Earth Surface Processes and Landforms
Earth Surf. Process. Landforms 28, 837–852INTERCHANNEL
(2003)
HYDRAULIC GEOMETRY
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/esp.497
837
INTERCHANNEL HYDRAULIC GEOMETRY AND HYDRAULIC
EFFICIENCY OF THE ANASTOMOSING COLUMBIA RIVER,
SOUTHEASTERN BRITISH COLUMBIA, CANADA
KEVIN K. TABATA1* AND EDWARD J. HICKIN2
2
1
Department of Geography, Simon Fraser University, Burnaby, British Columbia, Canada
Department of Geography and Department of Earth Sciences, Simon Fraser University, Burnaby, British Columbia, Canada
Received 30 May 2002; Revised 9 December 2002; Accepted 7 January 2003
ABSTRACT
The morphodynamics of the anastomosing channel system of upper Columbia River in southeastern British Columbia,
Canada, is examined using an adaptation of conventional hydraulic geometry termed ‘interchannel hydraulic geometry’.
Interchannel hydraulic geometry has some of the characteristics of downstream hydraulic geometry but differs in that it
describes the general bankfull channel form and hydraulics of primary and secondary channels in the anastomosing channel
system. Interchannel hydraulic geometry generalizes these relationships and as such becomes a model of the geomorphology
of channel division and combination. Interchannel hydraulic geometry of upper Columbia River, based on field measurements of flow velocity and channel form at 16 test sections, is described well by simple power functions: wbf = 3·24Qbf0·64;
dbf = 1·04Qbf0·19; vbf = 0·30Qbf0·17. These results, with other related measurements of flow resistance, imply that channel splitting
leads to hydraulic inefficiency (higher flow resistance) on the anastomosing Columbia River. Because these findings differ
from those reported in studies elsewhere, we conclude that hydraulic efficiency does not provide a general explanation for
anabranching in river channels. Copyright © 2003 John Wiley & Sons, Ltd.
KEY WORDS: hydraulic geometry; hydraulic efficiency; anastomosing river
INTRODUCTION
This paper is concerned with the morphodynamics of anastomosing channel systems in rivers and explores
an adaptation of conventional hydraulic geometry to describe the geomorphology of the anastomosing Columbia
River in southeastern British Columbia, Canada (Figure 1). Particular attention is given to hydraulic efficiency
in relation to the number and size of channels in the anastomosing system. The hydraulic geometry of a river
is the quantitative (mathematical and graphical) description of the channel cross-section size and shape, fluidflow properties and sediment-transport characteristics, in relation to the discharge being conducted by the
channel (Leopold and Maddock, 1953). It is a descriptive tool, derived from the empirical relationships of
regime ‘theory’ developed to aid canal design in India early last century (Lacey, 1930).
The principal equations of hydraulic geometry proposed by Leopold and Maddock (1953), and used in this
study, are simple power functions:
w = aQb
d = cQ f
v = kQ m
s = gQ z
ff = hQ p
where w, d, v, s, ff and Q are respectively width, mean depth, mean velocity, water-surface slope, Darcy–
Weisbach resistance coefficient and discharge. Because continuity must be satisfied in fluid flow (Q = wdv), the
* Correspondence to: K. K. Tabata, Department of Geography, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia,
V5A 156, Canada. E-mail: kevin_tabata@yahoo.com
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
838
K. K. TABATA AND E. J. HICKIN
Figure 1. Upper Columbia River and study reach
product of the coefficients and sum of the exponents in the width–, depth– and velocity–discharge relationships
must equal unity.
The adjustment of channel morphology and hydraulics in response to changes in discharge has been considered in two quite different contexts: at-a-station hydraulic geometry and downstream hydraulic geometry. Ata-station hydraulic geometry describes how channel geometry and flow hydraulics change as discharge increases
at an individual channel cross-section over time. In most rivers, discharge also increases in the downstream
direction as tributaries join the main channel. Downstream hydraulic geometry describes how this spatially
increasing discharge enlarges and shapes the channel and alters streamflow properties. In order to allow for
comparisons between channel sections, these changes are referred to a discharge of constant return period or
consistent relative stage. The most common reference discharge is bankfull discharge, which is often taken to
be the channel-forming discharge.
Hydraulic geometry forms an important core of fluvial geomorphology and much has been written on the
concept. It is not the present purpose to review this work (comprehensive reviews are available in Richards
(1977) and Knighton (1998)), but rather to briefly characterize hydraulic geometry as the point of departure for
the present study.
Because continuity is a fundamental and defining characteristic of downstream hydraulic geometry, application of this concept has excluded rivers with multiple channels, such as anastomosing rivers. It is argued in this
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
INTERCHANNEL HYDRAULIC GEOMETRY
839
paper, however, that the ideas of conventional hydraulic geometry can be usefully extended in a modified form
to include the morphodynamics of anastomosing (and other types of multiple-channelled) rivers. This extension,
introduced in this paper, is hereafter termed ‘interchannel’ hydraulic geometry.
Interchannel hydraulic geometry describes the general bankfull channel form and hydraulics of primary and
secondary channels in the anastomosing channel system. Given channel splitting and a particular reallocation of
discharge among the resulting channels, interchannel hydraulic geometry describes the morphology and hydraulics of divided channels at bankfull stage. The upper discharge limit of interchannel hydraulic geometry is
represented by the case in which all the flow at bankfull is confined to a single channel, while the lower
discharge limit is set by the size of the smallest secondary channel to form in the anastomosing system. At any
given valley cross-section in an anastomosing reach, discharges through the individual channels must sum to the
total system discharge. Interchannel hydraulic geometry generalizes these relationships and thus becomes a
model of the geomorphology of channel division and combination.
Although interchannel hydraulic geometry clearly is conceptually closer to downstream hydraulic geometry
than to at-a-station hydraulic geometry, there are some important differences. For example, in an anastomosing
reach, water-surface slope at bankfull discharge, and the size of boundary material, are sensibly constant in
distinct contrast to the typical circumstances of downstream changes in rivers.
