# Modeling and Predicting Carbon and Water Fluxes Using Data-Driven Techniques in a Forest Ecosystem
## 2 Materials and Methods  
### Site Description and Data Presentation  
As part of our on-going research, carbon and water flux measurements for a forest ecosystem are being carried out at a flux tower site in Canada. This study site (53.99\({}^{\circ}\) N, 105.12\({}^{\circ}\) W) is situated approximately 80 km east-northeast of Prince Albert National Park, Saskatchewan, Canada. This site belongs to the representative boreal evergreen needle-leaf forest and it is predominantly covered by black spruce regenerated after a fire in 1879. Its average canopy height was 7.2 m. It had an average stand age of 110 years in 2004, ranging from 91 to 130 years. Based on the statistics from the nearest long-term weather station during 1971 to 2000 [41], mean annual air temperature (\(T_{a}\)) and cumulative annual precipitation were 0.4 \({}^{\circ}\)C and 467 mm, respectively. More descriptions regarding the site history, topography, soil, and vegetation can be found in Swanson and Flanagan [42]. At this site, continuous half-hourly carbon and water vapor fluxes have been measured by using the eddy covariance technique. Half-hourly climate variables were also observed, mainly including \(T_{a}\), soil temperature (\(T_{s}\)), net radiation (\(R_{n}\)), relative humidity (\(R_{h}\)), wind speed and volumetric soil moisture content. Further details on the characteristics of the used instruments and measurement procedure of CO\({}_{2}\) flux can be found in [PERSON] et al. [43].  
The method of gap-filling for eddy covariance-measured NEE and its partitioning into gross primary productivity (GPP) and \(R\) was in accordance with the Fluxnet-Canada Research Network protocol [44]. In brief, \(R\) was calculated from nighttime and cold-season NEE. The gap-filling of night \(R\) and estimation of daytime \(R\) was based on an empirical relationship between \(R\) and \(T_{s}\) at a shallow depth (2 cm). GPP was derived according to the daytime \(R\) and daytime-measured NEE. During the cold season, GPP was set to zero. More details regarding NEE gap-filling and its separation scheme as well as the random errors in NEE, \(R\) and GPP are given in [PERSON] et al. [43]. In addition, as stated above, both GPP and \(R\) were not measured directly by the eddy covariance technique but were calculated from the eddy covariance-measured NEE. In the following sections, for the sake of distinguishing these calculated GPP and \(R\) from modeled or predicted GPP and \(R\) by our proposed models, the estimated GPP and \(R\) based on NEE are hereinafter referred to as measured or observed GPP and \(R\).  
Daily values of environmental variables during the study period are shown in Figure 1. The available data during the period of six years (2004-2009) were divided into three parts, respectively for training (2004-2007), validation (2008) and testing (2009). Table 1 shows the statistical parameters of daily data in the three datasets. Based on the table, it can be seen that each segment has similar statistical features. The climate variables correlate strongly with each flux. However, the correlation values for GPP, \(R\) and ET are generally greater than those of values for NEE, which may lead to