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Fluvial sediment-transport processes and morphology

Stephen E. Coleman1 and Graeme M. Smart21 Department of Civil and Environmental Engineering, The University of Auckland,

Auckland, New Zealand. Corresponding author: s.coleman@auckland.ac.nz2 NIWA, P.O. Box 8602, Christchurch 8440, New Zealand.

AbstractRivers convey water and sediment from catchments to the coast through channels that adapt to these flows. Society’s concerns about flood management and the potential effects of climate change must thus be matched with knowledge and appropriate management of fluvial sediment processes and the dynamic behaviour of river channels. This paper presents a synthesis of recent developments in our understanding of fluvial sediment processes and morphology, with an additional emphasis on the works of New Zealand researchers. We present frameworks and tools for predicting and interpreting these processes, from small to large scales, and also potential changes in morphology and in­channel sediment storage. The understanding derived from analyses of grain­scale concepts is presented in the context of larger­scale processes and also other aspects of the sediment­flux pathway from catchment to coast. The paper finishes with some comments on present issues and recommendations for research efforts.

IntroductionAll water flows in nature occur within boundaries that change over short or long time periods. Changes in channel boundaries and flow capacity are fundamentally controlled by rates of sediment erosion, deposition and transport, and channel morphologies arise that modulate these processes.

Given a blank earth­surface canvas, water energised by gravity will create a network of conduits in which to flow and in which sediment flux is concentrated (e.g., Willgoose et al., 1991; Dietrich et al., 1993; Tucker and Bras, 1998). As water is essential for maintaining life and ecosystems, societies have concentrated around these conduits, using them for many purposes, including food and water supply, waste removal, irrigation, transport, and energy. Understanding and appropriate management of these conduits, including their forms and the fluxes of water and sediment, is thereby essential for the ongoing needs of society (e.g., Day and Hudson, 2001).

Within the larger framework of sediment flux from catchment production to delivery to the coast, this paper provides an overview of sediment processes and morphologies within rivers (Fig. 1). Within this special issue on sediment flux, morphological adjustments, and river management, this paper complements other papers that consider larger scales, other aspects of the sediment­flux pathway from catchment to coast, and also river management examples from throughout New Zealand.

Many books and book chapters have been written on the topic of fluvial sediment transport and morphology (e.g., Schumm, 1977; Chang, 1992, Raudkivi, 1998; Julien, 1998; Knighton, 1998; García, 2008), and many conferences have been held on the topic. The extensive Carson and Griffiths

Journal of Hydrology (NZ) 50 (1): 37-58 2011© New Zealand Hydrological Society (2011)

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Figure 1 ­ Fluvial processes and morphologies.

(1987) paper on bedload transport in gravel channels is a particularly notable reference work for sediment flux and morphology in New Zealand. Other notable works in a New Zealand context include those of Henderson (1966), Mosley (1992), Mosley and Pearson (1997), Mosley and Jowett (1999), Harding et al. (2004), and Hicks and Gomez (2005). The present paper cannot cover in detail the extensive work to date on the subject matter, but instead we seek to synthesise recognised knowledge, and highlight and incorporate recent advances in understanding. In the framework of this special issue, we focus on work with a New Zealand context.

We begin by considering the river system as a whole to highlight the importance of the wide ranges of scales (from turbulence lengths and grain sizes, to cross­section widths, channel reach lengths and catchment scales) and variables affecting fluvial processes and morphologies. As a foundation for analyses of sediment flux, we then discuss new analytical frameworks based on the conservation of sediment mass and momentum within domains at the grain­size scale. These frameworks for the first time provide generalised equations that (a) explicitly reveal the interplay of forces acting to erode individual sediments, and (b) explicitly

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show the interplay between flux, sediment concentration and sediment accumulation at grain scales. More importantly, these frameworks can be analytically upscaled (averaged over larger domains to provide descriptions of sediment threshold, balance and movement at sediment­patch or channel­reach scales, revealing assumptions and limitations in conventional expressions for these processes at larger scales. The analyses leading to detailed versions of the general expressions of the “grain­scale” section are not given here, but can be found in Coleman and Nikora (2008, 2009).

We next discuss processes at cross­section to reach scales, outlining a general dimensionless­variable framework for analyses at these scales. Recent expressions for sediment threshold, deposition and transport are then presented, in line with the dimensionless­variable framework, along with understanding highlighted by upscaling of the earlier­presented fundamental

“grain­scale” expressions for threshold and transport. Analysis of sediment balance and channel adjustment and evolution at larger scales is then outlined and discussed, with earlier concepts complemented by the findings presented in recent international literature in these areas. A New Zealand case study is presented to illustrate application of these concepts for qualitative prediction of morphological adjustment. The paper finishes with comments on present issues and recommendations for research efforts in fluvial processes and morphologies.

Classification of rivers and their morphologyFigure 2 illustrates the scales and variables affecting fluvial processes. To predict river behaviour, we need to understand river processes at scales ranging from catchment size and larger down to the sizes of turbulent eddies and sediment particles.

Figure 2 – Scales and variables affecting fluvial processes, with the fluvial system discussed in this paper encircled.

