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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