## 2 Materials and Methods
### Site-Level VPP Observations from FLUXNET Measurements  
Based on the method proposed in [3], site-level VPP observations were extracted from daily GPP estimates derived from FLUXNET measurements. First, long-term daily GPP estimates of all years from the given site were smoothed using the Savitzky-Golay filter based on the embedded function in the MATLAB R2013a environment. The Savitzky-Golay filter has been successfully used for reconstructing high-quality normalized difference vegetation indices (NDVIs) and leaf area index time series datasets [29]. The general equation of the filter can be found in [29]. It has been used in numerous studies to extract vegetation phenology data [16; 17; 30]. Two parameters for the filter should be determined, including the degree of the polynomial and smoothing window. A suitably large smoothing window can more effectively smoothen the sharp peaks (outliers) caused by steep changes in environmental factors in the time series of daily GPP. Results from previous studies indicate an optimal smoothing window width of 9 (approximately 91 days) for reconstructing a high-quality 10-day NDVI time-series data set based on the Savitzky-Golay filter for 14 kinds of vegetation  
Figure 1: Distribution of the 145 flux sites used in the study. The plant functional types (PFTs) were: evergreen needle-leaf forest (ENF), deciduous broadleaf forest (DBF), mixed forest (MF), closed shrublands (CSH), open shrublands (OSH), savannas (SAV), woody savannas (WSA), grasslands (GRA), wetlands (WET), and croplands (CRO).  
types [29]. A data analysis also showed that differences in SOG and EOG observations using smoothing windows of 91 and 15 days were 3 and 5 days for DBF sites and 2 and 1 days for ENF sites, respectively. Therefore, based on data analysis and results from previous studies, in our study, the degree of the polynomial was 2 and the width of the smoothing window was 91 days [29; 31].  
Second, we calculated the amplitude of each year for the given site, equaling the maximum value of the smoothed daily GPP minus the minimum value. Finally, a relative threshold method was repeatedly used to extract the SOG and EOG [10]. Dates extracted using different thresholds represent different phases of the seasonal cycles of GPP [10], and a commonly used threshold equates to 10% of the growing season amplitude to represent the start and end of photosynthesis phenology from GPP [17; 32]. Previous studies have shown that LSPs derived from different methods have large discrepancies [33]. In our study, consistent with the threshold used to extract the latest MODIS-LSP product by [34], we set the threshold for extracting SOG and EOG at 15% of the long-term average amplitude for the given site. Thus, the SOG and EOG values for each year for each site were extracted based on the first and last dates, respectively, when the smoothed daily GPP reached a threshold of 15% (Figure S1). The SOG using a threshold of 15% occurred 5 and 6 days later than when using a threshold of 10%, while the EOG was 7 and 9 days earlier than when using a threshold of 10% for DBF and ENF sites, respectively. The definitions of the seasons for the Southern hemisphere were reversed to be consistent with the seasons for the Northern hemisphere. For example, the spring season is defined as March-April-May in the northern hemisphere and September-October-November in the Southern hemisphere. The seasons for the EVI and LST data sets were also reversed for the Southern hemisphere.