## Materials and Methods
### Remote Sensing Data and Processing  
Moderate Resolution Imaging Spectroradiometer (MODIS) datasets have been extensively used to explore large-scale phenology making use of their high quality and richness of available products. In this study, MODIS Surface Reflectance 8-Day L3 Global 500 m product (MOD9A1) during 2000-2016, acquired from the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC) ([[https://search.earthdata.nasa.gov/search](https://search.earthdata.nasa.gov/search)]([https://search.earthdata.nasa.gov/search](https://search.earthdata.nasa.gov/search))), was used to calculate NDVI (Equation (1)):  
\[NDVI=\frac{\text{Band2}-\text{Band1}}{\text{Band2}+\text{Band1}} \tag{1}\]  
Figure 1: Study region and the distribution of the three main grassland types. where Band 1 and Band 2 denote the reflectance values of red (620-670 nm) and near-infrared (841-876 nm), respectively. This NDVI product is derived from eight-day maximum value composites by choosing observations with minimal cloud cover and near-nadir views [49]. Further corrections for atmospheric gases, clouds, and aerosols have been routinely applied [50]. Although the highest-quality reflectance values have been selected, some poor quality values may still exist due to prolonged rainfall and cloudy weather periods. Eliminating these abnormal values in NDVI time series is of crucial importance to obtain credible phenological metrics. Usually, there are some sequential abnormal low points occurring at the start and end of the time series, and a few abrupt and extreme low points were observed in the middle of growing season (Figure 2a). We first addressed the issue of abrupt points [_NDVI_ (_t_)] in the middle of the growing season. If the difference between _NDVI_ (_t_) and _NDVI_ (_t_ \(\pm\) 1) is larger than (\(NDVI_{max}-NDVI_{min}\))/2, _NDVI_ (_t_) was replaced by the average value of _NDVI_ (_t_ \(-\) 1) and _NDVI_ (_t_ \(+\) 1). Then, we smoothed the entire time series with a nine-point moving average filter. Finally, abnormally low values at the start and end of the time series were replaced with the average NDVI value in March, when most NDVI values are approximately equal to the NDVI value of bare ground due to a lack of vegetation activities and little snow on the surface. Here, we assumed that the NDVI values during the non-growing season are approximately constant. Several methods have been developed to extract phenological information from NDVI curves [51; 52]. Among them, the logistic function can accurately simulate the growth process of vegetation and fit NDVI curves, and has been employed by National Aeronautics and Space Administration (NASA) to produce MODIS global vegetation phenology products [14]. The typical logistic function retrieves phenological metrics during spring and autumn separately, while the double logistic function can extract spring and autumn phenological events simultaneously [44; 53; 54; 55]. In this study, therefore, the reconstructed NDVI time series were fitted using double logistic function (Equation (2)) to obtain SOS and EOS based on Equations (3) and (4), respectively:  
\[NDVI(t)=NDVI_{min}+(NDVI_{max}-NDVI_{min})\times\left(\frac{1}{1+e^{I(S-t)}}+ \frac{1}{1+e^{D(E-t)}}-1\right) \tag{2}\]  
\[SOS =\frac{2\ln\left(\sqrt{3}-\sqrt{2}\right)}{I}+S \tag{3}\] \[EOS =\frac{2\ln\left(\sqrt{3}-\sqrt{2}\right)}{D}+E \tag{4}\]  
Figure 2: An illustration of processing NDVI time series (**a**) and GPP time series (**b**). The blue curve denotes the fitted curve by a double logistic function. The vertical blue lines represent the estimated SOS and EOS respectively. \(\times\) symbolizes abnormal NDVI values. where \(NDVI\) (\(t\)) is the reconstructed NDVI values at time \(t\); \(NDVI_{max}\) and \(NDVI_{min}\) are the maximum and minimum values in the NDVI time series, respectively; \(I\) and \(D\) represent the maximum rising and falling slopes (inflection points) on the fitted NDVI curve; and \(S\) and \(E\) represent corresponding dates of \(I\) and \(D\) on the fitted NDVI curve.