Environmental Engineering Reference
In-Depth Information
800
Q
K
S
V
700
600
500
400
300
200
−
100
0
−
100
−
75
−
50
−
25
0
25
50
75
100
−
100
% change in input variable
(a)
350
300
250
200
150
100
50
0
0
25
50
75
100
50
−
−
100
−
150
variability as % of input variable base value
(b)
kQ
m
S
n
e
−
iV
(where:
E
erosion [mm month
−
1
],
k
Figure 2.2
Example sensitivity analysis of the simple erosion model
E
=
=
=
soil
overland flow [mm month
−
1
],
m
tangent of slope [m m
−
1
],
n
erodibility,
Q
=
=
flow power coefficient [1.66],
S
=
=
slope constant
[2.0],
V
=
vegetation cover [%],
i
=
vegetation erosion exponential function [dimensionless]): (a) univariate sensitivity analysis.
100 mm month
−
1
,
k
Base values are
Q
=
=
0
.
2,
S
=
0
.
5,
m
=
1
.
66,
n
=
2
.
0,
i
=
0.07 and
V
=
30%. The variables
Q
,
k
,
S
and
V
are
varied individually from
−
100% to
+
100% of their base values and the output compared. Note that
k
has a positive linear response;
Q
a nonlinear response faster than
k
;
S
a nonlinear response faster than
Q
(because
Q
is raised to the power
m
=
1.66 while
S
is raised
to the power
n
2); and
V
a negative exponential response. The order of parameter sensitivity is therefore
V
>
S
>
Q
>
k
.; and
(b) Multivariate sensitivity analysis of the same model, where normally distributed variability is randomly added to each of the
parameters as a proportion of the base value. Note the large fluctuations for large amounts of variability, suggesting that the model is
highly sensitive where variability of parameters is
>
50% of the mean parameter value. No interactions or autocorrelations between
parameter variations have been taken into account.
=
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