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pressure applied to an enclosed sample of a porous medium in order to create unsaturated conditions that
immediately empty all the connected larger pores. They stay empty even if there is a hydraulic gradient
inducing flow. In the field, of course, there is no such imposed pressure and by-passing would be more
likely to take place during wetting if (locally) gravity is not dominated by capillary gradient effects. The
classical treatment of unsaturated soil water flows is, therefore, effectively predicated on an unrealistic
experiment! Air pressure effects could still be important perhaps when there is a continuous saturated
wetting front infiltrating into uniform soil, though even in this case air might escape through larger pore
pathways. This was recognised by Robert Horton, who also argued that the decline in infiltration rates
seen in experiments was more likely to be due to changes at the surface rather than a control due to
capillary gradient effects in the profile (see Beven (2004a) and Box 5.2).
Actually, the limitations of the theory of the Freeze and Harlan blueprint is not the only problem in
applying it in actual model applications. The greater problem is in the characterisation of the uniqueness
of individual catchments in terms of the parameters of the model. The argument, commonly made, that
the parameter values required by such models are more easily estimated because of the physical basis of
the concepts, does not really hold if the concepts are (at best) an approximation to the physics of flow in
heterogeneous domains (Beven, 2000, 2002a). As noted earlier, what is then needed is
effective
values
of the parameters that help compensate for the limitations of the physics incorporated into the model.
The effective values might be quite different from what can be measured or estimated from
pedotransfer
functions
derived from small scale measurements (see Box 5.5). Indeed, numerical experiments suggest
that where there is a strong interaction between surface and subsurface processes, it might not be possible
to find effective values consistent for all conditions (Binley
et al.
, 1989).
So, what should we conclude? That the Darcy-Richards equation might not be the best description
of flow in unsaturated soil in the field and that applying the Darcy-Richards equation as if the soil had
uniform soil properties is to ignore the implication of the physics that some other equation should be
being used. This, together with the difficulty of knowing the true boundary conditions and characteristics
of the subsurface in the field, may certainly be why it has proven rather difficult to show that models
based on the Freeze and Harlan blueprint can successfully reproduce the behaviour of real catchments
(see the case studies of Sections 5.4, 5.6 and 5.7). The real question then is can we do better? I think
we can.
9.2 Representative Elementary Watershed Concepts
In fact, the basis for a new generation of hydrological models already exists in the “representative
elementary watershed” (REW) concepts developed by Paolo Reggiani and others (Reggiani
et al.
1998,
1999, 2000, 2001; Reggiani and Shellekens, 2003; Reggiani and Rientjes, 2005). The REW framework
is based on physics, in that it sets out the fundamental balance equations for the processes underlying
the hydrological response of a control volume element of the landscape (Figure 9.1). It is normal for
hydrological models to consider the local or catchment water balance equation, of course, and some
models also make use of a surface energy balance equation in estimating evapotranspiration or snowmelt
fluxes. In this sequence of papers, Reggiani
et al.
take this further to consider the water balance, energy
balance and momentum balance equations for the processes in control volumes underlying any landscape
unit. This framework is discrete in space, resulting in ordinary differential equations in time, rather than
the continuum partial differential equation approach of the Freeze and Harlan blueprint. It is also scale
independent: soil profiles, small plots, hillslopes, or a zero-order or higher catchments can be treated as
REWs. Larger catchments could be made up of multiple REW elements, though these need not be of
the form of elements with simple geometry such as the grid squares of SHE or SWAT, or the triangular
or hexagonal elements of other distributed models. Within the REW framework they can be hillslope or
