Chaos, fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments

Abstract

Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Concepts of chaos, fractals and self-organization, originating from research in nonlinear dynamics, have proven to be powerful approaches to understanding and modeling the evolution and characteristics of a wide variety of landscapes and bedforms. This paper presents a brief survey of the fundamental ideas and terminology underlying these types of investigations, covering such concepts as strange attractors, fractal dimensions and self-organized criticality. Their application in many areas of geomorphological research is subsequently reviewed, in river network modeling and in surface analysis amongst others, followed by more detailed descriptions of the use of chaos theory, fractals and self-organization in coastal geomorphology in particular. These include self-organized behavior of beach morphology, the fractal nature of ocean surface gravity waves, the self-organization of beach cusps and simulation models of ripples and dune patterns. This paper further presents a substantial extension of existing dune landscape simulation models by incorporating vegetation in the algorithm, enabling more realistic investigations into the self-organization of coastal dune systems. Interactions between vegetation and the sand transport process in the model—such as the modification of erosion and deposition rules and the growth response of vegetation to burial and erosion—introduce additional nonlinear feedback mechanisms that affect the course of selforganization of the simulated landscape. Exploratory modeling efforts show tantalizing results of how vegetation dynamics have a decisive impact on the emerging morphology and—conversely—how the developing landscape affects vegetation patterns. Extended interpretation of the modeling results in terms of attractors is hampered, however, by want of suitable state variables for characterizing vegetated landscapes, with respect to both morphology and vegetation patterns. D 2002 Elsevier Science B.V. All rights reserved.