Integrating Fluxes of Carbon Dioxide and
Water Vapor From Leaf to Canopy Scales
Dennis Baldocchi
Ecosystem 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.
System Complexity:
Interconnection of Key Ecosystem Processes
PBL ht
Available
Energy
Transpiration/
Evaporation
Sensible Heat
LAI
Water
S
Con urface
duc
tan
ce
Photosynthesis/
Respiration
Carbon
Litter
Soil Moisture
ESPM 111 Ecosystem Ecology
Nutrients
Processes and Linkages:
Roles of Time and Space Scales
continent
Ecosystem
Dynamics
Weather model
Biogeochemistry
region/biome
landscape
Rn
ppt, T a,
P, e a,
u,Rg,L
E, H
Species,
Functional
Type
Ac,Gc
Leaf Area, N/C,
Ps capacity
canopy
Biophyscial Model
Biophysical model
centuries
years
days
seconds
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
ESPM 111 Ecosystem Ecology
After Hanson et al Ecol Appl 2004
Big-Leaf Model
A=Rne t-G
Big Leaf Model
eair
Tair
Ra,v
H
E
Ra,h
Rc
Ts fc
es(Ts fc)
g
G
2-Layer/Dual Source Models
Dual Source:
Layered Model
Tair
H
To
oil
G
Ra,air
Ra,air
Ra,c
Ra,s tom
Ra,c
E
eo
Ra,s oil
Hs
eair
Rnet
Tsoil
Ra,s oil
Rnet,soil
g
Rs,s oil
Dual Source:
Patch Model
Esoil
esoil
es(Tsoil)
Dual Source Model:
Discrete Form
Whole Canopy
Gsfc  LsunGsun  LshGsh
Lsun  (1  exp(  kL)) / k
Lsh  L  Lsun
Role of Proper Model Abstraction
ESPM 111 Ecosystem Ecology
Sunlit Leaf Area and Sun Angle
2.0
Lsun
1.5
1.0
0.5
G=0.5, sin=0.5
G=0.5; sin=0.75
G=0.5; sin
0.0
0
1
2
3
Leaf Area
4
5
6
Multi-Layer Models
CANOAK Schematic
Meteorological and Plant inputs
Rg,L in, T a, q a, [CO 2], u, P, ppt, 
LAI, h, d,l, z o
Radiative Trans fer:
Qpar ,Rnir
f( )
LongwaveRadiative
Trans fer:
f(T l,IR up ,IR dn ,
Stomatal
Conductace=
f(A,Ci,Tl, 
Leaf Energy
Balance:
H,E, T l
Boundary Layer
Conductace=
f(u,l
Leaf Photos ynthes is
and Res piration:
f(g s, T l,C i, g b, Q par )
Source/Sinks :
ST,S q,S C
Scalar
Profiles :
T,q,C
Basics of Ecosystem Models
EcoPhysiology:
Leaf area index, plant
functional type,
photosynthetic capacity,
canopy height, albedo
Weather:
Light Energy, Temperature,
Rainfall, Humidity, Wind
Velocity, CO2, soil
moisture
hours
Physiology:
Photosynthesis,
Respiration, Transpiration
hours/days
Growth and Allocation:
Leaves, Stems, Roots,
Light Interception, Water and
Nutrient Uptake
Soil:
Texture, DEM, C/
N,bulk density,
Hydraulic Properties
days/seasons
Biogeochemistry:
Decomposition,
Mineralization, Nitrification,
Denitrification
years
Ecosystem Dynamics:
Reproduction, Disperal, Recruitment,
Competition, Facilitation, Mortality,
Disturbance
ESPM 111 Ecosystem Ecology
Quantifying Sources and Sinks
(C(z)- Ci )
F
 S(C,z) = - a(z)
z
r b (z)+ r s (z)
• Biology: a(z), Ci, rs
• Physics: rb, C(z)
Weight Source/Sink by Fraction of Sunlit and
Shaded Leaves and Their Environment
S (C, z)  f ( I sun , Tsun , qsun , Csun )  psun ( z) 
f ( I shade , Tshade , qshade , Cshade )  pshade
Random Spatial Distribution:
Poisson Prob Distr.
