Energy balance of soil-plant-air system
Q* = QH + QE + QG +QS + QP + QA
QS - physical storage change due to
absorption or release of heat from air,
soil or plant biomass
QP - biochemical energy storage due to
photosynthesis
QA - horizontal sensible and latent heat
transport
Water balance of soil-plant-air system
p = E + r + S
S – net water storage of air, soil and plants
(internal and external)
Photosynthesis, P:
6CO2 + 6H2O + sunlight  C6H12O6 + 6O2
Respiration, R:
C6H12O6 + 6O2  6CO2 + 6H2O + energy
Surface
Radiation
Balance
for a
Plant
Canopy
Heat Storage by Photosynthesis
The net rate of CO2 assimilation (kgm-2s-1)
P = P – R
Heat storage by net photosynthesis is, therefore:
QP =  P
where  is the heat of assimilation of carbon (Jkg-1)
Values are very small compared to other fluxes
- up to ~10 Wm2 during the day
- about -3 Wm2 during the night
Transpiration through stomata
•increases the QE flux
•prevents overheating
•induces moisture and nutrient transport
Stomata
-
-
open during the day for gas exchange
closed at night
stomata open when there is enough
light, and appropriate levels of moisture,
temperature, humidity and internal CO2
concentration
10-30 m long, <10 m wide
50-500 stomata mm-2
Stomate (wheat)
Degree of opening
depends on light
intensity, moisture
availability,
temperature, humidity
and internal CO2
concentration
Stand Architecture and the Active Surface
Position of active surface lies at the zero plane
displacement:
d  2/3 h
Modified logarithmic wind profile equation:
uz = (u*/k) ln (z-d/z0)
For simplicity, energy exchange is considered at
a plane at the top of the system (‘big leaf’ approach)
Plant canopies
elevate the
position of the
active surface
Wavelength Dependence of Leaves
Leaves absorb photosynthetically-active radiation (PAR)
effectively for carbon assimilation
Better absorption in blue and red bands than in the green band
Leaves reflect and transmit near infra-red radiation (NIR)
This helps limit heating
Leaves are very efficient emitters of longwave radiation
due to their high water content (absorb L too)
This helps the leaves shed heat effectively
Leaf Radiation Balance
Q*leaf =
[(Kin(t) + Kin(b))(1--)]+
[(Lin(t)-Lout(t))+(Lin(b)-Lout(b))]
=
K*(t)+K*(b)+L*(t)+L*(b)
=
K*leaf + L*leaf
Leaf Energy Balance
Q*leaf
=
=
(QH(t)+QH(b))+(QE(t)+QE(b))
QH(leaf) + QE(leaf)
Sensible Heat Flux and Leaf Temperature
QH = Ca (T0-Ta)/rb
- rb is the diffusive resistance the laminar sublayer
-rb value higher for larger leaves as laminar layer grows
-higher resistance during calm conditions
T0 = Ta + (rb/Ca)  (Q*leaf – QE leaf)
-Air temperature is important for leaf temperature
-Leaf may be warmer or cooler than the air
-If rb is large, Q*leaf – QE leaf largely determine T0-Ta
-Hot, dry environments: plants develop small leaves, with
high albedo,or orient leaves vertically near solar noon
-Very cold environments: leaves grow close to ground,
have large rb, and, in the arctic, touch the warmer ground
The large leaf problem
(heats up more during
the day and cools off
more at night)
Number of degrees by
which the leaf temperature
exceeds the air temperature
during the daytime
Evapotranspiration from a Leaf
-Depends on vapour pressure deficit and diffusive resistance
of the laminar sublayer
E = (*v(To) - va)/ (rb + rst)
- rst is a variable stomatal resistance
Carbon flux from a Leaf
Fc = (ca - ci)/ (rb + rst)
Carbon dioxide must travel from atmosphere,
through mesophyll to chloroplasts
cuticle
upper epidermis
palisade mesophyll
spongy mesophyll
lower epidermis
Photosynthesis Measurement
Photosynthesis
Net photosynthesis (molm-2s-1)
Cloud forest, Cauca, Colombia
16
14
Miconia sp. (Melastomataceae)
12
10
1450 masl
8
6
4
2150 masl
2
0
-2 0
500
1000
1500
PAR (molm-2s-1)
2000
2500
40
VPD (kPa)
Tleaf (C)
35
30
25
20
180
210
240
3
2
1
270
20
gs (mmol m-2 s-1)
Amax (mol m-2 s-1)
150
16
12
8
4
0
120
150
180
210
240
270
120
150
180
210
240
270
120
150
180
210
240
270
120
150
180
210
240
270
800
600
400
200
0
120
150
180
210
240
270
E (mmol m-2 s-1)
0.9
ci/ca
4
0
120
0.8
0.7
0.6
10
8
6
4
2
0
150
180
210
240
270
Amax/E (mmol mol-1)
120
Amax/gs (mmol mol-1)
Photosynthesis
in Populus angustifolia
James, in 2006, at
Pearce, Corners
Cottonwood Grove.
