Land/Atmosphere Interface: Importance to Global Change

Size: px

Start display at page:

Download "Land/Atmosphere Interface: Importance to Global Change"

Justin Baker
5 years ago
Views:

1 Land/Atmosphere Interface: Importance to Global Change Chuixiang Yi School of Earth and Environmental Sciences Queens College, City University of New York

2 Outline Land/atmosphere interface Fundamental problems Progresses

3 Why land-atmosphere interactions are important to global change?

4 An example Boundary layer dynamics - and terrestrial CO2 fluxes Atmospheric CO 2 rectifier effect CO 2 SBL CO 2 Mixed Layer Sunset Shallow layer High CO 2 Respiration Sunrise Deep mixing Low CO 2 Photosynthesis

5 Why land-atmosphere interactions are important? Dynamic ABL Missing sinks Constant ABL ABL= Atmospheric boundary layer (Denning et al., 1995)

6 WLEF tall tower (447m) (Yi et al., JGR 2000 ) Measuring CO 2 by eddy flux tower Complex at night Simple in day CO2 (ppm) CO CO 2 at at m CO CO 2 at at m UTC 11m 30m 76m 122m 244m 396m

7 Measuring boundary layer evolution by 915-MHz ABL profiling radar Zi = a+ b* Γ Mixed layer depth Γ = t ( θ w ) s d t (Yi et al., JGR 2004 ) 0 (Yi et al., JAS 2001 )

Aerodynamics Classic theories do not work No transport

8 Photosynthesis, respiration CO 2 H 2 O VOC CH 4 Absorber and producer Turbulence nature affects reaction rate Aerodynamics Classic theories do not work No transport theory within canopy Canopy layer is more complex and important!

9 Why classic turbulent theories do not work within canopies?

= uw = u* = l, mixing length theory, developed by Prandtl in 1925, ρ z z 2

10 u( z) uw ( z) = u 2 * Height z Constant flux layer τ p = z x 0 Fundamental Characteristics u Km, K-theory, proposed by Boussinesq in 1877, z τ 2 2 u u = uw = u* = l, mixing length theory, developed by Prandtl in 1925, ρ z z 2 cu D, proposed by Prandtl in 1932 based on the velocity-squared law. Yi, 2007

11 Von Karman s s similarity hypothesis l = κ du / dz 2 2 du/ dz

12 Von Karman Prandtl l du / dz = κ du/ dz 2 2 l = κ z u z u z = κ z0 * ( ) ln κ 0.4 Z 0 is roughness

13 Edme Mariotte 1673 Christiaan Huygens 1699 Sir Issac Newton 1687 Velocity-Squared Law Drag = C ρsv D 2 Navier in 1822 Stokes in 1845 Prandtl in 1905

14 u( z) uw ( z) = u 2 * Height z u = w = u = u z l * l / = κ z Constant flux layer τ p = z x 0 u c z u z 2 2 * = D ( ) ( ) the friction velocity is the artificial but related velocity for which the square law holds exactly -Sutton (1953, pp.76) Taylor (1916) was first to test the validity of the velocity-squared law on the earth s s surface and estimated its drag coefficient values. The mixing length theory has achieved remarkable success. Thom (1971)( rationalized the physical connection between length scale and velocity scale.

15 u( z ) uw ( z) Height z Constant flux layer K-theory ML-theory τ p = z x 0 h d+z 0 Exponential flux layer τ F, D z F = ρc au D D 2 u( z ) uw ( z) Governing equation Yi, 2007

16 Why classic theories do not work within canopy. l K < = 0 m 0 Negative viscosity X Yi, 2007 u( z) Von Karman similarity rule l du / dz = κ du/ dz uw = 2 2 K m u z

17 New developments in canopy flow theory

18 τ = ρ uw [ τ ] -1 MLT mass velocity momentum 2 L T area time area time Momentum Transfer Rate Yi, 2007

19 τ = ρ uw ρu 2 momentum loss rate average velocity = u /2 momentum = ρu flow deceleration ρu u = u 2 /2 ρ /2 Yi, 2007 τ = cd ρ u 2

20 Local Equilibrium Hypotheses momentum transfer rate = momentum loss rate ρuw ( z) = ρc ( z) u ( z) D 2 uw z= c 2 D ( z ) a ( z ) u ( z ) (Yi, 2007) τ = ρ uw ( z)

21 Momentum Equations are closed uw c ( ) ( ) 2 = ( ) D z a z u z z uw ( z) = c ( z) u ( z) D 2 ( ( ) 2 ( )) D d c z u z dz = azc zu z 2 ( ) D ( ) ( ) du w ( z) + azuw ( ) ( z) = 0 dz (Yi, 2007)

22 Uniform Vegetation c ( z) = c D az ( ) = a D uw = ac 2 D u ( z ) z LAI z 1 τ( z) = τdqe( z) = u 2 e 2 h D h LAI z h 1 ( ) qz u( () z= ) cu( z) = uw( z) = aqz ( ) h dz z ( 1) h u( z) = u e α Inoue's model h (Yi, 2007)

