Floodplain persistence and dynamic-equilibrium conditions in a canyon environment

Geomorphology 250 (2015) 147–158

Contents lists available at ScienceDirect

Geomorphology journal homepage: www.elsevier.com/locate/geomorph

Floodplain persistence and dynamic-equilibrium conditions in a canyon environment Andrew W. Tranmer ⁎, Daniele Tonina, Rohan Benjankar, Matthew Tiedemann, Peter Goodwin Center for Ecohydraulics Research, University of Idaho, 322 E. Front St, Suite 340, Boise, ID 83702, USA

a r t i c l e

i n f o

Article history: Received 10 April 2015 Received in revised form 2 September 2015 Accepted 3 September 2015 Available online 9 September 2015 Keywords: Canyon rivers Dynamic-equilibrium Floodplains Extremal hypotheses Semiconfined rivers Floodplain evolution

a b s t r a c t Canyon river systems are laterally constrained by steep walls, strath terraces, and bedrock intrusions; however, semialluvial reaches are nested within these environments as discontinuous floodplains along the river margins. These semialluvial floodplains provide an example of dynamic-equilibrium set within high-energy fluvial systems, marking areas where the river is free to alter its boundary conditions. Most research has focused on hydraulic conditions necessary for floodplain formation and persistence in unconfined systems, whereas little is known about canyon streams. This paper focuses on (1) characterizing dynamic-equilibrium, (2) describing the controls on floodplain formation and distribution, and (3) evaluating the performance of extremal hypotheses to identify dynamicequilibrium and floodplain persistence in high-energy, semiconfined canyon environments. These objectives were addressed with field and numerical data derived from a one-dimensional hydraulic model for bankfull and 100-year return interval flood events, supported by closely spaced cross sections for the lower 38-km canyon reach of the Deadwood River (Idaho). Under bankfull conditions, critical energy thresholds for equilibrium floodplain persistence at this study site present the upper limits of: slope = 0.018, shear stress = 175 N/m2, and specific stream power = 400 W/m2. Channel and floodplains near equilibrium, quantified with a near-zero sediment transport divergence (Exner equation), were successfully identified by the minimum unit stream power extremal hypothesis and to a lesser degree by the other extremal hypotheses that minimize energy expenditure (minimum specific stream power, minimum total stream power, and minimum Froude number), provided backwater environments and major tributaries could be identified. Extremal results were compared to hydraulic geometry relations to evaluate how closely equilibrium floodplains approached values for unconfined alluvial river systems. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Fluvial canyon systems are characterized by high-energy, limited lateral extent, steep unstable walls, and tributaries prone to debris flows, with local addition of terrestrial materials to the valley floor providing diverse geomorphic features (Tinkler and Wohl, 1998; Benda et al., 2004b). Canyons have traditionally been thought of as disequilibrium landscapes that incur periodic disturbances from colluvial source zones and interrupt the equilibrium trajectory of channel evolution; however, rivers are dynamic features that respond quickly to changes in boundary conditions (Schumm, 1977; Pickup, 1986; Warner, 1987; Church, 2002). Given upstream boundary conditions, sufficient channel length, and mobile alluvial boundaries, a river will evolve toward dynamic-equilibrium in the downstream direction (Yalin and Da Silva, 1999, 2000). Within canyon river systems, such conditions may be present over short reaches (102 to 103 m) located between major tributary influences, and recent work has identified small floodplains inset within steep mountainous and ⁎ Corresponding author. E-mail addresses: [email protected] (A.W. Tranmer), [email protected] (D. Tonina), [email protected] (R. Benjankar), [email protected] (P. Goodwin).

http://dx.doi.org/10.1016/j.geomorph.2015.09.001 0169-555X/© 2015 Elsevier B.V. All rights reserved.

canyon environments that mark limited areas of semialluvial processes interspersed with geologic constraints (Reinfelds et al., 2004; Johnston and Brierley, 2006; Macnab et al., 2006; Jain et al., 2008). Geologic constraints consisting of canyon narrows, bedrock intrusions, and strath terraces can be present for numerous kilometers, limiting semialluvial floodplain development to discontinuous areas of canyon expansion. Controls on the presence and distribution of floodplains, their longevity in the fluvial network, or what leads to their occasional catastrophic stripping are not well understood within these expansion zones. Long-term floodplain persistence requires that the fluvial system (river and floodplain) attain dynamic-equilibrium, whereby the river channel erodes and deposits equal volumes of sediment along the river banks and floodplain surfaces during periods of high discharge (Wolman and Leopold, 1957; Lauer and Parker, 2008; Da Silva, 2009). Dynamic-equilibrium in canyon river systems is defined as time-averaged uniform sediment flux over the centurial scale and may be identified longitudinally in limited areas by the presence of discontinuous, coarse-grained, floodplains that represent the channel's ability to adjust its open boundary as a function of incoming sediment. Examined as a downstream series, discontinuous floodplains act as a single semialluvial unit that evolves toward dynamic-equilibrium until another tributary enters the canyon and resets

148

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

the boundary conditions. Therefore, after a significant tributary input a downstream progression of channel and floodplain will develop, subject to geologic constraints, from nonequilibrium configurations to that of equilibrium. Field identification of equilibrium floodplains is difficult as two general types of floodplains can form in canyon landscapes. Temporary depositional floodplains, made up of sand and fine gravel, form in backwater environments upstream from bedrock intrusions, canyon narrows, and major tributary debris fans (Benda, 1990; Davey and LaPointe, 2007; Swanson and Meyer, 2014). As the river evolves to erode bedrock controls or incise through debris fan material, these finer-grained features will be destroyed and redistributed downstream. Persistent equilibrium floodplains develop when channel geometry is able to adjust to upstream boundary conditions and maintain uniform sediment flux during free-channel flow. This occurs in canyon environments when four conditions are present: (i) adequate accommodation space is provided by an expansion in canyon width (Miller, 1990; Magilligan, 1992; Ferguson and Brierley, 1999), (ii) overbank flows are available to deposit/erode material along floodplain boundaries (Wolman and Leopold, 1957; Nanson, 1986; Nanson and Croke, 1992), (iii) energy gradients are below a critical erosional threshold (Bull, 1979; Church, 2002), and (iv) sufficient sediment is available for building and maintaining lateral storage zones (Nanson, 1986; Nanson and Croke, 1992; Johnston and Brierley, 2006; Lauer and Parker, 2008). Previous research into stable alluvial river channels suggested the use of extremal hypotheses to identify dynamic-equilibrium (Inglis, 1947; Leopold and Langbein, 1962; Huang and Nanson, 2000; Molnar and Ramirez, 2002; Eaton et al., 2004) and less information is available on how extremal hypotheses relate to high-energy, canyon systems (Griffiths and Carson, 2000). Extremal hypotheses are variational statements that optimize (i.e., maximize/minimize) one or more parameters within the fluvial system in an attempt to identify what controls the distribution of forces along the channel boundary and explain the evolutionary trajectory of the river at the macroscale. Extremal hypotheses were developed to provide an objective, one-dimensional closure criterion for the ‘indeterminate channel’ problem, by which channel dimensions could be predicted by simultaneously solving the four equations of continuity, resistance, sediment transport, and an unknown relation (Leopold et al., 1964; Henderson, 1966; Maddock. 1970; Parker, 1979; Ferguson, 1986; Phillips, 1991). When an extremal hypothesis is substituted for the unknown relation, the assumption is that the channel or fluvial network will alter its available degrees of freedom (width, depth, slope, and grain size) in order to satisfy the proposed extremal hypothesis; examples of these extremal statements include maximizing sediment transport or minimizing energy expenditure of the flow. Extremal hypotheses have been applied at the scale of single cross sections (USACE, 2002) to entire channel networks (RodriguezIturbe et al., 1992), yet little agreement has been reached on which extremal hypothesis is most appropriate. This paper (i) characterizes how dynamic-equilibrium occurs in semiconfined canyon environments, (ii) describes the four criteria that control floodplain distribution within canyons, and (iii) evaluates extremal hypotheses at the reach level to identify dynamicequilibrium and floodplain persistence. 2. Study site The Deadwood River basin is a snowmelt-dominated watershed (614 km2) located in the mountains of central Idaho, USA, and is a tributary of the larger Payette, Snake, and Columbia river systems (Fig. 1). For irrigation purposes, the U.S. Bureau of Reclamation built a reservoir in 1931 that moderates peak flows and traps sediment from the upper basin. The low sinuosity (1.03–1.30) lower Deadwood River runs 38 km between Deadwood Reservoir and the confluence with the South Fork Payette River. Canyon width fluctuates between 70 and 450 m; however, undated strath terraces 4–5 m above floodplains are evident throughout

