Geoscience Reference
In-Depth Information
The inert components in the model are described by the following equations:
Þ
B
10
¼
X
9
@
B
10
=@
t
þ
V
r
ð
ð Þ q
10
B
10
m
10
@
B
10
=@
z
B
10
k
1
;
10
R
1
P
1
þ
k
3
;
10
R
3
=
P
3
þ
k
4
;
10
R
4
=
P
4
M
s
þ
H
s
s¼1
þ
k
2
r
B
10
;
2
!
Þ
B
12
¼
q
10
B
10
þ q
1
T
9
þ
X
7
B
12
þ b
12
@
2
@
B
12
=@
t
þ
V
r
ð
T
s
d
12
R
2
þ
k
2
r
B
12
=@
z
;
ð
4
:
47
Þ
s
¼
1
Þ
B
13
¼ k
13
;
0
R
2
B
13
k
1
;
13
R
1
P
1
;
@
B
13
=@
t
þ
V
r
ð
Þ
B
14
¼
d
14
R
2
X
7
s¼1
n
s
T
s
n
9
T
9
þ
k
2
r
B
14
2
@
B
14
=@
t
þ
V
r
ð
d
10
q
10
B
10
þ
max 0
;
f
ð
z
14
z
Þ=
j
z
z
14
j
g
w
14
where
P
i
¼
X
j
2
S
i
k
i
;
j
B
j
;
ˁ
10
is the velocity of detritus decomposition per unit of biomass;
ʽ
10
is the velocity
of gravity settling; k
2
is the turbulent diffusion coef
cient;
ˁ
1
is the part of exchange
biomass losses transforming to nutrients;
ʴ
12
is the nutrient assimilation velocity by
the photosynthetic process per unit of the phytoplankton production;
ʴ
14
is the
oxygen production per unit of phytoplankton production;
7, 9) is the
oxygen losses at the expense of transpiration; z
14
is the maximal depth of oxygen
exchange of sea water with the atmosphere; w
14
is the difference between the
invasion and evasion processes.
The equation describing the changes in the size of birds is written as
ʾ
i
(i=1
-
@
B
8
=@
t ¼ 1
h
8
ð
Þ
R
8
M
8
;
where
z
z
Þ=
z
D
z
R
8
¼ max
f
0
; ðD
j
jg
k
8
;
0
B
8
1
exp
V
8
ð
½
Þ;
V
8
¼
X
7
0
8
k
8
;
s
B
s
þ
k
8
;
9
B
9
þ c
;
M
8
¼
l
8
B
8
s¼5
ʳ′
8
is the share of the non-
sh food in the ration of birds.
The Q
i
function of the age transitions is presented only for the anchovy elements
and written as a linear approximation:
Q
6
¼
k
56
B
5
k
69
B
6
;
Q
5
¼
k
95
B
9
;
Q
9
¼
k
69
B
6
k
95
B
9
:
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