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Author's personal copy
Geomorphology 116 (2010) 37–47
Contents lists available at ScienceDirect
Geomorphology
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / g e o m o r p h
Planform geometry and channel migration of confined meandering rivers on the
Canadian prairies
Tami J. Nicoll ⁎, Edward J. Hickin
Department of Geography, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6
a r t i c l e
i n f o
Article history:
Received 1 June 2009
Received in revised form 7 October 2009
Accepted 8 October 2009
Available online 17 October 2009
Keywords:
Confined meanders
Planform geometry
Channel migration
a b s t r a c t
The planform geometry and migration behaviour of confined meandering rivers at 23 locations in Alberta
and British Columbia are examined. Relationships among planform geometry variables are generally
consistent with those described for freely meandering rivers with small but significant differences because
of the unique meander pattern of confined meanders. These exceptions are the ratio channel wavelength
(l)/channel width (w) and the bend curvature (rm/w); in these confined meanders, the ratios exceed
(l/w ≈ 17; rm/w = 4.1) the free-meander norms (l/w = 8–14; rm/w = 2–3). In general, these migrating
confined meandering rivers do not develop cutoffs, and meander bends appear to migrate downstream
as a coherent waveform. Migration rates vary greatly, from 0.01 to 5.8 m/y, consistent with the general
distribution of published rates for freely meandering rivers. Attempts to seek correlations between
migration rate and channel flow and morphometry data are modestly successful. Stream power offers the
best statistical predictor of migration rate, accounting for up to 52% of variance in migration rate, greater
than that provided by valley slope (34%), bankfull width (32%), and mean annual flood (30%). Overall, the
findings indicate that confined meandering rivers within western Canada may be more usefully regarded as
part of a continuum of a meandering river pattern rather than as a unique river planform.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
Freely meandering rivers have attracted a great deal of attention
from river scientists and engineers over the last century. We now
know a great deal more about meander-planform geometry, bend
flow, bend-migration dynamics, and lateral accretion sedimentology
than we understood early last century (see Ikeda and Parker, 1989;
and the reviews in Leopold et al., 1964; and Knighton, 1998). That
understanding has come to us in part because of carefully designed
but selective laboratory and field studies of meandering so structured
as to avoid the complicating vagaries of nature (the special cases). But
as a result, however, we still know relatively little about one of those
special cases: that of confined meanders.
Confined meanders are those that are unable to fully develop the
planform geometry of free meanders because their lateral migration is
constrained by the walls of the relatively narrow valleys through
which they flow. Meander bends laterally migrate into the valley
walls; and the potentially sinuous channel loops are truncated to form
sharp right-angled bends, producing the distinctively asymmetric
sawtooth array of river bends that are uniquely associated with
meander confinement (Fig. 1).
⁎ Corresponding author. Present address: Northwest Hydraulic Consultants, 30 Gostick
Place, North Vancouver, BC, Canada V7M 3G3. Tel.: +1 604 980 6011; fax: +1 604 980 9264.
E-mail addresses: tnicoll@nhc-van.com (T.J. Nicoll), hickin@sfu.ca (E.J. Hickin).
0169-555X/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.geomorph.2009.10.005
This circumstance may seem like a special case but in some parts of
the world, such as the Canadian prairies, some degree of confinement
is normal for almost all meandering rivers. Here, many of the contemporary rivers occupy the large valleys of former glacial spillways
formed and abandoned by the meltwater from retreating continental
glaciers in the closing phase of the last glacial cycle. Many are classic
examples of manifestly underfit streams (Dury, 1964).
The distinctive planform of confined meanders suggests that the
channel geometry and migration dynamics of these river systems may
be quite different from those associated with freely meandering
channels. The purpose of this paper is to describe the planform geometry and migration behaviour of a set of confined meandering rivers
on the Canadian prairies and to relate the channel-migration rate of
these rivers to basic hydrologic and geomorphic controls. Although
the new data presented here are clearly of scientific interest to those
seeking to understand the dynamics of meander migration, they
are also significant to practical issues such as predicting channelmigration rates for engineering and planning purposes.
1.1. Planform geometry and river migration in freely meandering
rivers
The reference model for assessing the distinctiveness of confined
meander morphology and behaviour is the geomorphology of freely
migrating river meanders. Although the scale of river meandering varies
Author's personal copy
38
T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
Fig. 1. Aerial photographs of the Beaver, Fontas, Red Deer, and Wapiti Rivers showing characteristic planform of confined meanders.
widely, some aspects of channel-bend geometry in freely meandering
rivers are independent of scale (Leopold et al., 1964). Morphometric
relationships in the form of constant scaling ratios involving bend parameters [such as meander wavelength (l), bend radius (rm), and channel
width (w) as well as discharge (Q)] have been known for some time (for
pffiffiffiffi
example, l = w≈8−14w; rm = w≈2−3; l = Q ≈54) (Knighton, 1998), although the underlying causes are still being debated. We do not know
if these planform geometry relations apply also to confined meanders.
Meander migration rate depends on the force ratio: eroding force/
resisting force. Suggested factors for the eroding force (moderated by
channel curvature) include stream power (and therefore discharge and
water-surface slope) and surrogate measures, such as channel width
and drainage area (Hooke, 1980; Lawler, 1993); those for the resisting
force include bend geometry, bank height, calibre of bank sediment, and
bank vegetation (Hickin and Nanson, 1984). Some of these will be
examined here in relation to confined meanders.
Statistically, stream power has been shown to exert a strong influence on migration rate (Lewin, 1983; Hickin and Nanson, 1984;
Nanson and Hickin, 1986; Richard et al., 2005). Channel width has also
been shown to relate strongly to migration rate (Brice, 1982; Hickin and
Nanson, 1984; Nanson and Hickin, 1986; Richard et al., 2005). Using
drainage area as a proxy for river scale, Hooke (1980) and Brice (1984)
found that migration rate tends to increase with the square root of
drainage area. For rivers in western Canada, the calibre of bank sediment
was identified as being important (Nanson and Hickin, 1986). They
argued that migration rate was essentially limited by the rate of entrainment and transport of bed and basal bank material. Other authors
place more importance on cohesiveness of upper bank materials and
vegetation cover (Beeson and Doyle, 1995; Burckhardt and Todd, 1998).
