g leaf f(D, ) - FACE

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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).
 = 2.37 gC MJ-1 APAR
- Eucalyptus plantation:  = 3.85 gC MJ-1 APAR
- Loblolly pine:
GPP
LAI
+20%
, LAI =constant
, Clumping =constant
-20%
GPP
GPP
-20%
GPP
, Clumping =constant
LAI
+20%
, LAI =constant
-20% Clumping +20%
-20% Clumping +20%
Clumping, LAI =constant
Clumping, LAI =constant
-20%

+20%
GPP
GPP
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.
-20%

+20%
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:  = 2.37 gC MJ-1 APAR ;
- Eucalyptus plantation:  = 3.85 gC MJ-1 APAR
Monthly GPP
GPP, gC m-2 month-1
1200
1000
800
600
Pine
400
Euca
200
0
1
2
3
4
5
6
7
month
8
9
10 11 12
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.
5800
Pine & Euca
Pine & Euca
GPP, gC m-2 year-1
GPP, gC m-2 year-1
6600
5600
6200
5800
5400
5400
5200
5000
5000
4600
4800
4200
LAI-20%
LAI+20%
α-20%
BASE
α+20%
Pine & Euca
GPP, gC m-2 year-1
5800
BASE
5600
Actual GPPs
5400
Pine = 2500 gC m-2 year-1
Euca = 3300 gC m-2 year-1
5200
5000
4800
Ω-20%
BASE
Ω+20%
“Productivity” equation
Light supply and light capture
GPP =  {f(D)f(T)f() f(CO2)}*APAR
Maximum potential photosynthesis rate
Canopy quantum efficiency
Constraints to photosynthesis
 = Aleaf / PAR
Aleaf = ca (1- ci/ca) * gleaf
At the same time, H2O vapor moves
out of the leaf by diffusion (but really
H2O vapor moves both directions)
CO2 moves from the air to the leaf
to the chloroplast by diffusion (but
really CO2 moves both directions)
Some definitions ….
(note that this leaf has
stomata only on the
“abaxial” or bottom side.
Some leaves also have
stomata on the adaxial,
or upper surface. Leaves
with stomata on both
sides are called
“amphistomatous”)
Ci = internal CO2 concentration. This
value can be measured (indirectly) with
common gas exchange instruments
Ca = external CO2 concentration
CO2 diffuses into leaves, moving
“down” a concentration gradient
The CO2
concentration at
the site of
fixation
approaches “zero”
Ca = 370-400 ppm?
Typical
CO2
concentration
of a C3 plant at
midday is about
270-300 ppm
The diffusive movement of CO2 into and out of a
leaf can be described by Fick’s Law:
Net flux = D concentration * conductance
[xo] =
concentration
of “x” on the
“outside” of
“barrier”
Net flux of
“x” = Fx
(a membrane or barrier with a
“conductance” to substance “x” = gx)
Fx = ([xo] – [xi]) * gx
[xi] =
concentration
of “x” on the
“inside” of the
“barrier”
• Conductance is a PROPERTY of leaf, kind of analogous
to its “porosity” to CO2 or H2O vapor. It is NOT a “rate”!!!
Conductance is the inverse of resistance. Both quantities
are commonly used. The symbol “g” is commonly used for
conductance, “r” for resistance


gH2O = conductance to water vapor

gCO2 = conductance to CO2

gs = stomatal conductance (usually to water vapor)

gl = total leaf conductance (usually to water vapor)
The units used for conductance and resistance can be very
confusing 
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)
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
f(T)
f(D,  )
• Temperature, T
f(T)
f(D,  )
Humidity and
vapor pressure deficit
The portion of total air pressure
that is due to water vapor is
water vapor pressure (ea)
measured in kPa
When air has no extra capacity
for holding water, the vapor pressure
is termed:
saturation vapor pressure
(es, units kPa)
Saturation vapor pressure is mostly a
function of air temperature
When air temperature falls without
a change in water content, the
point of condensation is called the
dew point temperature
Relative Humidity
is the ratio between actual
vapor pressure (ea)
and saturation vapor pressure (es)
RH = ea/es
Vapor Pressure Deficit (D)
is the difference between saturation
vapor pressure (es)
and actual vapor pressure (ea)
D = es - ea
Relative conductance
gleaf/gleaf-maximum
Stomata (canopy) conductance
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.
D (kPa)
(Breda et al. 2006)
D (kPa)
(Oren et al. 1999)
1
gleaf/gleaf-maximum
0
1
1
5
2
3
4
Vapor pressure deficit, D (kPa)
gleaf/gleaf-maximum= 1
0.6
gleaf/gleaf-maximum
gleaf/gleaf-maximum= -0.6 LnD +1
0
0
LnD (Vapor pressure deficit)
(Oren et al. 1999)
 = Aleaf/PAR
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
Stomata respond to changes in soil moisture ( ). During
water
shortage, when  drops below ca. 0.2, gleaf declines gradually
down to very low values
0.1
0.2
0.3
0.4
Soil moisture,  (m3 m-3)
Modified after Breda et al. (2006)
1
0.2
gleaf/gleaf-maximum
0.08
0
0.1
0.2
0.3
0.4
0.5
1
gleaf/gleaf-maximum = 1
gleaf/gleaf-maximum = s +b
gleaf/gleaf-maximum
s
0
0.1
0.2
0.3
0.4
0.5
GPP =  {f(D)f(T)f(CO2)f()}*APAR
 = Aleaf/PAR
Stomata respond to changes in soil moisture ( ).
During water shortage, when  drops below ca. 0.2,
gleaf declines gradually down to very low values
If  > 0.2, then gleaf/gleaf-max = ?  Aleaf/Aleaf-max = ?   / max = ?
If  < 0.2, then gleaf/gleaf-max= ?  Aleaf/Aleaf-max < ?   / max < ?
• Temperature, T
f(T)
f(D,  )
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?)
0.6
Ci/Ca
Warren and Dreyer (2006)
0
5
20
30
Temperature (C)
40
1
A/Amax
0
5
20
30
Temperature (C)
40
GPP =  {f(D)f(T)f(CO2)f()}*APAR
 = Aleaf/PAR
ci/ca
respond to changes in temperature (T). Under low or
high T, ci/ca increases gradually to high values
If T <20C or T> 30 C, then ci/ca = ?  Aleaf/Aleaf-max = ?   / max = ?
If 20 C<T <30C, then ci/ca = ?  Aleaf/Aleaf-max = ?   / max = ?
Final assignment:
Just calculate GPP and have fun experimenting !
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.
Warren C.R. and E. Dreyer. 2006. Temperature response of photosynthesis and internal
conductance to CO2: results from two independent approaches. Journal of Experimental
Botany 57:3057-3067.

g leaf f(D, ) - FACE

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