Geoscience Reference
In-Depth Information
Predictability is related in part to whether a system is linear or non-linear. Systems that are linear
do not have any dependent variables to a power greater than one or they are not manipulated by
non-linear functions, for example, a cosine. They are deterministic in that the outputs are directly
proportional to the inputs and can be solved easily with exact equations, for example, a linear
regression equation (Antsaklis and Michel 2007). However, most phenomena (human and physical)
are characterised by non-linear behaviour. Some can be solved analytically, while others require
numerical solutions. But the problem arises when non-linear systems exhibit chaotic behaviour,
which means that the future state will be completely unpredictable (Albert 1995). Chaotic behaviour
can be observed in simple systems, for example, in the Lotka-Volterra models of predator-prey
systems (Sprott 2010), but also in the more complex dynamics of economies, cities and other social
as well as physical systems (Kiel and Elliott 1997). Approaches exist for determining when a sys-
tem becomes chaotic and after which point in time prediction will become impossible, for example,
the Lyapunov exponent and Kolmogorov-Sinai entropy, but even these have limits in quantifying
predictability (Boffetta et al. 2002).
Predictability and understanding can also be viewed from another perspective. Popper (2002)
argued that the future is unpredictable because it depends on knowledge that we do not yet have, for
example, newly discovered technologies and innovations. We might generalise this to any unknown
knowledge or
unknown unknowns
about changes or events in a system that could drastically alter
the outcome of our models. For example, the location of new roads/transport networks has an effect
on where deforestation or urbanisation will occur in the future. Where these networks will be built
in the future may be impossible to determine and yet may drastically change the results of future
scenarios from land change models. The presence of non-stationarity in temporal phenomena, that
is, changes in the means and/or variances of variables over time, for example, within climate and
hydrological systems, requires models that can handle the changing dynamics of these systems, or
they should be used with caution when making predictions in the future. Abrupt changes, tipping
points or bifurcations that result in a sudden radical change in behaviour are also not currently
handled well using conventional modelling approaches, for example, predicting the recent financial
crisis. Progress in this area will be limited by the rate at which new theoretical and empirical devel-
opments can be made.
We can also consider predictability in terms of the size and simplicity of our models. For exam-
ple, how many parameters are too many before the model becomes impossible to calibrate, vali-
date or explain? Clarke (2004) argues that simplicity is not always desirable, partly because good
reductionist methods do not yet exist but also because models have several components that interact,
each of which can be complex on their own. It may be better to have a complicated model that is
difficult to explain but produces good, credible results than a simple model which performs poorly.
We therefore need to consider limits at both ends of the simplicity-complexity spectrum and find a
balance. Clarke (2004) argues that it is more important to be ethical in modelling, do good science
and take responsibility for the modelling results, particularly when they pertain to critical systems,
all of which are relevant for GC research.
Finally, can we ever really model human behaviour, to what degree is this random, and will this
be an ultimate limit to predictability? Economics has traditionally treated individuals as rational
decision-makers who weigh up the costs and benefits before undertaking an action. In reality, this
is not the case and individuals have free will to pursue a range of choices that depend on many dif-
ferent factors. Farmer (2011) recognises a number of challenges in agent-based economic modelling
including the need to develop good agent decision rules, but where will these rules come from and to
what degree will they take free will into account? Other models of human activity have been largely
stochastic in nature (Castellano et al. 2009), implying that there are fundamental limits to predict-
ability. However, a recent study by Song et al. (2010) has shown that it is possible to predict individ-
ual behaviour in terms of where individuals travel in their daily lives based on historical data from
mobile phone usage. These latter issues highlight areas where advances in complementary fields will
benefit GC, but at present, they still represent fundamental limits to GC modelling and research.
