integrating fluxes of carbon dioxide and water vapor from leaf to canopy scales

Integrating Fluxes of Carbon Dioxide and Water Vapor From Leaf to Canopy Scales

Dennis BaldocchiEcosystem Science Division/ESPM

UC Berkeley

Outline

• Overview Leaf-Canopy Scaling and Integration Concepts

• Show Tests of Such Models over Multiple Time Scales

• Use the CANVEG Model to Ask Ecophysiological and Micrometeorological Questions Relating to Trace Gas Fluxes

Classes of Model Complexity

• The breadth and linkage of functional components that describe the biophysics of trace gas exchange.

• How driving variables are defined and used as inputs to non-linear model algorithms.

• The geometric abstraction of the canopy.

ESPM 111 Ecosystem Ecology

Water

SurfaceConductance

Transpiration/Evaporation

AvailableEnergy

Photosynthesis/Respiration

LAI

Carbon

NutrientsLitterSoil Moisture

PBL ht

Sensible Heat

System Complexity: Interconnection of Key Ecosystem Processes

Biogeo-chemistry

seconds

days

years

centuries

canopy

landscape

region/biome

continent

Weather model

Biophyscial Model

EcosystemDynamics

E, HRn

Species,Functional

Type

Leaf Area, N/C,Ps capacity

Biophysical model

ppt, Ta, P, e a,u,Rg,L Ac,Gc

Processes and Linkages:Roles of Time and Space Scales

ESPM 111 Ecosystem Ecology

3-d Representation of Canopy

Qi Chen and D. Baldocchi

ESPM 111 Ecosystem Ecology

Geometrical Abstraction of the Canopy

• One-Dimensional– Big-Leaf– Dual Source, Sun-Shade– 2-Layer

• Vegetation and soil– Multi-Layered

• Two-Dimensional– Dual source

• sunlit and shaded• Vegetated vs Bare Soil

• Three-Dimensional– Individual Plants and

Trees

After Hanson et al Ecol Appl 2004

g

E

eair

H

Tair

Ra,h

G

A=Rnet-G

Rc

es(Tsfc)Tsfc

Ra,v

Big Leaf Model

Big-Leaf Model

Dual Source:Patch Model

g

E

esoil

To

eair

H

EsoilHs

oilTsoil

Ra,cRa,c

Ra,stom

Ra,soil Ra,soil

eo

Tair

Ra,airRa,air

Rs,soil es(Tsoil)G

Rnet

Rnet,soil

Dual Source:Layered Model

2-Layer/Dual Source Models

Dual Source Model:Discrete Form

Whole Canopy

G L G L Gsfc sun sun sh sh

L kL ksun ( exp( )) /1

L L Lsh sun

ESPM 111 Ecosystem Ecology

Role of Proper Model Abstraction

Leaf Area

0 1 2 3 4 5 6

L sun

0.0

0.5

1.0

1.5

2.0

G=0.5, sin=0.5G=0.5; sin=0.75G=0.5; sin

Sunlit Leaf Area and Sun Angle

Multi-Layer Models

Meteorological and Plant inputsRg,Lin, Ta, qa, [CO2], u, P, ppt,

LAI, h, d,l, zo

StomatalConductace=

f(A,Ci,Tl,

LongwaveRadiativeTransfer:

f(Tl,IRup,IRdn,

Leaf EnergyBalance:H,E, Tl

Leaf Photosynthesisand Respiration:

f(gs, Tl,Ci, gb, Qpar)

Source/Sinks:ST,Sq,SC

ScalarProfiles:

T,q,C

Radiative Transfer:Qpar,Rnirf()

