## Materials and Methods
### Vegetation Indices  
PPI is a physically-based spectral index for retrieving plant phenology and is formulated to have a nearly linear relationship to green leaf area index (LAI) given a fixed soil effect [36]. The expression of PPI employs red and NIR reflectance and is based on modified Beer's law that describes the relationship between canopy reflectance and leaf area index (LAI) [36]. PPI (unit: \(m^{2}\ m^{-2}\)) is defined as:  
\[PPI\ =\ -K\ \times\ ln\frac{(M-DVI)}{(M-DVI_{s})}, \tag{1}\]  
where \(DVI\) (Difference Vegetation Index) is the difference between NIR and red reflectance; \(M\) is a site specific canopy maximum \(DVI\); \(DVI_{s}\) is the \(DVI\) of the soil. \(K\) is the gain factor that is formed as a function of sun zenith angle \(\theta\), a geometric function of leaf angular distribution and instantaneous diffuse fraction of solar radiation [36; 56]. \(K\) is formulated as:  
\[K\ =\ \frac{0.25\cos(\theta)}{(1\ -\ d_{\mathrm{c}})\ G\ +\ d_{\mathrm{c}}\ \cos(\theta)}\ \frac{1\ +\ M}{1\ -\ M}, \tag{2}\]  
where \(\theta\) is a sun zenith angle; \(\mathrm{d_{c}}\) is an instantaneous diffuse fraction of solar radiation for clear sky and standard atmosphere, when the sun is at zenith angle \(\theta\); G is a geometric function of leaf angular distribution; and M is a site-specific maximum \(DVI\).  
In this study, the inputs in the \(PPI\) formula were calculated as follows:  
* M--a maximum difference between NIR and red MODIS NBAR was calculated for each pixel, for the time period 2000-2014.
* DVI value was set to 0.09, which is an empirically defined value [36]. DVIs can cause negative values if canopy DVI is lower than \(DVI_{s}\), which can occur during snowy conditions or for an ecosystem with very bright soil. The empirical value of \(DVI_{s}\) was still considered to be applicable in this study, since negative \(PPI\) estimates will not alter linearity between PPI and LAI [36].
* zenith angle (\(\theta\)) value for each pixel location was acquired from \"Zenith Angle at local solar noon\" data layer in the MCD43C4 products.
* \(\mathrm{d_{c}}\) has been calculated for standard atmosphere from the equation formulated by [36] following [57; 58]: \[d_{c}\ =\ \ 0.0336\ +\ 0.0477\,/cos(\theta).\] (3)* G value was set to 0.5 based on [59] who found that for a spherical needle (leaf) orientation G is 0.5, regardless of directions of the solar beam (different view directions). According to [36], G 0.5 is also valid for a flat leaf, when assuming a spherical (uniform) leaf angle distribution and may therefore be used in the calculation of PPI. For a more complete description of the physical basis of PPI, we refer to [36]. NDVI, developed by [30], is a normalized ratio of the NIR and red bands. NDVI is defined as: \[\text{NDVI}\;=\;\frac{\rho_{\text{NIR}}\;-\;\rho_{\text{red}}}{\rho_{\text{NIR }}\;+\;\rho_{\text{red}}},\] (4) where \(\rho_{\text{NIR}}\) and \(\rho_{\text{red}}\) are the surface bidirectional reflectance for their respective MODIS bands. Enhanced Vegetation Index (EVI) is an index developed to improve the vegetation signal by incorporating the use of a soil adjustment factor, which ensures that the vegetation lines in the red-NIR space converts to a common point and a blue band that reduces the atmospheric influences [33]. EVI is defined as: \[\text{EVI}\;=\;\text{G}\frac{\rho_{\text{NIR}}\;-\;\rho_{\text{red}}}{\rho_{ \text{NIR}}\;+\;\text{C}_{1}\;\times\;\rho_{\text{red}}\;-\;\text{C}_{2}\; \times\;\rho_{\text{blue}}\;+\;\text{L}},\] (5) where \(\rho_{\text{blue}}\) is surface reflectance for the blue band, L is the canopy background adjustment factor, and C\({}_{1}\) and C\({}_{2}\) are the coefficients of the aerosol resistance term, which uses the blue band in diminishing the atmospheric aerosol scattering in the red band [33]. The coefficients employed in the EVI algorithm are empirically determined, L = 1, C\({}_{1}\) = 6, C\({}_{2}\) = 7.5, and G (gain factor) = 2.5 [33].