23 % τ = LAI e ( ζ 1) ζ = z/ h, % τ= τ(z)/ τ h ζ (Yi, 2007) τ%

24 (Yi, 2007) h z 2 uw ( h) = u* LAI L( z) z ( ) uw ( z) = uw (0) e L z = u 2 ( ( )) * ( h ) e LAI L z Lz ( ) = azdz ( ) 0 z uw(0) uw ( z) a (z) = leaf area density (m 2 /m 3 ) LAI = leaf area index = entire leaf area per m 2 ground

25 LAI = leaf area index = entire leaf area per m 2 ground z h τ = uw ( h) h (Yi, 2007) / = LAI 0 τ τ h e τ = uw (0) 0

26 (Yi, 2007) A Universal Relationship

27 (Yi, 2007) Dimensional Analysis (Buckingham Pi theorem) τ ρ u μ h a ml t ml lt ml t l l τ = f 1 (Re, LAI) ρu 2

28 Comparison with the High-Order Closure The high-order closure simulations (Yi, 2007) Observations CMT model uw () z u () h ( LAI L( z)) Observed Requirement High-order model leaf area CMT model Computing cost A super-computer density A calculator Adjustable constants Produced from one No constants dataset cannot be universal a (z) = leaf area density (m 2 /m 3 ) z = 0 a (z) = used leaf for area another density (m L( z) a( z ) dz 2 * = e

29 CMT predictions versus observations Shaw 1977 Wilson 1988 Amiro 1990 Baldocchi & Meyers 1988 Amiro 1990 Katul & Amiro 1990 Albertson 1998 (Yi, 2007) Kelliher et al. 1998

30 Conclusions The robust agreements between the theoretical predictions and observations indicate that the nature of momentum transfer within canopies can be well understood by the CMT theory. Questions What are canopy MASS and ENERGY transfer theories?

31 Super-Stable Layer Theory

32 Advection issues on eddy flux measurements Super-stable layer, flow separation (Yi et al., 2005) Courtesy to Jielun Sun

33 A super stable layer (1) Slow mean airflow; (2) Maximum drag elements; (3) Minimum vertical exchange; h Wind Speed Air Temperature Ri g T = T z 2 u z Vertical exchange zone Horizontal exchange zone (4) Maximum horizontal CO2 (or other scalar) gradient; (5) Maximum ratio of wake and shear production rate. (Yi, 2007; Yi et al., 2005)

34 SF 6 experiments Y Distance (m) X D istance (m ) Yi et al. 2005

35 Horizontal CO 2 gradient in summer Super stable layer Yi et al. 2007

36 Keeling Plot

37 Apply the computational fluid dynamics (CFD) approach to simulate canopy flow

38 Renormalization-group k-ε turbulence model Leaf area density and drag coefficient profile derived from the analytical model were used Yi et al. 2005

39 S -shaped wind profile θ < θ r Cold inflow Yi et al. 2005

40 Chimney phenomenon θ θ r Warm inflow Yi et al. 2007b

41 Oscillation θ θ r Yi et al. 2007b

42 Steady States du0 dt dθ dt 0 = = = 0 = f ( u, θ ), u f ( u, θ ). θ 0 0 g r 0 u ± θ θ 0 =±, cdl θr 2 cdll c0 θ0 = θr 1, 2 2 gγ sin α Stable Yi et al. 2007b Unstable

43 Synopsis γ sinα θr θ0 θc = l c D K + ( u0, θ0) ( u0, θ0) stable. unstable. 0 θ θ θ r 0 c Oscillation. Yi et al. 2007b

44 Acknowledgements to Monson lab, University of Colorado Davis lab, Penn State University Dean Anderson, USGS Andrew Turnipseed, NCAR Peter Bakwin, NOAA/CMDL Zhiqiang Zhai, University of Colorado Lamb lab, Washington State University Denning lab, Colorado State University

45 uw ( z) = c ( z) u ( z) D 2 Thank you! ( ( ) 2 ( )) D d c z u z dz = azc zu z 2 ( ) D ( ) ( ) du w ( z) + azuw ( ) ( z) = 0 dz

46 Science Law Hypothesis Deductions Facts Observations

47 Science stops Faith begins Logic Provable You cannot ask why. Law Deductions The holy property of science appears You can ask why.

48 Contact information Chuixiang Yi Assistant Professor School of Earth and Environmental Sciences Queens College, City University of New York Kissena Blvd Flushing, New York Phone: Fax:

J6.9 MODELING CANOPY TURBULENT FLOW OVER COMPLEX TERRAIN

J6.9 MODELING CANOPY TURBULENT FLOW OVER COMPLEX TERRAIN J6.9 MODELING CANOPY TURULENT FLOW OVER COMPLEX TERRAIN Chuixiang Yi 1, Russell K. Monson 1, Zhiqiang Zhai, Dean E. Anderson 3, Andrew A. Turnipseed 1,4, Sean P. urns 1, rian Lamb 5 1 Department of Ecology