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now. Other theories might be inconsistent, but that could just be because they have used the wrong initial
or external forcing conditions over the period of evolution considered. The concept is very similar to
equifinality of rainfall-runoff models in explaining catchment responses, though it should be pointed
out that Culling (1987) later reconsidered the concept to intepret it as a vague and transient concept
that will ultimately be subsumed into the well-defined apparatus of abstract dynamical systems. In this
interpretation, he suggested that geomorphological systems are nonlinear and subject to random forcings
of events of different magnitudes. Similarly to other nonlinear systems, they should be expected to
show significant sensitivity to initial conditions and random perturbations. He distinguishes between
equifinality
sensu strictu
, where a perturbed system will eventually return to its original form, and
weaker forms of equifinality which imply only persistence of some property (see the discussion in
Beven, 1996c).
A second issue is the uniqueness of catchment systems (see Beven, 2000). Even nearby catchments
that appear to be similar in geology, soils, and vegetation show different hydrological responses (though
they might be more similar than another nearby set of catchments that have developed on a different
geology, with different soils and vegetation). Where the development of a catchment has been subjected
to a catastrophic event (such as glaciation and the rather erratic deposition of glacial moraines), such
differences might be marked. This uniqueness of place, arising from natural variability in initial conditions
and the history of climatic forcings, is one of the issues that makes the ungauged catchment problem so
hard in hydrology (see Chapter 10). It also makes it difficult to provide a unified theory in any meaningful
way because, to be useful in practical applications, any such theory requires auxiliary conditions to deal
with the uniqueness of catchment characteristics. This is also why rainfall-runoff modelling has had to
rely so much on calibration against observed variables to either optimise or (much more appropriate)
constrain the uncertainty in the model parameters that reflect those characteristics.
Many hydrologists have suggested that uniqueness of place is a negative concept in that science works
initially by classification of similar entities, then by developing general theories to explain the generalities
underlying the classes, then by testing those theories against observations. Emphasising uniqueness
undermines the possibility of generalising in this way. There is certainly more yet to learn from the
classification approach, especially in the prediction of ungauged basins (see Chapter 10). The problem is,
as noted in previous chapters, there is that so much about catchment hydrology that is simply unknowable
and about which we can only speculate. This is true both at the small scale - the limited possibilities for
knowing about the subsurface characteristics of the different hillslopes in a catchment - and at the large
scale - the limited possibilities of knowing about the forcing inputs in many large catchments around the
world. These limitations are important in that they control the boundary conditions for the prediction we
are really interested in. That is the
next
event in the catchment of interest, with all the particularities of
both catchment and event, whether it be the next flood, the next drought, or some prediction of the future
impact of land or climate change. That is a different kind of science: because we are interested in the
particular, the general will only take us so far (Beven, 2002b). There is, however, a positive response to
uniqueness of place that we develop in Chapter 12.
9.8 Optimality Constraints on Hydrological Responses
One approach that has been proposed for providing additional constraints for the next generation of
hydrological models is to invoke optimality principles. The concept suggests that over a period of time
an open system will evolve so as to optimise the use of the available energy subject to the prevailing
constraints. This actually has a long history in hydrological research, instigated by the seminal series of
papers on the interaction of soil moisture and natural vegetation by Pete Eagleson (1982, 2002; Eagleson
and Tellers, 1982; Rodriguez-Iturbe and Porporato, 2004). There have now been a variety of applications
of optimality principles to hydrological systems (see, for example, recent papers by Schymanski
et al.
,
