China’s deserts greening and response to climate variability and human activities

Both the NDVI raster data and climate raster data were processed and analyzed by using ArcGIS10.5, MATLAB R2016a, and Python 3.7. Methods Theil-Sen estimator. The Theil-Sen estimator calculates the slope estimate as the median of the single-point slope and the intercept as the median of the single-point intercept. The Theil-Sen estimator can effectively eliminate the influence of outliers on the estimation results (Eq 1) [53,54]. In contrast to ordinary least squares used for linear regression, the Theil-Sen estimator is an unbiased estimate of a linear trend and is more robust; therefore, it has been widely used for estimating the slope of the NDVI [55–58]. slope ¼ Median NDVIj NDVIi j i � � ; 8j > i ð1Þ where NDVIi and NDVIj are the NDVI values at times i and j, respectively. The Theil-Sen esti- mator was used to calculate the trend for each pixel; in general, slope >0 indicates a positive trend in the NDVI value of the pixel during the period, and vice versa. Mann-Kendall test. The Mann-Kendall test, which is a nonparametric test, was applied to evaluate the significance of the trend of the Theil-Sen estimator [59,60]. And it has been widely used in analyses of NDVI trends [39,61–63]. The Mann-Kendall test was computed using Eqs (2–4). S ¼ X n 1 i¼1 X n j¼iþ1 sign NDVIj NDVIi � � ð2Þ sign NDVIj NDVIi � � ¼ 1 ðNDVIj NDVIi > 0Þ 0 ðNDVIj NDVIi ¼ 0Þ 1 ðNDVIj NDVIi < 0Þ 8 > < > : ð3Þ Z ¼ S 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi Var S ð Þ p ðS > 0Þ 0 S ¼ 0 ð Þ S þ 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi Var S ð Þ p ðS < 0Þ 8 > > > > > > <

> > > > > > : ð4Þ where n is the length of the time-series data (in this study, n = 18), S represents the Mann-Ken- dall statistic, and Z is a standardized statistic that follows a standard normal distribution. |Z| > 1.96 indicates that the time-series data change significantly at the 5% level. Combined with the Mann-Kendall statistic and the Theil-Sen estimator, a pixel shows a greening trend when slope > 0 and |Z| > 1.96, the pixel shows a browning trend when slope < 0 and |Z| > 1.96, and the pixel does not show a significant change when |Z| � 1.96. Correlation analysis of the NDVI and climatic factors. The Pearson correlation coeffi- cient (r) was commonly used in previous studies to evaluate the relationships between vegeta- tion dynamics and climatic factors [43,64,65]. In this study, this method was applied to calculate correlations between monthly, seasonal, and annual NDVI and climatic factors (i.e., temperature and precipitation). P-values were used to indicate the significance of the correlations. PLOS ONE China’s deserts greening and response to climate variability and human activities PLOS ONE | https://doi.org/10.1371/journal.pone.0256462 August 30, 2021 5 / 20