Geomorphology 38Ž. 2001 281–300 www.elsevier.nlrlocatergeomorph Logistic analysis of channel pattern thresholds: meandering, braiding, and incising Brian P. Bledsoe), Chester C. Watson 1 Department of CiÕil Engineering, Colorado State UniÕersity, Fort Collins, CO 80523, USA Received 22 April 2000; received in revised form 10 October 2000; accepted 8 November 2000 Abstract A large and geographically diverse data set consisting of meandering, braiding, incising, and post-incision equilibrium streams was used in conjunction with logistic regression analysis to develop a probabilistic approach to predicting thresholds of channel pattern and instability. An energy-based index was developed for estimating the risk of channel instability associated with specific stream power relative to sedimentary characteristics. The strong significance of the 74 statistical models examined suggests that logistic regression analysis is an appropriate and effective technique for associating basic hydraulic data with various channel forms. The probabilistic diagrams resulting from these analyses depict a more realistic assessment of the uncertainty associated with previously identified thresholds of channel form and instability and provide a means of gauging channel sensitivity to changes in controlling variables. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Channel stability; Braiding; Incision; Stream power; Logistic regression 1. Introduction loads, loss of riparian habitat because of stream bank erosion, and changes in the predictability and vari- Excess stream power may result in a transition ability of flow and sediment transport characteristics from a meandering channel to a braiding or incising relative to aquatic life cyclesŽ. Waters, 1995 . In channel that is characteristically unstableŽ Schumm, addition, braiding and incising channels frequently 1977; Werritty, 1997. Changes in the magnitude, threaten human infrastructure. relative proportions, and timing of sediment and Alluvial channel patterns form a continuum rather water delivery in these channels may affect water than discrete types and distinctions between morpho- quality via a wide variety of mechanisms. These logic types are fuzzy and complexŽ Ferguson, 1987; mechanisms include changes in channel morphology, Knighton and Nanson, 1993. Process and historical planform, bed material, and suspended sediment studies of individual streams suggest that switches between channel patterns may be historically contin- gent on how intrinsic variables have ‘primed’ a ) Corresponding author. Tel.: q1-970-491-8410; fax: q1-970- reach for instability and on the state of the channel at 491-8671. Ž. E-mail addresses: [email protected] the time of an impact Brewer and Lewin, 1998 . Ž.B.P. Bledsoe , [email protected] Ž. C.C. Watson . Because channel patterns are frequently transitional 1 Tel.: q1-970-491-8313; fax: q1-970-491-8671. and shaped by complex sequences of disturbance 0169-555Xr01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S0169-555XŽ. 00 00099-4 282 B.P. Bledsoe, C.C. WatsonrGeomorphology 38() 2001 281–300 events, stochastic alternatives to deterministic thresh- investigators have also suggested that bank resis- olds may be more useful and realistic for predictive tance is a confounding factor in the analysis of and postdictive work on the effects of geomorphic channel planformŽ Carson, 1984; Ferguson, 1987; changeŽ. Graf, 1981; Tung, 1985; Ferguson, 1987 . Bridge, 1993. Probabilistic discrimination of relatively stable and Several theoretical approaches to defining the unstable channel types using basic sedimentary and transition from meandering to braiding have also hydraulic variables offers improved predictions of been developedŽ e.g., Parker, 1976; Fredsøe, 1978; environmental impacts. Such predictions of risk help Fukuoka, 1989. These techniques have limited pre- establish priorities for management, planning, and dictive value, however, because the techniques rely policy. on parameters such as width, depth, and Froude number that are usually not available for a priori 1.1. Discriminators of braiding and meandering predictions of channel form. The theoretical ap- proaches do seem to suggest that braiding generally In the latter half of the twentieth century, geomor- occurs at channel width-to-depth ratios in excess of phologists and engineers attempted to predict the 50Ž.Ž. Fredsøe, 1978 . Bridge 1993 provides an excel- planform of rivers based on the slope and some lent review and summary of the various empirical measure of discharge or drainage area. The concept and theoretical thresholds that have been proposed of a threshold discharge–slope Ž.Q–S combination for the transition from braiding to meandering. that discriminates braiding rivers from meandering In an attempt to reconcile some of the issues ones has become firmly embedded in the doctrine of associated with the original empirical approaches, fluvial geomorphologyŽ. Carson, 1984 . The Q–S van den BergŽ. 