Journal of Sedimentary Research, 2005, v. 75, 844–860
DOI: 10.2110/jsr.2005.066
RADAR ARCHITECTURE AND EVOLUTION OF CHANNEL BARS IN WANDERING GRAVEL-BED RIVERS:
FRASER AND SQUAMISH RIVERS, BRITISH COLUMBIA, CANADA
C.L. WOOLDRIDGE* AND E.J. HICKIN
Department of Geography and Department of Earth Sciences, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada
e-mail: [email protected]
ABSTRACT: The alluvial architecture and evolution of two kilometer-scale
compound bars in the wandering gravel-bed Fraser and Squamish rivers,
British Columbia, Canada, are described. Integrating ground-penetrating
radar, bathymetry, and aerial photographs enables the internal architecture
to be linked to the evolution of the gravelly barforms over the previous 50
years. These linkages reveal the sedimentary mechanisms that formed the
various architectural packages within compound bars and unit bars. Growth
of compound bars is controlled by the accretion of unit bars onto discrete
segments along their gravelly edges. The attachment of unit bars deflects the
thalweg to impinge on and erode specific portions of bars and channel banks.
Bar growth leads to the stabilization of bars, vegetation colonization of bar
interiors, and island formation. It is the formation of islands, along with
channel avulsions, that maintains channel division in wandering rivers.
Seven styles of gravelly deposition are imaged in the alluvial architecture.
Vertical-accretion deposits formed from the deposition of gravelly bedload
sheets are the most common strata. A moderate abundance of slipface
deposits preserves high-relief bar margins. Lateral accretion dominates
point-bar deposits. Downstream-accretion deposits govern some phases of
down-bar growth. Partial and complete channel-fill and chute-fill deposits
are eroded into underlying sediments, as are scour-and-fill deposits.
Upstream-accretion deposits are uncommon.
A depositional model of gravelly channel bars in the two rivers is
presented and reveals that the architecture is made up of depositional styles
similar to those observed in braiding-river successions, although the
sedimentary packages are preserved in different proportions. Differences
in braiding-river and wandering-river sedimentology largely reflect the
relatively frequent migration of channels and bars in braiding rivers, which
preserve high proportions of channel fill and chute fill, and confluence scourand-fill deposits. Conversely, the moderately stable island and channel
network in wandering rivers limits channel shifting and consequently
preserves a low number of channel fills. Moderate proportions of slipface
strata and coherent patterns of sand deposition along bar tops provide
evidence of comparatively uniform flow patterns in independent channel
segments divided by islands. These patterns of bar sedimentation and
channel shifting preserved in the alluvial architecture appear to be signature
characteristics of wandering rivers. The occurrence of similar architecture in
both the Fraser and Squamish rivers suggests that the model likely applies
to most wandering gravel-bed rivers.
INTRODUCTION
The processes and dynamics of river behavior in wandering gravel-bed
rivers have become better understood in recent years, but the subsurface
sedimentary architecture (from channel base to bar-top deposits) has not
* Present address: EnCana Corporation, 421 7th Avenue SW, P.O. Box 2850,
Calgary, Alberta, T2P 2S5, Canada
Copyright E 2005, SEPM (Society for Sedimentary Geology)
been directly linked to formative flow processes and patterns of sediment
erosion and deposition. Work by Roberts et al. (1997) using groundpenetrating radar (GPR) to image gravelly channel and floodplain
subsurface structures in a modern wandering river, as well as Passmore
and Macklin’s (2000) description of the alluvial architecture exposed in
cut banks of late Holocene wandering-river deposits, has given some
insights into the architecture of wandering gravel-bed rivers. In both
cases, however, patterns of sediment transport and bar evolution were
inferred and not directly known.
For the purposes of this study, alluvial architecture is the geometry,
proportion, and spatial distribution of fluvial sediments within a storey
(or storeys). A storey is a deposit of a single channel bar and adjacent
channel fill (Bridge and Mackey 1993). Although the genetic classification
of channel bars is still unresolved (e.g., Best et al. 2003), compound bars
are complex sedimentary bodies that have been erosionally reworked and
are made up of amalgamated unit bars and/or compound bars, whereas
unit bars are simple depositional barforms that internally show unmodified depositional sedimentary structures (N.D. Smith 1974).
This study links the alluvial architecture of channel bars to patterns of
sediment transport and bar evolution over the previous 50 years in the
Fraser and Squamish rivers, British Columbia, Canada. Radar facies and
subsurface structures were imaged with GPR, and the migration history
and bed topography of barforms and channels were mapped and
interpreted from aerial photographs and bathymetry. Recent studies in
sand-bed and gravel-bed rivers have used similar methodologies to
elucidate patterns of channel migration and the deposits of braid bars,
which have informed and refined models of bar sedimentation in braiding
rivers (Best et al. 2003; Lunt et al. 2004). Differences in patterns of bar
evolution, bar sedimentation, and proportions of strata preserved in
braiding-river and wandering-river alluvial architecture led to the
development of a model of gravelly sedimentation on channel bars. Our
model provides the complement to sandy facies models in wandering
gravel-bed rivers that describe the sedimentology and facies assemblages
of sandy deposits preserved in floodplain and channel bar-top sediments
(Desloges and Church 1987; Brierley 1989, 1991a, 1991b).
STUDY AREA AND METHODS
Study Sites
The Fraser and Squamish rivers flow through the Coast Mountain
Range as wandering gravel-bed rivers for a portion of their length
(Table 1) prior to making an abrupt transition to meandering rivers
before they discharge into the Strait of Georgia and Howe Sound in
southwest British Columbia (Figs. 1, 2A). Two compound bars situated
in these wandering gravel-bed reaches are the study sites. In the Squamish
River, bank-attached TFLENT Bar (Tree Farm License Entrance;
Fig. 2A, B), 1.1 km long and up to 400 m wide, is located 2.1 km
upstream of the Ashlu River confluence at 34 to 35 m above sea level. In
the Fraser River, Wellington Bar (Fig. 2C, D) is a mid-channel island
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CHANNEL BARS IN WANDERING GRAVEL-BED RIVERS
TABLE 1.— Fraser and Squamish River statistics.
