Introduction
Information about the distribution of grain sizes within a volume of an
alluvial gravel river bed is sought for a variety of reasons. The focus here
is the relationship between grain size sorting in the river bed and bed
material transport rates, which is central to explaining, modeling and
predicting the morphological development of a river. The goal of the analysis
described in this paper is to characterize the grain size sorting of the
morphological active layer aggregated over an area of the full width of a
gravel-bed braided river in a non-aggrading or degrading state.
Gravel braided rivers have intricate patterns of size sorting driven by
complex flow structures at confluences and in shallow (typically the mean
depth/D90 in anabranches is 10 or less) flows associated with
bifurcations and sorting in low sinuosity bends and point bars as well as in migrating
bed-load sheets and low-amplitude bars . The
amplitude of topography, and therefore the turnover depth for gravel, related
to these local erosional and depositional features is commonly up to 20 times
D50 . The surface and near-surface
sorting of grain sizes associated with the active morphological processes of
braided rivers results in patterns of grain size related to local bed
elevation and flow structure. These patterns are preserved within the river
deposits as the anabranches migrate and rework previously deposited
material. Surface patchiness has been observed in flume experiments in
response to input sediment flux variations or topography control. The
importance of this patchiness has previously been considered mainly in
relation to the bed surface characteristics and the effect on local roughness
and bed material load .
We introduce the term “morphological active layer” to refer to the sediment involved
in the mixing, sorting and exchange over the full amplitude of the developing bed topography
over extended time periods. The core question addressed here is whether the morphological
active layer is homogeneous with respect to trends in grain size between layers and
aggregated at the scale of the braided channel. The answer to this question is important
for understanding the morphodynamic and sedimentary processes of braided rivers and
the methods for representing these processes in computational models .
Understanding the sedimentology of the morphological active layer is also important for calculation
of bedload transport rates using morphological methods from direct river survey that
integrate transport rates over morphologically significant events and extent .
Refining morphological transport estimates may require information on grain sizes encountered at
different depths below the bed or confirmation (or modification) of the simple assumption
that, during channel-forming processes, all grain sizes of the bulk grain size distribution are
available with equal probability.
Data on three-dimensional patterns of sorting within the bed are difficult to
acquire, especially for an entire volume of the bed in a river reach. In
sedimentological analyses, descriptions of braided river gravels have tended
to emphasize the sedimentary structure and sedimentological detail with
little direct analysis of grain size sorting except for limited vertical
sections, trenches or cores using direct physical grain measurement or
indirect grain size methods such as image-based automatic sizing
. Analyses have typically focused on facies
patterns and sedimentary structure, but several have mentioned that there is little
vertical trend in grain sizes in braided river gravels
e.g.,. Similarly, physical models of aggraded
braided gravel alluvium show patches and threads of distinct facies but no
clear trend in grain size e.g.,. However, these
generalities, while useful indications, are based on limited sampling and
quantification of trends in particle size sorting.
Analyses of the statistics of vertical tracer particle exchange for different
size fractions have been used in developing observations and theories of
particle kinetics for bedload prediction based on long-term mixing and
burial/exhumation within the particle exchange layer
. This relates partly to the development of bed
surface armor and the size of material available for transport at different
phases of particle mobility. These analyses are usually restricted to the bedload exchange layer, which is generally taken to extend to about 2×D90 beneath the river bed (although deeper exchange is possible;
) and is also observationally restricted by the
methods for locating tracer particles beneath the bed. These analyses provide
information for particle exchange and bedload theory for vertically stable
beds with limited topographic amplitude. In braided rivers, bed topography
can change rapidly during normal channel-forming events due to local bed
scour, deposition and channel avulsion so that exchange depths are likely to
extend through the entire range of bed elevation (of the order of 10×D90) rather than the relatively thin grain exchange layer of more stable
river beds. This is a primary reason to define a morphological active layer
that is distinct from the grain exchange active layer related to flood events
on a stable gravel bed with limited topographic amplitude.
