## 5 Conclusions  
This study investigated the grassland vegetation dynamic on the basis of multi-index and its response to droughts in the MP during 2000-2013 in terms of the relations between F\({}_{\mathrm{v}}\), F\({}_{\mathrm{b}}\), NPP, and scPDSI. The spatial distribution of grassland F\({}_{\mathrm{v}}\) and NPP decreases from  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Change Direction** & **Grassland Conditions** & **scPDSI** & **F\({}_{\mathrm{v}}\)** & **F\({}_{\mathrm{b}}\)** & **NPP** \\ \hline \multirow{4}{*}{control response} & \multirow{4}{*}{Grassland Restoration} & Slope \(>0\) & Slope \(>0\) & \multirow{4}{*}{Slope \(>0\)} \\  & & Slope \(>0\) & & & Slope \(>0\) \\  & & Slope \(>0\) & & & Slope \(>0\) \\  & & Slope \(>0\) & & & \\  & \multirow{4}{*}{Grassland degradation} & Slope \(<0\) & \multirow{4}{*}{Slope \(>0\)} & \multirow{4}{*}{Slope \(<0\)} \\  & & Slope \(<0\) & & & Slope \(<0\) \\ \hline \multirow{4}{*}{counter response} & \multirow{4}{*}{Grassland Restoration} & Slope \(<0\) & Slope \(>0\) & \multirow{4}{*}{Slope \(>0\)} \\  & & Slope \(<0\) & & & Slope \(>0\) \\ \cline{1-1}  & \multirow{4}{*}{Grassland degradation} & Slope \(>0\) & & & Slope \(>0\) \\ \cline{1-1}  & & Slope \(>0\) & & & Slope \(<0\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Scenarios to assess the role of F\({}_{\mathrm{v}}\), F\({}_{\mathrm{b}}\) and NPP responding to scPDSI in the MP.  
northeast to southwest, showing an increasing trend of 0.18 and 0.43, respectively. On the contrary, F\({}_{\rm b}\) increases from northeast to southwest, presenting a decreasing trend, with the value of \(-0.16\). The grassland degradation condition of the MP shows a restoration trend during the study period. F\({}_{\rm v}\) and NPP shows a positive relationship with scPDSI, whereas F\({}_{\rm b}\) is exactly on the country. The areas with a positive correlation between F\({}_{\rm v}\), NPP, and scPDSI are 84.08% and 93.88%. The grassland increase regions with control and counter response to drought account for 6.06% and 6.87%. However, the distribution of grassland decrease regions with control and counter response (0.44% vs. 0.29%) is minimal. The regions of grassland increase from control response mainly distribute in central MG, whereas the grassland increase regions with counter response are in the eastern and western MG and northeast IM. Such detailed analysis of grassland-related indexes and its responses to drought are useful to clarify the grassland condition, potential effect of drought, and is beneficial to help policymakers for develop proper measures for grassland protection.  
Conceptualization, Y.Z. and J.L.; Methodology, Z.W.; Software, Q.W.; Validation, Y.Z., Y.Y. and Z.W.; Formal Analysis, J.L. and Y.B.; Data Curation, Y.Z. and W.X.; Writing--Original Draft Preparation, Y.Z.; Visualization, Y.Z.; Supervision, J.L. and W.X.; Project Administration, J.L. and W.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (42067069), the Technology Innovation Leading Program of Shaanxi Province (2021 KJXX-53), the National Key Research and Development project (2018 YED0800201), the Natural Science Foundation of China (32060279) and the National Research Project of the State Ethnic Affairs Commission of China (2019-GMD-034). We are grateful to the editor and anonymous reviewers. We also appreciate the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC) for sharing a series of original remote sensing dataset and Climatic Research Unit in University of East Anglia for sharing climate dataset.  
Not applicable.  
The authors declare no conflict of interest.