Just as downstream hydraulic geometry can be used to deduce downstream changes in hydraulics, interchannel
hydraulic geometry can be used to deduce the morphologic and hydraulic consequences of channel division
within a reach. This facility is relevant to evaluating a recent general argument made by Nanson and Huang
(1999) from work in northern and central Australia that, in cases where river behaviour is constrained by very
low slopes, channel splitting may be a river response that leads to greater hydraulic and bedload-transport
efficiency.
In summary, the threefold purpose of this paper is:
1. to introduce the concept of interchannel hydraulic geometry of multiple-channelled rivers;
2. to describe the interchannel hydraulic geometry of the anastomosing reach of upper Columbia River in British
Columbia; and
3. to use the interchannel hydraulic geometry of upper Columbia River to provide a particular test of the general
hypothesis that anastomosis leads to more efficient hydraulic conductivity (to lower flow resistance).
PHYSICAL SETTING
Upper Columbia River is located in southeastern British Columbia within the Rocky Mountain Trench, an
intermontane valley flanked by the Rocky Mountains to the northeast and the Purcell Mountains to the southwest
(Figure 1). Its source is at Columbia Lake, near Canal Flats, BC, from which the river flows in a northwesterly
direction through the Trench for approximately 320 km before turning south towards the Canada–USA border.
Although there are numerous dams along the river, upper Columbia River retains much of its natural character
and provides an ideal ‘natural laboratory’ that serves to address the objectives of this study.
The 120 km anastomosing reach, situated between Radium Hot Springs and Golden, BC, is arguably the type
example of river anastomosis in North America. The geomorphology of the anastomosing Columbia River has
been the subject of numerous studies over the last few decades (see Smith, 1983; Galay et al., 1984; Makaske,
1998, 2001; Makaske et al., 2002). The most morphologically and sedimentologically significant portion of the
reach, according to Smith (1983), is a 55 km section between the communities of Spillimacheen and Nicholson
(Figure 1). The valley gradient is very low, estimated to be 9·6 cm km−1 by Smith (1983) and 11·5 cm km−1 by
Makaske (1998); mean elevation of the reach is 790 m a.s.l. The river changes to a wandering gravel-bed stream
pattern downstream from Golden.
The two major tributaries of upper Columbia River are Bugaboo Creek and Spillimacheen River (Figure 1),
which drain the Purcell Mountains and supply sediment to the valley. Rocks forming these mountains consist
of shales, sandstones, conglomerates and slates of Proterozoic age. Locally, the Purcell Mountains rise above
3000 m a.s.l. and are capped by glaciers. The Beaverfoot and Brisco Ranges of the Rocky Mountains provide
relatively little water and sediment to the valley. These glacier-free ranges rise to about 2700 m a.s.l. and consist
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
840
K. K. TABATA AND E. J. HICKIN
Figure 2. Upper Columbia River anastomosing reach downstream of Spillimacheen confluence. Aerial photos were taken during falling
stage (14 September 1999)
largely of calcareous shales and slates, limestones and dolomites of Palaeozoic age (Geological Survey of
Canada, 1972, 1979a,b, 1980).
The valley fill consists mostly of silts, sands and gravels, which were deposited during the complex geomorphic
history of the area. At the end of the last glaciation, ice dams remained at Canal Flats and to the north near
Donald, creating glacial Lake Invermere (Sawicki and Smith, 1992). Meltwater streams from remaining ice at
higher elevations on both sides of the valley transported large volumes of sediment, depositing silt into the lake
as well as forming gravel deltas. Galay et al. (1984) speculate that the ice dam failed first at Canal Flats causing
the lake to drain. A channel consequently incised through the lacustrine silts and deltaic gravels forming terraces
along the valley margins. Subsequently, the tributaries, which initially incised into the deltaic and lacustrine
deposits, formed alluvial fans and partially blocked the southeasterly flow. Eventually, the ice dam near Donald
retreated and flow reversed to its present northwesterly direction. At the same time, the Kicking Horse River
and Canyon Creek alluvial fans, upon which Golden and Nicholson are located, prograded into the valley and
aggraded to partially block flow. The resulting backwater effect caused sedimentation on the upvalley side of
the fans and a subsequent decline in the valley gradient (Smith, 1983). Other minor alluvial fans along the
Trench also blocked flow, creating low-gradient floodplains and anastomosing reaches between fans in a steplike fashion along the river profile (Smith and Putnam, 1980; Galay et al., 1984).
The anastomosing reach exhibits a pattern of interconnected sandbed channels within a 2 km wide valley
(Figure 2). This planform is maintained throughout the length of the reach except where large alluvial fans
encroach into the valley; for example, at Spillimacheen and Nicholson where Spillimacheen River and Canyon
Creek respectively enter the valley. Individual channels are generally narrow and deep, and possess steep-sided
banks, although progressively larger channels carrying greater flows tend to be significantly wider and only
slightly deeper. The characteristic cross-sectional shape is largely a function of the cohesive nature of the bank
material in combination with low stream power relative to bank strength. Stable channel banks allow dense
vegetation to become established, further reinforcing banks and effectively limiting lateral migration of the
channels (Smith, 1976).
Upper Columbia River experiences flooding during the summer months due to the highly seasonal snowmelt
regime and abundant summer precipitation, combined with the inability of channels to fully accommodate high
flows. Locking (1983) estimates that the anastomosing reach is flooded 45 days per year on average, and has
a flood frequency of every 1·01 years. Because of low channel slopes and thus low stream powers, a portion
of total bedload is deposited within the channels (Smith and Putnam, 1980; Locking, 1983; Makaske, 2001),
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
INTERCHANNEL HYDRAULIC GEOMETRY
841
Figure 3. Wetland environment showing a partially flooded marsh at centre and a lake in the foreground. River flow in the valley is from
right to left. Photo was taken in late May
reducing their flow capacity and promoting flooding (Knighton and Nanson, 1993; Nanson and Knighton, 1996;
Schumm et al., 1996; Nanson and Huang, 1999). Obstructions such as beaver dams (Gurnell, 1998), log jams
(Smith, 1983; Smith et al. 1989) and ice jams (Smith et al., 1989) may also create favourable conditions for
localized flooding. During overbank flows, suspended load is carried over adjacent wetlands (Figure 3). Much
of the load is deposited next to the channel and contributes to levee development. The remainder is deposited
on wetlands in such a manner that the volume of material declines with distance from the channel, producing
the characteristic concave-up cross-sectional wetland profile (Asselman and Middelkoop, 1995; Mackey and
Bridge, 1995). Consequently, a levee breach, which may begin in beaver drag trails (Smith, 1983), creates a local
gradient advantage so that a portion of channel flow is drawn into the wetland. If the crevasse persists and
enlarges over time, sand progrades into the wetland and is deposited as a splay (Smith and Putnam, 1980; Smith
and Smith, 1980; Smith, 1983). Moreover, if an increasingly greater proportion of channel flow is captured, the
splay becomes incised and a new channel may form, provided that the captured flow is connected to an existing
channel at some downstream point on the wetland (Smith and Putnam, 1980; Nanson and Knighton, 1996;
Nanson and Huang, 1999).
