Bedrock channel morphology

Abstract

Analyses of 41 bedrock channel reaches indicate quantifiable relationships between bedrock channel morphology and reach-scale hydraulic and substrate variables. Discriminant analysis was used to develop a discriminant criterion based on reach-averaged channel gradient, substrate heterogeneity, and Selby rock-mass strength. This criterion correctly classified 70% of the observations into one of five channel morphologic types. Channels formed at higher gradients have a morphology that effectively maximizes the erosional force, whereas a morphology that evenly distributes flow energy or dissipates flow energy internally is associated with lower gradients. These results suggest that bedrock channel morphology, like alluvial channel morphology, reflects a quantifiable balance between hydraulic driving and substrate resisting forces.

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q2001 Geological Society of America 1205
GSA Bulletin; September 2001; v. 113; no. 9; p. 1205–1212; 5 figures; 4 tables.
Bedrock channel morphology
Ellen E. Wohl*
David M. Merritt
†
Department of Earth Resources, Colorado State University, Fort Collins, Colorado 80523-1482, USA
ABSTRACT
Analyses of 41 bedrock channel reaches
indicate quantifiable relationships between
bedrock channel morphology and reach-
scale hydraulic and substrate variables.
Discriminant analysis was used to develop
a discriminant criterion based on reach-av-
eraged channel gradient, substrate hetero-
geneity, and Selby rock-mass strength. This
criterion correctly classified 70% of the ob-
servations into one of five channel morpho-
logic types. Channels formed at higher gra-
dients have a morphology that effectively
maximizes the erosional force, whereas a
morphology that evenly distributes flow en-
ergy or dissipates flow energy internally is
associated with lower gradients. These re-
sults suggest that bedrock channel mor-
phology, like alluvial channel morphology,
reflects a quantifiable balance between hy-
draulic driving and substrate resisting
forces.
Keywords: bedrock channels, channel clas-
sification, channel morphology, multivari-
ate statistics.
INTRODUCTION
Although neglected for many years relative
to alluvial river channels, channels formed in
bedrock have been the subject of increasing
research during the past decade (Tinkler and
Wohl, 1998). Research interest has stemmed
from the recognition that bedrock channels
differ in fundamental ways from alluvial chan-
nels, and from the recognition that bedrock
channel geometry has recurring forms that
may be explained by measurable physical
properties. The standard conceptual models
applied to alluvial channels do not adequately
*E-mail: ellenw@cnr.colostate.edu.
†
Present address: Department of Biology, Colo-
rado State University, Fort Collins, Colorado
80523-1482, USA.
describe the processes operating along bed-
rock channels. These alluvial channel models
include a logarithmic vertical velocity profile;
a suspended sediment load of sand size or fin-
er that is transported primarily during bankfull
discharge; a channel morphology that may be
characterized as straight, meandering, or
braided; and incision rates directly proportion-
al to stream power (Knighton, 1998). Whereas
alluvial channels have been described as the
authors of their own geometry in recognition
of the relatively continuous response to chang-
es in flow regime, the geometry of channels
formed in bedrock may reflect a stronger in-
fluence from resistant, heterogeneous sub-
strate. The temporal scale of formative events
may also differ for bedrock channels, infre-
quent high-magnitude flows exerting the dom-
inant influence on channel morphology be-
cause of the greater ability of these flows to
overcome channel-boundary resistance (Bak-
er, 1988).
Bedrock channels have also received in-
creasing attention because of recognition that
rates of incision along these channels may
govern both hillslope stability (Burbank et al.,
1996) and the transmittal of base-level change
along a drainage basin, and therefore rates of
landscape evolution (Howard, 1998; Sklar and
Dietrich, 1998). Understanding and being able
to determine parameters of the processes act-
ing along bedrock channels are critical to
modeling landscape evolution.
Examining the reach-scale morphology of
bedrock channels can provide insight into
rates and processes of channel incision. (We
define a channel reach as a length of channel
at least several times channel width, and gen-
erally tens of meters to tens of kilometers in
length, with consistent channel geometry in
the sense that the entire reach fits into one of
the categories in Fig. 1, such as pool riffle.)