Fig. 1. Study site on Deadwood River basin located in central Idaho, USA. Light gray stream channels are the upper system above the reservoir and dark gray channels depict the lower Deadwood River.

the canyon that locally limit river mobility and floodplain development. Average channel width at bankfull is 30 m, but ranges between 10 and 80 m at constrictions or irregular bends in the canyon. Inundation widths at the Q100, when floodplains are fully submerged, reach 217 m. The lower Deadwood River was divided into 16 hydromorphologically homogenous reaches, which present plane-bed, pool-riffle, and step-pool morphology (Fig. 2) following the Montgomery and Buffington (1997, 1998) stream classification. The channel substrate consists of cobble-sized clasts with occasional boulder features introduced from surrounding terrestrial sources and a substantial percentage of sand (b 2 mm) (Figs. 2 and 3). The average water surface slope of the river is 1.2% with higher values (3–8%) occurring locally because of geologic constraints (Fig 4). In Deadwood Canyon, 18 floodplains are adjacent to the river that vary between 90 and 1300 m, with average equilibrium floodplain length of 360 m. Floodplain sediments consist of gravel and cobbles with a veneer of sand and finer organics 5–60 cm in depth (Figs. 2 and 3). Field evidence suggests that these coarse-grained, noncohesive floodplains were formed by a combination of point bar, overbank vertical, and abandoned channel accretion processes (Nanson and Croke, 1992; Church, 2002). Trees and forbs have colonized floodplains since dam closure has effectively removed overbank flows. Deadwood Dam has altered the discharge and sediment regime in the lower river, limiting geomorphically significant flows and decoupling floodplain processes from the current river. Since dam completion, the highest flow ever recorded (May 1983) reached only 96% of bankfull discharge. The reduction of peak discharge has stabilized the cross-sectional and planform characteristics of the canyon, with the exception of the last 8 km that has undergone numerous tributary debris flows since 2000 and is considered a contemporary disturbance zone (CDZ). A coarse armor layer exists in the historically sediment supply-limited system; however, recent debris flows introduced finer material from tributary valleys (Fig. 3). Tributary confluences introduce sediment to the main channel as debris fans that can create an upstream backwater, reduce channel width, and increase slope downstream of the riffle/rapid feature. Depending upon the disturbance regime in the tributary basin, effects on the main channel can be minimal or extreme in the case of debris flow events. Channel slope in the lower Deadwood Canyon increases at tributary confluences and decreases downstream, with major alterations in slope occurring at historic debris flows (Fig. 4). Downstream of tributaries, floodplains are present where the canyon widens and deposition is allowed.

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

149

Fig. 2. (A) Floodplain along Deadwood River shown at height of white arrow. (B) Example model cross sections from the Deadwood River with and without floodplains. Dashed line indicates bankfull, stippled line marks 1 m above bankfull that defines floodplain extent.

3. Methods 3.1. Hydraulic model A one-dimensional MIKE11 hydraulic model was employed to quantify the hydraulic properties along the lower Deadwood River at bankfull (QBF) and 100-year flood (Q100) discharges. Marzadri et al.

Fig. 3. (A) Grain-size distributions, via Wolman pebble counts, in various reaches of the Deadwood Canyon with change in distribution from recent debris flows highlighted. (B) Distribution of D50 (boxes) and D84 (diamonds) in the canyon by reach. Reach 4 shows lower particle sizes owing to recent debris flows in 2002 and 2003.

Fig. 4. Longitudinal distribution of water surface slope in relation to major tributary inputs in the Deadwood River, (1) Sixmile Creek, (2) unnamed creek, (3) Sam's Creek, (4) Nellie's Basin Creek, and (5) Slim and Slaughterhouse creeks. Dashed line: water surface elevation at bankfull, points: water surface slope at each cross section, solid line: 15 point moving average of water surface slope to illustrate trend.

150

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

(2014) calibrated and validated the model with a Manning's n resistance parameter of 0.06. They reported a root mean square error of 20 cm between measured and predicted water elevations at low flows, and R2 of 0.98 between predicted and observed flood wave discharge. The model is supported by 30-m spaced cross sections extracted from a high resolution (1-m scale) LiDAR point cloud surveyed with the aquatic-terrestrial Experimental Advanced Airborne Research LiDAR in 2007. The aerial survey provides elevation data accurate on the order of centimeters (McKean et al., 2009a,b; Skinner, 2011) that is adequate for numerical modeling (McKean et al., 2014). Grain-size distribution (GSD) was measured with Wolman pebble counts at 10 of the 16 hydromorphologically homogenous reaches identified in the canyon (Fig. 3). Sand-sized material b 2 mm was identified, but boulders N300 mm were not accounted for in the particle counts. Upstream and downstream boundary conditions for the model were discharge and a field-derived, stage–discharge rating curve, respectively. Lateral inputs were derived from stage–discharge relationships based on water stage measured at each main tributary (Tiedemann, 2013). 3.2. Geomorphic characterization Pre-dam recurrence intervals of flood flows were calculated using a Log Pearson type III distribution based on reservoir inflows for the period of record (1931–2011). Bankfull flow has a recurrence interval in the Deadwood River of 6.3 years (QBF = 65.4 m3/s at canyon entrance, QBF = 108.2 m3/s at canyon outlet). Rarely is overbank inundation uniform over a floodplain surface, as spill occurs at low points along the channel and fills along the distal areas (Nanson, 1986; Pizzuto et al., 2008); therefore, bankfull discharge is that which begins to inundate the proximal areas of the floodplain. At each cross section, bankfull conditions were identified as a break in the area/width relation, where wetted width increases dramatically versus the relatively modest increase in cross-sectional area (Williams, 1978). Bankfull conditions in this study are used to evaluate the forces responsible for floodplain initiation (i.e., incipient overbank flow and deposition) and are comparable to bankfull values in the literature. Results from the 100-year flood (Q100 = 102.8 m3/s at canyon entrance, Q100 = 125.0 m3/s at canyon outlet) were also examined to discern differences between bankfull and catastrophic (overbank) discharge events. Floodplains were operationally defined as flat areas bordering the main river channel that when inundated by high flows (1 m of water above bankfull) had a wetted width N50% of the bankfull channel. To delineate the spatial domain of floodplains, GIS was used to detrend the elevation data using the River Bathymetry Toolkit (McKean et al., 2009b; U.S. Forest Service, 2013). Of the 1098 cross sections examined in the Deadwood River, 249 (23%) had floodplains present. Cross sections that intersected a continuous floodplain adjacent to the river were averaged across their spatial extent. Almost all floodplains are located within 1 km of sedimentcontributing tributaries (Fig. 5), which locally alleviates the sedimentsupply limitation and allows for potential channel-floodplain equilibrium to occur. To confirm that floodplain development occurred before dam closure while bankfull and overbank flows were still possible, historic aerial photographs were examined. The oldest available photographs were from August 1946, which was after dam completion; however, floodplains were fully vegetated, implying an extended period had passed. Given the dry conditions that persist throughout the short growing season in the canyon, vegetative repopulation of the former floodplains would be slow and confidence in the assumption that floodplains formed prior to dam closure is high. 3.3. Exner equation Dynamic-equilibrium is defined in the canyon as time-averaged, uniform sediment flux through a reach. An Exner-type computation

Fig. 5. Absolute sediment divergence through floodplains. Hollow circles are equilibrium floodplains and solid boxes are nonequilibrium floodplains. Vertical error bars show standard deviation of absolute divergence through a floodplain. CDZ marks contemporary disturbance zone.

was performed using model outputs to ensure sediment throughput. Assuming a dimensionless shear stress of 0.047 for incipient motion, sediment was routed through the system using the D50 and divergence was calculated for each cross section. The simplified one-dimensional Exner equation was formulated as: ∂η ∂Q S ¼ −ð1−λÞ ∂X ∂t

ð1Þ

where η = bed elevation (m), t = time (s), λ = porosity, Qs = sediment transport as calculated by the Meyer-Peter and Müller (1948) equation (m3/s), and X = distance downstream (m). Sediment transport relations contain substantial uncertainty because of their spatial variability and sensitivity to hydraulic and channel parameters (Gomez and Church, 1989; Haddadchi et al., 2012, 2013; Recking et al., 2012), yet order of magnitude estimates suffice in this study because results were used only to evaluate how channel geometry would accommodate full capacity transport. Over an entire reach, numerous geologic constraints restrict development of equilibrium channel geometry, causing relative sediment capacity to vary widely. Semialluvial floodplains inset within these reaches are free to adjust their boundaries to maintain uniform sediment flux and low divergence, thereby attaining dynamicequilibrium. Equilibrium floodplains were identified as having nearzero sediment divergence (b 0.0001 m/s) over their extent, whereas nonequilibrium floodplains show high sediment divergence. 3.4. Extremal hypotheses Select extremal hypotheses were assessed in their ability to discern dynamic-equilibrium of a fluvial system (river and floodplain) using the modeled QBF and Q100 results. Three categories of extremal hypotheses were identified from the literature (energy, conveyance/efficiency, resistance), and at least two representative hypotheses from each category were selected for evaluation (Table 1). To discern whether overbank flows were necessary to evaluate the extremal hypotheses, results were examined to see if trends appreciably changed under QBF and Q100 conditions. Eight extremal hypotheses were examined in this study (Table 1): MnSP ¼ ρgQS

minimum stream power

ð2Þ

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

151

Table 1 Extremal hypotheses classification. Values in bold are those selected for analysis in this study.

