Showing papers by "Stephen E. Darby published in 1995"

Effect of Bank Stability on Geometry of Gravel Rivers

Abstract: The authors analysis is an interesting and timely attempt to account for the effects of bank stability on the geometry of stable gravel rivers, as the neglect of the width dimension is a major limitation of channel morphology models. In the development of their model the authors encounter the problem that there are apparently more dependent variables than equations available for solution. To make the solution statistically determinate, they recognize that an additional equation is required and, therefore, use an extremal hypothesis. The authors acknowledge that the use of extremal hypotheses has been widely criticized on the grounds that the method lacks a physical basis. The main cause for concern is that the method only provides a method to calculate the channel width, although it does not suggest a mechanism by which width adjustment to a stable value is achieved (Bettess et al. 1988). In spite of this criticism, the authors argue that the use of an extremal hypothesis is justified on two grounds. First, they suggest that the method has enjoyed predictive success. Second, they argue that the inclusion of additional relations describing boundary shear stress and bank stability are insufficient to close the problem and that one extra relationship, in this case an extremal hypothesis, is still required. We would first like to discuss the apparent empirical success of the various extremal hypothesis approaches. There are a large number of extremal hypotheses to choose from, including the maximization of sediment transport rate, minimization of energy, and maximization of friction factor. Most studies have attempted to validate their results using comparisons between predicted and observed stable channel geometries, usually with a reasonable degree of success. However, no concerted effort was made until recently to directly verify the validity of various extremal hypotheses, by observing trends in the relevant parameters in unstable channels as they evolve toward equilibrium. Direct observations of the morphology and flow discharges of evolving channels were obtained in two diverse disturbed fluvial environments: the steep, high-energy coarse-grained Toutle River system in Washington, disturbed by the 1980 eruption of Mount Saint Helens; and the low-gradient, low-energy, fine-grained Obion-Forked Deer catchments in West Tennessee (Simon 1992), disturbed by channelization in the 1960s and 1970s. These data can be used in conjunction with step-backwater models to estimate temporal trends of flow energy and roughness variables in evolving channels. Simon (1992) showed that in both environments the stream power, total mechanical energy, and energy dissipation rate decreased with time toward minimum values, providing strong direct evidence in favor of the minimization of energy hypotheses. To illustrate this, Fig. 7 shows examples of temporal trends of the energy dissipation rate (energy slope) from the Toutle River system, in both aggrading and degrading reaches. As the authors recognized, the hypotheses of minimization of energy and maximization of sediment transport rate have been shown to be equivalent (Davies and Sutherland 1983); thus, this result also supports the maximization of sediment transport rate hypothesis, which was the one used by the authors in their analysis. However, support for other hypotheses is less clear. In particular, the estimated temporal trends of the Darcy-Weisbach friction factor in the Toutle River system following the 1980 eruption of Mount Saint Helens show a tendency to decrease or remain constant with time (Fig. 7), in contradiction to the maximization of friction factor hypothesis (Simon and Thorne, in press), which, according to Davies and Sutherland (1983), is also equivalent to the minimization of energy hypotheses. Shiqiang et al. (1986) conducted a comparison of the predictive abilities of the various extremal hypothesis methods. Of the tested hypotheses, the principles of minimum stream power, or maximum sediment concentration, gave the best agreement with the field data, which is consistent with the hypotheses. Although these results support the authors' choice of the maximization of sediment transport rate hypothesis, it appears that the basis of some of the extremal hypotheses may be open to question. Further, extremal hypotheses may give rise to very broad maximums or minimums, so that predicted channel equilibriums can exist over a large range, as is also suggested by the data shown in Fig. 7. This may make it difficult to obtain precise predictions of channel morphology when using the various extremal hypothesis approaches in practice. Independent of the validity and predictive power of the various extremal hypotheses, we