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When assessing a river and its behaviour, it is important to first consider the broader nature of the river, using river classification methods such as that of Rosgen (1994, 1996), the River Environment Classification (REC) system (e.g., Snelder and Biggs, 2002), or the River Styles framework of Brierley and Fryirs (2005), for example. The connectivity (e.g., Brierley et al., 2006) and significance of various apparent river morphologies can then be interpreted within the larger­scale context of the river.

Various fluvial morphologies can be evident within a river system (Fig. 1), including those for coarser sediments, planform morphologies, and morphologies at cross­section and bedform scales. Regime diagrams can also be used to interpret the morphologies of sand beds in terms of the river hydraulics (e.g., Simons and Richardson, 1966; Rubin and McCulloch, 1980; van Rijn, 1984a; García, 2000), with dune dimensions, significant in terms of hydraulic resistance, best described by Julien and Klaassen (1995). The dynamic New Zealand landscape gives rise to a wide variety of dramatic and captivating examples of fluvial morphologies, as shown in Figure 3.

Sediment processes at grain scalesAt fine scales, sediment motions may arise in response to local and instantaneous fluid velocities, fluid stresses, velocity gradients, accelerations, pressures and their gradients, energy transfers, shear instabilities, and turbulent structures such as vortices, ejection “bursts’’ and inrush “sweeps’’. The principal physical phenomena that act to move a sediment particle can furthermore change as the flows in a river change. Sediment dynamics are also influenced by the respective effects of the viscous sublayer (if present), hydrodynamic “added mass”, and sediment

density, size, shape, packing, concentration and exposure or hiding. The following subsections describe rigorous grain­scale frameworks and concepts for interpreting sediment entrainment, balance and transport. Upscaling of the grain­scale expressions of this section for threshold, transport and continuity are discussed later in regard to analysis and interpretation of processes at section to reach scales.

Sediment thresholdTo provide guidance as to the key hydro­dynamic properties acting to entrain particles, and for combining these properties to describe threshold conditions at a range of scales (e.g., Hofland et al., 2005; Detert et al., 2004, 2008), Coleman and Nikora (2008) for the first time derived a rigorous consistent framework for describing sediment­particle threshold directly from the equations for conservation of fluid and sediment momentum. They explicitly show that a particle is on the threshold of motion when:

instantaneous hydrodynamic forces > (weight + buoyancy + interparticle- contact) forces (1)

where the respective force vectors are linearly superposed, and the hydrodynamic forces arise from fluid accelerations and across­particle stress and pressure gradients. In general, bed shear stresses (parallel to the bed), across­particle differences in pressures and vertical fluxes of vertical momentum (normal to the bed), and sediment­bed characteristics such as porosity are shown to be the principal mechanisms leading to the hydrodynamic entrainment of individual grains or patches of particles. The results of the novel field experiments described in Smart (2005) and Smart and Habersack (2007) clearly illustrate the role of advecting pressure fluctuations in creating bed­normal pressure differentials that can act across the bed­surface layer to entrain gravel particles.

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Figure 3 – Fluvial morphologies: (a) an alluvial fan created by erosion arising from Cyclone Bola in 1988 (photo taken by John Johns ARPS, New Zealand Forest Service, courtesy of Catherine Chapman); (b) river braiding in Canterbury; (c) floodplains of the meandering Waipaoa River near Gisborne; (d) approximately 70­m high cliffs along the Manawatu River in Palmerston North; and (e) alternate bars along the Tongariro River.

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Sediment balance and transportThe equation of sediment­mass con serva tion, namely

the rate of change of mass in a volume = the sum of the mass transport rates occurring across the volume boundaries (2)

has been presented and used in various forms since the 1920s as the foundation for analyses of Earth surface morphodynamics (e.g., Raudkivi, 1976; Parker et al., 2000; Dietrich et al., 2003; Paola and Voller, 2005; Kubatko and Westerink, 2007; Parker, 2008).

In contrast to conventional “mixture­scale” control­volume approaches to deriving this equation, Coleman and Nikora (2009)

use spatial averaging of the subparticle­scale differential equation of mass conservation to give a general statement of sediment­mass balance that provides insight into sediment continuity at local­patch, bedform and larger scales. In an advance on earlier approaches, this general equation also includes the effects of fluctuations in sediment properties (e.g., density, velocity, and concentration or volume fraction) within analysis volumes, and readily enables calculations in terms of size fractions. The spatial­averaging approach furthermore readily allows analyses in terms of individual or successive layers, including bed, sus­pended and total loads, where layer interfaces

Figure 4 – Interface definitions for analysis of (a) total load, (b) bedload, and (c) suspended load; and (d) schematic variations of sediment concentration or fraction φst, and associated potential definitions of the bed surface z =ηbs, for patch­ and dune­scale averaging volumes Vo applied to the same riverbed.

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From a mechanical viewpoint, sediment motions can be governed by flow strength, turbulent motions, sediment availability, cohesion, flocculation, weathering, con­solidation, and particle clustering and orientations. At a fundamental level, the motions of fluvial sediments are driven by gravity g and further depend on the properties of the sediment, the fluid and the flow. Sediments are principally characterised by representative sizes, where dn is the size for which n% of the sediment is finer, and by densities ρs. The properties of fluid density ρ and dynamic viscosity µ are controlled by the water temperature. Relevant flow characteristics include velocities (and related pressures and turbulence magnitudes), depths and slopes, where U is a section­averaged streamwise velocity, H is section­averaged flow depth, and S is streamwise slope.