The idea that planform geometry (specifically bend curvature)
controls migration rate was first suggested by Bagnold (1960). He
reasoned that total resistance to flow around a meander bend depends
on bend-flow hydraulics that in turn are conditioned by bend curvature
(rm/w). Nanson and Hickin (1986) found maximum migration rates of
channel bends on meandering rivers in western Canada to be strongly
associated with bends having a bend curvature of 2 b rm/w b 3 with a
decrease in rates on either side of the optimum curvature (Hickin and
Nanson, 1975; Nanson and Hickin, 1986), although they did not
embrace Bagnold's explanation of this effect (Hickin, 1978). Other
authors have confirmed a similar role for bend curvature in controlling
channel migration (Hudson and Kesel, 2000; TRB, 2004; Hooke, 2007).
1.2. Confined meanders
Confined meanders are very common throughout much of southern
Canada. Indeed, they are so pervasive here that the distinctively
truncated and asymmetric planform noted above (Fig. 1) has been
taken as the planform norm for the region (Carson and Lapointe, 1983).
The effect of confinement on meander form has been discussed in the
literature for some time with various authors noting at least one of the
following: flattening of meanders where the channel impinges on valley
walls, acute bends at the point of contact, and a convex downvalley
asymmetry (Schattner, 1962; Yarnykh, 1978; Hooke and Harvey, 1983;
Hickin, 1988). Meander migration dynamics can also be affected by
confinement; downvalley translation without significant deformation
has only been observed within confined meanders whose amplitude is
restricted, as well as in certain bends of low curvature (Hooke, 1977;
Brice, 1982; Ferguson, 1984). Lewin and Brindle (1977) recognized
three degrees of confinement based on decreasing relative valley width.
The first and third degrees of meander confinement are not examined
here because the former involves only spatially intermittent confinement of the river so that surrounding unconfined meanders likely
influence the morphodynamics of the confined bend, while the extreme
confinement displayed in the latter type prevents any development of a
meandering planform. The confined meandering rivers examined here
display second-degree confinement, where every outside bend contacts
the confining medium; the potential amplitude of the meander is greater
than the width of its valley, and alluvial deposits are discontinuous.
Unlike the case of entrenched or incised meanders, however, an alluvial
plain forms the valley bottom allowing the confined stream to migrate.
Those properties intrinsic to confined meanders, such as planform
distortion, are the most pronounced with second-degree confinement.
Although little research exists on migration dynamics of confined
meanders, they have been the focus of research on the development of
concave-bank benches consisting of counterpoint deposits associated
with the sharp meander bends found on second-degree confined
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T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
rivers (Hickin, 1979; Page and Nanson, 1982; Hickin, 1988; Burge and
Smith, 1999). Indirectly, this research has shown that second-degree
confinement develops where the ratio of valley width to channel
width ranges from 3:1 to 10:1 (Hickin, 1986; Burge and Smith, 1999).
Lower ratios will result in first-degree confinement, while higher
ratios allow for some degree of unconfined meandering.
2. Regional setting
Twenty-three study sites are located throughout Alberta and
British Columbia (Fig. 2). With the exception of that on Kootenay
River, all sites are located east of the Rocky Mountains on the
Canadian prairies. The reaches are single thread, confined meandering, gravel- and sand-bed rivers that have available sequential aerial
photography covering a period of at least 30 years. Because only those
reaches where meander bends impinge on both valley walls are
considered, the length of channel examined for each location varies. A
minimum of three consecutive meander bends were examined at
each site, although typically a selection included nine bends and as
many as 25 bends in the case of Beaver River in Alberta. Because the
confined rivers in this study are located in lowland settings, they have
low channel slopes (0.0001–0.003). Sites span a range of channel
scale, with mean annual flood discharge varying over two orders of
magnitude (from 36 to 3870 m3/s).
Hydrologic regime is similar among the sites, generally characterised by snowmelt-related peak flows in late April to mid-June,
followed by a gradual decline in discharge to a minimum during the
winter months. Although it is not the aim of this study to determine
the origin of the confining valleys, most or possibly all are former
glacial–meltwater channels (Kellerhals et al., 1972; Mathews, 1980).
Sediment-size data for the study sites, based on previously published
data (Kellerhals et al., 1972; Nanson and Hickin, 1986; Burge and
Smith, 1999) and our field observations, indicate basal outer-bank,
sediment-size variation from fine sand to large cobbles.
39
3. Field and analytical methods
Measurement of planform geometry and migration rate for the
23 rivers in this study was completed through GIS analysis of historical aerial photography, a technique well established in the literature
(Nanson and Hickin, 1986; Petts, 1989; Gurnell, 1997; Wellmeyer
et al., 2005). Black and white contact prints providing stereo coverage
of all study sites were obtained from the government air photo libraries of Alberta and British Columbia. The number of time periods
examined for each river reach varies according to the availability of
suitable air photos. Those sites with a lengthy photo record have up to
four sets of air photos analysed while the limited photo record for
certain sites resulted in the examination of just two separate years of
photography. The scale of photography used varies between approximately 1:15,000 to 1:40,000.
Air photo prints were scanned at 1200 dpi and georectified using
the georeferencing tools available in ArcGIS 9.1. The ground control
points (GCPs) used for rectification were either collected through GPS
survey in the field or obtained from topographic maps. The most
recent photography for each study site was georeferenced using the
GCPs, and all other photography for the site was then registered to
this base layer and resampled to a 1-m cell size to coincide with the
lowest resolution data (the 1:40,000 scanned photography). Although
an effort was made to use the same set of GCP locations for rectifying
all photo sets for a site, this is not possible for all time intervals
because of landscape changes between photo surveys.
The RMS (root mean square) errors for georectification at all study
sites average 4.9 m and range from 1.1 to 10.9 m. These RMS errors are
comparable with those reported in similar studies elsewhere (Gurnell
et al., 1994; Gilvear et al., 2000; Winterbottom and Gilvear, 2000).
Gurnell et al. (1994) concluded that change in channel boundary
positions N5 m is likely due to genuine geomorphological change, a
guideline also applicable to Winterbottom (2000) and Gilvear et al.
(2000) as well as to this study.
Fig. 2. Study locations within Alberta and British Columbia, Canada.
