Chaos, fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments
Introduction
Research in nonlinear dynamic systems has grown rich and varied as notions of chaos, fractals and self-organization have been recognized in virtually all physical and human sciences, ranging from economics and linguistics to physics and geomorphology. This paper reviews the principal applications of these concepts in geomorphology, particularly in coastal geomorphology, and presents an exemplary self-organization model for the simulation of aeolian dune landscapes in vegetated environments. Although this paper is not intended as a rigorous and comprehensive review of chaos, fractals and self-organization in general, a brief overview of the basic ideas and terms involved is appropriate in order to appreciate their application in geomorphology. For comprehensive examination of these concepts, the reader is referred to Gleick (1987) and Kauffman (1995) for popular descriptions, while the more rigorous mathematical underpinning and specific algorithms may be found in Turcotte (1992) and Strogatz (1994).
Section snippets
Chaos theory
Chaos theory is epitomized by the so-called ‘butterfly effect’ detailed by Lorenz (1963). Attempting to simulate numerically a global weather system, Lorenz discovered that minute changes in initial conditions steered subsequent simulations towards radically different final states. This sensitive dependence on initial conditions is generally exhibited by systems containing multiple elements with nonlinear interactions, particularly when the system is forced and dissipative. A system is said to
Geomorphology
Geomorphology presents an obvious arena for the application of chaos theory, fractals and self-organization concepts, as nearly all landscapes exhibit a range of nonlinear dynamic interactions between system elements. Further, many features of the natural landscape have a fractal-like appearance. Indeed, one of conceptions of fractals evolved through an analysis of the set of measurements of Richardson (1961) of Britain's coastline by Mandelbrot (1967), who has subsequently described a host of
Coastal geomorphology
Coastal systems can be categorized as nonlinear dissipative complex systems as wind and wave energy is dissipated in the coastal zone and the interactions between morphology, sediment transport and fluid dynamics are strongly nonlinear. Southgate and Beltran (1998) and Southgate and Moller (2000) investigated the response of beach morphology to hydrodynamic forcing on monthly to decadal time scales in terms of self-organized behavior. By means of fractal analysis of beach-level time series at
Numerical simulation model
The simulation model is based on the original algorithm of Werner (1995), also outlined in Momiji et al. (2000). The principal feature of the algorithm is that batches of sand are transported across a simulated 3D surface based on a stochastic procedure, whereby the erosion, transport and deposition processes are determined by chance. The model area consists of a square cellular grid containing stacked slabs of sand of a fixed height that constitute the topography. The sand transport process is
Results
Initial investigations were conducted to reproduce the types of dune landscapes previously simulated by Werner without the vegetation influences in the environment. Fig. 6 shows an example of a barchan dune field simulation, evolved from an initially random undulating topography with no vegetation present. Other bare sand dune types, such as transverse dunes, seif dunes and star dunes, were successfully modeled as well. Since this class of simulations has already been described by Werner (1995)
Discussion
The above modeling efforts have been merely exploratory, but they have produced some tantalizing results. They clearly show the potential of this approach for simulating strikingly different and realistic dune patterns under the influence of vegetation dynamics. The great contrast in appearance between the landscapes of Fig. 7, Fig. 8, for example, shows the large impact of vegetation dynamics on the developing morphology. It illustrates how a change in parameters (here the growth functions)
Conclusion
Geomorphological research has been greatly enriched by the concepts of chaos, fractals and self-organization developed over the past few decades. Since nearly all geomorphic systems involve complex nonlinear dynamics, they are inherently amenable to these types of investigations. In coastal geomorphology, this has inspired research ranging from wave climates to shore profiles and beach cusps. The description of a system in terms of self-organization and attractors provides for an alternative
Acknowledgments
Part of this research was conducted during an MSc project at the University of Amsterdam, Department of Physical Geography and Soil Science, under the excellent and friendly supervision of Bas Arens. I am further grateful to Doug Sherman for valuable comments and discussions during the development of this paper. Constructive suggestions by two anonymous reviewers led to several improvements and are hereby greatly appreciated.
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