The grain size characteristics of the morphological active layer are needed
for implementing numerical models of braided river morphodynamics. Prior
studies of gravel bed stratigraphy under aggradation/degradation have used
plane beds in narrow flumes, rather than fully developed river models
. In the plane bed case, with no lateral or other
morphological sorting, the surface layers of the bed tend to be coarser than
the lower layers . The variety of sorting mechanisms at
work in laterally unstable rivers with substantial depths of scour and
deposition associated with, for example, confluences and braid bars may
modify this trend . New numerical model results have begun
to yield predictions of local grain size sorting in braided channels
, and physical experiments in small-scale models will be
valuable in developing and testing these numerical models.
We expect complex three-dimensional arrangements of patches of varying grain
composition in the morphological active layer that are locally heterogeneous ,
but the core objective here is to establish whether there is any systematic aggregate vertical
trend in the average grain sizes in a river reach. Braided river deposits and exposures in the
field might provide some of this information, but the sample requirements are Herculean and
would not, strictly, include the whole morphological active layer because our definition of
this layer (see above) makes it distinct from the lithosome that is of direct
interest for sedimentology. Formation of the morphological active layer requires a long period
of active braiding and reworking of the entire braided channel. Our solution is to use a small-scale
physical model of a gravel-bed braided river from which digital elevation maps and grain size maps can
be extracted over an extended time period. The sequence of DEMs (digital elevation models) and grain size maps was compiled to
produce the morphological active layer characteristics, using the idea and method developed by
based on photogrammetry image texture analysis. used this approach to characterize deposit
geometry in a small-scale flume model of a braided river (with topography acquired with a laser scanner), but
their models do not physically scale grain size distributions for gravel bed rivers and so do not yield
textural information. Laser scanning and other technologies may yield equivalent data in the field but
would still potentially require years of data acquisition, and periodically dry river bed, to reproduce
what is possible in tens of hours in a physical model.
Flume procedure and data collection
The experiment described here previously formed the basis for an analysis of
the topography, grain size and formation of the basal surface of braided
river deposits . Here we expand the analysis to focus on
grain size characteristics within the entire vertical extent of DEM data and
based on refinement of the topographic and textural data, extraction of
complete grain size maps, and extension of the time period analyzed from 20
to 40 h of model running time.
Flume procedure
The data are taken from a single experiment using a Froude-scale physical
model of a gravel-bed braided river in a flume 18 m long, 3 m wide and 0.3 m
deep. The grain size distribution was scaled at 1/30 from measurements of the
gravel (truncated at 8 mm in the field) particle size distribution of a
pro-glacial braided reach of Sunwapta River in the Canadian Rocky Mountains.
Consequently, bed material in the model was composed of sand with sieve sizes
ranging from 0.3 to 8 mm and a median size of about 1.3 mm. The geometric
sorting defined by σ=d84-d164+d95-d56.6 is equal to 1.3, with dX being the xth
percentile of the distribution. This grain size distribution was designed to
model the morphology and associated grain sorting mechanisms and patterns of
the gravel fraction of the sediments. The water discharge was maintained
constant at 2.1 L s-1 throughout the experiment and the bed slope was set at
1.5 %. These values maintain 1/30 Froude scaling of the Sunwapta River based
on known high-flow discharges, the bed material grain size distribution and
the surveyed gradient of the river . The
sediment system was closed to simulate long-term equilibrium conditions; a
sediment pump transferred the output material to the upstream end of the
flume, where it was returned continuously to the model river using a feed
chute that allowed excess water to drain away. The 40 h period analyzed in
this paper began at hour 140 of the experiment. Consequently, the flume bed
was fully braided at the time of the initial DEM, some bed features were
inherited from earlier in the experiment, and the braided pattern was
maintained throughout the experiment.