Energy

Conveyance/efficiency

Resistance

Investigators

Extremal Hypotheses

Leopold and Langbein (1962) Langbein and Leopold (1964) Brebner and Wilson (1967) Yang (1976) Chang (1979, 1980) Yang et al. (1981) Huang (1983, 1988) Grant (1997) Deng and Zhang (1994) Cao and Knight (1996) Cheema et al. (1997) Molnar and Ramirez (1998) Yalin and Da Silva (2000) Singh et al. (2003) Chang (2008) Da Silva (2009) Jefferson (1902) Inglis (1947) Rubey (1952) Pickup (1976) Kirkby (1977) Ramette (1980) White et al. (1982) Jia (1990) Huang and Nanson (2000) Nanson and Huang (2008) Tou (1964) Davies and Sutherland (1983) Davies (1987) Abrahams et al. (1995) Tinkler (1997) Eaton et al. (2004)

Maximum entropy + Uniform energy expenditure Minimum rate of work + Uniform energy expenditure Minimum energy degradation rate Minimum unit stream power Minimum stream power Minimum rate of energy dissipation Maximum rate of energy dissipation Critical energy dissipation Maximum entropy production Minimum stream power + Equal probability Minimum rate of change of unit stream power Minimum specific stream power Minimum Froude number Maximum entropy production + Minimum energy dissipation rate Uniform power expenditure + Uniform sediment load Maximum entropy + Minimum Froude number Maximum sediment transport per available energy slope Minimum energy expenditure per imposed sediment load Maximum hydraulic radius Maximum bedload transport Maximum sediment efficiency Maximum bedload discharge Maximum sediment transport capacity Minimum Froude number + Maximum stability Maximum flow efficiency Least action principle Minimum channel mobility Maximum friction factor Maximum shear stress Maximum flow resistance Critical flow resistance Maximum total friction factor

MnSSP ¼

ρgQ S B

minimum specific stream power

ð3Þ

MnUSP ¼

ρgQS ρgBh

minimum unit stream power

ð4Þ

minimum Froude number

ð5Þ

MnFr ¼

U 1=2

ðghÞ

MxHR ¼

A B

maximum hydraulic radius

3 = qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 hS MxSTC ¼ 8B ΔgD350 −0:047 ΔD50

ð6Þ

the variable assumptions of the original authors (Table 1) in deriving the condition of dynamic-equilibrium for unconfined, alluvial channels. For example, specific stream power describes the stream's response to energy expenditure per unit bed area (Bagnold, 1966; Bull, 1979), whereas unit stream power depicts energy expenditure per unit weight of water (Yang, 1976). 3.5. Hydraulic geometry relations A channel is considered competent to adjust its dimensions in line with hydraulic geometry relations when the ratio of stream power to D84 of the bed material is greater than the threshold value of Eq. (10) (Wohl, 2004):

maximum sediment transport capacity

ð7Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi  3 = 8B ΔgD350 2 hS −0:047 MxFE ¼ ΔD50 ρgQS MxSS ¼ ρghS maximum shear stress

maximum flow efficiency ð8Þ ð9Þ

where ρ = density of water (kg/m3), g = gravitational acceleration (m/s2), Q = discharge (m3/s), S = energy slope, B = channel width (m), h = average channel depth (m), A = cross sectional area (m2), U = average velocity (m/s), Qs = sediment discharge (m3/s), Δ = relative specific gravity of sediment (ρs − ρ) / ρ. If extremal hypotheses are able to indicate the presence/absence of dynamic-equilibrium for the channel and adjacent floodplain, they will be satisfied when their proposed parameters are optimized (i.e., maximal or minimal). The extremal hypotheses MnSP, MnUSP, MnSSP, and MnFr are based on energy minimization, while those of conveyance/ efficiency and resistance (MxHR, MxSTC, MxFE, and MxSS) suggest maximization. The different forms of extremal hypotheses represent

10; 000

kg ρgQ S N s3 D84

ð10Þ

where D84 = grain size that 84% of the distribution is finer (m). In the lower Deadwood River, the ratio did not exceed the critical value for only 18 of the 1098 cross sections, and none were located in floodplain sections. This suggests that hydraulic geometry (HG) relations could be used to quantify the equilibrium dimensions of the channel in reaches where floodplains are present. Typical values of hydraulic geometry coefficients and exponents (cf. Knighton, 1998; Agouridis et al., 2011) for alluvial riverine systems are: B ¼ 3:57Q 0:50

ð11Þ

h ¼ 0:40Q 0:40

ð12Þ

U ¼ 0:95Q 0:10

ð13Þ

S ¼ 0:044Q −0:38

ð14Þ

152

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

with Q = QBF because HG relations are limited to instream flows and bankfull discharge is required for incipient floodplain formation. The HG relations were computed for successful extremal hypotheses to check if semialluvial conditions in the canyon approached those of stable, unconfined, alluvial rivers. Extremal hypotheses quantified via Eqs. (11)–(14) (HG extremal hypotheses) provide the critical values for a stable fluvial configuration. This value can be compared with extremal hypothesis values computed with local fieldobserved or numerically calculated hydraulic values for B, h, U, and S. Comparison between HG extremal hypothesis values and those quantified with measured hydraulic values provide a method to check whether the reach is in equilibrium. Field-computed extremal hypothesis values near the HG extremal hypothesis values identify equilibrium reaches, whereas reaches with field-computed extremal hypotheses different from HG extremal hypothesis values have not reached equilibrium.

4. Results Because of the contemporary disturbance zone (CDZ) in the lower 8 km of the canyon, equilibrium floodplain analysis is limited to the area upstream. Recent debris flows and landslides have created backwater environments in much of the CDZ, initiating deposition of sand and fine gravel behind these channel blockages. With the contemporary reduction in peak discharge, channel and floodplain evolution in this section of river is uncertain.

4.1. Equilibrium and nonequilibrium floodplains The Exner-type equation, employed for QBF and Q100 to identify areas where channel and floodplain geometry have adjusted to uniform sediment flux and potential dynamic-equilibrium, indicate 7 of the 18 surveyed floodplains are below the threshold of 0.0001 m/s sediment transport divergence and thus in dynamic-equilibrium. The remaining 11 have divergence values above the threshold and have not adjusted their reach-scale geometry to sustain uniform sediment flux (Fig. 5). Exceptions are those floodplains located in the CDZ and one nonequilibrium floodplain (21,705 m) that is a depositional backwater directly behind a coarse debris fan at Sam's Creek. The two equilibrium floodplains near the threshold (19,140 and 24,405 m) have greater standard deviations of sediment divergence over their extents, possibly indicating recent small disturbances. Analysis of sediment divergence with QBF and Q100 shows negligible differences; consequently only the QBF results are presented in the upper half of Fig. 6, which shows the distribution of sediment divergence, averaged with 360-m moving windows (average floodplain length), through the system. White arrows indicate near-zero sediment divergence through individual floodplains and black arrows show floodplains with high fluctuations that are in nonequilibrium. A sensitivity analysis was performed to check if the pre-dam GSD affected the flux results, where the D50 was globally changed ±25% in the sediment transport equation (red and black dashed lines in Fig. 6). No major differences in the relative transport trends are apparent in the envelope curves.