Prob of Beam Penetration
LG
)
P0 = exp(sin 
Prob of Sunlit Leaf
sin  dP0
LG
 exp()
Pb = 
G dL
sin 
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
Vertical Profiles in Leaf Area
Deciduous Forest
30
25
Height (m)
20
15
10
5
0
0.0
0.5
1.0
2
1.5
-3
Leaf Area Density (m m )
Vertical Variation in Sunlight
0.0
30
0.5
d1411300
1.0
25
2.0
20
2.5
Height (m)
Leaf Area Index
1.5
3.0
Spherical Leaf Distribution
Clumped Leaf Distribution
3.5
15
10
4.0
4.5
PAR
NIR
5
5.0
5.5
0
0
6.0
0.0
0.1
0.2
0.3
0.4
0.5
Pbeam(f)
0.6
0.7
0.8
0.9
1.0
20
40
60
80
100
120
Diffuse Radiation Flux density (W m-2)
140
Carboxylation Velocity Profiles
D181 1200
25
Height (m)
20
15
Wc sun
Wc shade
Wj sun
Wj shade
10
5
0
0
5
10
15
Carboxylation Velocity (mol m-2 s-1)
20
Profiles of Ci/Ca
25
Ci/Ca sunlit
Height (m)
20
Ci/Ca shaded
15
10
5
0
0.65
0.70
0.75
0.80
0.85
Ci/Ca
0.90
0.95
1.00
Turbulence Closure Schemes
• Lagrangian
14
12
10
8
6
Y Data
4
2
0
-2
-4
-6
-8
-10
-12
-14
-20
0
20
40
60
80
100
120
X Data
• Eulerian
– Zero Order, c(z)=constant
– First Order, F=K dc/dz
– Second Order and ++ (dc/dt, dw’c’/dt)
Higher Order Closure Equations and Unknowns
ESPM 228 Adv Topics Micromet &
Biomet
Lagrangian Near- and Far-Field Theory
Far Field C profile
Source Profile
Total C profile
C( z )  Cn ( z )  C f ( z )
ESPM 228 Adv Topics Micromet &
Biomet
Dispersion Matrix
N
ci - cr =  S j ( c j ) Di, j
j=1
Ci  Cr
Dij 
S j z j
ESPM 228 AdvTopics Micromet &
Biomet
z
j
Turbulent Mixing
120
100
Height
80
60
40
20
0
0
20
40
60
80
Dij (s m-1)
100
120
140
Vertical Gradients in CO2
D1431100
80
Dij=f(z/L)
neutral
Height (m)
60
40
20
0
353.0
353.5
354.0
354.5
355.0
355.5
CO2 (ppm)
356.0
356.5
357.0
Vertical Gradients in q and T
D1431100
D1431100
80
80
Height (m)
Height (m)
60
Dij=f(z/L)
neutral
60
40
40
20
20
0
22.6
22.8
0
0.0113
0.0114
0.0115
0.0116
0.0117
0.0118
absolute humidity (kg m-3)
0.0119
0.0120
Dij = f(z/L)
23.0
23.2
Temperature (C)
neutral thermal stratification
23.4
23.6
13C
Profiles
80
70
1200 hours
0100 hours
Height (m)
60
50
40
30
20
10
0
340
360
380
400
420
440
460
480
500
CO2 (ppm)
80
70
Height (m)
60
50
40
30
20
10
0
3.6
3.8
4.0
4.2
4.4
13
4.6
CO2 (ppm)
4.8
5.0
5.2
5.4
CANOAK MODEL
Physiology
Photosynthesis
Stomatal Conductance
FCO2
LE
H
Transpiration
Albedo
Micrometeorology
Leaf/Soil Energy Balance
Radiative Transfer
Lagrangian Turbulent
Transfer
Gsoil
Examples: Non-Linear Biophysical
Processes
Photosynthesis
aI
dC
A~
;
b  cI e  fC
aA3  bA2  cA  d  0
es (T ) ~ exp(T )
Transpiration
aLE 2  bLE  c  0
Respiration
Rd ~ exp(T )
Leaf Temperature
A
4
s
L ~T
Why Non-linearity is Important?
