*2.6. Statistical Analysis*

Spatial trend of CUE was examined by applying a linear regression model with time as the independent variable and CUE as the dependent variables, respectively. The trend analysis method was used to analyze trend in seasonal CUE changes for the period 2001–2015. The outputs of the trend analysis are the maps of regression slope values, expressed by the following formula [19]:

$$\text{Slope} = \frac{\mathbf{n} \times \sum\_{i=1}^{n} \mathbf{i} \times \mathbf{A}\_{i} - \sum\_{i=1}^{n} \mathbf{i} \sum\_{i=1}^{n} \mathbf{A}\_{i}}{\mathbf{n} \times \sum\_{i=1}^{n} \mathbf{i}^{2} - \left(\sum\_{i=1}^{n} \mathbf{i}\right)^{2}} \tag{3}$$

where Slope is the slope of the fitted regression line at each pixel. n represents year range. i is 1 for the first year, 2 for the second year, and so on. Ai represents the CUE of the year i. A negative regression coefficient (Slope < 0) indicates a decline of CUE, whereas a positive value (Slope > 0) depicts an increase trend. F test was used to determine the significance of change trend.

To investigate the role of climate drivers and phenological factors affecting CUE, we analyzed the correlation between three phenological parameters (i.e., SOS, EOS and LOS) and CUE. In addition, Spearman partial correlation between CUE and two climate factors (i.e., precipitation and temperature) was calculated. The correlation coefficient and partial correlation coefficient were computed as follows [18]:

$$\text{tr}\_{\text{BC}} = \frac{\sum\_{i=1}^{n} \left( \mathbf{B}\_{i} - \overline{\mathbf{B}} \right) \left( \mathbf{C}\_{i} - \overline{\mathbf{C}} \right)}{\sqrt{\sum\_{i=1}^{n} \left( \mathbf{B}\_{i} - \overline{\mathbf{B}} \right)^{2}} \sqrt{\sum\_{i=1}^{n} \left( \mathbf{C}\_{i} - \mathbf{C} \right)^{2}}} \tag{4}$$

$$\overline{\mathbf{B}} = \frac{1}{\mathbf{n}} \sum\_{i=1}^{n} \mathbf{B}\_{\mathbf{i}} \ , \overline{\mathbf{C}} = \frac{1}{\mathbf{n}} \sum\_{i=1}^{n} \mathbf{C}\_{\mathbf{i}} \tag{5}$$

$$\mathbf{r\_{BC,D}} = \frac{\mathbf{r\_{BC}} - \mathbf{r\_{BD}}\mathbf{r\_{CD}}}{\sqrt{1 - \mathbf{r\_{BD}}^2}\sqrt{1 - \mathbf{r\_{CD}^2}}} \tag{6}$$

where rBC represents the correlation coefficient between B and C, its threshold ranges from −1 to 1, and rBC,D is the partial correlation coefficient between B and C when we controlled D values. If r < 0, B is negatively correlated with C. If r > 0, there is a positive correlation between B and C. Furthermore, B, C represent the average values of Bi and Ci, respectively. The significance of the results was examined by t-test.
