Geoscience Reference
In-Depth Information
Figure 9.4
Distribution of unsaturated zone (light grey), saturated zone (darker grey) and tracer (black)
particles in the MIPs simulation of a tracer experiment at G ardsj on, Sweden (after Davies et al., 2011, with
kind permission of John Wiley and Sons).
More explicit
particle tracking models
have been introduced by Beven
et al.
(1989) and in John
Ewen's SAMP model (Ewen, 1996). The former considered steady state flows only; the latter, infiltration
into a single soil profile, allowing for the effects of capillarity on particle movement. More recently,
Davies
et al.
(2011) have suggested that such an approach might also be used in a more explicitly
distributed model, tracking individual particle masses of water through a hillslope element. Their multiple
interacting pathways (MIPs) model assigns Lagrangian velocities to particles from distributions according
to whether they are in the unsaturated (vertical movement) or saturated (downslope movement) state. The
distributions must integrate to match the specified saturated hydraulic conductivity of the soil, which in
their application was a strongly nonlinear function of depth into the soil profile. In the initial application
of the model, interactions between particles are ignored so that particle movements can be treated in
parallel and bulk energy loss is assumed to be in equilibrium with the potential energy gained with loss
of elevation (equivalent to saying that capillary forces can be ignored as having only a local effect and
that the hydraulic gradient is equal to the slope angle). Figure 9.4 shows a snapshot of the particles
on a representation of a hillslope at the Gardsj on catchment in Sweden. More details of this modelling
experiment are in Chapter 11, but Davies
et al.
(2011) demonstrated that the MIPs approach could provide
good simulations of both flow and tracer concentrations at the site.
Having established that this model can reproduce the observed behaviour of the Gardsj on slope, Davies
and Beven (2010) also explored the effects of slope length scale on the nature of the storage-discharge
relationship, the constitutive relationships of the REW framework. Figure 9.5 shows, in an extension
of their original results, how the hydrographs and hysteresis in storage-discharge changes for slopes of
different length and different antecedent conditions. This work demonstrates how other approaches to
representing hillslope hydrology are possible, albeit as yet with simplifying kinematic assumptions.
Some of those assumptions will need to be relaxed in future. For example, in situations with deeper
subsurface flow systems, the change in hydraulic gradient with wetting and drying will be much more
important (although a kinematic assumption might still be a good approximation if the Lagrangian
velocities scale well with the total head differences in longer slower pathways). Alternatively, there is a
particle-based technique that allows the assessment of changes in pressure within the flow domain. This
is “smoothed particle hydrodynamics” (SPH), first introduced by Gingold and Monaghan (1977), which