120
100
Y Data
80
60
Expected Value, E[f(x)]
40
20
f(<x>)
0
<x>
0
2
4
6
X Data
8
10
12
Leaf Energy Balance
L
R
R
L
E
H
•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
35
Leaf Energy Balance, Wet, Transpiring Leaf
Rn  H  E
Net Radiation is balanced by the sum of
Sensible and Latent Heat exchange
B B
Q  (1  ) R L  Tl  H  E
ESPM 129 Biometeorology
4
36
Derivation
Rn  H  E
1: Leaf Energy Balance
2: Resistance
Equations for
H and E
E 
( mv / ma )  a g w (es ( Tl )  ea )
P
H   a Cp (Tl  Ta ) gh
es (Tl )  ea  D  es '(Tl  Ta ) 
3: Linearize
T4
and es(T)
E  P
 a  (mv / ma ) gw
Tl 4  Ta4  4Ta3( Tl  Ta )
ESPM 129 Biometeorology
37
Linearize with 1st order Taylor’s Expansion Series
df
f ( x ) ~ f ( x0 )  ( x  x0 )
dx
Tl  T  4T ( Tl  Ta )
4
4
a
3
a
ESPM 129 Biometeorology
38
Linearize the Saturation Vapor Pressure function
es ( Tl )  es ( Ta )  es' ( Tl  Ta )
des (T )
es (T )' 
dT
e"
es ( Tl )  ex ( Ta )  es' ( Tl  Ta )  s ( Tl  Ta )2
2
d 2 es (T )
es (T )' ' 
dT 2
ESPM 129 Biometeorology
39
Cc
*
)  min [ W c ,W j,Wp ](1-
•Wc, the rate of
carboxylation when
ribulose bisphosphate
(RuBP) is saturated
•
•Wj, the carboxylation rate
when RuBP regeneration is
limited by electron
transport.
)
Cc
Wc : demand limited by RUBISCO saturation
Wj : demand limited by RuBP regeneration
by electron transport
60
Carboxylation rate (mol m-2 s-1)
V c - 0.5V o =Vc (1-
*
50
40
30
20
supply
~stomatal conductance
(gs)
10
0
0
200
400
600
[CO2] (ppm)
•Wp carboxylation rate with
triose phosphate utilization
ESPM 228, Advanced Topics in
Micromet and Biomet
Ci
800
1000
Wc =
If Wc is minimal, then:
V C max C c
[ O2 ]
+
(1+
)
Cc K c
Ko
*
*
V C max( C c -  )
Vc  0.5Vo  Wc (1)=
[ O2 ]
Cc
)
C c + K c(1+
Ko
JCc
If Wj is minimal, then
Wj =
4 C c + 8 *
*
J( C c - * )
Vc  0.5Vo  W j (1- )=
4C c +8*
Cc
If Wp is minimal, then
Wp 
ESPM 228, Advanced Topics in
Micromet and Biomet
3Vtpu
*
1
Cc
Analytical Equation for Leaf Photosynthesis
Baldocchi 1994 Tree Physiology
ESPM 228, Advanced Topics in
Micromet and Biomet
Seasonality in Vcmax
70
60
White oak
-2
-1
Vcmax (mol m s )
50
40
30
20
10
0
100
125
150
175
200
225
250
Day of year
Wilson et al. 2001 Tree Physiol
ESPM 228, Advanced Topics in
Micromet and Biomet
275
300
325
Results and Discussion
