## Materials and Methods
### Data and Methods
#### 2.2.3 Indices Derived from MODIS Surface Reflectance Products  
Surface reflectance products in the red (620-670 nm), near-infrared (NIR: 841-875 nm), green (545-565 nm) and shortwave-infrared (SWIR: 1628-1652 nm) (MCD43A4 V005, spatial resolution 500 m) evaluated from MODIS measurements were used to provide a better match with the spatial footprint of the flux towers. To minimize potential seasonal effects of illumination geometry, we calculated the VIs from the MODIS surface reflectance product instead of using the MODIS VI product directly (Figure A2). Both Terra and Aqua data were used to generate this product. All the data were sampled every 8 days with an average over the 16-day period. We used the MCD43A4 surface reflectance product to calculate the VIs because of its comparable spatial resolution with EC-estimated GPP. NDVI is a normalized ratio of the NIR and red bands. The ratio concept of NDVI reduces many forms of multiplicative noise, such as illumination differences, cloud shadows, atmospheric attenuation, and certain topographic variations presented in multiple bands [47]. The equation takes the form:  
\[\mathrm{NDVI}=\frac{\rho_{NIR}-\rho_{red}}{\rho_{NIR}+\rho_{red}} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Site** & **Site name** & **Latitude** & **Longitude** & **IGBP** & **GPP duration** & **Reference** \\ \hline DK-ZaH & Zackenberg Heath & 74.47 & \(-\)20.55 & GRA & 2000–2014 & [35] \\ RU-Sam & Samoylov & 72.37 & 126.50 & GRA & 2002–2014 & [36] \\ US-Atq & Atqasuk & 70.47 & \(-\)157.41 & WET & 2004–2008 & [35] \\ RU-Cok & Chokurdakh & 70.83 & 147.50 & OSH & 2003–2014 & [37] \\ FI-Sod & Sodankyla & 67.36 & 26.64 & ENF & 2001 \(-\)2014 & [38] \\ DK-NuF & Nuuk Fen & 64.13 & \(-\)51.39 & WET & 2008–2014 & [39] \\ FI-Hyy & Hyytiala & 61.85 & 24.30 & ENF & 2000–2014 & [40,41] \\ FI-Kaa & Kaamanen & 69.14 & 27.30 & WET & 2000–2008 & [42] \\ SE-Deg & Degeró & 64.18 & 19.56 & GRA & 2001–2006 & [43,44] \\ SE-Nor & Norunda & 60.09 & 17.48 & ENF & 2003–2007 & [45] \\ SE-Sk1 & Skyttorp 1 & 60.13 & 17.92 & ENF & 2005–2008 & [45] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Eddy covariance tower sites used in this study. Location, data availability, and land-cover class according to the IGBP designations of the different sites. EVI was introduced to improve vegetation monitoring by decoupling canopy background signals and reducing atmospheric influences to increase the sensitivity of vegetation signals in high-biomass areas [47]. EVI was calculated as follows:  
\[\text{EVI}=G\frac{\rho_{NIR}-\rho_{red}}{\rho_{NIR}+C_{1}\times\rho_{red}-C_{2} \times\rho_{blue}+L} \tag{2}\]  
where \(L=1\), \(C_{1}=6\), \(C_{2}=7.5\), gain factor \(G=2.5\). Studies have shown the use of SWIR reflectance in VI constructions can improve LSP extraction from remote sensing data [48; 49]. Thus, to distinguish the effects of phenology from background contamination such as accumulation and melting of snow, NDII which is based on the NIR and SWIR reflectances has been examined. However, both NDVI and NDII respond not only to greenness, but also to other information such as brightness and wetness. Thus, PI was therefore developed to remove the effects of wetness and brightness on greenness. PI combines the advantages of NDVI and NDII to capture small changes in vegetation growth, as the shortcomings of these two indicators can be compensated for by the other [4]. \[NDII=\frac{\rho_{NIR}-\rho_{SWIR}}{\rho_{NIR}+\rho_{SWIR}} \tag{3}\]  
\[PI=0,\ if\ NDVI<0\ or\ NDII<0\ (NDVI+NDII)\times(NDVI-NDII)\ 0,\ if\ PI<0. \tag{4}\]  
PPI is a physical-based spectral VI for monitoring plant phenology that was formulated to highlight canopy leaf area index (LAI) and indicate canopy growth dynamics. Combining red and NIR reflectances, PPI is based on modified Beer's law, which describes the relationship between canopy reflectance and LAI [50].