Environmental Engineering Reference
In-Depth Information
Such implementations have been described, for
example, by Reggiani and Schellekens (2003),
Zhang et al. (2006), Varado et al. (2006) and Lee
et al. (2007) but have generally assumed scale
independence in REWs treated as homogeneous.
The problem of not having measurement techni-
ques for fluxes at the scale at which we wish to
make predictions means that developing better
representations of the closure fluxes will be both
difficult and uncertain, but this is what is required
tomake real progress in distributedmodelling (see
the more extended discussions in Beven 2002,
2006a). Until such progress is made, applications
of the REW concepts will essentially be subject
to much the same limitations as those for the
Freeze and Harlan blueprint described above.
Beven (2006a) has suggested that, while the REW
concept is physically consistent at any scale of
discretization, how to represent the boundary
fluxes on the basis of sub-element-scale properties
and patterns of storage remains the 'holy grail' of
hydrological modeling.
The third issue is knowing what the boundary
conditions are for the catchment. To predict the
pattern of hydrological fluxes we need to specify
input fluxes for precipitation, output fluxes for
evapotranspiration (which may depend on the
internal state of the system as well as vegetation
pattern), and we need to specify the initial
internal states at the start of a simulation for every
element in the catchment discretization. Binley
et al. (1989a) showed that the effects of the
initial conditions for simulations of this type can
affect predicted fluxes for periods of months;
while, in one of the earliest applications of
a distributed model to a real hillslope, Stephenson
and Freeze (1974) already recognized the difficulty
of validating such models when the initial and
boundary conditions were necessarily uncertain.
Representative Elementary Watershed
Reggiani et al. (1998, 1999, 2000) took this as the
basis for a quite different distributed description of
hillslope and catchment hydrology. They based
their 'Representative Elementary Watershed'
(REW) concept on the subdivision of a catchment
into landscape units, each of which might then
have different process domains. This was, in part,
similar to earlier semi-distributed approaches
based on hydrological response units (HRUs)
(e.g. Kite and Kouwen 1992). There is also an
analogy with the landscape 'tiles' used in repre-
senting the land surface hydrology in several mod-
ern climate models used at even larger scales.
Reggiani et al., however, took this concept a stage
further by listing the mass, energy and momen-
tum balance equations for each component of the
REW. These equations apply, without numerical
approximation, to any scale of REW from plot to
hillslope to landscape tile. The difficulty that then
arises, however, is that the balance equations
involve multiple boundary fluxes for mass, energy
and momentum. There is thus a 'closure' problem
of how to define these fluxes at a particular scale
(e.g. Reggiani and Rientjes 2005). What is clear is
that the definitionswill be scale and heterogeneity
dependent, something that has been neglected in
current implementations of the REW concepts.
Distributed flow routing and flood
inundation models
Similar issues have arisen in the development of
distributed hydraulic models since the first
explicit solution scheme for the 1D St-Venant
equations appeared in Stoker (1957). Once digital
computers became more widely available there
were many different finite difference implemen-
tations of the 1D equations (e.g. MIKE 11, ISIS,
HEC-RAS) and research on better solution
methods for these hyperbolic partial differential
equations (e.g. Abbott and Minns 1998). As more
and more powerful computers became available,
2D solutions were produced using finite differ-
ence, finite element and finite volume solution
methodologies, and solutions of the full Navier-
Stokes equations are now available for fully 3D
flow domains, although these are still limited to
small domains in any applications to rivers.
New distributed techniques, such as Smoothed
Particle Hydrodynamics, are also being explored
in applications to surface water flows (e.g.
