## 2 Materials and Methods
### GPP-Based Phenology  
In this study, the spring and autumn state-transition dates of GPP-based photosynthesis cycle, referred as the start (SOS) and end (EOS) of growing season, were adopted rather than the traditional phenological events of the plants. These phenological factor dates were derived at different spatial scales. First, they were derived at the site scale using both the FLUXNET daily GPP flux measurements and the MODIS 8-day GPP dataset at 1 km spatial resolution [30] for comparison between the ground and satellite observed phenology. Then, the phenological factors were calculated in each valid satellite-image pixel using the 8-day GPP dataset at 0.5\({}^{\circ}\) spatial resolution which was derived from the MODIS 8-day GPP dataset at 1 km spatial resolution.  
The Harmonic Analysis of Time Series (HANTS) model was used to smooth both the satellite-based and tower-based GPP measurements of each year. HANTS is an improved algorithm of the fast Fourier transform (FFT), which is described in detail in the work of [PERSON] et al. [40]. In this study, the HANTS algorithm was implemented in MATLAB R2013a (The Mathworks, Inc., Natick, MA, USA), and the code was provided by [PERSON] [41]. For the algorithm, the number of frequencies is set to 1, the fit error tolerance is set to 5.0, and the degree of overdeterminedness is set to 1. Then, the smoothed GPP time series were used to define the SOS and EOS in each pixel-year (site-year) data, with the dates on which the smoothed daily GPP reached 10% of the seasonal maximum in spring  
Figure 1: Spatial patterns of **(a)** Köppen climate classifications and **(b)** MODIS IGBP land cover types within the valid pixels of this study. The details regarding the codes of the climate and plant types are provided in Table 1. The white areas denote invalid satellite-image pixels in this study.  
and autumn used to indicate the onset and end of significant photosynthesis, respectively (Figure 2a). This 10% GPP threshold was determined because dynamic thresholds are more beneficial for capturing and comparing interannual variations in phenological events [42].  
To validate satellite-derived photosynthetic phenology, 13 sites (a total of 85 site-years) in the FLUXNET (the \"Fair Use\" LaThuile FLUXNET data set (V4)) [43] were identified, and the daily GPP fluxes were derived from 30-min eddy covariance measurements (net ecosystem exchange of CO\({}_{2}\), NEE) that were standardized and gap-filled using a set of common algorithms [44; 45]. Here, only summer active ecosystem sites which were identified by the same rule as the valid pixel were included in our analysis. In addition, the sites were filtered by data quality (less than 20% gap-filled records in each year; a lack of recent disturbances) and length of data record (a minimum of six years of continuous data since 2000). The details regarding these valid sites are provided in Table S1. According to the center geographic coordinates (latitude and longitude) of the selected field sites, the satellite-derived GPP time-series were extracted from 3 \(\times\) 3 MODIS pixels (\(\sim\)3 km \(\times\)\(\sim\)3 km) centered on the flux tower [42].