Environmental Engineering Reference
In-Depth Information
Fig. 9.2
Validation of a Dynamic Emulation Model (DEM) for the HEC-RAS (Hydrologic Engineering Center River
Analysis System) model at six downstream sites based on a new set of upstream level data.
persistently exciting in this complete theoretical
sense, it will normally provide sufficient excita-
tion to ensure identifiability (except for the case of
summer inactivity in ephemeral catchments). The
situation is less clear in the case of flow-flow or
level-level routing, since the upstream inputsmay
well be very smooth and relatively 'unexciting' in
some cases.
2 The number of parameters in the model: In a
lumped parameter model, the number of para-
meters is defined by the dynamic order and struc-
ture of the system, as well as any additional
parameters that, for example, are associated with
the characterization of nonlinear functions ap-
pearing in the model equations. However, the
most important parametric contribution is con-
cernedwith defining the order of the system, since
it is this that affects identifiability most critically
and links in with item 1 above. In the case of
distributed parameter partial differential equa-
tions, the parameterization is also connected with
the form of space-time discretization that is used.
In practice, each case has to be judged on its own
merits: a model becomes 'over-parameterized'
when clear signs of poor identifiability appear
during model parameter estimation, although
some methods of estimation or calibration are
better at detecting this than others (see the exam-
ple considered below).
3 The level and nature of noise on the data: In
statistical parameter estimation, the uncertainty
on the parameter estimates is a function of the
noise/signal ratio on the data and the nature of this
noise. If the noise level is high or the noise is not
well behaved in some manner, then the parameter
estimates may have high estimation error vari-
ance. This not only can produce effects that are
very similar to those encountered when themodel
