Agriculture Reference
In-Depth Information
Appendix 1: Derivation for Calculating Net Carbon Flow
From SCUAF simulation, the predicted changes in plant-soil system carbon at time
t
can be expressed as:
Cf
=
(
Cp Ca
+
)
-(
Ch
+
b Ce Co
+
+
)
(14.1)
t
t
t
t
t
t
t
where:
Cf
t
= annual carbon flow;
Cp
t
= carbon from biomass growth, calculated as
the annual net biomass accumulation multiplied by 0.50 - the proportion of carbon
in the biomass (Young et al. 1998);
Ca
t
= carbon from organic material additions;
Ch
t
= carbon losses from harvest;
Cb
t
= carbon losses from burning;
Ce
t
= carbon
losses due to erosion; and
Co
t
= carbon losses from oxidation. If harvesting follows
a clear cutting regime,
C
p
at time
t
can be calculated also as the carbon difference
between the biomass of the stand at the end of period
t
(i.e., at the start of period
t
+1),
C
t+1
, less the biomass of trees at the start of period
t
,
C
t
,
that is,
Cp
t
= 0.50
*
(
C
t
+1
−
C
t
).
When biomass is harvested, most of the sequestered carbon will ultimately be
emitted back to the atmosphere either through decay or burning. Carbon emission
was specified as a function of the decay rate of harvested biomass and the end-use
of its products and residues. Thus, the fate of carbon for the harvested biomass was
traced through a simple products' end-use equation. Let
Cw
t
be the net carbon stor-
age from all harvested products at time
t
. By definition
n
n
∑∑
(14.2)
Cw
=
r
Ch
−
We
;
i
=
12
, ,
,
n
(
outputs)
…
t
i
i
it
i
=
1
i
=
1
where:
Ch
i
= carbon from
i
harvested output;
= proportion of harvested biomass
used in the final product;
We
i t
= carbon emission from product
i
at time
t
.
An exponential decay function was applied to estimate the CO
2
emissions from
harvested biomass. Following Barson and Gifford (1990), a lumped parameter
exponential decay function has been specified, which varies according to the half-
life (after harvest) of product's end-use:
ρ
−λ
W=We
r
(14.3)
0
t
where:
W
rt
is the weight of carbon remaining after decay for time
t
;
W
o is the
weight of carbon sequestered by the forest (timber) at time of felling or harvest;
λ
is the decay constant. Using this approach, biomass was depreciated with a constant
proportion of the remaining biomass. The decay constant for timber products was
derived according to their half-life period using the relationship:
ln ln
=⇒=
l
2
2
(14.4)
t
l
12
/
t
12
/
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