Geology Reference
In-Depth Information
made to a sediment delivery ratio to express what
proportion of the sediment yield actually leaves
the cell and discharges into the river system. The
problems of obtaining a suitable relationship at
this scale between time and space increments at
which calculations are made precludes the possi-
bility of routing the water and sediment physi-
cally from one grid cell to another. Nevertheless,
this scale of modelling is seen as increasingly val-
uable because it allows the possibility of includ-
ing additional components, for example, the
ability to predict the growth of the plant cover in
relation to long-term changes in climate and
soils (Kirkby & Neale, 1987) or changes in
cattle-grazing regime (Biot, 1990; Thornes, 1990).
In the MEDALUS model (Kirkby
et al
., 2002),
feedback mechanisms are included to cover long-
term changes in the stoniness and roughness of
the surface soil as a result of erosion.
Some care needs to be taken in using and inter-
preting the results of models applied at different
scales. The scale at which the model operates is
the key, rather than the scale at which maps are
produced. For example, if the output from the
USLE is mapped at a national or European scale,
using 1 km or 10 km grid cells, the map shows the
predicted value of mean annual soil loss at a field
scale within each cell. It does not show the con-
tribution of sediment from each cell to the river
system. Nor can the values of each cell within a
catchment be summed to give a value for the sed-
iment yield from that catchment. This is because
the USLE does not predict sediment delivery to
rivers; nor does it predict erosion over 1-10 km
2
size areas.
the model can be evaluated to see whether it
yields realistic output.
2.8.1 Sensitivity analysis
An increasingly important aspect of model test-
ing is a sensitivity analysis that is designed to
determine how sensitive the output is to unit
changes in the value of one or more of the input
parameters. Different sensitivity indices are used
(Morgan, 2005), of which the average linear sensi-
tivity (Nearing
et al
., 1989a) is the most common.
The results provide a check on whether the sensi-
tivity of the different input parameters in the
model accords with that observed in field situa-
tions at the appropriate temporal and spatial
scales. If a parameter is found to be too sensitive
or not sensitive enough, the model may need to
be adjusted. Unfortunately, although conceptu-
ally simple, sensitivity analysis in reality can be
extremely complex, particularly when carried
out for process-based, distributed models. Since
these models allow for erosion to be limited by
either the detachment rate or the transport capac-
ity, parameter sensitivity depends upon which is
the limiting factor. Furthermore, many of the
relationships by which erosion is related to indi-
vidual parameters are non-linear, which means
that the output may be sensitive when the param-
eter values fall within a certain range, but not
when they are outside that range. Sensitivity may
also be different when a model is operated for
extreme conditions. A further issue is the inter-
action between the parameters so that a certain
parameter may only be sensitive when the values
of another parameter exist within a certain range.
Procedures for addressing these issues are dis-
cussed more fully in Chapter 3. Understanding
which parameters are most sensitive is also
important because the values of those parameters
need to be determined more accurately. There is
then the question of whether the procedures used
in field measurement are robust enough to give
the required level of accuracy.
The complex nature of sensitivity means that
the user cannot assume that the results of a
generic sensitivity analysis for a chosen model
2.8
Testing, Calibration and Validation
Once a model has been developed at the appropri-
ate temporal and spatial scale for meeting a spe-
cific objective, it needs to be tested to show that
it actually works. The first step is normally to
feed in arbitrary values of the input parameters to
check that the model functions mathematically
and is rational. Once errors have been corrected
and 'bugs' in the computer programming removed,