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T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
Measurements of planform geometry were conducted at a scale
of 1:1000 in GIS using ArcGIS 9.1 software. Channel outlines were
digitized using the water boundary to denote the edge of the channel
because it is clearly defined in the aerial photography. Although several
other studies use the limit of vegetation or change in vegetation type to
denote channel boundaries (Winterbottom, 2000; Richard et al., 2005),
initial overview of the sites indicated that this approach is difficult to
adopt here. The study sites span a large geographical area and therefore
include markedly different ecological zones with varying vegetation
types, preventing the use of the same boundary criteria at all sites. Photo
quality and therefore the ability to delineate exposed bars accurately
also vary between photos. To minimize the effect of varying water stage
between air photo dates, photographs were chosen for each site that
were taken within the same hydrologic phase of the year. Furthermore,
the two digitized channel boundary lines are used in ArcGIS to generate
a channel centreline (the line connecting the locus of points equidistant
from the two channel boundaries) used for subsequent analysis. This
protocol has an averaging effect that minimizes the error associated
with any change in water stage.
Planform geometry variables such as wavelength, bankfull width,
meander–belt width, sinuosity, and radius of curvature were measured
on the most recent set of aerial photos for each site. Bankfull width is
measured at meander inflection points and taken to be the distance
across the channel between vegetation boundaries. The arithmetic
averages of several measurements are used for analysis. To calculate
meander wavelength, a line defining the valley axis is split at each
crossing of the channel centreline. The length for each line segment is
multiplied by 2, and the average of these calculations is taken to be the
meander wavelength for that study reach. Sinuosity is calculated in
much the same way with the channel centreline split into segments at
each crossing of the valley axis. The length of each segment of the
channel centreline is multiplied by 2 to give equivalence of the channel
length over one wavelength then divided by the average wavelength of
the reach; the arithmetic average of all calculated sinuosity values is
used for analysis. In the case of confined meanders, the meander–belt
width is equal to the valley width. This distance is measured perpendicular to the valley bottom at a spacing of one-half wavelength. The
average of these lengths is taken to be representative for the reach.
To measure radius of curvature (rm) a series of circles is drawn in
ArcGIS, determined to be those that best fit the meander bends defined
by the channel centreline. The radius of that circle is then calculated
and taken to represent the radius of curvature for that bend. Because of
the convex downvalley asymmetry of the meanders, more judgement
may be involved in determining the best-fit circle for a confined
meander than in previous studies that have used this technique on
more symmetrical bends (Leopold and Wolman, 1960; Williams,
1986). To try to quantify the subjectivity involved in this method,
several operators independently determined rm values for one of the
river reaches. Where meander bends were regular, the rm values so
determined varied by ±7% among operators. If the rm values for the
more irregular bends (squared bends or those having very long,
convex downvalley arcs) are added to the sample, the average difference in measured rm values rises to ±13%. These values are comparable to those obtained by Williams (1986) in a similar consistency
check.
Downstream channel displacement is measured between successive
channel centrelines along the valley axis (Fig. 3). A further measurement
is taken between the centrelines of the earliest and most recent photography to obtain the total downstream movement over the period of
photo record. The measured movement is averaged for all bends in a
study reach for each time interval then divided by the number of years
between the sets of photographs to obtain an annual migration rate.
Where possible, channel slope values are taken from previously
published material. To be used, published values have to be calculated
for a section of river that includes the study reach; slopes obtained
using field-measured, water-surface elevations are preferred over those
obtained from topographic maps. The remaining channel and valley
slopes were calculated using NTS 1:50,000 topographic maps underlain
by Canadian Digital Elevation Data (CDED) in OziExplorer 3.95.4e
software.
Drainage areas for the study reaches are calculated using a combination of available watershed boundaries and 1:50,000 NTS topographic maps. Watershed boundary coverage is available through the
Prairie Farm Rehabilitation Administration (PFRA) for the Canadian
prairies and the corporate watershed base (CWB) for British Columbia.
In certain cases, either the PFRA or CWB drainage areas exactly
coincided with the drainage area for the study reach. For most study
sites, however, this is not the case. In these situations, as much of the
applicable watershed boundary available through the PRFA or CWB is
used and the missing portion is digitized using the drainage divides
visible on underlain topographic maps in ArcGIS. The area of the
resultant polygon is then calculated and used as the drainage area for
that site.
Bed material calibre was derived from previously published material
(Kellerhals et al., 1972; Hickin and Nanson, 1984; Burge and Smith,
1999) and from field visits to seven of the study sites. These data
are estimates of the bed material calibre at the site based on a visual
inspection.
The mean annual flood (Q mf) for the study sites was calculated using
peak flow data from the closest Water Survey of Canada (WSC) gauging
station. The arithmetic average of the annual record of instantaneous
maximum discharge (Q i) is calculated as the mean annual flood for
that gauge site. For sites with partial records of Q i, years without
instantaneous maximum discharge data are estimated from the
maximum daily discharge (Q max) adjusted by Q max(Q i/Q max). Where
applicable, data are scaled by drainage area (Ad). The relationship
between Q mf and Ad is assumed to be linear, although some studies
have indicated this may not be the most appropriate representation
Fig. 3. Successive channel centrelines showing channel migration (1952–2000) along a reach of the Beaver River, AB.
Author's personal copy
T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
of this relationship (see Eaton et al., 2002). Nevertheless, given the
accuracy of the calculated drainage area as well as the gauging data
used in this study, the simpler linear relation seems justified.
For sites with a WSC gauge within 15 km distance, Q mf at the
gauging site is used for the study reach. If the gauge is more than
15 km from the study site, Q mf/Ad was calculated and scaled to the
drainage area (Ad) of the study site. For those cases where WSC
gauges exist on either side of the study site, Q mf is regressed on Ad
and the resulting linear equation applied to the site. For rivers with
no WSC gauge, Q mf/Ad is calculated for the nearest gauged stream
of comparable drainage area and scaled to the study site in question.
4. Results
A summary of all environmental, planform geometry and
migration data for the 23 study reaches are shown in Table 1. All
planform and migration rate data are arithmetic values unless noted
otherwise.
41
discernable movement (a proportion very similar to the 24% of
stagnant bends noted by Hooke (1984) in a similar photo period on
the otherwise migrating River Dane in Cheshire, England).
Average channel-migration rate (M) varies from essentially no
movement (Clearwater River) to a high of 5.8 m/y on the Wapiti River.