Upper Columbia River valley at Golden has an annual temperature range of 39·3 °C. Temperatures reach a
mean monthly low of −10.1 °C in January and a mean monthly high of 17·2 °C in July (Environment Canada,
1998). Golden also receives an average of 490·7 mm of precipitation annually. Precipitation (mostly snow) peaks
in December and January, but significant amounts are also recorded during the remainder of the year with a
broad secondary peak centred on July. Mean annual precipitation gradually declines in a southeasterly direction
and Invermere receives about 300 mm (Makaske, 1998). In the adjacent mountains, particularly in the Purcell
Mountains, precipitation is markedly greater and provides most of the flow to upper Columbia River.
The drainage area above Nicholson gauging station is approximately 6660 km2 with most of the area located
in the Purcell Mountains (Figure 1). Because of greater snow accumulation at higher elevations, the flow regime
is dominated by snowmelt, which is enhanced by rain-on-snow events. Thus, discharge increases during the
spring months and reaches a maximum monthly mean of 322 m3 s−1 in June. A minimum monthly mean discharge of 24 m3 s−1 occurs in February, during which time ice covers much of the river. Mean annual discharge
is 108 m3 s−1 (Environment Canada, 2000). Figure 4 shows historic mean monthly discharges at Nicholson
gauging station (Environment Canada, 2000) and mean monthly discharges for 2000 (Environment Canada,
2001).
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
842
K. K. TABATA AND E. J. HICKIN
Figure 4. Mean monthly discharges for period 1902–1999 (Environment Canada, 2000) and for 2000 (Environment Canada, 2001) at
Nicholson gauging station (BC 08NA002)
METHODS
Field data consist mainly of measurements of cross-sectional form, water-surface width, flow depth and flow
velocity at a range of discharges during the summer of 2000 between June and August, a period during which
there is normally a considerable discharge range. At Nicholson gauging station (BC 08NA002), discharge
peaked at 351 m3 s−1 on 7 July (Environment Canada, 2001) and then rapidly declined. This time period enabled
measurements up to bankfull discharge on both the rising and falling stages so that measurements at discharges
missed during the rising stage could be obtained during the falling stage. Measurements during low-flow conditions were not obtained.
Data were collected at 16 stations in a 10 km reach of anastomosing channels between the communities of
Spillimacheen and Harrogate (Figure 5). Station selection was based on several criteria:
1. boat accessibility: many channels, particularly smaller ones, are either blocked at the entrance by log jams
making channel access difficult, or are unnavigable due to in-channel debris;
2. range of channel sizes: channels of various size, based on width, were required for sampling in order to derive
the interchannel hydraulic geometry;
3. fully equilibrated channel sections: only stable channel sections were considered; for example, channel
sections near a bifurcating junction were excluded;
4. straight or very low-sinuosity channel sections;
5. absence of flow irregularities at or near measurement stations: in smaller channels, subaerial beaver dams,
for example, reduce their cross-sectional areas and cause local increases in flow velocity.
A transect was established normal to flow direction at each measurement station. Six to ten verticals were used
along each transect, depending mainly on channel width. Point velocities were measured at each vertical with
a Price type AA current meter suspended from a 2·5 m inflatable boat. The first velocity measurement was made
at 0·15 m above the channel bed, which was as close to the boundary as the equipment would allow. Additional
point velocities were obtained at 0·31, 0·46, 0·76. 1·07, 1·53, 1·98, and 2·44 m above the bed so that increments
increase with height. Each point velocity was measured over 60 s. Flow depth was measured at each vertical and
water-surface width was measured with either a graduated survey line or a digital range finder.
The velocity–area method (Corbett, 1943) was employed to determine the discharge for each set of measurements. The mean velocity at each vertical was calculated by averaging the values obtained at 0·2 m intervals
above the channel bed. The values used for averaging were calculated with the equations derived by fitting a
polynomial curve through plots of velocity against height above bed. Because of some deviation of point
velocity measurements from the logarithmic profile, particularly near the water surface, this is a more accurate
method than calculating mean velocity using the point velocity measurement at 0·6d, or the average of the
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
INTERCHANNEL HYDRAULIC GEOMETRY
843
Figure 5. Study reach and measurement station locations
measurements at 0·2d and 0·8d. Mean flow-depth was calculated by spatially integrating the depth measurements
at each vertical over the cross-section.
Because the channel system at bankfull stage is ‘leaky’, with flow exchanges through bank crevasses between
the channel and flood basins on the floodplain surface, strict discharge continuity between adjacent measurement
stations on the channels is not met in all cases.
