## Results  
### Ground Measured NDVI Time-Series vs. Smoothed Satellite NDVI Time-Series  
RMSE values for the 987 runs with different settings for the smoothing of MODIS NDVI are displayed as averages (Table 3) and as boxplots for each of the sites and methods (Figure S2). Overall, for the ten test sites, average RMSE of the raw MODIS NDVI and ground-measured NDVI was 0.14 (Table 3). After applying smoothing, RMSE was on average reduced to 0.08, and the range of RMSE was 0.06. Most sites (89% of the 987 simulations) showed reduced RMSE compared to raw data, except at Sudan Barah. At the sites with high NDVI values and long growing season, such as Abisko Delta, Abisko Stordalen, Fajemyr, Hyytia and Norunda forest, the reductions in RMSE were larger than at the other sites that have lower NDVI or shorter growing seasons. The difference can be partly attributed to cloud effects. Clouds contribute to the majority of noise in the satellite received vegetation signal during the growing season. Hence, sites with high NDVI values are more strongly affected by cloud contamination than sites with low NDVI. In addition, the dry Sudanian sites have short growing season, and there is generally lower cloud contamination than in the humid areas. As a result, smoothing methods have a weaker effect on the RMSE than at the humid sites with high NDVI values and long growing seasons. When studying each smoothing method, we found that the minimum and median RMSEs of all methods differed relatively little, but that overall LO generated slightly lower RMSE than the other four methods (Table 3). Although window size \(q\) in SG/LO and smoothing parameter \(p\) in SP have different definitions, these methods produced similar smoothed time series (Figure S2). DL generated the smallest RMSE range of 0.035. The function fitting methods AG and DL also generated very similar results to one another. SP was closer to the local filtering methods. Cross validation (SGCV, LOCV and SPCV) generated RMSE values lower than median RMSE in most cases (87%), which means that CV is in many cases able to assist in selecting satisfying settings for a single pixel. In four out of the 30 cases, CV resulted in very poor results. When comparing the methods across the ten test sites, SG and LO produced the eight lowest RMSE values out of the ten test sites, except at the Hyytia\(\underline{\text{i}}\)a site and the Demokeya site where AG and SP produced the lowest RMSE respectively. The lowest median RMSEs varied between methods at the different sites, without any clear pattern. The smallest RMSE ranges were produced by the function-fitting methods (AG and DL) for nine sites. At one site, Sudan Barah, which had the lowest NDVI and the shortest growing season of all, this was not true. This may be due to the large NDVI uncertainties from measurement when NDVI is small [56]. The time-series patterns generated from each method are shown in Figure S3. SG, LO, SP were able to describe the variation \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Statistic** & **SG** & **LO** & **SP** & **AG** & **DL** & **Average** \\ \hline Minimum & 0.063 & 0.062 & 0.064 & 0.066 & 0.069 & 0.065 \\ Median & 0.076 & 0.075 & 0.085 & 0.076 & 0.077 & 0.078 \\ CV & 0.077 & 0.077 & 0.076 & - & - & - \\ Range & 0.069 & 0.068 & 0.071 & 0.038 & 0.035 & 0.056 \\ \hline \hline \end{tabular} Note: the RMSE between raw MODIS NDVI and ground measured NDVI is 0.142.  
\end{table} 
Table 3: The ten sites’ average of minimum, median and range of root mean squared error (RMSE) between smoothed moderate-resolution imaging spectroradiometer (MODIS) derived normalized difference vegetation index (NDVI) from all settings of each smoothing algorithm and ground measured NDVI. of NDVI during the growing seasons (e.g., year 2011 in Figure 8). However, AG and DL were more robust in reconstructing the general seasonal patterns when MODIS NDVI was noisy (e.g., year 2010 in Figure 8). For details of time-series patterns generated from each method for all 10 sites, see Figure S3.