# Annual Gross Primary Production from Vegetation Indices: A Theoretically Sound Approach
## 4 Results
### Calibration and Validation of the Semi-Empirical Model
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **Global** \\ \hline
**R** & 0.75 & 0.90 & 0.89 & 0.83 & 0.79 & 0.83 & 0.75 & 0.89 & 0.84 & 0.90 \\
**MBE** & 0.0011 & \(-\)0.005 & 0.007 & 0.006 & \(-\)0.002 & \(-\)0.0003 & \(-\)0.013 & \(-\)0.004 & \(-\)0.013 & \(-\)0.007 \\
**MAE** & 0.3 & 0.13 & 0.18 & 0.2 & 0.18 & 0.2 & 0.2 & 0.16 & 0.16 & 0.17 \\
**RMSE** & 0.4 & 0.18 & 0.2 & 0.3 & 0.2 & 0.3 & 0.3 & 0.2 & 0.2 & 0.2 \\
**rMBE** & 0.0008 & \(-\)0.007 & 0.005 & 0.004 & \(-\)0.0017 & \(-\)0.00018 & \(-\)0.015 & \(-\)0.004 & \(-\)0.018 & \(-\)0.007 \\
**rMAE** & 0.2 & 0.16 & 0.13 & 0.15 & 0.12 & 0.2 & 0.15 & 0.2 & 0.16 \\
**rRMSE** & 0.3 & 0.2 & 0.18 & 0.19 & 0.2 & 0.16 & 0.3 & 0.2 & 0.3 & 0.2 \\ \hline \hline \multicolumn{10}{c}{**EVI**} \\ \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **Global** \\ \hline
**R** & 0.76 & 0.90 & 0.90 & 0.84 & 0.81 & 0.85 & 0.80 & 0.90 & 0.87 & 0.91 \\
**MBE** & 0.005 & \(-\)0.009 & 0.0005 & 0.002 & 0.004 & \(-\)0.0019 & \(-\)0.007 & \(-\)0.006 & \(-\)0.008 & \(-\)0.009 \\
**MAE** & 0.3 & 0.13 & 0.18 & 0.2 & 0.17 & 0.18 & 0.19 & 0.16 & 0.14 & 0.16 \\
**RMSE** & 0.4 & 0.18 & 0.2 & 0.3 & 0.2 & 0.2 & 0.2 & 0.19 & 0.2 \\
**rMBE** & 0.004 & \(-\)0.011 & 0.0004 & 0.0015 & 0.004 & \(-\)0.0012 & \(-\)0.008 & \(-\)0.005 & \(-\)0.011 & \(-\)0.009 \\
**rMAE** & 0.2 & 0.16 & 0.13 & 0.14 & 0.14 & 0.11 & 0.2 & 0.15 & 0.19 & 0.16 \\
**rRMSE** & 0.3 & 0.2 & 0.18 & 0.18 & 0.19 & 0.15 & 0.3 & 0.19 & 0.3 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Validation statistics for each vegetation type and for the whole data set. 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. MBE, MAE and RMSE are expressed in kg\(\cdot\)m\({}^{-2}\).yr\({}^{-1}\). Results are shown NDVI and EVI. Figure 6: Mean rMBE (%) image showing the spatial distribution of the discrepancies between the estimated and the reference annual GPP: (**a**) Estimated annual GPP using the semi-empirical model with NDVI and with constant values of \(C_{1}\) and \(C_{2}\); and (**c**) considering \(C_{1}\) and \(C_{2}\) as a function of the land-cover type; (**b**) Estimated annual GPP using the semi-empirical model with EVI and with constant values of \(C_{1}\) and \(C_{2}\); and (**d**) considering \(C_{1}\) and \(C_{2}\) as a function of the land-cover type (red colors correspond to overestimates and blue color to underestimates). As mentioned above, Figure 6 shows average uncertainties for all the years when using the hybrid classification map. For the year 2011, the comparison between reference and estimated annual GPP data (Figure 7) shows a similar spatial pattern, although the model slightly underestimates GPP in highly productive areas corresponding to dense forests (Figure 5), more noticeable when using NDVI. Finally, as an example, Figure 8 shows the annual GPP images for the 2005-2012 period obtained using the proposed model with EVI and the coefficients in Table 4. The observed inter-annual variability in GPP is influenced mostly by changes in structural parameters of the vegetation, and thus by the EVI, which is connected with precipitation pattern. When precipitation diminishes, for example in 2005 [47], a reduction in GPP is observed. In a wetter year, such as 2010, an increase of GPP is shown. Figure 7: (a) Reference annual GPP and estimated GPP\({}_{\text{annual}}\) (in kg\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\)) for 2011 using: (b) NDVI; and (c) EVI. Figure 8: Images of GPP\({}_{\text{annual}}\) (in kg\(\cdot\)m\({}^{-2}\)\(\cdot\)yr\({}^{-1}\)) for the 2005–2012 period obtained using the semi-empirical model with EVI and the coefficients in Table 4.