Boundary LayerConductace=

f(u,l

CANOAK Schematic

ESPM 111 Ecosystem Ecology

Basics of Ecosystem Models

Physiology:Photosynthesis,

Respiration, Transpiration

Weather:Light Energy, Temperature,

Rainfall, Humidity, WindVelocity, CO2, soil

moisture

Growth and Allocation:Leaves, Stems, Roots,

Light Interception, Water andNutrient Uptake

Biogeochemistry:Decomposition,

Mineralization, Nitrification,Denitrification

Ecosystem Dynamics:Reproduction, Disperal, Recruitment,

Competition, Facilitation, Mortality,Disturbance

Soil:Texture, DEM, C/

N,bulk density,Hydraulic Properties

EcoPhysiology:Leaf area index, plant

functional type,photosynthetic capacity,canopy height, albedo

hours

days/seasons

years

hours/days

(z)r+(z)r)C-(C(z) a(z) -=z)S(C,

zF

sb

i

Quantifying Sources and Sinks

• Biology: a(z), Ci, rs

• Physics: rb, C(z)

Weight Source/Sink by Fraction of Sunlit and Shaded Leaves and Their Environment

shadeshadeshadeshadeshade

sunsunsunsunsun

pCqTIfzpCqTIfzCS

),,,()(),,,(),(

bP =G

dPdL

(- L G ) sin exp

sin

0

)G L(-=P0 sinexp

Random Spatial Distribution:Poisson Prob Distr.

Prob of Beam Penetration

Prob of Sunlit Leaf

Sources of Spatial Heterogeneity

• Vertical Variations in:– Leaf area index– Leaf inclination angles– Leaf Clumping– Leaf N + photosynthetic capacity– Stomatal conductance– Light, Temperature, Wind, Humidity,

CO2

Deciduous Forest

Leaf Area Density (m2 m-3)

0.0 0.5 1.0 1.5

Hei

ght (

m)

0

5

10

15

20

25

30

Vertical Profiles in Leaf Area

Vertical Variation in Sunlight

d1411300

Diffuse Radiation Flux density (W m-2)

0 20 40 60 80 100 120 140H

eigh

t (m

)

0

5

10

15

20

25

30

PARNIR

Pbeam(f)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Leaf

Are

a In

dex

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Spherical Leaf DistributionClumped Leaf Distribution

Carboxylation Velocity Profiles

Carboxylation Velocity (mol m-2 s-1)

0 5 10 15 20

Hei

ght (

m)

0

5

10

15

20

25

Wc sunWc shadeWj sunWj shade

D181 1200

Profiles of Ci/Ca

Ci/Ca

0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

Hei

ght (

m)

0

5

10

15

20

25

Ci/Ca sunlitCi/Ca shaded

Turbulence Closure Schemes

• Lagrangian

• Eulerian– Zero Order, c(z)=constant– First Order, F=K dc/dz– Second Order and ++ (dc/dt, dw’c’/dt)

X Data-20 0 20 40 60 80 100 120

Y Da

ta

-14-12-10

-8-6-4-202468

101214

ESPM 228 Adv Topics Micromet & Biomet

Higher Order Closure Equations and Unknowns

Sour

ce P

rofil

e

Far Field C profile

Total C profile

C z C z C zn f( ) ( ) ( )

Lagrangian Near- and Far-Field Theory

ESPM 228 Adv Topics Micromet & Biomet

i rj=1

N

j j i, j jc - c = S c D z( )

D C CS zij

i r

j j

Dispersion Matrix

ESPM 228 AdvTopics Micromet & Biomet

Turbulent Mixing

Dij (s m-1)

0 20 40 60 80 100 120 140

Hei

ght

0

20

40

60

80

100

120

D1431100

CO2 (ppm)353.0 353.5 354.0 354.5 355.0 355.5 356.0 356.5 357.0

Heig

ht (m

)

0

20

40

60

80

Dij=f(z/L)neutral

Vertical Gradients in CO2

D1431100

absolute humidity (kg m-3)

0.0113 0.0114 0.0115 0.0116 0.0117 0.0118 0.0119 0.0120

Heig

ht (m

)

0

20

40

60

80

Dij=f(z/L)neutral

D1431100

Temperature (C)22.6 22.8 23.0 23.2 23.4 23.6

Heig

ht (m

)

0

20

40

60

80

Dij = f(z/L)

neutral thermal stratification

Vertical Gradients in q and T

13C Profiles

CO2 (ppm)

340 360 380 400 420 440 460 480 500

Hei

ght (

m)

0

10

20

30

40

50

60

70

80

1200 hours0100 hours

13CO2 (ppm)

