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in wetting than in drying. I would encourage the reader to think about why there should be such an
expectation, starting with a block of soil in a lysimeter and working up to hillslope and catchment scales.
We also would expect the closure fluxes to be a function of spatial scale and geometry of the control
volumes. The time scale of the response will be longer when the hillslopes or channel reaches are longer
or the soil profile is deeper.
This type of hysteresis has been demonstrated in a number of field studies at different scales. Myrabø
(1997), Ewen and Birkinshaw (2006) and Beven (2006b) have all demonstrated hysteretic relationships
between storage and discharge in small catchments. Kendall
et al.
(1999) showed how the form of the
hysteresis might vary with position in the catchment. Clockwise hysteresis loops between flow and
groundwater levels were found in the riparian area in a small catchment in Vermont, while counter-
clockwise hysteresis was apparent in the data from sites on the contributing hillslopes.
Hysteresis is not a new concept to hydrologists. It has been used within soil physics in representing the
soil moisture characteristics which often show different behaviour in wetting and drying. This is often
forgotten when soil moisture characteristic curves are used in hydrological models based on the Darcy-
Richards equation, partly because of a limited amount of experimental information about hysteretic
characteristics (though the GRIZZLY database of Haverkamp
et al.
(2002) has gathered together what
information was available at that time). There are also multiple explanations of the causes of hysteresis
and no real consensus about how it should be parameterised (see the discussions by O'Kane, 2005; Flynn
et al.
, 2005; and Beven, 2006b).
9.3 How are the REW Concepts Different from Other Hydrological
Models?
In one sense nearly all previous rainfall-runoff models are implementations of the REW concepts in
that they provide flux relationships that allow closure of balance equations, whether they are the lumped
models of Chapter 4, the distributed models of Chapter 5 or the semi-distributed HRU models of Chapter
6. It would even be possible to analyse the flux relationships of such models to see what they imply
about energy or momentum balances (even if they are not considered explicitly in the original model
formulations). The difference is in the way in which the REW concepts require that the mass, energy
and momentum balance equations are considered in an integrated and consistent way at the scale of a
discrete partitioning of the landscape into REW elements. I consider the most important consequence
to be the way in which this focuses attention on the scale dependence of the relationships between
the boundary fluxes and the state of the system. This allows the theory of hydrological science to be
comprehensively rethought in ways in which scale, heterogeneity and nonlinearity are more properly and
explicitly reflected in the process representations and closures at the REW control volume. However, it
has to be said that most implementations of the REW concepts to date have not considered this scale
dependence in any way.
9.4 Implementation of the REW Concepts
There have been at least four implementations of the REW concepts reported in the literature: the
REWv4.0 model (Fenicia
et al.
, 2005; Reggiani and Rientjes, 2005; Varado
et al.
, 2006); the CREW
model (Lee
et al.
, 2007; Zehe
et al.
, 2006); the REWASH model (Zhang and Savenije, 2005); and the
THModel (Tian
et al.
, 2006; Mou
et al.
, 2008). The latter extends the REW concepts to low temperature
regions in which freeze-thaw processes have an important effect on the hydrology.
