# Annual Gross Primary Production from Vegetation Indices: A Theoretically Sound Approach
## 4 Results
### Calibration and Validation of the Semi-Empirical Model

Table 2: Regression coefficients \(C_{1}\) and \(C_{2}\) (in kg\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\)) for each iteration and their final values and errors. For each year, each coefficient has been obtained using the rest of the years. Results are shown for NDVI and EVI. Figure 5: The model underestimates the annual GPP in the lighter peixls when using NDVI. \begin{table}
\begin{tabular}{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** & **All** \\ \hline
**R** & 0.88 & 0.85 & 0.86 & 0.87 & 0.88 & 0.86 & 0.86 & 0.88 & 0.87 \\
**MBE** & 0.03 & \(-0.03\) & \(-0.05\) & \(-0.03\) & \(0.005\) & \(-0.02\) & 0.008 & 0.04 & \(-0.008\) \\
**MAE** & 0.18 & 0.20 & 0.2 & 0.20 & 0.19 & 0.19 & 0.19 & 0.19 & 0.19 \\
**RMSE** & 0.3 & 0.3 & 0.2 & 0.2 & 0.3 & 0.3 & 0.3 & 0.3 & 0.3 \\
**rMBE** & 0.03 & \(-0.03\) & \(-0.04\) & \(-0.03\) & 0.005 & \(-0.02\) & 0.0008 & 0.04 & \(-0.006\) \\
**rMAE** & 0.20 & 0.19 & 0.18 & 0.18 & 0.20 & 0.18 & 0.18 & 0.19 & 0.19 \\
**rRMSE** & 0.3 & 0.3 & 0.2 & 0.2 & 0.3 & 0.2 & 0.3 & 0.3 & 0.3 \\ \hline \multicolumn{10}{c}{**EVI**} \\ \hline  & **2005** & **2006** & **2007** & **2008** & **2009** & **2010** & **2011** & **2012** & **All** \\ \hline
**R** & 0.91 & 0.89 & 0.90 & 0.90 & 0.91 & 0.89 & 0.89 & 0.90 & 0.90 \\
**MBE** & 0.03 & \(-0.011\) & \(-0.017\) & \(-0.010\) & \(-0.012\) & \(-0.04\) & \(-0.03\) & 0.008 & \(-0.009\) \\
**MAE** & 0.16 & 0.17 & 0.17 & 0.17 & 0.17 & 0.17 & 0.18 & 0.17 & 0.17 \\
**RMSE** & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 \\
**rMBE** & 0.04 & \(-0.011\) & \(-0.015\) & \(-0.009\) & \(-0.013\) & \(-0.03\) & \(-0.03\) & 0.008 & \(-0.008\) \\
**rMAE** & 0.18 & 0.17 & 0.15 & 0.16 & 0.17 & 0.16 & 0.17 & 0.18 & 0.17 \\
**rRMSE** & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Validation statistics for each iteration and for the whole data set (in this case, using the mean values of \(C_{1}\) and \(C_{2}\) shown in Table 2). MBE, MAE and RMSE are expressed in kg\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\). Results are shown for NDVI and EVI. iteration and for each land-cover type. For the sake of brevity, Tables 4 and 5 summarize the mean value and standard deviation of \(C_{1}\) and \(C_{2}\) for each land-cover type, as well as the global validation statistics. The correlation between the estimates and the reference annual GPP using the coefficients in Table 4 is shown in Figure 4e,f for NDVI and EVI, respectively. In Figure 4e, the cluster corresponding to highest GPP pixels distributes also along the 1:1 line and, thus, the global correlation between NDVI estimated and reference annual GPP data increases from 0.87 to 0.90 (last column in Table 5) when considering different values of \(C_{1}\) and \(C_{2}\) for each land-cover type. However, when using the EVI the estimates hardly improve. Therefore, with EVI the uncertainties of the estimates are rather good even without using a vegetation map. The different vegetation types present rather similar statistics. Cultivated areas, croplands and herbaceous show high coefficient of correlation values, and irrigated lands and shrubs show the lowest values, though still relatively high. The lower rMBE values correspond to herbaceous and needle-leaved forest. When analyzing the spatial dependence of the estimates uncertainties (average for all the years), for example in terms of the rMBE, it is observed that most of the estimates present a bias around zero (Figure 6), and the different vegetation types present rather similar values. When using constant regressions coefficients, for the estimates from both NDVI (Figure 6a) and EVI (Figure 6b), 20% of the pixels have \(\mid\) rMBE \(\mid\)\(\leq\) 5% (and 68% of the pixels have \(\mid\) rMBE \(\mid\)\(\leq\) 20%).