Geoscience Reference
In-Depth Information
the MODFLOW groundwater code also use a gridded discretisation (e.g. IHMS (Ragab and Bromley,
2010) and GSFLOW Markstrom
et al.
, 2008).
5.2.3 Models Based on Hillslope Elements
The main alternative catchment discretisation strategy is to make a subdivision into hillslope planes
(Figure 5.4). Such a subdivision is ideally made along flow lines, such that any lateral exchanges
of water between adjacent hillslope elements can be neglected. Some early physically based dis-
tributed models which attempted solutions only for a single hillslope were essentially of this type
(e.g. Freeze (1972) used a finite difference solution and Beven (1977) used a finite element solution).
It is, of course, much easier to determine flow lines if the flow follows the form of the surface to-
pography. Hillslope elements may then be determined on the basis of a topographic analysis of the
catchment. Thus, this type of model works best where the hydrological activity is concentrated near
to the soil surface and no deeper regional aquifer flows are involved. For deeper systems, a two-
dimensional in plan (as in SHE) or fully three-dimensional solution of the subsurface flow domain is
more appropriate.
However, there are many catchments for which the hillslope element discretisation based on surface
topography provides a reasonable approximation to the flow directions. In some early catchment models
of this type, the variable width, variable depth and variable slope hillslope elements were represented by
“equivalent” planes of uniform width, uniform depth and uniform slope (and usually uniform soil and
surface parameters). Early versions of the Institute of Hydrology Distributed Model (IHDM) were of
this type, as well as some models based on Hortonian infiltration excess runoff generation that did not
include a full subsurface flow solution, but treated infiltration as a “loss” (e.g. the model of Smith and
Woolhiser (1971) that later developed into the KINEROS package described by Smith
et al.
(1995) - see
also Section 5.5.2).
The model of Beven (1977) showed that, using finite elements, it was relatively easy to follow the
actual shape of the hillslope and allow the depths of different horizons within a hillslope to vary (as in
the vertical plane discretisation of Figure 5.1). This study also introduced the simple idea of including
slope width in the equations so that convergent and divergent hillslopes could be represented (see also
Box 5.7). This was also introduced into Version 4 of the IHDM (Beven
et al.
, 1987) and there have
been further numerical improvements since (Calver and Wood, 1995). Applications are reported by
Calver (1988) and Binley
et al.
(1991) for the Wye catchment at Plynlimon in Wales and by Calver and
Cammeraat (1993) for an experimental hillslope in Luxembourg.
As a result of this form of discretisation, there is an implicit assumption that the soil and surface
parameters are considered to be constant across the width of the hillslope (in the same way as the SHE
model requires effective values for each grid element). Variations in parameter values between different
soil horizons or for individual elements in a discretisation, such as that of Figure 5.1, can be represented
but they must be effective values integrating over any heterogeneity across the slope. Thus, it may be
difficult to measure such values in the field and Calver and Wood (1995), for example, report that their
experience in using the model is that measured values of hydraulic conductivity tend to underestimate
the values required to represent fast subsurface stormflow in the model.
In Australia, two similar models, THALES and TOPOG have been developed based on the TAPES-C
topographic analysis package that identifies one-dimensional downslope sequences of hillslope elements
from contour data without any intervening interpolation onto a raster elevation grid (see, for example,
Figure 3.5). Both models use a kinematic wave approximation of downslope flows in the saturated zone
and are described in more detail in Section 5.5.3. The CATFLOW model also uses hillslope segments
but introduces the simulation of preferential flows in a dual porosity system (Zehe
et al.
, 2005; Klaus
and Zehe, 2010).