Model Test: Hourly to Annual Time Scale
1997 Walker Branch Watershed
15
measured
calculated
5
-2
-1
NEE (mol m s )
10
0
-5
-10
-15
-20
-25
0
100
200
300
400
500
600
700
b[0] 0.908
b[1] 1.085
r²
0.815
10
-2
-1
NEE computed (mol m s )
20
0
-10
-20
-30
-30
-25
-20
-15
-10
-5
0
5
NEE measured (mol m-2 s-1)
10
15
20
Model Test: Hourly Data
Temperate Deciduous Forest, 1997
400
Measured
Calculated
-2
LE (W m )
300
200
100
0
0
5
10
20
25
Week
500
Coefficients:
b[0]: 4.96
b[1]: 1.14
r ²:
0.83
400
-2
LE calculated (W m )
15
300
200
100
0
0
100
200
300
LE measured (W m
-2
400
)
500
Time Scales of Interannual Variability
10
nSwc(n)/w'c'
1
1997
canoak
data
0.1
0.01
0.001
0.0001
0.0001
0.001
0.01
n, cycles per hour
0.1
1
Spectra of Photosynthesis and
Respiration
1
Canopy Ps
Canopy Respiration
nSxx(n)/x
2
0.1
0.01
0.001
0.0001
0.0001
0.001
0.01
0.1
1
Frequency (cycles per hour)
10
nSxy(n)/xy
1
Covariance:
canopy photosynthesis and
respiration
0.1
0.01
nSxy(n)
0.001
-nSxy(n)
0.0001
0.0001
0.001
0.01
0.1
Frequency (cycles per hour)
1
Model Test: Daily Integration
calculated: -548 gC m-2 y-1
Measured: -668 gC m-2 y-1
1997
4
2
-2 -1
NEE (gC m d )
0
-2
-4
-6
-8
-10
-12
0
100
200
300
Day
-2 -1
NEE, calculated (gC m d )
4
2
0
-2
-4
-6
-8
-10
b[0]: 0.173
b[1]: 0.918
r ²:
0.556
-12
-12
-10
-8
-6
-4
-2
0
NEE measured (gC m-2 day-1)
2
4
Interannual Variability
Temperate Deciduous Forest: Canoak
Net Ecosystem C Exchange (g C m-2 yr-1)
-400
-450
-500
-550
CANOAK
Measured and Gap-Filled
-600
-650
1980
1982
1984
1986
1988
1990
Year
1992
1994
1996
1998
2000
Model Validation:
Who is Right and Wrong, and Why?
How Good is Good Enough?
Hansen et al, 2004 Ecol Monograph
ESPM 111 Ecosystem Ecology
Decadal Power Spectrum of CO2 and Water Vapor
Fluxes
1987-1997
Canoak
Temperate Deciduous Forest
1 year
1
daily CO2 flux
daily evaporation
124 days
nSxx/sx2
5.6 yrs
0.1
0.01
0.0001
0.001
0.01
f (cycles per day)
0.1
1
NEE and Growing Season Length
Temperate Deciduous Forests
0
-100
NEE (g C m-2 year-1)
-200
-300
-400
-500
-600
CANOAK, Oak Ridge, TN
Published Measurements, r2=0.89
-700
-800
120
140
160
180
200
Days with NEE < 0
220
240
GPP
CANVEG
EUROFLUX
Walker Branch Watershed
Duke: Ellsworth/Katul
Metolius Young: Law et al
Metolius old: Law et al
Harvard: Barford et al.
