## 3 Results
### Evaluation of the EMGPP Models under All Sky Conditions
#### 3.2.2 Evaluation of the EMGPP Model for S/Q \(\geq\) 0.5
Similarly, the standard error of the observed S/Q, 0.144 at S/Q \(\geq\) 0.5 also increased compared to 0.075 at S/Q \(<\) 0.5 during 2013-2016, implying the high atmospheric substance (e.g., aerosols, clouds, fog) loads and the complicated scattering processes in PAR transfer lead to large errors in observations and calculations at S/Q \(\geq\) 0.5 conditions. In addition, the averages of the observed hourly PAR values during 2013-2016 were 3.641 and 1.540 MJ m\({}^{-2}\) for S/Q \(\geq\) 0.5 and S/Q \(<\) 0.5, respectively. The monthly amounts of the calculated and observed GPP for S/Q \(\geq\) 0.5 are displayed in Figure 6 and Table 9. Overall, most monthly GPP estimates agreed with the observed values within 2 times the standard deviations of the observed values. Monthly amount GPP estimates overestimated by 32% (the range of the ratio of calculated to observed GPP was 0.28-1.90) and 27% (0.29-1.90) during 2013-2016 using 3-factor and 2-factor models, respectively. Both monthly amount GPP simulations using 3-factor and 2-factor models can also easily capture seasonal variations (higher in summer and lower in winter) and have similar GPP values, indicating that both models can be used to compute GPP for S/Q \(\geq\) 0.5. A scatter plot of calculated versus measured monthly amounts of GPP is given in Figure S1 (in Supplementary Material). Generally, the 3-factor model generates a better simulation than the 2-factor model. The 2-factor model can also be selected. Both the 3-factor and 2-factor models overestimated GPP with a relative bias of 45.91% and 45.66% from 2013-2016, respectively. The comparisons of annual amounts of GPP are given in Table S1 (In Supplementary Material), and EMGPP models generated reasonable simulations. The ratios of annual amounts of GPP calculated versus observed were 1.41 (ranging from 1.26 to 1.54) and 1.38 (1.25-1.50) using 3-factor and 2-factor models, respectively. It is evident that the estimation errors using 3-factor and 2-factor models increased the most compared to those of S/Q \(<\) 0.5 conditions, which is understandable and caused by the increased measurement errors accompanying high GLP loads (including aerosols, clouds, fogs, dews and smogs). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Time**} & \multirow{2}{*}{\(\delta_{\rm avg}\)} & \multirow{2}{*}{**NMSE**} & \multirow{2}{*}{\(\sigma_{\rm cal}\)} & \multirow{2}{*}{\(\sigma_{\rm obs}\)} & \multirow{2}{*}{**cal/obs**} & \multirow{2}{*}{\(n\)} & \multicolumn{2}{c}{**MAD**} & \multicolumn{2}{c}{**RMSE**} \\ \cline{5-10} \cline{6-10} \multicolumn{1}{c}{**Period**} & & & & & & & **(mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** & **(mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** \\ \hline
2013–2014 & 143.80 & 0.582 & 0.388 & 0.293 & 1.42 & 5759 & 0.295 & 70.83 & 0.543 & 130.46 \\
2015 & 156.93 & 0.653 & 0.387 & 0.287 & 1.54 & 3617 & 0.332 & 79.89 & 0.576 & 138.75 \\
2016 & 156.01 & 0.626 & 0.368 & 0.312 & 1.28 & 3552 & 0.349 & 73.65 & 0.591 & 124.73 \\
2013–2016 & 150.73 & 0.611 & 0.382 & 0.298 & 1.41 & 13031 & 0.320 & 73.93 & 0.402 & 92.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Same as Table 3, but for hourly GPP estimates in 2013–2016 using 3-factor EMGPP (S/Q \(\geq\) 0.5).