Geoscience Reference
In-Depth Information
7.13 Other Applications of GLUE in Rainfall-Runoff Modelling
To summarise, the GLUE methodology provides one way (and not necessarily the only way) of recognis-
ing the possible equifinality of models and parameter sets. The approach is conceptually simple, easily
implemented, and leads quite naturally to an assessment of the uncertainty of model predictions. There are
undoubtedly limitations of the method, of which the most important seems to be computing constraints
that restrict the number of runs that can be made in sampling the parameter space (although see the two
billion runs, of which 213 were accepted as behavioural, in the study by Iorgulescu
et al.
, 2005, 2007).
However, the type of calculations required is ideally suited to parallel computers. The GLUE methodol-
ogy also involves a number of subjective decisions, so that any uncertainty bounds or prediction limits
derived in this way are intrinsically qualitative. However, as noted earlier, all the subjective decisions
must be made explicit in the analysis so that they can be discussed or disputed and the analysis repeated,
if necessary, with alternative assumptions. Thus, despite the qualitative nature of the procedure, there
is some scientific rigour associated with it (and there are good reasons to suggest that the claims that a
Bayesian statistical approach might be more rigorous or objective are misleading when the sources of
error are epistemic rather than statistical in nature (Beven, 2006a, 2010).
Some recent applications of the GLUE methodology to rainfall-runoff modelling include those by
Beven and Freer (2001); Younger
et al.
(2009); Choi and Beven (2007); and Liu
et al.
(2009). Blazkova
et al.
(2002a, 2002b) and Gallart
et al.
(2007) have used internal measurements as well as discharges in
model evaluation. Thorndahl
et al.
(2008) have used it in the context of urban runoff modelling; Dean
et al.
(2009) have used it in runoff and water quality modelling. Iorgulescu
et al.
(2005, 2007) and Page
et al.
(2007) have combined runoff modelling with the use of tracers to identify the sources of runoff,
while Zhang
et al.
(2006b) examined uncertainty in the parameters of soil pesticide transport models.
Blazkova and Beven (2009) used a limits of acceptability approach to the prediction of flood frequencies
using continuous simulation in a catchment with multiple stream gauges. In an exercise that involved
several months of computation, Vazquez
et al.
(2009) used GLUE in an evaluation of the SHE model.
Buytaert and Beven (2009) have shown how the method can be applied in a regionalisation context to
predict the uncertain responses of ungauged catchments.
In other areas of hydrological and hydraulic modelling, Franks and Beven (1997a) and Schulz and
Beven (2003) have applied GLUE to the problem of estimating land surface to atmosphere fluxes; Brazier
et al.
(2000) looked at erosion modelling; and Schulz
et al.
(1999) have addressed the problem of estimat-
ing local nitrogen balances for regulation purposes. Romanowicz and Beven (2003) and Pappenberger
et al.
(2007a, 2007b) have used GLUE in an evaluation of the spatial predictions of flood inundation
models. Such a wide variety of applications has necessarily involved a great variety of likelihood mea-
sures, depending on the type of data available. This is another reason why Beven (2006a) suggested the
limits of acceptability approach to model evaluation as a common method that can be applied to a wide
range of different types of calibration data.
One interesting aspect of a number of these applications of GLUE is that the best model available might
not attain reasonable levels of acceptability (e.g. Choi and Beven, 2007, Page
et al.
, 2007; Brazier
et al.
,
2000, amongst others; see also Mroczkowski
et al.
, 1997). This suggests that all the models tried could
be rejected given the data with which they are being driven and the observations with which they are
being evaluated. This would not happen within a statistical framework (except as a result of judgement
by the modeller): the final error variance can always expand to satisfy the condition of bracketing the
observations to the required level, at least in calibration. A good example is provided by Freer
et al.
(1996) where an error in predicting the onset of snowmelt in one of the simulated years of data results in
the observations being outside the prediction limits of the simulations for several weeks (see Figure 7.16).
Thus, there would appear to be limitations on how far models can be validated as representations of the
real runoff processes. This is not to imply, however, that the model predictions might not be sufficiently
accurate to be useful for water resources management, flood forecasting or other purposes.
