HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

When t → ∞ we get the following,
0 ≤ N(t) ≤ a 19 (13)
This result tells us that the Nitrate concentration in this model will not exceed
the value of parameter 19 which is the Nitrate average deep concentration. (12) also
tells us that the maximum rate of decline of Nitrate will be that of Parameter 20
which represents the Nitrate maximum mixing rate. This means that the accuracy
of the Nitrate concentration is extremely dependent on how well the parameters are
selected. Since Iron has the same equation structures, the same analysis applies:
dF
dt = [
(a 21 − N)
−
[
P
(a 8 12.0107)
a
{ }}
22
{ ]
E T H2 O
a
max
− E T H2 O(t)
22
E T H2 O max
− E T H2 O min
[
]
(1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t))
M(t) +
]
a 15 D
(a 8 12.0107)
Using the same method as Nitrate the upper found for Iron is
F u (t) = a 21 + Q u e −a 22t
where Q u = F 0 − a 21 ,
Summarizing the bounds we get,
0 ≤ F (t) ≤ a 21 + Q u e −a 22t
(14)
When t → ∞ we get it to be,
∴ 0 ≤ F (t) ≤ a 21 (15)
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