122
maining SOM (Hayes 1982). The isotope effect is
proportional to the ratio of the decay constants of
the rare (k*) and common (k) isotopes, and can be
incorporated into Equation 8Ab above by adding a
fractionation term, a, to the decomposition of organic matter. For a given process, the fractionation
factor a is defined as the instantaneous ratio of the
isotopic composition of products and reactants:
k*
~rod
- = a = - -
k
~eoc!
(8.8)
Values of a in processes relevant to SOM are typically close to 1; if a < 1, there is a preferential loss
of 12C during a reaction, and if a > 1, there is a
preferential loss of l3C. A related relationship, useful if the 0 values of either a reactant or product are
known, is (Friedman and O'Neil 1977):
10 3 In a =:; o l3 C prod - o l3 C reac !
(8.9)
With respect to Equation 8Ab, the kinetic isotope
effect for the rare isotope l3C is incorporated in the
following manner:
dC*
"'dt = RrI - kaC*
(8.10)
If a soil has had time to reach steady state, the mass
balance equations can be greatly simplified. At
steady state, dC/dt and dC*/dt = 0, and Equations
8Aa and 8.10 become easy to solve algebraically.
The ratio of the solution is:
RrI
C*
ka
C
I
(8.11a)
k
where RSOM is the isotopic ratio in SOM. In delta
notation (Faure 1986), Equation 8.11a is expressed
as:
where the SOM is the same as in Equation 8.11a.
Thus, for this simple model, the isotopic ratio of
soil organic matter is related to the isotopic values
of the inputs (which in the absence of downward
transport is nearly constant with depth) (Wedin et
al. 1995) and the isotopic fractionation factors associated with decomposition (a).
Ronald Amundson and W. Troy Baisden
Uses of Well-Mixed Box Models in SOM
C Studies
One potential use of the well-mixed box model of
SOM is the establishment of geographic or climatic
variations in soil-ecosystem scale C isotope fractionations (i.e., the climatic dependence of the
value of a in Equation 8.11). If the steady state ol3C
values of SOM and plant inputs can be quantified
along climatic gradients, a can then be calculated.
Unfortunately, this proves to be difficult in practice
for several reasons. First, the ol3C value of the atmosphere (and plant inputs) has decreased by about
1.3%0 in the past 150 years due to global SOM decomposition, biomass burning, and fossil fuel consumption (a corollary of the Suess effect) (Freidli
et al., 1986). This shift in plant inputs is large relative to the approximate range of isotopic enrichment during decomposition (up to approximately
2%0 based on litter decomposition studies [e.g.,
Nadelhoffer and Fry 1988; Mary et al. 1992]).
Therefore, these ecosystem-scale comparisons may
not prove to be very rewarding for comparative
purposes.
In contrast, there has been enormous success using C isotopes to evaluate SOM turnover in agricultural settings where crop photosynthetic pathways differ from precultivation plants (Balesdent
and Mariotti 1996). In these approaches, the whole
soil can be viewed as a well-mixed pool or, more
commonly, each soil horizon can be viewed as a
separate pool and modeled individually. The model
used to calculate the fraction of new C added since
a crop change is (Balesdent et al. 1988):
o l3 C! - o l3 Ci
F = ol3C _ ol3e
p
1
(8.12)
where F is the fraction of SOM gained following
vegetation change, o l3 C! is the isotopic composition of SOM at time t, o l3 Ci is the isotopic composition of SOM prior to vegetation change, and
ol3C p is the isotopic composition of the cultivar.
