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‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications towards studying Methane Dennis Baldocchi University of California, Berkeley Workshop on ON THE RELEVANCE OF SURFACE AND BOUNDARY LAYER PROCESSES FOR THE EXCHANGES OF REACTIVE- AND GREENHOUSE GASES", Wageningen, The Netherlands 9-12th of October 2007.

‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

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Page 1: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon

Dioxide and Water Vapor Flux Measurement Systems and Applications towards studying Methane

Dennis BaldocchiUniversity of California, Berkeley

Workshop onON THE RELEVANCE OF SURFACE AND

BOUNDARY LAYER PROCESSES FOR THE EXCHANGES OF REACTIVE- AND

GREENHOUSE GASES", Wageningen, The Netherlands

9-12th of October 2007.

Page 2: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Outline

• Background – Coupled Carbon, Water and N Cycles– Eddy Covariance

• Long-Term Carbon Fluxes– Trends and Inter-annual Variability– Flux Partitioning– Disturbance

• Long-Term Water Vapor Fluxes– Mechanisms– Annual Fluxes

• Long-term Methane Fluxes – New Methane Measurements

Page 3: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Coupled Carbon, Water, Methane and Energy Fluxes

Page 4: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Eddy Covariance

• Direct measure of the flux density between the atmosphere and biosphere

• In situ

• Quasi-continuous

• Integrative of broad area

• Introduces no artifacts, like chambers

Page 5: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

F ws w sa ~ ' ' s c

a

( )

Eddy Covariance Technique

Mean

Fluctuation

Page 6: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

0

)('' dScwF wc

The Flux Density is defined by the integral of the CoSpectrum

n/u

0.001 0.01 0.1 1 10

nS

wc(

n)/

w'c

'

0.0001

0.001

0.01

0.1

1

D310 0900

Page 7: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Conservation Budget, Advection and Flux Divergence

Page 8: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

0 0

' '( ) ' '(0) ( )h h

a a a

sF w s h dt w s S z dz

t

Must Consider Storage in Air Layer, as at night or with Plume Impaction

1997Temperate Deciduous ForestOak Ridge, TN

Bi-Weekly Period after Jan 1., 1993

0 5 10 15 20 25

Sto

rag

e C

O2 F

lux

(m

ol m

-2 s

-1)

-5

-4

-3

-2

-1

0

1

2

3

4

5

Page 9: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

Longitude

-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Lat

itu

de

FLUXNET 2007

Page 10: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

FN (gC m-2 y-1)

-1500 -1000 -500 0 500 1000 1500

p(x)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

mean: -182.9 gC m-2 y-1

std dev: 269.5n: 506

Baldocchi, Austral J Botany, submitted

Probability Distribution of Published NEE Measurements, Integrated Annually

Page 11: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

FLUXNET Database: n ~ 300 in 2003; n ~ 430 in 2005

Does pdf change with time and/or as the Network Grows?

Page 12: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

FA (gC m-2 y-1)

0 500 1000 1500 2000 2500 3000 3500

FN (

gC m

-2 y

-1)

-1000

-800

-600

-400

-200

0

200

400

Baldocchi, Austral J Botany, submitted

Does Net Ecosystem Carbon Exchange Scale with Photosynthesis?

Page 13: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Length of Growing Season, days

50 100 150 200 250 300 350

FN (

gC

m-2

yr-1

)

-1000

-800

-600

-400

-200

0

200

Temperate and Boreal Deciduous Forests Deciduous and Evergreen Savanna

Baldocchi, Austral J Botany, submitted

Net Ecosystem Carbon Exchange Scales with Length of Growing Season

Page 14: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

FA (gC m-2 y-1)

0 500 1000 1500 2000 2500 3000 3500 4000

FR (

gC m

-2 y

-1)

0

500

1000

1500

2000

2500

3000

3500

4000

UndisturbedDisturbed by Logging, Fire, Drainage, Mowing

Baldocchi, Austral J Botany, submitted

Ecosystem Respiration Scales with Ecosystem Photosynthesis, with Offset by Disturbance

Page 15: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Conifer Forests, Canada and Pacific Northwest

Stand Age After Disturbance

1 10 100 1000

FN (

gC m

-2 y

-1)

-600

-400

-200

0

200

400

600

800

1000

Time Since Disturbance Affects Net Ecosystem Carbon Exchange

Page 16: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Harvard Forest

Year

1990 1992 1994 1996 1998 2000 2002 2004 2006

Ca

rbo

n F

lux

(gC

m-2

y-1

)

-600

-400

-200

0

1000

1200

1400

1600

1800

FNFAFR

Interannual Variation and Long Term Trends in Net Ecosystem Carbon Exchange, Photosynthesis and Respiration

Urbanski et al 2007 JGR

Page 17: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Interannual Variability in FN

d FA/dt (gC m-2 y-2)

-750 -500 -250 0 250 500 750 1000

d F

R/d

t (g

C m

-2 y

-2)

-750

-500

-250

0

250

500

750

1000Coefficients:b[0] -4.496b[1] 0.704r ² 0.607n =164

Baldocchi, Austral J Botany, submitted

Interannual Variations in Photosynthesis and Respiration are Coupled

Page 18: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Soroe, DenmarkBeech Forest1997

day

0 50 100 150 200 250 300 350

-10

-5

0

5

10

15

20

NEE, gC m-2 d-1

Tair, recursive filter, oC

Tsoil, oC

Data of Pilegaard et al.; Baldocchi et al. Int J. Biomet, 2005

Soil Temperature: An Objective Indicator of Phenology??