Fig. 6. Upper half with bankfull erosion/deposition as calculated via Eq. (1) for the Deadwood River. White arrows depict floodplains near dynamic-equilibrium and black arrows show nonequilibrium floodplains. Solid black line: 360-m moving average for D50 decreased by 25%, red dashed line: 360-m moving average for D 50 increased by 25%. Tributaries are indicated along the top (D.F.) representing debris flows. Lower half depicts 180-m moving average of four normalized, energy-based extremal hypotheses. Yellow: MnSSP, blue: MnUSP, orange: MnSP, and green: MnFr.

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

153

them evolving toward an equilibrium configuration and others being destroyed via erosion processes. 4.4. Extremal results

Fig. 7. Distribution of floodplains with respect to distance from contributing tributaries. Whiskers illustrate minimum and maximum values, whereas boxes depict 75th, 50th, and 25th quartiles.

4.2. Sediment availability The majority of floodplains were located within 1 km (median distance of 500 m) from tributary sources in Deadwood Canyon (Fig. 7, significant at α = 0.001). This is because in sediment-limited canyon systems, sediment availability is restricted to areas downstream of local tributaries, which are sediment sources via fluvial sediment transport or debris flows. These sediment inputs are essential for floodplain formation and maintenance.

4.3. Critical energy thresholds Values of specific stream power (SSP) in Deadwood Canyon reach 3550 W/m2 during QBF and Q100 in cross sections located at tributary confluences and canyon narrows. To investigate under what conditions floodplains may be maintained during QBF and Q100 events, Fig. 8 shows the cumulative distribution of floodplains with respect to SSP (Eq. (3)). During QBF (solid line) equilibrium floodplains are not present for SSP N 400 W/m2. To ensure that stream conditions do not drastically differ from bankfull during overbank floods of large magnitude, the dashed line illustrates the small difference in cumulative distribution of floodplains at Q100. The critical threshold of SSP during Q100 increases to 500 W/m2, but is skewed at the upper end by a few cross sections (7%) that increase the threshold value. These cross sections can be considered local phenomena as the rest of the distribution lies close to the bankfull values. The distribution of energy for nonequilibrium floodplains (boxes) is located between the equilibrium and no floodplain curves. Nonequilibrium floodplains are formed via canyon disturbances such as backwater deposition or coarse terrestrial inputs from landslides that got partially reworked by the flow. If high flows were currently available, these floodplains would be reworked with some of

No extremal hypotheses that attempt to maximize their parameter are successful in the Deadwood River (including MxHR, MxSTC, MxFE, and MxSS) and are not presented. The lower half of Fig. 6 presents a 180-m moving average (half of the average floodplain length) to illustrate the response of the four successful extremal hypotheses modeled with QBF; however, results from the Q100 are similar. The four normalized extremal hypotheses presented in Fig. 6 describe similar results for energy minimization: minimum stream power (orange), minimum specific stream power (yellow), minimum unit stream power (blue), and minimum Froude number (green). Median extremal values calculated within equilibrium floodplains are 90% lower than nonequilibrium floodplains and 153% lower than cross sections without floodplains for specific stream power. Findings are similar for other extremal hypotheses. Results indicate that floodplains form in low energy areas but are subject to geologic constraints of canyon width and sediment availability, so some low energy areas do not have floodplains (e.g., 20,300 m). 4.5. Comparison with equilibrium hydraulic geometry relations Because only the four extremal hypotheses that minimize their values identify floodplains, we calculated the theoretical HG extremal hypotheses for all 18 floodplains by substituting relations (11)–(14) into their extremal forms: MnSP ¼ ρgQS ¼ 1000

kg m  9:8 2  Q  0:044Q −0:38 ¼ 431:2Q 0:62 ð15Þ m3 s

kg m −0:38 ρgQS 1000 m3  9:8 s2  Q  0:044Q MnSSP ¼ ¼ 120:8Q 0:12 ð16Þ ¼ B 3:57Q 0:50

MnUSP ¼

ρgQS ¼ US ¼ 0:95Q 0:10  0:044Q −0:38 ¼ 0:042Q −0:28 ρgBh

U 0:95Q 0:10 MnFr ¼ pffiffiffiffiffiffi ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:48Q −0:10 : m gh 9:8 2  0:40Q 0:40 s

ð17Þ

ð18Þ

Field extremal hypothesis values that were below the theoretical HG values (Eqs. (15)–(18)) were considered to have reached minima in comparison with fully alluvial systems in dynamic-equilibrium. Percent differences were calculated between modeled extremal hypothesis and HG extremal hypothesis values, with negative values indicating extremal minima are below HG values (Fig. 9). In the seven equilibrium floodplains (white arrows in Fig. 6), three of the extremal hypotheses (MnSP, MnUSP, and MnSSP) fall below the theoretical threshold of HG values, whereas MnFr values do not. Exceptions are cross sections located in the CDZ that fall below the threshold in backwater environments and MnUSP at 24,405 m that lies just above the line. Assuming that extremal values closest to the HG values can be considered nearest the equilibrium condition of fully alluvial channels, percent differences for extremal hypotheses are: MnUSP (~ 18%), MnSP (~ 27%), MnSSP (~ 27%), and MnFr (~ 59%). For the purpose of identifying dynamicequilibrium in semialluvial floodplain environments, primary support is provided for MnUSP. 5. Discussion

Fig. 8. Cumulative distribution of floodplains with specific stream power. Solid line: equilibrium QBF, dashed line: equilibrium Q100, boxes: non-equilibrium QBF, triangles: no floodplains QBF.

In canyon systems, tributaries and unstable walls provide sediments as debris fans that can impinge on river width, create an upstream backwater, and increase water surface slope downstream (Benda et al., 2003,

154

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

Fig. 9. Percent difference of extremal hypotheses with respect to relations. Diamonds: MnSP, boxes: MnSSP, triangles: MnUSP, circles: MnFr. Hollow symbols portray equilibrium floodplains and solid symbols nonequilibrium.

2004a; Ferguson et al., 2006; Swanson and Meyer, 2014). During high discharge these debris fans get incised and mobile material gets redistributed downstream. Sediment that is transported downstream becomes available for lateral exchange and may develop equilibrium floodplains where sufficient canyon width is available. The river and floodplains mutually evolve in the downstream direction toward dynamic-equilibrium until either (i) canyon confinement constrains channel-floodplain processes or (ii) another tributary perturbation enters the main channel. 5.1. Canyon width In wide alluvial valleys, flood waters undergo divergence over local bathymetry and lose competence that allows for vertical and lateral accretion to occur (Wolman and Leopold, 1957; Nanson and Croke, 1992). In canyons and gorges, width is a function of the geologic and lithologic properties that must be treated in a stochastic manner for riverine studies (Baker and Costa, 1987; Magilligan, 1992; Miller and Parkinson, 1993; Burbank and Anderson, 2001; Tooth et al., 2002; Pillans, 2007; Perez-Peña et al., 2009; Fryirs and Brierley, 2010). It is considered here as the primary independent variable that controls the distribution of floodplains, which all other criteria must be subject to. While canyon width is a primary control, secondary geologic controls (bedrock, strath terraces, etc.) limit sediment deposition and floodplain formation to discontinuous and irregular expansion zones (Miller, 1990, 1995; Warner, 1992; Grant and Swanson, 1995; Ferguson and Brierley, 1999; Tooth et al., 2002; Brierley and Fryirs, 2005; Johnston and Brierley, 2006; Cohen and Nanson, 2008; Fryirs and Brierley, 2010). In Deadwood Canyon, valley width is relatively constant; yet geologic constraints and secondary controls induce convective steering of flows and provide protection for small floodplains to form on the lee side of barriers. As long as geologic intrusions are present in canyon systems, some form of floodplain feature that scales with the size of intrusion will be likely. 5.2. Overbank discharge The large bankfull recurrence interval in Deadwood Canyon (R.I. = 6.3 years) is thought to be caused by the coarse grain size, configuration of bed particles, and addition of boulders from terrestrial sources that require higher discharges to initiate bedload motion. Under the condition of sediment supply limitation, gravel and cobble beds armor via selective transport and winnowing of finer sediments (Proffitt and Sutherland, 1983; Church et al., 1998; Hassan and Church, 2000; Hassan et al., 2006; Pitlick et al., 2008). While flood recurrence varies by system, the formative floodplain recurrence interval (QBF) may be greater in canyons than unconfined alluvial settings because the coarse bed material from terrestrial sources like walls and tributaries may not be a function of fluvial competence. Floodplain formation and

