2.3.2. Mann–Kendall Test

The Mann–Kendall trend test is a nonparametric statistical test used to test significant trends of change. The samples do not need to have a specific distribution, nor are they affected by a few outliers [46]. Equation (3) is as follows:

$$\begin{aligned} S\_k &= \sum\_{i=1}^k \sum\_{j=1}^i \text{sgn}\left(X\_i - X\_j\right) \\ \text{LIF}\_k &= \left[S\_k - E(S\_k)\right] / \sqrt{\text{Var}(S\_k)} \end{aligned} \tag{2}$$

where *Xi* and *Xj* represent the NDVI values of time i and j, respectively. *Sk* is the cumulative count of *Xi* > *Xj*. *E*(*Sk*) and Var(*Sk*) are the mean and variance of *Sk*, respectively. *UFk* > 0 indicates an upward trend of the NDVI sequence, while *UFk* < 0 indicates a downward trend of the NDVI sequence. Combining the NDVI trend classification results (Table 2), the non-significant decrease and non-significant increase are classified into one category (i.e., no change). The results are divided into the following five levels [47]: significant decrease, moderate decrease, no change, moderate decrease, and significant decrease.