5
Male
Female
0.08
0.06
0.04
0.02
0.00
120
150
180
210
DOY
240
270
5
4
3
2
1
0
DOY
Photosynthesis in
Artemisia cana
(sagebrush), Prunus
virginiana (chokecherry),
Ribes aureum (golden
currant) and Rhus
trilobata (skunkbush).
60
Light-saturated net
photosynthesis (Amax)
rate rebounds with
early autumn moisture
impulse & low VPD
SW-facing
Θv (m3·m-3)
50
NW-facing
40
30
20
10
0
May
Amax (µmol·m-2·s-1)
Amax (µmol·m-2·s-1)
Jul
Aug
Sep
Oct
16
16
12
8
4
SE
NW
0
May
-4
Jun
Jun
12
8
4
SW
NE
PK
0
Jul
Aug
Sep
Oct
May
-4
Jun
Jul
Aug
Sep
Oct
Leaf temperature (ºC)
Leaf Temperature
34
34
30
30
26
26
22
22
18
18
SW
SE
14
10
NE
14
NW
May
Jun
Jul
Aug
Sep
10
PK
May
Jun
Jul
Aug
Sep
VPD (kPa)
Chamber H2O Vapour Pressure Deficit
5
5
4
4
SW
NE
PK
3
3
2
2
SE
1
0
1
NW
May
Jun
Jul
Aug
Sep
0
May
Jun
Jul
Aug
Sep
Net photosynthesis rate decreases in hot,
dry air (large VPD reduces Amax)
16
Amax (µmol CO2·m-2·s-1)
SE
14
SW
12
NW
NE
10
8
6
4
PK
VPD
Amax = -3.7311 (VPD) + 13.393
(0.9<VPD<4.1; R2 = 0.51)
2
0
-2 0
5
4
3
2
1
H2O Vapour Pressure Deficit (kPa)
Late summer acclimation to drought and
VPD stress: Stomatal closure reduces
water loss, but also lowers photosynthesis
rates. Recovery by early October.
300
300
SW
NE
NW
250
Gs (mmol·m-2·s-1)
Gs (mmol·m-2·s-1)
SE
200
150
100
50
0
May
Jun
Jul
Aug
Sep
Oct
250
PK
200
150
100
50
0
May
Jun
Jul
Aug
Sep
Oct
ci/ca ratios peaked in mid-season
and were more variable in S-facing
species
0.90
0.90
0.80
SE
NE
NW
SW
Poly. (NW)
0.80
0.70
0.60
R = 0.71
ci/ca
ci/ca
Poly. (SE)
R2 = 0.38
Poly. (SW)
2
Poly. (NE)
0.70
R2 =1.00
0.50
03-May 23-May 12-Jun 02-Jul
DOY
R2 = 0.72
0.60
22-Jul 11-Aug 31-Aug
0.50
03-May 23-May 12-Jun 02-Jul
DOY
22-Jul 11-Aug 31-Aug
•Due to stomatal closure, less water is transpired in August
and early September, despite high temperature and VPD.
•Contrasts with Fischer et al. (2002), who found that tight stomatal
control led to similar E during wet and dry periods in Limber Pine
of an Arizona meadow
•Photosynthetic WUE is high in cool autumn temperatures
(low E, but moderately high Amax)
5
5
SE
SW
NW
4
E (mmol·m-2·s-1)
E (mmol·m-2·s-1)
NW
3
2
1
0
3
2
1
0
May
Jun
Jul
Aug
Sep
Oct
PK
4
May
Jun
Jul
Aug
Sep
Oct
12
10
SE
NW
8
6
4
2
0
-2
-4
-6
May
Jun
Jul
Aug
Sep
Oct
WUE (µmol CO2·mmol-1 H2O)
WUE (µmol CO2·mmol-1 H2O)
•Seasonal pattern of
photosynthetic water
use efficiency (Amax/E)
12
10
SW
8
NE
PK
6
4
2
0
-2
-4
-6
May
Jun
Jul
Aug
Sep
Oct
a.
20
Modelled LMCF
Observed LMCF
Pn
16
Modelled UMCF
Observed UMCF
µmol CO2
m2 s 1
LMCF
RMSE = 1.10 µmolm-2 s -1
R2 = 0.77; N=820
12
8
UMCF
RMS E = 1.69 µmolm-2 s -1
R2 = 0.55; N=500
4
0
0
600
1200
1800
2400
PAR (µmolm-2 s -1 )
-4
b.
14
Modelled LMCF
Observed LMCF
12
Modelled UMCF
Pn
Observed UMCF
10
µmol CO2
m2 s 1
8
6
4
2
0
0
-2
50
100
150
PAR (µmolm-2 s -1 )
200
250
Anthurium sp.
25
Pn
The short-term
influence of
increased
CO2 concentration.
Cecropia sp.
25
Pn
20
mol 15
m2 ·s 10
20
15
2xCO2
2xCO2
Ambient
Ambient
Mod 2xCO2
Mod Ambient
Mod Ambient
5
5
0
0
0
-5
0
500 1000 1500 2000 2500
PAR
Mod 2xCO2
10
-5
( mol·m-2 ·s -1 )
500
1000 1500 2000 2500
PAR ( mol·m-2 ·s -1 )
Clusia sp.