maintenance therefore requires higher flows to release the fine particles trapped in the coarse armor layer and build floodplains (Williams, 1978; Warner, 1987; Wilcock and DeTemple, 2005; Yanites et al., 2006; Clayton and Pitlick, 2008). Alternatively, as floodplains increase in height a concomitant increase in recurrence interval is required to maintain sediment exchange with the floodplain (Moody et al., 1999; Pizzuto et al., 2008). In canyon streams this process is believed to progress until catastrophic stripping removes large sections of floodplain and rebuilding begins (Nanson, 1986; Ferguson and Brierley, 1999). With the removal of high flows and instantaneous conversion of floodplains to terraces upon dam closure, catastrophic stripping has not occurred in the contemporary environment. This illustrates the mature nature of these floodplains in the pre-dam era. 5.3. Sediment availability In canyon settings, active floodplains are supported downstream of tributary confluences, by which material originating in the tributary valleys becomes accessible for lateral exchange and storage (Dietrich and Dunne, 1978; Magilligan, 1992; Melis, 1997; Meyer et al., 2001; Yanites et al., 2006; Wright and Kaplinski, 2011). Floodplains will persist until the upstream sediment supply is exhausted and floodwaters induce lateral channel erosion and widening that removes previous floodplain deposits down to the coarsest grain sizes (Parker, 1978; Williams and Wolman, 1984; Ferguson and Brierley, 1999; Moody et al., 1999; Benda et al., 2004b; Brierley and Fryirs, 2005; Lauer and Parker, 2008). Hence, floodplain distribution in sediment supplylimited systems is fundamentally linked to the availability of sediment, where persistent long-term floodplains require periodic replenishment of material. Tributary confluences are dynamic mixing zones that often constitute geologic fractures and variable lithology, where sediment production in tributaries varies from diffuse waves to acute inputs from debris flows. As tributary sediment output increases, downstream channel and floodplain geometry will respond to the changing boundary conditions. Stream confluences combine disturbance regimes from disparate areas in a watershed, with increasing basin size increasing activity of these areas (Benda et al., 2003, 2004a). Certain tributaries of the Deadwood River range from b1 to 20 km2 and are ideal for sustaining downstream floodplains owing to the lower disturbance regime, expansion in canyon width, and moderate sediment supply. In contrast, steep low-order tributaries can incur debris flows that deliver substantial quantities of sediment into the main river and cause perturbations upstream and downstream. While debris flows occur infrequently, their respective sediment yield may constitute several thousand years of normal annual erosion rate in a basin and supply significant quantities of material for floodplain exchange (Webb et al., 2000, Meyer et al., 2001; Yanites et al., 2006). Debris fans at these confluences can be considered major drivers of system disequilibrium, affecting slope for numerous kilometers downstream (Fig. 4). These major perturbations to the system provide an opportunity to assess how far their influence reaches before fluvial processes can adjust to equilibrium. 5.4. Energy thresholds High-energy canyon environments can have very high erosive power during flood events, preventing sediment storage along the channel margins and stripping incipient floodplain features that developed during lower flows (Nanson, 1986; Magilligan, 1992; Nanson and Croke, 1992; Ferguson and Brierley, 1999; Macnab et al., 2006; Cohen and Nanson, 2008). Many authors have proposed threshold values for soil/bank erosion or floodplain persistence (Table 2) using field measurements, GIS applications, and hydraulic models set in different environments. Previous investigations report rivers developing in

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

155

Table 2 Threshold values reported in the literature and this study (values are for QBF and [Q100]: C = canyon, A = alluvial, C–A = mixed canyon and alluvial settings). Table modified from Tranmer et al. (2013). Author

Year

Stream type

Substrate

Slope (–)

Shear stress (N/m2)

Specific stream power (W/m2)

This study Reinfelds et al. Church Macnab et al. Jain et al. Magilligan Booth Williams Brookes Miller Magilligan Nanson and Croke McEwen Lecce Kale

2015 2004 2002 2006 2008 1992 1990 1983 1987 1990 1992 1992 1994 1997 2008

C C–A A C C–A C–A A A A C C–A C A A A

Coarse Coarse Coarse Coarse Coarse Unknown Unknown Coarse Coarse–Fine Coarse Unknown Coarse Coarse Coarse Coarse

0.018–[0.018] 0.01 0.02 0.05 0.015–0.03

175–[200]

400–[500]

semiconfined canyons and unconfined alluvial valleys, with critical values for slope and applied shear stress close to those in the Deadwood River. Similar threshold values between canyon and alluvial systems imply that slope and shear stress may not properly identify critical thresholds between diverse river types. Conversely, SSP for canyon rivers is higher than those reported for alluvial streams, with the exception of the unconfined Narmada River in India that is recovering from a very large flood decades before (Kale, 2008). Floodplains in high-energy, semiconfined canyons like the Deadwood and others (Miller, 1990; Magilligan, 1992; Nanson and Croke, 1992) may have unique critical thresholds described by specific stream power.

5.5. Extremal hypotheses and stable hydraulic geometry Examination of extremal hypotheses within semialluvial canyon sections show that no equilibrium floodplains formed where extremal hypotheses display a maximum (MxHR, MxSTC, MxFE, and MxSS), which occur in deep backwater areas upstream of debris fans or at steep, debris-fan-induced rapids. As seen in the threshold section, energy metrics are very sensitive to channel geometry and hydraulics that make them ideal for identifying changes in fluvial systems. Figure 6 shows the longitudinal trends of erosion/deposition in relation to normalized extremal hypotheses, and the presence of semialluvial, equilibrium floodplains in areas of energy minimization. Concerning floodplain formation, it is rational that areas of deposition would coincide with energy minimization as it is a surrogate for sediment transport competence. Equilibrium floodplains can be discerned from surrounding nonequilibrium floodplains because they have lower minima. While absolute minimization of the extremal hypotheses depends on geologic conditions in the basin that set limits on channel slope and valley width, values also depend upon upstream boundary conditions. The addition of water and sediment at major tributaries will affect GSD and subsequent channel geometry (Benda et al., 2004b; Swanson and Meyer, 2014), thereby changing boundary conditions and the respective minima. These changes will be incorporated by extremal hypotheses to varying degrees as they scale locally with discharge, slope, and channel dimensions. Total stream power (Eq. (2)) will increase with respective increases in discharge and slope; however, it does not account for channel geometry. The other extremal hypotheses directly incorporate aspects of channel geometry and may better represent the energy expenditure at a cross section. Specific stream power for example (Eq. (3)) accounts for channel width and therefore scales the energy expenditure to the size of the stream. If consistent relations exist for the width, depth, and slope of alluvial channels, such as those of hydraulic geometry, a universal minimum may be possible to identify that

100 175

200 90 35 500 300 600 100 100 527

represents true dynamic-equilibrium conditions for both semi- and fully alluvial systems. Assuming self-organizing, semialluvial channel processes are present along the adjustable, open floodplain boundary and that hydraulic geometry relations represent the collective empirical findings of over 60 years of alluvial research, an approximate comparison will indicate if the extremal hypotheses are approaching dynamic-equilibrium for bankfull discharge (Leopold and Maddock, 1953; Parker, 1979; Cao and Knight, 1998; Camporeale et al., 2005; Hooke, 2007; Parker et al., 2007; Agouridis et al., 2011). Comparing extremal results to the hydraulic geometry values (Fig. 9) for the equilibrium floodplains, MnUSP provides the best agreement and may be the most appropriate for identifying dynamic-equilibrium within the semiconfined canyon environment because of its incorporation of channel width and depth. Given the variable influence of tributary inputs, identifying absolute minima of extremal hypotheses is complicated for long sections of river. In Deadwood Canyon, extremal hypotheses are applicable for identifying equilibrium floodplains outside of backwater conditions and between major tributary influences. Application of energy-based extremal hypotheses between tributary disturbances can illustrate a downstream trend in how the hydraulics and geometry adjust to those new boundary conditions. Identification of low energy areas can predict potential floodplain construction or persistence of existing floodplains. In other semiconfined and fully alluvial river systems, major tributary inputs enter main channels on the scale of 101 to 103 m, whereby the extremal approach could be applicable. Further research is needed to see how extremal hypotheses respond over multiple series of equilibrium floodplains without major tributary inputs to find absolute minima. 6. Conclusions Floodplain distribution in canyon environments depends upon four limiting conditions: (i) sufficient canyon width providing accommodation space, (ii) overbank flows available for channel–floodplain material exchange, (iii) sediment readily accessible for transport and building processes, and (iv) an energy gradient below critical thresholds that permits deposition. Of these four criteria, canyon width is treated as a function of geologic properties that changes on a millennial timescale and is therefore considered an independent controlling variable. Overbank flows are dependent upon regional hydrology, which is increasingly being manipulated by human impacts of dams and diversions, as well as uncertainty from future climate change. Sediment availability in supply-limited rivers is a function of tributary sediments derived from local instabilities along the canyon periphery. Sediment availability is manifested in the main channel by distance downstream from tributary inputs, which locally alleviates the supply limitation

