## 3 Results
### GPP Simulations and Measurements under All Sky Conditions during 2013-2016  
To fully investigate GPP levels and variations under all sky conditions, all hourly GPP was calculated by the 2-factor and 3-factor EMGFP models and combined coefficients for S/Q < 0.5 and S/Q \(\geq\) 0.5 (all hourly GPP during 1 January 2013-21 May 2013 was calculated using the 2-factor EMGFP model, as the direct radiation and S/Q values were not available). All statistical metrics are shown in Tables S2 and S3 (in Supplementary Material) for the 3-factor and 2-factor models, respectively. Under all sky conditions, hourly GPP estimates (including S/Q < 0.5 and S/Q \(\geq\) 0.5) were generally larger than the observed values, and simulation errors (\(\delta\)avg, \(\sigma_{\rm cal}\), MAD, RMSE) were larger than those for S/Q < 0.5 conditions and slightly smaller than those for S/Q \(\geq\) 0.5 conditions. Specifically, the mean simulated hourly GPP was overestimated compared to observed GPP by 31% (ranging from 15% to 43%) from 2013-2016; RMSE values were 0.398 mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\) and 87.60% when using the 3-factor model, and the corresponding values were 29% (17%-39%), 0.378 mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\), 83.23% when using the 2-factor model. Generally, the EMGFP models showed similar performance over the model development and nonmodel development periods. Thus, the EMGPP model can be applied to simulate GPP under all skies. Likewise, the mean simulated daily GPP overestimated the observed GPP by 31% during 2013-2016; RMSE values were 3.55 g C m\({}^{-2}\) and 87.60% when using the 3-factor model, and the corresponding values were 29%, 3.43 g C m\({}^{-2}\) and 83.23% when using the 2-factor model. Monthly amounts of calculated and observed GPP for S/Q = 0-1 are displayed in Figures S2 and S3 (in Supplementary Material) and Table S4 (in Supplementary Material). Most monthly amounts of GPP estimates showed reasonable agreement with the observations within 2 times the standard deviations of the observed. For using 3-factor and 2-factor models: (1) The estimated monthly amounts of GPP were overestimated compared \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**3-F** & \multirow{2}{*}{\(\delta_{\text{avg}}\)} & \multirow{2}{*}{\(\delta_{\text{max}}\)} & \multirow{2}{*}{\(\delta_{\text{PD}}\)} & \multirow{2}{*}{\(\text{GPP}_{\text{obs}}\)} & \multirow{2}{*}{cal/obs} & \multicolumn{2}{c}{**2-F**} & \multirow{2}{*}{\(\delta\)**avg**} & \multirow{2}{*}{\(\delta\)**max**} & \multirow{2}{*}{\(\text{GPP}_{\text{cal}}\)} & \multirow{2}{*}{\(\text{GPP}_{\text{obs}}\)} & \multirow{2}{*}{cal/obs} \\
**Time Period** & & & & & & & & & \\ \hline
2013 & 43.62 & 77.66 & 169.86 & 134.17 & 1.19 & 2013 & 42.62 & 74.40 & 169.71 & 134.17 & 1.19 \\
2014 & 51.87 & 92.51 & 183.79 & 121.52 & 1.37 & 2014 & 50.90 & 90.06 & 178.56 & 121.52 & 1.31 \\
2015 & 50.20 & 95.21 & 193.13 & 125.12 & 1.45 & 2015 & 48.70 & 89.28 & 187.62 & 125.12 & 1.39 \\
2016 & 36.99 & 65.80 & 179.30 & 140.17 & 1.20 & 2016 & 39.15 & 70.01 & 175.86 & 140.17 & 1.16 \\
2013-2014 & 48.83 & 92.51 & 178.66 & 126.18 & 1.30 & 2013–2014 & 47.85 & 90.06 & 175.30 & 126.18 & 1.26 \\
2013-2016 & 45.91 & 95.21 & 182.87 & 129.79 & 1.32 & 2013–2016 & 45.66 & 90.06 & 178.89 & 129.79 & 1.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Same as Table 5 and for simulations of monthly amounts of GPP (mg CO\({}_{2}\) m\({}^{-2}\)) (S/Q \(\geq\) 0.5). Figure 6: Observed and calculated monthly amounts of GPP using the 3-factor and 2-factor EMGFP models (GPP\({}_{\text{obs}}\), GPP\({}_{\text{cal}\,3\text{F}}\) and GPP\({}_{\text{cal}\,2\text{F}}\), respectively) with error bars showing 2 times standard deviations in the observed GPP during 2013–2016 (S/Q \(\geq\) 0.5). to observed GPP by 22% (the range of the ratio of calculated to observed GPP was 0.28-1.90) and 18% (0.23-1.86) from 2013-2016, respectively. (2) The R\({}^{2}\) values between the estimated and observed monthly amounts of GPP were 0.86 and 0.87, respectively.