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A new empirical river pattern classification system is established based on the generalization of the famous Darcy-Weisbach equation. A parameter ψ for representing river shape is derived and defined as the river pattern discriminant criteria. After transformation, the discriminant thresholds are expressed as dimensionless form relating the resistance factor to the relative roughness factor of the channel, which reflect the channel slope, sediment size, bank strength and channel geometry integrated. Adopting the most promising discriminant mode that combines both regime theory and linear stability theory, a threshold function is used to separate single-thread channels (including straight and meandering) from multi-thread channels, and another one is employed to distinguish stable and unstable multi-thread channels (i.e., anabranching and braided) in this paper. A novel bank strength impact factor (μ) is proposed herein and turns out to be rather representative. Some channel patterns are redefined using this method and proved to be reasonable enough. Analysis of various data sets reveals that riparian vegetation condition is a sensitive part of this classification system, in particular for single-thread channels, but not braided channels, because overlarge width-depth ratio(W/d) would have strongly weaken this impact. Moreover, we support that transient anabranching or braiding pattern could also occur in single-thread typical zone following external disturbance, but would eventually go back dynamic equilibrium state. Despite some construction mechanism shortcomings, our discriminant method is supported by the selected existing data sets and could effectively distinguish three distinct types of channels by just a few hydrodynamic parameters.
Keywords: river pattern; Darcy-Weisbach equation; river shape; bank strength
River pattern reveals the physical geometry and dynamic behavioral process of a river system (Schumm, 1985; Nanson and Knighton, 1996). It is well understood that an alluvial channel could adjust itself to the ever-changing water flow and sediment conditions. Thus river patterns could exhibit a series of continuous variations, described as straight, meandering and braided patterns in tradition (Leopold and Wolman, 1957). It is pretty necessary to distinguish several distinct types of channels for better understanding the consistent changing progresses of river channels in different environment conditions. Numerous classification schemes using discriminant functions have been proposed, based on a set of typical properties, such as discharge, channel slope, width-depth ratio, sediment grain size, etc. Noteworthy is that the still least well-known multi-thread river pattern, anabranching pattern, has been attracting considerable attention (e.g., Schumm, 1981, 1985; Nanson and Knighton, 1996; Wende and Nanson, 1998; Tooth and Nanson, 1999; Burge, 2006; Eaton et al., 2010; Kleinhans and van den Berg, 2011). It makes great contribution to the diversity of river systems (Wende and Nanson, 1998). Then based on tradition, following the popular discriminant mode and developing a novel river pattern discriminant method comprise the focus of this paper, and lead to the capture of different channel patterns, including single-thread, anabranching and braided.
Many early empirical attempts used Leopold and Wolman (1957)’s method as base model, to improve understanding quantitative process of rive pattern transformation. Most of them focused on the critical discharge to construct discriminant function, later also included critical channel slope and bed grain size (Henderson, 1963; Millar, 2000). For a given bankfull discharge, braided usually corresponds to increased slope, while which in turn usually result in stronger sand transport rate, increased bank erosion and coarser bed surface sediment (Eaton et al., 2010). Due to powerful impediment that almost all channel properties have been varying desultorystrickly or methodically with flow progression downstream, some newly threshold schemes successively appear on related research hotspot topics, of which critical specific stream power(Nanson and Croke, 1992; Van den Berg, 1995; Lewin and Brewer, 2001; Petit et al., 2005) is outstanding. It can be viewed as a potential status with maximum flow energy and minimum sinuosity condition (Van den Berg, 1995). The classification between braided and meandering channels with high sinuosity in unconfined alluvial floodplains is well acceptable. But the argument about it also exists all the while. Lewin and Brewer (2001) argued that the analysis of potential bankfull stream power and grain size by Van den Berg (1995) is virtually ineffective; the classification of river pattern should not be limited to obtain an all-sided discriminant method, but the thresholds integrated with patterning process domain. Petit et al. (2005) conducted experiments on different sized rivers and concluded that critical specific stream power is the smallest for the largest river, while turns to the higher value in intermediate rivers, then becomes the highest in head water streams. The reasons are down to the bedform’s larger resistance that consumes energy for bedload transport. Recently, Kleinhans (2010) emphasized that channel pattern is directly bound up with the presence of bars. Then, Kleinhans and van den Berg (2011) combined the empirical stream power-based discrimination method and a physics-based bar pattern prediction method to undertake bold exploration about the underlying reasons of different river channel patterns. It was found that the range of specific potential stream power is rather narrow in gravel-bed meandering channel due to nonlinearity of sediment transport; anabranching channel is irrelevant to stream power but subject to additional factors such as bank strength, lateral confinement, avulsion, and vertical morphodynamics change; river pattern can actually be defined by bar pattern, channel division number, and bifurcation condition.
