Stability and Instability in the Management of Mediterranean Desertification - Environmental Modelling: Finding Simplicity in Complexity - page 392

arguing that species mixtures may lead to conditions
that are 'unstably contagious' by virtue of their genetic
evolutionary potential and population dynamics.

and Kirkby, 1979). The MEDRUSH model (Kirkby et al .,
2002) operates at the large catchment scale and uses the
technique of a statistical ensemble of a 'characteristic' flow
strip whose hydrology, vegetation growth and erosion are
modelled by physical process laws and applied to the
representative strips which thus change its morphology.
The theory developed permits this changed morphology
to cause the strips to migrate within a basin and the
sediment is routed down the channel. In this model, the
initial vegetation cover is provided in the catchment GIS
from remotely sensed imagery and themodels can be used
to predict the impacts of different physical (rainfall) and
human (land-use) perturbations on runoff and sediment
yields from the catchment.
Empirical models have also been used to examine the
effects of climate change on land degradation and runoff,
both over space (Kirkby and Cox, 1995) and over time
(Arnell, 1996). These examples have the usual problems
of such models. Time series that have been parameterized
by particular data sets and so are not readily transportable.
They often have (and should have) error bands attached to
them that may be quite wide. This rather ancient technol-
ogy is highly speculative and often misleadingly simple.
Even further down the line are analogue studies in
which the authors seek contemporary or historical ana-
logues for supposed climate changes among existing or
past environments. Thus one might expect parts of the
south shore of the Mediterranean to be suitable analogues
for the northern shore. The problem is obvious. Obtain-
ing suitable analogues is very difficult especially when the
systems are only weakly understood. This is the kind of
approach that enables us to hope that southern Britain
might be like southern Spain 70 years from now and
therefore the farmers of Sussex can change their potato
fields for vineyards.
A special version of this argument that has become
popular in recent years is the gradient analogue. Where
there is a strong climatic gradient, detailed studies of
geomorphological and ecological processes with their
respective responses can be used to demonstrate how
the changing climatic parameters along the gradient
control the erosion rates. When these are coupled with
plot studies, the linkages so made can be confirmed. An
outstanding study of this type was carried out by Lavee
and Pariente (1998) between Jerusalem and Jericho, a
gradient of strongly decreasing rainfall from the uplands
of central Israel to the Dead Sea. The methodology is
to seek along the gradients for analogues of expected
future climate conditions. It might reveal what the future
processes and responses will be, but does not reveal the

24.3.2 Temporal variability

Of course the very word dynamical implies that the ana-
lytical models are evolutionary (changing through time)
according to their internal mechanism, but the external
controls are also changing through time. Theoretically,
it should be possible to use the equations of dynamical
behaviour to determine how long the system will take to
adjust to a perturbation or external change (the relax-
ation time: Brunsden and Thornes, 1979). This delay has
important impacts in dynamical systems and external
changes can be scaled. High frequency changes (sudden
storms) may have significantly different impacts from
lower frequency changes (such as internal variations in
storm intensities).
In desertification studies, these continue to be a preoc-
cupation, with climate change as a major cause in spite of
the overwhelming evidence that socio-economic controls
are probably more important. In this respect, Allen and
his colleagues developed the human-dimensions aspect
of dynamical systems models in desertification studies
(Allen, 1988). There also, thresholds, attractors, intrinsic
and extrinsic forces all have their roles.
Climate changes can also be regarded as perturbations
operating over a long time scale (tens of years). The main
effects, in terms of the models outlined above are on
the overall carrying capacities ( V cap ), the instantaneous
growth-rate coefficient in the logistic equations ( k 1 ), the
soil moisture constraining plant growth and the direct
production of overland flow through varying rainfall
intensities and therefore the rate of erosion. The variabil-
ity in rainfall is also important, as indicated in the previous
section. Temperature and CO 2 concentrations also affect
plant growth and are therefore an integral component of
modelling the impacts of climate change on desertifica-
tion, as used by Diamond and Woodward (1998).
There are several ways of attempting to model the
impacts of climate change on desertification. The most
common is direct digital simulation of the impacts of
change. For the Mediterranean, the MEDALUS team
at Leeds University under Mike Kirkby has produced
a variety of simulation models for different space and
time scales. The MEDALUS hillslope model (Thornes
et al ., 1996) investigates field-scale erosion in semi-arid
environments and operates at an hourly event scale. It is
essentially based on the principles of TOPMODEL (Beven