156

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

and provides mobile material for exchange with floodplain surfaces. An energy gradient that allows for deposition of tributary sediments is a function of width and slope in the canyon environment, which is controlled by geologic constraints. This can be addressed by a critical threshold approach, in which floodplains are formed and maintained when conditions are less than specific values. Threshold values at bankfull flow for the Deadwood River are energy slope (0.018), shear stress (175 N/m2), and specific stream power (400 W/m2); however, SSP may better differentiate semialluvial floodplains in canyons than slope or shear stress. Results from the extremal hypotheses illustrate that those based on energy minimization performed well, providing depositional backwater environments and major tributary influences can be accurately identified. When compared with hydraulic geometry relations, minimum unit stream power showed the closest agreement in the equilibrium floodplains, with secondary support for minimum stream power and minimum specific stream power. No significant difference was found between extremal hypotheses calculated at QBF and Q100, implying instream measurements are sufficient for evaluating extremal methods. Acknowledgments The authors would like to acknowledge Carolyn Bohn of the U.S. Rocky Mountain Research Station for her assistance with some of the GIS work and Elowyn Yager for her helpful discussions on the paper. Special thanks to DHI for providing the modeling software. This work was made possible by funding from the U.S. Forest Service (Grant 08JV-11221659-036). Any opinions, conclusions, or recommendations expressed in this material are solely those of the authors and do not necessarily reflect the views of the supporting institutions and agencies. We thank the editor and anonymous reviewers for their critical and constructive comments. References Abrahams, A.D., Li, G., Atkinson, J.F., 1995. Step-pool streams: adjustment to maximum flow resistance. Water Resources Research 31 (10), 2593–2602. Agouridis, C., Brockman, R., Workman, S., Ormsbee, L., Fogle, A., 2011. Bankfull hydraulic geometry relationships for the Inner and Outer Bluegrass Regions of Kentucky. Water 3, 923–948. Bagnold, R.A., 1966. An approach to the sediment transport problem from general physics. United States Department of the Interior, U.S. Geological Survey Professional Paper 422-I, 37 pp. Baker, V.R., Costa, J.E., 1987. Flood power. In: Mayer, L., Nash, D. (Eds.), Catastrophic Flooding. Allen and Unwin, Winchester, pp. 1–21. Benda, L., 1990. The influence of debris flows on channels and valley floors of the Oregon Coast Range, U.S.A. Earth Surface Processes and Landforms 15, 457–466. Benda, L.E., Veldhuisen, C., Black, J., 2003. Debris flows as agents of morphological heterogeneity at low-order confluences, Olympic Mountains, Washington. Geological Society of America Bulletin 115 (9), 1110–1121. Benda, L.E., Andras, K., Miller, D.J., Bigelow, P., 2004a. Confluence effects in rivers: interactions of basin scale, network geometry, and disturbance regimes. Water Resources Research 40. http://dx.doi.org/10.1029/2003WR002583 W05402. Benda, L., Poff, N.L., Miller, D., Dunne, T., Reeves, G., Pess, G., Pollock, M., 2004b. The network dynamics hypothesis: how channel networks structure riverine habitats. Bioscience 54 (5), 413–427. Booth, D.B., 1990. Stream-channel incision following drainage basin urbanization. AWRA Water Resources Bulletin 26 (3), 407–417. Brebner, A., Wilson, K.C., 1967. Derivation of the regime equations from relationships for pressurized flow by use of the principle of minimum energy-degradation rate. Proc Institute Civil Engineering 36, 47–62. Brierley, G.J., Fryirs, K., 2005. Geomorphology and River Management: Applications of the River Styles Framework. Blackwell Publishing, Oxford, UK 398 pp. Brookes, A., 1987. River channel adjustments downstream from channelization works in England and Wales. Earth Surface Processes and Landforms 12, 337–351. Bull, W.B., 1979. Threshold of critical power in streams. Geological Society of America Bulletin 1 (90), 453–464. Burbank, D.W., Anderson, R.S., 2001. Tectonic Geomorphology. Blackwell Science, Malden Massachusetts 274 pp. Camporeale, C., Perona, P., Porporato, A., Ridolfi, L., 2005. On the long-term behavior of meandering rivers. Water Resources Research 41. http://dx.doi.org/10.1029/ 2005WR004109 W12403. Cao, S., Knight, D.W., 1996. Regime theory of alluvial channels based upon the concept of stream power and probability. Proc Institution of Civil Engineers 100, 160–167.

Cao, S., Knight, D.W., 1998. Design for hydraulic geometry of alluvial channels. J Hydraulic Engineering 124, 484–492. Chang, H.H., 1979. Minimum stream power and river channel patterns. J. Hydrology 41, 303–327. Chang, H.H., 1980. Geometry of gravel streams. ASCE J. Hydraulics Division 106 (9), 1443–1456. Chang, H.H., 2008. River morphology and river channel changes. Transactions of Tianjin University 14 (4), 254–262. Cheema, M.N., Marino, M.A., De Vries, J.J., 1997. Stable width of an alluvial channel. J. Irrigation and Drainage Engineering 123 (1), 55–61. Church, M., 2002. Geomorphic thresholds in riverine landscapes. Freshwater Biology 47, 541–557. Church, M., Hassan, M.A., Wolcott, J.F., 1998. Stabilising self-organized structures in gravel-bed stream channels: field and experimental observations. Water Resources Research 34, 3169–3179. Clayton, J.A., Pitlick, J., 2008. Persistence of the surface texture of a gravel-bed river during a large flood. Earth Surface Processes and Landforms 33, 661–673. Cohen, T., Nanson, G.C., 2008. Topographically associated but chronologically disjunct late Quaternary floodplains and terraces in a partly confined valley, south-eastern Australia. Earth Surface Processes and Landforms 33, 424–443. Da Silva, A.M.F., 2009. On the stable geometry of self-formed alluvial channels: theory and practical application. Canadian J Civil Engineering 36, 1667–1679. Davey, D., Lapointe, C., 2007. Sedimentary links and the spatial organization of Atlantic salmon (Salmo salar) spawning habitat in a Canadian Shield river. Geomorphology 83 (1), 82–96. Davies, T.R.H., 1987. Problems of bed load transport in braided gravel-bed rivers. In: Thorne, C.R., Bathurst, J.C., Hey, R.D. (Eds.), Sediment Transport in Gravel-bed Rivers. John Wiley and Sons, Chichester, pp. 793–828. Davies, T.R.H., Sutherland, A.J., 1983. Extremal hypotheses for river behavior. Water Resources Research 19 (1), 141–148. Deng, Z., Zhang, K., 1994. Morphologic equations based on the principle of maximum entropy. International J Sedimentary Research 9 (1), 31–46. Dietrich, W.E., Dunne, T., 1978. Sediment budget for a small catchment in mountainous terrain. Zeitschrift für Geomorphologie, Supplement Band 29, 215–230. Eaton, B.C., Church, M., Millar, R.G., 2004. Rational regime model of alluvial channel morphology and response. Earth Surface Processes and Landforms 29, 511–529. Ferguson, R.I., 1986. Hydraulics and hydraulic geometry. Progress in Physical Geography 10, 1–31. Ferguson, R.I., Brierley, G.J., 1999. Downstream changes in valley confinement as a control on floodplain morphology, lower Tuross River, New South Wales: a constructivist approach to floodplain analysis. In: Miller, A.J., Gupta, A. (Eds.), Varieties of Fluvial Form. John Wiley & Sons, Chichester, UK, pp. 377–407. Ferguson, R.I., Cudden, J.R., Hoey, T.B., Rice, S.P., 2006. River system discontinuities due to lateral inputs: generic styles and controls. Earth Surface Processes and Landforms 31, 1149–1166. Fryirs, K., Brierley, G.J., 2010. Antecedent controls on river character and behavior in partly confined valley settings: upper Hunter catchment, NSW, Australia. Geomorphology 117 (1–2), 106–120. Gomez, B., Church, M., 1989. An assessment of bedload sediment transport formulae for gravel bed rivers. Water Resources Research 25, 1161–1186. Grant, G.E., 1997. Critical flow constrains flow hydraulics in mobile-bed streams: a new hypothesis. Water Resources Research 33 (2), 349–358. Grant, G.E., Swanson, F.J., 1995. Morphology and processes of valley floors in mountain streams, Western Cascades, Oregon. In: Costa, J.E., Miller, A.J., Potter, K.W., Wilcock, P.R., (Eds.), Natural and Anthropogenic Influences in Fluvial Geomorphology. American Geophysical Union Geophysical Monograph 89, Washington DC, pp. 83–101. Griffiths, G.A., Carson, M.A., 2000. Channel width for maximum bedload transport capacity in gravel-bed rivers, South Island, New Zealand. J. Hydrology 39 (2), 107–126. Haddadchi, A., Omid, M.H., Dehghani, A.A., 2012. Assessment of bed-load predictors based on sampling in a gravel bed river. J. Hydrodynamics 24 (1), 145–151. Haddadchi, A., Omid, M.H., Dehghani, A.A., 2013. Bedload equation analysis using bed load-material grain size. J. Hydrology and Hydromechanics 61 (3), 241–249. Hassan, M.A., Church, M., 2000. Experiments on surface structure and partial sediment transport on a gravel bed. Water Resources Research 36, 1885–1895. Hassan, M.A., Egozi, R., Parker, G., 2006. Experiments on the effect of hydrograph characteristics on vertical grain sorting in gravel bed rivers. Water Resources Research 42(9). http://dx.doi.org/10.1029/2005WR004707. Henderson, F.M., 1966. Open Channel Flow. Macmillan, New York 522 pp. Hooke, J.M., 2007. Complexity, self-organization and variation in behaviour in meandering rivers. Geomorphology 91, 236–258. Huang, H.Q., Nanson, G.C., 2000. Hydraulic geometry and maximum flow efficiency as products of the principle of least action. Earth Surface Processes and Landforms 25, 1–16. Huang, W.L., 1983. The extremity law of hydro-thermodynamics. Applied Mathematics and Mechanics 4 (4), 501–510. Huang, W.L., 1988. The law of maximum rate of energy dissipation. International Symposium on Hydraulics for High Dams, Beijing, China, 159–165. Inglis, C.C., 1947. Meanders and Their Bearing on River Training. Maritime and Waterways Engineers Division. Institution of Civil Engineers, London. Jain, V., Fryirs, K., Brierley, G.J., 2008. Where do floodplains begin? The role of total stream power and longitudinal profile form on floodplain initiation processes. Geological Society of America Bulletin 120 (1–2), 127–141. Jefferson, M.S.W., 1902. Limiting width of meander belts. The National Geographic Magazine 13, 373–384. Jia, Y., 1990. Minimum Froude number and the equilibrium of alluvial sand rivers. Earth Surface Processes and Landforms 15, 199–209.

