Environmental Engineering Reference
In-Depth Information
ities and nonlinearities of distributed hydrological
models, however, it is not possible to propagate
these uncertainties analytically. One way of ap-
proximating the calculations required to estimate
prediction uncertainties is to use Monte Carlo
simulation.However, thiscreates acomputational
difficultybecauseof thehighdimensionalityof the
potential uncertainties and the lack of knowledge
of covariation between the different uncertainties.
In principle, the spatial patterns of all parameters
and the space-time error characteristics of the
boundary conditions can all be uncertain. Thus,
a very high number of Monte Carlo simulations
would be required, even if we assume only a single
model structure is feasible, and that the error char-
acteristics of the parameter values and boundary
conditions are known.
verymany state or flux predictions of a distributed
rainfall-runoff or hydraulic model.
Two simpler approaches are then possible. The
first is to update only a model of the prediction
errors for the distributed model, using, for exam-
ple, a simple gain adaptation or stochastic error
model. The latter is used, for example, in the
Norwegian flood forecasting system (see Skaugen
et al. 2005). The second is not to worry about
a distributed model at all for real-time forecasting
but touseamuchsimplermodel for eachsubcatch-
ment. Since the model will be used purely
for forecasting, with real-time updating, it is not
even necessary to maintain a hydrological mass
balance; Romanowicz et al. (2008), for example,
have used rainfall-water level and water-level to
water-level nonlinear transfer function models in
forecasting (see also Chapter 9). A network of sub-
catchment transfer functions and reach transfer
functions, with local updating at sites with real-
time data availability, can be used to extend the
lead time of forecasts in larger catchments. This
has the advantage of not needing to use the rating
curve to convert level to discharge, which neces-
sarily introduces uncertainty into the modelling
process, particularly for overbankflooddischarges,
when the rating curve may be poorly controlled or
changing during an event. It is also often predic-
tions of level that are required in forecasting. It is
level rather than discharge that determineswheth-
er a flood embankment is overtopped.
Computational issues
By definition, distributed models have a large
number of computational elements and produce
a large number of predicted variables. Thus, as
with other distributed forecasting and simulation
systems, such as atmospheric models, there is
always a need to compromise between using the
available computing power to reduce the size of
the elements of the discretization and increasing
the accuracy of the approximation, or to make
more Monte Carlo realizations of the model. This
perhaps would not be such an issue if we could be
sure that feasible models were limited to a small
region of the high-dimensional space of potential
model parameter sets and boundary conditions,
but Monte Carlo experiments have shown that
this is often not the case. Given the various
sources of uncertainty, models that give accept-
able fits to any evaluation data may be scattered
through the space of feasiblemodels and boundary
conditions. This is what Beven (2006b) calls
the
PredictionUncertainty inDistributedModels
It is clear from the previous discussion in this
chapter that in any application of a distributed
model there are likely to be many sources of un-
certainty that might impact onmodel predictions.
Thereareuncertainties inmodel representationsof
the relevant processes; there are uncertainties in
effective parameter values; there are uncertainties
in the initial and boundary data required; and there
are uncertainties in the observations used in eval-
uating model predictions. It would therefore be
useful to evaluate the effects of these uncertainties
on the model predictions. Because of the complex-
issue.
1
equifinality
Equifinality has been
1
In other disciplines non-identifiability and ambiguity are also
used. Equifinality, the idea that many different conditionsmight
lead to similar results, was introduced to indicate that this was a
generic problem rather than a problem of identifying the best
model, following Von Bertalanffy (1968; see also Beven 2009).