3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4

Hei

ght (

m)

0

10

20

30

40

50

60

70

80

PhysiologyPhotosynthesis

Stomatal Conductance

Transpiration

MicrometeorologyLeaf/Soil Energy BalanceRadiative TransferLagrangian Turbulent Transfer

Albedo

LEH

Gsoil

FCO2

CANOAK MODEL

Examples: Non-Linear Biophysical Processes

L TsA~ 4

e T T

aLE bLE cs ( ) ~ exp( )

2 0

A aIb cI

dCe fC

aA bA cA d

~ ;

3 2 0

Leaf Temperature

Transpiration

Photosynthesis

Respiration R Td ~ exp( )

X Data0 2 4 6 8 10 12

Y Da

ta

0

20

40

60

80

100

120

Expected Value, E[f(x)]

f(<x>)

<x>

Why Non-linearity is Important?

ESPM 129 Biometeorology 35

R

R

L

L

H E

Leaf Energy Balance

• R: is shortwave solar energy, W m-2

• L: is Longwave, terrestrial energy, W m-2

• E: Latent Heat Flux Density, W m-2

• H: Sensible Heat Flux Density, W m-2

ESPM 129 Biometeorology 36

Leaf Energy Balance, Wet, Transpiring Leaf

R H En

Net Radiation is balanced by the sum of Sensible and Latent Heat exchange

Q R L T H El B B ( )1 4

ESPM 129 Biometeorology 37

R H En

H C T T ga p l a h ( )

e T e D e T T E Pm m gs l a s l a

a v a w

( ) ' ( )( / )

Derivation

1: Leaf Energy Balance

2: Resistance Equations for H and E

3: Linearize T4 and es(T)

T T T T Tl a a l a4 4 34 ( )

E

m m g e T eP

v a a w s l a( / ) ( ( ) )

ESPM 129 Biometeorology 38

f x f x x x dfdx

( ) ~ ( ) ( )0 0

T T T T Tl a a l a4 4 34 ( )

Linearize with 1st order Taylor’s Expansion Series

ESPM 129 Biometeorology 39

e T e T e T T e T Ts l x a s l as

l a( ) ( ) ' ( ) " ( ) 2

2

Linearize the Saturation Vapor Pressure function

e T de TdTss( )' ( )

e T d e TdTs

s( )' ' ( )

2

2

e T e T e T Ts l s a s l a( ) ( ) ' ( )

ESPM 228, Advanced Topics in Micromet and Biomet

* *

min ,c o c jc pc c

-0.5 =V (1- ) [ , W ](1- )V V W WC C

[CO2] (ppm)

0 200 400 600 800 1000

Car

boxy

latio

n ra

te (

mol

m-2

s-1

)0

10

20

30

40

50

60

Ci

supply~stomatal conductance (gs)

Wc : demand limited by RUBISCO saturation

Wj : demand limited by RuBP regenerationby electron transport

• Wc, the rate of carboxylation when ribulose bisphosphate (RuBP) is saturated

• • Wj, the carboxylation rate

when RuBP regeneration is limited by electron transport.

• Wp carboxylation rate with triose phosphate utilization

ESPM 228, Advanced Topics in Micromet and Biomet

If Wc is minimal, then:

* *max0.5 C c

c o c2c

cco

( - )V CV V W (1- )= [ ]OC + (1+ )C KK

If Wj is minimal, then

* *

*0.5 cc o j

c c

J( - )CV V W (1- )=4 +8C C

*

3

1

tpup

c

VW

C

If Wp is minimal, then

maxC cc

2cc

o

V CW = [ ]O+ (1+ )C KK

*c

jc

JCW =4 +8C

ESPM 228, Advanced Topics in Micromet and Biomet

Analytical Equation for Leaf Photosynthesis

Baldocchi 1994 Tree Physiology

ESPM 228, Advanced Topics in Micromet and Biomet

Day of year

100 125 150 175 200 225 250 275 300 325

Vcm

ax (

mol

m-2

s-1

)

0

10

20

30

40

50

60

70

White oak

Seasonality in Vcmax

Wilson et al. 2001 Tree Physiol

Results and Discussion

0 100 200 300 400 500 600 700

NEE

( mol

m-2 s-1 )

