## Materials and Methods  
### MODIS NDVI Data and Ground Reference Data  
The MODIS/Terra MOD09Q1 land surface reflectance dataset of 8-day interval and 250 m spatial resolution [54] was used as an example in this study. We used the binary MODIS quality flags to set weights for each observation. NDVI time-series from 2000 to 2014 were calculated using near-infrared (NIR) and red reflectance from MOD09Q1 for the 10 field sites and the test area with elevation reference data. For each field site, the reflectance data of single pixels were used rather than the mean value of several neighboring pixels, so that the performance of smoothing methods on single pixel time-series data could be fully evaluated. For ground reference, NDVI data from sensors mounted on masts at 10 sites (Figure S1 in Supplementary Material), located in Scandinavia, Greenland and Africa, were used [42; 55]. These sites cover different environments: arctic, sub-arctic, deciduous forest, evergreen forest, grassland, savanna, and clear-cut forest (Table 1) and the sites were established in homogeneous areas in terms of vegetation coverage and topography. The sensor pairs were calibrated following [PERSON] and [PERSON] [56]. Ground-based NDVI was computed from daily nontime reflectance in red and NIR bands, and it agreed very well with MODIS data during the growing season [42]. For further information about the field measurements, see [PERSON], et al. [42]. To agree with the time step of MOD09Q1 NDVI, daily NDVI were converted to 8-day NDVI values by median filtering. Due to the high latitude of sites 1-7, snow cover in winter disturbed both spectral NDVI sensors on the ground and MODIS. For this reason, we only compared them during the non-winter period: April-October at the Hyytiala and Norunda sites and June-September at the Abisko and Zackenberg sites [57; 58; 59; 60]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Site** & **Latitude** & **Longitude** & \begin{tabular}{c} **Elevation** \\ **a.s.1. (m)** \\ \end{tabular} & \begin{tabular}{c} **Spectral Sensor** \\ **Footprint Area (m\({}^{2}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Biome** \\ **(CO\({}_{2}\) Flux Data** \\ \end{tabular} \\ \hline Abisko Delta & 68.36 & 18.80 & 340 & 2000 & Deciduous forest & 2009–2011 \\ \hline Abisko Stordalen & 68.36 & 19.05 & 360 & 2000 & Sub-arctic mire & 2009–2011 \\ \hline Fajemyr * & 56.27 & 13.55 & 140 & 3000 & Permanent wetlands & 2009–2011 \\ \hline Zackenberg * & 74.48 & \(-\)20.56 & 1300 & 10,000 & Arctic mire & 2008–2010 \\ \hline Hyytiala * & 61.85 & 24.29 & 170 & 7000 & Coniferous forest & 2009–2012 \\ \hline Norunda Clear-cut & 60.09 & 17.47 & 70 & 300 &
\begin{tabular}{c} Coniferous forest \\ (Clear-cut in 2009) \\ \end{tabular} & 2011–2014 \\ \hline Norunda Forest * & 60.09 & 17.48 & 70 & 1500 & Coniferous forest & 2010–2012 \\ \hline Sudan Barah & 13.82 & 30.36 & 500 & 10,000 & Grassland & 2008–2010 \\ \hline Sudan Dilling & 11.86 & 29.72 & 720 & 10,000 & Grassland & 2008–2009 \\ \hline Sudan Demokeya & 13.27 & 30.49 & 530 & 10,000 & Cropland & 2008–2009 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ground-based spectral observation sites and flux tower sites (more information available in Table S1). We used flux-tower measured GPP from sites Fajemyr, Zackenberg, Hyytiala and Norunda Forest (Table 1) to evaluate the performance of the time-series smoothing methods for estimating vegetation temporal dynamics from the satellite images. Weekly (8-day) GPP data for these sites were acquired from Fluxnet ([[http://www.eosdis.ornl.gov/FLUXNET](http://www.eosdis.ornl.gov/FLUXNET)]([http://www.eosdis.ornl.gov/FLUXNET](http://www.eosdis.ornl.gov/FLUXNET))). Besides using ground reference data from point locations, we used spatial data from the Ammar region, located in Vasterbotten, Sweden, and having a significant elevation gradient (approximately 1980 m). Elevation data (50 m spatial resolution) were obtained from the Swedish mapping, cadastral and land registration authority, Lantmateriet (Figure 1).