River
Drainage Area (km2)
Mean Annual Flow (m3 s21)
Flood of Record (m3 s21)
Wandering Reach (km)
Mean Width (m)
Mean Depth (m)
Slope
Surface D16 (mm)
Surface D50 (mm)
Surface D84 (mm)
Fraser
Squamish
250 000
3 4101
, 17 2002
55
5123
6.63
0.000184
5–84
11–184
17–294
3 600
2395
2 6106
10.5
, 707
, 2.57
0.00158
25–388
55–808
93–1388
1
at Mission (Water Survey of Canada Station 08MH024); 229 May 1894; 3at
Agassiz (McLean et al. 1999); 4at Wellington Bar (McLean et al. 1999); 5at
Brackendale (Water Survey of Canada Station 08GA022); 68 October 1984; 7at
Ashlu Bridge; 8at TFLENT Bar (Brierley and Hickin 1985).
about 1.1 km wide and 3.2 km long, positioned 6.6 km downstream of
the Harrison River confluence at 7 to 8 m above sea level.
Aerial Photographs
Channel bars, vegetation, and channel boundaries were mapped from
rectified aerial photographs to identify patterns of channel and bar
change from 1943 to 2001 using ArcView software. The photographs were
rectified digitally using ER Mapper software (Leys and Werritty 1999).
Analyzed photographs were taken at unevenly spaced intervals of ten
years or less in which discharge was relatively low and bars were
emergent.
Channel-Bar Topography and Bathymetry
Bar-top surfaces were surveyed at each site using a level and stadia rod
to topographically correct the GPR profiles. The topographic surveys
were tied to UTM coordinates through GPS surveys, to align the GPR
grids with the bathymetry, and to position the grids on rectified aerial
photographs.
Channel-bottom surveys of the Squamish River were completed in 2001
using a Lowrance X-16 chart recorder mounted on a 3-m-long inflatable
boat. Channel-bottom surveys of the Fraser River were completed in
1952, 1984, and 1999 (McLean 1990; McLean and Church 1999).
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Ground-Penetrating Radar
Ground-penetrating radar enabled the examination of the entire bar
thickness, from channel base to bar top. In contrast, trenching provided
incomplete data because high water tables limited sedimentary analysis to
bar-top deposits, which are a small proportion of the bar thickness.
A pulseEKKO IV GPR system was used with a 400 V transmitter.
Three antenna frequencies (200, 100, and 50 MHz) were used at each bar
to vary the depth of penetration and image resolution of subsurface
structures. The 100 and 50 MHz antennas imaged sedimentary structures
to depths of about 15 and 25 m, respectively, whereas 200 MHz radar
profiles were limited to 10 m.
Approximately 1 km of ground was profiled in rectilinear grids
(, 200 m 3 , 200 m) on each bar in October 2000. The antennas were
oriented perpendicular to the direction of travel at fixed trace spacings
with constant separation between antennas (Table 2). An average velocity
of 0.085 m ns21 was calculated from common-midpoint surveys at each
site. The radar profiles were processed for: time-zero adjustment, dewow
to correct for signal saturation, 7-point down-trace and 2 trace-to-trace
averaging to improve the signal-to-noise ratio, and automatic gain
control to compensate for signal attenuation with depth. All traces were
stacked 128 times.
Radar Interpretation
Radar facies and radar elements were identified using the principles of
radar stratigraphy (Beres and Haeni 1991; Jol and Smith 1991) derived
from seismic stratigraphy (Mitchum et al. 1977). Radar facies are
mappable, 3D units composed of reflections whose internal reflection
configuration (e.g., shape, orientation), continuity, amplitude, polarity,
spacing, and external 3D geometry differ from adjacent units. Radar
elements combine closely related facies into facies associations, and are
characterized by the facies assemblage, their external form, and internal
geometry (cf. Allen’s (1983) architectural elements).
To avoid frequency-dependent radar interpretations (Woodward et al.
2003), we imaged the subsurface with three antenna frequencies to allow
GPR profiles of the same strata to be interpreted at three different scales.
This process of interpretive redundancy aids in identifying facies and the
subsurface architecture.
Genetic interpretations of radar facies and elements are derived from
observations of bedform and barform morphology, geometry, sediment
organization seen in cut-bank exposures and trenched sections, patterns
FIG. 1.— Location of TFLENT Bar (TB) and Wellington Bar (WB) sites in the Squamish and Fraser rivers,
British Columbia.
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C.L. WOOLDRIDGE AND E.J. HICKIN
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FIG. 2.—Aerial views of the channel bar sites. A) TFLENT Bar (TB) in the wandering reach upstream of the abrupt transition to a meandering planform, Squamish
River. B) GPR grid imaged on TFLENT Bar. The thicker line segments show the locations of the GPR profiles shown in Figures 6 and 7. C) Wellington Bar (WB) and
other islands dividing flow in the Fraser River. D) GPR grid imaged on Wellington Bar. The thicker line segments show the locations of the GPR profiles shown in
Figures 10, 11, and 12. British Columbia Government photographs (A) 5012:244, (B) 96036:19, and (C) 99001:22,29. Photograph (D) SRS6164:90 courtesy of the
Department of Geography, UBC.
of bar change mapped from aerial photographs, scour-and-fill patterns,
and channel-bed topography mapped from bathymetry.
Reflection orientations are stated in reference to mean flow directions
with respect to the orientation of the channel belt (river-scale flow, not
local flow). All dip angles reported are apparent dip angles.
MORPHOLOGY AND SEDIMENTATION IN WANDERING GRAVEL-BED RIVERS
Wandering rivers have a morphology that is intermediate between
braiding and meandering with multiple channels separated by islands
(islands are vegetated bars; Neill 1973; Lewis and McDonald 1973;
Kellerhals et al. 1976) rather than channel division by bars common to
TABLE 2.— GPR parameters.
Frequency,
f (MHz)
Trace
Spacing (m)
Antenna
Separation (m)
Sampling
Rate (ps)
200
100
50
0.10
0.25
0.50
0.5
1.0
2.0
800
800
1600
braiding rivers. Wandering rivers have an irregularly sinuous, single
dominant channel with one or two secondary channels that have reduced
velocities and carry reduced flow volumes. This channel arrangement,
along with moderate bedload transport rates, leads to the stabilization of
mid-channel bars and their subsequent evolution to islands (Morningstar
1987; Desloges and Church 1989). The planform of wandering gravel-bed
rivers contrasts with that of braiding rivers, where pervasive channel
splitting leads to individual threads of flow shifting frequently as bar
deposition and erosion occur (Ashmore 1991).