Previous work has demonstrated that the ero-
sion rate law first proposed by Howard and
Kerby (1983) and subsequently applied by
several investigators (Seidl and Dietrich,
1992; Rosenbloom and Anderson, 1994;
Howard et al., 1994) is not the same among
basins or along a basin (Seidl et al., 1994;
Wohl and Ikeda, 1998; Stock and Montgom-
ery, 1999; Snyder et al., 2000; Whipple et al.,
2000). The erosion rate law may be expressed
as:
mn
2(dz/dt)5kAS, (1)
where zis the distance above some arbitrary
datum, tis time, Ais contributing drainage
area, Sis surface slope, k is an erodibility con-
stant, and m and n are constants. Changes in
the (m/n) ratio have been interpreted to result
from different erosive processes (e.g., debris
flow versus fluvial erosion) (Seidl and Die-
trich, 1992). The spatial differentiation of ero-
sive processes will be governed by interac-
tions among rock type, uplift style and rate,
and river discharge. This raises the question
of whether it is possible to predict the erosive
processes or channel geometry likely to be
present along different parts of a basin, which
would allow more effective parameterization
of erosion rates within a basin.
Examining the reach-scale morphology of
bedrock channels may also provide insight
into how channels adjust to critical flow.
Grant (1997) proposed that during high dis-
charges, steep, competent alluvial channels
adjust to maintain flow conditions close to
critical, the interactions between hydraulics
and channel geometry preventing supercritical
flow for more than limited spatial and tem-
poral scales. Tinkler (1997) made a related
proposal for bedrock channels, hypothesizing
that sites of critical flow dictate the hydraulics
and dependent channel geometry elsewhere in
the system. In pools with lateral constrictions,
for example, the geometry of the constriction
interacts with discharge to determine the
strength of the jet of critical flow, which forms
at the constriction. The characteristics of the
jet in turn determine both the rate of flow-
energy dissipation, via shearing between the

1206 Geological Society of America Bulletin, September 2001
WOHL and MERRITT
Figure 1. Bedrock channel morphologic classification (after Wohl, 1998, Fig. 1).
TABLE 1. SUBSTRATE HETEROGENEITY INDEX
1. Homogeneous
Single lithologic unit and
One to two Selby categories per unit and
Bedrock dips in a consistent direction (,208variability) and
Joint orientation and spacing consistent (two or fewer Selby categories)
2. Moderately homogeneous
Single lithologic unit and
More than two Selby categories within unit or
Bedrock dip is variable (channel trends updip and downdip, or .208variability) or
Joint characteristics variable (more than two Selby categories)
3. Moderately heterogeneous
More than one lithologic unit with one to two Selby categories of difference
4. Heterogeneous
More than one lithologic unit and more than two Selby categories of difference between units or
Bedrock dip is variable or
Joint characteristics are variable
jet and lateral eddies (Tinkler, 1997), and sed-
iment deposition in the eddies and at the pool
exit slope (Thompson et al., 1999). If bedrock
channels tend to maintain critical flow at
channel irregularities such as lateral constric-
tions or downsteps in the channel bed, study
of reach-scale channel morphology may indi-
cate the factors that govern (1) the distribution
of critical flow zones and (2) the adjustments
in dependent channel geometry.
Alluvial channel morphology is commonly
acknowledged to result from specific combi-
nations of control variables such that channel
morphology can be predicted if the control
variables can be quantified (Knighton, 1998).
A similar relationship has not previously been
proposed for bedrock channels. The primary
objective of the research summarized here is
to empirically define the occurrence of differ-
ent bedrock channel morphology using vari-
ous measures of the basic control variables:
hydraulics and substrate. If bedrock channel
geometry reflects some balance between these
variables, then channel morphologic types
should correspond to the characteristics of hy-
draulics and substrate as reflected in several
quantitative descriptors of these variables. We
hypothesized that some measure of the hy-
draulic driving force and some measure of the
substrate resisting force would explain to
some degree reach-scale channel morphology.
We also hypothesized that channel-bed gradi-
ent would be correlated with channel mor-
phology. If driving forces greatly exceed re-
sisting forces, we expect to see a graded
stream with a concave-upward longitudinal
profile and a lower gradient. If driving forces
are much lower than resisting forces, we ex-
pect to see a higher gradient, a straight or con-
vex longitudinal profile, and some form of
channel adjustment that has the effect of max-
imizing erosive force, such as the presence of
an inner channel (Wohl, 1992).
