Methods
### LSMA Method  
Due to the NDVI (Normalized Difference Vegetation Index) and other vegetation indexes being highly affected by seasonal vegetation changes and rainfall variation [14; 15], the rangeland degradation \begin{table}
\begin{tabular}{c c c c c} \hline
**Year** & **Path/Row** & **Landsat Scene ID** & **Acquisition Date** & **Spatial Resolution (m)** \\ \hline
1996 & 131/35 & LTS1310351994200 BJC00 & 19 July 1996 & 30 \\
2001 & 131/35 & LTS13103520012038 JC00 & 22 July 2000 & 30 \\
2006 & 131/35 & LTS1310352006217 JKR00 & 6 August 2006 & 30 \\
2011 & 131/35 & LTS1310352011199 IKR00 & 18 July 2011 & 30 \\ \hline \end{tabular}
\end{table} 
Table 1: Metadata of Landsat Thematic Mapper (TM)/ETM+ (Enhanced Thematic Mapper Plus) images cover the Linxia rangeland, northwest China. \begin{table}
\begin{tabular}{c c c c} \hline
**Type** & **Vegetation Coverage (\%)** & **Vegetation Pattern** & **Bare-Land Rate (\%)** & **Bare-Land Pattern** \\ \hline Non-DR & \textgreater{}80 & No shrub or inedible grass & \textless{}20 & Almost no land bare \\ \hline SI-DR & 50–60 & \begin{tabular}{c} Shrub or inedible grass become \\ the main accompany species \\ \end{tabular} & 30–45 & Bare-land sporadically exists \\ \hline M-DR & 30–50 & \begin{tabular}{c} Shrub or inedible grass become \\ the dominant species \\ \end{tabular} & 45–60 & \begin{tabular}{c} Relatively large area \\ bare-land exists \\ \end{tabular} \\ \hline Se-DR & \textless{}30 & \
\begin{tabular}{c} Sparse vegetation or no \\ edible meadow \\ \end{tabular} & \textgreater{}60 &
\begin{tabular}{c} Bare-land dominates \\ the landscape \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 2: Remote sensing derived system of rangeland degradation in the study region. Non-DR, non-degraded rangeland; SI-DR, slightly degraded rangeland; M-DR, moderately degraded rangeland; and Se-DR, severely degraded rangeland. results tend to be overestimated in sparse vegetation areas. Here, the LSMA (Linear Spectral Mixture Analysis) method was selected to extract the vegetation coverage and bare-land rate in the study region for its simplicity, effectiveness, and interpretability [14; 16]. In LSMA, the reflectance of each image pixel is presented as a linear combination of the reflectance of each endmember and its residual [17], which can be presented as Equation (1). \[R_{b}=\sum_{i=1}^{n}f_{i}R_{i,b}+e_{b} \tag{1}\]  
where \(i=1,2,\,\ldots,\,n\) is the endmember, \(b=1,\,2,\,\ldots,\,m\) represents the spectral band, \(n\leq m+1\); \(R_{b}\) is the reflectance of pixels for each band, \(R_{i,b}\) is the reflectance of endmember \(i\) at band \(b\), and \(e_{b}\) is the residual. Among all the parameters, \(f_{i}\) is the one to be determined, it represents the best fit fraction of endmember \(i\) in the pixel, which minimizes the RMSEs calculated by Equation (2); the RMSE should be as small as possible. In addition, all \(f_{i}\) are subject to the unity constraint of Equation (3). \[\text{RMSE}=\sqrt{\frac{1}{n}\left(\sum_{i=1}^{n}e_{b}\right)} \tag{2}\]  
\[\sum_{i=1}^{n_{2}}f_{i}=1,\,\,f_{i}\geq 0 \tag{3}\]  
The accurate application of LSMA techniques requires delineation of meaningful and accurate endmembers [18]. Before the LSMA techniques were processed, a mask was made for other land cover types (e.g., water body, farmland, human settlements) by visual interpretation to remove their spectral interference. Then a comprehensive field investigation covering the study region was conducted in July 2012 to identify suitable sites for developing a spectral library from the images. Images for the four years were then spectral normalized [19], and Minimum Noise Fraction and Purity Pixel Index transformation were conducted to locate the \"pure\" endmembers of shade, vegetation, and bare-land by iteratively testing different endmember combinations [20; 21].