## 2 Study Region and Methodology
### Methodology
#### 2.2.3 Quantitative Impact Calculation  
A function of vulnerability and resilience of the sites where earthquake-induced geohazards occurred could be applied for NPP assessment. [PERSON] [30] listed various definitions for vulnerability and resilience [6]. In this paper, we propose a new assessment indicator, with vulnerability (\(S\)) and resilience (\(R\)) representing the degree of vegetation damage degree and restoration, which could be quantified by NPP reduction during the earthquake and the ratio of NPP increment in 2018 to dur-earthquake level, respectively. In addition, taking into consideration the advocation of the Jiazhaigou Administration that \"ecosystem natural restoration as the primary, manual intervention as an adjunct\", without considering the artificial intervention and hemeroby index mentioned by [PERSON] et al. [31] and [PERSON] et al. [32], the impact coefficient (\(I\)) of quake-induced geohazards on vegetation without self-recovering was proposed, and it can be calculated by Formula (9). \[I=S\cdot(1-R) \tag{9}\]  
Scholars have shown that NPP change was mainly attributed to natural factors such as temperature and precipitation [33; 34; 35], which could be regarded as long-term factors in a certain aspect. Nevertheless, the M\({}_{s}\)7.0 earthquake caused instantaneous damage to the ecosystem and was devastating. Therefore, this research principally analyzed the driving factor that affected NPP in a short time, namely seismic intensity (\(SI\)). The \(SI\) could be determined by referring to \"the distribution map of the M\({}_{s}\)7.0 Jiazhaigou earthquake and the characteristics of the earthquake damage\" released by the Sichuan Earthquake Administration, from which we knew that the seismic intensity in the whole study region is VII+. Vegetation NPP changes (calculated by Formula (10)) within one month after the earthquake were mainly attributed to earthquake damage, seasonal turnover, and self-restoration, among which earthquake damage and seasonal turnover had negative effects on NPP, while self-restoration exerted positive effects. Thus, we reclassified the NPP change into positive part (\(\Delta NPP>0\)) and negative part (\(\Delta NPP<0\)) so that we could determine whether the vegetation was recovered or destroyed in the study region. Then, the value of NPP change was normalized (Formula (11)). \[\Delta NPP(x)=NPP^{*}(x)-NPP^{**}(x) \tag{10}\]  
\[N^{*}(x)=[\Delta NPP(x)-N_{min}]/[N_{max}-N_{min}] \tag{11}\]  
where \(\Delta NPP(x)\), \(NPP^{*}(x)\) and \(NPP^{**}(x)\) are the NPP change values of pixel \(x\) during the month when the earthquake occurred, in the month after the earthquake and in the month before the earthquake, respectively; \(N^{*}(x)\) is the normalized NPP change value of pixel \(x\); \(N_{max}\) and \(N_{min}\) are the maximum and minimum value of NPP change within the whole region. \[S\;(\text{or}\;R)=\sum_{i=1}^{5}(A_{i}\times B_{i}) \tag{12}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Vegetation Type** & \(\textit{SR}_{max}\) & \(\textit{E}_{max}\) \\ \hline Needleleaved deciduous forest & 6.63 & 0.485 \\ Needleleaved evergreen forest & 4.67 & 0.389 \\ Broadleaved evergreen forest & 5.17 & 0.985 \\ Broadleaved deciduous forest & 6.91 & 0.692 \\ Bush & 4.49 & 0.429 \\ Sparse woods & 4.49 & 0.542 \\ Alpine and sub-alpine grassland & 4.46 & 0.542 \\ Lake & 4.46 & 0.542 \\ Rock & 4.46 & 0.542 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The maximum light energy utilization efficiency (\(E_{max}\)) of typical vegetation types. The computed normalized values were divided into 0-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8, 0.8-1 (5 groups), with the gradient being 0.2, and then the area proportion of each group was calculated. Due to the principle of class mid-value, the median value (0.1, 0.3, 0.5, 0.7, 0.9) was taken as coefficient \(A\), and the corresponding area proportion value of each group was regarded as coefficient \(B\).