Environmental Engineering Reference
In-Depth Information
High Order
Model
:
(e.g. 17th order and
circa 180 parameters)
Reduced Order
Model
:
(e.g. 3rd order and
27 parameters)
Parameterized
State-Dependent
Parameter
Regression
(SDR)
Relationships
.
.
.
.
.
High Dynamic
Order Model
Estimated
Parameters
Reduced
Dynamic
Order Model
Parameters
.
.
.
.
.
.
Fig. 9.1
The process of dynamic emulation model synthesis.
order of the system:
5
for instance, in the case of
linear systems, it can be shown that a single pure
sinusoid will only provide sufficient excitation to
identify a system described by a first-order differ-
ential or difference equation; in general, the input
should contain at least n sinusoids of distinct
frequencies to allow for the identification of an
n
th
-order system. In the case of rainfall-flow or
level data, although the rainfall may not be
parametrically identifiable from the available da-
ta. In simple terms, a model is identifiable from
data if there is no ambiguity in the estimates of its
parameters. In relation to input-output models of
the kind used in catchment modelling, identifia-
bility is affected by the following interrelated
factors.
1 The nature of the input signal: It can be shown
that, ideally, the input signal should be
'persistently exciting' in the sense that it remains
bounded in mean and variance, while continuing
to perturb the system sufficiently to allow for
unambiguous estimation of the model para-
meters: see, for example, Young (1984). This re-
quirement is linked strongly with the dynamic
5
In a hydrological system, the dynamic order is linked to the
number of 'tanks' or 'reservoirs': so a typical first-order model
would be a first-order differential equation of single river reach or
storage reservoir; and a second-order model would be two such
reservoirs connected in series, parallel or feedback.