RESEARCH METHODS
The data set used for this analysis includes
41 different bedrock channel reaches from riv-
ers in the United States, Canada, Japan, Aus-
tralia, and Israel. Data for 21 of these reaches
were taken from previous work on bedrock
channels by Wohl. The remaining 20 reaches
were chosen specifically for this study as be-
ing representative of types of bedrock channel
morphology. The resulting data set represents
small- to medium-scale bedrock channels
across a range of lithologic, tectonic, and hy-
droclimatic conditions (Table 1).
For each reach, channel geometry was char-
acterized through field surveys. Reach-aver-
aged width/depth ratios were calculated using
paleostage indicators of maximum discharge.
Flow hydraulics were estimated using the
step-backwater model HEC-RAS (Hydrologic
Engineering Center, 1995). Total stream power
and unit stream power provided measures of
the hydraulic driving force. Total stream pow-
er here is for maximum discharge, as estimat-
ed at each site by use of paleohydrologic in-
dicators, multiplied by the specific weight of
water and the channel-bed gradient. Unit
stream power is bed shear stress multiplied by
flow velocity; here, this number represents an
average of all the cross-sectional average val-
ues within the reach as estimated via step-
backwater modeling. This number is thus a
coarse estimate of a parameter that is highly
spatially variable along bedrock channels.
Channel substrate was characterized via Selby
rock-mass strength (Selby, 1980), a substrate
heterogeneity index (Table 2), and coarse-clast
measurements (Wolman, 1954).
The data matrix included Selby rock-mass
strength, substrate heterogeneity index, total
stream power, unit stream power, channel-bed
gradient, flow width/depth ratio, drainage
area, maximum discharge, the ratios of unit
stream power to Selby index and total stream
power to Selby index, and channel morphol-
ogy (Table 3). Three sets of variables (Selby
rock-mass strength, total stream power, and
unit stream power; Table 1) were normalized
(e.g., normalized unit stream power, v
n
5[(v
2v
mean
)/std.dev.]), so that the mean and stan-
dard deviation of all the observations were 0
and 1, respectively.
Channel morphology was categorized using
the classification scheme in Wohl (1998) (Fig.

Geological Society of America Bulletin, September 2001 1207
BEDROCK CHANNEL MORPHOLOGY
TABLE 2. BEDROCK CHANNEL DATA USED IN DISCRIMINANT ANALYSIS
Channel Location Channel Upstream Reach Selby rock- Substrate Reach Maximum Total stream Unit stream Width/depth ratio
morphology drainage area gradient mass hetero. length discharge power power for maximum
(km
2
) (m/m) strength index (m) (m
3
/s)* (W) (W/m
2
) discharge
Shichiri Japan Plane bed 10 0.009 50 3 1131 150 13 230 480 16.5
Torii 1 Japan Plane bed 0.3 0.02 57 3 360 4.4 2200 180 5
Rio Puerco New Mexico Plane bed 610 0.022 55 3 320 108 23280 2350 6.2
New River W. Virginia Plane bed 17380 0.002 76 2 310 4770 93 570 350 44
Anacostia 2 Maryland Plane bed 120 0.002 62 2 60 490 9600 360 11.1
20 Mile Cr. Canada Plane bed 296 0.007 67 3 27 130 8920 410 8
Swayze Cr. Canada Plane bed 6 0.025 55 2 30 6 1470 690 5.6
Deep Run
†
Maryland Plane bed
(
undulating
)16 0.007 52 1 300 140 9600 190 12.7
Paran 2 Israel Plane bed 2950 0.018 47 4 450 2500 171 500 2150 12.2
Piccaninny 3
†
Australia Inner channel
(
pool-riffle
)61 0.003 60 1 100 100 2940 300 22
Piccaninny 2
†
Australia Inner channel
(
pool-riffle
)61 0.004 60 1 85 100 2940 300 21.7
Piccaninny 1
†
Australia Inner channel
(
pool-riffle
)61 0.004 60 1 4000 100 2940 300 12.5
Paran 1
†
Israel Inner channel
(
pool-riffle
)2950 0.008 65 1 1000 2500 171 500 2150 5.3
Futama 2 Japan Inner channel 3.8 0.094 56 1 60 56 45 000 1360 2.5
Muddy R. Washington Inner channel 345 0.036 80 1 56 90 31 750 7410 7.8
Cheat R.
