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February 6, 2001
ESPM254 Ecosystem Modeling
Lectures on Respiration and Decomposition
Respiration is another important ecological process which uses organic carbon to produce
CO2.
6CO2 + 6H2O = C6H12O6 + 6O2
30-70% of the carbon assimilated during photosynthesis is lost as CO2 through the
respiration process. Respiration is not simply a reverse process of photosynthesis. It is
more likely a continuous process of photosynthesis because it is through respiration
plants can maintain the ion gradients, protein synthesis and replacement, membrane
repair and develop new tissues. Photorespiration occurs with photosynthesis under
sunlight, which happens in the chloroplasts. For C3 plants, carboxylation of RuBP
produces two molecules of PGA (3-C) that are then utilized in the reactions of the Calvin
cycle to regenerate RuBP. Photorespiration happens when O2 compete RuBP.
Photoresiration is out of the range of this talk. We will focus on dark respiration, which
happens in mitochondria (Krebs cycle) and cytoplasm (Glycolysis or called EMP
pathway).
C6H12O6 + 6O2 = 6CO2 +6H2O +686,000 calories/mol
If you burn a mole glucose in the lab you get that amount of energy released as heat. If it
happens in living cells about two-thirds of the energy is captured and stored in ATP from
which it later can be released to do chemical work. In living cells, this process requires
about 25 enzymes and numerous steps. It can be as complex as this Figure 6.1, 6.2.
Aerobic respiration:
Glucose + O2 = CO2 + H2O + 686,000 calories/mol
Anaerobic respiration:
Anaerobic respiration happens under the limitation of O2 availability.
Glucose (no O2) = alcohol/organic acids + CO2 + 15,200 calories/mol
Autotrophic respiration (Ra) vs. heteotrophic respiration (Rh).
Factors affecting respiration
1. tissue age
small twigs have a greater respiration rate per unit of dry weight than big branches and
young leaves are higher than older leaves.
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2. water content
respiration rate is much small for dry seeds, and it immediately increases when the seeds
are wetted.
3. temperature
nonlinear relationship. Insert figure from Amthor Page 521.
4. mechanical injuries
repair cost
5. air pollution
Ozone increases respiration
Sulfur dioxide may increase or decrease respiration depending on dosage.
Nitrogen oxides (NO2) inhibits respiration.
Modeling respiration
Total respiration is the sum of growth and maintenance respiration. McGree (1970) and
Thornley (1970) first partitioned respiration into growth/construction and
maintenance/basal respiration. Growth respiration is required for synthesis of new
tissues; maintenance respiration provides the energy needed to keep existing tissues
healthy. Protein turnover is the maintenance process that uses the greatest amount of
respiratory products. The proportion of growth respiration to the total respiration varies
among species (Figure 6.3).
A simple model for whole plants:
Where R = whole-plant respiration rate (gC/day), M = biomass (amount of carbon in
structure plus long-term storage gC), dM/dt = absolute growth rate (gC/day), growth
respiration coefficient gC/gC added to M), and m = maintenance respiration coefficient
(gC/gBiomassC).
Maintenance respiration
1. Quadratic equation
R = a + bT + cT2
(regression to fit parameters)
Kinerson (1977, Oecologia 29, 1-10) fitted for stem and branch respiration
2. Exponential or Q10 equation
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van't Hoff (1898) developed an exponential equation to describe the temperature
dependency of chemical reactions. The Q10 function has been widely used to study
respiration process.
R Re
 ( T  Ts )
s
 RQ
s
T T
s
10
10
Linearization and using regression
Q
10

e
10

where Ts is reference temperature in degree Celsiss, and Rs is respiration rate at Ts. Beta
is a constant, a fitted parameter.
Although the Q10 function is successful in many studies, some people argue that Q10
itself is a function of temperature. Q10 values generally decrease with the increase of
temperature. See figure 1 of Kirschbaum 1995.
In some models, such as TEM, Q10 is allowed to vary with temperature. By assuming a
linear increase of Q10 from 2.0 to 2.5 between 5 and 0oC, a constant of 2.0 between 5 and
20oC, an linear decrease from 2.0 to 1.5 between 20 and 40oC, a third order polynomial
regression is fitted to adjust the Q10 values:
Q10=2.35665 - 0.05308t + 0.00238T2 - 0.00004T3
T is mean monthly air temperature (TEM).
3. Arrhenius equation
In 1884 van't Hoff derived an equation :
d (ln k )
E