-25

-20

-15

-10

-5

0

5

10

15

measuredcalculated

1997 Walker Branch Watershed

NEE measured (mol m-2 s -1)

-30 -25 -20 -15 -10 -5 0 5 10 15 20

NEE

com

pute

d (

mol

m-2 s-1 )

-30

-20

-10

0

10

20

b[0] 0.908b[1] 1.085r ² 0.815

Model Test: Hourly to Annual Time Scale

Week0 5 10 15 20 25

LE (W

m-2 )

0

100

200

300

400MeasuredCalculated

Temperate Deciduous Forest, 1997

LE measured (W m-2)

0 100 200 300 400 500

LE c

alcu

late

d (W

m-2 )

0

100

200

300

400

500Coefficients:b[0]: 4.96b[1]: 1.14r ²: 0.83

Model Test: Hourly Data

Time Scales of Interannual Variability

n, cycles per hour

0.0001 0.001 0.01 0.1 1

nSw

c(n)/w

'c'

0.0001

0.001

0.01

0.1

1

10

canoakdata

1997

Spectra of Photosynthesis and Respiration

Frequency (cycles per hour)0.0001 0.001 0.01 0.1 1

nS xx(n)/ x2

0.0001

0.001

0.01

0.1

1Canopy PsCanopy Respiration

Frequency (cycles per hour)0.0001 0.001 0.01 0.1 1

nS xy(n)/ x y

0.0001

0.001

0.01

0.1

1

10

nSxy(n)-nSxy(n)

Covariance:canopy photosynthesis andrespiration

1997

Day0 100 200 300

NEE

(gC

m-2 d-1 )

-12

-10

-8

-6

-4

-2

0

2

4

calculated: -548 gC m-2 y-1

Measured: -668 gC m-2 y-1

NEE measured (gC m-2 day-1)

-12 -10 -8 -6 -4 -2 0 2 4

NEE,

cal

cula

ted

(gC

m-2 d-1 )

-12

-10

-8

-6

-4

-2

0

2

4

b[0]: 0.173b[1]: 0.918r ²: 0.556

Model Test: Daily Integration

Interannual Variability

Year

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

Net

Eco

syst

em C

Exc

hang

e (g

C m

-2 y

r-1)

-650

-600

-550

-500

-450

-400

CANOAKMeasured and Gap-Filled

Temperate Deciduous Forest: Canoak

ESPM 111 Ecosystem EcologyHansen et al, 2004 Ecol Monograph

Model Validation: Who is Right and Wrong, and Why?

How Good is Good Enough?

1987-1997CanoakTemperate Deciduous Forest

f (cycles per day)0.0001 0.001 0.01 0.1 1

nSxx

/s x2

0.01

0.1

1 daily CO2 fluxdaily evaporation

1 year

5.6 yrs124 days

Decadal Power Spectrum of CO2 and Water Vapor Fluxes

Temperate Deciduous Forests

Days with NEE < 0

120 140 160 180 200 220 240

NEE

(g C

m-2 yea

r-1 )

-800

-700

-600

-500

-400

-300

-200

-100

0

CANOAK, Oak Ridge, TNPublished Measurements, r2=0.89

NEE and Growing Season Length

Vcmax LAI/fpar0 100 200 300 400 500

GPP

(gC

m-2

yr-1

)

400

600

800

1000

1200

1400

1600

1800

CANVEG

EUROFLUXWalker Branch WatershedDuke: Ellsworth/Katul Metolius Young: Law et alMetolius old: Law et alHarvard: Barford et al.