To estimate mean flow resistance, the law of the wall was first used to determine boundary shear stress at each
vertical across the channel. Spatially integrating point boundary shear stress values over the cross-section
produced the mean boundary shear stress for the station. Mean flow resistance was then calculated as the Darcy–
Weisbach resistance coefficient:
ff =
8τ 0
ρv 2
(1)
8gRs
v2
(2)
Equation 1 can be rewritten as:
ff =
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
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K. K. TABATA AND E. J. HICKIN
since:
τ 0 = ρgRs
The variables ρ, g, R and s are respectively water density (kg m−3), acceleration due to gravity (m s−2), hydraulic
radius (m) and slope. Equation 2 provides an alternative way to calculate mean flow resistance, but it may also
produce less reliable results in this study because channel slope, which approximates the slope of the energy
grade line, is assumed to be equal to the valley slope of 0·0001 and constant over the discharge cycle. This
expediency is necessary because it is not possible to measure directly the very low channel slopes to any
acceptable degree of accuracy. Regardless, the two methods of calculating flow resistance provide two independent results for comparison. Hereafter, flow resistance calculations using Equation 1 are referred to as the ‘law
of the wall’ method, and those using valley slope in Equation 2 are referred to as the ‘constant slope’ method.
At-a-station hydraulic geometry relationships were determined by plotting width, depth, velocity and flow
resistance respectively against discharge on log–log graphs and fitting least-squares regression lines through the
plots. To derive interchannel hydraulic geometry relationships, bankfull values of width, depth, velocity and flow
resistance were calculated for each station. This required specifying the bankfull discharge for each station.
Bankfull stage was taken as the height at which a break in bank slope occurred near the top of the bank,
corresponding to the minimum width/depth ratio (Wolman, 1955). When the bankfull heights of opposite banks
differed, the lower of the two was selected as the bankfull stage for that station. By plotting discharge against
stage, it was possible to estimate bankfull discharge for the specified bankfull stage. For all 16 stations, nearbankfull flow measurements were obtained in the field so that extrapolation of stage relations was actually
minimal. Width, depth, velocity and flow resistance were then calculated by entering the bankfull discharge
value into the regression equations from the respective at-a-station relationships. Anti-log bias correction (Sprugel,
1983; Miller, 1984; Ferguson, 1986) was applied to the final values so that true values were not underestimated.
Once bankfull values were determined for each channel, they were plotted as power functions of bankfull
discharge. Finally, linear regression was used to derive quantitative descriptions of the interchannel hydraulic
geometry relationships.
STATION AND CHANNEL DESCRIPTIONS
In general, all stations possess trapezoidal cross-sections, although some approach a rectangular shape. Width/
depth ratio (the form ratio) therefore is a suitable measure of cross-sectional shape. Bankfull width and depth
measurements and form ratios are listed in Table I together with brief descriptions of the channels at their
respective stations. Clearly, narrow channels tend to have low form ratios and small cross-sectional areas while
wider channels have higher form ratios and larger cross-sections.
Table I shows that all channels are generally straight (linear bank alignment) at their respective stations.
Moreover, channel banks are characteristically colonized by dense vegetation, although some variability exists
among stations. For example, Station 3, in addition to having densely vegetated banks, has small trees growing
on the channel bed near both banks, and Stations 1, 12 and 15 have trees leaning into the channel as a result
of bank failure. Stations 7 and 15 have only one bank with dense vegetation while the other is lined mainly with
grass, and Stations 4 and 6 have a sub-bankfull bench with grass growth. Overhanging vegetation is present at
all stations except 4, 12 and 15. These overhangs become significant contributors to flow resistance when stage
approaches bankfull conditions.
RESULTS: INTERCHANNEL HYDRAULIC GEOMETRY
Width, depth and velocity
In order to describe the interchannel hydraulic geometry relationships, bankfull values of width, depth and
velocity were plotted as power functions of bankfull discharge. Bankfull values of the dependent variables are
shown in Table II together with bankfull values of the form ratio.
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
INTERCHANNEL HYDRAULIC GEOMETRY
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Table I. Cross-sectional shape of channels at each station, expressed as width/depth ratio, and general channel descriptions
Station
Bankfull
width (m)
Bankfull w/d ratio
depth (m)
1
52·48
2·67
19·6
2
46·06
2·25
20·5
3
29·80
2·24
13·3
4
24·75
1·11
22·2
5
17·24
1·49
11·6
6
15·07
1·93
7·8
7
131·22
2·16
60·7
8
41·73
2·02
20·7
9
23·89
3·26
7·3
10
14·91
2·39
6·2
11
18·01
2·64
6·8
12
25·73
2·99
8·6
13
13·36
1·87
7·1
14
50·11
2·09
23·9
15
20·76
2·11
9·8
16
23·80
1·51
15·8
Comments
Very slight s-curve planform with station at middle; dense growth on both
banks; slumping trees and overhangs affect surface flow
Slightly sinuous upstream, straight downstream; dense growth with some
overhangs on right bank; less growth on left bank, few overhangs
Slight reverse s-curve planform, straight at station; dense growth and few
overhangs on both banks; small trees on bed near both banks
Straight channel; dense growth on both banks; sub-bankfull bench with
grass growth at right bank
Straight channel; dense growth on both banks with overhangs on both
banks upstream of station
Straight channel; dense growth with few overhangs on left bank;
sub-bankfull bench with grass growth at right bank
Very slight s-curve planform; mostly grass with few trees on right bank;
more tree growth with few overhangs on left bank
Slight s-curve planform; mostly flow from Spillimacheen River; dense
growth and overhangs on both banks
Slight reverse s-curve planform; dense growth with some overhangs on
both banks
Straight channel; dense tree growth on both banks; overhangs and slumping
tree on left bank; few overhangs just upstream on right bank
Straight at station, curves to left 100 m upstream (viewed upstream); dense
growth on both banks with overhangs upstream
Straight at station; dense growth on both banks; some tree growth from
side of right bank; fallen tree 15 m upstream on left bank
Straight channel with sharp bend 50 m downstream; dense growth with
overhangs on both banks; crevasse 20 m upstream on left bank
Straight at station, slight curve to right upstream (viewed upstream); dense
growth on both banks; overhangs on right bank
Slight s-curve; tree growth from right bank side 5 m upstream; mostly grass
growth on left bank; crevasse 30 m upstream from right bank
Slight channel curvature with right bank on inside of curve; dense growth
on both banks; overhang 20 m upstream from left bank
Despite some scatter, the interchannel hydraulic geometry relationships in Figure 6 conform to power function
relationships between width, depth and velocity respectively and bankfull discharge. Among the three variables,
bankfull width exhibits the greatest rate of change (b = 0·64), while the rates of change of depth ( f = 0·19) and
velocity (m = 0·17) are considerably less. In other words, if a comparison is made between two typical anastomosing
channels with different bankfull discharges, the greatest difference would be in bankfull width, while differences
in bankfull depth and velocity would be relatively small. As with at-a-station and downstream hydraulic geometry, both the product of the coefficients and the sum of the exponents equal unity.