C
dT
RT
2
Where k is the chemical reaction rate, R prime is the universal gas constant, 8.314 Jmol1 -1
K , T is the absolute temperature (K), E and C are constants for a particular reaction. In
1889, Arrhenius suggested that C=0, considering the energy distribution of reacting
molecules. He wrote:
k  de
E
RT
Linearization form
Where d is a constant and E is the activation energy, kJmol-1. The above equation can be
rewritten with a reference temperature:
R Re
E 1 1
(  )
R T Ts
s
Linearized form
4. Lloyd and Taylor equation
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R  Ae
 E0
T T0
Where T0 is a temperature between T and 0K, E0 is no longer an activation energy with a
unit of K, and A is a constant.
With a reference temperature the above equation can be rewritten:
R Re
 E0 (
1
1

)
T T0 Ts T0
s
R e
308.56 (
1
1

)
56.02 T  227.13
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Advantage: fitting better for most data sets
Disadvantages:
a. one more parameter
b. can not be linearized, therefore, least square technique can not be applied.
c. Using computer program to find the values for the parameters, so the solution may be
not unique.
5. Power function
R  AT
b
Where A and b are fitted parameters.
Linearized form
6. using plant nitrogen content
Rm and tissue N content are strongly correlated because most of the organic N in plants
is in protein and about 60% of Rm supports protein repair and replacement. Micheal
Ryan derived an empirical relationship based on a wide variety of species and plant
tissues:
Rm = 0.0106 N
Where Rm is maintenance respiration (moles C per hour), and N is plant Kjeldahl
nitrogen in moles of N. see Ryan 1991, Ecological Applications, figure 1, page 159.
Growth respiration (Rg)
Maintenance respiration is temperature dependent, and growth respiration is generally
considered to be independent of temperature and is proportional to GPP:
n
n
R   R   r r GPP
g
i 1
g ,i
i 1
g ,i
a ,i
Where rg,I is a growth respiration coefficient for plant component I, and ra,I is the carbon
allocation fraction for plant component i. Micheal Ryan used 25% for overall and root
growth respiration coefficient. In TEM 20% of GPP is applied to growth respiration.
Running and Coughlan (1988) applied a 40% of root carbon allocation fraction in their
model.
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Growth respiration can also be estimated based on construction cost, in g glucose g-1 of
tissue dry weight (Williams et al. 1987):
kN 180.15  1

C   (0.0698H  0.065)(1  A) 