In wandering rivers portions of compound bars are actively reshaped
every year, but numerous bars and islands have persisted for more than
50 years and are deemed to be stable channel elements (with many of
them formally named in both rivers). The reoccupation and excavation of
preexisting channels is likely more frequent than the development of new
channels in wandering rivers (Gottesfeld and Johnson Gottesfeld 1990).
Wandering rivers tend to develop laterally unstable ‘‘sedimentation
zones’’ in which channel-bar growth, bank erosion, and bar shifting
occurs (Church 1983). Eroded sediment is transported through stable
channel zones and deposited downstream in another sedimentation zone,
initiating channel instabilities and bar growth (Desloges and Church
1987; McLean and Church 1999; McLean et al. 1999).
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FIG. 3.— Typical barforms, bedforms, and surface features of wandering gravel-bed Fraser and Squamish rivers. A) Definitions of barforms and channel types in
wandering rivers, Squamish River. B) Slipface margin (1 m thick) of a kilometer-scale unit bar, Wellington Bar, Fraser River. Note sandy dunes and ripples in
foreground. C) Bedload sheet (0.10 to 0.15 m thick) prograding over an older, armored bar surface, Fraser River. Hand trowel (0.15 m high) is circled for scale.
Photograph by D.G. Ham. D) Island cut-bank exposure with gravels (deposited by bedload sheets) encased in horizontally bedded and structureless bar-top sands
overlying crudely, horizontally bedded sandy gravels, Fraser River. 0.3 m ruler is circled for scale. Photograph by M.C. Roberts. E) Logjam instigating scour-hole
development, TFLENT Bar, Squamish River.
The magnitude of channel-forming discharge is important in governing
bar formation because gravel transport appears to increase exponentially
above the critical threshold of motion for gravel (McLean et al. 1999).
The two rivers have different hydrologic regimes, and in consequence,
contrasting bed-material transport regimes. In the Squamish River,
sediment is episodically mobilized by high-magnitude, short-duration,
autumn rains (events that last on the order of days). In the Fraser River,
the annual, early summer snowmelt flood transports bedload for
a number of weeks.
Figure 3A shows morphological features common to wandering rivers
including unit bars (Fig. 3B), and gravelly bedload sheets on bar surfaces
(Fig. 3C) and encased in bar-top sands (Fig. 3D). Bar surfaces are usually
armored with a layer of open-framework gravels (Fig. 3C), but subsurface
deposits are matrix-filled sandy gravels (Fig. 3D). The surface and
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C.L. WOOLDRIDGE AND E.J. HICKIN
subsurface gravel clasts are similar in size (McLean et al. 1999). Channel
sands (1 to 3 m thick) overlie the gravelly deposits (Fig. 3D) on the
highest portion of the bars and are colonized by alder and cottonwood
(Boniface 1985). Surface deposits of sand (dunes and ripples, Fig. 3B) are
also found on lower bar areas, such as on the downstream margins of
bars, in cross-bar chutes, along secondary channels, and in sloughs.
Chutes are shallow channels (up to 3 m deep) that cut across bar
interiors, and sloughs are abandoned channels that receive moderate- and
high-stage flows (Fig. 3A). Secondary channels are either former main
channels that are still active or chutes that were excavated but never
occupied by the main channel (Fig. 3A). Logjams (Fig. 3E) affect
sediment transfer and influence bar growth in the Squamish River
(Hickin 1984), but they are not as important in governing bar growth in
the much larger Fraser River.
EVOLUTION AND STRATIGRAPHY OF TFLENT BAR, SQUAMISH RIVER
Evolution of TFLENT Bar
TFLENT Bar evolved from an assemblage of small mid-channel
islands and bars separated by multiple channels in 1951, to a large bankattached compound bar in a single-thread channel (with subordinate
sloughs) by the 1970s (Fig. 4). In 1984, the flood of record eroded islands
in the reach and locally deposited gravel onto the bar head but did not
immediately reorganize the reach (Hickin and Sichingabula 1988).
Subsequently, however, the enlarged bar head forced the thalweg against
the western bank, instigating bank retreat over the next decade (Fig. 4).
During this time, two unit bars (labeled 1 and 2 in the 1996 panel of Fig. 4)
accreted to the western edge of TFLENT Bar. Unit bar 1 was deposited
by 1994, and between 1994 and 1996 unit bar 2 (the site of GPR profiling)
aggraded vertically to become a prominent barform. After 1996, the
growth of unit bar 2 deflected formative flows away from unit bar 1,
enabling a dense cover of 3-m-high willow to become established on unit
bar 1 by 2000. Willow was beginning to colonize the surface of unit bar 2
by 2000 as well.
Radar Facies and Elements of TFLENT Bar
The GPR grid imaged on TFLENT Bar is shown in Figure 2B, with
two GPR lines displayed in Figures 6 and 7. The interpretation of the
stratigraphy is uniquely derived from the grid of GPR profiles,
bathymetry (Fig. 5), and aerial photographs (Fig. 4).
Radar Facies 1: Subhorizontal, Continuous, Subparallel Reflections
Radar facies 1 is characterized by stacked (1 to 5 m thick), horizontal
to subhorizontal, continuous (20 to 150 m long), parallel to subparallel
reflections (Figs. 6, 7). The facies is preserved at all levels within the
stratigraphy, and in some cases its ubiquitous extent dominates the
succession. Reflections can be traced in both flow-parallel (Fig. 6) and
flow-normal (Fig. 7) GPR profiles because their subhorizontal, subparallel character is three-dimensional.
Interpretation: Vertical-Accretion Deposits.—Radar facies 1 is interpreted as vertically accreted gravelly sheets deposited from bedload sheets
migrating across bar surfaces and channel floors. Bedload sheets (Whiting
et al. 1988; Livesey et al. 1998), formerly described as diffuse gravel sheets
by Hein and Walker (1977), are low-amplitude, relatively planar features,
up to 0.2 m thick (Fig. 3C), composed of ‘‘normally loose’’ sediment
(Church 1978). Individual sheets may be imaged in 200 MHz profiles
(Fig. 7) because their thickness is roughly equivalent to the vertical
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resolution of the reflections. The subparallel nature of the facies is
probably due to the intermittent nature of bedload transport whereby
bedload sheets overtake and bury other stalled sheets (Ashmore 1991),
creating subdued topographic relief. Sheets are commonly preserved on
bar-top surfaces (Ferguson and Werritty 1983) because, during falling
stages as discharge drops below the threshold of motion for gravel, flows
are not competent to rework the sediments, stranding the sheets on bar
tops. The facies occurs at all stratigraphic levels because it likely
represents the dominant process of deposition in these and other
wandering gravel-bed rivers.
