## 3 Results
### Evaluation of the EMGPP Models under All Sky Conditions  
#### 3.2.1 Evaluation of EMGPP Models for S/Q < 0.5 Conditions  
First, we investigated the performance of 3-factor and 2-factor EMGPP models for GPP estimates from 22 May 2013 to 31 December 2016. The hourly GPP calculated using the coefficients in Tables 1 and 2 was compared with the observations for S/Q < 0.5. To thoroughly investigate performance in detail, we also show the results for the periods of 2013-2014, 2015, 2016 and 2013-2016. The results in Tables 3 and 4 and Figure 4 show that the estimated monthly GPP using 3-factor and 2-factor models overestimated GPP with a relative bias of 78.41% and 76.19% during 2013-2016, respectively, and their corresponding ratios of the mean calculated hourly GPP to the observed were 1.03 and 1.05. Hourly GPP  
\begin{table}
\begin{tabular}{l l c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{\(\mathbf{B_{1}}\)} & \multirow{2}{*}{\(\mathbf{B_{2}}\)} & \multirow{2}{*}{\(\mathbf{B_{3}}\)} & \multirow{2}{*}{\(\mathbf{B_{6}}\)} & \multirow{2}{*}{\(\mathbf{R^{2}}\)} & \multirow{2}{*}{\(\delta_{\mathbf{mag}}\)} & \multirow{2}{*}{\(\delta_{\mathbf{mag}}\)} & \multirow{2}{*}{**NMSE**} & \multirow{2}{*}{\(\sigma_{\mathbf{cal}}\)} & \multirow{2}{*}{\(\sigma_{\mathbf{abs}}\)} & \multicolumn{2}{c}{**MAD**} & \multicolumn{2}{c}{**RMSE**} \\ \cline{5-12}  & & & & & & & & & & & & **(mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** & **(mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** \\ \hline
3 factor & 0.012 & 1.128 & \(-\)0.092 & 0.072 & 0.994 & 15.52 & 47.91 & 0.035 & 0.228 & 0.226 & 0.12 & 15.21 & 0.15 & 18.74 \\ \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{\(\mathbf{C_{1}}\)} & \multirow{2}{*}{\(\mathbf{C_{2}}\)} & \multirow{2}{*}{\(\mathbf{C_{6}}\)} & \multirow{2}{*}{\(\mathbf{R^{2}}\)} & \multirow{2}{*}{\(\delta_{\mathbf{mag}}\)} & \multirow{2}{*}{\(\delta_{\mathbf{mag}}\)} & \multirow{2}{*}{**NMSE**} & \multirow{2}{*}{\(\sigma_{\mathbf{cal}}\)} & \multirow{2}{*}{\(\sigma_{\mathbf{abs}}\)} & \multicolumn{2}{c}{**MAD**} & \multicolumn{2}{c}{**RMSE**} \\ \cline{5-12}  & & & & & & & & & & & & **(mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** & **(mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** \\ \hline
2 factor & 0.005 & 1.171 & 0.027 & 0.993 & 16.20 & 67.15 & 0.037 & 0.235 & 0.226 & 0.13 & 15.66 & 0.16 & 19.35 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Same as Table 1 but for S/Q \(\geq\) 0.5 (\(n=985\)).  
Figure 3: Scatter plot of calculated versus measured hourly GPP at Qianyanzhou subtropical conifer plantation under atmospheric conditions S/Q \(\geq\) 0.5 (\(n=985\)), using the 3-factor (**left**) and 2-factor (**right**) EMGPP models.  
Figure 2: Scatter plot of calculated versus measured hourly GPP in Qianyanzhou subtropical conifer plantation under atmospheric conditions S/Q < 0.5 (\(n=91\)), using the 3-factor (**left**) and 2-factor (**right**) EMGPP models.  
summer and lower values in winter [72]. Generally, the 3-factor model performs better than the 2-factor model. The 2-factor model can also be used when the scattering factor (e.g., direct or diffuse solar radiation) is not available. The estimated monthly GPP using 3-factor and 2-factor models overestimated GPP with relative biases of 35.66% and 33.19% during 2013-2016, respectively.  
Similarly, comparisons of annual amounts of GPP are given in Table 6, and better estimates were also performed, e.g., the ratios of annual amounts of GPP calculated as observed were 1.03 (ranging from 0.91 to 1.12) and 1.05 (0.95-1.13). Additionally, the relative errors were 2.66% (7.20-12.17%) and 5.06% (4.00-13.46%), respectively, for using 3-factor and 2-factor models.