Page 19: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Temperate Deciduous Forests

Day, Tsoil =Tair

70 80 90 100 110 120 130 140 150 160

Day

FN=

0

70

80

90

100

110

120

130

140

150

160

Canopy Photosynthesis Starts when Soil Temperature Matches Mean Annual Air Temperature

Baldocchi et al 2005 Int J Biomet

Page 20: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Spatialize Phenology with Flux-Based Transformation & Climate Map

Mean Air Temperature, C

4 6 8 10 12 14 16 18

Day

of N

EE

= 0

60

80

100

120

140

160

Coefficients:b[0]: 169.3b[1]: -4.84r ²: 0.691

White, Baldocchi, Schwartz, JGR, submitted

Page 21: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

White, Baldocchi and Schwartz, JGR, submitted

Flux Based Phenology Patterns with Match well with data from Independent Phenology Network

Page 22: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Penman Monteith Equation

Function of:

•Available Energy (Rn-S)•Vapor Pressure Deficit (D)•Aerodynamic Conductance (Gh)•Surface Conductance (Gs)

E

s R S C G D

sGG

n p H

H

s

( )

Page 23: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Rcanopy (s m-1)

10 100 1000 10000

E/

Ee

q

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

wheatcornjack pineoak-savanna

Effects of Functional Types and Rsfc on Normalized Evaporation

Rc is a f(LAI, N, soil moisture, Ps Pathway)

Page 24: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

A (mol m-2 s -1)

0 1 2 3 4 5 6 7 8

gs

(mm

ol

m-2

s-1

)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

oak, varying lightCa: 360 ppmTa: 25 C

Stomatal Conductance Scales with Photosynthesis

Wilson et al. 2001, Tree PhysiologySchulze et al 1994. Annual Rev Ecology

Na (g m-2)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Vcm

ax ( m

ol m

-2 s

-1)

0

20

40

60

80

Photosynthetic Capacity Scales with Nitrogen

after Schulze et al (1994)

leaf nitrogen (mg g- 1̀)

5 10 15 20 25 30 35 40

ma

xim

um

sto

ma

tal

co

nd

uc

tan

ce

(m

m s

-1)

0

2

4

6

8

10

12

14

Stomatal Conductance scales with Nitrogen

Stomatal Conductance Scales with N, via Photosynthesis

Page 25: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Boreal Forest

Vcmax*LAI

0 20 40 60 80 100 120 140 160 180 200

QE/Q

E,e

q

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

k=8.0

k=10

k=7.0

Effects of Leaf Area and Photosynthetic Capacity on Normalized Evaporation:

Watered-Deficits

Page 26: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Eco-hydrology:ET, Functional Type, Physiological Capacity and Drought

?

?

?

E/

Eeq

Page 27: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Use Appropriate and Root-Weighted Soil Moisture

Soil Moisture, arthimetic average

0

0

z

z

z dP z

dP z

Chen, Baldocchi et al, in prep.

Soil Moisture, root-weighted

Page 28: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Interannual Variation ET

Vaira 2004

Day

0 50 100 150 200 250 300 350

E (

mm

d-1

)

0

1

2

3

4

5

2001: 301 mm 2002: 292 mm 2003: 353 mm 2004 : 284 mm

Oak Savanna

Day

0 50 100 150 200 250 300 350

ET

(m

m d

-1)

0

1

2

3

4

5

2002: 389 mm2003: 422 mm2004: 340 mm2005: 484 mm

Page 29: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Gs (mm s-1)

0 2 4 6 8 10 12 14 16

LE/L

Eeq

0.0

0.2

0.4

0.6

0.8

1.0

Savanna WoodlandAnnual Grassland

Monthly Averages

Landscape DifferencesOn Short Time Scales, Grass ET > Forest ET

Ryu, Baldocchi, Ma and Hehn, JGR-Atmos, submitted

Page 30: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

California Savanna

Hydrological Year

02_03 03_04 04_05 05_06 06_07

Eva

pora

tion

(mm

y-1

)

240

260

280

300

320

340

360

380

400

420

440

Oak WoodlandAnnual Grassland

Role of Land Use on ET:On Annual Time Scale, Forest ET > Grass ET

Ryu, Baldocchi et al, JGR-Atmos, submitted

Page 31: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

•Savanna Uses More Water than Grassland•Savanna Soil holds about 78 mm more Water•Annual ET Decreases with Rg•Rg is negatively correlated with Rain and Clouds•System is Water not Radiation Limited

Different Land Use

<Rg> (MJ m-2 d-1)

17.4 17.6 17.8 18.0 18.2 18.4

Eva

po

ratio

n (

mm

y-1

)

