*2.3. Methods*

2.3.1. Extraction of Vegetation Phenology

The NDVI time series involves some noise caused by clouds or poor atmospheric conditions and needs to be smoothed using a filter. In this study, NDVI was smoothed using a seven-parameter double logistic function proposed by Gonsamo et al. [31] to reconstruct the NDVI time series at a daily temporal resolution:

$$\mathbf{f}(\mathbf{x}) = \alpha\_1 + \frac{\alpha\_2}{1 + \mathbf{e}^{-\partial\_1(\mathbf{x} - \beta\_1)}} - \frac{\alpha\_3}{1 + \mathbf{e}^{-\partial\_2(\mathbf{x} - \beta\_2)}} \tag{1}$$

where f(*x*) is the fitted NDVI at day *x*; *x* is a specific day of year (DOY); *α*1, *α*2, *α*3, *∂*1, *∂*2, *β*1, *β*2 are smoothing parameters; *α*1 is the background NDVI value; *α*2 is the early summer plateau; *α*3 is the amplitude of the late summer plateau; *∂*1 and *∂*2 represent the transitions in the slope coefficient; and *β*1 and *β*2 are the midpoints at the start and end of the growing season transitions, respectively.

For the fitted *NDVI* time series, the dynamic threshold derived from each pixel was used to determine the SOS and EOS. In this method, the SOS and EOS are defined as the DOY when the *NDVIratio* reaches a certain threshold during the *NDVI* rising stage in spring and decline stage in autumn. The *NDVIratio* is calculated as:

$$NDVI\_{ratio} = \frac{NDVI\_x - NDVI\_{min}}{NDVI\_{max} - NDVI\_{min}} \tag{2}$$

where *NDV Ix* represents the *NDVI* value on day *x* and *NDV Imax* and *NDV Imin* are the maximum and minimum *NDVI* values in the annual NDVI time series, respectively. In this study, the dynamic threshold was defined as *NDVIratio* values of 30% and 50% to determine the SOS and EOS, respectively. The LOS was the difference between the SOS and EOS.
