## Materials and Methods
### Data Analysis  
In this study, we first analyzed spatial patterns of SOS/EOS and compared SOS/EOS differences among meadow steppe, typical steppe, and desert steppe with one-way analysis of variance (ANOVA). The accuracy of MODIS-based SOS/EOS was assessed with R\({}^{2}\) (goodness of fit) and RMSE (root mean square error) by regressing them with GPP-based SOS/EOS.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Site Name** & **Latitude (\({}^{\circ}\)N)** & **Longitude (\({}^{\circ}\)E)** & **Observation Time** & **Vegetation Type** & **Data Source** \\ \hline Duolun & 42.05 & 116.28 & 2008 & Typical steppe & FLUXNET2015 \\ Siwangziq & 41.79 & 111.90 & 2012 & Desert steppe & FLUXNET2015 \\ Xilinhot\_1 & 44.13 & 116.33 & 2004, 2006 & Typical steppe & [PERSON] et al., 2014 [57] \\ Xilinhot\_2 & 43.55 & 116.67 & 2003, 2004 & Typical steppe & [PERSON], 2006 [58] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic information of GPP observation sites, including geographical coordinate, observation time, vegetation type, and data source.  
Secondly, we calculated the Pearson correlation coefficient between SOS/EOS and pre-season average temperature/total precipitation (defined as 90-day and 60-day before multi-year average SOS/EOS) in each grid. As 90-day and 60-day results were similar, we only presented the former in this study. For clearly distinguishing, the 90-day periods prior to SOS and EOS were named as 'pre-SOS' and 'pre-EOS', respectively. Finally, we established linear regression models to obtain the sensitivity of SOS/EOS to temperature/precipitation in each grid. One-way ANOVA was taken to compare the sensitivity of SOS/EOS to these main climatic variables among the different vegetation types. It is worth noting that regression analysis between SOS/EOS and climate factors only covers the period of 2000-2015 (data for 2016 was not available). When conducting regression analyses between SOS/EOS and climate factors, we used the average SOS/EOS of all pixels falling in a climate grid.  
The variation trends analysis of SOS/EOS was conducted in both pixel scale and vegetation type scale. In pixel scale, variation trends of SOS/EOS during 2000-2016 were computed with the Theil-Sen median method in each pixel, which chooses the median of the slopes of all lines through pairs of two-dimensional sample points. The non-parametric Mann-Kendall test was employed to assess the significance of trends. Compared with linear regression, the Theil-Sen median method is more robust and not affected by outliers.  
In vegetation type scale, however, we chose to directly compare SOS/EOSs in the head and tail of the studying period instead of computing trends of multi-pixel average SOS/EOS, with the aim to reduce calculation errors. To eliminate the effects of SOS/EOS in possibly abnormal years, we first obtained multi-year average SOS/EOS during 2000-2004 and 2011-2015 in each pixel. We then compared the overall SOS/EOS differences between 2000-2004 and 2011-2015 with two-sample \(t\)-test in meadow steppe, typical steppe, and desert steppe separately. Meanwhile, for investigating the possible reasons that resulted in SOS/EOS variations, we also analyzed the variations of pre-SOS/EOS temperature and precipitation from 2000-2004 to 2011-2015 with the same methods in each of the three grassland types, respectively. Notably, the significance of all statistical analyses in this study were tested at the 95% level (i.e., \(p=0.05\)).