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158 Johnston, P., Brierley, G.J., 2006. Late Quaternary river evolution of floodplain pockets along Mulloon Creek, New South Wales, Australia. The Holocene 16 (5), 661–674. Kale, V.S., 2008. A half century record of annual energy expenditure and geomorphic effectiveness of the monsoon-fed Narmada River, Central India. Catena 75, 154–163. Kirkby, M.J., 1977. Maximum sediment efficiency as a criterion for alluvial channels. In: Gregory, K.J. (Ed.), River Channel Changes. Wiley, Chichester, pp. 429–442. Knighton, A.D., 1998. Fluvial Forms and Processes: A New Perspective. Arnold, London 383 pp. Langbein, W.B., Leopold, L.B., 1964. Quasi-equilibrium states in channel morphology. American J. Science 262, 782–794. Lauer, J.W., Parker, G., 2008. Net local removal of floodplain sediment by river meander migration. Geomorphology 96, 123–149. Lecce, S.A., 1997. Nonlinear downstream changes in stream power on Wisconsin's Blue River. Annals of the Association of American Geographers 87, 471–486. Leopold, L.B., Langbein, W.B., 1962. The concept of entropy in landscape evolution. U.S. Geological Survey Professional Paper 500-A, 20 pp. Leopold, L.B., Maddock, T., 1953. The hydraulic geometry of stream channels and some physiographic implications. U.S. Geological Survey Professional Paper 252, pp. 57. Leopold, L.B., Wolman, M.G., Miller, J.P., 1964. Fluvial Processes in Geomorphology. Freeman Press, San Francisco 522 pp. Macnab, K., Jacobson, C., Brierley, G.J., 2006. Spatial variability of controls on downstream patterns of sediment storage: a case study in the Lane Cove catchment, New South Wales, Australia. Geographical Research 44 (3), 255–271. Maddock, T., 1970. Indeterminate hydraulics of alluvial channels. ASCE J. Hydraulics Division 96 (11), 2309–2323. Magilligan, F.J., 1992. Thresholds and the spatial variability of flood power during extreme floods. Geomorphology 5, 373–390. Marzadri, A., Tonina, D., McKean, J.A., Tiedemann, M.G., Benjankar, R., 2014. Multi-scale streambed topographic and discharge effects on hyporheic exchange at the stream network scale in confined stream. J. Hydrology 519, 1997–2011. http://dx.doi.org/ 10.1016/j.jhydrol.2014.09.076. McEwen, L.J., 1994. Channel planform adjustment and stream power variations on the middle River Coe, Western Grampian Highlands, Scotland. Catena 21, 357–374. McKean, J.A., Isaak, D.J., Wright, C.W., 2009a. Improving stream studies with a smallfootprint Green Lidar. EOS. Transactions of the American Geophysical Union 90 (39), 341–342. McKean, J.A., Nagel, D., Tonina, D., Bailey, P., Wright, C.W., Bohn, C., Nayegandhi, A., 2009b. Remote sensing of channels and riparian zones with a narrow-beam aquatic–terrestrial LIDAR. Remote Sensing 1, 1065–1096. http://dx.doi.org/10.3390/rs1041065. McKean, J.A., Tonina, D., Bohn, C., Wright, C.W., 2014. Effects of bathymetric lidar errors on flow properties predicted with a multi-dimensional hydraulic model. J. Geophysical Research: Earth Surface. http://dx.doi.org/10.1002/2013JF002897. Melis, T.S., 1997. Geomorphology of Debris Flows and Alluvial Fans in Grand Canyon National Park and Their Influences on the Colorado River Below Glen Canyon Dam, Arizona, Ph.D. Dissertation, Univ. of Arizona. Meyer, G.A., Pierce, J.L., Wood, S.H., Jull, A.J.T., 2001. Fire, storms, and erosional events in the Idaho batholith. Hydrological Processes 15, 3025–3038. Meyer-Peter, E., Müller, R., 1948. Formulas for bed-load transport. Proc. 2nd Meeting of the International Association for Hydraulic Structures Research, IAHR, Delft, Netherlands, 39–64. Miller, A.J., 1990. Flood hydrology and geomorphic effectiveness in the central Appalachians. Earth Surface Processes and Landforms 15 (2), 119–134. Miller, A.J., 1995. Valley morphology and boundary conditions influencing spatial patterns of flood flow. In: Costa, J.E., Miller, A.J., Potter, K.W., Wilcock, P.R. (Eds.), Natural and Anthropogenic Influences in Fluvial GeomorphologyGeophysical Monograph 89. American Geophysical Union, Washington DC, pp. 57–81. Miller, A.J., Parkinson, D.J., 1993. Flood hydrology and geomorphic effects on river channels and flood plains: the flood of November 3–5, 1985, in the South Branch Potomac River Basin of West Virginia. U.S. Geological Survey Bulletin 1981-E, 96 pp. Molnar, P., Ramirez, J.A., 1998. Energy dissipation theories and optimal channel characteristics of river networks. Water Resources Research 34 (7), 1809–1818. Molnar, P., Ramirez, J.A., 2002. On downstream hydraulic geometry and optimal energy expenditure: case study of the Ashley and Taieri Rivers. J. Hydrology 259, 105–115. Montgomery, D.R., Buffington, J.M., 1997. Channel-reach morphology in mountain drainage basins. Geological Society of America Bulletin 109, 596–611. Montgomery, D.R., Buffington, J.M., 1998. Channel processes, classification, and response. In: Naiman, R., Bilby, R. (Eds.), River Ecology and Management. Springer-Verlag, New York, pp. 13–42. Moody, J.A., Pizzuto, J.E., Meade, R.H., 1999. Ontogeny of a flood plain. Geological Society of America Bulletin 111 (2), 291–303. Nanson, G.C., 1986. Episodes of vertical accretion and catastrophic stripping: a model of disequilibrium floodplain development. Geological Society of America Bulletin 97 (12), 1467–1475. Nanson, G.C., Croke, J.C., 1992. A genetic classification of floodplains. Geomorphology 4, 459–486. Nanson, G.C., Huang, H.Q., 2008. Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels. Earth Surface Processes and Landforms 33, 923–942. Parker, G., 1978. Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel bed. J Fluid Mechanics 89, 127–146. Parker, G., 1979. Hydraulic geometry of active gravel rivers. ASCE J Hydraulics Division 105, 1185–1201. Parker, G., Wilcock, P.R., Paola, C., Dietrich, W.E., Pitlick, J., 2007. Physical basis for quasiuniversal relations describing bankfull hydraulic geometry of single-thread gravel bed rivers. J. Geophysical Research 112. http://dx.doi.org/10.1029/2006JF000549 F04005.

