Geoscience Reference
In-Depth Information
Table 1 First-order sensitivity index
S
i
of the dead zone model parameters
Sub-reach
K
x
(m
2
/s)
A
(m
2
)
A
S
(m
2
)
Flow rate
a
(1/s)
1-2
Q
1
0.296
0.702
0.015
0.000
Q
2
0.317
0.677
0.014
0.000
Q
3
0.318
0.682
0.012
0.000
Q
1
2-3
0.315
0.680
0.008
0.000
Q
2
0.303
0.701
0.009
0.000
Q
3
0.315
0.684
0.007
0.000
3-4
Q
1
0.310
0.690
0.007
0.000
Q
2
0.316
0.677
0.007
0.000
Q
3
0.318
0.680
0.006
0.000
4-5
Q
1
0.314
0.681
0.009
0.000
Q
2
0.325
0.656
0.010
0.000
Q
3
0.313
0.684
0.006
0.000
Table 2 Total sensitivity index
S
Ti
of the dead zone model parameters
Sub-reach
K
x
(m
2
/s)
A
(m
2
)
A
S
(m
2
)
Flow rate
(1/s)
a
1-2
Q
1
0.298
0.701
0.015
0.000
Q
2
0.320
0.674
0.016
0.000
Q
3
0.320
0.682
0.012
0.000
2-3
Q
1
0.320
0.682
0.008
0.000
Q
2
0.304
0.699
0.009
0.000
Q
3
0.318
0.684
0.008
0.000
3-4
Q
1
0.313
0.690
0.007
0.000
Q
2
0.324
0.680
0.007
0.000
Q
3
0.323
0.681
0.007
0.000
4-5
Q
1
0.320
0.683
0.009
0.000
Q
2
0.342
0.666
0.010
0.000
Q
3
0.319
0.685
0.007
0.000
no impact on the model output. Hence, the dead zone model could be simplified
by neglecting transient storage parameters. Omitting transient storage parameters
results in reducing the dead zone model to the Fickian model, which takes
the form:
@
C
@
Q
A
@
C
1
A
@
AK
x
@
C
@
t
¼
x
þ
(4)
@
@
x
x
In Fig.
6
a comparison of the dead zone model results and the Fickian model
results is presented. The comparison indicates that results of both models are in very
good agreement with each other.
Additionally, the uncertainty analysis was performed for the Fickian model. The
95% confidence limits are the same as for the dead zone model (Fig.
5
), which
verifies the statement that transient storage parameters do not affect the output
uncertainty, and the uncertainty is dependent on parameters
A
and
K
x
.