1800
GPP (gC m
-2
-1
yr )
1600
1400
1200
1000
800
600
400
0
100
200
300
Vcmax LAI/fpar
400
500
Component C Fluxes
1.2
1.1
Rplant/Ps
1.0
0.9
0.8
0.7
Gifford (1994)
0.6
0.5
0.4
0
100
200
300
Vcmax*LAI/fpar
10/19/2000
Rpl = Rleaf+Rbole+1/2 Rsoil
400
500
Light Use Efficiency
and
Net Primary Productivity
NPP=f Qp
Tree
Tree
Tree
Tree
LUE and Leaf Area
crop canopy
Vcmax = 100 mol m-2 s-1
50
LAI=5
LAI=3
40
LAI=1
Pc (mol m-1 s-1)
30
20
10
0
-10
0
500
1000
1500
PAR (mol m-2 s-1)
2000
LUE and Ps Capacity
crop canopy
LAI = 5
50
Vcmax = 100 mol m-2 s-1
Vcmax = 50
40
Vcmax = 25
Pc(mol m-1 s-1)
30
20
10
0
-10
0
500
1000
1500
-2
PAR (mol m
-1
s )
2000
Emergent Processes: Impact of Leaf Clumping on
Canopy Light Response Curves
Deciduous forest
Fc (mol m-2 s-1)
-40
(a)
-30
-20
-10
0
model: spherical leaves
10
0
500
1000
1500
2000
2500
-2 -1
Fc (mol m s )
-40
-30
(b)
-20
-10
measured
model: clumped leaves
0
10
0
500
1000
PPFD
1500
2000
(mol m-2 s-1)
2500
Role of Leaf Clumping on Annual C and H2O Fluxes
Temperate Deciduous Forest
-200
-1
NEE (gC m year )
-300
-2
-400
-500
Clumped Foliage
Spherical Foliage
-600
-700
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
950
Clumped Foliage
Spherical Foliage
900
-1
ET (mm year )
850
800
750
700
650
600
1980
1982
1984
1986
1988
1990
Year
1992
1994
1996
1998
2000
Interaction between Clumping and Leaf Area
Temperate Deciduous Forest
1.1
Fluxsph/Flux clp
1.0
0.9
0.8
0.7
canopy photosynthesis
E
NEE
0.6
0.5
0
1
2
4
3
LAI
5
6
7
How Sky Conditions Affect NEE?
Temperate Broad-leaved Forest
Spring 1995 (days 130 to 170)
10
Sunny days
diffuse/total <= 0.3
5
Cloudy days
diffuse/total >= 0.7
0
NEE (mol m-2 s-1)
-5
-10
-15
-20
-25
-30
-35
-40
0
500
1000
PPFD (mol m-2 s-1)
1500
2000
0
1
/2
Pdiffuse  2  P0 cos sin   d
2
LAI
0
Diffuse Radiation
Beam Radiation,  = pi/2
Beam Radiation, =pi/3
3
4
5
6
0.0
0.2
0.4
0.6
P0
0.8
1.0
NEEmeas / NEEstat [ - ]
1.4
A
Hainich (m = 0.54 +/- 0.06, r2 = 0.61)
Leinefelde (m = 0.45 +/- 0.11, r2 = 0.26)
1.2
1.0
0.8
0.6
NEEmeas / NEEstat [ - ]
1.4
Hainich (measured, m = 0.54 +/- 0.06, r2 = 0.61
Hainich (modelled, m = 0.51 +/- 0.05, r2 = 0.70
B
1.2
1.0
0.8
0.6
0.0
0.2
0.4
0.6
Rd/Rs [ - ]
Knohl and Baldocchi, JGR Biogeosci 2008
0.8
1.0
Diffuse light effect (slope) [ - ]
0.5
0.4
0.3
0.2
0
2
4
6
Leaf area index [m2 m-2]
Knohl and Baldocchi, 2008 JGR Biogeosci
8
10
30
A
-2
-1
CO2 Flux [µmol m s ]
25
20
15
10
Canopy photosynthesis
Net ecosystem exchange
5
4.4
0
8
B
4.0
3.8
4
3.6
3.4
2
Transpiration
Water use efficiency
0
0.1
0.2
0.3
0.4
0.5
Rd/Rs [ - ]
Knohl and Baldocchi, 2008 JGR Biogeosci
0.6
0.7
3.2
3.0
0.8
Water use efficiency
-1
[µmol CO2 mmol H2O]
6
-2
-1
Transpiration [mmol m s ]
4.2
Potential Impact of Aerosols/Clouds on NEE
Direct Radiation is reduced by 20%: NEE = -627 gC m-2 yr-1
Ambient Conditions: NEE= -553 gC m-2 yr-1
4
NEE (gC m -2 day-1)
2
0
-2
-4
-6
-8
-10
0
50
100
150
200
Day
250
300
350
400
Oxygen and NEE: Paleoclimates
4
NEE (gC m-2 d-1)
2
0
-2
-4
-6
LAI: 6
O2=35% : -224 gC m-2 y-1
-8
-10
0
50
100
150
200
Day
250
300
350
Do We Need to Consider Canopy Microclimate [C]
Feedbacks on Fluxes?
