1. Eddy covariance (EC) is the most direct method for estimating fluxes of energy, heat, and mass. The fundamental theory of EC relies on the conservation of energy (the balance of incoming and outgoing energy). This states that the sum of sensible (H) and latent heat fluxes (lE) measured by EC should equal net radiation (Rn) less energy stored in the soil (G, soil heat flux):
Rn – G = H + lE
Unfortunately, many researchers have found that (Rn - G) is usually greater than (H + lE), often referred to as the “energy balance closure problem”. Foken et al. (2006) outlined three factors that may contribute to the closure problem: 1) measurement and post-processing errors, 2), errors resulting from the turbulent fluxes (H and lE) being measured at different scales than Rn and G, and 3) errors resulting from advection and low frequency fluxes caused by heterogeneity of the land surface.
Objective
Measure energy balance closure for tallgrass prairie at two landscape positions using EC, taking extra precautions to minimize measurement error and to reduce the effect of sampling scale (to maximize closure).
Parameter Location Instrument
H Main tower CSAT3 (Campbell Scientific, Inc., Logan, UT)
lE Main tower CSAT3 and LI-7500 Open-Path Infrared Gas Analyzer (Licor, Inc., Lincoln, NE)
Rn 1 Near tower Q*7.1 Net radiometer (Radiation & Energy Balance Systems, Pullman, WA)
Rn 2 In footprint CNR2 Net radiometer (Kipp & Zonen, Delft, The Netherlands)
G Tower, footprint HFT3 Soil heat flux plates at 7.5cm (Radiation & Energy Balance Systems)
Tsoil Tower, footprint TCAV Type E Thermocouple (Campbell Scientific)
Soil Moisture Tower, footprint Theta Probe (Delta-T Devices, Inc., Cambridge, UK)
HLAS Transect (Fig. 1) Large Aperture Scintillometer (Fig. 2) (Kipp & Zonen)
Fluxes of H and lE were calculated from the 20-Hz time series data
using Matlab (The Mathworks Inc.) and EdiRe (Rob Clement,
University of Edinburgh). Post processing included:
• Despiking
• Planer fit coordinate rotation
• Sonic temperature correction
• Density corrections (i.e., Webb‑Pearman‑Leuning corrections)
• Lag removal
• Frequency response corrections
• Filtering for wind direction, friction velocity, and Rn (Rn > 125 W m-2)
Data Processing
Energy Balance Closure When Using Eddy Covariance: How Good is Good Enough?
Kira B. Arnold1,*, Jay M. Ham1, Nathaniel A. Brunsell2
1Dept. of Agronomy, Kansas State University; 2Dept. of Geography, University of Kansas
Results and Discussion
The lowland site had slightly greater lE and smaller H compared to the upland, but overall landscape position had a very small effect on the energy balance (Fig. 3).
Latent heat flux was the dominant form of energy loss early in the 2007 growing season as precipitation was above normal in June and July (H / lE << 1).  Sensible and latent heat fluxes were nearly equal in August and September as soils dried (Fig. 3).
The energy balance regression coefficient, a, (Rn - G) = a (H + lE), showed that turbulent heat fluxes measured by the EC instrumentation accounted for 83 to 89 % of the available energy (Fig. 4). Landscape position had little impact on the degree of closure.  
Conclusions
Site Description and Materials
Research was conducted at the Konza Prairie Biological Station south of Manhattan, Kansas in the summer of 2007.  Data were collected simultaneously at upland and lowland landscape positions on an annually burned watershed (Fig. 1). Vegetation at the site was dominated by native C4 grasses big bluestem (Andopogon gerarardii Vitman) and indian grass (Sorgastrum nutans L.). Soils were silty clay loams. Peak leaf area index in 2007 was 3.59 and 2.96 m2 m-2 at the lowland and upland, respectively.
Instrumentation
Fluxes of H and lE were measured using open-path EC. Net radiation and G were measured at two locations, near the tower and in the source area footprint to reduce uncertainty in (Rn – G). A large aperture scintillometer (LAS, Fig. 2) was positioned upwind of the EC towers to provide a spatially integrated measure of H.
