# The Resilience of Vegetation to the 2009/2010 Extreme Drought in Southwest China
## 2 Materials and Methods
### Methods
#### 2.3.3 The Calculation of Vegetation Resilience and Recovery Time  
To assess the response of vegetation to the extreme drought, we adopted the vegetation resistance, recovery, and resilience indices, which were proposed by [PERSON] et al. (2011) [37]. Firstly, we calculated the ratios of detrended indexes (i.e., NDVI, LAI, and GPP) in each month during the extreme drought to those of the same month before and after the extreme drought in the regions where the extreme drought occurred. Then, the mean values of resistance, recovery, and resilience in the base periods of 4 years were calculated. At the same time, to compare the spatial heterogeneity and determine the stability with time, we also calculated the mean values of resistance, recovery, and resilience in the base periods of 2 years and 8 years. The formulas of resistance, recovery, and resilience are as follows:  
\[Rt_{ij}=\frac{Dr_{i}}{PreDr_{ij}} \tag{1}\]  
\[Rc_{ij}=\frac{PostDr_{ij}}{Dr_{i}} \tag{2}\]  
\[Rs_{ij}=\frac{PostDr_{ij}}{PreDr_{ij}}=Rt_{ij}\times Rc_{ij} \tag{3}\]  
where \(Rt_{ij}\) is resistance, \(Rc_{ij}\) is recovery, \(Rs_{ij}\) is resilience, \(Dr_{i}\) is the value of the detrended index for each month during the extreme drought, \(PreDr_{ij}\) is the value of the detrended index for each month before the extreme drought, \(PostDr_{ij}\) is the value of the detrended index for each month after the extreme drought, \(i\) is the detrended index, \(j\) is the month in the 2 years, 4 years, and 8 years before or after the extreme drought, which corresponds to the same month during the extreme drought. The lower \(Rt_{ij}\), the more seriously the vegetation was affected by the extreme drought. The lower \(Rc_{ij}\), the worse the vegetation recovered after the extreme drought. Resilience was determined based on resistance and recovery.  
Moreover, vegetation resistance, recovery, and resilience are closely related to water availability and temperature changes during the extreme drought [38]. First, we calculated  
Figure 2: The temporal changes of standardized scPDSI and detrended NDVI. The gray and green areas represent the period of the extreme drought (**a**) and the 4 year mean value before the extreme drought (**b**), respectively. A threshold of 0.28 was used for the beginning and end of the extreme drought.  
the variance inflation factor (VIF) values of all water indices and temperature indices. If there were any indices with VIF values greater than 10, this indicated that multicollinearity existed, which needed to be eliminated. Then, we deleted the indices with the largest VIF values and recalculated the VIF values of the remaining indices until all the VIF values of the remaining indices were less than 10 [39; 40]. Finally, the contribution percentages of water indices and temperature indices to vegetation resistance, recovery, and resilience were calculated based on the standardized regression coefficients using multiple linear regression. The formulas are as follows:  
\[y=a_{0}+a_{1}x_{1}+a_{2}x_{2}+a_{3}x_{3}+a_{4}x_{4}+a_{5}x_{5} \tag{4}\]  
\[cp_{i}=\frac{|a_{i}|}{|a_{1}|+|a_{2}|+|a_{3}|+|a_{4}|+|a_{5}|}\times 100\% \tag{5}\]  
where \(y\) is the resistance, recovery, and resilience of vegetation to the extreme drought based on 2, 4, and 8 years, respectively; \(x_{1}\) is precipitation; \(x_{2}\) is surface soil moisture; \(x_{3}\) is root-zone soil moisture; \(x_{4}\) is LST; \(x_{5}\) is mean air temperature; \(a_{i}\) is the standardized regression coefficient; and \(cp_{i}\) is the contribution percentage.