The average dimensionless migration rate (M/w) varies from
negligible to 0.05 and averages 0.02. The maximum migration rate
varies from a low of 0.4 m/y on the Petitot River to a peak rate of about
17.5 m/y on the Wapiti and Muskwa Rivers. In general, maximum
migration rate (the most mobile single bend in any photo period) is
about three times the spatially averaged migration rates for the study
reaches (based on the movement observed between the earliest and
the most recent photography for each study site). Clearly, the average
migration rate integrates considerable spatial and particularly
temporal variability.
The average migration rate for all study reaches is about 1.7 m/y.
Because the valley confinement directs all migration downvalley, the
average migration rate is also the average rate of planform translation
on these rivers.
4.1. Planform geometry
5. Discussion
Bankfull width ranges from 21 to 288 m. Fort Nelson River
(downstream site) represents the largest of the rivers examined
and, at 288 m in width, is nearly 84 m wider than the next largest river
(Muskwa River). Channel wavelength ranges from 456 to 4578 m;
and meander–belt width, equivalent to the valley width in these
confined meanders, ranges from 167 to 1491 m. In both cases the
downstream site on Fort Nelson River yields the largest measurement.
The smallest values for bankfull width, meander wavelength,
and meander–belt width were measured on Baptiste River, respectively 21, 456, and 167 m. Sinuosity values (Si) are closely grouped,
ranging from 1.1 to 1.8 across the full range of river scale. The degree
of confinement of these rivers limits the sinuosity to values
that are low relative to those generally found for meandering rivers
(Si ~ 2.0–3.0).
The overall shape of the rm/w distribution is positively skewed,
with values from 1.1 up to a maximum rm/w of 13 and an overall
median of 4.1. Because of the positively skewed distribution, median
rather than mean rm and rm/w values are used as the representative
values for each river in subsequent analyses.
4.2. Downstream migration
One of the limitations of using the 30–50 years of photo record to
determine long-term average migration rate on these rivers is that
the period is barely long enough to fully capture the complete process
of lateral migration. On the freely migrating reaches of Beatton River
in northeastern British Columbia, Nanson and Hickin (1986) used
dendrochronology to show that individual scroll bars on migrating
channel bends take ~30 years to mature and that the process of bend
migration is distinctly intermittent, particularly at the timescale of
typical aerial photo coverage. Furthermore, very slowly migrating
channel bends may involve displacements too small to be resolved by
the methods used here. Since mobile bends may exhibit no movement
during a photo period for the reasons noted, zero migration rates are
excluded from the analysis. Note that this approach does not inflate
the calculated average migration rate for those rivers with a significant proportion of stationary bends; rates for such rivers (Clearwater,
Petitot, Hay (upstream), and Fontas study reaches) remain among the
slowest channel migrations observed.
Sixteen of the 23 study sites had at least one bend that did not
move during the air photo period. Of these 16 reaches, the proportion
of bends displaying no discernable movement on each study reach
varied from 3 to 83% of the total bends examined, with Clearwater
River and Petitot River study reaches remaining very stable over the
air photo period. For the data set as a whole, 22.5% of bends had no
5.1. Planform geometry relations
In general, the planform geometry relations established for freely
meandering rivers appear to apply to confined meanders as well,
although there are some minor but noteworthy differences.
For these confined meanders, l/w ≈ 17 on average is a higher
coefficient than the more commonly reported l/w = 8–14 for freely
meandering rivers (Nanson and Hickin, 1986; Williams, 1986). The
median bend curvature calculated in this study is also slightly higher
(rm/w = 4.1) compared to rm/w = 2–3 that is generally reported as
being typical for freely meandering rivers (Nanson and Hickin, 1986;
Williams, 1986).
Several reasons are apparent as to why the related planform
properties of channel wavelength and curvature are higher for rivers
of given width in this study. First, examination of the pattern of
meander migration over the photo period reveals that the river
meanders generally tend to translate downstream as a package (see
Fig. 3), and cutoffs are relatively uncommon compared to the case of
freely meandering rivers. Bend overtightening commonly precedes
the generation of a cutoff in meandering rivers, leading to a decrease
in the channel curvature. As this process appears to be relatively rare
on these confined rivers, the corresponding reduction in l/w and rm/w
does not occur. Secondly, freely meandering rivers may migrate
outward (toward the bend apex) rather than downstream, a process
that also leads to a decrease in channel-bend radius. That is, the
meander inflection points remain stationary while the bend moves
outward, tightening the bend curvature. This outward movement is
not possible for confined meanders. As the bends migrate downstream, the inflection points move with the bend and the bend
curvature remains relatively constant. Furthermore, although these
confined meanders have very sharp bends at the point of impingement on the valley wall, most of each meander is comparatively open.
In the “best-fit” circle method of measurement adopted here, the bend
curvature of the larger, convex downvalley arc has the greatest
influence on the value of rm.
The well-documented relationship between bankfull width and
the square root of discharge is also evident for these confined
meanders. The relationships of bankfull width and channel wavelength to mean annual flood (Q mf) are described well by respective
2
0.42
power functions (w = 4.5Q 0.5
mf ; R = 0.88; P b 0.0001; l = 116Q mf ;
2
R = 0.74; P b 0.0001).
