## 3 Results
### Impact of Bias in Phenology on Simulated Productivities  
Figures 5 and 6 show the GPP and NEP simulated in the Dynamic Onset and Dynamic Offset runs, respectively. The GPP and NEP from experimental simulations have similar inter-annual variability as the control; however, their magnitude was overall increased or decreased compared with the control. This corresponds to the overall advanced or delayed phenology in the experimental simulations because the environmental conditions are the same. In general, higher GPP and NEP were found for earlier onset and later offset, mainly due to the extra days of photosynthesis. Our regression analysis showed a strong negative linear correlation between the bias in the onset (_i.e._, difference between modeled onset and observed onset) and the error in simulated productivities (_i.e._, difference in simulated GPP and NEP between the Dynamic Onset experiment and the control) (Figure 7a,b). It should be noted that, because our control simulation does not perfectly reproduce the observation (Figure 2), the difference between the experimental and control run might not perfectly represent the overall error (_i.e._, the difference between simulation and reality). Instead, the difference represents a component of the overall error due to inaccurate phenology, which we refer to as error in this paper for simplicity. The slopes for GPP (R\({}^{2}\) = 0.98, \(p\) \(<\) 0.01) and NEP (R\({}^{2}\) = 0.93, \(p\) \(<\) 0.01) were \(-\)9.48 and \(-\)5.02, respectively, indicating that a one-day bias in the leaf onset would result in an error of 9.48 g C m\({}^{-2}\) yr\({}^{-1}\) in GPP and 5.02 g C m\({}^{-2}\) yr\({}^{-1}\) in NEP. The difference in simulated GPP and NEP between the Dynamic Offset and the control can be represented as a quadratic function of the difference between modeled and observed leaf offset (Figure 7c,d). As the coefficients of the quadratic term were small (\(-\)0.05 for GPP and \(-\)0.02 for NEP), the relationship is approximately linear when the bias in offset is small (e.g., when the bias is less than 10 days). The quadratic relationship also implies that the magnitude of errors in productivities resulting from a negative bias (_i.e._, earlier offset) is larger than that resulting from a positive bias (_i.e._, later offset). Moreover, the correlation between the errors in simulated GPP and the bias in phenology is slightly stronger than that between the errors in NEP and the bias in phenology. Since NEP is the difference between GPP and Re, this implies that the Re is not as strongly controlled by the phenology as the photosynthesis. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Leaf Offset**} & \multicolumn{2}{c}{**NDVI**} & \multicolumn{2}{c}{**EVI**} \\ \cline{2-5}  & **RMSD** & \(\rho\) & **RMSD** & \(\rho\) \\ \hline LOGISTIC1 & 18.1 & 0.53 & 49.5 & 0.50 \\ LOGISTIC2 & 17.1 & 0.47 & 3.4 & 0.40 \\ MIDPOINT & 18.1 & 0.50 & 9.6 & 0.04 \\ MOVING & 56.3 & 0.39 & 29.0 & 0.23 \\ DERIVATIVE & 22.6 & 0.52 & 10.3 & 0.02 \\ CAMELBACK & 34.1 & 0.50 & 37.3 & 0.35 \\ \hline \end{tabular} The RMSD and \(\rho\) between the onset simulated using the original Agro-IBIS algorithm and observations are 10.9 days and 0.43, respectively.  
\end{table} 
Table 6: Performance of modeled offset. Figure 5: Simulated annual Gross Primary Productivity (GPP) and Net Ecosystem Production (NEP) from Dynamic Onset experiment. Leaf onset dates were simulated using the “Sequential” model with the parameters optimized against remotely sensed onset using NDVI (**a**,**b**), and EVI (**c**,**d**). Figure 6: Simulated annual GPP and NEP from Dynamic Offset experiment. Leaf offset dates were simulated using the “Delpierre” model with the parameters optimized against remotely sensed offset using NDVI (**a**,**b**), and EVI (**c**,**d**). Figure 6: _Cont._  
Figure 7: Relationship between errors in phenology and errors in simulated productivities. Leaf onset _vs._ GPP (**a**); leaf onset _vs._ NEP (**b**); leaf offset _vs._ GPP (**c**) and leaf offset _vs._ NEP (**d**).