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Here a
1
is the maximal rate of the absorption of nutrients by the phytoplankton
(day
−
1
), a
2
is the index of the rate of saturation of photosynthesis, and
T
c
T
T
c
T
opt
exp 1
T
c
T
T
c
T
opt
K
0
ð
T
;
t
Þ
¼
a
3
max 0
;
ð
6
:
5
Þ
where a
3
is the weight coef
cient, and T
c
and T
opt
are the critical and optimal
temperatures for photosynthesis, respectively (
°
C).
fits the laboratory data. The relationships (
6.4
) and
(
6.5
) make the description of the phytoplankton production more accurate for
critical environmental conditions when the concentration of nutrients and the
temperature have high
Equation (
6.3
) adequately
fl
fluctuations. The coef
cients of these relationships are
de
ned on the basis of estimates given by Legendre and Legendre (1998).
The dynamic equation for the phytoplankton biomass in the environment A has
the following form:
B
2
;
A
.
B
2
;
A
@u þ
v
A
B
2
;
A
@k þ
v
z
@
B
2
;
A
@
t
þ
v
A
@
@
u
@
k
@
z
z
k
Zp
R
ZA
.
h
Z
þ
k
Fp
R
FA
.
i
B
2
;
A
ð
6
:
6
Þ
A
p
M
p
þ
k
2
@
2
B
2
;
A
A
A
F
¼ R
pA
h
@
n
n
F
are the production (the food spectrum) of zooplankton
B
3
and nekton B
5
, respectively; M
p
Z
and R
ZA
A
A
where R
ZA
n
n
A
p
is the rate of exchange.
The balance equations for the other ecological elements of Fig.
6.6
are given by
Krapivin (1995, 1996).
The energy source for the entire system issolar radiation energy E
A
(t,
is the mortality; and
h
φ
,
ʻ
,z), the
intensity of which depends on time t, latitude
, and depth z. The
equations that describe the biomass dynamics of the living elements are:
φ
, longitude
ʻ
¼ R
i
T
i
M
i
H
i
X
j
2C
i
@
B
i
@
t
þ n
i
V
u
@
B
i
þ
V
k
@
B
i
@k
þ
V
z
@
B
i
@
z
C
ij
R
j
þ n
i
@
@u
D
u
@
B
i
@u
@u
þ
@
þ b
V
@
B
i
@
z
þ
@
@k
D
k
@
B
i
@k
@
z
D
z
@
B
i
; ð
i ¼ 1
;
3
;
4
;
5
Þ
;
@
z
ð
6
:
7
Þ
where V(V
ˆ
, V
ʻ
, V
z
) are the components of the water current velocity V
u
¼ v
W
u
;
V
k
¼ v
W
k
;
V
z
¼ v
z
Þ
; R
i
is the production; Mi
i
is the mortality; Hi
i
is non-assimilated
food; and
ʓ
i
is the set of the trophic dependence of the i-th component:
C
ji
¼ k
ji
F
i
=
P
m
2
S
i
k
jm
F
m
; S
i
is the food spectrum of the j-th component; k
jm
is the
index of satisfaction of the nutritive requirements of the j-th component at the expense
of the m-th component biomass; Fi
i
¼ max 0
;
B
i
B
i
;
min
; B
i,min
is the minimal
biomass of the i-th component consumed by other trophic levels;
are
DD
u
; D
k
; D
z
components of the turbulent mixing coef
cient (on the assumption of isotropism of
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