Curvature-migration relations and planform dynamics of meandering rivers

Theoretical approaches to understanding the planform dynamics of meandering rivers have attempted to relate planform migration to channel curvature. Deterministic meander migration models that have a simple exponential decay spatial convolution form characterizing the effect of upstream curvature on migration behavior generally yield fairly realistic predictions of patterns of bend translation and evolution. However, these models are incapable of reproducing complex terms of bend development, such as double heading or compound looping. Higher-order deterministic models, which incorporate relations between channel curvature and migration rate that are more complex than exponential decay, can reproduce complex meander forms, lending support to the notion that the spatial structure of upstream planform effect is more complex than a simple exponential decay. In any case, deterministic spatial-convolution models of planform dynamics embody theoretical assumptions that have not been extensively evaluated and verified empirically. Moreover, these deterministic models do not take into account the effects of random spatial variability in environmental conditions, which may significantly affect planform evolution. Thus, there is also a need to explore the effects of this variability on migration behavior.;The ultimate goal of this research is to advance understanding of the planform dynamics of meandering rivers by exploring the spatial relationship between planform geometry and meander migration patterns. To achieve this goal, I first develop a methodology that provides a continuous characterization of planforms using aerial photography data. The method overcomes the reliance on discrete and density-dependent characterization—a major limitation of previous studies—and affords the basis for a rigorous empirical evaluation of the planform curvature—migration relation. Using the continuously characterized planform geometry and curvature, I explore empirically the influence of planform curvature on migration dynamics. For this purpose, I use the refined autoregressive form of the planform curvature—migration relation. I then employ Digital Signal Processing (DSP) methodology to derive empirically the spatial planform curvature—meander migration relation and to compare the empirical relation with the spatial convolution structure embodied in deterministic models. Finally, I evaluate the effects of random variability in environmental heterogeneity on the planform evolution. The evaluation of the refined bend data extracted from continuously characterized planforms reveals important information on the spatial character and time evolution of the planform curvature—migration rate relationship. I empirically show that a linear autoregressive relationship, which corresponds to pure exponential decay convolution structure of curvature—migration relation, is not sufficient to characterize the spatial structure of the effect of upstream planform curvature on migration patterns. Bends present complex trajectories of spatial autoregressive relation. To gain knowledge of the underlying processes that give rise to these complex trajectories, there is a need for further empirical exploration of the spatial autoregressive relation for a wide range of meandering rivers.;DSP methodology is a novel approach to the study of the spatial relationship between planform curvature and migration. The methodology allows for direct empirical derivation of the effect of upstream planform curvature on local migration rates. In this respect, being purely empirical, this research is significantly different from previous modeling work where a spatial convolution structure is specified a priori. From the empirical explorations of the spatial planform curvature—migration relation of three reaches of natural rivers, I find that upstream planform curvature—migration rate relation is more complex than simple exponential decay. For a study reach consisting of compound loops, the spatial structure of this relationship coincides with that of higher-order deterministic meander migration models, providing empirical support for theoretical assumptions underlying these models. Empirically derived impulse-response functions do not always capture satisfactorily the planform dynamics of highly complex meandering rivers, suggesting that other factors, such as random or downstream effects may be important in some circumstances.;Finally, evaluation of the effects of random variability in environmental conditions on planform dynamics using a deterministic model with a random component reveals that this variability has an important influence on planform migration dynamics. I demonstrate that both the spatial variation and the variation in the magnitude of random component increase the irregularity of the planform geometry. To rigorously explore if the planforms simulated with a random component can replicate the dynamics of natural meandering rivers, a comparative analysis of the irregularity amongst natural rivers and models with and without random components is necessary. Spectral analysis may be helpful for such a comparison.;In conclusion, this research contributes to the field of fluvial geomorphology by advancing knowledge of the planform dynamics of meandering rivers. The intellectual merit of the research is the identification of the role of the spatial structure of planform curvature in the dynamics of meander migration. The new knowledge gained from the research provides an improved framework for understanding and predicting patterns of planform change along meandering rivers.