Bed topography
Vertical stereo images of the dry bed were taken at 1 h intervals and
DEMs were derived photogrammetrically (using Leica Photogrammetry Suite
software v. 9.1) with a mean elevation error of ν=-0.02 mm, standard
deviation of σ=0.78 mm and a cell size of 3 mm . We
consider an absolute error on height of 3σ=2.3 mm, which corresponds
to a confidence interval of 99.7 % for a normal distribution. The DEM extent
in this analysis was 10 m long and 2.5 m wide to remove photogrammetric
artifacts apparent near the edges and ends of the raw DEMs while covering the
full braided river width. The final size on the DEM is 3334 × 868 cells. The
flow increase and decrease lasted only a few minutes, and changes induced
during that period are considered as negligible at the experiment scale.
Grain size analysis
The grain size analysis and mapping used the image texture method developed
and tested by and for
field mapping of gravel-bed rivers but adapted for the sand texture in the
physical model. The image texture calculation was made using the
co-occurrence gray matrix level based on 64 gray level vertical bed images.
The sampling window size of 7 × 7 pixels was chosen due to the median grain
size (1.3 mm) and the camera resolution, and the best fit of the data was
found using the entropy index. The entropy measures the quantity of common
pattern on a picture. To calibrate the predictive relationship between an
entropy value and the real grain size, two sets of measurements were used.
Surface patches on the model river bed were sampled using adhesive and grain
size was measured using physical sieving. The first set of 58 samples
corresponded to patches with uniform grain size covering the range of sizes
in the distribution . This first set of 58 was extended
with an additional 125 samples spread over an image area regardless of the
surface composition and covering the full range of grain sizes and
gradations. The 183 grain samples were split randomly into two sets: the
first set was used to calibrate the linear relationship between sampled grain
size and texture value (Fig. a) and the second set was
used to validate the relationship and estimate the measurement error (Fig. b). With the validation set, we find that the mean value of the
absolute error is 0.38 mm with a standard deviation of 0.61 mm. The relative
error on the absolute value ranges from 0 to 100 % and half of the set had
error less than 20 %.
Calibration (a) and validation (b) data set for
the predictive relationship between the surface grain size and the picture
texture (entropy). A simple linear equation is used. The error estimation on
the validation data set is 0.38 mm on the absolute mean value and 0.61 mm
for standard deviation of the absolute value.
We refer to the estimated grain size from the textural calibration as the
“equivalent texture” because it is a texture value calibrated to only the
median grain size (not the full distribution) for a patch and is not strictly
a grain size value as conventionally defined in physical measurements of
grain size.
A grain size map is associated with each DEM, and for every bed location the
bed elevation and local bed texture is known (Fig. ).
Summary of data acquisition. (a) Orthoimage: vertical pictures are
taken at 1 h interval (note patterns of sorting of fine and coarse
material). (b) DEM: the topography is derived photogrammetrically, the cell
size is 3 mm, and the flume slope is removed. (c) Equivalent texture map: the
map is derived from the texture calculation of vertical pictures, and the median
grain size error is less than 20 %.
Dimensionless bed depth
During the 40 h of experiment time the bed elevation varied over a range
of values at each location. From the minimum and maximum values at each point
we define two specific surfaces: the minimum surface and the maximum surface
denoted by the lowest and highest elevations at that point over the 40 h
. The difference between these two surfaces over the areal
extent of the data is the morphological active layer (Fig. ). The morphological active layer differs
from deposit thickness because it is a virtual layer developed over time with
virtual vertical extent larger than the deposits at any time. Moreover, the
deposit thickness is time-related and changes with successive topography,
whereas for a certain time interval the morphological active layer is
constant. The morphological active layer is also different from the active
layer involved in particle exchange during bedload transport because it
extends over a depth related to overall scour and deposition of the river bed
over the time-scale of reworking of the bed by braiding processes, rather
than the near-surface particle exchange on a vertically stable bed during
single bed-mobilizing events.