GPP

Component C Fluxes

Vcmax*LAI/fpar0 100 200 300 400 500

Rpla

nt/P

s

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

10/19/2000Rpl = Rleaf+Rbole+1/2 Rsoil

Gifford (1994)

Light Use Efficiency and

Net Primary Productivity

Tree

TreeTree

Tree

NPP=f Qp

PAR (mol m-2 s-1)

0 500 1000 1500 2000

P c (m

ol m-1 s-1 )

-10

0

10

20

30

40

50

crop canopyVcmax = 100 mol m-2 s-1

LAI=5

LAI=3

LAI=1

LUE and Leaf Area

PAR (mol m-2 s-1)

0 500 1000 1500 2000

P c(m

ol m-1 s-1 )

-10

0

10

20

30

40

50

crop canopyLAI = 5

Vcmax = 100 mol m-2 s-1

Vcmax = 50

Vcmax = 25

LUE and Ps Capacity

Emergent Processes: Impact of Leaf Clumping on Canopy Light Response Curves

Deciduous forest

model: clumped leaves

PPFD (mol m-2 s-1)

0 500 1000 1500 2000 2500

F c ( mol

m-2 s-1 )

-40

-30

-20

-10

0

10

measured

(b)

0 500 1000 1500 2000 2500

F c ( mol

m-2 s-1 ) -40

-30

-20

-10

0

10

(a)

model: spherical leaves

Temperate Deciduous Forest

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

NEE

(gC

m-2 y

ear

-1 )

-700

-600

-500

-400

-300

-200

Clumped FoliageSpherical Foliage

Y ear1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

ET (m

m y

ear

-1 )

600

650

700

750

800

850

900

950

Clumped FoliageSpherical Foliage

Role of Leaf Clumping on Annual C and H2O Fluxes

Interaction between Clumping and Leaf Area

Temperate Deciduous Forest

LAI0 1 2 3 4 5 6 7

Flux

sph/F

lux cl

p

0.5

0.6

0.7

0.8

0.9

1.0

1.1

canopy photosynthesisENEE

PPFD (mol m-2 s-1)0 500 1000 1500 2000

NEE

( mol

m-2 s-1 )

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10Sunny daysdiffuse/total <= 0.3

Cloudy daysdiffuse/total >= 0.7

Temperate Broad-leaved ForestSpring 1995 (days 130 to 170)

How Sky Conditions Affect NEE?

P0

0.0 0.2 0.4 0.6 0.8 1.0

LAI

0

1

2

3

4

5

6

Diffuse RadiationBeam Radiation, = pi/2 Beam Radiation, =pi/3

2

002

/

diffuse dsincosPP

NE

Em

eas /

NE

Est

at [

- ]

0.6

0.8

1.0

1.2

1.4 Hainich (m = 0.54 +/- 0.06, r2 = 0.61)Leinefelde (m = 0.45 +/- 0.11, r2 = 0.26)

Rd/Rs [ - ]

0.0 0.2 0.4 0.6 0.8 1.0

NE

Em

eas / N

EE

stat

[ - ]

0.6

0.8

1.0

1.2

1.4 Hainich (measured, m = 0.54 +/- 0.06, r2 = 0.61Hainich (modelled, m = 0.51 +/- 0.05, r2 = 0.70

A

B

Knohl and Baldocchi, JGR Biogeosci 2008

Leaf area index [m2 m-2]

0 2 4 6 8 10

Diff

use

light

effe

ct (s

lope

) [ -

]

0.2

0.3

0.4

0.5

Knohl and Baldocchi, 2008 JGR Biogeosci

CO

2 Fl

ux [µ

mol

m-2

s-1

]

0

5

10

15

20

25

30

Canopy photosynthesisNet ecosystem exchange

Rd/Rs [ - ]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Tran

spira

tion

[mm

ol m

-2 s

-1]

0

2

4

6

8

Wat

er u

se e

ffici

ency

[µm

ol C

O2

mm

ol-1

H2O

]

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

TranspirationWater use efficiency

A

B

Knohl and Baldocchi, 2008 JGR Biogeosci

Potential Impact of Aerosols/Clouds on NEE

Day

0 50 100 150 200 250 300 350 400

NEE

(gC

m-2

day

-1)

-10

-8

-6

-4

-2

0

2

4

Direct Radiation is reduced by 20%: NEE = -627 gC m-2 yr-1

Ambient Conditions: NEE= -553 gC m-2 yr-1

Oxygen and NEE: Paleoclimates

Day

0 50 100 150 200 250 300 350

NEE

(gC

m-2

d-1

)