†
W. Virginia Inner channel
(
pool-riffle
)2600 0.007 76 1 610 2640 181 100 5760 7.9
Wire Pass Utah Undulating walls 200 0.043 50 1 510 70 29 500 430 1.3
Upper 40 Mile
†
Utah Undulating walls
(
inner channel
)50 0.021 63 1 3378 320 65 860 1600 0.2
Lower 40 Mile 2 Utah Undulating walls 75 0.026 48 1 1500 340 49 980 1600 0.3
Coyote Utah Undulating walls 65 0.026 56 1 1330 16 3290 290 1.2
Buckskin 1 Utah Undulating walls 790 0.008 52 1 2115 100 7840 540 0.4
Buckskin 2 Utah Undulating walls 1,000 0.021 52 1 164 105 21 610 1170 0.4
Pawnee 1 Colorado Undulating walls 0.2 0.019 53 1 160 1.4 260 530 0.7
Pawnee 2 Colorado Undulating walls 0.2 0.098 49 1 120 3.7 3550 3600 1.1
Lower 40 Mile 1 Utah Meander 75 0.018 44 1 900 340 49 980 1600 0.5
Torii 2
†
Japan Step-pool
(
plane-bed
)0.3 0.02 54 3 90 4.4 2 200 180 4
Futama 1
†
Japan Step-pool
(
inner channel
)3.8 0.103 57 1 100 56 45 000 1360 2.5
Big Box Arizona Step-pool 72 0.107 83 2 790 60 62 920 14 680 3
Little Box Arizona Step-pool 4 0.139 83 2 690 25 34 060 10 670 3.6
Swamp Run
†
Maryland Step-pool
(
inner channel
)1.2 0.161 63 1 20 13 20 500 3310 4.3
Difficult Run
†
Maryland Step-pool
(
inner channel
)151 0.025 85 1 310 680 166 600 5880 4.2
Tacoma Cr.
†
Washington Step-pool
(
inner channel
)2.5 0.107 72 1 52 9 9440 4840 3.3
Forsythe Colorado Step-pool 15 0.199 55 1 160 3.7 2570 760 10
NF Poudre Colorado Pool-riffle 950 0.011 78 1 3000 290 31 260 820 5.2
Anacostia 1 Maryland Pool-riffle 120 0.009 73 1 70 490 43 220 1730 17.4
Greenbrier 1 W. Virginia Pool-riffle 3790 0.002 73 1 520 1772 34 730 500 18.5
Greenbrier 2 W. Virginia Pool-riffle 3790 0.001 43 1 540 1770 17 370 410 8.4
St. Charles Colorado Pool-riffle 430 0.012 67 1 150 230 27 050 1680 6
Buckhorn Colorado Pool-riffle 120 0.010 75 1 33 13 1270 200 6.5
N. St. Vrain Colorado Pool-riffle 312 0.014 77 1 51 25 3380 220 18.9
S. St. Vrain Colorado Pool-riffle 210 0.008 77 1 42 21 1610 160 10.3
*Maximum discharge was computed from paleostage indicators (PSI) identified in the field. The PSI were input with surveyed channel geometry into the HEC-RAS
model to calculate maximum discharge.
†
Misclassified data, with misclassification in italics.
TABLE 3. VARIABLES USED IN DATA ANALYSES
Hydraulic variables Substrate variables Other variables Bedrock channel stream types
(range) (range) (number)
Maximum discharge Selby rock-mass strength Drainage area plane-bed
(1.4 to 4770 m
3
/s) (43 to 85) (0.2 to 17 380 km
2
) (9)
Total stream power Substrate heterogeneity Reach gradient inner channel
(260 to 171 500 W) (1 to 4) (0.001 to 0.199) (7)
Unit stream power Total stream power/Selby rock-mass strength undulating walls
(160 to 14 680 W/m
2
) (–36.7 to 68.0) (8)
Unit stream power/Selby rock-mass strength pool-riffle
(–17.1 to 48.2) (8)
Width/depth ratio step-pool
(0.20 to 44.0) (8)
meandering
(1)

1208 Geological Society of America Bulletin, September 2001
WOHL and MERRITT
Figure 2. Canonical discriminant analysis (CDA) of channel type classified by Selby rock-
mass strength, gradient, and substrate heterogeneity. (A) Plot of first two axes from CDA
of bedrock channel data from 41 stream reaches. Symbols represent the six channel types
from the classification scheme in Wohl (1998). Weightings of the independent variables
Selby rock-mass strength, gradient, and substrate heterogeneity are 0.12, 0.68, and 0.62
on canonical axis 1 and 0.40, 0.66, and 20.78 on canonical axis 2, respectively. Contours
are constructed from channel-bed gradient, at an interval of 0.02 m/m. Canonical axes 2
and 3 are plotted in B. Canonical weightings for axis 3 are 0.91, 20.33, 0.06 for Selby
rock-mass strength, gradient, and substrate heterogeneity, respectively. Contours arecon-
structed from Selby rock-mass strength, at an interval of 10. Wilks’s lambda for the
discriminant function analysis using within-class covariance matrices is F 59.66, p ,
0.0001, and the classification error rate is 0.32.