14.0067 24  E

c
c
g
Where Cc is construction cost in g glucose g-1 Dry mass, Hc is the ash-free heat of
combustion in KJg DW-1, A is the ash content in g g DW-1, N is the organic nitrogen
content in g gDW-1, k is the oxidation state of the nitrogen substrate (-3 for ammonium,
and +5 for nitrate), and Eg is the growth efficiency of conversion (0.89 used by
Williams).
Construction cost estimates are based on the energy contained in chemical bonds of the
tissue combusted. When expressed in units of glucose required for synthesis of an equal
unit of dry weight, these estimates include both carbon incorporated structurally into the
tissue and that respired during construction. The energy cost of constructing organic
compounds includes both the carbon incorporated into structure and the metabolic energy
expended to assemble the compound. These cost vary substantially among compounds.
For example, 1 g lignin requires 2.5 g glucose, while 1 g cellulose requires only 1.2 g
glucose. Construction respiration is equal to the total carbon cost minus carbon
incorporated into structure. Growth/construction respiration in mol CO2 kg DW-1 is
calculated from construction cost in g glucose g-1 tissue by converting to units of CO2
and subtracting the carbon fraction of the tissue.
Heteotrophic respiration (Rh) / decomposition
Insert figure flow chart from Li Yiqing's thesis.
Modeling Rh
1. linear/nonlinear model
Fung et al. (1987, JGR, 92, d3, 2999-3015) used a linear relationship at global scale.
Figure 3 on page 3003. The Frankfurt Biosphere Model (FBM) uses this relationship
adjusted with soil moisture. Page 81 FBM paper.
2. moisture temperature combined models
R  A e   A Q
T
v
v
T / 10
10
A is a constant, theta is soil volumetric moisture (m3/m3, %), T is soil temperature at 10cm. Epron et al. 1999, Ann. For. Sci. 56:221-226.
Using Blodgett data Ye and I fitted a function:
R  A e   A Q
b
v
T
b
v
T / 10
10
We use a power function for soil moisture part.
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In TEM a more complex function is used for soil moisture adjustment:
Rh  K C f (M )e
d
s
0.0693T
v
Where Kd is Rh at 0oC, in new version of TEM Kd changes with litter quality, the C/N,
Cs is carbon storage in soils, f(Mv) is a function of soil volumetric moisture on
decomposition, T is monthly mean air temperature.
f ( Mv) 
( Mv  Mv min)( Mv  Mv max)
( Mv  Mv min)( Mv  Mv max)  ( Mv  Mvopt )
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Where Mvmin =0%, Mvopt = 50%, and Mvmax = 100% of field capacity.
3. process-based model
Fang and Moncrieff (1999, Agri. For. Meteor. 95: 225-236).
Figure 1 of Fang 's paper on Page 227.
4. century approach
Parton et al. (1987, Soil Sci. Soc. Am. J. 51: 1173-1179) developed the model to describe
the dynamics of soil organic matter. Figures from CASA model.
Litter production
Other methods in estimating soil respiration
1. isotope approach
Estimates the total soil surface CO2 efflux, and separates the root respiration from the
total. Amundson et al. (1998, Geoderma, 82: 83-114) has a good review on this topic.
2. Stream chemistry approach
Jones and Mulholland (1998, Ecosystems, 1:183-196) estimate the soil respiration (root +
decomposition) of a whole catchment in a hardwood forest stream.
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Energy balance
The sun has a temperature of about 6000K. Spectral curve of solar radiation (Rosenberg
page 9).
Short wave/solar radiation: 0.15-3.0 um. Solar constant 1370 Wm-2.
Long wave radiation: 3.0-100um.
Radiation incident upon a substance must either be transmitted through it, or be reflected
from its surface, or be absorbed. The conservation of energy.
     1
Transmissivity, reflectivity, and absorptivity.
Albedo (Fig. 1.22 Rosenberg, P47)
Transmissivity varies greatly among species and leaf ages of the same species. E.g.
aquatic leaves transit 4-8% of incident light, deciduous tree leaves and grasses may
transmit 5-10%.
Diffuse radiation: the portion of the incoming solar radiation that is reflected and
scattered, together with that multiple-reflected between the surface and the atmosphere
(back scattered). (D)
Beam/direct radiation: the portion of the incoming solar radiation that arrives at the
Earth's surface without being absorbed or diffused. (B)
PAR:
Par = 0.52 S (total radiation)
PAR = 0.42 Sb + 0.6 Sd
1. Lambert's cosine law
I = I0 cos (gama)
Fig. 1.7 in Oke on p15
2. Beer's Law
I
e
I
 kx
0
I0 is the initial flux density of the beam, I is the flux density after passing through a depth
x of a medium of extinction coefficient k.
3. Monsi and Saeki model
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Monsi and Saeki adapted the Beer's law and applied it to the penetration of light into
plant canopies.
I
e
I
 kF
0
K is an extinction coefficient for plant leaves and F is the downward cumulative leaf area
index.
This model assumes that the plant canopy is a homogeneous medium, sky is isotropic (all
radiation is diffuse), and k is a constant. Errors may be caused by : 1, 2, 3, light quality
changes, 4, sunflecks. K may range from 0.3-0.5 for vertical leaves and from 0.7-1.0 for
horizontal leaves. Chartier (1966) proposed an equation to improve the estimate of k:
K=(1-t) cos i for i<beta
T is a transmission factor for the leaf and wavelength considered, i is the angle of leaf
with respect to the horizontal, beta is the solar elevation eagle.
4. energy balance equation
a) for vegetation layer
Rn  LE  H  Qs  Qd  IA
Rn = net radiation, LE= latent heat, L is the latent heat of vaporization, at 20oC,
L=2.45MJ kg-1, so 1 mm of evaporation requires an energy density of 2.45 MJ m-2, Qs =
conduction to or from the underlying soil (soil heat flux), Qd = effective storage in
above-ground biomass, IA is photosynthetic energy.
b) for soil surface
Rn  LE  H  Qs
Rn = K - K + L + L
c) for a single leaf
Rnl  Ras  Ral  2Tl 4  2H l  LEl   l cl
dTl
M
dt
Rnl = total energy absorbed by the leaf (Wm-2), Ras = solar radiation absorbed by the leaf
(Wm-2), Ral = absorbed longwave radiation (Wm-2),  is the leaf emissivity,  is StefanBoltzman constant (5.67*10-8 Wm-2K-4), L is latent heat of vaporization, l is the specific
gravity of the fresh leaf (gm-3), cl is the specific heat capacity of the fresh leaf (Jg-1K-1), 
is the volume to surface area ratio of the leaf which has a dimension of distance and
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equals the thickness of the leaf for a flat leaf, M is the energy stored in biochemical
reactions / photosynthesis (Wm-2), t is time in s.
M < 5% of the net radiation (shortwave + longwave) absorbed by the leaf.
5. Diffusion Exchange of sensible heat, water vapor, and CO2 at the leaf level
H
 c (T  T )
a
p
l
a
r
bh
m e (T ) / RT  m e / RT
LE 
r r
*
v
l
l
v
bw
a
a
sw
m e / RT  m e / RT