25
Also:
Stomatal
conductance
tends to decrease
(enough CO2),
leading
to increased
water use
efficiency
Pn
Miconia sp.
25
Pn = 0.0442 (PAR) - 0.3025
R2 = 0.93; 7<PAR<570
20
Pn
15
20
15
2xCO2
Ambient
Ambient
2xCO2
10
Linear (Ambient)
Pn = 0.0364 (PAR) - 0.2994
Mod Ambient
Linear (2xCO2)
R2 = 0.88; 30<PAR<350
5
5
0
0
0
-5
200
PAR
400
0
600
-5
( mol·m-2 ·s -1 )
Psychotria sp.
25
Pn
Mod 2xCO2
10
Pn
15
2xCO2
PAR
800
1200
( mol·m-2 ·s -1 )
All genera
25
20
400
20
15
2xCO2
Ambient
Mod 2xCO2
10
Mod Ambient
5
Ambient
Mod Ambient
5
0
0
0
-5
Mod 2xCO2
10
500 1000 1500 2000 2500
PAR
( mol·m-2 ·s -1 )
0
-5
500 1000 1500 2000 2500
PAR ( mol·m-2 ·s -1 )
Leaf-level net photosynthesis modelling
  PAR  Pmax
Pn 

  PAR  Pmax
(Thornley and Johnson, 1990)
Plant Canopies and Carbon Dioxide Flux
At night:
- flux directed from canopy to the atmosphere
- respiration from leaves, plant roots, soil
Daytime:
- CO2 assimilation rate exceeds respiration rate
Seasonal Variation in Temperate Environments
Spring:
Assimilation increases with leaf area index and
increasing solar radiation availability/day length
Midsummer: Fc drops despite sun, due to soil moisture
depletion – flux higher in morning
Winter:
Small, negative flux
Vertical flux of
carbon dioxide
(FC) over a prairie
grassland
What causes the
midday minimum in
August?
Canopy Radiation Budget
-
Incident light greatest at crown and decreases
logarithmically with depth in the canopy
-
Approximated by Beer’s Law for canopy extinction
K(z) = K0e-kLAI
(z)
k is a canopy-specific extinction coefficient (0.4-0.9)
(‘a’ in Oke)
LAI is the leaf area index (m2 leaf m-2 ground) accumulated
from the top of the canopy to the level in question
(‘A1(z)’ in Oke)
Q* influences
the temperature
and humidity
structure within
a canopy
Energy balance
over an English
barley field
QE dominated in
dissipating radiative
surplus
cloud cover
Leaf temperature
remained cool
due to evaporation
Decreasing light
intensity or increasing
water stress
Dew present
Net canopy photosynthesis (Pc)
  PAR  Pmax [1  e
Pc 
  k  PAR  Pmax
(  k  LAI )
]
   LAI
Charles-Edwards (1986)
Photosynthetically-active radiation
(“direct” portion,0.3-0.4 CI, 0400h-1200h)
0400-0500h
0500-0600h
0600-0700h
0700-0800h
0800-0900h
0900-1000h
1000-1100h
1100-1200h
Effect of LAI on Pc
Relative productivity (%)
20
10
0
-10
-20
-30
-40
August
-50
November
-60
-70
0
1
2
3
4
5
6
Leaf Area Index (LAI)
7
8
Relative productivity (%)
Effect of Respiration Parameter on Pc
40
30
20
10
0
-10
-20
-30
-40
-50
-60
August (1400m)
November (1400m)
August (1600m)
November (1600m)
0
0.2
0.4
0.6
0.8
1
Canopy leaf respiration rate (molCm-2 s -1 )
Effect of Extinction Coefficient, k, on Pc
Relative productivity (%)
10
5
0
-5
-10
August
-15
November
-20
-25
0.2
0.4
0.6
0.8
Extinction coefficient, k
1
Soil respiration measurements
There is a much easier way to
assess productivity…
A micrometeorological solution:
Eddy correlation
NEE = A + R
A=
Gross Photosynthesis (-)
R=
Total Ecosystem
Respiration (+)
Night-time NEE = Total Ecosystem Respiration
NEE (mol CO2m-2s-1)
10
8
Mer Bleue Bog,
Eastern Ontario
6
4
2
0
-2 0
-4
-6
5
10
15
20
NEE = 0.1223 (soil temp) - 0.0525
2
-8
-10
R = 0.2477
Soil Temperature at 5cm depth (C)
25
30
NEE (mol CO2m-2s-1)
Daytime NEE
Gross Photosynthesis – Total Ecosystem Respiration
8
4
0
-4 0
1000
2000
-8
-12
Photosynthetically-active radiation (molm-2s-1)
CO2 rich
Dry, Cool
Low CO2
Humid, Warm
Source: Dr. Larry Flanagan
Footprint: Area affecting measurements at the tower varies with
wind speed, wind direction, roughness, stability etc.
Top View
c
The black area has the greatest
influence on tower measurements
Profile
c
Dist ance
View