# Simulation of Gross Primary Productivity Using Multiple Light Use Efficiency Models
## 3 Results
### The BMA Based GPP Estimation  
The determinant coefficient and RMSE were calculated between the simulated GPP and the EC-measured GPP (Table 4). As expected, the results from the trained BMA method had the highest accuracy. Averaging the R\({}^{2}\) and RMSE among all of the sites indicated that BMA had the highest R\({}^{2}\) and the lowest RMSE among all the models during the training and validation stages (Table 4). However, if one looks at one of the five sites, the BMA was not always the highest-accuracy method, and some LUE models performed better than the BMA. The LUE models performed differently at different sites. At a specific site, the performance of the LUE models varied greatly. For example, the R\({}^{2}\) of the C-fix model in 2014 at the Dashalong site was 0.73, but the R\({}^{2}\) was 0.97 in 2015 at the Daman site. At the Arou site, the MODIS-PSN model performed better than other LUE models, but the C-fix model performed better than other LUE models at the Sidaoqiao site. Overall, at each site, the BMA method was close to the best one of the LUE models. To further explore the performance of these methods, the residual is plotted for each method (Figure 3). The residuals of the BMA method were uniformly distributed around 0 and were less than the standard deviation (SD) of the measurements. The residuals of the BMA method were  
Figure 2: Seasonal carbon flux dynamics at the five study sites.  
smaller than all the LUE models. All the LUE models had values outside the 1x standard deviation range. Even GLO-FEM and EC-LUE had values outside the 2x standard deviation range. The convergence trajectory of the coefficients for LUE models at the Arou site is shown in Figure 4. The initial coefficients for each LUE model were assigned a fixed value, and the value changed during the iteration and quickly reached a steady-state (Figure 4).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Site**} & \multicolumn{8}{c}{**R2**} & \multicolumn{8}{c}{**RMSE (gC/m2/8 day)**} \\ \cline{2-13}  & \multirow{2}{*}{**VPM**} & **EC-LUE** & **GLO-FEM** & **MODIS** & **BMA** & **VPM** & **EC-LUE** & **C-Fix** & **GLO-FEM** & **MODIS** & **BMA** \\ \hline \multirow{2}{*}{Arou} & Training & 0.95 & 0.95 & 0.95 & 0.95 & **0.97** & 0.96 & 6.7 & 8.1 & 8.4 & 26.0 & 6.0 & **4.8** \\  & Validation & **0.95** & 0.94 & 0.94 & 0.94 & **0.95** & **0.95** & 10.1 & 7.0 & 10.9 & 23.8 & 10.3 & **6.9** \\ \hline \multirow{2}{*}{Dashalong} & Training & 0.83 & 0.79 & **0.73** & 0.79 & 0.79 & 0.8 & 8.8 & 7.1 & 10.7 & 10.9 & 9.6 & **6.0** \\  & Validation & 0.88 & **0.91** & 0.84 & 0.82 & 0.76 & 0.87 & 7.1 & **3.9** & 8.2 & 13.2 & 8.4 & 4.7 \\ \hline \multirow{2}{*}{Daman} & Training & 0.95 & 0.94 & 0.95 & 0.94 & **0.96** & 0.95 & 11.5 & 13.6 & 9.6 & 23.9 & 10.9 & **8.4** \\  & Validation & 0.96 & 0.96 & 0.97 & 0.95 & **0.98** & 0.97 & 15.7 & 8.4 & 8.2 & 41.5 & **6.7** & 8.6 \\ \hline \multirow{2}{*}{Shidi} & Training & 0.83 & **0.85** & 0.87 & 0.81 & 0.82 & 0.84 & 9.9 & 15.5 & 14.7 & 39.5 & 13.6 & **8.6** \\  & Validation & 0.75 & 0.82 & 0.79 & **0.83** & 0.82 & 0.81 & 18.4 & 16.1 & 17.0 & 40.9 & **13.5** & 15.1 \\ \hline \multirow{2}{*}{Sidaoqiao} & Training & 0.93 & 0.91 & 0.94 & 0.93 & 0.91 & **0.95** & 5.7 & 7.2 & 4.8 & 24.3 & 8.5 & **3.4** \\  & Validation & 0.85 & 0.84 & **0.87** & 0.85 & 0.78 & **0.87** & 9.3 & _9.7_ & **7.4** & 25.7 & 11.6 & 7.6 \\ \hline \multirow{2}{*}{All sites} & Training & 0.90 & 0.90 & 0.89 & 0.90 & **0.91** & 9.5 & 11.0 & 10.2 & 21.6 & 10.8 & **5.8** \\  & Validation & 0.88 & 0.90 & 0.89 & 0.88 & 0.85 & **0.90** & 12.7 & 9.9 & 10.9 & 25.1 & 11.3 & **8.1** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Determinant coefficients and RMSEs between the simulated GPP and the EC-measured GPP. (Data measured during 2014/2015 was used to train/validate the BMA method. The highest R2 and the smallest RMSE were bolded.).  
Figure 3: \(Cont.\)