World-wide variations in hydraulic geometry exponents of stream channels: An analysis and some observations

: A framework for channel restoration design is presented that attempts to bridge the divide between reconnaissance level geomorphological designs at one extreme and numerical modeling of hydrodynamics, sediment transport and morphological change at the other Reestablishing equilibrium between the sediment supply and available transport capacity in the restored reach is the primary objective of the design framework A geomorphic engineering approach is presented, which recognizes that the river is ultimately the best restorer of its natural morphology and should be allowed to participate in its own recovery This is accomplished through designing an approximate channel mould, based on the broad dimensions of the river, and then allowing the river itself to develop the intricate cross-sectional detail and intra-reach morphological features to complete the recovery process Geomorphic engineering provides a practical solution by striking a balance between empirical-statistical and analytical (process-based) methods The range of techniques that comprise the design approach facilitate a realistic solution to the indeterminacy problem and confidence bands applied to typed' morphological equations provide a mechanism through which natural rivers can be used as realistic analogues for channel restoration design By accounting for natural systems variability, the design framework is an appropriate platform for generating restoration design solutions that mimic the natural channel morphologies and environmental attributes in undisturbed systems, while meeting multifunctional goals of channel stability and low maintenance commitments Rather than constructing physical habitats that constitute form without function, geomorphologically, the types and levels of physical habitat diversity that are sustainable in the restored reach are defined by the type of river, the nature of the sediment and flow regimes and the catchment context

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Channel Restoration Design for Meandering Rivers

Hydraulic geometry is of fundamental importance in planning, design, and management of river engineering and training works. Although some concepts of hydraulic geometry were proposed toward the end of the nineteenth century, the real impetus toward formulating a theory of hydraulic geometry was provided by the work of Leopold and Maddock (1953). A number of theories have since been proposed.Some of the theories are interrelated but others are based on quite different principles. All theories,however, assume that the river flow is steady and uniform and the river tends to attain a state of equilibrium or quasi-equilibrium. The differences are due to the differences in hydraulic mechanisms that the theories employ to explain the attainment of equilibrium by the river.

On the theories of hydraulic geometry

Effects of catchment size on runoff relationships

Few studies have attempted to examine explicitly the factors that produce variation in hydraulic geometry parameters. A continuously varying parameter model of downstream hydraulic geometry is formulated to address this issue. Parameter variation is viewed as a function of channel sediment characteristics and flood magnitude. Results for the Missouri River basin show that these factors are strongly associated with variation in hydraulic geometry coefficients and exponents. The results also indicate that bivariate relationships are biased by these associations. The analysis yields site-specific parameters that uniquely describe the relationship between active channel form and mean discharge at a particular location within the basin. The continuously varying parameter approach has several advantages: (1) it isolates the separate influences of each explanatory variable on each hydraulic geometry parameter, (2) it maintains the precision of parameter estimates by including the entire data set in the analysis, and (3) it allows testing of the conception that hydraulic geometry parameters vary continuously rather than discretely, yet permits analysis of discrete change through the use of dummy variables.

A Continuously Varying Parameter Model of Downstream Hydraulic Geometry

The hypothesis that channel perimeter sediment characteristics exercise control over the shape (width-to-depth ratio) of alluvial channels is well established in the literature. Schumm9s analyses of Great Plains streams constitute a particularly important set of evidence in this regard. A reanalysis of Schumm9s data using multiple regression techniques suggests that channel perimeter sediment characteristics play a minor role in the development of channel shape. Discharge appears to be the dominant factor controlling width-to-depth ratio in Great Plains streams.

The relationship between channel shape and sediment characteristics in the channel perimeter

Sixteen hydromorphic variables, with observations grouped by stream order, were subjected to principal components analysis to investigate the manner in which variables interact in a downstream direction within a drainage basin. The degree of intercorrelation between variables in a fluvial system is influenced by geology, structure, and variation in the physical characteristics of stream basins. The contention here is that since the degree to which these factors are effective varies downstream in an orderly way, the intensity of interaction between variables should also be so ordered. The results of the analysis support this because the variance accounted for by the first and second principal components increased systematically downstream, whereas that associated with principal components three through six generally decreased. The structure of the data is also examined in the context of varimax rotated components, and the changes that occur between lower- and higher-order stream basins are identified.

Patterns of variation in a fluvial system

The relationship between stream order and hydraulic geometry was tested using multivariate discriminant analysis. Data on the hydraulic geometry variables were collected for 103 streams of order 3 through 6 in the Pecatonica River drainage network in southwestern Wisconsin. The results indicate that the relationship is not as strong as suggested by L. R. Leopold and J. P. Miller. Channel width, depth, and gradient appear to account for the existing strength, whereas velocity and roughness make only a negligible contribution.

Multivariate empirical test of the Leopold and Miller stream order–hydraulic geometry hypothesis

Channel networks for 103 drainage basins ranging in size from 0.65 to 199 km2 were classified according to 9 topologic systems ranging from Strahler's order and Shreve's magnitude to those recently derived by Werner and Smart. Correlation coefficients and coefficients of determination were calculated to test the relationship between these systems and 10 characteristics of drainage basins and stream channels. The results suggest that (1) network properties are closely associated with basin area and with other characteristics primarily determined by area, (2) the hydraulic variables are essentially unrelated to all topologic systems analyzed, and (3) certain newly proposed topologic systems are unrelated to all characteristics tested, including area.

Topological classifications of drainage networks: An evaluation

Stream channel development is a complicated process involving many factors. A major goal of research in fluvial geomorphology is to develop an understanding of the relations between channel form, water discharge, and sediment discharge characteristics. The concept of thresholds has been introduced as an element in fluvial processes, with the implication that the factors involved in a process might change in some way as threshold boundaries are passed. This study is focused on the extent to which a particular regional boundary represents a threshold in the process of stream channel development. Twenty-four alluvial stream channels from the Great Plains region and 24 from the Central Lowlands region are compared with regard to the distributional form, central tendency and dispersion characteristics, and correlation structure of ten variables, including indicators of discharge, channel sediment, and channel morphology. The results suggest that these aspects of the data are very similar between the regions, except for certain differences in central tendency characteristics, which are assumed to reflect underlying differences between the regions in geology and climate. In general, the results support the idea that this regional boundary is not an effective threshold with respect to the stream channel development process, and that, therefore, stream channels develop in these environmentally distinct regions by way of a similar process.

Lawrence J. Onesti

Papers

The relationship between channel shape and sediment characteristics in the channel perimeter

Patterns of variation in a fluvial system

Multivariate empirical test of the Leopold and Miller stream order–hydraulic geometry hypothesis

Topological classifications of drainage networks: An evaluation

Interregional Comparison of Alluvial Stream Channel Morphology: Great Plains Versus Central Lowlands