Environmental Engineering Reference
In-Depth Information
F
λ
h m
N = 1
w
K
d
N = 2
K
w
N = 3,....,38
Polar
sinking:
π
Meridional
overturning
stream
function
Figure 7.5 Ocean Heat Model (Modified with
permission from Eickhout B., den Elzen
M.G.J. and Kreileman G.J.J. (2004) The
Atmosphere-Ocean System of IMAGE 2.2: a
global model approach for atmospheric
concentrations, and climate and sea level
projections. RIVM report no. 481508017/
2004).
w
K
w
N = 39
K
N = 40
or, in full differential equation form:
d 3 Tt
dt 3
replacements for the model in those applications, such
as forecasting and control, where the internal descriptive
aspects of the complex model are of lesser importance. In
other applications, such as 'what-if' studies, environmen-
tal planning and risk analysis, however, the reduced-order
model does not disclose clearly those physically mean-
ingful parameters of the large model that control the
dominant reduced order modes of behaviour and are,
therefore, important in such applications. Fortunately,
this limitation can be obviated by converting the simple
reduced order model into a 'dynamic emulation model',
in which the parameters of the large model are linked
with those of the reduced order model, as discussed in
the next section.
06575 d 2 T ( t )
dt 2
00103 dT ( t )
dt
+
0
.
+
0
.
+ 1 . 0981 × 10 6 T ( t )
10 5 d 2 Q ( t 7)
dt 2
000153 dQ ( t 7)
dt
=−
.
×
+
.
1
094
0
10 7 Q ( t
+
8
.
5911
×
7)
(7.7)
where T(t) is the temperature simulated at time t the
decomposed residence times in the case of the parallel
model are:
τ 1 =
.
τ 2 =
.
τ 3 =
24
0 years;
43
5 years; and
871
years.
The model (7.6) was, as in the example of the previous
section, identified and estimated using the RIVCBJ rou-
tine in the CAPTAIN Toolbox. Its ability to emulate the
behaviour of the large diffusion model is demonstrated
in Figure 7.6, which compares the emulated and simu-
lation model temperatures at four of the layers. In all
cases, the DBM emulation model mimics the large model
temperature behaviour to a level greater than 99.9%.
Model-reduction exercises of the above kind demon-
strate rather dramatically how the superficial complexity
of large and complex simulation models can, as in the real
data example described in Section 7.6, conceal underlying
simple dynamics that are the main engine for the observed
behaviour of the model in its response to input variations.
Such reduced-order models can function, therefore, as
7.8 The dynamic emulation of large
computer-simulation models
The reduced-order model considered in the previous
section can be considered as a 'nominal' emulation model,
in the sense that it closely mimics the behaviour of its
large model progenitor when the parameters of this large
model are fixed at some nominal values. In full dynamic
model emulation (DME), on the other hand, it is assumed
that, while the large model may be characterized in it ially
in terms of such a 'nominal' parameter vector, say X, the
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