HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

Model A
Where,
dP
dt
dZ
dt
dD
dt
dN
dt
dF
dt
=
=
=
=
=
[ [ ]
(1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t))
M(t) (1 − a 6 ) − a 9 − a 17
]P (1)
} {{ }
(
−
P Growth
)
Rate
a 13 (1 − e (−a 14P ) ) Z
} {{ }
Z Grazing Rate
[
a 12 a 13 (1 − e (−a 14P ) ) −a
} {{ } 11 − a 16
]Z (2)
Z Grazing Rate
(
) (
)
(1 − a 10 )a 11 P + (1 − a 10 )a 11 Z
(
)
+ (1 − a 10 )(1 − a 12 ) a 13 (1 − e (−a 14P ) ) Z
} {{ }
− D(a 15 + a 18 )
Z Grazing Rate
[
]
E T H2 O
(a 19 − N) a
max
− E T H2 O(t)
20
E T H2 O max
− E T H2 O
} {{ min
}
N Mixing Rate
−
[
−
[
P
(a 7 12.0107)
[
]
(1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t))
M(t)
} {{ }
P Growth Rate
]
E T H2 O
(a 21 − F ) a
max
− E T H2 O(t)
22
E T H2 O max
− E T H2 O
} {{ min
}
F Mixing Rate
[
P
(a 8 12.0107)
[
]
(1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t))
M(t)
} {{ }
P Growth Rate
(3)
(4)
]
+ a 15D
(a 7 12.0107)
(5)
]
+ a 15D
(a 8 12.0107)
{
F
M(t) = min
(F + a 5 ) , N
(N + a 4 ) , E P UR (t)
(e− a 2 )(1 − e −E P UR (t)(1+a 3 e(E P UR (t)e1.089−2.12log 10 (a 1
} ) ) )
a 1 ))
} {{ }
Phytoplankton Growth Limitation
35