Because of its similarity to downstream hydraulic geometry, it is useful to compare the interchannel relationships with those typically found in downstream studies. A fundamentally distinctive characteristic of anastomosing
channels, which contrasts with changes downstream in a single channel, is that neither water-surface slope nor
boundary materials vary in any significant way with changes in bankfull discharge. The similarity in bank
materials from one sandbed anastomosing channel to another in the upper Columbia River means that changes
in bank height and flow depth are quite conservative ( f = 0·19) and much lower than those for the typical
downstream case ( f ≈ 0·4).
The mean velocity exponent for the anastomosing channels (m = 0·17) is not unlike the exponents found in
the corresponding downstream cases (m = 0·0–0·2), but the reasons for the change clearly are not the same.
Copyright © 2003 John Wiley & Sons, Ltd.
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846
K. K. TABATA AND E. J. HICKIN
Table II. Various channel characteristics at bankfull stage
Station
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Qbf (m3 s−1)
wbf (m)
dbf (m)
vbf (m)
ffbf(lw)
ffbf(cs)
(w/d)bf
ω bf (W m−2)
87·79
63·48
43·93
10·81
10·73
12·78
200·56
42·51
34·56
15·77
15·92
44·68
11·10
46·14
16·67
15·65
52·20
46·16
29·75
24·53
16·96
14·88
131·31
41·72
23·25
14·77
17·53
25·51
13·15
49·43
20·52
23·76
2·55
2·30
2·19
0·94
1·33
1·89
2·20
2·01
3·03
2·29
2·48
2·85
1·73
1·72
1·69
1·49
0·66
0·56
0·68
0·47
0·48
0·46
0·69
0·51
0·49
0·47
0·37
0·62
0·49
0·54
0·48
0·44
0·046
0·044
0·075
0·053
0·059
0·065
0·040
0·048
0·066
0·072
0·056
0·059
0·053
0·066
0·062
0·051
0·045
0·050
0·037
0·034
0·045
0·069
0·036
0·059
0·096
0·078
0·139
0·057
0·055
0·046
0·056
0·058
20·5
20·1
13·6
26·0
12·8
7·9
59·6
20·8
7·7
6·5
7·1
9·0
7·6
28·7
12·1
16·0
1·68
1·19
2·96
0·67
0·81
0·80
1·67
0·82
1·01
0·97
0·36
1·76
0·80
1·32
0·88
0·57
Qbf = bankfull discharge; wbf = bankfull water-surface width; dbf = bankfull mean flow depth; vbf = bankfull mean flow velocity; ffb(lw) = bankfull
flow resistance (law of the wall method); ffbf(cs) = bankfull flow resistance (constant slope method); (w/d)bf = bankfull width/depth ratio;
ω bf = bankfull specific stream power
Figure 6. Interchannel hydraulic geometry relationships of bankfull width (A), bankfull depth (B) and bankfull velocity (C) to bankfull
discharge
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
INTERCHANNEL HYDRAULIC GEOMETRY
847
Among the anastomosing channels, velocity increases in response to increasing flow depth at a constant watersurface slope, and in the downstream case, the velocity exponent reflects mainly the competing effects of
declining slope and the declining grain size (roughness) of channel boundary materials.
Changes in flow depth and velocity exhibited by the anastomosing channels are conservative with only about
one-third of the increase in discharge in the range 10–200 m3 s−1 being accommodated by combined adjustments
in these variables. The width of the anastomosing bankfull channels accommodates most (two-thirds) of the
change in this discharge range; b = 0·64 is a significantly higher exponent than the b ≈ 0·5 typical of downstream
hydraulic geometry.
Unlike downstream changes in width, depth and velocity, interchannel changes are independent of changes
in drainage area. Rather, the reach comprises a number of channels that carry a proportion of total discharge
and each channel independently adjusts to its imposed discharge. The manner in which total discharge is
apportioned to each channel is seemingly stochastic so that the possible range of channel sizes varies from small
to large in any particular anastomosing system. If total discharge is divided equally among a number of channels,
the bankfull discharge for each component channel would be identical and therefore interchannel relationships
become difficult to define. The upper Columbia River anastomosing reach, however, comprises channels with
a range of bankfull discharges and power laws adequately describe the interchannel relationships.
Flow resistance
Table I indicates that the two versions of the Darcy–Weisbach resistance coefficient [ ffbf(lw) (based on Equation 1 and the ‘law of the wall’) and ffbf(cs) (based on Equation 2 and an assumed water-surface slope = a constant (0·0001) valley floor slope) ] yield generally consistent results. For the 16 stations, the ratio ffbf(lw)/ffbf(cs) has
the following statistical properties: median = 0·993, mean = 1·069, standard deviation = 0·377 and standard error = 0·094.
Because the log-linear velocity gradients are well defined and averaged, there is greater stability and less
uncertainty associated with the bankfull values of ffbf(lw) than there is with the bankfull values of ffbf(cs). Velocity
gradients at each station are based on an average of four velocity measurements in each of six to ten verticals.
Semi-logarithmic regressions for velocity and height above the bed for each cross-section average R2 = 0·96
(0·85–0·99).
The bankfull flow resistance–discharge relationship is shown in Figure 7. Regardless of the basis for computing flow resistance, the Darcy–Weisbach coefficient tends to decline as discharge increases. The related
changes in the shape of the channel cross-section probably explain this tendency; the relation of flow resistance
at bankfull stage to the channel form ratio is shown in Figure 8. These pronounced inverse relationships (based
on the law of the wall and the constant slope methods) are consistent with the field observations that small,
relatively narrow anastomosing channels with lower form ratios are more influenced by bank roughness (bank
irregularities and vegetation) than their larger counterparts.
