Geology Reference
In-Depth Information
Table 5.4
Generalised Likelihood Uncertainty Estimation (GLUE) setup. All subjective assumptions are made explicit:
the choice of the prior parameter distribution (see Table 5.3 for its bounds); the choice of performance measures;
the number of parameter sets sampled; the initial performance thresholds; and whether or not input and output
uncertainties are acknowledged.
Parameter sets
Prior parameter distribution
Input uncertainty
10
9
uniform
no
Output uncertainty
Initial performance threshold
Discharge
Suspended solids
Discharge
Suspended solids
yes
no
0.4
150
Performance measure for discharge
QQ
Q
N
-
-
=
å
1
sim,i
obs,i
()()
sup
inf
Q
i
=
obs,i
obs,i
D
|
N
where
Q
sim,i
and
Q
obs,i
are simulated and observed discharges at time-step
i
=
1, . . . , N
, sup (
Q
obs,i
) and inf (
Q
obs,i
) are upper and lower interval
bounds and
()
()
() ()
()
ì
Q
sup
Q
if
Q
sup
Q
-
>
sim,i
obs,i
sim,i
obs,i
ï
-=
QQ
0
if
inf
Q
Q
sup
Q
££
ï
sim,i
obs,i
obs,i
sim,i
obs,i
()
Q
inf
Q
if
Q
inf
Q
-
<
î
sim,i
obs,i
sim,i
obs,i
Performance measure for suspended solids
N
=
å
1
CC
-
sim,i
obs,i
MAE
i
=
N
where
C
sim,i
and
C
obs,i
are simulated and observed concentrations at time-step
i
=
1, . . . , N
.
independently and performance statistics calcu-
lated. The performance statistics are compared
with a predefined performance threshold (see
below). If the simulation exceeds the required per-
formance threshold then the parameter set is
retained and declared behavioural (or good) at
simulating the observed behaviour; if it is lower
than the performance threshold the parameter set
is rejected. The procedure is then repeated a large
number of times (one billion randomly selected
parameter sets per event, in this study). This proc-
ess is called Monte Carlo simulation. The retained
parameter sets, weighted by their performance,
are then used to construct new (posterior) param-
eter distributions. The model output for the mul-
tiple runs can be used to demonstrate uncertainty
in model output and model parameters. The gen-
eral framework for refining simulations with new
data can be summarized as follows:
●
The initial uniformly weighted prior parameter
sets (from the Monte Carlo sampling) are weighted
(updated) using the performance statistic calcu-
lated from the 1st storm event information (in
this case discharge and sediment). These provide
the first iteration of posterior parameter distribu-
tions conditioned on this event information, in
that only the good simulations (as defined by the
performance measure) are retained for further
simulations.
●
These posterior parameter distributions can
then be subsequently updated using data from
second and/or additional events in the same way
that the initial uniform prior distributions were
updated previously (Beven & Freer, 2001).
