Environmental Engineering Reference
In-Depth Information
System boundary
j
mode 2
recycle
j
j
j
i
j
j
j
j
mode 1
first passage
mode 3
dissipation
f
(0)
+f
(1)
+f
(2)
=f
(2)
+f
(3)
+f
(4)
Fig. 5.2 Schematic of flow partitioning for a central node i, in relation to other network
compartments. Flow reaches the node directly across the boundary, f
(0)
, by passing through
other compartments before reaching i, f
(1)
, and leaving i to cycle back again, f
(2)
. Outflows
symmetrically mirror these inputs
Example: Cone Spring Ecosystem Model
A classic example is the Cone Spring ecosystem model developed by Tilly [
10
]. In
this model, there are five compartments representing: (1) plants, (2) bacteria,
(3) detritivores, (4) carnivores, and (5) detritus (
Fig. 5.3
). There are 2 external
inputs (to plants and detritus), 8 internal flows, and each compartment has boundary
outflow representing metabolic or egestion losses. The internal flows from columns
j to rows i are given by:
2
3
0
0
0
0
0
4
5
8881
0
1600
200
167
F
¼
0
5205
0
0
0
0
2309
75
0
0
0
0
0
370
0
Compartmental throughflows are: T = [11 184, 11 484, 5 204, 2 384, 370] and
TST = 30 627.
The nondimensional flow fractions are given by:
2
4
3
5
0
0
0
0
0
:
:
:
:
0
794
0
0
308
0
0840
0
451
¼
:
G
00
453
0
0
0
00
:
201
0
:
014
0
0
0
0
0
0
:
155
0