240

260

280

300

320

340

360

380

400

420

440

460

Oak Savanna WoodlandAnnual Grassland

Ryu, Baldocchi, Ma, Hehn, JGR-Atmos, submitted

Page 32: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Anoxic Sediments

Water

Fluxes, Sources andSinks of Methane

Air-WaterExchange

Air

Ebullition

MethanogenicBacteria

XylemTransport

Oxidation:Methanotropic

Bacteria

CO2

Page 33: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Whiting and Chanton, 1993 Nature

Methane Efflux Scales with NEP

McMillan et al 2007 JGR

Rice in Ca

Shurpali and Verma, 1998

Page 34: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Whalen 2005 Env Eng Sci

Methane Fluxes Experience Much Seasonality and transcend several

Orders of Magnitude

McMillan et al 2007 JGR

Page 35: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Hendricks et al 2007 Biogeoscience

Role of Landscape in Holland

Page 36: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Interannual Variation in Methane Fluxes due to Water Table

Shurpali and Verma, 1998

Page 37: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Methane Emission and Water Table

Roulet et al, 1992 TellusBubier and Moore, TREE, 1994

Page 38: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Measuring Methane with Off-Axis Laser Spectrometer

Los Gatos Research

Page 39: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

HI Tran Methane Spectra1651 nm band IR absorption for Laser system

Wavelength (microns)

1.6500 1.6505 1.6510 1.6515 1.6520

Line

Abs

orpt

ion

(cm

mol

ecul

e-1

)

0.0

2.0e-22

4.0e-22

6.0e-22

8.0e-22

1.0e-21

1.2e-21

1.4e-21

Page 40: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Methane power spectrum

f/U

0.0001 0.001 0.01 0.1 1 10

Scc

/cc

0.00001

0.0001

0.001

0.01

0.1

Page 41: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Flux detection limit

F rwc w c rwc ~ 0.5

w ~ 0.125 m s-1

c ~ 0.84 ppb

minimum methane flux density on the order of 4.68 nmol m-2 s-1 (0.27 mg CH4 m

-2 h-1),

Methane Lab Calibration

Time

260 280 300 320 340 360 380 400

Met

hane

Sen

sor

1880

1890

1900

1910

1920

Mean: 1897.4277StdDev: 0.8411Std Err 0.0219

Page 42: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Methane Fluxes over a Peatland

Detto and Baldocchi, unpublished

Page 43: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Methane Fetch Daytime, Ideal

Page 44: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Methane Fetch at Night, Patchy and Complex

Page 45: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Day and Night Footprints over Peatland

Detto and Baldocchi, unpublished

Page 46: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Conclusions

• Net Ecosystem Carbon Exchange is a result of close coupling between photosynthesis and respiration

• Disturbance produces an additional respiratory source• Long-term measurements are showing trends in CO2 exchange due

to ecosystem dynamics• Methane Fluxes transcend several orders of magnitude and

experience much seasonality due to modulation in water table and net primary productivity

• New opportunities to measure other traces gases, like methane, with new generation of tunable diode laser spectrometers

• Fluxes of trace gases is more complicated due to plume impaction, over small background signal, and patchy sources

Page 47: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications
Page 48: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications
Page 49: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications
Page 50: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

WU

U

U

Page 51: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Fc, 1d rotation

-30 -20 -10 0 10

Fc

3D r

otat

ion

-30

-20

-10

0

10

2% difference or 15 gC m-2 y-1

Page 52: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

wind direction

0 40 80 120 160 200 240 280 320 360

w/u

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Page 53: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Filtering Functions

• High pass filtering• Low pass filtering• Digital sampling• Sensor response time• Attenuation of signal via

sampling• Line or volume averaging• Sensor separation

w c H Co dmeasured wc' ' ( ) ( )z 0

H H H H Hn nn

N

( ) ( ) ( )... ( ) ( ) 1 2

1

Page 54: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Frequency

0.00001 0.0001 0.001 0.01 0.1 1 10 100

T(f

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Low Pass FilterHigh Pass Filter

Page 55: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

F w w wc c c ' '

a

a

T

T

' '

F wT

w Tcc ' ' ' '

Many sensors don’t measure mixing ratio, they measure molar density

1st order assumption, Boussinesq Approximation

w w a a ' ' /

Page 56: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

a

a

v

vm m

p

RT

w wm

m

w m

m

w T

Ta a

a

v

v

a

v a

a v

' ' /'

( )' ''

1

‘correction’ for moist air

Page 57: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

Closed Path TDL

,c nat c qca

w w w

After Detto and Baldocchi

, ,ex

, ,ex

c c nat c t

c c nat c t

Page 58: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

0 a B

w s

zS z

' '( )

Ideal, steady-state, infinite fetch, no advection

Integrate and Define Constant Flux Layer

a a

h

w s h w s S z dz' ' ( ) ' ' ( ) ( ) z00

Page 59: ‘Breathing’ of the Terrestrial Biosphere: Lessons Learned from a Global Network of Carbon Dioxide and Water Vapor Flux Measurement Systems and Applications

a a Bus

xw

s

z

w s

zS x z t

LNM

OQP

LNM

OQP

', ,b g

Advective conditions