Environmental Engineering Reference
In-Depth Information
4
4
3
cs 82
cs 79
cs 77
2.5
3
3
2
2
2
1.5
1
1
1
0.5
0
0
0
0
500
1000
0
500
1000
0
500
1000
5
5
6
cs 73
cs 68
cs 70
5
4
4
4
3
3
3
2
2
2
1
1
1
0
0
0
0
500
1000
0
500
1000
0
500
1000
Time (hours)
Time (hours)
Time (hours)
Hec-Ras
DBM fit
±
95%
Figure 7.10
Validation of the DME for the HEC-RAS model at the six cross sections, based on data not used for identification and
estimation.
more sophisticated mapping procedures must be used,
such as the GASP technique mentioned above. In the case
of the examples presented in Young and Ratto (2011),
alternative smoothing spline ANOVA models (e.g. Gu,
2002) provided good DME results.
Finally, in this case, the emulation model (7.8) can be
reconciled with DBM models obtained from the analysis
of real data from the River Severn (Romanowicz
et al
.,
2006; Young
et al
., 2006), where the river 'routing' models
between upstream and downstream locations, as obtained
by RIVBJ identification and estimation, are of the same
basic first order, nonlinear form as this model.
all areas of the discipline. In general, such 'bottom-
up', reductionist models are normally overparameter-
ized and so not statistically identifiable in relation to
the information content of the experimental data, and
their determinism sits uncomfortably with the acknowl-
edged uncertainty that characterizes most environmental
systems. This chapter has argued that parsimonious,
'top-down' models provide a more appropriate, iden-
tifiable parameterization in most situations and that the
uncertainty that pervades most environmental systems
demands an alternative stochastic approach. In particu-
lar, stochastic, dynamic models and statistical modelling
procedures provide a means of acknowledging this uncer-
tainty and quantifying its effects. Most often, however,
the conventional statistical approach to stochastic model
building is posed in a 'black-box' manner (e.g. Ljung,
1999), which often fails to produce models that can be
interpreted directly in physically meaningful terms. The
7.9 Conclusions
For too long in the environmental sciences, deterministic
reductionism has reigned supreme and has had a dom-
inating influence on mathematical modelling in almost
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