## 2 Materials and Methods  
### Site Description and Data Used  
Measurements of carbon fluxes were conducted at three sites in Canada. The three sites were chosen for this study because they represent different types of forests and have obvious differences in stand age and biological structure. In addition, continuous multi-year half-hourly measurements of CO\({}_{2}\) flux with EC technique were collected from these sites. The two forest sites, CA-Oas and CA-Obs, are situated near the southern boundary of the boreal plain ecological region in north-central Saskatchewan, Canada. The two sites were established based on the dominant boreal tree species. The two forest sites have the similar characteristics of synoptic meteorological forcing, while present the remarkable differences in their soil texture, topography and tree stem density. CA-Oas site is located in Prince Albert National Park, Saskatchewan, Canada. This mature trembling aspen site is s a boreal deciduous broadleaf forest generated from a fire in 1919, and had a mean canopy height of 22 m and an average stand age of 75 years in 2004 [34]. CA-Obs site is located about 80 km east-northeast of CA-Oas, and is predominately covered by black spruce with an average canopy height of 7.2 m. According to the statistics from the nearest long-term weather station during 1971 to 2000, the mean annual air temperature and cumulative annual precipitation are 0.4 \({}^{\circ}\)C and 467 mm, respectively, for both CA-Oas and CA-Obs sites [34]. CA-Gro site is situated about 80 km southwest of Timmins in northeastern Ontario, Canada. The site is a representative of the boreal mixed wood forest and was regenerated after the high level logging which primarily occurred in the 1930s. This site is primarily covered by five different types of species, including black spruce, balsam fir, trembling aspen, white spruce and white birch. At the CA-Gro site, the mean annual air temperature and cumulative annual precipitation during the study period (2004-2006, 2008-2010) are 3.29 \({}^{\circ}\)C and 784 mm, respectively. More details on the sites are presented in Table 1.  
Based on the EC technique, continuous half-hourly carbon fluxes for six or more years were measured at each site. Positive NEE stands for a loss of CO\({}_{2}\) to the atmosphere, while negative NEE implies an uptake of CO\({}_{2}\) by the ecosystem. The method of gap-filling for eddy covariance-measured \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Site** & **Latitude** & **Longitude** & **Elevation** & **MAT** & **TAP** & **Vegetation** & **Period** & **Reference** \\ \hline CA-Obs & 53.63 & \(-\)106.20 & 601 & 1.82 & 343 & DBF & 2003–2008 & [PERSON], et al. [35] \\ CA-Obs & 53.99 & \(-\)105.12 & 629 & 1.00 & 373 & ENF & 2004–2009 & [PERSON], et al. [36] \\ CA-Gro & 48.22 & \(-\)82.16 & 341 & 3.29 & 784 & MF & 2004–2006, 2008–2010 & [PERSON], et al. [37] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Site characteristics used in this study. The mean annual temperature (MAT, \({}^{\circ}\)C) and total annual precipitation (TAP, mm year\({}^{-1}\)) are for the time period (Period). Vegetation types are deciduous broadleaf forest (DBF), evergreen needle-leaf forest (ENF) and mixed forest (MF). NEE and its partitioning into GPP and \(R\) was according to the Fluxnet-Canada Research Network protocol [38]. Briefly, \(R\) was obtained from both nighttime and cold-season NEE. The gap-filling of missing \(R\) during nighttime and calculation of \(R\) during daytime were on the basis of an empirical relationship between \(R\) and soil temperature. Finally, GPP was estimated based on the daytime-observed NEE and calculated daytime \(R\). During the cold season, GPP was set to zero. More details regarding the EC instrument characteristics, NEE gap-filling and its separation scheme as well as the random errors in NEE, \(R\) and GPP have been provided for CA-Oas and CA-Obs in [PERSON] et al. [35] and [PERSON] et al. [34], and CA-Gro in [PERSON] et al. [37].