# Annual Gross Primary Production from Vegetation Indices: A Theoretically Sound Approach
## 4 Results
### Calibration and Validation of the Semi-Empirical Model  
The density scatterplot of GPP\({}^{\mathrm{REF}}_{\mathrm{annual}}\) as a function of both \(\overline{\mathrm{NDVI}}^{Y}\) and \(\overline{\mathrm{EVI}}^{Y}\) for all the image pixels and all years (Figure 4a,b, respectively) evidences a practically linear correlation. Therefore, in a first step, the regression coefficients \(C_{1}\) and \(C_{2}\) (Equation (4), using reference annual GPP data) are obtained assuming a constant conversion efficiency value \(\varepsilon\). The cross-validation procedure is applied to these data to obtain \(C_{1}\) and \(C_{2}\) using NDVI and EVI (Tables 2 and 3). The corresponding estimated GPP\({}_{\mathrm{annual}}\) values using NDVI and EVI are shown in Figure 4c,d, respectively. Most of the estimates distribute along the 1:1 line, which indicates a good agreement between the reference and the estimated GPP. However, when using the NDVI, there is a cluster located at high levels of GPP that does not lie along the 1:1 line, which indicates an underestimation of the model for high GPP values. The corresponding  
Figure 3: Coefficient of variation among the eight-year dataset of: (**a**) annual PAR; (**b**) annual mean NDVI; and (**c**) annual mean EVI. \(p\)-value of correlations between inter-annual variations for the eight years of annual GPP and those from: (**d**) annual PAR; (**e**) annual mean NDVI; and (**f**) annual mean EVI. \(\mathrm{R}^{2}\) for the above correlations: (**g**) GPP/PAR; (**h**) GPP/NDVI; and (**i**) GPP/EVI. pixels are located in dense forest areas (Figure 5). The last column in Table 3 shows the statistics of the correlation between estimated and reference annual GPP using the mean values of \(C_{1}\) and \(C_{2}\). Figure 4: A density plot including all image pixels and all years evidences the correlation between: (**a**) \(\mathrm{GP_{annual}^{REF}}\) and \(\overline{\mathrm{NDVI}}^{Y}\); and (**b**) \(\mathrm{GP_{annual}^{REF}}\) and \(\overline{\mathrm{EVI}}^{Y}\). Correlation between \(\mathrm{GP_{annual}^{REF}}\) and \(\mathrm{GP_{annual}}\) estimated by the semi-empirical model with a constant conversion efficiency using: (**c**) NDVI; and (**d**) EVI. Correlation between \(\mathrm{GP_{annual}^{REF}}\) and \(\mathrm{GP_{annual}}\) estimated by the semi-empirical model with a conversion efficiency depending on the land-cover type using: (**e**) NDVI; and (**f**) EVI (Reddish areas correspond to the highest point density. The dashed line is the 1:1 bisector). The consideration of different vegetation types implies adjusting the distributions in Figure 4a,b using different regression lines. The hybrid land-cover map for the study area [44] has been used to apply the cross-validation procedure for each vegetation class: (1) irrigated lands; (2) cultivated areas; (3) cropland mosaic; (4) broad-leaved forest; (5) needle-leaved forest; (6) mixed forest; (7) shrubs; (8) herbaceous; and (9) sparse vegetation. As a result, values of \(C_{1}\) and \(C_{2}\) have been obtained for each \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**NDVI**} \\ \hline  & **2005** & **2006** & **2007** & **2008** & **2009** & **2010** & **2011** & **2012** & **Mean** & **Std** \\ \hline \(C_{1}\) & \(-1.031\) & \(-1.050\) & \(-1.030\) & \(-1.027\) & \(-1.021\) & \(-1.029\) & \(-1.038\) & \(-1.022\) & \(-1.031\) & \(0.009\) \\ \(C_{2}\) & 3.843 & 3.862 & 3.819 & 3.818 & 3.818 & 3.826 & 3.848 & 3.828 & 3.833 & \(0.017\) \\ \hline \multicolumn{10}{c}{**EVI**} \\ \hline  & **2005** & **2006** & **2007** & **2008** & **2009** & **2010** & **2011** & **2012** & **Mean** & **Std** \\ \hline \(C_{1}\) & \(-1.611\) & \(-1.625\) & \(-1.615\) & \(-1.619\) & \(-1.592\) & \(-1.605\) & \(-1.613\) & \(-1.604\) & \(-1.160\) & \(0.010\) \\ \(C_{2}\) & 6.97 & 6.99 & 6.96 & 6.98 & 6.91 & 6.93 & 6.96 & 6.94 & 6.96 & \(0.03\) \\ \hline \hline \end{tabular}
\end{table}