A plot of valley width to channel width shows that the type of
confined meanders examined in this study generally develops where
the ratio of floodplain width to channel width ranges between 3:1
20,320
39,680
2830
840
7120
5730
20,300
23,820
11,830
610
8450
35,280
11,300
1560
1276
506
65
92
690
97
2161
778
511
58
1141
454
1205
89
0.0013
0.0001
0.0007
0.0003
0.0007
0.0013
0.0024
0.0008
0.0003
0.0012
0.0026
0.0003
0.0002
0.0005
0.0028
0.0003
0.0002
0.0018
0.0030
0.0002
0.0001
0.0001
0.0003
S
0.0019
0.0002
0.0009
0.0004
0.0009
0.0013
0.0026
0.0015
0.0005
0.0013
0.0039
0.0006
0.0003
0.0009
0.0037
0.0004
0.0005
0.0019
0.0038
0.0008
0.0004
0.0004
0.0004
Sv
1182
974
625
6366
5065
6331
1348
9310
1188
13,788
2235
214
860
6097
964
128
265
10,107
3163
782
192
173
12,365
ω
(Wm− 1)
G
G/S:S
G/S:S
G
G
G
G
G
G/S:S
G
G
S
G/S:S
G/S:G
G
S
G/S:S
G
G
S
G/S:G
S
G/S:G
Bed grain
size
43
123
74
205
140
99
33
142
140
139
39
44
86
163
21
32
44
117
57
126
28
68
288
Wbf(m)
663
1825
1219
2441
2214
662
591
2109
3063
2032
571
627
1673
2036
456
991
757
2098
642
1958
750
1208
4578
L (m)
15.4
14.8
16.4
11.9
15.8
6.7
17.9
14.9
21.9
14.6
14.6
14.3
19.4
12.5
21.7
31.0
17.2
17.9
11.3
15.5
26.8
17.7
15.9
L/Wbf
1.2
1.4
1.2
1.3
1.2
1.2
1.8
1.7
1.2
1.2
1.8
1.6
1.4
1.6
1.4
1.4
1.5
1.1
1.5
1.7
1.3
1.6
1.4
Si
223
991
318
1032
598
255
192
990−
816
469
345
312
770
802
167
412
337
403
279
1380
236
582
1491
WMB (m)
217
479
231
471
435
158
77
428
823
464
93
120
434
622
135
213
213
785
191
467
165
320
863
rm (m)
5.1
3.9
3.1
2.3
3.1
1.6
2.4
3.0
5.9
3.3
2.4
2.8
5.0
3.8
6.4
6.6
4.9
6.7
3.3
3.7
5.8
4.7
3
rm/w
1.8
0.6
1.6
5.5
1.6
0.2
0.8
3.3
1.6
5.8
0.9
0.3
0.8
4.1
0.6
0.6
1.2
1.5
3.0
0.01
0.2
0.6
2.5
Mav
(my− 1)
0.042
0.005
0.022
0.027
0.011
0.002
0.024
0.023
0.012
0.042
0.023
0.006
0.009
0.025
0.030
0.019
0.028
0.013
0.053
0.0001
0.007
0.009
0.009
Mav/w
(my− 1)
2.3
3.9
4.0
17.5
12.4
0.4
2.8
11.1
11.0
17.6
7.6
1.5
2.2
10.4
2.2
1.4
3.5
3.1
9.5
1.3
1.1
3.9
7.0
Mmax
my− 1)
6
10
8
8
8
16
13
9
12
7
10
26
9
15
9
9
29
6
10
6
18
20
12
Bend (#)
24
52
44
44
47
31
50
31
51
51
49
39
41
31
46
53
48
48
45
46
41
30
30
Photo period
(years)
42
a
Coordinates referenced to WGS84 datum; Qmf = mean annual flood; Ad = drainage area; S = water-surface slope; Sv = valley slope; ω = stream power; bed grain size (G = gravel; S = sand; G/S:S a gravel–sand transition dominated by
sand; G/S:G = a gravel–sand transition dominated by gravel); Wbf = bankfull channel width; L = meander wavelength; Si = channel sinuosity; WMB = meander–belt width; rm = channel-bend radius of curvature; M = migration rate; and
Mmax = maximum migration rate.
420
17,800
14,500
15,370
2880
30,800
1940
7400
52,230
36
42
115
569
108
399
186
320
3867
Baptiste (52.5442/−115.4598)
Battle (53.0605/−110.7035)
Beaver (54.2562/−110.7035)
Bow (50.8130/−113.7418)
Clear (56.2125/−119.6795)
Clearwater (56.6890/−111.2997)
Doig (56.9092/−120.2597)
Fontas (58.2684/−121.4650)
Fort Nelson (downstream)
(59.2325/−123.1503)
Fort Nelson (upstream)
(58.5018/−122.1095)
Hay (downstream)
(59.3927/−117.2663)
Hay (upstream)
(58.4073/−119.7492)
Klua (58.2653/−122.0325)
Kootenay (49.7615/−115.7488)
Milk (49.1363/−111.0991)
Muskwa (58.7975/−122.6372)
Oldman (49.8422/−112.3195)
Petitot (59.6604/−121.0775)
Pinto (53.7979/−117.7957)
Prophet (58.7101/−122.7790)
Red Deer (50.9635/−111.9258)
Wapiti (55.0679/−119.0049)
Wildhay (53.7091/−117.7105)
Ad
(km2)
Qmf
(m3s− 1)
River (latitude/longitude)
Table 1
Environmental information, planform geometry, and migration rates for all study reachesa.
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T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
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T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
and 10:1 (Fig. 4A), consistent with ratios suggested by Hickin (1986)
and Burge and Smith (1999) for similarly confined meandering rivers
elsewhere.
5.2. Comparison with published migration rates
To provide a regional context for the channel-migration measurements, additional data were extracted from the Hickin (1988)
compilation for rivers located in Alberta and British Columbia.
Fig. 4B shows the migration rates of these rivers with the mean and
maximum rates for confined meanders scaled to bankfull width. The
mean migration rate for the confined meanders is consistent with
those of other rivers within the same region. (M/w averages 0.02 for
the confined meanders and averages 0.03 for unconfined meanders).
A few of the mean migration rates appear to be lower than other rivers
of the same size, including the very low outlying Clearwater River.
Notably, however, the majority of the Alberta and British Columbia
migration rates used in these graphs were calculated for meanders
with a bend curvature (rm/w) between 2 and 4 (Nanson and Hickin,
1986), a range designed to capture the maximum migration rates
observed for those rivers. For this reason the maximum migration
rates observed on the confined meanders were also examined. With
the exception of the Petitot River, the few sites with mean migration
rates that appear to be lower than other rivers of the same size have
maximum migration rates that fall within the general distribution of
the data. Overall, the maximum values generally plot on the high
boundary of the distribution, although they do not appear to be
abnormally high for the region. They may indicate an upper threshold
for migration rates on comparably sized rivers. Certainly the confined
meanders of this study do not appear to have migration rates that
exceed those found in freely meandering rivers of comparable size. On
the other hand, because channel migration in these confined meanders is directed downvalley, the rate of downvalley planform
translation is almost certainly faster; but comparative migration rate
data for freely meandering rivers are not available.
Fig. 4. (A) Confinement ratio of the study sites. (B) Mean and maximum migration rates
for the 23 study locations plotted with data extracted from Hickin (1988) for western
Canadian rivers.
43
5.3. Controls on migration rate
To supply a statistical description of confined meanders that
provides the basis for prediction of migration rate, relations among
migration rate and drainage area, mean annual flood, channel and
valley slope, stream power, bed material, and planform geometry
were examined.