Adopting d as a single representative grain size for a sediment mixture of standard deviation of sizes σg, and considering ρ solely in relation to kinematic viscosity ν  =   µ/ρ and submerged gravity g(s­1) = g(ρs – ρ)/ρ, then section­averaged sediment motions can be expected to be of the form

Process = f(d,σg,g(s–1),ν,U,H,S) (4)

Setting two of the three parameters U, H and S defines the third term for flow over a roughness height ks (here taken to be proportional to d), and so only two of U, H and S need to be specified. S can be taken to be equal to the bed slope for steady uniform flow, and the energy slope of the flow otherwise. For local processes, the section­averaged parameters U, H and S can be replaced by local equivalents. Channel width W (or wetted perimeter P) can also be included in equation (4) for section­averaged considerations (e.g., Henderson, 1966; Griffiths, 1983). For a uniform sediment of σg → 1, any process dependency on σg can be neglected in equation (4). In addition to the independent variables of equation (4),

(e.g., at general elevations z = η1 and z = η2, at the bed surface z = ηbs and the water surface z = ηw) are clearly shown to be defined based on isosurfaces of sediment concentration, or other sediment properties (e.g., densities or transport rates) within regions of constant concentration (see Figure 4, where z = ηc and z = ηt are crest and trough levels, and Vo is the averaging volume used in analyses).

Importantly, the spatially­averaged approach presented by Coleman and Nikora (2009) highlights the effects of the scale of consideration, which can be straightforwardly varied over wide ranges, on defining and interpreting macroscopic (mixture­scale) sediment and layer properties such as averaged densities, volume concentrations or fractions, velocities, transport modes and rates, interfaces and bed layers (Fig. 4). As an example, double­averaged (in space and time) sediment­mass transport rate (per unit width) in direction x between surfaces at z = η1 and z = η2, gsx, is explicitly shown to be given by

(3)

where φst is the volume concentration or fraction of sediment, ρs is the sediment solid density, usx is the sediment velocity in direction x, and the overbar and angled brackets indicate averaging of the product over the time and spatial analysis domains, respectively.

Sediment and river processes at section to reach scalesDimensionless frameworksFrameworks for analyses at section to reach scales can be constructed by upscaling expressions used for finer scales, such as those of equations (1) to (3). Alternatively, empirical expressions for sediment and river processes at section to reach scales can be established by considering the parameters governing the processes.

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cohesion is very important in controlling the behaviour of sediments with a significant clay content (e.g., Raudkivi, 1998).

Equation (4) can be expressed non dimension ally as

(5)

where d and g(s­1) have been chosen as re­peat ing variables to represent the dimensions of length and time respectively, dimension­less shear stress θ  = gHS/[g(s–1)d], H/d is relative grain submergence, grain Froude number Fg=U2/[g(s–1)d], and dimensionless grain size D*=[g(s–1)/ν2]1/3d. Based on the definitions of equations (4) and (5), the following sections consider the processes of sediment threshold, deposition, transport and balance, and morphological adjustment.

Sediment thresholdSediment is on the threshold of being eroded when the parameters of equation (5) achieve critical values. For a uniform sediment (σg→1), erosion threshold is then defined by:

θc = f(D*,H/d) (6)

where Fg (representing U) has been omitted and θ and H/d (representing S and H) retained.

For large relative grain submergence (H/d →  ∞), equation (6) can be simplified as:

θc = f(D*) (7)

Soulsby and Whitehouse (1997) used collected experimental data to derive the empirical expression

(8)

for unidirectional currents and 0.1 < D* < 1000. The functionality θc=f(D*) can alternatively be expressed as θc=f(R*), as originally presented in the seminal work on sediment threshold of Shields

(1936), where grain Reynolds number

. The reach­

averaged hydraulic conditions leading to sediment erosion consequently can be pre­dicted using equation (8), or by using equi­valent expressions such as the Shields curve

or as given by Brownlie

(1981). Soulsby and Whitehouse (1997) show that threshold conditions for finer sediments (D* < 10) are better predicted using equation (8) than by the conventional Shields curve. The effects of particle protrusion, sediment size distribution and bed slope on the con­ditions for sediment erosion are not included in conventional reach­averaged expressions for sediment threshold, e.g., equation (8) and the Shields curve, but they can be included in subsequent analyses (e.g., Fenton and Abbott, 1977; García, 2008). Bed armouring can also influence threshold conditions for a bed consisting of a mixture of sediment sizes (e.g., Carson and Griffiths, 1987). With equations (7) and (8) determined for H/d → ∞, threshold is more generally also a function of relative submergence (e.g., Bettess, 1984; Coleman and Nikora, 2008).

