## 2 Materials and Methods
### Methodology  
The monthly time-series of NDVI anomalies at the 250 m pixel level of resolution was calculated for the period from February 2000 to April 2017. Then, [PERSON]'s correlations and linear regressions were performed between the NDVI anomalies and PDSI for each pixel. The NDVI-PDSI regression slopes represent the vegetation sensitivity to drought, and the NDVI-PDSI correlation coefficients indicate the strength of the relationships between the vegetation greenness and water availability. Correlation and regression analyses between NDVI and PDSI were also calculated for different seasons: winter, December-February; spring, March-May; summer, June-August; and fall, September-November. All the correlation and regression coefficients were tested at a 95% confidence level. To detect long-term trends in the browning or greening of the vegetation over the past 17 years, a Theil-Sen estimator was utilized to measure the changing trends of the pixel-wise NDVI. The Theil-Sen algorithm is a robust trend detection approach, which gives the median changing slope of a time-series and, thus, is less affected by outliers than parametric approaches [81; 82]. Though the NDVI time-series also contains some fluctuations induced by short-term disturbances (e.g., fire or diseases), the Theil-Sen method is appropriate for capturing the long-term greenness trends attributed to climate change. The Mann-Kendall test was applied to identify the significance of the NDVI trends. As a non-parametric test, the Mann-Kendall test is a reasonable method for detecting monotonic trends in series of environmental data, climate data, or hydrological data, regardless of the distribution of the data [83; 84; 85]. Given that autocorrelations commonly exist in environmental time-series, we used the pre-whitening algorithm proposed by [86] to remove the lag-1 serial correlations in the anomaly NDVI time-series before trend detection. Existence of a serial correlation can increase the probability that the Mann-Kendall test detects a significant trend, leading to a disproportionate rejection of the null hypothesis of no trend [87]. We also applied the same trend detection procedure to the monthly time-series of maximum temperature, minimum temperature, and precipitation, which indicated the recent climate change background in Southern California. To compare the relative sensitivity of the five vegetation communities to drought, a dummy variable regression was performed, which uses the regression slopes between NDVI anomalies and PDSI as the dependent variable and vegetation as the unique predictor. Vegetation in developed land was selected as the reference category, as it showed the smallest seasonal variations. The dummy regression model gives the relative changes in NDVI-PDSI regression slopes for forest, chaparral, CSS, and grassland, as compared to developed land. By comparing the drought sensitivity of natural and developed-land vegetation, we may estimate how human activities mitigate the drought impact on urban vegetation and verify the assumption that natural vegetation is more vulnerable to drought than vegetation in developed lands. Moreover, we employed multiple linear regression to further investigate the geographically different vegetation response to drought caused by climate, using the regression slopes between NDVI anomalies and PDSI as the dependent variable, while normal temperature and precipitation were the independent variables. As multiple linear regression assumes the independent variables are not highly correlated with each other, we used variance inflation factor (VIF) to detect multicollinearity [88]. A general rule is that the VIF should not exceed 10 to avoid severe multicollinearity [89]. Based on the two-fold regression, we can identify the impact of changing temperature and precipitation on the drought sensitivity of the vegetation types. To remove the influence of wildfire, we discarded all burned pixels over the study period, which were identified according to the FRAP fire perimeter data.