Post on 24-Dec-2015
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
Lsu
n
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,Rnir
f()
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,
z
F
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
pCqTIf
zpCqTIfzCS
),,,(
)(),,,(),(
bP =G
dP
dL(-
L G)
sinexp
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
Heig
ht
(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
Lea
f A
rea
Ind
ex
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
Heig
ht
(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
gh
t (m
)
0
5
10
15
20
25
Ci/Ca sunlit
Ci/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 D
ata
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
ESPM 228 Adv Topics Micromet & Biomet
Higher Order Closure Equations and Unknowns
So
urc
e P
rofi
le
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( )
DC C
S ziji 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
gh
t
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
He
igh
t (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
Hei
ght (
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
Hei
ght
(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
Heig
ht
(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
Heig
ht
(m)
0
10
20
30
40
50
60
70
80
Physiology
Photosynthesis
Stomatal Conductance
Transpiration
Micrometeorology
Leaf/Soil Energy Balance
Radiative Transfer
Lagrangian 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
AaI
b cI
dC
e fC
aA bA cA d
~ ;
3 2 0
Leaf Temperature
Transpiration
Photosynthesis
Respiration R Td ~ exp( )
X Data
0 2 4 6 8 10 12
Y D
ata
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
• lE: 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 TE P
m m gs l a s l aa v a w
( ) ' ( )( / )
Derivation
1: Leaf Energy Balance
2: Resistance Equations for H and lE
3: Linearize T4 and es(T)
T T T T Tl a a l a4 4 34 ( )
E
m m g e T e
Pv a a w s l a
( / ) ( ( ) )
ESPM 129 Biometeorology 38
f x f x x xdf
dx( ) ~ ( ) ( )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 Te
T Ts l x a s l as
l a( ) ( ) ' ( )"
( ) 2
2
Linearize the Saturation Vapor Pressure function
e Tde T
dTss( )'( )
e Td e T
dTss( )' '( )
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
Ca
rbo
xyl
ati
on
ra
te
(m
ol
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 regeneration
by 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 K
K
If Wj is minimal, then
* *
*0.5 c
c o jc 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 K
K
*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
(m
ol 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
NE
E ( m
ol
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
NE
E c
om
pu
te
d (
mo
l 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
Week
0 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
ca
lcu
late
d (
W m
-2)
0
100
200
300
400
500
Coefficients: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
nS
wc(
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 x
x(n
)/
x
2
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 x
y(n
)/
x y
0.0001
0.001
0.01
0.1
1
10
nSxy(n)
-nSxy(n)
Covariance:canopy photosynthesis andrespiration
1997
Day
0 100 200 300
NE
E (
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
NE
E,
ca
lcu
late
d (
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
han
ge
(g C
m-2
yr-1
)
-650
-600
-550
-500
-450
-400
CANOAKMeasured and Gap-Filled
Temperate Deciduous Forest: Canoak
ESPM 111 Ecosystem Ecology
Hansen 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
nS x
x/s x
2
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
NE
E (
g C
m-2 y
ea
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/fpar
0 100 200 300 400 500
GP
P (
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/fpar
0 100 200 300 400 500
Rp
lan
t/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= e f Qp
PAR (mol m-2 s-1)
0 500 1000 1500 2000
Pc (
mo
l 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
Pc( 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
Fc (m
ol m
-2
s-1 )
-40
-30
-20
-10
0
10
measured
(b)
0 500 1000 1500 2000 2500
Fc ( m
ol 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
NE
E (g
C m
-2 ye
ar
-1 )
-700
-600
-500
-400
-300
-200
Clumped FoliageSpherical Foliage
Y ear
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
ET
(m
m ye
ar
-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
LAI
0 1 2 3 4 5 6 7
Flu
xsp
h/F
lux
clp
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
NE
E ( m
ol
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
LA
I0
1
2
3
4
5
6
Diffuse Radiation
Beam Radiation, = pi/2
Beam Radiation, =pi/3
2
0
02/
diffuse dsincosPP
NE
Em
eas
/ NE
Est
at [
- ]
0.6
0.8
1.0
1.2
1.4Hainich (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
ligh
t e
ffec
t (s
lop
e)
[ -
]
0.2
0.3
0.4
0.5
Knohl and Baldocchi, 2008 JGR Biogeosci
CO
2 F
lux
[µm
ol 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
Tra
nsp
iratio
n [m
mo
l m-2
s-1
]
0
2
4
6
8
Wa
ter
use
effi
cie
ncy
[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
NE
E (
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
NE
E (
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
Av
e D
ail
y 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
Av
e D
ail
y 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
Av
e D
ail
y F
c,
q(z
)= q a; T
(z)
= T
a; C
(z)=
Ca
-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
pd
f
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
Tleaf
0 10 20 30 40
Pro
ba
bil
ity
0.00
0.02
0.04
0.06
0.08
pdf tsun ambient CO2=1500 ppm, 100 mm leaf
pdf 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
pro
ba
bil
ity d
en
sit
y
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
Rn
et (
W m
-2
)
-50
0
50
100
150
200
250
300
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 15
enbmod.spw
12/8/99: 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
QE
,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 )
-50
0
50
100
150
200
Ponderos PineForest Floor
Figure 16
enmodstb.spw
12/8/99
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 17
enmodlit.spw
12/8/99
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