## 2 Experiment Description
### Methodology  
To better understand changes in extreme weather and vegetation growth in the Loess Plateau from 1982 to 2015 (period S), we divided the long-time series into two segments using the year 2000 as the cut-off point. This year was selected because China's national policy of \"returning farmland to the forest\" began in 2000 in the Loess Plateau. Therefore, two sub-periods of 1982-1999 (S1) and 2001-2015 (S2) were separately considered to ensure that specific change patterns in vegetation growth under extreme weather and human intervention in these corresponding periods would not be overridden by long-term trends. To understand the change trends of the NDVI during the experimental period, the average value, linear trend, and F-test of the NDVI were calculated over the three selected periods. Here, the annual change rate in NDVI was calculated; a positive value was considered to represent an increasing trend of vegetation, whereas a negative value represents a decreasing trend. Three levels of significance were evaluated for the F-test, i.e. ; P = 0.1, P = 0.05, and P = 0.01. In addition, the percentages of pixels with decreasing and increasing trends for different significance levels were counted. To analyze the spatiotemporal distribution of PWV, RHU, and SSD in the Loess Plateau over the experimental period, several processes were performed. The 5-year sliding averages of PWV, RHU, and SSD were introduced to directly reflect the change trends of the corresponding time series, and the spatial distribution of the average PWV, RHU, and SSD was calculated over the period of 1982-2015. To better understand changes in extreme climate indices in the Loess Plateau, the first derivatives of 7 extreme precipitation indices and 13 extreme temperature indices were calculated over the three periods of S, S1, and S2. In addition, the year in which an abrupt change in trend occurred was also calculated using the Mann-Kendall trend and abrupt analysis method. The Mann-Kendall test is a nonparametric method that does not require a certain distribution and is minimally affected by outliers [31]. The Pearson correlation coefficient was introduced to calculate correlations between NDVI and the meteorological factors (i.e. ; PWV, RHU, and SSD) observed through the weather stations. The formula of calculating Pearson correlation coefficient is give as follows:  
\[\text{r}=\frac{\sum\limits_{i=1}^{n}{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}} {\sqrt{\sum\limits_{i=1}^{n}{(X_{i}-\overline{X})^{2}}}\sqrt{\sum\limits_{i=1}^ {n}{(Y_{i}-\overline{Y})^{2}}}} \tag{1}\]  
where r is the correlation coefficient, and r > 0 is a positive correlation, r < 0 is a negative correlation, the greater the absolute value of r, the stronger the correlation. \(X\) and \(Y\) are variables, \(n\) is the number of samples, \(\overline{X}\) and \(\overline{Y}\) are the average values of \(X\) and \(Y\), respectively. Considering that the relationship between precipitation and NDVI has been widely investigated, we do not discuss precipitation in this paper. A comprehensive analysis between extreme climatic indices and NDVI was performed to explain the response of vegetation growth to climate change. The F-test was also performed to determine the significance level of vegetation change in the different subregions of the Loess Plateau during the three specified periods. To better understand the time delay impacts of extreme climatic indices on vegetation growth, the monthly time series of the factors TXn, TNn, TXx, TNx, mean of max temperature (TMAXmean) mean of min temperature (TMINmean), RX1 day, RX5 day, and diurnal temperature range (DTR) were calculated using the RClimDex model. Their Pearson correlation coefficients were also analyzed along with the corresponding NDVIs for the current month and after 1-3 months during the growing season (April-October) in the Loess Plateau. In this paper, the correlation degree was defined based on previous studies on the relationship between climatic indices and ecological factors [32; 33; 34].