As indicated above, upscaling of the fundamental grain­scale framework for sediment threshold can be used to provide valuable insight into sediment entrainment mechanics and prediction at section­to­reach scales. Although as­yet­unavailable closure terms are required to apply the upscaled framework to specific entrainment problems, Coleman and Nikora (2008) demonstrate

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through the upscaled framework that bed shear stress, rather than alternatives of average velocity, stream power or flow rate, e.g., as discussed in Carson and Griffiths (1987) and Clausen and Plew (2004), is the appropriate hydraulic parameter for describing sediment threshold at section­to­reach scales. Non dimensionalised bed shear stress, also referred to as the Shields entrainment parameter θ, is furthermore explicitly shown to describe averaged en masse entrainment by steady uniform two­dimensional flows, with conditions outside of these shown to introduce extra factors into the balance of forces leading to sediment entrainment. Through upscaling of the grain­scale framework, Coleman and Nikora (2008) explicitly show how various forms of equation (7), such as the Shields curve, equation (8), and alternative expressions for threshold conditions, arise due to fluid and sediment properties such as the sediment and matrix characteristics discussed in Carson and Griffiths (1987).

Sediment depositionConsidered at a fine scale, sediment deposition typically occurs in an environment of turbulent flow dynamics (in terms of statistics and structure), varying particle velocities and concentrations, and sediment advection and diffusion processes. Large­scale sediment deposition is commonly in the form of fan and delta growth, floodplain accretion, and the growth of in­channel deposits.

According to Bagnold (1973), suspension ceases when the particle fall velocity relative to the surrounding fluid exceeds the upward turbulent eddy velocity components relative to the bed. For uniform sediment (σg → 1) falling in still water (for which U, H and S can be neglected), a nondimensional expression for the sediment fall velocity ω can be expected from equation (5) to be of the form

(9)

Soulsby (1997) and Cheng (1997) give the following alternative expressions for the fall velocity of naturally­shaped sediments:

(10)

Sediment fall velocity consequently can be predicted using one of the expressions of equation (10), or by using equivalent expressions such as those given in van Rijn (1984b). Sediment fall velocity is reduced from equation (10) for larger sediment concentrations C, with expressions to incorporate this effect given in Soulsby (1997) and van Rijn (1984b). In assessing fall velocities in relation to turbulent eddy velocity components, and thereby potential sedimentation, the standard deviation of the bed­normal velocity fluctuations w´can be assumed to take a value in the near­bed region of about σw = u*b (Nezu and Nakagawa, 1993; Lopez and García, 2001), where bed shear velocity u*b is defined as

.

The critical flow intensity for sediment deposition is less than that for sediment entrainment (e.g., Carson and Griffiths, 1987). Figure 5 illustrates this, in an averaged perspective, for gravel sediments, using critical average velocity Uc based on

Uc = CI[2g (s – 1) d50]0.5 (11)given by Isbash (1936) for sediment deposition, where CI = 1.20 for low­ turbulence conditions (0.86 for high turbulence). Figure 5 also shows respective

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velocity thresholds for bed scour and non­scouring transport.

Sediment transportAside from transport in the form of debris flows or turbidity currents, sediment is conventionally considered to be transported as bedload, suspended load and wash load. The wash load comprises very fine sediments that are directly washed through river reaches and thus form only a minor component of bed sediments. Except where streamflow is ponded, the wash load has little influence on channel morphology for New Zealand rivers. The wash load furthermore tends to be uncorrelated with streamflow, and so it is typically neglected in analyses of sediment transport. The suspended (bed­material) load comprises sediments present in the bed that are carried along in suspension by the flow turbulence, with rare contact with the bed. Near­bed sediments that move by rolling, sliding or saltating (bouncing) along the bed are classified as bedload. Bedload and suspended load may move simultaneously, and the borderline between them is not well defined. Abrasion and sediment sorting generally result in bed materials becoming finer and sediment being transported in­

Figure 5 – Critical average velocities for entrainment and deposition of gravels.

creasingly in suspension downstream along a river.

The different transport processes and distributions of sediment within the flow mean that it is important to differentiate between transport as bed and suspended load (e.g., Fig. 4). Material is predominantly transported as suspended load for

u*b / ω   >1 (12)(e.g., van Rijn, 1984b; García, 2000), where, as noted above, the standard deviation of the bed­normal velocity fluctuations w´ takes a value in the near­bed region of about σw = u*b. The ratio of equation (12) accordingly expresses the balance between suspending and depositing velocities for a near­bed sediment, with bedload dominating for relatively large fall velocities and u*b/ω < 1. The related Rouse number Ro=ω/(κu*b), defines the distribution of sediments in the water column for a flow, where κ is the von Karman constant (κ ≈ 0.4) and sediments are increasingly concentrated near the bed for larger values of Ro (e.g., García, 2008).

