## 3 Results  
### Energy Balance Analysis and Daily Cumulative Carbon Fluxes  
The simple linear regression models used in the energy balance/closure analysis indicated great correlation between the available energy (Rn-G) and the sum of the turbulent fluxes (H + LE; Figure 3).  
In particular, the first growing season data yielded an R\({}^{2}\) value of 0.91 and an RMSE value of 57 W m\({}^{-2}\), and the second growing season yielded an R\({}^{2}\) value of 0.83 with an RMSE value of 79 W m\({}^{-2}\). The slope results from both seasons indicated partial energy balance closure (<1), indicating that measured turbulence fluxes accounted for 74% and 62% of available energy loss during each growing season, respectively. The rest of the available energy was primarily transferred to the above-heat-flux-sensor soil layer, vegetation canopy (mainly used for photosynthesis), and the atmospheric air layer between the soil horizon and the IRGA.  
Figure 2: The overall data analysis scheme and logic flow of the net ecosystem exchange (NEE) and latent heat flux (LE) gap-filling and uncertainty analysis.  
Foot-print analysis [23] indicated that at least 70-80% of flux data was from within the research field throughout the entire growing season. The overall patterns of daily cumulative NEE, GPP, and ER for the entire pasture ecosystem are depicted in Figure 4.  
Figure 4: Thirty-minute average net ecosystem exchange (NEE) and the partitioned gross primary production (GPP) and ecosystem respiration (ER) of a cool-season grass-dominated grassland ecosystem from the 2016–2017 and 2017–2018 growing seasons located in Middle Tennessee. Dashed lines separate calendar years from each other.  
Figure 3: Energy balance closure for the 2016–2017 and 2017–2018 growing seasons of a cool-season grass dominated grassland ecosystem located in Middle Tennessee. Rn, G, H and LE represent net radiation, soil heat flux, sensible heat flux, and latent heat flux; respectively. Data points used were based on 30 min average values.  
The daily maximum NEE reached up to 21.1 and 20.7 g C m\({}^{-2}\) for the first (early fall 2016 to late summer 2017) and second growing seasons (early fall 2017 to late summer 2018), respectively; and the minimum NEE reached up to \(-\)33.5 and \(-\)43.6, g C m\({}^{-2}\), respectively. The seasonal average daily NEE was \(-\)5.2 and \(-\)7.8 g C m\({}^{-2}\). Large fluctuation was observed in daily cumulative GPP, with the average values of \(-\)21.7 and \(-\)23.9, maximum values of \(-\)0.02 and \(-\)0.37, and minimum values of \(-\)49.3 and \(-\)49.8 g C m\({}^{-2}\), for the first and the second growing seasons, respectively. Following similar trends, the average, maximum, and minimum ER values were 16.5, 41.3, and 0.07 g C m\({}^{-2}\), respectively, for the first growing season; and 11.8, 36.9, and 0.61 g C m\({}^{-2}\), respectively, for the second growing season. The seasonal cumulative NEE, GPP, and ER were \(-\)1.23, \(-\)3.46, and 2.23 kg C m\({}^{-2}\), respectively, for the first growing season; and \(-\)1.95, \(-\)2.98, and 1.03 kg C m\({}^{-2}\), respectively, for the second growing season. Again, the negative signs indicate carbon fluxes from the atmosphere into the ecosystem and vice versa.