## 4 Results and Discussion
### Second-Step Optimization - Phenological and Standing Biomass Parameter Estimates  
The relationship between modeled and observed NDVI for the two growing seasons is reported in Figures 5a and 5b. NDVI\({}_{\text{PROSAILH}}\) explained about 75% of NDVI\({}_{\text{MODIS}}\) variance and showed good agreement between observed and modeled data (Figure 5b). For low NDVI values an underestimation of modeled NDVI was observed. \begin{table}
\begin{tabular}{c c c c} \hline \hline _Parameter_ & _Unit_ & \(\theta_{or}\) & \(\theta_{opt}\) \\ \hline FRC:LC & - & 0.333 & 1.969 (\(\pm\)0.420) \\ Leaf C:N & \(kgC\)\(kgN^{\text{-1}}\) & 15.59 & 20.93 (\(\pm\)2.50) \\ PLNR & - & 0.088 & 0.1050 (\(\pm\)0.011) \\ g\({}_{\text{s,MAX}}\) & \(m\)\(s^{\text{-1}}\) & 0.006 & 0.0041 (\(\pm\)0.001) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Original (\(\theta_{or}\)) and optimized (\(\theta_{opt}\)) parameters of the PROSAILH-BGC model. Standard errors of parameter estimates, calculated with the bootstrap algorithm, are shown in parentheses. ONDAY, OFFDAY and LCMAX estimated with second-step optimization for 2002 and 2003 showed good agreement with the values observed at the experimental site (Table 3). With regard to ONDAY, we found 3 and 8 days of displacement between modeled and observed dates for 2002 and 2003, respectively, whereas for OFFDAY, the displacement was 7 and 6 days for 2002 and 2003, respectively. Conversely, the phenological dates estimated with the internal phenological model of BIOME-BGC led to higher offset between modeled and observed dates with an \begin{table}
\begin{tabular}{c|c c c c} \hline \hline _Year_ & & _ONDAY_ & _OFFDAY_ & _LCMAX_ \\ \cline{3-5}  & & _DOY_ & _DOY_ & _kgCm\({}^{\text{-2}}\)_ \\ \hline
2002 & Obs. & 91 & 267 & 0.164 \\  & Second-step & 88 & 260 & 0.159 \\  & Internal phenology & 100 & 289 & - \\
2003 & Obs. & 78 & 315 & 0.155 \\  & Second-step & 70 & 309 & 0.147 \\  & Internal phenology & 107 & 297 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Start (ONDAY) and end (OFFDAY) of growing season, maximum leaf carbon (LCMAX) observed and estimated with second-step model optimization. The ONDAY and OFFDAY estimated with the internal phenological model (Internal phenology) were also reported. DOY is Day Of Year. Figure 5: a) Time series of NDVI\({}_{\text{MODIS}}\) (full circles) and NDVI\({}_{\text{PROSAILH-BGC}}\) (open circles) for the time period 2002-2003. b) Scatterplot of NDVI\({}_{\text{MODIS}}\) and NDVI\({}_{\text{PROSAILH-BGC}}\). Black triangles are the NDVI data for the growing season (for the days between ONDAY and OFFDAY) while open triangles are data for the dormant period. The black straight line is the regression line calculated on the whole dataset, the dashed lines represent the 95 confidence intervals, the grey line is the 1:1 line. b[0] is the intercept, b[1] is the slope and \(p\) is the significance of the linear regression analysis observed vs modeled. average displacement of 17 days for the ONDAY and 20 days for the OFFDAY. Moreover, LC\({}_{\rm MAX}\) values were estimated with good accuracy (mean error = 4.1%) as shown in Table 3.  
The discrepancy between modeled and observed NDVI, as well as the offset between the estimated and observed phenological dates, may be due to the influence of the understory on the NDVI\({}_{\rm MODIS}\) signal, particularly noteworthy in the period immediately before the beginning and after the end of the growing season as shown in Figure 5a. However, these discrepancies between observed and modeled phenological dates are similar to those reported in others studies [52]. The effect of correct phenological parameterization on the determination of the annual GPP budget is reported in Table 4 where the yearly GPP estimated with the reference models and the two-step optimized model are listed. It is to be noted that by using the Reference Model 1 we obtained sensible underestimation of yearly GPP (-21% for the 2002, -26% for 2003).