The Gravel River Bankfull Channel Estimator

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A tool from the NCED Stream Restoration Toolbox
The Gravel River Bankfull Channel Estimator Gary
Parker, 10/2004
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CAVEAT

• This tool is provided free of charge.
• Use this tool at your own risk.
• In offering this tool, none of the following
  accept responsibility or liability for its use by
  third parties
• the National Center for Earth-surface Dynamics
• any of the universities and institutions
  associated with the National Center for
  Earth-surface dynamics or
• any of the authors of this tool.

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The Gravel River Bankfull Channel Estimator
This tool consists of a set of regression
relations for predicting bankfull geometry of
mobile-bed single-thread gravel bed streams in
terms of bankfull discharge and bed surface
median grain size. These relations can be used to
a) help optimize the design of a restored channel
to be as close as possible to its natural
bankfull geometry, and b) help speed along the
development toward this geometry by providing
guidelines for preconstruction.
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RIVERS ARE THE AUTHORS OF THEIR OWN GEOMETRY

• Given enough time, rivers construct their own
  channels.
• A river channel is characterized in terms of
  its bankfull geometry.
• Bankfull geometry is defined in terms of river
  width and average depth at bankfull discharge.
• Bankfull discharge is the flow discharge when
  the river is just about to spill onto its
  floodplain.
• A river restoration scheme is likely to become
  more successful in a shorter amount of time if
  it takes into account the natural bankfull
  geometry of a channel.
• This tool helps predict bankfull geometry for
  single-thread gravel- bed rivers with definable
  floodplains that actively move the gravel on
  their beds from time to time.

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THIS TOOL IS FOR GRAVEL-BED STREAMS
Little Wekiva River, Florida, USA a sand-bed
river.
Raging River, Washington, USA a gravel-bed river
This tool addresses gravel-bed streams. Typical
gravel-bed streams have bed surface median sizes
Ds50 in the range from 8 to 256 mm. Boulder-bed
streams have median sizes in excess of 256 mm.
Sand-bed streams have median sizes between 0.062
and 2 mm.
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THIS TOOL ADDRESSES SINGLE-THREAD RATHER THAN
MULTIPLE-THREAD RIVERS
Raging River, Washington, USA a single-thread
gravel-bed river
Sunwapta River, Canada a multiple-thread
(braided) gravel-bed river
This tool addresses single-thread streams. A
single-thread stream has a single definable
channel, although mid-channel bars may be
present. A multiple-thread, or braided stream
has several channels that intertwine back and
forth.
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THIS TOOL ADDRESSES MOBILE-BED RATHER THAN
THRESHOLD CHANNELS
Trinity Dam on the Trinity River, California,
USA. A threshold channel forms immediately
downstream.
Raging River, Washington, USA a mobile-bed river
This tool addresses mobile-bed gravel streams.
Such streams are competent to modify their beds
because they mobilize all or nearly all gravel
sizes on the bed from time to time during floods.
Threshold channels are defined in the next slide.
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THRESHOLD CHANNELS
Threshold gravel-bed channels are channels which
are barely not able to move the gravel on their
beds, even during high flows. These channels
form e.g. immediately downstream of dams, where
their sediment supply is cut off. They also
often form in urban settings, where paving and
revetment have cut off the supply of sediment.
Threshold channels are not the authors of their
own geometry. The relations presented in this
tool do not apply to them.
Trinity Dam on the Trinity River, California,
USA. A threshold channel forms immediately
downstream.
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PARAMETERS USED IN THIS TOOL

• This tool uses the following parameters
• Bankfull discharge Qbf in cubic meters per second
  (m3/s) or cubic feet per second (ft3/s)
• Bankfull channel width Bbf is meters (m) or feet
  (ft)
• Bankfull cross-sectionally averaged channel
  depth Hbf in meters (m) or feet (ft)
• Down-channel slope S (meters drop per meter
  distance or feet drop per feet distance).
• Bed surface median grain size Ds50. This
  parameter is usually measured in millimeters
  (mm) the value must be converted to meters or
  feet in using the tool presented here.
• These parameters are defined before the tool is
  introduced. If you are familiar with the
  parameters, click the hyperlink to jump to the
  tool.