1). This classification is best applied at the
scale of a channel reach. Figure 1 is organized
along a decreasing spatial scale from reach-
length planform to variability at the scale of a
single cross section. Selection of a category
reflects the dominant channel morphologic
feature. The classification is descriptive, but
the different channel morphologic types reflect
different balances between driving and resist-
ing forces, and different dominant erosional
processes and rates of erosion (Wohl, 1998).
Six of the 10 channel morphologic types in
Figure 1 are included in the data set analyzed
here. We do not have field data to adequately
represent anastomosing channels or channels
with longitudinal grooves, potholes, or knick-
points. We have only one example of a me-
andering channel; this was included in the ca-
nonical discriminant analysis for illustration,
but it was not included in the discriminant
function analysis.
As was previously mentioned, our primary
goal was to develop an understanding of the
relationships between measurable physical
factors (such as stream hydraulics and local
bedrock characteristics) and channel form.
Discriminant analysis was employed to (1) de-
rive a discriminant criterion based on mea-
sured independent variables (i.e., hydraulic
driving and substrate resisting forces) that best
separates the previously classified bedrock
channel forms, and (2) to use this function to
assign membership to one of the six bedrock
channel types by using this discriminant cri-
terion. In discriminant analysis, a set of quan-
titative variables is used to develop a discrim-
inant criterion that classifies each observation
into one of several groups (in this case, bed-
rock channel morphologies). Stepwise dis-
criminant analysis was used to develop the
best possible discriminant function from a
subset of the independent variables (SAS In-
stitute, 1990). Whereas all seven hydraulic
and substrate variables, including the normal-
ized ratios of unit stream power and total
stream power to Selby rock-mass strength,
were initially entered into the model selection
routine, the final model was constrained to
contain a maximum of three independent var-
iables. This limit was established so that the
final model did not exceed the recommended
3:1 ratio of group sample sizes to quantitative
variables (Williams and Titus, 1988). Variable
entry into and retention in the final model
were based upon the significance of the F-sta-
tistic from an analysis of covariance between
the groups, the variables already chosen acting
as covariates. Variables with p ,0.05 were
entered into the model; only those contribut-
ing to the explanatory power of the model

Geological Society of America Bulletin, September 2001 1209
BEDROCK CHANNEL MORPHOLOGY
TABLE 4. P-VALUES FROM TUKEY’S TEST FOR PAIRWISE DIFFERENCES IN LEAST SQUARES MEANS
OF GRADIENT AND LOG
10
SELBY ROCK-MASS STRENGTH FOR FIVE BEDROCK CHANNEL TYPES
Channel type LS mean Inner channel Plane bed Pool riffle Step pool
Gradient
Inner channel 0.022
Plane bed 0.012 0.9773
Pool riffle 0.008 0.9298 0.9991
Step pool 0.108 0.0002 ,0.0001 ,0.0001
Undulating walls 0.033 0.9743 0.7291 0.6036 0.0008
Log
10
Selby
Inner channel 1.82
Plane bed 1.77 0.5523
Pool riffle 1.85 0.9208 0.1225
Step pool 1.84 0.9788 0.2074 0.9988
Undulating walls 1.73 0.1133 0.8151 0.0122 0.0241
Note
: Significant differences at p ,0.05 are indicated in bold (no significant differences for width/depth ratio
and total stream power/Selby).
Figure 3. Mean and standard error of the mean of independent variables used in discrim-
inant function and canonical discriminant analyses. Channel morphologies: SP—step pool,
UW—channels with undulating walls, IC—inner channel, ME—meandering, PB—plane
bed, PR—pool riffle. Reach gradient, Selby rock-mass strength, and W/D ratio were log
10
transformed prior to statistical analyses to comply with the assumption of multivariate
normality; raw values are presented here. Scale on the abscissa is logarithmic with the
exception of the ratio of total stream power/Selby rock-mass strength.
