Geology Reference
In-Depth Information
need to be characterized by either its dominant
soil type, slope steepness or land cover, or by
some weighted average of these conditions
(Wood
et al
., 2006). As grid cells approach 1 km ×
1 km in size, the model simulations are less
likely to resemble the observed landscape (see
also Section 6.4). A further problem with large
grid cells is that the equations used in the models
to calculate flow depths and flow velocities
and to describe the processes of detachment and
transport of soil particles are strictly valid
only for virtually instantaneous conditions or
extremely short time periods. It is difficult to
see how these can be used to describe average
conditions when the time taken for water to
flow from the highest to the lowest point within
a grid cell exceeds the time for which the equa-
tion may be expected to operate reliably. Smith
(1979) stated that flow velocity equations can be
averaged over time periods as long as 5 minutes,
but only over slope lengths of 2 to 5 m. With a
typical velocity for unchannelled overland flow
of 0.01 m s
−1
averaged over 5 minutes, water will
have travelled 3 m in that time. The situation is
somewhat better for flow in small channels or
rills; with a velocity of 2 m s
−1
, water will have
travelled 600 m over 5 minutes. The use of large
grid cells, say 1 km × 1 km, may be just about
workable if it is accepted that flow velocities can
be averaged for periods up to 10 minutes and
velocities are no greater 3-4 m s
−1
.
The decision on whether to select a lumped or
distributed approach may depend on the degree of
complexity at which erosion processes need to be
modelled. As noted earlier, Meyer and Wischmeier
(1969) described erosion in terms of four separate
processes but, in reality, the detachment and
transport of sediment by runoff is more compli-
cated because it can take place by both unchan-
nelled flow and channelled flow, such as rills and
gullies. When dealing with practical problems, it
is important to decide how much information is
needed on the processes by which sediment gets
detached, transported and deposited. If it is suf-
ficient to know only the quantity of material
eroded over a given time, there is no need to
assess the different processes and a lumped model
is likely to suffice. If, however, it is necessary to
know whether conservation measures should be
targeted at controlling the detachment or the
transport of sediment and, if the latter, whether
the transport is relatively uniform over the area
or is concentrated along selected flow paths,
a more detailed modelling of the separate
processes is essential; a distributed model will
therefore be required. At present, many erosion
models separate the processes of detachment and
transport, but few will separate unchannelled
overland flow from rill flow. Indeed, one of the
challenges for modelling research is to develop a
dynamic rill erosion model which will simulate
the processes by which rills develop and infill at
different locations on a hillslope at different times
during a storm (Favis-Mortlock
et al
., 2000). From
a geomorphological viewpoint, most erosion
models are still rather incomplete in respect of
processes since they are restricted to rainsplash,
unchannelled overland flow and rill flow. A fully
integrated model incorporating processes such as
gully erosion, subsurface piping, mass move-
ments (ranging from soil creep to mudflows and
landslides) and wind erosion has yet to be devel-
oped (but see Chapter 14). Fortunately, most
erosion-control problems do not require this level
of complexity.
The above discussion has focused on the con-
ditions within the area being modelled. It is also
important to consider the nature of the boundary
of the area and how models deal with this. In the
simplest situation, the boundary is usually clearly
defined, it being the edge of an erosion plot or a
field, or the divide of the catchment. It is assumed
that the location of the boundary is static over
time and that, except for the lower boundary,
there is no transfer of water or sediment across it.
Most erosion models allow for the transfer of
material across the lower boundary either to an
area downslope or into the river system. Once the
material leaves the area being modelled, no fur-
ther account is taken of it. This approach is gen-
erally acceptable for relatively short time periods
ranging from individual storms to a few years.
Over longer time periods, the boundary condition
can become more complicated. For example, the
