## 4 Discussion
### Soil Drought as the Main Driver of GPP Anomalies
Now, when focusing on our study site, and quantifying the potential errors related to the FPAR canopy instead of fraction of photosynthetic active radiation absorbed by the photosynthetic elements, we are not alarmed by this bias as GPP MODIS and measured GPP are actually in close agreement during the non water-limited periods. In addition, as our model explained the error rate with R\({}^{2}\) = 0.71, we can also attribute to an additional error rate of 0.29 for the FPAR bias. In turn, we could also claim that refining drought is twice more important than the bias due to erroneous FPAR. The comparison of different GPP outputs when using FPAR or refined photosynthetic active interception in [64] illustrates large discrepancies in croplands/grassland test sites, but a lower bias for evergreen or mixed forests. [PERSON], [PERSON] _et al_. [36] were the first to report that MODIS GPP was significantly overestimated during the water-limited periods, but gave reasonable estimates during the wettest seasons in the savanna ecosystem where rainfall amount and timing exclusively controls plant productivity. In the _Eucalyptus_ spp. forest, they found that rainfall was a key-control factor in explaining inter-annual variations of productivity, while evaporation fluxes were less affected by drought than carbon uptake. The lack of a soil water limitation term in MODIS GPP algorithm may result in significant overestimation in productivity particularly during extreme drought. [PERSON] _et al_. and [PERSON] _et al_. [56, 72] advocated for the development of such soil water modifier. [PERSON] _et al_. [36] and [PERSON] _et al_. [73] examined the possible benefits of modifying the MODIS algorithm by adding simple water balance scalar from the ratio of antecedent rainfall and potential evapotranspiration PET data. [PERSON], [PERSON] _et al_. [36] proposed a modifier based on the ratio of the sum of rainfall on the sum of PET over a given time window. Their estimate of PET is the equilibrium evapotranspiration and the optimal time window is three months. Further, [PERSON] _et al_. [74] successfully applied this modifier with the same integration period for a Douglas-fir needle leaf forest. A similar time window of 100 days is also adopted by [75] in developing their new drought index for grasslands, the \"local dryness\". Alternatively, [PERSON] _et al_. [73] proposed a soil water correction index at a yearly scale. They first calculated the monthly course of soil water availability with a soil bucket model receiving monthly rainfalls minus PET. For evergreen coniferous, their correction index is integrated over the whole-year because they assumed that photosynthesis occurs throughout the year. For deciduous forests only the growing season is concerned. All found that the modifiers significantly improved the predictions. For our _Q.__ilex_ forest, we develop a modifier depending on daily values of the soil RWC integrated over the rooting depth that we further average over eight days to facilitate comparison with MODIS GPP. This modifier explains more than 75% of the variance (Figure 4). The use of soil water content as driver for a modifier has already been suggested by [74]. They observed that [36]'s modifier paralleled the eight-day averaged measurements of the relative extractable soil water content REW over the 0-60 cm layer. This layer contains most of the roots of the dominant species of their study forest, _Pseudotsuga menziesii_. Interestingly, we observed two characteristic values in the course of GPP anomalies against RWC. First there exists a plateau for values of \(\mathrm{RWC}<0.7\) during which we do not observe significant effect of soil water limitation. Most of the errors sources from the previously discussed parameters. Finally, we observed an asymptote for \(\mathrm{RWC}=0.4\). For \(0.7<\mathrm{RWC}<0.4\) large anomalies may be related to the soil water limitation.