Interpreting these inverse relationships, however, warrants caution because they obviously are characterized
by considerable scatter in the data. For example, it was observed in the field that some smaller channels are more
influenced by backwater effects above channel confluences than larger channels. These backwater effects probably explain the increase in the variability of ff with declining bankfull discharge evident in Figure 7.
Bedforms appear to be present in most Columbia River channels and must influence the pattern of flow
resistance shown in Figure 7. Dunes increase in size as channels become larger and reach their maximum size
where the river is most confined to a single channel (Station 7). In consequence, form roughness increases with
bankfull discharge. Bedform effects do not appear to dominate the flow resistance regime, however, and the
inverse relationships in Figure 7 are consistent with the conventional view that boundary roughness is drowned
out as discharge and cross-sectional area of channels increase.
DISCUSSION: CONDUCTIVITY OF ANASTOMOSING CHANNELS
Developing the fundamental notion of river channel equilibrium that ‘the average river channel system tends to
develop in a way to produce an approximate equilibrium between the channel and the water and sediment it must
transport’ (Leopold and Maddock, 1953, p. 1), Nanson and Knighton (1996) and Nanson and Huang (1999)
Copyright © 2003 John Wiley & Sons, Ltd.
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848
K. K. TABATA AND E. J. HICKIN
Figure 7. Interchannel relationship between bankfull flow resistance and bankfull discharge. Flow resistance values are calculated using (A)
the law of the wall method and (B) the constant slope method
Figure 8. Interchannel relationship between bankfull flow resistance and bankfull width/depth ratio. Flow resistance values are calculated
using (A) the law of the wall method and (B) the constant slope method
argue that anabranching rivers (including anastomosing rivers) form and persist over time in order to maintain
or enhance water- and sediment-transport efficiency. They argue that a river can increase stream power and
therefore water- and sediment-transport efficiency by increasing its slope (Nanson and Knighton, 1996; Nanson
and Huang, 1999). In most environments, this increase in efficiency can be accomplished by reducing channel
Copyright © 2003 John Wiley & Sons, Ltd.
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849
INTERCHANNEL HYDRAULIC GEOMETRY
Table III. Bankfull width, depth, cross-sectional area, velocity and flow resistance values for channels of various size (Qbf).
Values are calculated using the regression equations describing the interchannel relationships.
Qbf (m3 s−1)
wbf (m)
dbf (m)
Abf (m2)
vbf (m s−1)
ffbf(lw)
ffbf(cs)
100
90
80
70
60
64·39
2·58
166·1
0·65
0·050
0·047
60·18
2·53
152·3
0·63
0·051
0·048
55·80
2·48
138·4
0·62
0·052
0·049
51·21
2·41
123·4
0·61
0·052
0·050
46·39
2·34
108·6
0·59
0·053
0·051
50
41·26
2·26
93·2
0·58
0·054
0·052
40
30
20
10
35·76
2·17
77·6
0·55
0·055
0·054
29·73
2·06
61·2
0·53
0·057
0·056
22·92
1·90
43·5
0·49
0·059
0·059
14·69
1·67
24·5
0·44
0·064
0·065
wbf = 3·24Qbf0·64; dbf = 1·04Qbf0·19; Abf = wbf × dbf ; vbf = 0·30Qbf0·17; ffb(lw) = 0·07Qbf−0·06; ffbf (cs) = 0·09Qbf−0·13
sinuosity, but when valley slope is low, a river has little opportunity to increase its slope. Nanson and Knighton
(1996) and Nanson and Huang (1999) argue that a single-channelled river may be able to achieve the same
outcome by anabranching. In doing so, they argue, water and sediment are conveyed in multiple channels that
are collectively at least as efficient as a single channel. To test this idea, Nanson and Huang (1999) developed
a model based on anabranching rivers of northern and central Australia and they found that divided channels
have a lower total width, greater depths and thus a lower total cross-sectional area and higher mean velocities.
Furthermore, they assert that this condition maximizes sediment transport capacity, and specifically bedload
transport, since it is directly related to velocity.
We do not challenge the findings of Nanson and Huang (1999) for the specific Australian cases they examined, but on the basis of our observations of upper Columbia River behaviour, we do question the generalization
that, in slope-constrained environments, river channels develop anabranching channel patterns in order to achieve
hydraulic efficiencies. The interchannel hydraulic geometry of the anastomosing Columbia River presented in
the previous section does not support this generalization.
Table III presents modelling data, based on the interchannel hydraulic geometry relationships for upper
Columbia River, which illustrate the consequences of several combinations of channel splitting. For example,
a single channel with a bankfull discharge of 100 m3 s−1 has a width of 64·39 m, a depth of 2·58 m, and a velocity
of 0·65 m s−1. If this channel divides into two equal channels with bankfull discharges of 50 m3 s−1 each, the
aggregate channel width becomes 82·52 m, and the channel depth and velocity in each channel becomes 2·26 m
and 0·58 m s−1 respectively. Clearly, the aggregate width becomes greater and both depth and velocity decline
in each divided channel, indicating that the system becomes hydraulically less efficient. Put another way, this
simple channel division into two equal-size secondary channels requires a 12 per cent increase in aggregate
cross-sectional area of the channel in order to maintain the discharge. These changes are accompanied by
increases in flow resistance in both divided channels. The same pattern emerges when other combinations of
bankfull discharge are used. For example, if a channel with 100 m3 s−1 discharge divides into three channels
with discharges of 60, 30 and 10 m3 s−1 (Table III), an even greater increase in aggregate cross-sectional area
(17·5 per cent) is required to maintain the flow at 100 m3 s−1. Because of the nature of the governing equations
of interchannel hydraulic geometry, upper Columbia River becomes hydraulically less efficient as a single
channel divides into a progressively larger number of subchannels.
Unfortunately there are not sufficient bedload transport measurements at bankfull flow available for upper
Columbia River secondary channels to unequivocally specify the accompanying changes in bedload-transport
capacity. Nevertheless, any changes in bedload-transport efficiency are likely to be quite small because the
modest increase in aggregate bed width through channel splitting is accompanied by significant reductions in
flow depth, velocity, and specific stream power (Table III). Consequently, modelling of bedload transport
through the channel system using the Meyer-Peter and Muller, Engelund and Hansen, and Shields bedload
formulae, for example, implies that there is no significant change in the total bedload-transport capacity accompanying anastomosis (Tabata, 2002).
