CO2 moves from the air to the leaf to the chloroplast by diffusion (but really CO2 moves both directions)
At the same time, H2O vapor moves out of the leaf by diffusion (but really H2O vapor moves both directions)
The diffusive movement of CO2 into and out of a leaf can be described by Fick’s Law:
Net flux = concentration * conductance
(a membrane or barrier with a “conductance” to substance “x” = gx)
Net flux of “x” = Fx
[xo] = concentration of “x” on the “outside” of “barrier”
[xi] = concentration of “x” on the “inside” of the “barrier”
Fx = ([xo] – [xi]) * gx
Applying Fick’s Law to carbon assimilation :
Net C assimilation = (ca-ci) * gleaf
Or: Aleaf = ca (1- ci/ca) * gleaf
(Norman 1982; Franks & Farquhar 1999)
Modeling Canopy Photosynthesis(GPP)
GP
P (
Mg
ha-1
)
Absorbed PAR (MJ ha-1)
α max
(CO2)
(soil moisture)(D, temperature)
How can we describe the response of α to changes in the environment?
α = A / PAR
α is light-use efficiency; units: g C / Joule light energy
A is for C assimilation (or photosynthesis, GPP of a leaf); units: g C / m2 leaf area
PAR is light on the leaf surface (think APAR); unit: Joule light energy / m2 leaf area
We know a lot about the response of A to changes in the Environment!!!
A = gs * (Ca – Ci)
This is Fick’s diffusion equation describing that the flux (here of CO2) is proportion to the conductance (here leaf conductance through the stomata) and the difference in concentration (here of CO2 between the inside and outside of the leaf)
How can we describe the response of α to changes in the environment?
We begin with α = A / PAR
And know that A = gs * (Ca – Ci)
Which can be re-written A = gs * Ca * (1 – Ci / Ca)
Now we can ask:
What do we know about the responses of gs, Ca, and Ci / Ca to changes in the environment??
As a simple example, we begin with Ca.
Two examples of the RELATIVE change in A (and therefore α):
(1)only Ca changes
(2)changes in Ca affects gs and Ci / Ca
Begin with setting the ratio of response
AE = gsE * CaE * (1 – Ci / Ca)E
AA = gsA * CaA * (1 – Ci / Ca)A
R =
(1)only Ca changes – increases by 50%
R = 1 * 1.5 * 1 = 1.5;
α increases by a factor 1.5
(2) Ca increases 50%; plants respond by decreasing gs by 10% and increasing Ci / Ca (from 0.7) by 5%
R = 0.9 * 1.5 * ((1 – 0.735) / (1 – 0.70)) = 0.9 * 1.5 * 0.88 = 1.19
α increases by a factor ~1.2
Modeling Canopy Photosynthesis(GPP)
GP
P (
Mg
ha-1
)
Absorbed PAR (MJ ha-1)
α max
(CO2)
(soil moisture)(D, temperature)
Factors affecting net assimilation (A) and stomatal conductance (gleaf):
• Vapor pressure deficit, D (that is related to the humidity of the air)
• Soil Moisture, • Temperature, T
Aleaf = ca (1- ci/ca) * gleaf
f(D, )f(T)
Factors affecting net assimilation (A) and stomatal conductance (gleaf):
• Vapor pressure deficit, D (that is related to the humidity of the air)
• Soil Moisture, • Temperature, Temperature, TT
Aleaf = ccaa (1- (1- ccii/c/caa)) * gleaf
f(D, )f(T)
Stomata respond to the vapor pressure deficit between leaf and air (D). Stomata
generally close as D increases and the response is often depicted as a nonlinear
decline in gs with increasing D.
(Breda et al. 2006) (Oren et al. 1999)
Sto
mat
a (c
anop
y) c
ondu
ctan
ce
D (kPa)
Rel
ativ
e co
nduc
tanc
eg l
eaf/g
leaf
-max
imum
D (kPa)
LnD (Vapor pressure deficit)
Vapor pressure deficit, D (kPa)
0
1
0
1
Relative conductancegleaf/gleaf-maximum
1
0
532 4
Relative conductancegleaf/gleaf-maximum
gleaf/gleaf-maximum= -0.6 LnD +1
0.6
gleaf/gleaf-maximum= 1
(Oren et al. 1999)
Stomata respond to the vapor pressure deficit between leaf and air (D). Stomata generally close as D increases and the
response is often depicted as a nonlinear decline in gs with increasing D.