An exploratory multiple regression analysis of the data in this
study using various combinations of slope, mean annual flood, and
width as independent variables provided no significant improvement
in the level of explanation that could be achieved by bivariate
regression, so the discussion below is focused on the simpler bivariate
relations.
Several studies have demonstrated elsewhere a close relation
between channel-migration rate and drainage area (Hooke, 1980;
Brice, 1984). In Hooke's (1980) study, 53% of the variance in migration
rate is explained statistically by variation in drainage area. In this
study, no clearly-defined relation between migration rate and
drainage area is evident (Fig. 5A), although the highest migration
rate is associated with the larger drainage areas (the data envelope
has a positive slope). When the migration rate is scaled to bankfull
width the trend reverses: the largest migration rates per unit width
occur in smaller watersheds (Table 1). Many of these rivers are small
but with actively mobile channels so that a comparatively small
absolute movement will have a proportionally larger impact on the
scaled migration rate compared to those in larger rivers. Much of the
data scatter here likely relates to the confounding influence of variable
bend curvature and to the air photo sampling problem noted earlier.
The present data are not inconsistent, however, with a general and
broadly based relation linking migration rate with drainage area
(Fig. 5B). Nevertheless, that general trend is not likely evident in data
sets that span less than a few orders of magnitude in drainage area.
The relation between migration rate and bankfull width is one of
the strongest exhibited in this study, a result consistent with those
obtained elsewhere. In a study of Rio Grande channel migration,
Richard et al. (2005) found that width explained over 50% of the
migration rate variance on that river, while Nanson and Hickin (1986)
reported a level of 44% explained variance for a sample of western
Canadian rivers. In the present study, migration rate increases linearly
with bankfull width (Fig. 5C), although the relationship is confounded
by other factors, such as the channel slope. Bankfull width alone
explains 31% of variance in the migration rates observed. Many of the
study sites, particularly the Petitot and Clearwater Rivers, have
relatively slow migration rates for their size. If maximum rather than
average migration rate is regressed on bankfull width, there is a slight
strengthening of the statistical explanation (33%).
Channel migration of these confined channels is also closely
related to the magnitude of the mean annual flood (Fig. 5D). Migration rate increases with discharge, although there is considerable
data scatter (30% of the variation in migration rate is explained by
variation in Q mf). If the study sites are split into their respective bed
material types, a strong relationship between the migration rate
of gravel-bed rivers and mean annual flood is evident (explained
variance increases to 61%), although most of this increase depends
heavily on the Fort Nelson (downstream) site with its bed material of
transitional gravel. If gravel and transitional gravel sites are combined
into one classification, the explained variance in the migration rate
drops to 26%. Sites with sand and transitional sand-bed material have
average migration rates that are in the lower range of data but no
strong regression relation is evident for these sites. Although only
nine sites are to some extent sand-bedded, sites with similar mean
annual floods in the transitional sand-bedded rivers consistently
display higher rates of migration than those that are fully sandbedded. No general trend is observed for average migration rates of
sand-bed rivers. If scaled to bankfull width, the sand-bedded rivers
display a general linear decrease (R2 = 0.35) in migration rate per unit
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T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
Fig. 5. Relations between migration rate and controlling factors: (A) drainage area for this study; (B) a comparison with published migration rates (Van De Wiel, 2003); (C) bankfull
width; (D) mean annual flood; (E) channel slope (migration rates scaled to bankfull width); and (F) stream power.
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T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
width with increases in mean annual flood. The sand-bed rivers still
generally plot in the lower range of the data after scaling.
Physical reasoning suggests that increasing slope should increase
migration rate, all else being equal. Fig. 5E shows the relation between
slope and migration rate for the study sites, with migration scaled
to bankfull width. Study sites with relatively high slopes do display
higher migration rates. Overall, channel slope explains 33% of variation
in migration rate; this increases slightly (to 34%) when valley slope is
used.
A more comprehensive measure of the erosive forces for seeking a
correlation with migration rate is stream power because it incorporates
both discharge and slope. Stream power is the rate of potential energy
expenditure per unit channel length, expressed as a product of discharge and channel slope. In the interests of optimising predictive
power of the statistical model, stream power and specific stream power
are calculated using valley slope rather than channel slope.
Stream power provides the best explanation for variation in
migration rate of any factor examined within this study (Fig. 5F). This
result supports the findings of Nanson and Hickin (1986) and Richard
et al. (2005) who achieved very similar stream-power-based levels of
statistical explanation (respectively 48% and 52%) in channel-migration
rates in earlier studies. Stream power here explains 52% of the variation,
greater than that provided by valley slope (34%), bankfull width (31%),
and mean annual flood (30%). No improvement in this level of explanation can be achieved by separating the study sites by their bed
material type. Using exclusively gravel-bedded rivers, the explanation
level decreases to 40%; no trend exists when the sand-bed rivers are
considered separately. The sand-bed rivers within this study have relatively low stream power and somewhat lower migration rates overall
(Fig. 5F), largely because of their lower gradients. When migration rate
is scaled to bankfull width, only two of the transitional sand-bed study
sites are migrating at a rate N2% of their bankfull width per year. In
comparison, a large proportion of gravel-bedded rivers are migrating at
rates N2%.
A factor that modulates the erosive forces as well as the resisting
forces in channel migration is the curvature of the channel bend.
Numerous authors have recognized a non-linear relationship between
bend curvature and migration rate in which the maximum rates are
generally found with rm/w ratios of 2 to 3 (Hickin and Nanson, 1984;
Nanson and Hickin, 1986; Hooke, 2007). The same association is
found with the confined meanders in this study. Fig. 6A shows the
45
average channel-migration rate for each time interval for each bend in
relation to the channel curvature. The envelope curve is much the
same shape as that reported elsewhere. Migration rate increases
sharply to a maximum for rm/w between 2 and 4, followed by a
general decline in rate for smaller and larger bend curvatures. Scaling
the bend-radius measurements to bankfull width yields the same
general shape of the envelope curve (Fig. 6B). Both graphs in Fig. 6
exhibit a large amount of internal scatter within the relation so that
very low rates of migration are also found between rm/w of 2 to 4.