Copyright © 2003 John Wiley & Sons, Ltd.
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K. K. TABATA AND E. J. HICKIN
These results in relation to hydraulic and bedload-transport efficiency on Columbia River are contrary to the
findings of Nanson and Huang (1999) based on Australian anabranching rivers. Nanson (personal communication, December 2002) argues that these contrary results are difficult to interpret because, unlike the Australian
anabranching rivers studied, Columbia River is in disequilibrium in the sense that bedload input to the anastomosing
reach exceeds output. It is difficult for us to envision how channel splitting can occur in any river, however,
unless channel capacity is not locally reduced by shoaling and bar formation resulting from such a disequilibrium
state in the sediment flux.
The reason for the usually single-channelled Columbia River developing an anastomosing reach has
been suggested by others (Smith, 1983; Smith and Putnam, 1980, Galay et al., 1984) and it is a view not
contradicted by the results of the present study. Downstream control in the form of large tributary alluvial
fans have reduced the channel slope upstream in the backwater zone so that the capacity of the channel to
transport the sediment being supplied from upstream to it is exceeded. The resulting aggradation locally raises
the channel above the floodplain so that annual floods often spill out of the channel onto the wetlands with
enhanced erosive force, sometimes resulting in permanent channel avulsions. The reduced hydraulic efficiency of these new secondary channels and the oversupply of sediment lead to further cycles of avulsion
until a fully developed anastomosing channel system is in place. Secondary channels remain in place on
the floodplain until isolated by further avulsions because the very low water-surface slope and the strong
cohesive channel banks prevent significant channel migration. Anastomosis is essentially caused by the imbalance between sediment supply and sediment transport capacity that leads to superelevation of the channel, and
to the avulsive behaviour of the aggrading channel. The decline in hydraulic efficiency caused by channel
splitting is simply a passive accompaniment to anastomosis and cannot be construed as the cause of river
adjustment.
The defining system of interconnected channels in anabranching rivers does suggest some general underlying
cause. It is prudent to recognize, however, that the pronounced planform differences between the anastomosing
Columbia River in British Columbia and the anabranching rivers in northern and central Australia (for examples,
see Nanson et al., 1986; Rust and Nanson, 1986; Tooth, 1997; Wende and Nanson, 1998) speak to strong sitespecific elements in the formative processes.
CONCLUSIONS
A new type of hydraulic geometry is introduced to describe the morphodynamics of multiple-channelled rivers.
Interchannel hydraulic geometry describes the changes in hydraulic variables as channels at bankfull discharge
become progressively larger in an anastomosing reach of a river. For the upper Columbia River anastomosing
reach, the interchannel hydraulic geometry, like conventional downstream hydraulic geometry, in general is
adequately described by power functions. The highest rate of change in channel geometry, expressed in the
conventional power-function relationships, is found in width (b = 0·64), followed by depth ( f = 0·19) and velocity (m = 0·17). That is, the range of channel widths among channels in the upper Columbia River anastomosing
reach is much greater than those for mean depth and mean flow velocity.
Interchannel flow resistance–discharge relationships display a tendency for flow resistance to decline with
progressively larger bankfull channels. This inverse trend is consistent with physical reasoning that suggests
larger channels can be expected to be more hydraulically efficient because of the reduced relative contribution
of bed and bank roughness to flow resistance.
The idea proposed by Nanson and Knighton (1996) and Nanson and Huang (1999), that anabranching is a
way to maintain or enhance water and sediment transport efficiency in an environment where slope adjustments are not possible, does not appear to apply to the upper Columbia River anastomosing reach. Compared to a single channel, water conveyance is less efficient in the anastomosing reach. Bedload transport
also is probably less efficient. On Columbia River, the cause of anastomosis more likely relates to local
oversupply of sediment, channel aggradation, and consequent enhancement of channel avulsion behaviour.
Any change in hydraulic efficiency of anastomosing channels on Columbia River appears to be independent
of the channel splitting process; change in channel conductivity is a result of anastomosis, not the cause of
it.
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
INTERCHANNEL HYDRAULIC GEOMETRY
851
Clearly, there is a need for additional studies of anastomosing stream morphology in order to establish the
range of interchannel hydraulic geometry exhibited by this pattern of river and to inform any further discussion
of the general cause of river anastomosis.
ACKNOWLEDGEMENTS
We acknowledge an intellectual debt to Derald Smith and Gerald Nanson whose ideas have led to the present
work. We thank Gerald Nanson and Rob Ferguson for their helpful reviews of the original manuscript and He
Qing Huang, Gerald Nanson and John Jansen for their insights and forbearance in discussions to reconcile the
disparate results of the studies discussed in this paper. In addition, we thank Sarah Baines, Sean Todd and Chris
Braybrook for their invaluable assistance in the field. This research forms part of a study of the morphodynamics
of rivers in British Columbia funded by the Natural Sciences and Engineering Research Council of Canada
(NSERC).
REFERENCES
Asselman NEM, Middelkoop H. 1995. Floodplain sedimentation; quantities, patterns and processes. Earth Surface Processes and Landforms
20(6): 481–499.
Corbett DM. 1943. Stream-gaging procedure: a manual describing methods and practices of the Geological Survey. United States Geological Survey Water-Supply Paper 888.
Environment Canada. 1998. Canadian Climate Normals: Golden Airport, British Columbia. http://www.msc-smc.ec.gc.ca/climate/climate/
climate_normals_e_cfm?station_id=99&prov=BC [5 October 2001]
Environment Canada. 2000. HYDAT CD-ROM (version 99–2·00).
Environment Canada. 2001. Daily mean discharge data for 2000. Water Survey of Canada hydrometric station 08NA002.
Ferguson RI. 1986. River loads underestimated by rating curves. Water Resources Research 22(1): 74–76.