Radar Facies 3: Low-Angle (2 to 8u ), Downstream-Dipping, Subparallel
Reflections
Radar facies 3 is characterized by low-angle (2 to 8u), offlapping,
divergent to subparallel reflections (1 to 7 m thick, 25 to . 200 m long)
that dip downflow (Fig. 6). Extensive sets of downlapping tangential
reflections occur at all stratigraphic levels. The flow-normal radar image
is made up of subhorizontal and undulose reflections (Fig. 7).
Interpretation: Downstream-Accretion Deposits.—Radar facies 3 is
interpreted as downstream-accretion deposits in which bedload sheets are
deposited on the downstream margins of bars (Fig. 6). The facies
documents the migration of gravelly bedload sheets over bar tops or
along channel floors onto downstream bar margins, causing barforms to
aggrade and translate downstream. The subhorizontal and undulose flownormal reflections indicate that sedimentation is influenced by mean flow
conditions depositing extensive sheet-like strata, as well as by more
variable local flow conditions depositing larger low-relief bedforms
(Livesey et al. 1998).
Radar Facies 5: Small- to Medium-Scale (0.5 to 3 m), Steeply Inclined (13
to 26u ), Oblique Reflections
Radar facies 5 is characterized by continuous sets (10 to . 90 m long)
of small- to medium-scale (0.5 to 3 m thick), roughly parallel, steeply
inclined (13 to 26u ), oblique reflections that dip downflow (Fig. 6) and
normal to flow (Fig. 7). The facies is typically found in packages that are
bounded above and below by radar facies 1 and in some instances the
packages thicken downflow. The facies is found at all stratigraphic levels,
but it rarely dominates the entire succession.
Interpretation: Bar-Margin Slipface Deposits.—Radar facies 5 is
interpreted as bar-margin slipface deposits indicative of gravelly bedload
sheets periodically avalanching and passing over high-relief bar margins
into deeper water at high-stage flows. Bar margins are typically oriented
downflow, but in many cases flow crosses the bar top obliquely, causing
the barform to prograde cross-flow and downstream.
Changes in flow competency during bar formation cause the angle of
the slipfaces to vary, such that the angle typically declines downstream
along a set of slipfaces. Reactivation and erosion of bar margins during
falling stages reduces the angle of the slipface, as does sand deposition on
the slipface and at its toe when discharge falls below the threshold of
motion for gravel.
Radar Facies 6: Large-Scale (4 to . 10 m), Steeply Inclined (11 to 28u ),
Oblique Reflections
Radar facies 6 is characterized by large-scale (4 to . 10 m thick),
parallel, steeply inclined (11 to 28u ), oblique reflections that dip
downvalley and in some cases can be traced up-dip into horizontal
R
FIG. 4.—Evolution (1951 to 1996) of TFLENT Bar, Squamish River. Changes in channel position and bar morphology superimposed on GPR grid (dashed box) and
1996 British Columbia Government photograph 96036:19, Q (discharge) 5 364 cumecs (m3 s21). Flow is to the bottom of the page.
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CHANNEL BARS IN WANDERING GRAVEL-BED RIVERS
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C.L. WOOLDRIDGE AND E.J. HICKIN
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FIG. 5.—Bathymetry across TFLENT Bar, Squamish River. Sounding locations are shown in the photograph. A) Sounding across a riffle in a straight reach adjacent
to GPR line (Fig. 7) along the bar top. B) Cross-channel sounding across a subaqueous mid-channel bar. C) Sounding along a steeply dipping (19u) 4-m-deep scour hole.
D) Cross-channel sounding across the scour (dipping 10 to 13.5u). 0.0 m depth is the water level at low stage flow (discharge < 50 m3 s21).
FIG. 6.—GPR profile (100 MHz), TFLENT Bar, Squamish River. A) Flow-parallel profile. B) Interpreted profile. Radar facies 1 (vertical accretion), 3 (downstream
accretion), 5 (slipface accretion), 6 (delta foresets and topsets), and radar elements Ia (channel deposits) and I(3) (chute filled with downstream-accretion deposits) are
delineated. Storeys 1 and 2 record the thickness of the Holocene channel-belt deposits. Intersection with Figure 7 is shown.
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CHANNEL BARS IN WANDERING GRAVEL-BED RIVERS
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FIG. 7.— GPR profile (200 MHz), TFLENT Bar, Squamish River. A) Flow-normal profile. B) Interpreted profile. Radar facies 1 (vertical accretion), 5 (slipface
accretion), 6 (delta foresets and topsets), and radar elements I (chute deposits) and I(3) (chute filled with downstream-accretion deposits) are delineated. Intersection with
Figure 6 is shown.
reflections (Fig. 6). The flow-normal radar image is composed of
subhorizontal reflections (Fig. 7).
Interpretation: Delta Foreset (and Topset) Deposits.—Radar facies 6 is
interpreted as delta foresets in which the inclined reflections dip close to
the 25u angle of repose of gravel found on gravelly delta fronts (D.G.
Smith 1991). The large-scale character of the deposit, both its thickness
and widespread extent, suggests that local channel scouring did not
produce the foresets. Also, the stratigraphic thickness of the facies varies
from 4 to 10 m, but the top of the facies always occurs at , 200 ns
(, 8.5 m depth), indicating progradation into a standing body of water.
Further, some of the steeply dipping reflections can be traced up-dip into
horizontal reflections suggestive of depositional topset strata (Jol and
Smith 1991).
Radar Element I: 2D, Bounding, Concave-Up Reflections
Radar element I is distinguished by a 2D, basal, concave-up reflection
that truncates adjacent reflections and is filled with a mix of
subhorizontal and/or steeply inclined reflections (Figs. 6, 7). The element
extends 30 to 45 m laterally, with depths approaching 4 m, and the
concave-up edges dip 6 to 11u into the center of the form. There are few
preserved forms, and they occur within the middle and upper portions of
the bar stratigraphy.
Interpretation: Channel and Chute Deposits.—Radar element I is
interpreted as main-channel and chute-channel fills bounded by erosional
concave-up channel edges. The chutes and main channels were filled by
a number of depositional events during abandonment.