(significant at p ,0.10 after the entry of cov-
ariates) were retained in the final model.
Data were transformed when necessary to
comply with assumptions of within-group
multivariate normality (Johnson and Wichern,
1992). Whereas the semiquantitative variable
substrate heterogeneity was not univariate nor-
mal, inclusion of this variable in the final
model significantly reduced the classification
error rate, and it was therefore included. The
quadratic discriminant function was computed
using individual within-group covariance ma-
trices. Prior probabilities were specified to be
proportional to group sample sizes. Because
there was only one meandering stream, this
channel type was excluded from the analysis.
The explanatory strength of the discriminant
functions was evaluated by comparing pre-
dicted to actual classifications and recording
classification error, as well as cross-validation
error rate. The proportion of correct classifi-
cations indicates how well the channel types
may be separated using the measured
variables.
Following discriminant function analyses,
canonical discriminant analysis (CDA) was
employed for graphical and exploratory pur-
poses. CDA is a technique used to derive lin-
ear combinations of the independent variables
that have the highest possible multiple corre-
lation with the groups (in this case bedrock
channel types), thereby achieving the greatest
possible separation of the groups (SAS Insti-
tute, 1990). For illustrative purposes, the me-
andering stream was included in the explor-
atory CDA plots to examine the position of
this single reach relative to the other reach
types. Means of independent variables used in
discriminant function analyses were compared
between channel morphologies using one-way
analysis of variance (ANOVA). Tukey’s test
was used to adjust for pairwise comparisons
in cases of significant differences in the
means.
RESULTS
Substrate heterogeneity, gradient, and Selby
rock-mass strength generate a model with the
best discrimination of channel morphology.
Of the 40 data points included in the analysis,
28 (70%) are correctly classified by the dis-
criminant function as being the channel mor-
phologic type that we defined in the field (Ta-
ble 1). Cross-validation error rate is 0.49 for
the model containing Selby rock-mass
strength, substrate heterogeneity, and gradient.
CDA results in good separation of the channel
types on the first three canonical axes. The
first axis is strongly related to channel gradi-
ent, the second to substrate heterogeneity, and
the third to Selby rock-mass strength (Fig. 2).
Step-pool channels form a cluster on the high
end of axis 1 (high stream gradient), whereas
pool-riffle channels are on the low end of the
axis (low gradient), and channels with undu-
lating walls, an inner channel, meandering, or
a plane bed tend to have intermediate gradi-
ents. Differences in mean gradient among
channel types indicate that step-pool channels
are significantly different from all other chan-
nel types (Table 4, Fig. 3). Step-pool and
plane-bed channels tend to form in more het-
erogeneous substrates, whereas pool-riffle, un-
dulating wall, meandering and inner channels
are associated with homogeneous substrates.
Channels with meanders or with undulating
walls are associated with lower values of Sel-
by rock-mass strength, pool-riffle channels
tend to have higher values of Selby, and the
other channel types span the range of Selby
values. Differences in mean value of Selby
rock-mass strength among channel types in-
dicate that channels with undulating walls are
significantly different from pool-riffle and
step-pool channels (Table 4, Fig. 3).

1210 Geological Society of America Bulletin, September 2001
WOHL and MERRITT
Figure 4. Canonical discriminant analysis of channel type classified by Selby rock-mass
strength, gradient, and channel width/depth ratio. (A) Plot of first two axes from CDA of
bedrock channel data from 41 stream reaches. Symbols are as in Figure 1. Weightings of
the independent variables Selby rock-mass strength, gradient, and W/D are 0.41, 20.28, 0.99
on canonical axis 1 and 0.44, 0.91, and 0.05 on canonical axis 2, respectively. Contours
are constructed from channel width/depth ratio, at an interval of 2.5. Canonical axes 2
and 3 are plotted in B. Canonical weightings for axis 3 are 0.80, 20.31, 20.13 for Selby
rock-mass strength, gradient, and W/D, respectively. Contours are constructed from Selby
rock-mass strength, at an interval of 2. Wilks’s lambda for the discriminant function
analysis using within-class covariance matrices is F 512.5, p ,0.0001, and the classifi-
cation error rate is 0.29.
Inner channels are the most misclassified of
all of the channel types; only two of the seven
were correctly classified in the analysis, the
remainder being misclassified as pool-riffle
channels (Table 1). This is not unreasonable,
because an inner channel may have the down-
stream alternations between deeps and shal-
lows that also characterize pool-riffle chan-
nels. Five of the eight step-pool channels are
misclassified, mostly as inner channels. Seven
of the eight undulating-wall channels and
eight of the nine plane-bed channels are cor-
rectly classified.