As indicated in the discussions above based on grain­scale understanding, fluvial sediment is transported in an environment of turbulent flow dynamics (in terms of statistics and structure), varying particle velocities and concentrations, sediment layers, transport as cellular elements, and sediment advection and diffusion processes. On a broad scale, however, sediment transport rate per unit channel width qs can be nondimensionalised in line with equation (5) as the Einstein number qs* = qs / [(s – 1)gd3]1/2. From equation (5), transport rate can then be expressed as

(13)

where only two of θ, Fg and H/d (together representing S, U and H) are required for flow over roughness of ks ∝ d. Different empirical relations for the prediction of sediment

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transport arise through varying assumptions of relative parameter significance, e.g.

qs* = 0.05Fgθ1.5  (14) qs* = 3.97(θ – 0.0495)1.50 (15)

(16)

for total load (Engelund and Hansen, 1967), bedload (Meyer­Peter and Müller, 1948, as amended by Wong and Parker, 2006), and flows including steep channels (Smart, 1984), respectively. Both the bedload and steep­slope formulae given above relate the dimension­ less shear stress to a reference value, where only equation (16) includes the effects of sediment gradation σg (through the ratio of sediment sizes) and viscosity (through θc), with CU = U/(gHS)0.5 = (Fg/ θ)0.5, and S, Fg and (θ – θc) representing the variables S, U and H (relative to a threshold value). Cheng (2011) presents a sensitivity analysis that indicates θ, Fg and D* to be the most significant independent variables of equation (13) in predicting total bed­material load, with H/d the next most important variable. Note that the exponent of 1.5 in equations similar to equation (15) means that small errors in θ when it is near θc will produce large errors in qs*. From the writer’s experience, sediment transport often occurs at values of θ not much larger than θc in New Zealand gravel­bed rivers.

In an alternative approach to that following from equation (13), if σg is neglected, and g(s­1) and H are replaced by fall velocity ω (e.g., through equations (9) and (10) and bed shear velocity u*b = (gHS)0.5, respectively, then equation (4) becomes

C = f(d,ω,ν,U,u*b,S) (17)where sediment concentration C is qs normalised by (water) flow rate per unit width q. Selecting u*b and stream power per unit weight of water US as the two variables to represent U, S and H(u*b), then equation (17) becomes

(18)

where variables have been normalised by d and ω. Yang (1973, 1979, 1984) gives total sediment load aslog C = 5.435 – 0.286log (ω d/ν) – 0.457log(u*b/ω)

+[1.799 – 0.409log(ω d/ν) – 0.314log(u*b/ω)]

log C log [(US/ω) – (US/ω)c] (19)

log C = 6.681 – 0.633log (ω d/ν) – 4.816log(u*b/ω)

+[2.784 – 0.305log(ω d/ν) – 0.282log(u*b/ω)]log C log [(US/ω) – (US/ω)c] (20)

for sands and gravels, respectively, with (US/ω)c = (Uc S/ω) and Uc/ω = f(R*).

Carson and Griffiths (1987) note that for sediment mixtures, calculation of transport in terms of sediment fractions or size classes will theoretically improve prediction of transport rates. Expressions for fractional transport of sand­gravel mixtures are given in Parker and Sutherland (1990) and, more recently, Wilcock and Crowe (2003). The stream power approach can also be extended to sediment mixtures as outlined in Yang (1979, 1984).

In general, there are many alternative expressions available to calculate sediment transport loads (e.g., Carson and Griffiths, 1987; García, 2008), where equations (14) to (16), (19) and (20) are given here for estimating bed and total loads, as they are recognised to perform consistently well in tests (e.g., Yang and Wan, 1991; Vanoni, 2006).

In terms of determining suspended load, this sediment fraction is influenced by sediment supply to a greater degree than

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bedload and is generally measured directly rather than estimated using empirical equations (e.g., Hicks and Griffiths, 1992). Sediment concentrations are accordingly measured at a section and suspended load calculated using equation (3), or, more typically, the depth­averaged equivalent (for constant ρs)

qs = gs / ρs = CUH = Cq (21)This approach for estimating suspended

sediment load provides further evidence of the value and insight provided by upscaling the fundamental grain­scale framework for sediment continuity and transport to section­to­reach scales. In this regard, for constant solid density of sediment particles ρs , the solid­volume flux in a layer between η1 and η2  in direction x (per unit width) is given by equation (3) as the product of volume concentration or fraction φst and double­averaged (in time and space) velocity, i.e.

(22)

where usx is the sediment velocity in direction x. Coleman and Nikora (2009) show that this general expression can be integrated over depth to describe any of bedload, total load, or suspended load, depending on the integration boundaries (e.g., Fig. 4), where equation (21) arises for the assumption of both flow velocity and suspended­sediment concentration being constant over the flow depth. The general relation of equation (22)also provides a valuable tool for estimating bedload from measurements of bed surface variations with time, where these can be readily measured today through acoustic and laser technologies. In this regard, if the bed sediment velocity is taken to be approximately constant with depth, then equation (22) becomes

(23)where c is the bulk celerity of bed movement, which can be simply evaluated through cross­

correlation of successive surfaces, and the vertical integral of the volume fraction of sediments φst can be simply determined from the surfaces of measured bed elevations (e.g., Aberle et al., 2011). Applying equation (23) with a dune­scale analysis volume Vo (Fig. 4d) to a surface of steadily propagating triangular­shaped dunes, then the conventional (e.g., Simons et al., 1965; Crickmore, 1970) relation for bedload as a function of the dimensions and movement of the waves

(24)

is recovered, where k is bed porosity, volume fraction of sediment φst = k[1–(z/h)], and wave height h = ηc – ηt (Fig. 4d). As identified by Coleman and Nikora (2009), upscaling of the grain­scale expression for transport to dune and larger scales allows insights into the definitions of the reach­scale terms (e.g., averaged densities, volume concentrations or fractions, velocities, transport modes and rates, interfaces, and sediment layers), and also understanding of how conventional expressions for transport such as equation (24) might be appropriately adapted for different assumptions, e.g., for an element of sediment suspension and inter­wave transport (e.g., Mohrig and Smith, 1996), or an elevation of zero transport occurring above the wave troughs (e.g., Crickmore, 1970).