Linking Radar Stratigraphy to the Evolution of TFLENT Bar
A prominent undulating reflection , 9 m below the surface of the bar
partitions the stratigraphic succession into two sedimentary bodies
(Figs. 6, 7). Below 9 m, the radar stratigraphy images facies 6 with
large-scale, steeply inclined reflections dipping downvalley that trace
delta-front progradation into a flooded Squamish River valley in the late
Pleistocene (Friele et al. 1999). The delta foresets are overlain by
subhorizontal reflections recording the deposition of topset beds before
relative sea level dropped and alluvial sedimentation commenced.
Above 9 m, the radar stratigraphy images the alluvial fill, which we
interpret to be made up of two storeys whose thicknesses are roughly
equivalent to the depth of formative flows in the modern channel. The
storeys are separated by bounding surfaces defined by systematic
reflection terminations such as erosional truncation of the chute edges
in storey 1 (radar element I(3) in Fig. 7), and the depositional onlap of
slipface deposits between 120 and 140 m in storey 2 (radar facies 5 in
Fig. 6). The pervasive extent of these bounding surfaces differentiates
them from internal scour surfaces within a storey such as the erosional
surface bounding the chute channel (radar element I(3) in Fig. 7) which
locally scoured into the bar strata. Further evidence of this bipartite
division is the preservation of the chute element I(3) in storey 1 and its
absence in the photographic record (Fig. 4). The 3D geometry of the fill
shows that the chute was filled with downstream-accretion deposits (radar
facies 3), yet there is no evidence of a chute directing flow to the
southwest between 1951 and 1996. Moreover, the floodplain occupied
that location prior to 1951, indicating that storey 1 represents Holocene
deposits laid down before 1951.
In contrast, the GPR-imaged stratigraphy in storey 2 matches the
depositional history traced in the photographic record and preserves
the style of unit-bar sedimentation and history of compound-bar
development. The channel form , 7 m below the bar surface (radar
element Ia in Fig. 6) is the subsurface expression of the channel
locally scouring into storey 1 in response to bar growth, which constricted
the channel after the flood of 1984. The position of the buried
paleochannel coincides with the western edge of the former floodplain
up to 1967 and records a flow direction that matches the main channel
across the site up to 1984. Subsequent channel shifting, bank erosion, and
bar deposition after 1984 displaced the channel farther westward, forcing
flow away from the site. The growth of unit bar 2 after 1984 (the
uppermost 3 m of strata in storey 2) was achieved by bedload sheets
migrating along the surface of the bar, which caused it to aggrade
vertically and form high-relief bar margins. Sediment avalanched over
and filled the lee of the bar margins, forcing the barform to prograde
downstream and override the paleochannel. The contrasting modes of
sedimentation within the storey illustrate the multidirectional growth of
the larger compound bar.
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CHANNEL BARS IN WANDERING GRAVEL-BED RIVERS
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EVOLUTION AND STRATIGRAPHY OF WELLINGTON BAR, FRASER RIVER
Evolution of Wellington Bar
In 1943, Wellington Bar was a large, bank-attached, unvegetated bar
(Fig. 8). A 100 year flood in 1948 eroded a chute channel across the bar
head adjacent to the southeastern channel margin. By 1952 the chute had
incised into the bar (evident in the 1952 bathymetry in Fig. 9A) and
detached it from the bank, forcing it to a mid-channel position. During
the next decade, high-stage flows excavated the chute and shifted the
thalweg to the southeast channel. The avulsion reduced flow volumes and
velocities in the former main channel, leading to the episodic deposition
and erosion of several mid-channel bars and the accretion of sediment to
the northwest margin of Wellington Bar by 1979. Continued bar growth
from 1967 to 1993 broadened the bar head (the site of GPR profiling) and
enabled vegetation to colonize the higher (more stable), central portion of
Wellington Bar by 1986. The bar head vertically aggraded 2 m (between
the 1984 and 1999 bathymetry in Fig. 9A), causing the tip of the bar to
migrate upstream until 1999, where it remained relatively unchanged
through 2001.
Radar Facies and Elements of Wellington Bar
The GPR grid imaged on Wellington Bar is shown in Figure 2D with
three GPR lines displayed in Figures 10, 11, and 12.
Radar Facies 2: Low-Angle (1 to 6u ), Cross-Stream Dipping, Subparallel
Reflections
Radar facies 2 is characterized by continuous sets (55 to . 150 m long,
1 to 8 m thick) of stacked, low angle (1 to 6u, typically 5 to 6u), parallel to
subparallel reflections that dip normal to flow (Fig. 10). The facies makes
up a minor portion of the alluvium on Wellington Bar, but on point bars
it dominates the stratigraphy from channel base to bar top (Wooldridge
2002). The flow-parallel radar expression is made up of continuous,
parallel, subhorizontal to horizontal reflections (Fig. 12).
Interpretation: Lateral-Accretion Deposits.—Radar facies 2 is interpreted as lateral-accretion deposits that record the progressive onlap of
gravelly bedload sheets onto bar surfaces, causing barforms to build out
laterally into the channel. This interpretation is supported by the flownormal apparent dip angle of the reflections matching, and being
coincident with the dip angle of the upper bar surface. Stalled bedload
sheets on bar surfaces and the flow-parallel, subhorizontal reflections
document the continuous nature of sheet-like sedimentation.
Radar Facies 4: Low-Angle (, 1u ), Upstream-Dipping, Parallel
Reflections
Radar facies 4 is characterized by stacked (. 6 m thick), continuous
(. 200 m long), low-angle (, 0.5u), parallel reflections that dip upstream
(Fig. 11). The facies is found across the bar head, but it is limited to the
upper portion of the stratigraphy. The reflections onlap an upstreamdipping lower bounding surface and hence the thickness of the radar
facies increases upflow. The flow-normal radar profiles show subhorizontal reflections (Figs. 10, 12).
Interpretation: Upstream-Accretion Deposits.—Radar facies 4 is
interpreted as upstream-accretion deposits. The migration of gravelly
bedload sheets onto an upstream-dipping bar surface causes the strata to
dip upstream and the bar to accrete upstream. The apparent dip angle of
the reflections is coincident with the , 1u upstream dip of the bar surface.
