Soil and Hillslope (Eco)Hydrology - Environmental Modelling: Finding Simplicity in Complexity - page 164

arrangement of other vegetated and bare areas. However,
these larger scale patterns will interact with outside factors
such as the intensity and duration of rain storms (Boer
and Puigdef abregas, 2005; Puigdef abregas, 2005). For
example, consider the case where a given amount of rain
falls either as a single event or as a series or three, well-
spaced (in time) small events. In the former scenario, rain
falling in upslope areas may first be absorbed by the soils
there, but, as these soils begin to fill (with water), there
may be a surplus that finds its way via overland flow to
the base of the hillslope. In the shorter storms, most rain
falling on the upper parts of a hillslope may be absorbed
by vegetated patches there and there may be no surplus
for downslope areas. If the soils dry out between the small
events, the lower slopes will receive much less water than
in the case of the single event, even though the amount of
rainfall in each scenario is the same. Scenarios in which
patchiness leads to more water reaching the hillslope base
also exist (Boer and Puigdef abregas, 2005).
The empirical evidence points strongly to dryland hill-
slopes being CAS. As well as self-formed patterns of
fundamental units, we know there are localized flows
of resources, that these flows are controlled by the bio-
physical properties of the hillslope soil, and that they
are mediated by larger scale patterns. Similarly, strong
empirical evidence has been presented for peatlands by
Belyea and Baird (2006) and Belyea (2009). Although
such empirical knowledge is essential for a clearer under-
standing of how hillslopes function ecologically and
hydrologically (and also geomorphologically), models
are needed to formalize this understanding. Nevertheless,
a problem of modelling dryland slopes and peatlands in
which vegetation patterns have formed, is that of know-
ing which processes to include in a model and which
to exclude. The problem for the modeller is this: how
simple can we go in simulating ecohydrological processes
in drylands and peatlands? Part of the answer to this
question depends on the purpose of the model. If what
is required is an accurate prediction of water discharge
at the base of a hillslope it may be enough to know the
attributes and distribution of patches which means that
no 'eco' would be needed; the characteristic hydraulic and
storage properties of the different fundamental units and
their spatial distribution might prove sufficient. However,
treating what are clearly dynamic biophysical entities as
static physical ones might be unsatisfactory if the hills-
lope develops or evolves over relatively short timescales
such as periods of 5-10 years. Changes in hydrological
functioning may be driven by internal feedbacks within
the hillslope or may arise as responses to external forcing

such as the introduction of grazers like cattle or a shift
in climate (e.g. Gao and Reynolds, 2003). Change might
be normal under some circumstances and it may be of
sufficient magnitude to warrant an ecohydrological treat-
ment of the hillslope even if predicting hillslope response
to storm events is the main purpose of the model. It is
worth noting, too, that the ecohydrological dynamics of
a hillslope may show threshold behaviour, such that a
switch from one vegetation type or pattern to another
may occur and may be associated with a change in hydro-
logical behaviour (e.g. Abrahams et al . 1995; Turnbull
et al ., 2008).
A range of ecohydrological models of drylands and
peatlands have been proposed and developed. The sim-
plest are CA such as that used by Dunkerley (1997) in
which simple sets of rules can be developed that represent
water uptake by soil, the redistribution of water via over-
land flow, and plant dieback and growth. Such models are
attractive because of their simplicity, and their patterns
could be used as the basis for more detailed hydrological
models (see discussion in Chapter 3). However, in using
simple rules, it is often the case that a single rule repre-
sents two or more processes, and some key feature of the
dynamics (for example, feedbacks between two processes)
might be lost in such a treatment. Another problem is
that CA models often have simple binary states (plants,
bare - no plants), and this may not always provide a good
reflection of reality where the fundamental units (see
Section 10.1) may actually show more subtle variability
in their properties (in for example, biomass). Thus, more
complicated models have been proposed and used. These
include the model of Rietkerk et al . (2002) (see also van de
Koppel and Rietkerk, 2004) where three partial differen-
tial equations (pde) were used to simulate plant density,
subsurface water transfers and surface water transfers.
Whichever approach is used, there remains the problem
of pattern attribution. As Grimm et al . (2005) show in a
review of agent-based models (ABMs) - that is, bottom-
up models that include CA and those that simulate
shoaling fish and bird flocking - it is possible to obtain
similar particular patterns from different rule sets (see
also Chapters 13 and 18). This sounds like the familiar
problem of model equifinality in catchment hydrology
discussed in detail by Beven on many occasions (e.g.
1996, 2001b). The problem might be posed thus: how do
we know we are getting the right pattern for the right
reasons? Most systems display multiple patterns both in
space and time, and models developed to simulate one of
those patterns - such as vegetation distribution - should
also be tested for the other patterns they may predict