## 3 Results
### Evaluation and Application of the EMRe Models under all sky Conditions during 2013-2016
#### 3.2.2 Daytime and Nighttime Re Simulations Using Re (DDR) Method  
Based on some studies where the daytime Re was extrapolated from the nighttime Re [37], the EMRe model at nighttime was further applied to calculate the Re at daytime during 22 May 2013-31 December 2016 using Equation (3) and observation data at daytime (water vapor). This Re (DDR) method was used for the Re simulation in the daytime and nighttime. The detailed results for the averages of the hourly, daily, monthly, and annual sums of Re are given in Tables 8-10 and Figures 8 and 9.  
For daytime + nighttime Re, (1) the EMRe also exhibited acceptable performances, and most of the estimations were within a one time standard deviation of the observed Re; (2) the estimation errors of Re were smaller than that at nighttime (e.g., MAD, RMSE); thus, it may be caused by that \(\sigma_{\rm obs}\) (observed Re) decreased with the increase in sampling number (i.e., from 16,836 to 31,606 for 2013-2016). Data quality of observed Re at daytime and nighttime, as well as only at nighttime in 2016, were the worst with the largest standard deviations (\(\sigma_{\rm obs}\), Tables 5-10), which caused larger simulation errors in 2016 than in other years. The best Re estimates were performed for nighttime and daytime + nighttime Re in 2014 than in other years. It reveals that better observational data are very necessary for accurate Re evaluations.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Time** & \multirow{2}{*}{**\(\delta\)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{1-1} \cline{5-10} \cline{7-10} \multicolumn{1}{c}{**Period**} & & & & & & & **(mgCO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** & **(mgCO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\))** & **(\%)** \\ \hline
2013 & 10.64 & 0.009 & 45.22 & 41.61 & 0.92 & 7 & 9.952 & 7.95 & 7.041 & 11.51 \\ \hline
2014 & 10.44 & 0.009 & 30.31 & 47.42 & 1.03 & 12 & 8.096 & 7.76 & 5.433 & 10.55 \\ \hline
2015 & 8.06 & 0.007 & 41.05 & 41.06 & 0.93 & 12 & 8.419 & 7.06 & 5.221 & 8.76 \\ \hline
2016 & 20.68 & 0.066 & 40.83 & 51.73 & 0.79 & 12 & 28.303 & 20.64 & 32.733 & 23.88 \\ \hline
2013–2016 & 12.67 & 0.026 & 42.02 & 47.09 & 0.91 & 53 & 14.13 & 11.67 & 17.156 & 14.17 \\ \hline \end{tabular}
\end{table}
Table 10: Same as Table 7, but for mean monthly sums of Re at daytime and nighttime during 2013–2016.  
Figure 8: Observed and calculated monthly sums of daytime and nighttime Re (Reobs, Recal) with error bars showing one time standard deviation of the observed Re during 2013–2016.  
Figure 9: Observed and calculated annual sums of daytime and nighttime Re (Reobs, Recal) with error bars showing one time standard deviation of the observed Re during 2013–2016.  
For the consistency, the units used for the hourly, daily, monthly, and annual sums of Re were the same as mgCO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\). A coefficient can be multiplied by (3600 \(\times\) 12/44)/1000 \(\approx\) 0.982 to convert the hourly sums of Re to the widely used unit (gC m\({}^{-2}\)) for monthly and annual sums of Re.  
Based on the above results, the Re values calculated by the EMRe model (Re (DDR) method) were multiplied by a factor 1.1 to best fit the hourly, daily, monthly, and annual Re values in averages and sums for each year and four years 2013-2016, so as to reduce the estimation error in the extrapolation of the respiration from nighttime to daytime; therefore, the updated Re estimates were improved at different time scales to some extent. As a brief summary, the ratios of the mean calculated to the observed Re were 1.000, 1.003, 1.001, and 1.001 for hourly, daily, monthly, and annual sums, respectively, from 2013 to2016. Then, the updated EMRe (i.e., using a modified coefficient 1.1) was applied in the later Re calculations.