Planform geometry and channel migration of confined meandering rivers on the Canadian prairies

Geomorphology 116 (2010) 37–47

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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: [email protected] (T.J. Nicoll), [email protected] (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

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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

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.

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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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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.

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.

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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

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Table 1 Environmental information, planform geometry, and migration rates for all study reachesa. Qmf (m3s− 1)

Ad (km2)

S

Sv

ω (Wm− 1)

Bed grain size

Wbf(m)

L (m)

L/Wbf

Si

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)

36 42 115 569 108 399 186 320 3867

420 17,800 14,500 15,370 2880 30,800 1940 7400 52,230

0.0028 0.0003 0.0002 0.0018 0.0030 0.0002 0.0001 0.0001 0.0003

0.0037 0.0004 0.0005 0.0019 0.0038 0.0008 0.0004 0.0004 0.0004

964 128 265 10,107 3163 782 192 173 12,365

G S G/S:S G G S G/S:G S G/S:G

21 32 44 117 57 126 28 68 288

456 991 757 2098 642 1958 750 1208 4578

21.7 31.0 17.2 17.9 11.3 15.5 26.8 17.7 15.9

1.4 1.4 1.5 1.1 1.5 1.7 1.3 1.6 1.4

1276

20,320

0.0005

0.0009

6097

G/S:G

163

2036

12.5

506

39,680

0.0002

0.0003

860

G/S:S

86

1673

65

2830

0.0003

0.0006

214

S

44

92 690 97 2161 778 511 58 1141 454 1205 89

840 7120 5730 20,300 23,820 11,830 610 8450 35,280 11,300 1560

0.0013 0.0001 0.0007 0.0003 0.0007 0.0013 0.0024 0.0008 0.0003 0.0012 0.0026

0.0019 0.0002 0.0009 0.0004 0.0009 0.0013 0.0026 0.0015 0.0005 0.0013 0.0039

1182 974 625 6366 5065 6331 1348 9310 1188 13,788 2235

43 123 74 205 140 99 33 142 140 139 39

G G/S:S G/S:S G G G G G G/S:S G G

WMB (m)

rm (m)

rm/w

Mav (my− 1)

Mav/w (my− 1)

167 412 337 403 279 1380 236 582 1491

135 213 213 785 191 467 165 320 863

6.4 6.6 4.9 6.7 3.3 3.7 5.8 4.7 3

0.6 0.6 1.2 1.5 3.0 0.01 0.2 0.6 2.5

0.030 0.019 0.028 0.013 0.053 0.0001 0.007 0.009 0.009

1.6

802

622

3.8

4.1

19.4

1.4

770

434

5.0

627

14.3

1.6

312

120

663 1825 1219 2441 2214 662 591 2109 3063 2032 571

15.4 14.8 16.4 11.9 15.8 6.7 17.9 14.9 21.9 14.6 14.6

1.2 1.4 1.2 1.3 1.2 1.2 1.8 1.7 1.2 1.2 1.8

223 991 318 1032 598 255 192 990− 816 469 345

217 479 231 471 435 158 77 428 823 464 93

Mmax my− 1)

Bend (#)

Photo period (years)

2.2 1.4 3.5 3.1 9.5 1.3 1.1 3.9 7.0

9 9 29 6 10 6 18 20 12

46 53 48 48 45 46 41 30 30

0.025

10.4

15

31

0.8

0.009

2.2

9

41

2.8

0.3

0.006

1.5

26

39

5.1 3.9 3.1 2.3 3.1 1.6 2.4 3.0 5.9 3.3 2.4

1.8 0.6 1.6 5.5 1.6 0.2 0.8 3.3 1.6 5.8 0.9

0.042 0.005 0.022 0.027 0.011 0.002 0.024 0.023 0.012 0.042 0.023

2.3 3.9 4.0 17.5 12.4 0.4 2.8 11.1 11.0 17.6 7.6

6 10 8 8 8 16 13 9 12 7 10

24 52 44 44 47 31 50 31 51 51 49

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.

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River (latitude/longitude)

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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.

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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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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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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

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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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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.

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