If D <1, then gleaf/gleaf-max = 1 Aleaf/Aleaf-max = 1 / max = 1
If D > 1, then gleaf/gleaf-max= -0.6 LnD +1 Aleaf/Aleaf-max < 1 / max < 1
GPP = {f(D)f(f(TT)f()f() ) f(COf(CO22))}*APARAPAR = Aleaf/PAR
Aleaf = ca (1- ci/ca) * gleaf
Stomata respond to changes in soil moisture ( ). During water
shortage, when drops below ca. 0.2, gleaf declines gradually
down to very low values
Soil moisture, (m3 m-3)
0.1 0.30.2 0.4
Modified after Breda et al. (2006)
Soil moisture, (m3 m-3)
0
1
0.1 0.50.30.2 0.4
gleaf/gleaf-maximum = s +bRelative conductancegleaf/gleaf-maximum
gleaf/gleaf-maximum = 1
s
0
1
0.1 0.50.30.2 0.4
0.2
0.08
Soil moisture, (m3 m-3)
Relative conductancegleaf/gleaf-maximum
If > 0.2, then gleaf/gleaf-max = ? Aleaf/Aleaf-max = ? / max = ?
If < 0.2, then gleaf/gleaf-max= ? Aleaf/Aleaf-max < ? / max < ?
GPP = {f(f(DD)f()f(TT)f(CO)f(CO22))f()}*APARAPAR
= Aleaf/PARAleaf = ca (1- ci/ca) * gleaf
Stomata respond to changes in soil moisture ( ). During water shortage, when drops below ca. 0.2, gleaf declines gradually down
to very low values
Factors affecting net assimilation (A) and stomatal conductance (gleaf):
• Vapor pressure deficit, Vapor pressure deficit, DD (that is related to (that is related to the humidity of the air)the humidity of the air)
• Soil Moisture, Soil Moisture, • Temperature, T
Aleaf = ccaa (1- ci/ca) * * ggleafleaf
f(D, )f(T)
Temperature effect on Ci/Ca and on net assimilation
Ci : Typical CO2 concentration is about 270-300 ppm
Ca = external CO2 concentration (Ca = 380-400 ppm?)
Temperature (C)
0
A/Amax
Ci/Ca
5 3020 40
Temperature (C)
0
0.6
5 3020 40
1
If T <20C or T> 30 C, then ci/ca = ? Aleaf/Aleaf-max = ? / max = ?
If 20 C<T <30C, then ci/ca = ? Aleaf/Aleaf-max = ? / max = ?
GPP = {f(f(DD))f(T)f(CO2)f(f())}*APARAPAR
= Aleaf/PARAleaf = ca (1- ci/ca) * gleaf
ci/ca respond to changes in temperature (T). Under low or high T, ci/ca increases gradually
to high values
Next week’s assignment:1) Using clumping indexes, LAI and values for a conifer stand (Loblolly pine forest, Duke Univ.) and for a Eucalyptus plantation (New Zealand), calculate their Monthly GPP (potential GPP).
- Loblolly pine: = 0.05 molC molAPAR-1 (2.74 gC MJ-1 APAR )
- Eucalyptus plantation: = 0.07 molC molAPAR-1 (3.85 gC MJ-1 APAR)
2) Assuming that all of the above parameters vary by plus or minus 20%, calculate how Annual GPP would be affected for each forest type.
GP
P
-20% +20%LAI
, Clumping =constant
GP
P
-20% +20%Clumping
, LAI =constant
GP
P
-20% +20%
Clumping, LAI =constantG
PP
-20% +20%LAI
, Clumping =constant
GP
P
-20% +20%Clumping
, LAI =constant
GP
P
-20% +20%
Clumping, LAI =constant
Lobl
olly
pin
e
Euc
alyp
tus
References
Breda N. et al. 2006. Temperate forest trees and stands under severe drought: a review. Annals of Forest Science. 63:625-644.
Dye, P.J. et al. 2004. Verification of 3-PG growth and water-use predictions in twelve Eucalyptus plantation stands in Zululand, South Africa. For. Ecol. Management. 193:197–218
Franks PJ, Farquhar GD. 1999. A relationship between humidity response, growth form and photosynthetic operating point in C3 plants. Plant, Cell Environment 22:1337–1349.
Norman J. M. 1982. Simulation of microclimates, in Biometeorology in integrated pest management, edited by J. L. Hatfield and I. J. Thomason, p. 65-99, Academic, New York.
Oren R. et al. 1999. Survey and synthesis of intra- and interspecific variation in stomatal sensitivity to vapour pressure deficit. Plant, Cell and Environment 22: 1515-1526
Waring W.H. and S.W. Running 1998. Forest ecosystem analysis at multiple scales. 2nd Ed. Academic press. San Diego, CA 370p.