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fluxes in an arbitrary surface or subsurface flow domain. We would expect this to depend on the nature
of the soil horizons, the spatial heterogeneity of the soil characteristics, the degree and connectivity of
any macroporosity, and other complexities of the perceptual model for a particular site (see Section 1.4).
Where there are observations of actual discharges then some calibration of the velocity distributions might
be possible, but as with other parameterisations, we would expect there to be no unique calibration but
rather some equifinality of representations. This will make it more difficult in estimating what velocity
distribution characteristics might be suitable for an ungauged site, but the same problem arises in any
modelling framework (see Chapter 10). Thus, it would be advantageous if other constraints on possible
parameterisations could be imposed.
9.7 Catchments as Complex Adaptive Systems
There is an intellectual movement in hydrology that aspires to a grand unified theory of catchments as
complex adaptive systems. This movement has its origins in the classic paper of Horton (1945) on the
evolution of hillslope and catchment structures as a result of erosion and transport of sediments in surface
runoff. The work was given impetus by Pete Eagleson in his topic on dynamic hydrology and papers on the
interaction of soil moisture and vegetation (Eagleson, 1978, 1982; Eagleson and Tellers, 1982) and later
by Ignacio Rodriguez-Iturbe and many colleagues, work that has been summarised by Rodriguez-Iturbe
and Rinaldo (1997) and Rodriguez-Iturbe and Porporato (2004). Modern interpretations of this theme,
including taking account of the anthropomorphic effect on hydrological and ecological systems, have
been expressed by, for example, Wagener
et al.
(2010) as the “future of hydrology”. This is to evaluate
catchment systems as complex adaptive systems, with co-evolving soil, vegetation and water components
with or without significant human influence. A particular driving force in this effort has been to borrow
concepts from nonlinear dynamics and complexity theory such as self-organisation, criticality, complex
trajectories in phase space, etc. (e.g. Kumar, 2007).
I have long been sceptical of such an effort. This is not because I do not think of catchments as
complex adaptive and co-evolving systems. Far from it, catchments exhibit their history both before
and after significant human influence, only too obviously in many cases. But providing a meaningful
unifying theory with predictive capability has two main issues. One is that the history of a catchment is
unknowable; it is lost in the past. What we see at the present time is the result of millenia of different
external forcings which might have had different
relaxation times
, that is the periods over which their
impacts can be identified. In some cases, such as a storm event on a badland landscape, the relaxation time
might be rather short, not much longer than the event itself. A significant flood might have a relatively
short relaxation time in humid temperate landscapes (e.g. see the Anderson and Calver (1977) study on
the 1952 Lynmouth flood in Devon, UK, or the different types of response to two major floods on the
Plynlimon catchments described by Newson, 1980). In other cases, such as in a glaciated landscape, the
relaxation time may be much longer. The flow pathways in the catchment may still be dominated by the
results of periglacial and glacial processes of 10 000 years or more ago and have not necessarily changed
much since. Some relaxation times may be even longer, such as the relict soils that are found in some
landscapes, for example in the deep lateritic soils of western Australia which pre-date the Pleistocene
(even if more recent events such as deforestation for cereal production has had a dramatic impact on the
hydrology over large areas).
We cannot know very much detail about the patterns of external forcing that “evolved” the present
landscape, nor about the “initial” conditions at the point of departure for evaluating that evolution. This
problem has been recognised in geomorphology for decades. Bill Culling (1957) borrowed the word
“equifinality” from Ludwig von Bertalanffy (1951, 1962) to describe the logical multiplicity of potential
explanations of the evolution of landforms when their true initial conditions and history development are
unknowable. Multiple theories of that development might be consistent with the landforms as observed
