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parameters based on this detailed information
were worse than in the original (calibrated) model
of Loague and Freeze (1985). Later, VanderKwaak
and Loague (2001) and Loague and VanderKwaak
(2004) applied the more complete 3D subsurface/
2D surface finite element InHM model to the R5
site. The resultswere better but still suggested that
improved results might be obtained with a better
representation of the subsurface flow processes. In
a final paper, Loague et al. (2005) extended the
subsurface flow domain to deeper layers. They
were able to report a further improvement but that
their storm by storm simulations were still very
sensitive to the specification of the initial condi-
tions for each event, which are difficult to define in
the subsurface: the same issue of model validation
recognized by Stephenson and Freeze (1974)
30 years earlier.
There has been another interesting application
of the InHMmodel to the Coos Bay site inOregon.
This is a small (860-m
2
), steep, channel head hol-
low that was extensively studied by Bill Dietrich
and others until it failed. Again, where possible the
soil and sapprolite parameters used in the model
were based on the extensive database of field
measurements. Therewere not enough pointmea-
surements in this case to interpolate a field of soil
parameters, so these were treated as homogeneous
in each of three layers, even though individual
measurements of hydraulic conductivity in the
sapprolite ranged over four orders of magnitude.
It was found that while themodel could reproduce
the discharge from the site reasonably well, it
could not reproduce the internal piezometer
observations (Ebel et al. 2008). It was suggested
that one reason for this was that the piezometers
were affected by flow through fractures in the
underlying bedrock, the presence of which had
been revealed by the slope failure and which were
thought to have played an important role in the
failure (Montgomery et al. 2002).
These case studies both demonstrate that even
in small catchments with detailed experimental
information available, there are limitations as
to how far a distributed rainfall-runoff model
can predict the internal responses of the hydrolog-
ical processes. All models should be treated as
measures. Because of input and boundary condi-
tion error, the optimummodel in calibration may
also not give the best performance in validation
(even if the model structure provides a good repre-
sentation of the processes). We also know that for
many commonly used performance measures
there may be many different parameter sets that
give nearly the same level of performance
(Beven 1993; Beven and Freer 2001a). Thus, there
are persuasive arguments that retaining only an
'optimum' model may be inadequate, even if the
prediction uncertainty around that optimum is
explored (Beven 2006b).
One of the early arguments for pursuing a strat-
egy of distributed rather than lumped modelling
was to avoid the problems that had been encoun-
tered in the calibration of lumped models. The
argument was that if the model parameters were
physically based and could be estimated by field
measurement or on the basis of the physical char-
acteristics of a catchment, then not onlywouldwe
move towards a more realistic representation of
the spatial pattern of hydrological processes
but also we would avoid these difficult calibration
issues. Hydrological science would become
more realistic - see the discussion between
Beven (1996a, 1996b) and Refsgaard et al. (1996).
This has, in the end, been difficult to demonstrate,
and even the applications of distributed models
to small catchments have had to resort to some
calibration.
One of the most interesting studies in this
respect is the application of several generations
of distributed models to the R5 catchment at
Chickasha, Oklahoma, by Keith Loague and col-
leagues. This is not a large catchment (9.6 ha). It
was originally modelled as an infiltration excess
overland flow runoff generation system using the
QPBRRMmodel, with parameter estimates based
on 26 point infiltration experiments (Loague and
Freeze 1985; Loague 1990, 1992). Later, this was
extended to a further 247 measurements on a grid
of 25m with additional transects of 2m and 5m
spacing, with geostatistical interpolation to 1m
and 959 hillslope planes in the runoff model
(Loague and Kyriakidis 1997). The results using
only the measured and interpolated infiltrated
