2.3.2. Trend Analysis

The temporal trends in the time series of the vegetation phenology were calculated by the Theil–Sen median slope estimator [32] at the pixel level. The Theil–Sen median slope estimator is a nonparametric median-based slope estimator that is less susceptible to noise and outliers [33]. A positive Theil–Sen slope indicates a delayed or extended trend, while a negative value indicates an advanced or shortened trend. The Mann–Kendall (MK) method [34] was used to determine the significance of the long-term advanced/delayed trend in vegetation phenology. In our study, the significance level was based on the MK test value, and *p* < 0.05 was defined as statistically significant. The combined use of the Theil–Sen median slope and MK trend test classified vegetation phenological parameters into five categories, namely, "significant advanced/shortened", "insignificant advanced/shortened", "no change", "insignificant delayed/extended", and "significant delayed/extended".

#### 2.3.3. Partial Correlation Analysis

Partial correlation coefficients were calculated to examine the correlation between vegetation phenology and seasonal driving factors (temperature, precipitation, and soil moisture). In our analysis, the seasons were defined as spring (March–May), summer (June–August), and autumn (September–November). The second-order partial correlation coefficient was calculated as follows:

$$r\_{12,34} = \frac{r\_{12,3-}r\_{14,3} \times r\_{24,3}}{\sqrt{(1-r\_{14,3}^2) \times (1-r\_{24,3}^2)}}\tag{3}$$

where *<sup>r</sup>*12,34 represents the partial correlation coefficient of variables 1 and 2 after controlling for variables 3 and 4. *<sup>r</sup>*12,3 represents the first order partial correlation coefficient and was computed as follows:

$$r\_{12,3} = \frac{r\_{12} - r\_{13} \times r\_{23}}{\sqrt{(1 - r\_{13}^2) \times (1 - r\_{23}^2)}}\tag{4}$$

where *r*12,*r*13,*r*23 represent the Pearson's correlation coefficients between variables 1 and 2, 1 and 3, and 2 and 3, respectively. After we calculated the partial correlation coefficient values, Student's t-test was used to identify the significance of the coefficient, and only the pixels with a significance level of *p* < 0.05 were considered significant. To determine the influence of terrain and vegetation types on the linkage between vegetation phenology and seasonal driving factors, the partial correlation coefficients in different elevation zones and different vegetation types were also analyzed in our study. The elevation was reclassified into four classes (1: <3000 m a.s.l., 2: 3000–3500 m a.s.l., 3: 3500–4000 m a.s.l., and 4: >4000 m a.s.l.).
