1. Thermal stratification, organized motion, and the onset of counter-gradient flows within canopies Daniela Cava 1, Gabriel Katul 2, Antonio Scrimieri 1,3, Davide Poggi 2,4, Alessandro Cescatti 5, and Umberto Giostra 6 1 CNR - Institute of Atmosphere Sciences and Climate section of Lecce, Lecce, Italy. 2 Nicholas School of the Environment and Earth Sciences, Duke University, Durham, N.C., U.S.A. 3 Material Science Department, University of Lecce, Lecce, Italy. 4 Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili, Politecnico di Torino, Torino, Italy. 5 Centro di Ecologia Alpina, 38040 Viote del Monte Bondone (Trento), Italy 6 Environmental Science Department, University of Urbino, Urbino, Italy

2. Update on Daniela Out of the hospitalAnd back to Lecce

3. Historical Perspective In 1988, Raupach 1 concluded his review by noting that the reasons for the failure of gradient-diffusion theory inside uniform canopy on flat terrain are now understood…. “looking further ahead, several thorny problems await systematic investigation…., the problem of buoyancy effects …..” 1 Raupach, M., 1988, Canopy Transport Processes, in Flow and Transport in the Natural Environment: Advances and Applications Ed. W.L. Steffen and O.T. Denmead, Springer Verlag, pp.95-127.

4. A decade later In 1998, Mahrt 2 ended his review on the Stable Boundary Layer by noting that: “formulation of turbulence in the very stable boundary layer is uncertain and the stable boundary layer contains a number of physical influences not present in any of the existing models….” “…even small future advances justify more work”. 2 Mahrt, L., 1998, Stratified Atmospheric Boundary Layers and Breakdown of Models, Theoret. Comput. Fluid Dynamics, 11: 263–279.

5. Introduction Failure of gradient-diffusion theory inside canopies is often linked to three inter-related factors: Variable scalar source distribution within the canopy strongly impacts the apparent diffusivity (near-field effects). Lack of local balance between turbulent production and dissipation. Vertical transport occurs by organized eddy motion whose size is comparable to the canopy height.

6. Objective Investigate the interplay between ejections and sweeps (often used as signatures of large-scale organized motion) and local thermal stability in the onset of zero- or counter-gradient flows inside canopies. A necessary first step towards a ‘small advance’.

7. 25 m 33 m 17.5 m 11 m 4 m Mixed hardwood forest Lavarone, Italy Aerial View of the Site Tower

8. Lavarone Experiments Unstable Near-neutral Stable

9. Theory – 1:Budget Equations Mean Continuity Equation: Heat Flux – Budget Equation:

10. Theory – 2:Closure Models Flux-Gradient Closure for Triple Moment: (e.g. Donaldson, 1973 1 ) Scalar-Pressure Interaction (Andre et al., 1979 2 ) STST 1 Donaldson, C., 1973, Construction of a dynamic model for the production of atmospheric turbulence and the dispersal of atmospheric pollutants, in Workshop on Micrometeorology, American Meteorological Society, 313-392. 2 Andre, J.C., G. De Moor, P. Lacarrere, G. Therry, and R. du Vachat, 1979, The clipping approximation and inhomogeneous turbulence simulations, Turbulent Shear Flows – I, Springer Verlag, 307-318.

11. Result:Second-Order Closure Model Result ‘Near field’ Effects from canopy heat source vertical variations Buoyancy effects (+ve) Production Term Model is not explicit in terms of ejection-sweep cycle

12. Organized Motion The interest in ejections and sweeps dates back to early experiments by Kline et al. (1967) who demonstrated via flow visualization that fluid motion near a wall is “far from being completely chaotic in nature” revealing a definite “sequence of ordered motion”.

13. Conditional Sampling, Ejections- Sweeps & Quadrant Analysis W’ U’ Ejections Sweeps Quadrant 2 Quadrant 4 Frenkiel and Klebanoff (1967), Lu and Willmarth (1973), Antonia (1981) – Conditional sampling and quadrant analysis Relative contribution of ejections and sweeps to Momentum flux: Nakagawa and Nezu (1977) & Raupach (1981):

14. Connecting the Ejection-Sweep Cycle with the Flux-Transport Using 3 rd order cumulant expansion methods (CEM) in Nakagawa and Nezu (1977) and Raupach (1981), and a sensitivity analysis in Katul et al. (1997), an ‘Incomplete CEM’ (or ICEM) was proposed by Poggi et al. (2004).

15. Validation of ICEM From Katul, G.G., D. Poggi, D. Cava, and and J.J. Finnigan, 2005, BLM, in Press

16. Further Simplification * Value from a Pine Forest experiment

17. From Cava et al. (2006) Sweeps dominate heat flux Ejections dominate heat flux Equate Gradient-Diffusion Model and ICEM representation of

18. z/h c 2 1 0 0 Daytime Nightime Ejections Sweeps All Sweeps Canonical Profiles From Kaimal and Finnigan (1994)

19. Prognostic Equations From Poggi et al. (2006) – Flume experiments From Katul et al. (2001) – IREX [rice] and Siqueria and Katul (2002) - pine From triple moments

20. Three Variants on the Model K-theory [Dummy model] No buoyancy Full Model

21. Lavarone Experiments Unstable Neutral Stable Data K-theory g=0 Full model

22. Thorny issue 1 : Very Stable Conditions 1) Flow is not high Reynolds # (and Peclet #..) 2) Flow is not stationary 3) Standard turbulence closure scheme that assume independence of Reynolds number need not apply. 4) Flow may not be independent of transients in the upper boundary conditions 1 From Cava et al. (2004) DUKE FOREST

23. Conclusions Two analytical expressions relating For neutral to slightly stable flows, neglecting the buoyancy contribution is preferred given that the temperature variance is always finite. Prognostic Diagnostic

24. Publications Cava et al., 2006, Buoyancy and the sensible heat flux budget within dense canopies, Boundary Layer Meteorology, to appear. Poggi, et al. 2006, Scalar Dispersion within a Model Canopy: Measurements and Three-Dimensional Lagrangian Models, Advances in Water Resources, to appear Katul, G.G., D. Poggi, D. Cava, and J.J. Finnigan, 2006, The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer. Boundary Layer Meteorology, to appear. Cava et al., 2004, Organized motion and radiative perturbations in the nocturnal canopy sublayer above an even-aged pine forest, Boundary-Layer Meteorology, 112, 129-15