FIG. 9.— Bathymetry across Wellington Bar, Fraser River. A) 1999, 1984, and
1952 soundings show typical wandering river cross-channel geometries. 0 m
elevation is mean sea level. 1999 water level is at low stage flow (discharge 5
677 m3 s21). Extent of bar surface profiled with GPR is shown. Bathymetry
courtesy of the Department of Geography, UBC. B) 1952 (British Columbia
Government photograph 1622:24 taken 2 October 1952, discharge 5 2350 m3 s21),
and C) 1999 sounding locations (NNNN) (British Columbia Government photographs
99001:22, 29 taken 20 March 1999, discharge 5 701 m3 s21).
r
FIG. 8.—Evolution (1943 to 1999) of Wellington Bar, Fraser River. Changes in channel position and bar morphology superimposed on GPR grid (dashed box) and
1999 British Columbia Government photograph 99001:29 taken 20 March 1999, Q (discharge) 5 701 cumecs (m3 s21). Flow is from top right to bottom left.
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C.L. WOOLDRIDGE AND E.J. HICKIN
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FIG. 10.— GPR profile (50 MHz), Wellington Bar, Fraser River. A) Flow-normal profile. B) Interpreted profile. Radar facies 1 (vertical accretion), 2 (lateral
accretion), 4 (upstream accretion), 5 (slipface accretion), 6 (delta foresets), and radar elements II and IIa (scour and fill) are delineated. Storeys 1 and 2 record the
thickness of the Holocene channel-belt deposits. Intersection with Figure 11 is shown.
Radar Element II: 3D, Steep-Sided (5 to 19u), Scallop-Shaped Reflections
Radar element II is bounded by 3D, scallop-shaped reflections. The
steep-sided reflections dip , 7u downstream (Figs. 11, 12) and 5 to 18u
cross-flow (Fig. 10) into the center of the element, which is up to 16 m
thick, . 150 m long (parallel to flow), and . 180 m wide (normal to flow).
The radar stratigraphy records two sets of reflection packages with the
smaller set (radar element IIa, up to 6.5 m thick, 30 m long parallel to
flow, and 50 m wide normal to flow) locally entrenched within the larger
set (radar element II; Figs. 10, 12). Radar element IIa shows flow-parallel,
scallop-shaped reflections dipping downstream between 13 and 19u
(Fig. 12). The reflections truncate each other in a downstream direction at
similar depths (, 13.5 m below bar surface) and are filled with reflections
showing variable dip. Flow-normal profiles record symmetrical, troughshaped bounding reflections that dip , 18u into the center of the element
and are filled with a set of steeply dipping reflections (Fig. 10).
Interpretation: Scour-and-Fill Deposits.—Radar elements II and IIa
are interpreted as scour-and-fill structures. The continuous, highamplitude bounding reflections are erosional scours that have truncated
the adjacent strata. This interpretation is contingent on the threedimensional scallop-shaped bounding form of the element (Figs. 12,
5C, D), because in two dimensions the troughs appear as channel forms
(Figs. 10, 5D). The scours are filled by strata that show changes in dip
angle, a consequence of the unsteady process of sediment avalanching
into the scours from both the upstream edge and the sides of the
scours.
FIG. 11.— GPR profile (50 MHz), Wellington Bar, Fraser River. A) Flow-parallel profile. B) Interpreted profile. Radar facies 1 (vertical accretion), 3 (downstream
accretion), 4 (upstream accretion), 5 (slipface accretion), 6 (delta foresets), and radar element II (scour and fill) are delineated. Intersection with Figure 10 is shown.
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CHANNEL BARS IN WANDERING GRAVEL-BED RIVERS
855
FIG. 12.—Three-dimensional GPR profile (50 MHz), Wellington Bar, Fraser River. A) 3D profile. B) Interpreted profile. Radar facies 1 (vertical accretion), 2 (lateral
accretion), 3 (downstream accretion), 4 (upstream accretion), 5 (slipface accretion), 6 (delta foresets), and radar elements II and IIa (scour and fill) are delineated.
Linking Radar Stratigraphy to the Evolution of Wellington Bar
A wavy reflection , 17 m below the surface of the bar separates
deeper, low-amplitude radar reflections from high-amplitude reflections
in the Wellington Bar stratigraphy (Figs. 10, 11, 12). Similarly to
TFLENT Bar, the deeper stratigraphy shows steeply inclined foresets
(radar facies 6) dipping downvalley, tracing the progradation of a delta
front into a flooded Fraser Lowland in the late Pleistocene during
deglaciation (Clague et al. 1982). As alluvial sedimentation commenced,
the Fraser River incised into and partly eroded the delta foresets. The
foresets were likely preserved here because of their mid-valley position
where the river is unconfined (the channel belt is not impinging on hard
points) and scour depths are limited.
The upper 17 m of the stratigraphy is split into two storeys by
a subhorizontal bounding surface about 8 m below the bar surface. The
bounding surface erosionally truncates the scour-and-fill structures and
corresponds very closely to the depth of the channel floor mapped in the
1952, 1984, and 1999 bathymetry (Fig. 9A). This suggests that the
architecture of storey 2 (above 8 m depth) should match the evolution of
the bar recorded in the photographic record (Fig. 8). The deposits in
storey 2 are the product of flow divergence across the mid-channel bar
head with gravelly bedload sheets laterally accreting to the northwest bar
margin, depositing low-angle strata after the thalweg had switched to the
southeast channel by 1967. As flow diverged across the southeast portion
of the bar, it cut a high-relief bar margin over which sediments
avalanched to form slipface deposits. Subsequent sheet-like deposition
associated with an extensive (, 1 km wide) gravelly unit bar prograding
over the bar between 1984 and 1999 caused the barform to grow upstream
and laterally. Neither storey images the architecture of Wellington Bar
when it was a bank-attached barform in 1943 (Fig. 8), so it is not possible
to reconstruct the transition of the bank-attached bar to a mid-channel
bar.
Storey 1 is made up of nested scour-and-fill structures (radar elements
II and IIa) eroded into downstream-accretion and slipface-accretion
deposits. The smaller scours are locally entrenched into the fill of the
larger scour and were likely formed in response to barforms migrating
through and constricting a secondary channel, causing it to overdeepen.
In contrast, the larger scour undoubtedly records the constriction of the
main channel because it scales to modern scours that erode up to 16 m
and extend across most of the width of the main channel.
A MODEL OF GRAVELLY CHANNEL-BAR DEPOSITION IN WANDERING
GRAVEL-BED RIVERS
Figure 13 summarizes the geometries of the six radar facies and two
radar elements identified in the TFLENT and Wellington Bar stratigraphies. These same facies and elements were observed at four other sites
that we analyzed on two compound bars in the Fraser River, bankattached Queens Bar and a point bar, Calamity Bar (Wooldridge 2002).