Isotopic fractionations associated with decomposition are commonly ignored in these comparisons
due to the large difference in 0 l3C values between
C 3 ( - 27 ± 4%0) and C 4 (-12 ± 3%0) plants
(Bender 1968; Smith and Epstein 1971). When
combined with total C measurements, the total
quantity of cultivar-derived C in the soil can be
determined. Additionally, the dynamics of the loss
maining SOM (Hayes 1982). The isotope effect is
proportional to the ratio of the decay constants of
the rare (k*) and common (k) isotopes, and can be
incorporated into Equation 8Ab above by adding a
fractionation term, a, to the decomposition of organic matter. For a given process, the fractionation
factor a is defined as the instantaneous ratio of the
isotopic composition of products and reactants:
k*
~rod
- = a = - -
k
~eoc!
(8.8)
Values of a in processes relevant to SOM are typically close to 1; if a < 1, there is a preferential loss
of 12C during a reaction, and if a > 1, there is a
preferential loss of l3C. A related relationship, useful if the 0 values of either a reactant or product are
known, is (Friedman and O'Neil 1977):
10 3 In a =:; o l3 C prod - o l3 C reac !
(8.9)
With respect to Equation 8Ab, the kinetic isotope
effect for the rare isotope l3C is incorporated in the
following manner:
dC*
"'dt = RrI - kaC*
(8.10)
If a soil has had time to reach steady state, the mass
balance equations can be greatly simplified. At
steady state, dC/dt and dC*/dt = 0, and Equations
8Aa and 8.10 become easy to solve algebraically.
The ratio of the solution is:
RrI
C*
ka
C
I
(8.11a)
k
where RSOM is the isotopic ratio in SOM. In delta
notation (Faure 1986), Equation 8.11a is expressed
as:
where the SOM is the same as in Equation 8.11a.
Thus, for this simple model, the isotopic ratio of
soil organic matter is related to the isotopic values
of the inputs (which in the absence of downward
transport is nearly constant with depth) (Wedin et
al. 1995) and the isotopic fractionation factors associated with decomposition (a).
Ronald Amundson and W. Troy Baisden
Uses of Well-Mixed Box Models in SOM
C Studies
One potential use of the well-mixed box model of
SOM is the establishment of geographic or climatic
variations in soil-ecosystem scale C isotope fractionations (i.e., the climatic dependence of the
value of a in Equation 8.11). If the steady state ol3C
values of SOM and plant inputs can be quantified
along climatic gradients, a can then be calculated.
Unfortunately, this proves to be difficult in practice
for several reasons. First, the ol3C value of the atmosphere (and plant inputs) has decreased by about
1.3%0 in the past 150 years due to global SOM decomposition, biomass burning, and fossil fuel consumption (a corollary of the Suess effect) (Freidli
et al., 1986). This shift in plant inputs is large relative to the approximate range of isotopic enrichment during decomposition (up to approximately
2%0 based on litter decomposition studies [e.g.,
Nadelhoffer and Fry 1988; Mary et al. 1992]).
Therefore, these ecosystem-scale comparisons may
not prove to be very rewarding for comparative
purposes.
In contrast, there has been enormous success using C isotopes to evaluate SOM turnover in agricultural settings where crop photosynthetic pathways differ from precultivation plants (Balesdent
and Mariotti 1996). In these approaches, the whole
soil can be viewed as a well-mixed pool or, more
commonly, each soil horizon can be viewed as a
separate pool and modeled individually. The model
used to calculate the fraction of new C added since
a crop change is (Balesdent et al. 1988):
o l3 C! - o l3 Ci
F = ol3C _ ol3e
p
1
(8.12)
where F is the fraction of SOM gained following
vegetation change, o l3 C! is the isotopic composition of SOM at time t, o l3 Ci is the isotopic composition of SOM prior to vegetation change, and
ol3C p is the isotopic composition of the cultivar.
Isotopic fractionations associated with decomposition are commonly ignored in these comparisons
due to the large difference in 0 l3C values between
C 3 ( - 27 ± 4%0) and C 4 (-12 ± 3%0) plants
(Bender 1968; Smith and Epstein 1971). When
combined with total C measurements, the total
quantity of cultivar-derived C in the soil can be
determined. Additionally, the dynamics of the loss