1995 devised a simple parameter discriminator was first suggested by LaneŽ. 1957 and representing potential specific stream power that en- Leopold and WolmanŽ. 1957 . Many other investiga- ables discrimination of braiding and meandering tors have provided support for the notion of a thresh- riversŽ. sinuosityG1.3 in unconfined alluvium. Us- old between meandering and braiding types and have ing a data set of 126 streams and rivers, he arrived at used this approach to interpret a variety of field and a discriminant function of the form: flume dataŽ Schumm and Khan, 1972; Chitale, 1973; g . v( SQ0.5s900D 0.42 Ž.1 Osterkamp, 1978; Begin, 1981; van den Berg, 1995 . a Õ bf 50 Critical examination of the early work on mean- dering to braiding thresholds has subsequently re- where specific stream power Ž.v is a function of vealed several limitations of the original approach. valley slope, estimated bankfull dischargeŽ m3rs,. Critical stream power for braiding appears to vary and a regression coefficient Ž.a computed for a with bed material size; i.e., the critical slope for particular collection of streams that varies between braiding at a given discharge is higher for gravel sand bed and gravel bed rivers. The discriminate than for sand bed channelsŽ Carson, 1984; Ferguson, function applies to both sand and gravel bed rivers 1987. The threshold suggested by Leopold and Wol- with median bed material ranging from 0.1 to 100 manŽ. 1957 is too high for sand bed channels and too mm. Potential specific stream power and median low for gravel bed channels because it is based on a particle size Ž.D50 are expressed in Watts per square combination of the two channel types. Other con- meterŽ Wrm2 . and meters, respectively. The result- cerns with the original stream power approach arise ing specific stream power represents the maximum from bias associated with using channel slope and potential specific stream power for a particular val- bankfull discharge parametersŽ. van den Berg, 1995 . ley slope. Channel slope and bankfull discharge are not neces- sarily independent of planform. Braided channels are 1.2. Stream power and eÕolution of incising sand bed inherently steeper than meandering channels for a streams given valley slope because of generally low sinuos- ity. Braided channels may also have larger bankfull Channel incision, or bed lowering by erosion, cross-sections as a consequence of braiding. Some results from an imbalance in the power aÕailable to B.P. Bledsoe, C.C. WatsonrGeomorphology 38() 2001 281–300 283 move a sediment load and the power needed to such as specific stream power, the size of bed mate- move the sediment loadŽ. Bull, 1979; Galay, 1983 . rial, sediment load, and bank resistance. Logistic Where banks are cohesive and resistant to hydraulic regressionŽ. Menard, 1995; Christensen, 1997 is a forces, bed erosion is initially dominant over channel statistical technique that allows comparison of binary widening. As an incising channel deepens, flow and continuous parameters. The research described events of increasingly greater magnitudes are con- below is targeted at developing a risk-based ap- tained within the channel banks. This process may proach for predicting the occurrence of stable mean- create a positive feedback wherein shear stress on dering, braiding, and incising channel forms as a the bed and toe of the banks during large events is function of simple hydraulic and sedimentary at- magnified through incision. If bed degradation con- tributes. The specific objectives of the proposed tinues until banks reach a critical height for geotech- research were the following. nical failure, radical channel widening may be initi- Ž.i To use a very large data set from actual ated. Such widening can proceed at a staggering rate, streams with logistic regression methodology to with tenfold increases in cross-sectional areas re- identify probabilities of occurrence of braiding or ported in some instancesŽ. Harvey and Watson, 1986 . incising channels versus meandering channels using Conceptual models of the temporal response or simple indices of specific stream power and charac- evolutionary sequence of incised channels have been teristics of bed material. described by various investigatorsŽ Schumm et al., Ž.ii To contrast the logistic regression results with 1984; Harvey and Watson, 1986; Watson et al., van den Berg’sŽ. 1995 previously defined geomor- 1988a,b; Simon, 1989; Simon and Hupp, 1992. The phic threshold between meandering and braiding models