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.