Spatial scales resolved. Four hierarchical scales: Leaf. Plant. Canopy. Landscape

Spatial scales resolved Four hierarchical scales: Leaf Plant Canopy Landscape Canopy embedded in a turbulent air stream - extracting momentum and releasing/uptaking scalars at the solid-fluid interface.

Photosynthesis: Biochemical Models CO + H O + light CH O + O 2 2 2 2 A J Light-limited E = min J J c s Rubisco-limited Sucrose-limited

Photosynthesis Model parameters A n = f( C ) Mathematical Form i A n = α 1 ( C Γ * ) i C i + α 2

Photosynthesis - Transpiration

Leaf Equation for CO2/H2O A n α1 = C ( * C ) i Γ i + α ARH n gs = m + b CO2 2 Farquhar model Collatz et al. model Fickian diffusion A = g ( CO2 C ) n s i 3 unknowns: An, gs, Ci

Leaf Transpiration [ ] Transpiration = c g e e e i = f( T) l s i a If leaf stomata are saturated, then Clausius-Clapeyron

Leaf equations: A parsimonious model for well-watered soils *Given atmospheric state outside the leaf: CO2, PAR, e a (or RH) & Tl *Given physiological properties of the leaf: Vcmax, m & b Solve for: Ci, An, gs, and transpiration

Spatial Scales in Water Transport Leaf-Air Exchange Through Stomata Ecosystem scale Biosphere-atmosphere Water Exchange Meso-Scale Landscape- Atmosphere Exchange Xylem Water Transport

Xylem An Engineering Solution

J. Sperry

Data from Hubbard et al. (2001) Relationship between stomatal conductance (g s ) and photosynthesis (A) and plant hydraulic conductivity (K L ). K L = Soil to leaf

Leaf-level Equations - Modified 1.0 A RH g = m n f( ψ ) + b s leaf CO ( ) f ψ leaf 2 Cavitation occurs ψ leaf

A Problem in Biosphere- Atmosphere Exchange Given the state of the atmosphere above the canopy, and given the physiological, radiative, and drag properties of the canopy, Can we predict sources, sinks, Concentrations, and fluxes within and Above the canopy?

INPUT FORCING VARIABLES Atmospheric Forcing a(z) PAR S T a, RH, C a, U dz Gs R E Soil

S c z q t C + = = c o o S t z t z p C ),, ( b s i c r r C C z a S + = ) ( ρ,..., ),, ( w o o U t z t z p σ > Time-averaged Equations Time averaging ~ 30 minutes

Include all three scalars: T, H2O, and CO2 3 scalars 9 unknowns (flux, source, and conc.) 3 conservation equs. for mean conc. 3 equations to link S conc. (fluid mech.) 3 equations for the leaf state 3 internal state variables (Ci, qs, Tl) 1 additional unknown - stomatal resistance (gs)

Farquhar/Collatz model for A-Ci, gs (2 eq.) Assume leaf is saturated (Claussius-Claperon q & Tl, 1 equ.) Leaf energy balance (Tl, 1 equ.) PROBLEM IS Mathematically tractable

Linking concentration to source strength: p( z, t zo, to) > U, σ w,... Lagrangian Fluid Mechanics du a i i, = a ( x, u, t) dt + b ( x, u, t) b ij i ij dω Determined from Thomson s (1987) model - Require first and second moments of the turbulent velocity j

Canonical Form of the CSL THE FLOW FIELD IS A SUPERPOSITION OF THREE CANONICAL STRUCTURES Displaced wall Boundary Layer Mixing Layer REGION III REGION II Real wall d REGION I

Toy Model for Momentum Transport a(z) uwin du w = CazU d ( ) dz 2 F d = C a( z) U d 2 uwout 1 equ. 2 unknowns

Toy Model for Momentum Transport z = du uw Kt dz du K = l l t dz w ' > 0 l u ' < 0 u ' > 0 uw< ' ' 0 w ' < 0 U

Toy Model for Momentum Transport d dz du K = CazU ( ) t d dz 2 2 nd order nonlinear & non-homogeneous ODE

Drag Coefficient From Poggi, Porporato, Ridolfi, et al. (2004, BLM)

Second-order closure models

From Poggi, Katul, and Albertson (2004, BLM)

From Katul and Chang (1999, JAM)

Massimo Cassiani Well, it's not Brunello di Montacino... But ok, it can be drank

Channel Bottom

Scalar Transport Thomson (1987) From Poggi, Katul, & Alberson (2005, AWR; to appear) Model Measured

Field testing using temperature at The FACE-FACTS Duke Forest

From Siqueira & Katul (2002)

Photosynthesis Model parameters Maximum quantum efficiency ~ 0.08 J E = α e PAR C p m i C i ( Γ * ) + 2Γ Leaf absorptivity Compensation for PAR ~ 0.8 point (ppm) *