r
*
s
v
l
v
a
for transpiration or,
a
bw

m e (T ) / RT  m e / RT
r
LE 
m e (T ) / RT  m e / RT
r
*
v
l
l
v
s
a
sw
*
v
l
l
v
a
a
for evaporation or condensation
bw
Fc  

C l / RTl  C a / RTa
* 10 6
rbc  rsc
C s / RTl  C a / RTa
* 10 6
rbc
C l / RTl  C s / RTl
* 10 6
rsc
a is air density (gm-3), cp is specific heat of air at constant pressure (Jg-1K-1), Tl and Ta
are leaf and air temperature (K, outside the laminar boundary layer of the leaf), rbh, rbw,
and rbc are the leaf boundary layer resistances (sm-1), rsw and rsc are the stomatal
resistance for water vapor and CO2 (sm-1), H, LE, and Fc are the source density for heat,
water vapor, and CO2 (molm-2 leaf area s-1), mv is molar mass of H2O (18 g mol-1), R is
universal gas constant (JK-1mol-1), ea and Ca are the water vapor and CO2 partial
pressure outside the laminar boundary layer (Pa), Cl is CO2 partial pressure in the
stomatal cavity (Pa), es and Cs are the water vapor and CO2 partial pressure at leaf
surface, e*(Tl) is the saturation vapor pressure at a temperature of Tl, given by Buck
1981:

e * (T )  (1.0007  3.46  10  Pa)  611.21e
8
17.502 ( T  273.15 )
T  32.18
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Pa is atmospheric pressure (Pa).
There are 3 unknown variables in the previous equations, which are Tl, rsw, and Cl
(internal CO2 partial pressure). Therefore, three independent equations are required to
solve for the 3 variables. The three independent equations are based on leaf energy
balance, stomatal conductance model, and biochemical model of photosynthesis. By
coupling the three equations we get:


 f (T , g , C )  2T 4  2 H  LE   c  dTl  M  R  R  0
l
l
l
l l
as
al
 1 l sw l
dt

g s1 Fc Pa

 g s0
 f 2 (Tl , g sw , C l ) 
Ds

(C s  )(1 
)

D0

 f (T , g , C )   C l / RTl  C a / RT a *10 6  F  0
c
 3 l sw l
rbc  rsc
In the Ball-Berry Leuning model, gs0 is stomatal conductance for water vapor when Fc is
0. Pa is atmospheric pressure (Pa), Ds is vapor pressure deficit at leaf surface (Pa), D0
and gs1 are empirical constants,  is CO2 compensation point (Pa), and Cs is calculated
as:
Cs  Ca
Tl
g sc
T

(Cl  Ca l )
Ta g sc  g bc
Ta
6. Shortwave radiation transfer in plant canopies
Factors have to be considered:
a) LAI
b) Leaf characteristics (reflectivity, transsimity)
c) Leaf orientation (facing the Sun or not, heliotropic leaves, sunflowers receive about
40% more solar radiation than would a plant with a fixed leaf distribution)
d) Leaf angle (leaf angle distributions with respect to the sun also differ by species.
Vertical leaves receive 44% less solar radiation than horizontal leaves)
e) Leaf clumping
f) Light quality in canopies
7. Longwave radiation transfer in plant canopies
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More complex because leaf elements are also longwave radiation sources. And even
more complex because the leaf temperature from the leaf energy balance equation
depends on the temperature of the concerned leaf and its neighboring leaves.