Sediment balance, aggradation and degradationSediment balance, aggradation and degrada­tion for a reach are governed by the mass conservation equation (2), where the sediment inputs to and outputs from a reach are commonly determined by sediment supply (e.g., Davies and McSaveney, 2006) and system connectivity (Brierley et al., 2006) rather than simply the expected upstream or downstream transport capacity (as given by equations (14) to (16), (19) and (20) for example). Where the long­term transport

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capacity of a reach exceeds the long­term sediment input, channel degradation, incision and/or widening occur. Whether the bed or the banks of a reach erode depends on their relative erodibility (which in turn depends on local slope, cohesion, and particle size and grading, etc.). When supplies of finer bed particles are exhausted, the bed surface may become armoured with the remaining larger grains. In this situation, channel degradation can cease and channel widening may commence.

Equation (2) can be used to determine whether a reach is aggrading or degrading. Importantly, the Coleman and Nikora (2009) spatially­averaged formulation of equation (2) that is described above in the grain­scale discussions can be straightforwardly applied over wide ranges of scales (e.g., Coleman, 2010). Upscaling of this approach to analyses of continuity, aggradation and degradation at section to reach scales provides important insights into the effects of the scale of consideration on defining and interpreting macroscopic (mixture­scale) sediment and layer properties and their changes, including averaged densities, volume concentrations (e.g., porosity) or fractions, velocities (e.g., grain or bedform), transport modes (e.g., bed, suspended or total loads) and rates, interfaces and bed layers (Fig. 4).

Channel evolutionTo understand river behaviour, it is important to consider the present stage of river development and likely development trajectories. A principal approach to providing a quantitative understanding of channel form and response to changes involves comparing the existing river channel with regime geometries for alluvial rivers. Regime for a river represents a dynamic equilibrium in which average channel dimensions remain approximately constant over time, and the river can thereby be considered stable in a broad sense, despite local and temporal vertical and planform fluctuations.

Regime configurations arise with rivers being free to adjust their hydraulic geometries to achieve optimum configurations (e.g., Davies and McSaveney, 2006; Millar, 2005; Nanson and Huang, 2008). Extremal hypotheses leading to prediction of expected regime geometries have been presented in terms of minimum stream power (e.g., Yang, 1976; Chang, 1979), minimum rate of energy dissipation (e.g., Yang and Song, 1979), minimum energy (Huang et al., 2004), maximum sediment­transport rate (e.g., Kirkby, 1977; Millar, 2005, Davies and McSaveney, 2006), maximum friction factor (e.g., Davies and Sutherland, 1980, 1983), maximum bed shear stress (Davies and Sutherland, 1983; Davies and McSaveney, 2006), and maximum flow efficiency (Huang and Nanson, 2000). Interrelations between these approaches are discussed in Davies and Sutherland (1983), Knighton (1998), Davies and McSaveney (2006), and Nanson and Huang (2008).

Approaches based on both empirical and semi­theoretical analyses indicate that regime rivers can be described by the downstream hydraulic geometry relations

W = aWQξW, H = aHQξH, S = aSQξS U = aUQξU, and QSS = aSSQξSS (25)

where W is average channel width, H is average channel depth, Qss is suspended­sediment load, and Q is channel­forming discharge, which is usually considered to be the bankfull discharge or a frequency­based flow such as the mean annual flood (e.g., Leopold and Maddock, 1953; Blench, 1957; Henderson, 1966; Charlton et al., 1978; Bray, 1982; Andrews, 1984; Hey and Thorne, 1986; Carson and Griffiths, 1987; Mosley and Jowett, 1999; Huang et al., 2002; Millar, 2005; Biedenharn et al., 2008). Griffiths (1980) cites the classic (e.g., Leopold and Maddock, 1953) exponent values ξW = 0.5, ξH = 0.4, ξS = –0.5, ξU = 0.1, and ξSS = 0.8, with Parker (1979) noting that

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the exponents are relatively constant and apparently independent of location and only weakly dependent on channel type. Knighton (1998) presents the results of a range of studies with ξW = 0.45–0.56, ξH = 0.31–0.46, ξU = 0.08–0.20, and ξS = –(0.09–0.55). Millar (2005) similarly summarises gravel­bed rivers as being of ξW = 0.41–0.53, ξH = 0.33–0.42, and ξS = –(0.15–0.42), with coefficients aW, aH and aS that are functions of grain size, bed­material load, bank materials and stability, and bank vegetation. In terms of New Zealand rivers, Griffiths (1980) finds ξW = 0.48, ξH = 0.43, ξS = –0.49, ξU = 0.11, and ξSS = 1.31 for six steep, wide, coarse gravel­bed rivers. Jowett (1998) further calculated hydraulic geometry relationships for 73 New Zealand river reaches, finding ξW = 0.5, ξH = 0.25, and ξU = 0.25 on average.

