Empirical analysis of the planform curvature-migration relation of meandering rivers
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abstract
Meandering rivers are among the most dynamic Earth surface systems, exhibiting progressive change in channel location as they migrate across their floodplains over time. Theoretical models of meandering have defined the influence of planform curvature on meandering in the form of a spatial convolution function that expresses migration at any point along the channel as a weighted aggregate of local, upstream, and, most recently, downstream curvature. This study evaluates empirically the spatial planform curvaturemigration relation of meandering rivers using data obtained from natural meandering rivers with varying degrees of planform complexity and compares the empirical results with the assumed relationships embodied in the theoretical meander migration models. The study is based on a framework that views a meandering river as a dynamical inputoutput system where the migration process is characterized by a spatial filter through which planform curvature produces migration. Discrete signal processing is used to derive the spatial planform curvature-migration relation for each study reach and to analyze the characteristics of this relation via transfer function models. The results demonstrate that the spatial structure of the planform curvature effect on migration rates depends on the complexity of the planform geometry. A first-order difference equation, in which the planform curvature effect is characterized as an exponential decay, can satisfactorily describe the migration process of a planform containing simple bends, but a high-order difference equation, which includes oscillatory terms superimposed on exponential decay, is necessary to capture the development of complex meander forms. The findings support recent theoretical studies that suggest that high-order terms are required in spatial convolution models to generate complex bend geometries. Copyright 2009 by the American Geophysical Union.
