Geoscience Reference
In-Depth Information
The closure schemes that have been used in these implementations of the REW concepts as hydrological
models have largely ignored both hysteresis and scale issues. Instead, they have taken a path similar to
models based on the Freeze and Harlan blueprint by assuming that small scale physics can be used at larger
scales only with a change of effective parameters. This, however, gives an even greater approximation
in the discrete framework of the REW than in the numerical solution of the partial differential equations
of the Freeze and Harlan blueprint. The distributed nature of a direct numerical solution, at least, shows
the effects of length scales and wetting and drying implicitly (and could be thought of as a form of REW
model within which the REW elements are defined by the spatial discretisation of the numerical solution;
there might also be the possiblity of transforming the orginal differential equations to boundary element
form in cases where suitable continuum equations can be defined).
An interesting application in this respect is that of Zehe
et al.
(2006) and Lee
et al.
(2006). The aim
of their papers was to provide constitutive relationships for predicting the response of ungauged basins
within the REW framework (see Chapter 10). To do so, they looked initially at modelling a single small
catchment, the Weiherbach catchment (3.6 km
2
) in Germany. Erwin Zehe had already implemented a
distributed model for this catchment (CATMOD) that produced reasonably accurate predictions of the
discharge hydrograph and of the averaged soil moisture observations in the catchment (Zehe
et al.
, 2005).
CATMOD is based on the Darcy-Richards equation, but with the option of additional macropores as
local zones of high hydraulic conductivity in the solution domain. Zehe
et al.
(2006) then used this model
as a dynamic upscaling tool to develop constitutive relationships for storage-discharge at the REW scale
in the CREW model. They used the existing model to do so, as well as alternate representations of
the hillslopes in terms of both soil types and macroporosity. They showed how the relationships could
be derived from integrated values of storage and predicted discharges. The relationships showed some
limited hysteresis in this case, but a non-hysteretic relationship could provide almost as good predictions.
They allow that the limited range of soil moisture values simulated at this site might have limited the
hysteresis in the response, so that this might not be a general conclusion. Lee
et al.
(2007) then take the
relationships to provide closure in a REW model of the catchment, demonstrating predictive capability
of equivalent accuracy to the orginal model.
In the application of the REW concepts to the Weiherbach catchment, the CREW model is emulating
the CATMOD simulation rather than the real catchment. Zhang
et al.
(2006) have taken an alternative
strategy, calibrating the effective parameter values of their REWASH model (where the closures are also
based on small scale Darcian physics) directly against data from the Geer catchment in Belgium. In both
cases, there is still a limited degree of accuracy in reproducing the behaviour of the real catchment that
is similar to that achieved with other hydrological models calibrated against observations.
There may be two primary reasons why these new concepts might seem to perform no better than
traditional models. One is that the level of performance that is achievable is limited by the uncertainties
in the observations against which they are being calibrated or evaluated. As discussed in Chapter 7,
rainfall-runoff models should not be expected to perform better than the quality of the data that is
available to drive and evaluate them. The second is that the types of closure scheme that are being used
in the first implementations of the REW concepts might still be improved, beyond the range of concepts
that have been used in the rainfall-runoff models currently available.
The question is how this might be achieved in future research and practice. We cannot get around the
fact that while experiments such as those in Figure 1.1 reveal the complexity of subsurface flow pathways,
it is not generally possible to examine how water flows in the subsurface (and even how it might flow
over the surface) everywhere in a landscape unit. It is clear, however, that to ignore such complexity and
assume that small scale theory can simply be scaled up to the REW is not the correct response, even
if it might appear to produce acceptable results in some cases. It would be better to try to account in a
more general way for such complexity. It is not yet clear how this might be done, but two possibilities
are considered here, one in which a scale-dependent hysteresis is inferrred from simplified theory and
one which tries to represent the heterogeneity of flow pathways directly as distributions of velocities