The exponent ξU of the hydraulic geometry relation for U in equation (25) has specific morphologic implications. According to Bathurst (1993), the exponent increases moving up a channel network from sand bed channels (ξU < 0.40) via gravel (ξU = 0.45 ­0.55), cobble and boulder­bed channels (ξU = 0.45 ­0.55) to steep pool/fall streams and pool­riffle sequences (ξU > 0.55). Aberle and Smart (2003) also showed that limits for the exponent ξU depend on the channel cross­sectional shape.

As noted above, existing river geometries can be compared with those indicated by regime theory (e.g., equation (25)) to provide initial guidelines as to potential future river developments. However, regime relationships are empirical, usually dimensionally inconsistent, and are thereby strictly applicable only to the data sets from which they were derived. In addition, the relationships of equation (25) do not completely represent the factors influencing channel form. In particular, sediment characteristics can be expected to influence channel form, with Schumm (1977), Mosley (1981), and Millar (2005) including in equation (25) the

effects on channel form of sediment size and bank material types and stability. Riparian vegetation can also modify channel geometry in a manner akin to the more obvious effects of bank protection and river control works.

Morphological adjustmentA framework for the response of rivers to natural or man­made disturbances can be formulated based on equation (4) and empirical relationships derived for rivers in nature (e.g., equation (25)). If σg is neglected, g(s­1) and ν are taken to be approximately invariant, and q = UH and S are taken to represent U and S, then for sediment transport qs equation (4) becomes qs = f (d,q,S). This can be approximated as qs = cd–α qβ Sγ for incomplete self similarity in qs with each of d, q and S, where c is a coefficient, and α > 0, β > 0 and γ > 0 are indicated by typical empirical sediment transport relations (e.g., the Engelund­Hansen relation of equation (14)). The proportionality

qs dα ∝ qβ Sγ   (26)can then be stated, where equation (26) reflects that a change in the product qsdα will give rise to a similar change in the pro­duct qβ Sγ, and equation (26) is consistent with the indications of regime geometries, for which QSS ∝   QξSS and Millar (2005) gives S ∝ Q–(0.15­0.42)d(0.59­1.15).

The empirical regime geometries of equation (25), conventional relations for sediment transport, e.g., equations (14) to (16), and the balance of equation (26), all apply to equilibrium (or quasi­equilibrium) channels. For channels in equilibrium, long­term sediment input matches the long­term transport capacity. Thus both capacity formulae and empirical regime equations can be used to indicate changes required to return a disturbed channel to equilibrium. The balance nature of equation (26) was accordingly first proposed by Lane (1955) in his discussion of a qualitative assessment of the response of a natural stream in order

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to restore equilibrium when changes are made that make it depart from equilibrium. An elegant derivation leading to the proportionality of equation (26) is given by Henderson (1966). The sediment discharge qs in equation (26) is the bed­material or total load (bedload and suspended load) that interacts with and moulds the channel boundaries. For an increase in sediment supply qs, for example, equation (26) indicates that restoration of equilibrium for the stream will require a decrease in the sediment size being transported, or increases in flow rate q or the channel slope S, where the last can be regulated by the river itself and is typically how the river will respond (e.g., Davies and McSaveney, 2006). Expressing equation (26) in terms of volume sediment­transport and flow rates Qs and Q, the channel width W or aspect ratio W/H becomes an addi­tional independent variable in the balance relation of equation (26). The proportionality (W/H)∝Q–(0.12­0.19)d–(0­0.03) of Millar (2005) might suggest an appropriately­revised balance relation of

Qsdα  ∝  QβSγ (W/H)δ  (27)

Nanson and Huang (2008) provide a more detailed discussion of the role of W/H in a revised form of Lane’s balance.

Based on the balance relation of equation (26) and regime relations such as those of equation (25) and meander wavelength λ  ∝  Q0.5(e.g., Schumm, 1977; Mosley, 1981; Knighton, 1998), Schumm (1969, 1977) pioneered the qualitative prediction of channel adjustment (in terms of W, H, S, λ, channel aspect ratio F = W/H, and sinuosity P) in response to changes in governing parameters. Table 1 presents example process­response relations given by this approach, where the superscripts in the relations indicate the relative variations in the associated parameters. Changes in channel slope indicated by the regime relations leading to the process­response relations in

Table 1 can furthermore be used together with empirical relations for the threshold between braiding and meandering, namely

Sth = 0.0125Q–0.44 or Sth = 0.0002Q–0.25 d0.61φ´1.75 (28)

and also channel sinuosity variation with slope (e.g., Schumm et al., 1972) to consider associated changes in planform morphology and accompanying lateral instability and erosion. The first relation of equation (28) is the original expression for threshold slope Sth given by Leopold and Wolman (1957). The second relation is given by Millar (2000), where Q and d are in SI units, the bank sediment friction angle φ´ (degrees) is an index of bank stability and resistance to erosion, and this relation satisfies the observation of Carson and Griffiths (1987) that particle size needs to be included in such a criterion. Rivers categorized as braided are generally steeper than Sth, while meandering rivers are less steep. Earlier equations along the line of equation (28) are discussed in a New Zealand context in Henderson (1966) and Carson and Griffiths (1987). Eaton et al. (2010) provide updated versions of equation (28) to give respective criteria demarcating between single­thread (straight and meandering) and multiple­thread (anabranching) channels, and also anabranching and braided channels.