This suggests that the results presented here are representative of bars
typically found in wandering rivers. The geometry, proportion, and
spatial distribution of the facies and elements are used to construct
a model of gravelly channel-bar deposition in the two wandering gravelbed rivers (Fig. 14). The model also depicts the hierarchical arrangement
of bedload sheets, unit bars, and compound bars, along with morphologic
features such as logjams, hard points (bedrock), chutes, sloughs,
856
C.L. WOOLDRIDGE AND E.J. HICKIN
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CHANNEL BARS IN WANDERING GRAVEL-BED RIVERS
857
FIG. 14.— A model of gravelly channel-bar
deposition in the Fraser and Squamish
wandering gravel-bed rivers based on the
integration of GPR, bathymetry, and aerial
photograph data.
secondary and main channels, and bar-top sands colonized by vegetation
common to wandering gravel-bed rivers. Sandy deposits were not
examined or included in the model because channel-sand facies have
already been described on TFLENT Bar, and in a wandering gravel-bed
river facies model (Brierley 1989, 1991b).
The model reflects our observation that vertical-accretion deposits
constitute , 40% of channel-bar strata and thus dominate the
architecture of wandering rivers. This pattern is also the most prevalent
in the Roberts et al. (1997) GPR images of floodplain and channel-bar
sediments in a wandering river. Observations of massive or crudely
horizontally bedded cobble and gravelly strata in wandering-river cutbank exposures further suggest that vertical accretion is the prevailing
mode of sediment deposition (Ferguson and Werritty 1983; Desloges and
Church 1987; Passmore and Macklin 2000).
The model shows that slipface deposits make up , 20% of bar deposits.
Ferguson and Werritty (1983) note that well defined foresets are rare in
cut-bank exposures, but Roberts et al. (1997) also imaged slipface
deposits, indicating that high-relief bar margins occur on many bars but
are not present on all bars.
Lateral-accretion deposits constitute , 70% of point-bar deposits but
only , 10% of the alluvial architecture. Downstream-accretion deposits
make up the bulk of distal unit-bar sediments (, 60%), but only , 10% of
the architecture. Roberts et al. (1997) also imaged thick sets of lateralaccretion and downstream-accretion deposits, although low-angle inclined strata (either lateral or downstream) are not commonly observed in
cut-bank exposures.
Partial and complete channel-fill deposits are preserved in the
architecture (, 7%), and similar deposits have also been imaged in
floodplain sediments (Roberts et al. 1997).
The model synthesizes the first descriptions of upstream-accretion
deposits, and scour-and-fill structures in wandering rivers. Upstreamaccretion deposits make up the smallest proportion of the architecture
(, 4%), suggesting that this style of sedimentation is not a primary
mechanism of bar growth. Scour-fill deposits are more commonly
preserved in the architecture (, 7%), but the process of scouring does
not appear to be widespread in wandering rivers.
DISCUSSION
The integration of GPR, bathymetry, and aerial photographs links largescale depositional processes and subsurface alluvial architecture for the
first time in wandering gravel-bed rivers. Yet, questions remain regarding
the uniqueness of wandering-river style. The multiple-channel character of
wandering rivers identifies them as braiding rivers (Galay et al. 1998),
although Nanson and Knighton (1996) refer to them as a type of
anabranching river. Braiding rivers are defined by multichannel flow
separated by bars, whereas anabranching rivers (of which wandering rivers
are a specific type) are characterized by multiple channels divided by stable
islands (up to bankfull stage). The division of flow around islands creates
independent flow patterns in adjacent channels, unlike those in braiding
rivers (Bridge 1993). The maintenance of stable islands reduces the
frequency of flow bifurcation and convergence and preserves different
proportions of sedimentary packages in braiding and wandering rivers.
The nature of frequent channel shifting in braiding rivers preserves
moderate amounts of complete and truncated, partial channel fills in the
sedimentary record (Ramos and Sopena 1983; Vandenberghe and van
Overmeeren 1999; Ekes 2000). This contrasts with wandering rivers,
where the infrequent occurrence of channel avulsions does not permit
many channels to be abandoned, filled, and potentially preserved within
the alluvial architecture. Similarly, the excavation and reoccupation of
abandoned channels also limits opportunities to preserve channel fills.
The deepest scours in wandering rivers (excluding scours caused by
bedrock impingements) occur adjacent to recently accreted unit bars that
have constricted the channel. Scouring deepens channel floors, before
r
FIG. 13.— Radar configurations in the wandering gravel-bed Squamish and Fraser rivers. Radar facies 1 to 5 and radar elements I and II are typical channel-bar
reflection configurations. Radar facies 6 images deltaic sedimentation. The facies are depicted at different antenna frequencies because these reflection profiles provide the
clearest images of the structures.
858
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C.L. WOOLDRIDGE AND E.J. HICKIN
flow laterally erodes opposing channel banks or island margins. Scour
deposits make up a smaller proportion of the architecture, because of the
infrequent accretion of unit bars. Confluence scours are not a significant
depositional mechanism, because island stability maintains established
channel networks and limits channel avulsions and bar migration. In
braiding rivers, however, rapid bar migration and frequent channel
shifting form numerous confluence scours across the channel belt (Best
1987; Bridge 1993). The scour-fill deposits are preserved in the
architecture (Siegenthaler and Huggenberger 1993), unlike other facies
that are reworked as barforms are mobilized (Salter 1993; Best and
Ashworth 1997).
Lateral accretion is locally significant in directing point-bar growth and
the enlargement of mid-channel bars in both wandering and braiding
rivers (N.D. Smith 1974; Ori 1982; Ramos and Sopena 1983; Ashmore
1991). It is a significant and widespread depositional style in braiding
rivers with slowly migrating bars (Lunt et al. 2004). The accretion of
sediment onto gently dipping bar-tail margins is important in directing
down-bar growth during some phases of bar migration (S.A. Smith 1990;
Lunt et al. 2004). Of less importance in these rivers is the case where flow
expansion across a bar head enables unit bars to accrete onto the bar
head, which in turn forces the upstream translation of the compound bar.
This style of bar formation is not commonly preserved in wandering-river
or braiding-river successions (Lunt and Bridge 2004).
