## 4 Discussion  
### Why is Annual Mean LAI the Best Satellite-Derived Estimator of Annual GPP?  
LAI showed the highest correlation with annual GPP among the satellite metrics presented in this study (Table 4). This strong connection between annual GPP and annual mean LAI has previously been  
Figure 6: Average and standard deviation of estimated LAI-based and MOD17 annual GPP for each forest type: Evergreen Needleleaf Forest (EN), Evergreen Broadleaf Forest (EB), Deciduous Needleleaf Forest (DN), Deciduous Broadleaf Forest (DB), and mixed forest. The statistics are calculated from all the available 0.5-degree pixels grouped by forest type using the MODIS Land Cover MCD12C1 V005 IGBP classification scheme data.  
Figure 7: Contour plots of estimated GPP against temperature and precipitation (**a**) and against precipitation and diurnal temperature range (DTR) (**b**).  
documented through ground measurements by [PERSON] _et al._[70] and [PERSON] _et al_.[71], who showed high correlations between GPP and Leaf Area Duration (LAD = growing season LAI \(\times\) the number of growing season months). The relationship can be explained biophysically with the observation that larger canopies and longer growing seasons allow more carbon to be assimilated. Conversely, as more carbon is fixed as GPP, more carbon is allocated to leaf production. Although annual mean LAI correlates well with annual GPP, seasonal LAI correlates poorly with seasonal GPP because it does not respond to short term stresses such as anomalous heat waves.  
The high correlation across different forest types can be explained by the functional convergence hypothesis [72]. The functional convergence hypothesis states that plants tailor their photosynthetic capacity to the amount of the most limiting resource so that optimal use is made of all resources [72]. The hypothesis has been well examined at the leaf level and is used to explain the convergence of leaf traits, such as the high correlation between photosynthetic capacity and leaf nitrogen content [73,74]. At the landscape or global level, the functional convergence hypothesis can be extended to explain the high correlation between absorbed PAR (APAR) and net primary production, and leads to assuming a constant LUE ([PERSON], 1991). [PERSON] _et al._[75] concluded that, because of the wide variability of carbon use efficiency (NPP/GPP), it is the LUE of GPP that should converge rather than the LUE of NPP. Since APAR is a function of LAI, the functional convergence theory should apply also for the relation between annually integrated GPP and LAI. Hence, we expect the annual GPP and LAD to be tightly correlated, even though over shorter time periods there can be a discrepancy between GPP and LAI, as shown in Table 3. Similar results were found when calculating GPP and LAI using prognostic ecosystem models [65].  
Vegetation indices plots (Figure 3) showed non-linear relationship with GPP and a very different scatter from LAI plots (Figure 4). Vegetation indices do not monotonically increase with LAI mainly because of (1) canopy structural parameterization in the radiative transfer model of the MOD15 algorithm and (2) higher sensitivity of LAI to the reflectances in the saturation range of vegetation indices [35].