In assessing potential river behaviour in response to a known disturbance, con­sideration of the stages of evolution of a river channel as outlined in Schumm et al. (1984), Simon and Rinaldi (2006) and Simon and Castro (2003) is also important.

Example analysis of morphological adjustment: The Bulls Road BridgeThe failure of the Bulls Road Bridge over the Rangitikei River (e.g., Coleman and Melville, 2001) provides an interesting case study of river response to human disturbance – instream mining. As shown in Figure 6,

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the river was significantly braided in 1947, with numerous channels upstream of the bridge site. Because of instream mining upstream and downstream of the bridge from 1949, there was a decrease in sediment transport supply rate qs. Equation (26)pre dicts a decrease in stream slope S, with accompanying degradation at the bridge site owing to the reduced sediment supply. The process­response relations in Table 1 further indicate expected decreases in channel width and aspect ratio, with deeper flows and an increase in channel sinuosity. The decrease

Table 1 – Process­response relations given by Lane’s balance of Equation (26) and regime geometry relations. Superscripts indicate relative increase (+) or decrease (­).

Process Description Response

Q+ Increase in Q alone W+H+F+λ+S­

Q­ Decrease in Q alone W­H­F­λ­S+

Qs+ Increase in Qs alone W+H­F+λ+S+P­

Qs­ Decrease in Qs alone W­H+F­λ­S­P+

Q+Qs+ Increase in Q and Qs together W+H±F+λ+S±P­

Q­Qs­ Decrease in Q and Qs together W­H±F­λ­S±P+

Q+Qs­ Increase in Q with decrease in Qs W±H+F±λ±S­P+

Q­Qs+ Decrease in Q with increase in Qs W±H­F±λ±S+P­

Figure 6 – Schematic of channel development for the Rangitikei River at the Bulls Road Bridge: (a) July 1947, (b) March 1971, and (c) June 1973, with flow from top to bottom.

in slope could also lead to a transition from channel braiding to meandering based on the threshold slope criteria of equation (28).

As shown in Figure 6, the river did change form as a result of the mining, with the number of channel branches reducing to 1–2 deeper and narrower main channels meandering within the wider channel by the early 1970s. With the increasing sinuosity of the river channels, river control works were developed to protect the meander bends upstream of the bridge. The resulting controlled flows passed underneath the southern end of the bridge in

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the early 1970s (Fig. 6). The concentration of these flows at a pier contributed to the failure of the pier in 1973 for what was essentially an annual flood (Fig. 6).

The implications for the river of such interventions are significant for many regions in which sediment mining has been and is presently taking place.

Summary and future directionsThe challenge of analyzing fluvial sediment transport and morphology has been likened to attempting to treat a chronic skin irritation in the absence of effective medications (Kennedy, 1971). Kennedy identified five principal aspects contributing to the fluvial sediment­transport “itch” – initiation of motion, bed and channel stability, channel roughness, bed­load transport, and sediment suspension, where only the last of these was considered to have any solid foundation.

This paper provides a synthesis of more recent developments in the understanding of fluvial sediment processes and morphology, with an additional emphasis on the works of New Zealand researchers. Despite a wealth of understanding having been accumulated, many needs and interesting questions still remain. The present development of analysis frameworks and today’s means of generating and collecting data give rise to great hope for significant developments in understanding in the years to come.

Many critical itches can be identified, based on present needs and also potential for progress in the coming years (e.g., Church, 2010). A number of these areas requiring further work are noted here. In terms of sediment production, the role of relative submergence on erosion potential needs to be quantified, particularly for coarse sediments in steep channels. Quantifying the role of cohesion on sediment erodibility also requires further significant work. In terms of sediment transport, further work is required to develop

a satisfactory physically­based framework for the prediction of transport. Measurements to date can then be interpreted within this framework, with contemporary improvements in measurement systems giving increased confidence in confirming trends by comparing theoretical predictions with the more recent data of lesser uncertainties. In terms of river morphology, secondary flow effects on sediment dynamics, channel morphology and also hydraulic resistance remain under debate, with the promise of notable advances to come with the recent development of advanced frameworks within which to interpret these flows (Nikora, 2009; Nikora and Roy, 2010). In a separate vein, morphological modelling needs to be significantly improved to provide tools for improved modelling of channel response to disturbance. Such models need to link fine­scale expressions for transport to the larger­scale constraints of sediment availability and landscape connectivity, and need to be able to describe the development of morphological units (e.g., bends, bars) and channel forms (e.g., meanders, braiding). As a final comment, vegetation interactions with sediment transport and morphology is a rapidly­developing field, with significant developments in analysis frameworks and understanding already appearing (e.g., Nikora and Nikora, 2009), but with much more work remaining to be done.

AcknowledgementsThe support of the University of Auckland Cross­faculty Research Initiatives Fund (Grant 3624991) and the New Zealand Ministry of Science and Innovation (FRST Contract C01X0812) for Coleman and Smart, respectively, is gratefully acknowledged. The writers also greatly appreciate the review comments provided by Joe Aberle and Grant Webby that have acted to focus and strengthen the paper.

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