Although the river reworked the whole flume width during the experiment, some
areas of the river bed were not active during the 40 h. Those areas
corresponded mainly to the tops of stable braid bars developed in earlier
stages of the experiment. We define the areas that showed no measurable
change by setting a uniform threshold of 4.6 mm according to the precision of
the DEM. These “no-change” areas have been removed from DEMs and grain size
maps so as to retain only the active part of the braided pattern in the analysis.
The minimum surface, the maximum surface and the morphological
active layer. The minimum surface (a) is defined at the lowest elevation for
each location throughout 40 h. The maximum surface (b) is the highest
elevation for each location throughout 40 h. The morphological active
layer (c) is the difference between the maximum surface (b) and the minimum
surface (a). Whites parts are the no-change areas. The arrow indicates flow
direction, and the flume slope is removed.
In a single set of DEM/equivalent texture maps, there is no clear link
between the surface grain size and the bed elevation (Fig. ). The longitudinal bed slope or the local
bed topography might induce a complex relation even on a single set of bed
elevation and local features (bar vs. channel). Yet, to study the grain
sorting in the morphological active layer, the layer should be scaled
relative to the absolute elevation to remove residual local topographic
effects.
The raw bed topography was scaled by the local morphological active layer
thickness (Eq. ), where h‾(x,y) is the
dimensionless bed elevation, H(x,y) the bed elevation in meters, Hmin(x,y) the minimum elevation in meters, and Δh(x,y) the morphological
active layer thickness in meters. Dimensionless bed value ranges from 0 to 1.
h‾(x,y)=H(x,y)-Hmin(x,y)Δh(x,y)
The normalization allows analysis of grain size changes in relation to the
active layer thickness and local position within the vertical extent of the
active layer.
Example of equivalent texture as a function of bed elevation for a
part of a single DEM: there is no clear trend between the equivalent texture
and the local elevation for one set of measurements.
Analysis and results
Natural and modeled surface grain sorting
During the period of analysis, a large proportion of the bed area was reworked by
processes typical of braided rivers, i.e., channel avulsions, bar migration, bedload
transport, confluence and bifurcation evolution, and active and non-active anabranches e.g.,.
Natural grain sorting is observed over the entire bed surface; fine and
coarse sediments are organized in relation to local topography, flow
bifurcation, bed roughness or flow constriction, which lead to a complex
pattern of different surface grain size e.g.,. Figure shows a bar located at the downstream end of a confluence
from a field site (Fig. a) and on the 1/30 downscaled
flume model (Fig. b). In both pictures, small uniform
fine grain units are observed on the bar surface, with a longitudinal shape
in bar length direction. The longitudinal shape of bars on the edge define a
developed sorting pattern, as also described in .
The braided channel in the flume also showed complex and diverse grain sorting patterns of
the kind seen in full-scale braided rivers, including lateral sorting at confluences, coarse
deposits on bar heads at bifurcations, fine-grained lateral bars on the downstream margins of
braid bars, and lateral fining in bends and on bars (see also ).
Grain sorting and natural pattern. (a) Vertical view of the
Sunwapta River in the Canadian Rockies and (b) on the 1/30 model.
Flow is from left to right in both bar pictures. Fine sediments are lighter
gray than coarse sediments.
Bed layer construction
Construction of the texture maps: (a) the bed topography derived
from the photogrammetry process, (b) the normalized bed topography using Eq. (), (c) normalized bed topography sorted in 10 layers (the
minimum and maximum surface are not included in the layers), (d) 400
equivalent texture maps, and (e) 10 median equivalent texture maps for each
normalized bed depth.
From the normalized bed topography, 10 classes of dimensionless bed depth
(Eq. and Fig. a and b) are
considered: ]0,0.1], ]0.1,0.2] ...]0.9,1[. Values 0 and 1, which
correspond respectively to the minimum surface and the maximum surface, are
not included in the sublayer division to avoid imbalance in the amount of
data within each layer – the maximum and the minimum values always exist for
each cell, whereas the intermediate values do not necessarily.