The tallgrass prairie is an ideal ecosystem to perform EC measurements.  The vegetation is uniform in annually burned watersheds, and the upland and lowland terrains are often flat enough to provide adequate sampling range.  Kansas is windy in the summer, which provides reliable turbulent transport of energy, heat, and mass for EC measurement. In this study, every effort was made to minimize any effect of measurement and processing errors. Nevertheless, energy balance closure was between 0.84 and 0.90, a range consistent with that reported in other studies (Wilson et al., 2002; Oncley et al., 2007). Some conclusions from the study were:
The surface energy balance and the degree of closure were not strongly affected by landscape position within the watershed.  
Energy balance closure improved as lE decreased and the Bowen ratio increased.
Sensible heat flux measured by the LAS was in relatively good agreement with the EC measurements.
Latent heat fluxes computed by the residual of the energy balance were 15 to 18 % greater than those measured directly with the EC instruments (Fig. 8).
Integrating the time series data over periods longer than 30 min to account for low frequency transport (ogive analysis) did not improve daytime closure (see Ham et al., poster ).
Until the energy balance closure problem is fully resolved, researchers are likely to underestimate field‑scale evapotranspiration using the EC technique.
Fig. 2. Photo of the LAS transmitter.
The energy balance residual flux, Residual = Rn – G – H - lE, showed a distinct diurnal pattern with a maximum value around 80 W m-2 near midday (Fig. 5).
Energy balance closure, expressed as (H+ lE +G)/Rn, was 87% on average.  Closure tended to improve later in the growing season as soil moisture became more limiting and the Bowen ratio (H / lE) increased (Fig. 6).
Sensible heat flux measured by the LAS was slightly greater than H measured at the lowland and smaller than H measured at the upland (Fig.7).  The agreement is good considering the differences in scales and techniques.
There is no clear evidence that H is being underestimated by the EC instruments. The LAS estimates of lE, which are a residual calculation, lELAS= (Rn – H – G), were always larger than those from the EC systems.
Fig. 5. Composite of the average residual energy by time of day.
References
Foken, T.; Wimmer, F.; Mauder, M.; Thomas, C. and Liebethal, C Some aspects of the energy balance closure problem. Atmos. Chem. Phys : 4395 – 4402.
Oncley, S.P.; Foken, T.; Vogt, R.; Kohsiek, W.; DeBruin, H.A.R.; Bernhofer, C.; Christen, A.; van Gorsel, E.; Grantz, D.; Feigenwinter, C.; Lehner, I.; Liebethal, C.; Liu, H.; Mauder, M.; Pitacco, A.; Ribeiro, L. and Weidinger, T The energy balance experiment EBEX2000. Part I: overview and energy balance. Boundary-Layer Meteorol. 123: 1-28.
Wilson, K.; Goldstein A.; Falge, E.; Aubinet, M.; Baldocchi, D.; Berbigier, P.; Bernhofer, C.; Ceulemanst, R.; Dolman, H.; Field, C.; Grelle, A.; Ibrom, A.; Law, B.E.; Kowalski, A.; Meyers, T.; Moncrieff, J.; Monson, R.; Oechel, W.; Tenhunen, J.; Valentini, R. and Verma, S Energy balance closure at FLUXNET sites. Ag. For. Meteorol. 113:
Acknowledgements
Technical support was provided by Kristen Baum, Fred Caldwell, and Jamey Duesterhaus.
Funding provided by National Science Foundation (EPSCoR).
*Kira Arnold:
Contact Information
Fig. 1. (a) Relief map of the Konza prairie watershed showing the locations of the upland and lowland EC towers and the LAS beam,
(b) A photo of the vegetation in the lowland footprint. Up
Low
LAS transect
(a)
(b)
Background
Fig. 6. Closure as a function of the Bowen ratio and day of year.
Fig. 7. Comparison of turbulent fluxes measured by the LAS to those measured at the EC towers.
Fig. 8. EC-derived evapotranspiration (ET) compared with residual-derived ET. ET_Residual: (lE_Residual = Rn – H – G).
Fig. 4. Analysis of energy balance closure at the upland and lowland towers during early, mid, and late summer.
Fig. 3. Comparison of the average diurnal energy balance at the upland and lowland sites in early and later summer.