To investigate further the cause of the scatter in Fig. 6, the migration
rate/curvature relation was examined for individual study sites. A
few of the study sites (such as those on the Kootenay, Wapiti, and
Wildhay Rivers) display expected behaviour based on published
findings (migration rate maxima at rm/w ratios between 2 and 4
flanked by declining rates). In contrast, other study reaches, notably
the Battle River site, have bends with relatively high curvature exhibiting the highest rates of migration. Still other sites exhibit a
maximum migration rate between 2 and 4, but they also vary greatly
over a small range of bend curvature. Taken as a whole, the results
indicate that bend curvature modulates migration rate but obviously
other factors, particularly others relating to the resisting forces in the
migration process, are at work as well.
An explanatory component shown elsewhere to be important
(Hickin and Nanson, 1984) is the resistance to lateral erosion offered
by the boundary sediment within the meanders. While Nanson and
Hickin (1986) find sediment size at the base of the outer bank to be a
useful measure of erosion resistance, other studies place more importance on percentage of silt/clay in the banks (Hooke, 1980), presence of vegetation (Burckhardt and Todd, 1998), and height of the
outer bank (Hickin and Nanson, 1984).
Because of the remote nature of many of the study reaches and lack
of published data, quantitative estimates of basal sediment calibre at
the study sites are not available. This missing element likely explains a
significant proportion of the variation in migration rate left unexplained
in this study. Supporting this suggestion are the probable bank characteristics of the five sites recording the lowest absolute migration rate:
the Clearwater, Doig, Petitot, Hay (upstream), and Fontas River reaches.
Each of these rivers flows through areas of muskeg; and the river banks
here likely have abundant fine-grained sediment and dense root mats,
making them highly resistive to lateral erosion and thereby lowering
migration rate.
Fig. 6. Rate of channel-migration (A) and migration rate per unit channel width (B) versus bend curvature (rm/w).
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T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
6. Conclusions
Planform appearance notwithstanding, the planform geometry and
migration behaviour of confined meandering rivers examined here
generally are consistent with those exhibited by freely meandering
rivers. Nevertheless, the unique meander pattern of confined meanders is reflected in small but significant differences within the overall
planform relations (l/w ≈ 17 rather than the more commonly reported
l/w = 8–14 for freely meandering rivers, and the median bend curvature is also slightly higher at rm/w = 4.1 rather than rm/w = 2–3).
In general, these migrating confined meandering rivers do not
develop cutoffs, and meander bends appear to migrate downstream
as a coherent waveform. Migration rates fall within the general distribution of published migration rates, although they vary greatly
among sites, from highly stable reaches such as the Clearwater River
migrating at a rate of just 0.01 m/y, to decidedly active reaches such
as the Wapiti River that migrates downstream at 5.8 m/y. The relation
of peak migration rate to bend curvature displays the same characteristic asymmetric form with a maximum at 2.0 b rm/w b 4.0 as
reported elsewhere for freely migrating river bends.
Statistical explanations for the rate of migration in terms of environmental controls are also similar to those achieved in published
studies of freely meandering rivers. Although bankfull width, discharge, and slope each by themselves explains about 30% of the
variance in migration rate, the explanatory power of the integrative
measure of stream power accounts for more than half of the migration
rate behaviour.
For the region examined here, sand-bed rivers have lower stream
power and lower migration rate relative to similarly sized gravel-bed
rivers.
Overall, the findings of this study in western Canada indicate that
confined meandering rivers here might be more usefully regarded as
part of a continuum of meandering river pattern rather than as
something completely different. Although the unique meander pattern of confined rivers has an effect on their meander morphometry
and kinematics, they also have much in common with their freely
meandering counterparts. Of course the usual caveat with respect to all
empirical work applies here as well: caution needs to be exercised
when exporting these particular results beyond this study region.
The new data and geomorphic relationships introduced in this
study represent a contribution to the understanding of channelmigration dynamics. They also provide a basis for testing predictive
channel-migration models.
Acknowledgements
This project, based on the M.Sc. thesis of the lead author (Nicoll,
2008), is part of a larger study on the morphodynamics of rivers
in western Canada funded by the Natural Sciences and Engineering
Council of Canada (NSERC Discovery Grant) to Hickin. This work
was also supported in part by research grants to Nicoll from NSERC
and Simon Fraser University. We thank the reviewers for their useful
suggestions that have been incorporated into the present paper.
References
Bagnold, R.A., 1960. Some Aspects of the Shape of River Meanders. U.S. Geological
Survey Professional Paper 282E, Washington, DC.
Beeson, C.E., Doyle, P.F., 1995. Comparison of bank erosion at vegetated and non-vegetated
channel bends. Journal of the American Water Resources Association 31 (6), 983–990.
Brice, J.C., 1982. Stream channel stability assessment. Final Report, U.S. Department of
Transportation, Federal Highway Administration, Washington, DC.
Brice, J.C., 1984. Planform properties of meandering rivers. In: Elliott, C.M. (Ed.), River
Meandering. Proceedings of the Conference on Rivers 1983. ASCE, New York, pp. 1–15.
Burckhardt, J.D., Todd, B.L., 1998. Riparian forest effect on lateral stream channel migration
in the glacial till plains. Journal of the American Water Resources Association 34,
179–184.
Burge, L.M., Smith, D.G., 1999. Confined meandering river eddy accretions: sedimentology,
channel geometry and depositional processes. Special Publications of the International
Association on Sediment 28, 113–130.
Carson, M.A., Lapointe, M.F., 1983. The inherent asymmetry of river meander planform.
Journal of Geology 91, 41–55.
Dury, G.H., 1964. Principles of underfit streams. U.S. Geological Survey Professional
Paper 452-A, Washington, DC.
Eaton, B., Church, M., Ham, D., 2002. Scaling and regionalization of flood flows in British
Columbia, Canada. Hydrological Processes 16 (16), 3245–3263.
Ferguson, R.I., 1984. Kinematic model of meander migration. In: Elliott, C.M. (Ed.),
River Meandering. Proceedings of the Conference on Rivers 1983. ASCE, New York,
pp. 942–951.
Gilvear, D., Winterbottom, S., Sinchingabula, H., 2000. Character of channel planform
change and meander development: Luangwa River, Zambia. Earth Surface Processes
and Landforms 25, 421–436.
Gurnell, A., 1997. Channel change on the River Dee meanders, 1946–1992, from the
analysis of air photographs. Regulated Rivers: Research and Management 13,
13–26.
Gurnell, A., Downward, S.R., Jones, R., 1994. Channel planform change on the River Dee
meanders, 1876–1992. Regulated Rivers: Research and Management 9, 187–204.