Canoak
Oak Ridge, TN 1997
Ave Daily LE,
q(z)= qa; T(z) = Ta
200
b[0]: -0.753
b[1]: 0.983
r ²:
0.9463
150
100
50
0
0
20
40
200
Ave Daily H,
q(z)= qa; T(z) = Ta
60
80
100
120
140
160
180
200
Ave Daily LE, f(z,w) (W m-2)
b[0] 2.72
b[1] 0.615
r ²
0.860
150
100
50
0
0
50
100
150
200
Ave Daily Fc,
q(z)= qa; T(z) = Ta; C(z)=Ca
Ave Daily H, f(z,w) (W m-2)
4
b[0] 0.0119
b[1] 0.985
r ²
0.998
2
0
-2
-4
-6
-8
-8
-6
-4
-2
0
Ave Daily Fc, f(z,w) (W m-2)
2
4
Leaf Temperature and Isoprene
Emission?
Temperate Broadleaved Forest
Days 100 to 273
0.12
0.10
1993
1981
1982
1984
1994
1997
1995
0.08
pdf
0.06
0.04
0.02
0.00
0
10
20
Tleaf
30
40
Leaf size, CO2 and Temperature: why oak
leaves are small in CA and large in TN
pdf tsun ambient
CO2=1500 ppm, 100 mm leaf
pdf tsun small leaves
0.08
sunlit leaves, daytime
Oak Ridge, TN 1997
Probability
0.06
0.04
0.02
0.00
0
10
20
Tleaf
30
40
Physiological Capacity and Leaf Temperature: Why Low
Capacity Leaves Can’t Be Sunlit::or don’t leave the
potted Laurel Tree in the Sun
Temperate Deciduous Forest
Sunlit leaves, 1997
0.08
probability density
Vcmax = 73 mol m-2 s-1
Vcmax = 10 mol m-2 s-1
0.06
0.04
0.02
0.00
0
10
20
Tleaf (oC)
30
40
Below Canopy Fluxes
300
Rnet (W m-2)
250
Ponderosa Pine
Forest Floor
D187-205, 1996
200
150
measured
calculated
100
50
0
-50
E (W m-2)
75
50
25
0
-25
200
-2
H (W m )
150
100
50
G (W m-2)
0
150
125
100
75
50
25
0
-25
-50
-75
0
4
Figure 15
enbmod.spw
12/8/99: laieff=1.8, zlitter=0.08
8
12
Time (hours)
16
20
24
Below Canopy Fluxes and Canopy Structure
and Function
0.30
0.25
QE,soil/QE
0.20
0.15
0.10
0.05
0.00
0
20
40
60
80
100
120
LAI * Vcmax
140
160
180
200
Impact of Thermal Stratification
Ra=f(stability)
Ra: neutral
300
250
200
150
100
50
0
-50
70
60
50
40
30
20
10
0
-2
H (W m )
-2
E (W m )
-2
Rn (W m )
Ponderos Pine
Forest Floor
150
125
100
75
50
25
0
-2
G (W m )
200
150
100
50
0
-50
0
4
8
12
Time (hours)
Figure 16
enmodstb.spw
12/8/99
16
20
24
Impact of Litter
Litter depth, 0.01 m
litter depth, 0.02 m
Ponderos Pine
Forest Floor
-2
H (W m )
-2
E (W m )
-2
Rn (W m )
litter depth, 0.05 m
300
250
200
150
100
50
0
-50
60
50
40
30
20
10
0
150
125
100
75
50
25
0
-2
G (W m )
150
100
50
0
-50
0
4
8
12
Time (hours)
Figure 17
enmodlit.spw
12/8/99
16
20
24
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