Galay VJ, Tutt DB, Kellerhals R. 1984. The meandering distributary channels of the upper Columbia River. In River Meandering:Proceedings
of the Conference Rivers 1983, New Orleans, Louisiana, October 24–26, 1983, Elliott CM (ed.). American Society of Civil Engineers:
New York; 113–125.
Geological Survey of Canada. 1972. Map 1326A; Geology; Lardeau (East Half ), British Columbia; Scale 1:250,000. Geological Survey
of Canada: Ottawa.
Geological Survey of Canada. 1979a. Map 1501A; Geology; McMurdo (East Half ), British Columbia; Scale 1:50,000. Geological Survey
of Canada: Ottawa.
Geological Survey of Canada. 1979b. Map 1502A; Geology; McMurdo (West Half ), British Columbia; Scale 1:50,000. Geological Survey
of Canada: Ottawa.
Geological Survey of Canada. 1980. Diagrammatic Structure Sections A-A′, B-B′, C-C′, D-D′, E-E′, 4 and 5 to accompany Map 1501A,
McMurdo (East Half ) and Map 1502A, McMurdo (West Half ); Scale 1:50,000. Geological Survey of Canada: Ottawa.
Gurnell AM. 1998. The hydrogeomorphological effects of beaver dam-building activity. Progress in Physical Geography 22(2): 167–189.
Knighton AD, Nanson GC. 1993. Anastomosis and the continuum of channel pattern. Earth Surface Processes and Landforms 18: 613–625.
Knighton, D. 1998. Fluvial Forms and Processes: A New Perspective. Arnold: London.
Lacey, G. 1930. Stable channels in alluvium. Proceedings of the Institute of Civil Engineers 229(1): 259–384.
Leopold LB, Maddock Jr. T. 1953. The hydraulic geometry of stream channels and some physiographic implications. United States
Geological Survey Professional Paper 252.
Locking T. 1983. Hydrology and Sediment Transport in an Anastomosing Reach of the Upper Columbia River, B.C. Masters Thesis,
University of Calgary, Calgary.
Mackey SD, Bridge JS. 1995. Three-dimensional model of alluvial stratigraphy; theory and applications. Journal of Sedimentary Research
65(1): 7–31.
Makaske B. 1998. Anastomosing Rivers: Forms, Processes and Sediments. Faculteit Ruimtelijke Wetenschappen, Universiteit Utrecht: Utrecht.
Makaske B. 2001. Anastomosing rivers: a review of their classification, origin and sedimentary products. Earth-Science Reviews 53: 149–196.
Makaske B, Smith DG, Berendsen HJA. 2002. Avulsions, channel formation and floodplain sedimentation rates of the anastomosing upper
Columbia River, British Columbia, Canada. Sedimentology 49: 1049–1071.
Miller DM. 1984. Reducing transformation bias in curve fitting. The American Statistician 38(2): 124–126.
Nanson GC, Huang HQ. 1999. Anabranching rivers: divided efficiency leading to fluvial diversity. In Varieties of Fluvial Form, Miller AJ,
Gupta A (eds). John Wiley and Sons: New York; 477–494.
Nanson GC, Knighton AD. 1996. Anabranching rivers: their cause, character and classification. Earth Surface Processes and Landforms 21:
217–239.
Nanson GC, Rust BR, Taylor G. 1986. Coexistent mud braids and anastomosing channels in an arid-zone river: Cooper Creek, central
Australia. Geology 14: 175–178.
Richards, KS. 1977. Channel and flow geometry: a geomorphological perspective. Progress in Physical Geography 2: 87–95.
Rust BR, Nanson GC. 1986. Contemporary and palaeochannel patterns and the Late Quaternary stratigraphy of Cooper Creek, southwest
Queensland, Australia. Earth Surface Processes and Landforms 11: 581–590.
Sawicki O, Smith DG. 1992. Glacial Lake Invermere, upper Columbia River valley, British Columbia: a paleogeographical reconstruction.
Canadian Journal of Earth Sciences 29: 687–692.
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)
852
K. K. TABATA AND E. J. HICKIN
Schumm SA, Erskine WD, Tilleard, JW. 1996. Morphology, hydrology, and evolution of the anastomosing Ovens and Kings Rivers,
Victoria, Australia. Geological Society of America Bulletin 108(10): 1212–1224.
Smith DG. 1976. Effect of vegetation on lateral migration of anastomosed channels of a glacial meltwater river. Geological Society of
America Bulletin 87: 857–860.
Smith DG. 1983. Anastomosed fluvial deposits: modern examples from Western Canada. In Modern and Ancient Fluvial Systems, Collinson
JD, Lewin J (eds). Special Publication No. 6 International Association of Sedimentologists. Blackwell Scientific Publications: Oxford;
155–168.
Smith DG, Putnam PE. 1980. Anastomosed river deposits: modern and ancient examples in Alberta, Canada. Canadian Journal of Earth
Sciences 17: 1396–1406.
Smith DG, Smith ND. 1980. Sedimentation in anastomosed river systems: examples from alluvial valleys near Banff, Alberta. Journal of
Sedimentary Petrology 50(1): 157–164.
Smith ND, Cross TA, Dufficy JP, Clough SR. 1989. Anatomy of an avulsion. Sedimentology 36: 1–23.
Sprugel DG. 1983. Correcting for bias in log-transformed allometric equations. Ecology 64(1): 209–210.
Tabata KK. 2002. Character and conductivity of anastomosing channels, upper Columbia River, British Columbia, Canada. MSc thesis,
Simon Fraser University, Burnaby, Canada.
Tooth S. 1997. The morphology, dynamics and late Quaternary sedimentary history of ephemeral drainage systems on the Northern Plains
of central Australia. PhD thesis, University of Wollongong, Australia.
Wende R, Nanson GC. 1998. Anabranching rivers: ridge-forming alluvial channels in tropical northern Australia. Geomorphology 22: 205–
224.
Wolman MR. 1955. The natural channel of Brandywine Creek, Pennsylvania. United States Geological Survey Professional Paper 271.
Copyright © 2003 John Wiley & Sons, Ltd.
Earth Surf. Process. Landforms 28, 837–852 (2003)