Random Porous Media Light Representation Crown Clumping

FACE, Duke Forest, NC, USA Leaf Area Density [m 2 m -3 ] B A PAR

Meteorological Forcing (~30 min) a(z) T a, RH, C a PAR S <U> dz Soil

Modeled S c CO 2 H 2 O Fluxes at z/h=1 Model ecophysiological parameters are independently measured using porometry (leaf scale). T

Comparison between measured and modeled mean CO 2 Concentration CO 2 measured by a 10 level profiling system sampled every 30 minutes. Sources and sinks and transport mechanics are solved iteratively to compute mean scalar concentration

Elevated CO2: Duke Forest CO2 increased from 380 to 550 ppm. No significant increase in LAI, Vcmax, or other above-ground ecophysiological variable (as measured by porometry). Sap-flux measurements suggest that elevated CO2 did not impact bulk canopy conductance (Schafer et al., 2002).

CO 2e /CO 2a =1.45 1999 2000 C-Cycle (g C m -2 year -1 ) a CO 2 e CO 2 a CO 2 a CO 2 Photosynthesis (Model) 2405 3378 2435 3508 Ecosystem Respiration (Model) 1711 1750 1832 1850 Net Ecosystem C Exchange (Model) 694 1628 603 1658 Net Ecosystem Productivity (C pools) 576 872 653 1030 Net Ecosystem C Exchange (EC) 661 792 H2O Cycle (mm year -1 ) Precipitation (Measured) 1214 1006 Transpiration (Sapflux Measured) 497 501 478 516 Latent Heat Flux (EC) 575 615 Transpiration (Model) 530 530 510 510

Summary: Elevated CO2 It is clear that elevated CO2 has not altered the water cycle - but drastically altered the C cycle and its relationship with the water cycle. Ecosystem Water Use Efficiency nearly increased by 1.4

N-Fertilization and C uptake Fertilization can increase leaf area index (LAI) and leaf carboxylation capacity (which increases leaf photosynthesis). Fertilization can also increase respiring biomass.

Experiment: SETRES II SouthEast Tree Research and Education Site (SETRES) 2. A large-scale genotype nutrition interaction experiment designed to quantify the effects of fertilization on C- cycling in a managed southern pine forest in North Carolina (operated by the U.S. Forest Service).

SETRES: FIRST RESULTS After 6 years of fertilization Fertilization Rate (~11 g N m -2 y -1 ): Leaf Area Index Doubled (1.5 3) Maximum Leaf Carboxilation Capacity Increased by 20%. Respiring Biomass Increased by ~ 48%.

CO2 From Lai et al. (2002,PCE) H2O EC = Eddy-covariance measurements. T CV = CANVEG Model calculations

Annual carbon balances (g C m -2 yr -1 ) Variable Control Fertilized Gross Primary Productivity -1220-1795 Respiration Components (i) Forest Floor 1107 1140 (ii) Above-ground Woody 156 395 (iii) Foliar 63 133 Total Ecosystem Respiration 1326 1668 Net Ecosystem Exchange (NEE) +106-127 Daytime NEE -525-993 Nighttime Ecosystem Respiration 695 901 Woody Increment 121 403

Summary: Fertilization impacts the timing at which the forest switches from a source to a sink of carbon. With shorter rotations, such timing in terms of source-sink transition becomes even more critical.

Uh (m/s) 1 0.5 0-0.5-1 T' (K) 50 40 30 20 10-10 0-20 -30-40 -50 q' (Kg/m 3 ) Gravity Waves: Stable Boundary Layer at z/h = 1.12 (Duke Forest) 0 2 4 6 8 10 12 14 Time (minutes) 4 3 2 1 0 w' (m/s) 0.6 0.4 0.2 0-0.2-0.4-0.6 CO2 u'w' (m/s) 2 0.2 0.1 0-0.1-0.2-0.3 Fc 6E-005 4E-005 2E-005 0-2E-005 0.0001-4E-005 0-0.0001-0.0002-0.0003-0.0004-0.0005-0.0006 0 2 4 6 8 10 12 14 RN (W/m 2 ) Time (minutes) 0.4 0-0.4-0.8-1.2 w't' (K m/s) 20 15 10 5 0-5 -10 w'q' -20-25 -30

Night-Time Nonstationarity Uh (m/s) 4 3 2 1 u'w' (m/s) 2 0.4 0-0.4-0.8 1 0.5 0-0.5-1 T' (K) 50 40 30 10 20-10 0-20 -30-40 -50 q' (Kg/m 3 ) 0 4 8 12 16 20 24 28 Time (minutes) 0 w' (m/s) 2 1.5 1 0.5 0-0.5-1 -1.5-2 CO2 0.2 0.1 0-0.1-0.2-0.3 Fc 0.0002 0.0001 0-0.0001-0.0002 0.0008-0.0003 0.0006 0.0004 0.0002 0-0.0002-0.0004-0.0006 0 4 8 12 16 20 24 28 RN (W/m 2 ) Time (minutes) -1.2 w't' (K m/s) 20 15 10 5 0-5 -10 w'q' -20-25 -30