-10

-8

-6

-4

-2

0

2

4

LAI: 6O2=35% : -224 gC m-2 y-1

Ave Daily LE, f(z,w) (W m-2)

0 20 40 60 80 100 120 140 160 180 200

Ave

Dai

ly L

E, q

(z)=

q a; T(z

) = T

a

0

50

100

150

200

b[0]: -0.753b[1]: 0.983r ²: 0.9463

CanoakOak Ridge, TN 1997

Ave Daily H, f(z,w) (W m-2)

0 50 100 150 200

Ave

Dai

ly H

,q(

z)=

q a; T(z

) = T

a

0

50

100

150

200

b[0] 2.72b[1] 0.615r ² 0.860

Ave Daily Fc, f(z,w) (W m-2)

-8 -6 -4 -2 0 2 4

Ave

Dai

ly F

c, q(

z)=

q a; T(z

) = T a; C

(z)=

C a

-8

-6

-4

-2

0

2

4

b[0] 0.0119b[1] 0.985r ² 0.998

Do We Need to Consider Canopy Microclimate [C] Feedbacks on Fluxes?

Tleaf

0 10 20 30 40

pdf

0.00

0.02

0.04

0.06

0.08

0.10

0.12

1993198119821984199419971995

Temperate Broadleaved ForestDays 100 to 273

Leaf Temperature and Isoprene Emission?

sunlit leaves, daytimeOak Ridge, TN 1997

Tleaf0 10 20 30 40

Prob

abili

ty

0.00

0.02

0.04

0.06

0.08

pdf tsun ambient CO2=1500 ppm, 100 mm leafpdf tsun small leaves

Leaf size, CO2 and Temperature: why oak leaves are small in CA and large in TN

Temperate Deciduous ForestSunlit leaves, 1997

T leaf (oC)

0 10 20 30 40

prob

abili

ty d

ensi

ty

0.00

0.02

0.04

0.06

0.08

Vcmax = 73 mol m-2 s-1

Vcmax = 10 mol m-2 s-1

Physiological Capacity and Leaf Temperature: Why Low Capacity Leaves Can’t Be Sunlit::or don’t leave the

potted Laurel Tree in the Sun

Ponderosa PineForest FloorD187-205, 1996

Rne

t (W

m-2

)

-500

50100150200250300

measured

calculated

E (W

m-2

)

-25

0

25

50

75

H (W

m-2 )

0

50

100

150

200

Time (hours)

0 4 8 12 16 20 24

G (W

m-2

)

-75-50-25

0255075

100125150

Figure 15enbmod.spw12/8/99: laieff=1.8, zlitter=0.08

Below Canopy Fluxes

Below Canopy Fluxes and Canopy Structure and Function

LAI * Vcmax

0 20 40 60 80 100 120 140 160 180 200

Q E,so

il/QE

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Rn

(W m

-2 )

-500

50100150200250300

E (W

m-2 )

010203040506070

Ra=f(stability)Ra: neutral

H (W

m-2 )

0255075

100125150

Time (hours)

0 4 8 12 16 20 24

G (W

m-2 )

-500

50100150200

Ponderos PineForest Floor

Figure 16enmodstb.spw12/8/99

Impact of Thermal Stratification

Rn

(W m

-2 )

-500

50100150200250300

E (W

m-2 )

0102030405060

Litter depth, 0.01 mlitter depth, 0.02 m

H (W

m-2 )

0255075

100125150

Time (hours)

0 4 8 12 16 20 24

G (W

m-2 )

-50

0

50

100

150

Ponderos PineForest Floor

Figure 17enmodlit.spw12/8/99

litter depth, 0.05 m

Impact of Litter

Conclusions

• Biophysical Models that Couple Aspects of Micrometeorology, Ecophysiology and Biogeochemistry Produce Accurate and Constrained Fluxes of C and Energy, across Multiple Time Scales

• Models can be used to Interpret Field Data – LUE is affected by LAI, Clumping, direct/diffuse

radiation, Ps capacity– NEE is affected by length of growing season– Interactions between leaf size, Ps capacity and position

help leaves avoid lethal temperatures– Below canopy fluxes are affected by T stratification and

litter