The features common in empirical methods are that more is based on statistical correlation derivation, less to clearly expound inherent processes for discriminating river pattern. These models may really be questioned about application to broader scope, due to original data restrictions. Considering the shortcomings, many researchers have been contributing to develop physically based theories, and explore the relationship variables controlling river evolution process and pattern. Leading theories are regime theory and linear stability models. Rational regime model is developed for predicting reach-averaged channel pattern response to the controlled environment variables in equilibrium, such as width-depth ratio, relative roughness and channel slope (Eaton et al., 2004). This concept employs optimization theory to achieve relative stability of the fluvial system by assessing the resistance and energy expenditure, meanwhile adjusting channel geometry to given flow conditions (Valentine et al., 2001; Huang et al., 2004). It has been proved much more successful than statistical empirical equations in predicting the variation of width and slope along downstream area and helping understanding the influence of bank stability on channel geometry (Chew and Ashmore, 2001; Millar and Eaton, 2011). While, linear stability models are used for discriminating river pattern which based on physically morphodynamic equations. This theory explains that meandering is formed along with bend instability from planimetric perturbation (van Dijk et al., 2012). As perturbation propagates downstream, pattern transition towards braided occurs associated with multiple bars. In addition, this theoretical method could predict the threshold that bifurcation occurs by width-depth ratio (W/d) (Parsons et al., 2007; Crosato and Mosselman, 2009). A significant disadvantage in this theory is that we cannot establish a typical relationship about channel geometries, such as slope with discharge and sediment size, only if the channel dimensions have been obtained (Eaton et al., 2010). However, when combining regime theory with linear stability models, means that morphodynamic condition and fluvial system stability are together considered to describe pattern transition progress, has recently been given particular attention, represented by Eaton (Eaton and Church, 2004; Eaton, 2006; Eaton et al., 2004, 2010).
In this paper, we attempt to develop a physical based classification system combining regime theory and linear stability theory, just like Eaton et al. (2010). A threshold could be used to distinguish single-thread and stable multi-thread channels, and another one could be used to distinguish stable and unstable multi-thread channels, from a stability perspective. However, when rereading the original work by Eaton et al. (2010), some limitations of subjectivity becomes clear that a threshold value of W/d =50 originally recommended for discriminating braided channels was employed to derive bifurcation criteria, and the number of channel divisions exceeding four was subjectively assumed as the beginning of system instability. We hold that this treatment should be regarded warily due to lack of absolute objective stability or instability criterion in fact.
We turn in another new way. The famous Darcy-Weisbach equation (Weisbach, 1848; Darcy, 1857) is generalized from artificial rectangular channel case to natural alluvial channel cases and expressed as functions of assumed river shape parameter, resistance factor and relative roughness factor. A relevant scatter diagram reveals that several typical channel patterns correspond to differentiable distribution mode. Based on strictly fitting, river shape parameter is determined and defined as river pattern discrimination criterion. After transformation, we develop a new dimensionless style threshold for distinguishing different river patterns. Then the classification system based on two dimensionless threshold equations is established. However, it is also, by necessary, practically restricted to certain subjectivity, especially the judgment of system instability. Considering the data fitting dependency, this method may be better treated as an empirical method.