157

Perez-Peña, I.V., Azañon, I.M., Azor, A., Delgado, J., Gonzáez-Lodeiro, F., 2009. Spatial analysis of stream power using GIS: SLk anomaly maps. Earth Surface Processes and Landforms 34, 16–25. Phillips, J.D., 1991. Multiple modes of adjustment in unstable river channel cross-sections. J. Hydrology 123, 39–49. Pickup, G., 1976. Adjustment of stream-channel shape to hydrologic regime. J. Hydrology 30, 365–373. Pickup G., 1986. Fluvial landforms. In: Australia — A Geography, 2nd edition, Jeans D.N., (Ed.). Sydney University Press, 148–179. Pillans, B., 2007. Pre-Quaternary landscape inheritance in Australia. J Quaternary Science 22, 439–447. Pitlick, J., Mueller, E.R., Segura, C., Cress, R., Torizzo, M., 2008. Relation between flow, surface-layer armoring and sediment transport in gravel-bed rivers. Earth Surface Processes and Landforms 33, 1192–1209. Pizzuto, J.E., Moody, J.A., Meade, R.H., 2008. Anatomy and dynamics of a floodplain, Powder River, Montana, U.S.A. J Sedimentary Research 78, 16–28. http://dx.doi.org/ 10.2110/jsr.2008.005. Proffitt, G.T., Sutherland, A.J., 1983. Transport of non-uniform sediment. J. Hydraulic Research 21 (1), 33–43. Ramette, M., 1980. A theoretical approach on fluvial processes. Proc. International Symposium River Sedimentation, Beijing, China Recking, A., Liébault, F., Peteuil, C., Jolimet, T., 2012. Testing bedload transport equations with consideration of time scales. Earth Surface Processes and Landforms 37, 774–789. Reinfelds, I., Cohen, T., Batten, P., Brierley, G.J., 2004. Assessment of downstream trends in channel gradient, total and specific stream power: a GIS approach. Geomorphology 60, 403–416. Rodriguez-Iturbe, I., Rinaldo, A., Rigon, R., Bras, R., Marani, A., Ijjasz-Vasquez, E., 1992. Energy dissipation, runoff production, and the three-dimensional structure of river basins. Water Resources Research 28 (4), 1095–1103. Rubey, W.W., 1952. Geology and mineral resources of the Hardin and Brussels quadrangles (in Illinois). U.S. Geological Survey Professional Paper 218, 179 pp. Schumm, S.A., 1977. The Fluvial System. John Wiley & Sons, New York 338 pp. Singh, V.P., Yang, C.T., Deng, Z.Q., 2003. Downstream hydraulic geometry relations: 1. Theoretical development. Water Resources Research 39 (12), 1337. http://dx.doi.org/10. 1029/2003WR002484. Skinner, K.D., 2011. Evaluation of LiDAR-acquired bathymetric and topographic data accuracy in various hydrogeomorphic settings in the Deadwood and South Fork Boise Rivers, West-Central Idaho, 2007. U.S. Geological Survey Scientific Investigations Report 2011-5051, 30 pp. Swanson, B.J., Meyer, G., 2014. Tributary confluences and discontinuities in channel form and sediment texture: Rio Chama, NM. Earth Surface Processes and Landforms 39, 1927–1943. Tiedemann, M.G., 2013. Examining a Functional Flow Regime and Accompanying Thermal Regime in a Regulated Mountain Canyon River Under Varying Climatic Conditions. MS Thesis, University of Idaho, USA Tinkler, K.J., 1997. Critical flow in rockbed streams with estimated values for Manning's n. Geomorphology 20, 147–164. Rivers over rock: fluvial processes in bedrock channelsTinkler, K.J., Wohl, E.E. (Eds.), 1998. Geophysical Monograph 107. American Geophysical Union, Washington, DC 323 pp. Tooth, S., McCarthy, T.S., Brandt, D., Hancox, P.J., Morris, R., 2002. Geological controls on the formation of alluvial meanders and floodplain wetlands: the example of the Klip River, Eastern Free State, South Africa. Earth Surface Processes and Landforms 27, 797–815. Tou, K.J., 1964. Hydromorphology of alluvial channels of lowland rivers and tidal estuaries (translation). Scientia Sinica 14 (8), 1212–1227. Tranmer, A.W., Tonina, D., Godwin, P., Benjankar, R., Tiedemann, M., 2013. Stream power changes in an alluvial canyon — Deadwood River, USA. Proc. 2013 IAHR Congress, Tsinghua University Press, Beijing, China. pp. 11. U.S. Army Corps of Engineers, 2002. SAM Hydraulic Design Package for Channels. Thomas, W.A., Copeland, R.R., McComas, D.N., Coastal and Hydraulics Laboratory Vicksburg, MS, September U.S. Forest Service, 2013. http://www.fs.fed.us/rm/boise/AWAE/projects/river_ bathymetry_toolkit.shtml. Last accessed: 04/10/2015. Warner, R.F., 1987. Spatial adjustments to temporal variations in flood regime in some Australian rivers. In: Richards, K.S. (Ed.), River Channels — Environments and Processes. Blackwell, Oxford, pp. 14–39. Warner, R.F., 1992. Floodplain evolution in a New South Wales coastal valley, Australia: spatial process variations. Geomorphology 4, 447–458. Webb, R.H., Griffiths, P.G., Melis, T.S., Hartley, D.R., 2000. Sediment delivery by ungaged tributaries of the Colorado River in Grand Canyon, Arizona. U.S. Geological Survey Water Resources Investigations Report, 00-4055, 67 pp White, W.R., Bettess, R., Paris, E., 1982. Analytical approach to river regime. ASCE J. Hydraulics Division 108 (10), 1179–1193. Wilcock, P.R., DeTemple, B.T., 2005. Persistence of armor layers in gravel-bed streams. Geophysical Research Letters 32. http://dx.doi.org/10.1029/2004GL021772 L08402. Williams, G.P., 1978. Bank-full discharge of rivers. Water Resources Research 14 (6), 1141–1154. Williams, G.P., 1983. Paleohydrological methods and some examples from Swedish fluvial environments. I. Cobble and boulder deposits. Geografiska Annaler 65A (3–4), 227–243. Williams, G.P., Wolman, M.G., 1984. Downstream effects of dams on alluvial rivers. U.S. Geological Survey Professional Paper 1286, 83 pp. Wohl, E., 2004. Limits of downstream hydraulic geometry. Geology 32 (10), 897–900. Wolman, M.G., Leopold, L.B., 1957. River flood plains: some observations on their formation. U.S. Geological Survey professional Paper 282-C, 107 pp.

158

A.W. Tranmer et al. / Geomorphology 250 (2015) 147–158

Wright, S.A., Kaplinski, M., 2011. Flow structures and sandbar dynamics in a canyon river during a controlled flood, Colorado River, Arizona. J Geophysical Research 116. http://dx.doi.org/10.1029/2009JF001442 F01019. Yalin, M.S., Da Silva, A.M.F., 1999. Regime channels in cohesionless alluvium. J. Hydraulic Research 37 (6), 725–742. Yalin, M.S., Da Silva, A.M.F., 2000. Computation of regime channel characteristics on thermodynamic basis. J. Hydraulic Research 38 (1), 57–64.

Yanites, B.J., Webb, R.H., Griffiths, P.G., Magirl, C.S., 2006. Debris flow deposition and reworking by the Colorado River in Grand Canyon, Arizona. Water Resources Research 42. http://dx.doi.org/10.1029/2005WR004847 W11411. Yang, C.T., 1976. Minimum stream power and fluvial hydraulics. ASCE J 102 (HY7), 919–934. Yang, C.T., Song, C.S., Woldenberg, M.J., 1981. Hydraulic geometry and minimum rate of energy dissipation. Water Resources Research 17 (4), 1014–1018.