## 3 Results
### Evaluation and Application of the EMRe Models under all sky Conditions during 2013-2016  
#### 3.2.1 Nighttime Re Simulations Using Re (DR) Method  
We used the EMRe model (Equation (3)) for Re estimations from 22 May 2013 to 31 December 2016; the hourly Re values calculated using the coefficients in Table 3 were compared with the measurements. To fully evaluate the model performance, detailed results for each year and 2013-2016 are displayed in Table 5 and Figure 5 (a scatted plot of calculated versus measured nighttime hourly Re during 2013-2016). Generally, hourly Re simulations exhibited suitable performances at nighttime with little underestimations for 2013 and 2015. A little larger underestimation (~20%) in 2016 may be caused by instrument problems during June-October.  
Similarly, the daily sums of the nighttime Re values were also estimated and shown in Table 6. The daily sums of the Re simulations were also in line with the observations.  
Furthermore, the mean monthly sums of the nighttime Re values for each year and four years over 2013-2016 were also computed (Table 7 and Figure 6), and were also in agreement with the observations.  
Figure 7 shows the simulations of the annual sums of Re at nighttime during 2013-2016. The ratios of the mean annual sums of the calculated to the observed Re were 0.93, 1.01, 0.93, and 0.81 for 2013, 2014, 2015, and 2016, as well as 0.91 for 2013-2016.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Time** & & & & & & & & & & **MAD** & & **RMSE** \\ \hline
**Period** & **savg** & **NMSE** & **\(\sigma_{\text{cal}}\)** & **\(\sigma_{\text{obs}}\)** & **cal/obs** & **\(n\)** & \multicolumn{2}{c}{**(mgCO2 m\({}^{-2}\) s\({}^{-1}\))**} & **(\%)** & **(mgCO2 m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** \\ \hline
2013 & 15.35 & 0.029 & 0.656 & 0.553 & 0.92 & 224 & 0.248 & 12.34 & 0.329 & 16.37 \\ \hline
2014 & 19.50 & 0.036 & 0.688 & 0.751 & 1.01 & 365 & 0.242 & 14.31 & 0.321 & 18.96 \\ \hline
2015 & 12.14 & 0.024 & 0.602 & 0.582 & 0.93 & 365 & 0.210 & 10.73 & 0.290 & 14.78 \\ \hline
2016 & 20.34 & 0.078 & 0.677 & 0.814 & 0.81 & 366 & 0.463 & 19.82 & 0.588 & 25.16 \\ \hline
2013–2016 & 16.99 & 0.046 & 0.658 & 0.737 & 0.91 & 1320 & 0.296 & 14.79 & 0.407 & 20.36 \\ \hline \end{tabular}
\end{table}
Table 6: Same as Table 5, but for daily sums of Re at nighttime during 2013–2016.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Time** & & & & & & & & & **MAD** & & **RMSE** \\ \hline
**Period** & **savg** & **NMSE** & **\(\sigma_{\text{cal}}\)** & **\(\sigma_{\text{obs}}\)** & **cal/obs** & **\(n\)** & \multicolumn{2}{c}{**(mgCO2 m\({}^{-2}\) s\({}^{-1}\))**} & **(\%)** & **(mgCO2 m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** \\ \hline
2013 & 11.69 & 0.013 & 45.22 & 41.61 & 0.92 & 7 & 5.517 & 9.02 & 7.041 & 11.51 \\ \hline
2014 & 11.23 & 0.010 & 30.31 & 47.42 & 1.03 & 12 & 4.506 & 8.75 & 5.433 & 10.55 \\ \hline
2015 & 7.75 & 0.008 & 41.05 & 41.06 & 0.93 & 12 & 4.244 & 7.12 & 5.221 & 8.76 \\ \hline
2016 & 18.99 & 0.056 & 40.83 & 51.73 & 0.79 & 12 & 13.626 & 19.11 & 15.780 & 22.13 \\ \hline
2013–2016 & 12.50 & 0.025 & 18.28 & 21.07 & 0.91 & 53 & 7.143 & 11.74 & 9.337 & 15.34 \\ \hline \end{tabular}
\end{table}
Table 7: Same as Table 6, but for mean monthly sums of Re at nighttime during 2013–2016.  
Figure 6: Calculated and observed monthly sums of nighttime Re (Re\({}_{\text{cal}}\), Re\({}_{\text{obs}}\)) with error bars showing one time standard deviation of the observed Re during 2013–2016.  
In a brief summary for the estimates of the nighttime Re from the hourly to annual time scales, the EMRe model exhibited a reasonable performance and most of the simulations were within a one time standard deviation of the observed Re.