We also performed CDA including the
reach-averaged width/depth ratios (Fig. 4) and
the ratio of total stream power to Selby rock-
mass strength (Fig. 5) in order to determine
how well these measures separate the channel
morphologic types. Channels with undulating
walls or with meanders have low width/depth
ratios, step-pool channels and inner channels
are intermediate, and pool-riffle and plane-bed
channels tend to have higher width/depth ra-
tios (Figs. 3 and 4; Table 4). The ratio of hy-
draulic driving to substrate resisting forces, as
measured by the ratio of total stream power to
Selby rock-mass strength, is lowest for step-
pool channels, and it increases through me-
andering, pool-riffle, plane-bed, and inner
channels, reaching a high value for channels
with undulating walls (Figs. 3 and 5). Al-
though CAN axis 3 in Fig. 5B is driven large-
ly by two extreme values of the ratio of total
stream power to Selby rock-mass strength
(weighting 50.89) and provides little infor-
mation about the remaining reaches, it is pre-
sented here to maintain consistency with the
other sets of CDA plots. The two outlying
reaches, Upper 40 Mile (undulating walls and
a total stream power/Selby of 56.5) and
Swamp Run (step-pool with total stream pow-
er/Selby of 231.5), lie further than nine stan-
dard deviations away from mean total stream
power/Selby ratio of all of the reaches (mean
51.39, SD 53.48).
DISCUSSION AND CONCLUSIONS
Alluvial bedforms and variations in channel
geometry have been interpreted as roughness
elements that increase the expenditure of flow
energy by generating flow separation and tur-
bulence (Nelson et al., 1995). Changes in al-
luvial channel configuration in response to
water and sediment discharge reflect changes
in energy availability. Similarly, channel ge-
ometry in bedrock channels may reflect ener-
gy availability and the competence of the flow
to erode the channel boundaries. This problem
may be addressed by considering channel gra-
dient. Reach-averaged channel gradient may
be taken as a surrogate for the ratio of hy-
draulic driving to substrate resisting forces. In
regions of active tectonic uplift, small chan-
nels with lower discharge are unable to keep
pace with uplift and become progressively
steeper with time, whereas larger channels
with higher discharge may be able to incise at

Geological Society of America Bulletin, September 2001 1211
BEDROCK CHANNEL MORPHOLOGY
Figure 5. Canonical discriminant analysis of channel type classified by Selby rock-mass
strength, gradient, and the ratio of total stream power to Selby rock-mass strength. (A)
Plot of the first two axes from CDA of bedrock channel data from 41 stream reaches.
Symbols are as in Figure 1. Weightings of the independent variables Selby rock-mass
strength, gradient, and the ratio of total stream power (TSP) to Selby rock-mass strength
are 0.38, 0.94, 20.29 on canonical axis 1 and 0.81, 20.33, and 20.35 on canonical axis 2,
respectively. Contours are constructed from channel-bed gradient, at an interval of 0.02
m/m. Canonical axes 2 and 3 are plotted in B. Canonical weightings for axis 3 are 0.45,
20.12, 0.89 for Selby rock-mass strength, gradient, and the ratio of total stream power
to Selby, respectively. Contours are constructed from the ratio of total stream power to
rock-mass strength, at an interval of 10. Wilks’s lambda for the discriminant function
analysis using within-class covariance matrices is F 55.25, p ,0.0001, and the classifi-
cation error rate is 0.31.
a rate equal to uplift and maintain lower gra-
dients (Merritts and Vincent, 1989). In an
analogous manner, channels with a constant
discharge have steeper gradients through
reaches of more resistant substrate (Hack,
1957; Wohl, 2000). Figures 2, 3, and5 suggest
that step-pool channels, with high gradients
and heterogeneous substrates, form where
there is a fairly low ratio of driving to resist-
ing forces. The presence of steps and plunge
pools, which may result from differential ero-
sion associated with substrate heterogeneity,
localizes and maximizes erosional force in the
plunge pools.
The differences among the remaining chan-
nel types are much subtler. ANOVA indicates
that the mean gradients for channel groups
with undulating walls, an inner channel, a
plane-bed, and pool-riffle sequences are not
statistically different (Table 4), although these
values do show some separation in Figure 3.
