## Results
### Relationships between Vegetation Indices and Environmental Stresses  
To understand how VIs respond to environmental stresses, we examined the relationships between the VIs and two environmental scalars - f\({}_{\rm{f}opt}\) and f\({}_{\rm{f}VD}\) (representing temperature stress and water stress, respectively) at the monthly scale for each site separately. On average, NDVI, EVI, EVI2, \(\rm{NIR_{V}}\), \(\rm{NDVI_{B}RDF}\), \(\rm{EVI_{B}RDF}\), \(\rm{EVI_{B}RDF}\), and \(\rm{NIR_{V,B}RDF}\) explained 58%, 45%, 61%, 55%, 59%, 53%, 64%, and 62% of the variance in temperature stress across the 121 sites. This indicates that these VIs responded to temperature stress fairly well, and three VIs (EVI2, \(\rm{EVI2_{B}RDF}\) and \(\rm{NIR_{V,B}RDF}\)) could capture temperature stress almost as well as the MODIS GPP product (average R\({}^{2}\) = 0.67, p \(<\) 0.001). Figure 6 summarizes the R\({}^{2}\) values for the relationships between the VIs and the f\({}_{\rm{f}opt}\) scalar across all sites in each biome. In general, the correlation of the VIs to temperature stress was high for ENF (R\({}^{2}\) = 0.39-0.70, p \(<\) 0.0001), DBF (R\({}^{2}\) = 0.59-0.73, p \(<\) 0.0001), MF (R\({}^{2}\) = 0.57-0.81, p \(<\) 0.0001), COSH (R\({}^{2}\) = 0.16-0.53, p \(<\) 0.0001), GRA (R\({}^{2}\) = 0.61-0.70, p \(<\) 0.0001), and WET (R\({}^{2}\) = 0.49-0.64, p \(<\) 0.0001), medium for EBF (R\({}^{2}\) = 0.27-0.44, p \(<\) 0.0001) and CRO (R\({}^{2}\) = 0.50-0.60, p \(<\) 0.0001), and low for WSA (R\({}^{2}\) = 0.06-0.14, p \(<\) 0.005) and SAV (R\({}^{2}\) = 0.04-0.2, p \(<\) 0.5). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**IGBP** & **NDVI** & **EVI** & **EVI2** & **NDVI\_BRDF** & **EVI\_BRDF** & **EVI2\_BRDF** & **NIR\_** & **NIR\_** & **NIR\_** \\ \hline ENF & 0.79 *** & 0.28 * & 0.65 *** & 0.76 *** & 0.46 *** & 0.66 *** & 0.52 *** & 0.66 *** & 0.70 *** \\ EBF & 0.85 * & 0.68 * & 0.86 * & 0.75 & 0.53 & 0.55 & 0.84 & 0.52 & 0.46 \\ DBF & 0.59 *** & 0.11 & 0.25 * & 0.45 *** & 0.25 * & 0.16 & 0.00 & 0.12 & 0.00 \\ MF & 0.63 * & 0.10 & 0.35 & 0.70 * & 0.46 * & 0.61 * & 0.29 & 0.50 * & 0.23 \\ COSH & 0.84 *** & 0.02 & 0.76 * & 0.84 * & 0.75 & 0.76 * & 0.51* & 0.75 * & 0.75 * \\ WSA & 0.79 * & 0.72 * & 0.69 * & 0.82 * & 0.70 * & 0.69 * & 0.64 & 0.69 * & 0.60 * \\ SAV & 0.02 & 0.13 & 0.22 & 0.04 & 0.24 & 0.29 & 0.28 & 0.35 & 0.00 \\ GRA & 0.76 *** & 0.74 *** & 0.72 * & 0.76 *** & 0.71 *** & 0.73 *** & 0.73 *** & 0.73 *** & 0.72 *** \\ WET & 0.37 * & 0.39 * & 0.42 * & 0.39 * & 0.32 * & 0.42 * & 0.14 * & 0.42 * & 0.31 * \\ CRO & 0.27 & 0.83 * & 0.81 * & 0.69 * & 0.03 & 0.56 & 0.00 & 0.69 * & 0.05 \\ \hline \end{tabular}
\end{table} 
Table 1: The coefficient of determination (R\({}^{2}\)) values for the relationships of the VIs and MODIS GPP with tower GPP at the annual scale across all sites within each biome in Figure 4. The asterisks - *, ** and *** stand for the significance level p \(<\) 0.05, p \(<\) 0.01 and p \(<\) 0.001, respectively. Figure 6: The boxplots of the R\({}^{2}\) values for the relationships of monthly averaged VIs and MODIS GPP with temperature stress (f\({}_{\rm{f}opt}\)) for each biome with the total of 121 sites. The letters on the x axis stand for: A - NDVI, B - EVI, C - EVI2, D - NDVI\({}_{\rm{B}RDF}\), E - \(\rm{EVI_{B}RDF}\), F - \(\rm{EVI_{B}RDF}\), G - \(\rm{NIR_{V}}\), H - \(\rm{NIR_{V,B}RDF}\), and I - MODIS GPP. The biome types are as follows: evergreen needleleaf forest (ENF); evergreen broadleaf forest (EBF); deciduous needleleaf forest (DNF); mixed forest (MF); closed and open shrublands (COSH); woody savannas (WSA); savannas (SAV); grasslands (GRA); wetlands (WET); croplands (CRO). NDVI, EVI, EVI2, NIRV, NDVIIBRDF, EVIBRDF, EVI2 BRDF, and NIRV, BRDF explained 29%, 26%, 32%, 32%, 29%, 31%, 34%, and 34% of the variance in water stress at the monthly scale across 121 sites, respectively. This indicates that these satellite-derived VIs were more strongly correlated with temperature stress than with water stress.