Electric equivalence models - ODE VPD Porous media models PDE VPD, LAI VPD Soil-air VPD Stomata resistance Soil-air VPD Stomata resistance Soil-wood resistance Soil-wood resistance Wood capacitance Soil-tree water flux Soil-tree water flux 1. 2R model 2. RC model 3. Simple beam model 4. Branching model linked to dynamic turbulent closure

1-D Richard s equation with H2O sinks Solved by Finite Element Methods Stem hydraulics based on cavitation curves from Sperry et al. (2000) G. Bohrer Maximum H2O loss from CANVEG Stomatal shut-down: From Sperry - Critical pressure

H2O Pressure Simulations Movie file (mpeg) Mean conductive Xylem Movie file (mpeg) Poorly conductive Xylem

Norway Spruce Flakeliden, Sweden From Chuang, Oren, Bertozzi, Phillips, and Katul (2005; Ecological Modeling)

Emerging Areas and Advances

Michele Holbrook Rob Jackson Stomata & Plant Hydrodynamics How does water enter an embolized conduit? How does positive pressure needed for refilling coexist with tension? How is hydraulic continuity restored? Does elevated CO2 alter xylem hydraulic properties? How will elevated CO2 alter stomatal density of a given species?

Monitoring CO2/H2O fluxes from a wide range of Biomes - linking atmospheric (flux) measurements to biological processes requires detailed understanding of fluid dynamics and biophysical processes in complex terrain.

Preliminary WT Modelling (Hughes and Finnigan, 2002)

Seed Release experiments Liriodendron tulipifera Pinus taeda

Remote Sensing Methods Leaf Area Index (m 2 leaf area m -2 ground area): TERRA-the Earth Observing System (EOS) satellite: Moderate Resolution Imaging Spectroradiometer (MODIS) onboard, provides LAI on an 8-day time step and at a spatial resolution of 1 km. IKONOS (Quick-Bird) 1 m x 1 m resolution (qualitative). Leaf Area Density (m 2 leaf area m -3 ) FOCUS OF THIS TALK: Laser Altimetry: terrain and vegetation from ground and aircraft (LVIS/SLICER). Portable LIDAR system (bottom-up scanning)

Portable Canopy LIDAR G. Parker (personal communication) developed a portable laser rangefinding system. Riegl-LD90-3100HS first-return laser rangefinder (operating at 890 nm and 1 khz, laser safety class I) mounted to the front of a frame at 1 m above the ground and pointed upward. The laser made approximately 1000 measurements per second; these were automatically averaged in groups of five to yield about 200 data points per second.

Hardwood Stand (Duke Forest) 25 15 5 50 100 150 200 250 Loblolly Pine (Duke Forest) 25 15 5 50 100 150 25 15 5 Thinned Loblolly Pine (Duke Forest) 50 100 150 200 250 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Surface Area Density (m 2 m -3 )

30.5 25.5 20.5 30 meter-transects in a loblolly pine plantation A 30.5 25.5 20.5 180 meter-transects in a loblolly pine plantation B 15.5 15.5 10.5 10.5 5.5 5.5 0.5 30.5 25.5 20.5 15.5 0 0.2 0.4 0.6 0.8 1 1.2 300 meter-transects in a thinned loblolly pine plantation C 0.5 30.5 25.5 20.5 15.5 0 0.2 0.4 0.6 0.8 1 1.2 260 meter-transects in a hardwood forest D 10.5 10.5 5.5 5.5 0.5 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 Surface Area Density (m 2 m -3 ) 0.5

SLICER = Scanning LIDAR Imager of Canopies by Echo Recovery From Lefsky et al., 2002

Lidar Measurements of the TwinTower Sites

Comparison between SLICER and field measurements Data from Lefsky et al. (2002) BioScience, Vol. 52, p.28

~1 km

Data from Katul et al. (1998) Near-convective scaling r Ts,u =-0.38

COMPUTATIONAL LES of water- carbon- energy fluxes LES: 3-D, transient integration of filtered Navier- Stokes Canopy is embedded in flow field Radiation excites vegetation energy balance Water and Energy exchange based on results of Farquhar (A) and Leuning (g c ) Canopy temperature evolves and forces heat exchange Eddy motion and the fluxes control canopy environment

Flow and Transport Equations ( ) jui iu j = i p jτ ij + βδi fi oui + u j 3 i u i = 0 o θ + u j jθ = jπ j + θ h o q + u j jq = jπ j + q e o c + u j j c = j c j π +η From Albertson, Katul, and Wiberg, (2001, AWR)

Water Vapor Transport: Vertical Slice of the region J. Albertson LES Simulation of H2O Exchange

Subgrid Models?

From Katul et al. (2004) Distance (m)