# Annual Gross Primary Production from Vegetation Indices: A Theoretically Sound Approach
## 5 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**NDVI**} & \multicolumn{2}{c}{**EVI**} \\ \cline{2-5}  & **Constant Values** & \(\boldsymbol{C_{1}}\) **and \(\boldsymbol{C_{2}}\) Values** & **Constant Values** & \(\boldsymbol{C_{1}}\) **and \(\boldsymbol{C_{2}}\) Values** \\  & **of \(\boldsymbol{C_{1}}\) and \(\boldsymbol{C_{2}}\)** & **Depending on Vegetation** & **of \(\boldsymbol{C_{1}}\) and \(\boldsymbol{C_{2}}\)** & **Depending on Vegetation** \\ \hline \multirow{4}{*}{**REFERENCE**: \(\text{GPP}_{\text{APMT}}\)} & R = 0.87 & R = 0.90 & R = 0.90 & R = 0.91 \\  & rRMSE = 0.3 & rRMSE = 0.2 & rRMSE = 0.2 & rRMSE = 0.2 \\  & rMBE = \(-\)0.008 & rMBE = \(-\)0.007 & rMBE = \(-\)0.009 & rMBE = \(-\)0.009 \\  & rMAE = 0.19 & rMAE = 0.16 & rMAE = 0.17 & rMAE = 0.16 \\ \hline \multirow{4}{*}{**REFERENCE**: \(\text{GPP}_{\text{MODIS}}\)} & R = 0.87 & R = 0.84 & R = 0.86 \\  & rRMSE = 0.3 & rRMSE = 0.3 & rRMSE = 0.3 & rRMSE = 0.3 \\ \cline{1-1}  & rMBE = \(-\)0.07 & rMBE = \(-\)0.05 & rMBE = \(-\)0.07 & rMBE = \(-\)0.05 \\ \cline{1-1}  & rMAE = 0.17 & rMAE = 0.16 & rMAE = 0.2 & rMAE = 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of the validation statistics (R, rRMSE, rMBE and rMAE) of the semi-empirical model estimates when driven by NDVI and EVI (with and without a vegetation map) and using as reference \(\text{GPP}_{\text{annual}}^{\text{REF}}\) the aforementioned GPP product optimized for the study area (\(\text{GPP}_{\text{OPT}}\)) as well as the official MODIS GPP product MOD17A3 (\(\text{GPP}_{\text{MODIS}}\)). and EVI. The time series of EVI is shorter than the NDVI one and it is limited to sensors with the blue band. Nevertheless, a longer series could be generated using the two-band enhanced vegetation index, EVI2 [51], which is an acceptable and accurate substitute of EVI without the blue band. Annual GPP could be obtained even when no classification map is available with similar uncertainty when using EVI (and with a slightly higher uncertainty in the case of using NDVI), or even in global studies using lower spatial resolution images such as SEVIRI-MSG. On the other hand, there is no need to work with daily images. It is possible to work directly with the original MODIS products, for example, the NDVI at 16-day temporal resolution, or even with a monthly NDVI without losing functionality. To assess their performance, the annual GPP has been calculated using both products with constant \(C_{1}\) and \(C_{2}\). The validation statistics using the 16-day and 30-day products are exactly the same as those from the daily product shown in Table 3. Only a negligible change in the bias (from \(-0.008\) to \(-0.007\)) is observed when using monthly NDVI values. The model, mainly when it is driven with NDVI, overestimates the annual GPP in semiarid areas and slightly underestimates it in dense forest areas. This conclusion has been reached when using both a vegetation class map and an ecosystem functional type map. The overestimation in semiarid areas when using NDVI might be a consequence of NDVI sensitivity to canopy background variations, especially important in sparse vegetation areas (as bare soil NDVI does not equal to zero, then \(f_{\text{APAR}}\) is slightly overestimated). This overestimation, although reduced, is not completely removed when using EVI. A light, general, GPP overestimation is found in semiarid areas. It could be a consequence of the photosynthesis reduction due to water stress that is not completely taken into account by the semi-empirical model, which evidences that the hypothesis H3 might be somehow inaccurate, that is, the vegetation index decrease does not fully characterize the photosynthesis reduction by water stress. However, the GPP in these areas is very low and therefore the absolute value of the uncertainty is low. On the other hand, the underestimation in dense forest areas could be attributed to the NDVI saturation at high LAI levels.