To create the texture map of layers, normalized bed topography of each DEM is
distributed into the 10 classes of dimensionless bed depth
(Figs. b
and b). For each class, within each DEM, cells
corresponding to the layer are associated with their equivalent texture value
(Fig. c). From this process we get, for each
class of normalized bed topography, 40 partial equivalent texture maps
corresponding to each DEM (Fig. d). The
resulting map is created by calculating the median value for each cell
throughout the 40 partial maps (Figs. e and a–j).
Equivalent texture distribution
The equivalent textures of the different layers all cover the same range of
values. Within the morphological active layer each equivalent texture can be
found in every layer, every layer has the full range of equivalent texture
values, and the proportion of equivalent textures is almost identical for all
layers (Fig. ).
The bed elevation is normalized by the morphological active layer
thickness. On initial topography (a), local topographic gradients affect
local elevation of features. On normalized topography (b), equivalent features
all have elevation shown by the same range of color over the model extent; for example, channels are blue and high bar tops dark red. The flume slope is
removed.
Equivalent texture maps: layer 1 (a), layer 2 (b), layer 3 (c),
layer 4 (d), layer 5 (e), layer 6 (f), layer 7 (g), layer 8 (h), layer 9
(i), and layer 10 (j). The white part of the color scale is centered around the median
value (2.7) of the distribution combined.
Equivalent texture histogram. The dashed lines represent the lower
layers: layers 1 and 2. The shift of the equivalent distribution of those two
layers indicates that the median equivalent texture is slightly higher close
to the minimum surface.
The shift of the equivalent texture distribution for the first two layers
just above the minimum surface indicates that the average equivalent texture
is slightly coarser for layers near the minimum surface (Fig. ). The total number of data points is small
compared to other layers due to the slight local aggradation in part of the
flume during the experiment. Nevertheless, among those points, this small
coarse shift reflects the increased presence of coarse patches in the lower
parts of the morphological active layer.
In this study we assessed the grain size variation vertically within the
morphological active layer of a physical model of a gravel-bed braided river.
To avoid slope and topography bias, the bed topography was normalized and the
results demonstrate that, aggregated at the scale of the major morphological
units of a braided channel, there is no strong vertical trend in the median
size. Every equivalent texture occurs in each layer with approximately equal
frequency. However, focusing on the coarse end of the equivalent texture
distribution, there is a slight tendency for more coarse patches in the lower
part of the morphological active layer. The presence of these coarse patches
may relate to particular morphological features inherited from
morpho-textural patterns on the river bed. For example, Fig. shows the localization of the coarse patches (regardless
of bed depth) and anabranch confluences. Confluences were identified manually
, and the map (Fig. ) shows
time-integrated confluence positions. The majority of coarse patches are
located on the confluence area or in the downstream channel. These coarse
patches may correspond to “fixed” grain patches because of their location
close to confluences . Further analysis of
these and other features is needed to understand the relationship between
texture and channel morphology at the reach scale to explain details of
size sorting within the morphological active layer.
Confluence and coarse patches map. Black lines are the boundaries of
confluence areas over 40 h. Gray dots are coarse patches.
Discussion
Overall the results indicate that, while local sorting patterns are complex,
the morphological active layer can be considered, on aggregate at
reach scale, to be homogeneous with respect to median grain size between
sedimentary layers of the bed. In other words, there is nearly equal
probability of encountering any texture value at any relative elevation
within the morphological active layer. This is consistent with some
observations suggesting very little general vertical sorting trends within
gravelly braided alluvium . In morphological
approaches to computing bedload transport in braided rivers
it is implicit that transport involves the entire
morphological active layer. From our results a good first-order approximation
of grain sizes available for transport is that all grain sizes are equally
available at all elevations in the morphological active layer over relevant
morphodynamic timescales.
Therefore, available sediments at any location and time match the bulk size
distribution of the morphological active layer. This also provides both an
initial basis for numerical modeling of bedload transport in braided rivers
with mixed sediment sizes e.g., and a means for mutual
testing of grain size sorting in physical and numerical models, for which
limited and strategic field sampling could provide validation.