The majority of bar deposits in wandering river successions are made
up of horizontal, parallel, continuous strata (vertical-accretion deposits).
This has also been observed in gravelly deposits of ancient and modern
braiding rivers, indicating that gravels are generally transported as
individual bedload sheets in these rivers (N.D. Smith 1974; Hein and
Walker 1977; Ramos and Sopena 1983; S.A. Smith 1990). Trough crossstrata deposited by gravel dunes typically constitute a very small
proportion of braiding-river architecture (Morison and Hein 1987; S.A.
Smith 1990), although the work of Lunt et al. (2004) provides an
exception; they suggest a model of braid-bar sedimentation in which
trough cross-strata make up a high proportion of the architecture, with
planar strata rarely preserved.
The moderate abundance of continuous sets of slipface deposits in
wandering rivers is much greater than the limited sets typically observed
in braiding-river deposits (Eynon and Walker 1974; N.D. Smith 1974;
Steel and Thompson 1983; Ramos and Sopena 1983; Morison and Hein
1987; S.A. Smith 1990; Lunt et al. 2004). Extensive sets of continuous
slipfaces are not formed in braiding rivers because frequently changing
flow and sediment transport in developing flow expansions interrupts
the unidirectional growth of bars (Ashmore 1991). In contrast, stable
bars and islands in wandering rivers hinder flow expansion and maintain
the directionality of flow and routing of sediment to bar edges and
slipfaces.
The spatial distribution of bar-top sand deposits described by Brierley
(1991a, 1991b) also reveals this differential pattern of sediment deposition. In braiding reaches, sandy facies assemblages are complexly
arranged across bar tops in highly discontinuous patterns. Chutes and
channels adjusting their orientation at different flow stages deposit
variable thicknesses of sand atop dissected and irregular gravel-bar
surfaces. The same sandy facies assemblages are observed in wandering
reaches, except that the sands are deposited in consistent down-bar trends
but irregular across-bar trends. The relative stability of the channels
directs more uniform flow orientations depositing sands atop gravelbar surfaces that have not been dissected or incised into by chute
channels.
These patterns of bar sedimentation demonstrate that compound bars
in braiding rivers evolve and respond to changes in local flow conditions,
while compound bars in wandering rivers react to decadal changes in
river-scale flow and/or sediment input (Church and Jones 1982; Church
1983). Correspondingly, large floods affect the stability of bars and
channels in wandering rivers, but floods do not produce immediate largescale changes such as channel avulsions. Rather, unit bars attached to
compound bars deflect flood-stage flows onto the edges of bars and banks
and erode small portions of the bars and banks, creating small-scale
channel changes. These changes are amplified by successive flows
transporting pulses of eroded sediment onto well-defined depositional
zones (sites of unit-bar attachment), which ultimately cause channel
shifting and bar growth.
While our model points to key differences between braiding and
wandering rivers, it also illustrates that concepts proven in braiding rivers
are also present in wandering ones. The idea that styles of bar
sedimentation occur independently of river size (scale independence)
has recently been demonstrated in the architecture of sand-bed and
gravel-bed braiding rivers (Best et al. 2003; Lunt et al. 2004). Scale
independence is also observed in these wandering rivers, in which the
same depositional styles are preserved in the Squamish River and in the
much larger Fraser River. Further, the geometry and type of facies
preserved in the lower storeys match those observed in the upper storeys,
indicating that the style of bar sedimentation and channel depths have not
changed in either river during the deposition of the two storeys.
The unequal size of the two wandering rivers is evident in the higher
stacking density of facies in the Squamish River architecture. Shorter sets
of facies indicate narrower channel and channel-belt widths, while thinner
facies point to shallower channels and lesser scour depths in the Squamish
River (, 7 m) than the Fraser River (. 16 m). The depth of scour has
also been found to control the geometry and stacking of channel and bar
deposits in the architecture of gravelly braiding rivers (Ashworth et al.
1999).
CONCLUSIONS
This study has presented detailed descriptions of all of the radar facies
and elements imaged in the alluvial architecture of the Fraser and
Squamish rivers. For the first time the internal structure of gravelly
sediments in wandering gravel-bed rivers has been linked to patterns of
deposition that control the evolution of barforms. It has been shown that
the evolutionary history of bars is fully revealed only if their study
integrates GPR profiles, bathymetry, and aerial photographs in order to
synthesize complete descriptions of bar architecture. A depositional
model of gravelly channel bars in the two rivers is presented and reveals
that the architecture is made up of depositional styles similar to those
observed in braiding-river successions, although there are some important
differences as well. In both river types, upstream-accretion deposits are
uncommon, lateral-accretion dominates point-bar deposits, downstreamaccretion deposits govern some phases of down-bar growth, and verticalaccretion deposits formed by the deposition of gravelly bedload sheets are
the most prevalent strata.
Differences in the sedimentology of braiding rivers and wandering
rivers largely reflect the relatively frequent migration of channels and bars
in braiding rivers, which preserve high proportions of channel and chute
fill, and confluence scour-and-fill deposits. The network of moderately
stable islands and channels in wandering rivers, on the other hand, limits
channel shifting and consequently preserves a low number of channel fills.
Moderate proportions of slipface strata and coherent patterns of sand
deposition along bar tops in wandering rivers provide evidence of
comparatively uniform flow orientations directing the attachment of
gravelly unit bars onto the margins of compound bars. These patterns of
bar sedimentation and channel shifting preserved in the alluvial
architecture appear to be signature characteristics of wandering
rivers. The occurrence of similar architecture in both the Fraser and
Squamish rivers suggests that the model likely applies to most wandering
gravel-bed rivers, but further testing is needed to confirm this wider
application.
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CHANNEL BARS IN WANDERING GRAVEL-BED RIVERS
ACKNOWLEDGMENTS
We thank the reviewers for their constructive critiques. Sean Todd, Joel
Epp, Sarah Baines, Solvej Patschke, Scott Babakaiff, Matt Cleary, Tim
Johnsen, Quinn Jordan-Knox, Channa Pelpola, Crystal Huscroft, and Greg
Matsuo are gratefully thanked for providing assistance in the field. Fraser
River bathymetry was graciously supplied by Dr. M. Church from the
Department of Geography, University of British Columbia. The project was
partly funded by the Natural Sciences and Engineering Research Council of
Canada and the Association of Professional Engineers and Geoscientists of
British Columbia.
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Received 7 February 2004; accepted 22 February 2005.