Agriculture Reference
In-Depth Information
Φ
ij
,
J
ij
) denote properties and functions of depth
z
and time
t
integrated
over the unitary area of the model (usually at least 1 m
2
, commonly as
much as 10
4
m
2
). In most models,
K
i
is an invariant property of SOM pool
i
; in the cohort model, it is a function of the age of the cohort. Equations 1
and 2 are actually over-generous in the degree of flexibility they accord to
most existing SOM transformation models. Rate modifier functions
F
i
(
T
,
,
C
) are almost universally assumed to be simple products of
individual modifier functions
F
T
(
T
),
F
Θ
(
Θ
Θ
) and
F
C
(
C
) equally applicable
to all reactions, while partition functions
Φ
ij
(
T
,
Θ
,
C
) are generally taken to
depend only on the clay content
C
.
Underlying assumptions
Equations 1 and 2 invoke soil properties, concentrations and reaction rates
averaged over areas of 1 m
2
or more. Microbial biomass does not feature
in the formulae. Yet (i) SOM decomposition is known to be microbially
mediated and (ii) microbial populations and metabolic reaction rates are
known to be markedly heterogeneous over distances considerably smaller
than 1 m. How are these apparent contradictions to be resolved?
Spatial variability and reaction kinetics
Consider a microsite small enough to be treated as homogeneous. Let
T
,
,
c
and
y
i
represent microsite temperature, moisture content, clay fraction
and substrate concentration (and
T
,
θ
Θ
,
C
and
Y
i
, as before, their macro-
scale equivalents). Let
µ
i
represent the microbial biomass responsible for
bringing about Y
i
-decomposition, with local (microsite) rate
v
i
. In general:
v
i
=
v
i
(
T
,
θ
,
c
,
y
i
,
µ
i
)
(3)
(i.e.
v
i
is a function of
T
,
θ
,
c
,
y
i
and
µ
i
) and the corresponding macroscopic
rate
V
i
is:
V
i
=
∫
v
i
(
T
,
θ
,
c
,
y
i
,
µ
i
)
p
(
T
,
θ
,
c
,
y
i
,
µ
i
)
d
(
T
,
θ
,
c
,
y
i
,
µ
i
)
(4)
where
p
(
T
,
µ
i
) is the probability of an individual microsite having the
particular set of controlling properties
T
,
θ
,
c
,
y
i
,
µ
i
. Assuming - and it is
quite a big assumption - that the microsite-scale influences of temperature,
moisture content and clay fraction can be disentangled from those of
biomass and substrate supply, Equation 3 may be written:
θ
,
c
,
y
i
and
v
i
=
f
i
(
T
,
θ
,
c
)
g
i
(
y
i
,
µ
i
)
(5)
and Equation 4 becomes:
V
i
=
∫
f
i
(
T
,
θ
,
c
)
p
(
T
,
θ
,
c
)
d
(
T
,
θ
,
c
)
∫
g
i
(
y
i
,
µ
i
)
p
(
y
i
,
µ
i
)
d
(
y
i
,
µ
i
)
(6)
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