Environmental Engineering Reference
In-Depth Information
are not commensurate because of scale or other
observational considerations (e.g. Beven 2010). It
is usually only possible to test whether a combi-
nation of model, input and boundary condition
data provide adequate simulations, and because
the input and boundary condition data are pro-
cessed nonlinearly by themodel, it is very difficult
to separate out the different sources of uncertainty
(Beven 2006b, 2008, 2009; Beven et al. 2008).
It is perhaps a problem resulting from inade-
quate characterization of inputs and boundary
conditions in hydrologicalmodels that in applying
the limits of acceptability approach in practice it
has been found that often
no
models produce
predictions that are everywhere within reasonable
limits of acceptability. Invoking a statistical anal-
ogy and allowing for some 'outlier' observations so
that acceptability is relaxed to a condition of sat-
isfying only 90% or 95% of the limits is a possible
response to this. This can also, however, be prob-
lematic. The nature of hydrological records is
such that the other 10% or 5% of time steps may
actually be some of the most hydrologically inter-
esting periods. An alternative is to relax the limits
until at least somemodels become acceptable, and
then decide whether the resulting predictions are
fit for purpose.
Effectively the error variance will expand to
ensure that the uncertainty associated with the
model predictions is sufficient to enclose (usually)
the required fraction of the observations.
It is possible to compare the performance of
different model structures in a statistical frame-
work, for example by using Bayes ratios, but
ultimately the user must make a subjective
decision as to whether the performance of the
'best' model is actually good enough for the pur-
pose of the particular application. In this aspect,
current practice is not so different from traditional
model optimization. The calibration process was
always a way of being able to demonstrate some
success in a hydrological model in the face of all
the potential sources of uncertainty and error in
both data and model structures (even if there was
no real guarantee that the best model in calibra-
tion would perform equally well in prediction of
future responses).
This lack of model rejection is perhaps unfor-
tunate in terms of progressing hydrological sci-
ence. It is one reason why Beven (2006b) suggested
an alternative approach within the GLUE frame-
work of setting limits of acceptability associated
with each observation prior to making any model
runs. The limits of acceptabilitymight be based on
what would be fit for purpose in an application or
on a consideration of different sources of input and
observation error. Models that fell consistently
within the limits of acceptability would then be
used in prediction (perhaps with some weighting
based on past performance), those that did not
would be rejected.
This idea of feasible models being treated as
multiple working hypotheses about catchment
functioning, to be rejected as new tests are made,
has some resonances with the Popperian model of
the scientific method, where the emphasis is on
testing and falsification of hypotheses. The prob-
lem in applying such a principle in hydrological
modelling is that we must be very careful not to
make a Type II error of rejecting a good model
because it does not give a good simulation of the
available observations, when that may only be
a result of driving the model with poor input data
or comparing the outputs with observations that
Implications for distributed flood
routing models
In flood management, the purpose of a distributed
hydrological model is often to provide discharge
predictions that can be used as the upstream and
lateral boundary conditions for flood routing mod-
els. The flood routing models might then be used
with design storms or historical data to map areas
at risk of flooding, or they might be used in real-
time forecasting to get a better spatial pattern of
changing flood risk during an event.
In the past, the accuracy of hydraulic models
has been limited by the availability of good flood-
plain geometry data. This has greatly improved
with themorewidespread synthetic aperture radar
(SAR) and light detection and ranging (LiDAR)
datasets, though there are still issues about how
well floodplain infrastructure of embankments,
