Environmental Engineering Reference
In-Depth Information
Fallout
Deposition
Plant surface
Plant interior
Translocation
Vegetation
Weathering
Root uptake
Resuspension
Fast comprtm.
Slow comprtm.
Fixation
Soil
Infiltration
Infiltration
Deep layer
Fig. 18.6
Graph for the migration of nuclides in the plant-soil environment after a fallout, as used
by Amano et al. (
2003
); modified by E.H.
coincide. Where the transpose of the adjacency matrix
A
T
has unit entry, there is
a positive entry in
B
of (
18.4
), too. Opposite to the adjacency matrix there are
nonzero entries in the diagonal of the compartment matrix. In the donor-controlled
cases these entries are negative. The sign of the matrix entries corresponds to the
sign in the formulae given above, because the fluxes
Q
i
denote absolute values and
are thus positive.With such compartment matrices general networks of connected
compartments can be described. Each upstream compartment corresponds with
a positive off-diagonal entry in the matrix. Each downstream compartment leads
to a negative contribution in the diagonal. Sidebar 18.1 outlines the idea how
a linear model can be used for indoor air quality modeling. Figure
18.6
depicts
a graph of the compartment concept used for the migration of radionuclides after
the fallout in the plant-soil environment. The concept, which was presented by
Amano et al. (
2003
), leads to a linear system of equations.
We note the compartment matrix for the system, shown in Fig.
18.2
,asan
example. It looks as follows:
0
@
1
A
Q
VS
þQ
VC
ð
Þ=V
V
0
0
0
0
Q
VS
=V
V
Q
SSo
þQ
SC
ð
Þ=V
S
0
0
0
B
¼
0
Q
SSo
=V
S
Q
SoG
þQ
SoC
ð
Þ=V
So
0
0
0
0
Q
SoG
=V
So
Q
GC
=V
G
0
Q
VC
=V
V
Q
SC
=V
S
Q
SoC
=V
So
Q
GC
=V
G
0
(18.5)