Hickin, E.J., 1978. Hydraulic factors controlling channel migration. In: Davidson-Arnott, R.E.,
Nickling, W. (Eds.), Research into Fluvial Systems. Proceedings of the 5th Guelph
Symposium on Geomorphology 1977. GeoAbstracts, Norwich, UK, pp. 59–66.
Hickin, E.J., 1979. Concave-bank benches on the Squamish River, British Columbia, Canada.
Canadian Journal of Earth Sciences 16 (1), 200–203.
Hickin, E.J., 1986. Concave-bank benches in the floodplains of Muskwa and Fort Nelson
Rivers, British Columbia. Canadian Geographer 30 (2), 111–122.
Hickin, E.J., 1988. Lateral migration rates of river bends. In: Cheremisinoff, P.N., Cheng, S.L.
(Eds.), Handbook of Civil Engineering. Hydraulics/Mechanics, vol. 2. Technomic
Publishing, Lancaster, PA, pp. 419–445.
Hickin, E.J., Nanson, G.C., 1975. The character of channel migration on the Beatton River,
northeast British Columbia, Canada. Geological Society of America Bulletin 86, 487–494.
Hickin, E.J., Nanson, G.C., 1984. Lateral migration rates of river bends. Journal of Hydraulic
Engineering-ASCE 110, 1557–1567.
Hooke, J.M., 1977. The distribution and nature of changes in river channel patterns: the
example of Devon. In: Gregory, K.J. (Ed.), River Channel Changes. Wiley, Chichester,
UK, pp. 206–220.
Hooke, J.M., 1980. Magnitude and distribution of rates of river bank erosion. Earth
Surface Processes and Landforms 5, 143–157.
Hooke, J.M., 1984. Changes in river meanders: a review of techniques and results of
analyses. Progress in Physical Geography 8 (4), 473–508.
Hooke, J.M., 2007. Complexity, self-organization and variation in behaviour in meandering
rivers. Geomorphology 91, 236–258.
Hooke, J.M., Harvey, A.M., 1983. Meander changes in relation to bend morphology and
secondary flows. In: Collinson, J., Lewin, J. (Eds.), Modern and Ancient Fluvial Systems.
Blackwell, Oxford, UK, pp. 121–132.
Hudson, P.F., Kesel, R.H., 2000. Channel migration and meander-bend curvature in the
lower Mississippi River prior to major human modification. Geology 28 (6), 531–534.
Ikeda, S., Parker, G. (Eds.), 1989. River Meandering. Water Resources Monograph, vol. 12.
American Geophysical Union, Washington, DC.
Kellerhals, R., Neill, C.R., Bray, D.I., 1972. Hydraulic and geomorphic characteristics of
rivers in Alberta. River Engineering and Surface Hydrology Report 72-1, Alberta
Research Council, Edmonton.
Knighton, D., 1998. Fluvial Forms and Processes: A New Perspective. Oxford University
Press Inc., New York.
Lawler, D.M., 1993. Measurement of river bank erosion and lateral channel change: a
review. Earth Surface Processes and Landforms 18, 777–821.
Leopold, L.B., Wolman, M.G., 1960. River meanders. Bulletin of the Geological Society of
America 71, 769–794.
Leopold, L.B., Wolman, M.G., Miller, J.P., 1964. Fluvial Processes in Geomorphology. W.
H. Freeman, San Francisco, CA.
Lewin, J., 1983. Changes of channel patterns and floodplains. In: Gregory, K.J. (Ed.),
Background to Paleohydrology. Wiley, Chichester, UK, pp. 303–319.
Lewin, J., Brindle, B.J., 1977. Confined meanders. In: Gregory, K.J. (Ed.), River Channel
Changes. Wiley, Chichester, UK, pp. 221–233.
Mathews, W., 1980. Retreat of the Last Ice Sheets in Northeastern British Columbia and
Adjacent Alberta. Geological Survey of Canada Bulletin 331, Ottawa, ON.
Nanson, G.C., Hickin, E.J., 1986. Statistical analysis of bank erosion and channel migration
in western Canada. Geological Society of America Bulletin 97, 497–504.
Nicoll, T.J., 2008. Planform geometry and kinematics of confined meandering rivers on
the Canadian prairies. M.Sc. Thesis, Simon Fraser University, Burnaby, BC, Canada.
Page, K., Nanson, G., 1982. Concave-bank benches and associated floodplain formation.
Earth Surface Processes and Landforms 7, 529–543.
Petts, G.E., 1989. Historical analysis of fluvial hydrosystems. In: Petts, G.E., Muller, H.,
Roux, A.L. (Eds.), Historical Change of Large Alluvial Rivers: Western Europe. Wiley,
Chichester, UK, pp. 1–18.
Richard, G.A., Julien, P.Y., Baird, D.C., 2005. Statistical analysis of lateral migration of the
Rio Grande, New Mexico. Geomorphology 71, 139–155.
Schattner, I., 1962. The lower Jordan valley. PhD. Thesis, Hebrew University, Jerusalem,
Israel.
TRB (Transportation Research Board of the National Academies of the U.S.), 2004.
Methodology for Predicting Channel Migration. NCHRP Web-Only Document 67
(Project 24-16). http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w67.pdf.
Van De Wiel, M.J., 2003. Numerical modelling of channel adjustment in alluvial
meandering rivers with riparian vegetation. PhD. Thesis, University of Southampton,
UK.
Author's personal copy
T.J. Nicoll, E.J. Hickin / Geomorphology 116 (2010) 37–47
Wellmeyer, J., Slattery, M., Phillips, J., 2005. Quantifying downstream impacts of
impoundment on flow regime and channel planform, lower Trinity River, Texas.
Geomorphology 69, 1–13.
Williams, G.P., 1986. River meanders and channel size. Journal of Hydrology 88, 147–164.
Winterbottom, S., 2000. Medium and short-term channel planform changes of the
Rivers Tay and Tummel, Scotland. Geomorphology 34, 195–208.
47
Winterbottom, S., Gilvear, D., 2000. A GIS-based approach to mapping probabilities of
river bank erosion: regulated River Tummel, Scotland. Regulated Rivers: Research
and Management 16, 127–140.
Yarnykh, N.A., 1978. Channel and bank deformations in an acute meander. Soviet
Hydrology Selected Papers 17, 278–281.