1. Reducing uncertainty in NEE estimates from flux measurements D. Hollinger, L. Mahrt, J. Sun, and G.G. Katul Ameriflux Meeting, Boulder CO., October 20, 2005

2. Organizing Framework  Uncertainty in flux measurements (random and systematic errors) over sampling intervals needed to average out turbulence.  Gap-filling missing data when averaging over extended time scales (relevant to impact of carbon allocation on ecosystem properties).  Linking measured fluxes to biological sources and sinks (main issues – stable flows; topography).

3. All recent reviews concerning measurements and modeling of surface-atmosphere mass, energy, and momentum exchange expressed the need to confront the problem of turbulent flows within plant canopies on non-flat terrain. Background

4. Field Studies [Mainly forests, stable flows, mild topography] Aubinet et al. (2003; 2005); Yi et al. (2004); Staebler and Fitzjarrald, (2004); Feigenwinter et al., (2004); Fokken et al., (2005); Laboratory Studies: [steep topography] Finnigan and Brunet (1995) Previous Studies

5. Results from Recent Field Experiments  CO 2 advection study at the Niwot Ridge AmeriFlux site by Yi et al. (2004) suggested that: 1)Both longitudinal and vertical advective fluxes are important and often larger than the turbulent flux. 2)They often act in opposite direction

6. Feigenwinter et al 1. (2004)  “ The opposite sign of horizontal and vertical advection supports the idea that the two fluxes will cancel out each other in the long-term carbon balance”.  “The mean advective fluxes at night have magnitudes comparable to the daily NEE ”. 1 Feigenwinter et al., 2004, Boundary-Layer Meteorology.

7. Aubinet et al 1. (2005)  “The advective fluxes strongly influence the nocturnal CO2 balance, with the exception of almost flat and highly homogeneous sites”.  Storage - significant “only during periods of both low turbulence and low advection”.  “All sites where advection occurs show the onset of a boundary layer characterized by a downslope flow, negative vertical velocities and negative vertical CO2 concentration gradients during nighttime”. 1 Aubinet et al., 2004, Boundary-Layer Meteorology.

8. Hill Properties: Four hill modules Hill Height (H) = 0.08 m Hill Half Length (L) = 0.8 m Canopy Properties Canopy Height = 0.1 m Rod diameter = 0.004 m Rod density = 1000 rods/m 2 Flow Properties: Water Depth = 0.6 m Bulk Re > 1.5 x 10 5 Polytechnic of Turin (IT) Flume Experiments

9. Velocity Measurements Sampling Frequency = 300 Hz Sampling Period = 300 s Laser Doppler Anemometer

10. Displaced Coordinates Coordinate Systems

11. Mean Velocity (m/s) Turbulent Stress (m 2 /s 2 )

12. Model Formulation: 2-D Mean Flow Fluid Continuity: Mean Momentum Equation: Two equations with two unknowns – after appropriate parameterization Produced by the Hill Canopy Drag

13. Finnigan and Belcher (2004) Analytical Model Closure for Reynolds Stress Constant mixing length inside canopy: Linearized Adv.: Closure for Linearized Drag:

14. Mixing Length Model

15. Linearized Advective Term Linearized Drag Force Deep Inside the Canopy

17. Advection Drag Turbulent Stress Pressure Gradient Mean Momentum Balance

18. w u EJECTIONS SWEEPS Ejection-Sweep Cycle

19. Canopy Surface

20. Smooth Surface (no canopy)

22.  Advective fluxes are opposite in sign  They are often larger than Photosynthesis (Sc)

23. Advective terms are (individually) of the same order of magnitude as photosynthesis, consistent with field experiments to date. Note that the model does not consider atmospheric stability. The effects of advective terms on CO 2 fluxes at a particular point can be as large as 100%. Both advective terms must be considered in any flux-correction treatment due to topography. Conclusions

24. ~1 km (b): Tower relief map Tumbarumba, AU (a): SLICER Data from Duke Forest (c): Eucalyptus vegetation Tumbarumba, AU

25. Gap-Filling What new information is being added in the Gap-filling? How much are the distributional and spectral properties altered by gap-filling?

26. Distributional and Autocorrelation Properties fBm process with Hurst exponent =1/3

27. Shannon-Entropy p=Empirical probability density function OR Energy distribution (e.g. from spectral analysis) Maximum Entropy: Entropy = Information Content (Shannon, 1948)

28. Wavelet-Based Spectra Haar wavelet, localized in time domain – can remove gaps from spectral calculations. Schimel & others – use Entropy measures for assessing New information injected by gap-filling.

29. PP = Pine Plantation OF = Old Field HW = Hardwood Forest Duke Forest Ameriflux Sites

30. SpectraProbability Entropy, Gap filling, ET

31. Entropy, Gap filling, Daytime NEE SpectraProbability

32. Night-time NEE SpectraProbability

33. Remarks  If after gap-filling, the is large (>20%), the ‘long-term’ estimates of NEE are going to be sensitive to gap-filling and are likely to have significant artificial correlation with the gap-filling drivers.

34. Extra References Katul et al., 2001, Advances in Water Resources, 24, 1119. Katul et al., 2001, Geophysical Research Letters, 28, 3305. Katul et al., 2001, Physics of Fluids, 13, 241. Wesson et al., 2003, Boundary-Layer Meteorology, 106, 507. Mahrt et al., 1999, Journal of the Atmospheric Sciences, 48, 472.