Environmental Engineering Reference
In-Depth Information
implausibility I ( x )ofaninput x to be:
t ( x ) in Equation 26.13 equal to zero to help identify
some 'nonimplausible' inputs with which to help assess
model discrepancy error, which in turn can be used
to assess whether the model is worth calibrating and
adequate for prediction.
In the runoff example, we selected 203 candidate runs
from the emulated values at the 100 000 point design
used in Section 26.3.4.1, using an implausibility cutoff
value of 6.5. We then evaluated these 203 runs on the
actual runoff model and computed the implausibility
in Equation 26.7 with
σ
max 1 t N
z t
E[ f t ( x )]
σ t ( x )
I ( x )
=
(26.13)
where E[ f t ( x )] denotes the mean of the emulator at time t
for input x and
t ( x ) is the sumof three variances, those of
measurement error, model discrepancy and the emulator
at x : in our example N
σ
13. Cutoff considerations for
I ( x ) are similar to those for fast models. Note that,
as internal model-error assessment is not possible for
slow computer models, external model error implicitly
includes the internal contribution.
An emulator run time will be fast compared to that
for the computer model it emulates, so we can evaluate
it at many inputs (as we did for fast models) to help
determine implausible inputs. As for fast models, we
set the model discrepancy variance component term of
=
t equal to measurement error
variance, and found that their implausibility values were
all greater than 8.5. We then chose the eight best of these
203 runs having implausibility less than 10. These eight
runs were used to assess the external model discrepancy,
exactly as in Section 26.3.4.1. Figure 26.7 shows the
results.
σ
Observed discharge
250 Original runs
203 Candidate runs
0
200
400
Time in hours
600
800
Fast Internal
Fast External
Fast Total
Slow External
0
200
400
Time in hours
600
800
Figure 26.7 The upper panel shows the 250 runs used to build the 13 emulators the 203 candidate runs, the observed discharges and
the error bars are based on the sum of the external model discrepancy and measurement error. The vertical dotted lines are the 13
emulator hours. The lower panel compares the fast and slow model results, showing standard deviations for fast internal model
discrepancy, fast external model discrepancy, fast total model discrepancy (black) and slow external model discrepancy.
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