Similarly, ANOVA indicates no statistically
significant differences among the mean values
for the ratio of total stream power to Selby
rock-mass strength, although there is a slight
decline from channels with undulating walls
through inner channels, plane-bed, pool-riffle,
and meandering to step-pool channels (Figs. 3
and 5). Selby values for channels with undu-
lating walls are significantly different from
those for other channel types (Table 4, Fig. 3).
The remaining channel types have similar
mean values, although pool-riffle channels
tend to form in more resistant substrates and
plane-bed channels in less resistant substrates.
The deep, narrow parts of channels with un-
dulating walls or an inner channel may effec-
tively maximize the erosional force by con-
centrating the flow. As in the plunge pools of
step-pool channels, these channel morpholog-
ic types that enhance localized erosion are as-
sociated with channels at the higher range of
the gradient spectrum. The primary difference
in potential control variables among channels
with undulating walls and those with an inner
channel appears to be that channels with un-
dulating walls form in less resistant substrates.
At the lower range of the gradient spectrum,
channels formed in fairly soft, heterogeneous
substrates are likely to have a plane bed. The
relatively hydraulically smooth boundaries of
a plane-bed channel suggest that flow is able
to evenly erode the substrate. Channels in this
gradient range that form in more resistant, ho-
mogeneous substrates are likely to have a
pool-riffle sequence, which may dissipate the
energy of flow passing over the undulating
channel bed. The pools associated with pool-
riffle sequences do not create hydraulic distri-
butions that increase local bed erosion as ef-

1212 Geological Society of America Bulletin, September 2001
WOHL and MERRITT
fectively as the plunge pools of step-pool
sequences. As suggested by the higher width/
depth ratio of pool-riffle channels, much of the
energy of flow passing through these broader
pools is expended in internal shear rather than
in work against the channel bed. In summary,
a channel morphology that has the effect of
increasing bed erosion for a given discharge
(step pool, undulating walls, inner channel)
tends to be associated with higher gradient
reaches, whereas a morphology that evenly
distributes flow energy (plane bed) or that dis-
sipates flow energy internally (pool riffle)
tends to be associated with lower gradient
reaches. The specific type of channel mor-
phology present along a higher or lower gra-
dient channel appears to be a function of sub-
strate resistance and heterogeneity.
Although we have long been able to differ-
entiate alluvial channel types on the basis of
gradient, sediment load, discharge regime, and
bank erodibility (Schumm, 1960; Leopold et
al., 1964), such differentiation has not previ-
ously been proposed for bedrock channels.
The correct classification in the analysis, using
independent variables, reported here of 70%
of the data suggests that we may be able to
predict bedrock channel morphology if we can
obtain channel-bed gradient and substrate
characteristics for a channel reach. If we can
predict likely channel morphology at the reach
scale, this will improve our understanding of
processes of erosion at this scale, and thus our
ability to apply the erosion-rate law. The as-
sumption here is that channel morphology re-
flects the balance between driving and resist-
ing forces as expressed through different
erosive processes such as plunge-pool scour
or the erosion of wall undulations. If we can
determine parameters for rates of erosion at
the channel-reach scale, we should be able to
improve models of bedrock channel incision
and landscape evolution. We will also improve
our understanding of reach-scale segmentation
and inter-reach adjustment along bedrock
channels.
The results presented here represent an in-
triguing start. It is now necessary to enlarge
the data set used to develop the model and to
test the model against independent data. How-
ever, these preliminary results suggest that
bedrock channel morphology, like alluvial
channel morphology, results from an adjust-
ment between the controlling variables of sub-
strate and hydraulics, and that the manner of
this adjustment is predictable if the controlling
variables can be quantified.
ACKNOWLEDGMENTS
About half of the data used in the analyses pre-
sented here come from previously published papers
resulting from studies funded by the National Geo-
graphic Society, the Japan Society for the Promo-
tion of Science, the U.S.-Israel Educational Foun-
dation, NCASI (National Council of the Pulp and
Paper Industry for Air and Stream Improvement),
and the Geological Society of America Gladys W.
Cole Award. New data have been collected for this
paper with the assistance of Karen Prestegaard,
Keith Tinkler, Gregory Springer, Stephanie Phippen,
and Sara Rathburn. The manuscript benefited sub-
stantially from thorough reviews by Keith Tinkler,
Peter Knuepfer, and David Harbor.
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