Geoscience Reference
In-Depth Information
Figure 5.4
Schematic diagram of a hillslope plane catchment discretisation as in the IHDM model (after
Calver and Wood, 1995, with kind permission from Water Resource Publications).
(TIN) discretisation of the topography such as tRIBS (Ivanov
et al.
, 2004, 2008) and PIHM (Qu and
Duffy, 2007). This can give rise to numerical problems in coupling the solutions at a boundary which
moves up and down with the water table as the soil wets and dries. The solution of the saturated zone
problem depends on the profile of water content in the unsaturated zone of each grid element and
vice versa. Normally some iterations are required to achieve convergence of the two solutions. Similar
iterations may be required to achieve convergence at nodes on the soil surface, where the boundary may
be changing from infiltration to ponded conditions during a storm.
An alternative strategy is to avoid decoupling the unsaturated and saturated zones and instead make
the split along lines of greatest slope in the catchment to make a number of hillslope planes that are then
solved separately “in parallel”. The vertical section along each plane is then discretised in two dimensions,
assuming that conditions across each plane can be considered uniform. This is the approach adopted by
the IHDM model (Figure 5.4; see Calver and Wood, 1995) and, more recently, the CATFLOW model
of Zehe
et al.
(2005). Then there are models, such as TOPOG (Vertessy
et al.
, 1993), that use variable
width hillslope planes but separate the unsaturated zone and saturated zone; VSAS2 uses variable width
hillslope planes but has a time variable separation of a saturated contributing area to ease the numerical
problems of solving the Richards equation when part of the flow domain is fully saturated (Bernier,
1985; Prevost
et al.
, 1990; Davie, 1996); and the model of Duffy (1996), which also uses hillslope
planes but solves for the moisture storage at each point, integrated over the profile of both saturated and
unsaturated zones.
However, the computer power available to hydrological modellers continues to increase, and in the next
decade this will result in more and more use of three-dimensional solutions of the continuum equations.
