# Annual Gross Primary Production from Vegetation Indices: A Theoretically Sound Approach
## 4 Results
### Calibration and Validation of the Semi-Empirical Model
When using coefficients depending on the vegetation type, the 24% of pixels have \(\mid\) rMBE \(\mid\)\(\leq\) 5% (and 73% have \(\mid\) rMBE \(\mid\)\(\leq\) 20%) for NDVI (Figure 6c) and EVI (Figure 6d). The rMBE image using both constant and vegetation-type dependent values of \(C_{1}\) and \(C_{2}\), shows that in the second case the red and blue areas (overestimation and underestimation) are reduced (Figure 6). That is, when considering variable \(C_{1}\) and \(C_{2}\), the bias of the semi-empirical model is slightly reduced. However, when using NDVI some areas located in W (small area with very low vegetation cover) and SE Spain still present overestimates of ca. 100%. Something similar occurs in the semiarid Ebro basin in NE Spain when using instead the EVI. Those areas located in SE and NW Spain comprise semiarid lands with a very low productivity (see Figure 1c). Then, although the bias is important in relative terms, it is not so in absolute terms because the aforementioned areas have very low GPP. Other areas presenting bias between 20% and 40% can also be identified, which are not clearly associated with a vegetation type. The presence of some areas with significant bias might be associated with the thematic map used. However, the use of an ecosystem functional type map [38] produces no improvement. The global statistics for the validation when using this alternative map with NDVI are R = 0.88, rMBE = \(-\)0.010, rMAE = 0.18, and rRMSE = 0.2. That is, the correlation between the model estimates and the reference GPP is \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & & & & \\ \hline \multirow{2}{*}{\(C_{1}\)} & \(-1.610\) & \(-1.143\) & \(-1.190\) & \(-1.50\) & \(-1.046\) & \(-1.44\) & \(-0.975\) & \(-1.194\) & \(-1.019\) \\  & (0.009) & (0.007) & (0.017) & (0.03) & (0.011) & (0.02) & (0.009) & (0.013) & (0.008) \\ \hline \multirow{2}{*}{\(C_{2}\)} & 5.682 & 4.164 & 4.20 & 4.68 & 3.561 & 4.40 & 3.302 & 4.15 & 3.62 \\  & (0.018) & (0.018) & (0.03) & (0.04) & (0.019) & (0.04) & (0.017) & (0.02) & (0.02) \\ \hline \multicolumn{10}{c}{**EVI**} \\ \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline \multirow{2}{*}{\(C_{1}\)} & \(-1.825\) & \(-1.562\) & \(-1.311\) & \(-1.15\) & \(-1.498\) & \(-1.01\) & \(-1.421\) & \(-1.337\) & \(-1.735\) \\  & (0.011) & (0.007) & (0.018) & (0.02) & (0.009) & (0.02) & (0.007) & (0.013) & (0.007) \\ \hline \multirow{2}{*}{\(C_{2}\)} & 7.99 & 6.68 & 6.25 & 6.15 & 6.95 & 5.77 & 6.319 & 6.25 & 7.29 \\  & (0.03) & (0.02) & (0.04) & (0.05) & (0.03) & (0.06) & (0.017) & (0.03) & (0.03) \\ \hline \end{tabular}
\end{table} 
Table 4: Mean value and standard deviation (below each value, between brackets) of the regression coefficients for each land-cover type. Code: (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. \(C_{1}\) and \(C_{2}\) are expressed in kg\(\cdot\)m\({}^{-2}\).yr\({}^{-1}\). Results are shown for NDVI and EVI. decreased, and the uncertainties are slightly increased, with respect to those obtained using the hybrid classification map.