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BANKFULL PARAMETERS THE RIVER AND ITS FLOODPLAIN
floodplain
A river constructs its own channel and floodplain.
channel
At bankfull flow the river is on the verge of
spilling out onto its floodplain.
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THE DEFINITION OF BANKFULL DISCHARGE Qbf
Let ? denote river stage (water surface elevation
in meters or feet relative to an arbitrary datum)
and Q denote volume water discharge (cubic meters
or feet per second). In the case of rivers with
floodplains, ? tends to increase rapidly with
increasing Q when all the flow is confined to the
channel, but much less rapidly when the flow
spills significantly onto the floodplain. The
rollover in the curve defines bankfull discharge
Qbf.
The floodplain is often somewhat poorly-developed
in mountain gravel-bed streams. Bankfull stage,
however, can often still be determined by direct
field inspection.
Minnesota River and flooded floodplain, USA,
during the record flood of 1965
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CHARACTERIZING BANKFULL DISCHARGE Qbf

• Bankfull discharge Qbf is used as a shorthand
  for the characteristic flow discharge that forms
  the channel.
• One way to determine it is by means of direct
  measurement of the flow in a river. Since
  bankfull flow is not frequent, this method may be
  impractical in a river restoration scheme.
• Another way to estimate it is from a
  stage-discharge curve, as described in the
  previous slide. In order to implement this, the
  river must be gaged near the reach of interest.
• Another way is to estimate it using stream
  hydrology. It has been found that in gravel- bed
  streams bankfull flow is often reasonably
  estimated in terms of a peak flood discharge
  with a recurrence of 2 years (e.g. Williams, 1978
  ). This corresponds to a flow discharge that
  has a 50 probability of occurring in any given
  year.
• When none of the above methods can be
  implemented, Qbf can be estimated from bankfull
  channel characteristics using the tool
  BankfullDischargePredictor.ppt of this toolbox.

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CHARACTERIZING BANKFULL CHANNEL
GEOMETRY BANKFULL WIDTH Bbf AND BANKFULL DEPTH
Hbf
Bankfull geometry is here defined in terms of the
average characteristics of a channel
cross-section at bankfull stage, i.e. when the
flow is at bankfull discharge. Here the key
parameters are bankfull width Bbf and
cross-sectionally averaged bankfull depth Hbf.
These parameters should be determined from
averages of values determined at several
cross-sections along the river reach of interest.
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CAVEAT NOT ALL RIVERS HAVE A DEFINABLE BANKFULL
GEOMETRY!
Rivers in bedrock often have no active
floodplain, and thus no definable bankfull
geometry.
Wilson Creek, Kentucky a bedrock stream. Image
courtesy A. Parola.
Highly disturbed alluvial rivers are often
undergoing rapid downcutting. What used to be
the floodplain becomes a terrace that is almost
never flooded. Time is required for the river to
construct a new equilibrium channel and
floodplain.
Reach of the East Prairie Creek, Alberta, Canada
undergoing rapid
downcutting due to stream straightening. Image
courtesy D. Andres.
The relations presented in this tool do not apply
to bedrock streams, or disturbed alluvial streams
with no active floodplain. They may, however, be
used to estimate characteristics of the ultimate
equilibrium alluvial channel that will evolve in
time.
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FIELD MEASUREMENT OF BANKFULL CHANNEL GEOMETRY
Not all field channels have definable bankfull
geometries. Even when a channel does have a
definable bankfull geometry, some experience and
judgement is required to measure it. In the
future a worked example complete with photographs
and data files will be added to the toolbox.
Until this is done, the user is urged to spend
some time to determine how bankfull geometry
should be determined.
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CHARACTERIZING BED SEDIMENT IN GRAVEL-BED
STREAMS MEDIAN SURFACE SIZE Ds50
Armored surface
Gravel-bed streams usually show a surface armor.
That is, the surface layer is coarser than the
substrate below.
substrate
Bed sediment of the River Wharfe, U.K., showing a
pronounced surface armor. Photo courtesy D.
Powell.
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SURFACE AND SUBSTRATE MEDIAN SIZES
Here the surface median size is denoted as Ds50
and the substrate median size is denoted as
Dsub50. The surface is said to be armored when
Ds50/Dsub50 gt 1. This ratio also provides a
rough estimate of ability of the stream to move
its own gravel. Low values of Ds50/Dsub50 (e.g.
lt 1.3, i.e. relatively weak armoring) are
generally indicative of relatively high mean
annual sediment transport rates, whereas high
values of Ds50/Dsub50 (e.g. gt 4, relatively
strong armor) are generally indicative of
relatively low mean annual sediment transport
rates (Dietrich et al., 1989). Notes on bed
sampling, grain size distributions and the
determination of median sediment size are given
in and Appendix (slides 35-41) toward the end of
this presentation. To jump to them click the
hyperlink bed sampling.
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CHARACTERIZING DOWN-CHANNEL SLOPE S
Down-channel bed slope should be determined from
a survey of the long profile of the channel
centerline. The reach chosen to determine bed
slope should be long enough to average over any
bars and bends in the channel, which are
associated with local elevation highs and lows.
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CHANNEL SLOPE VERSUS VALLEY SLOPE
In the figure to the left, down-channel bed slope
S is the difference in bed elevation from A to B
divided by the along-channel distance from A to B
(red line). Down-valley bed slope Sv is the
difference in elevation from A to B divided by
the along-valley distance from A to B (blue
line). The ratio between the down-channel
distance from A to B and the down-valley distance
from A to B is known as channel sinuosity ?. For
a channel that is parallel to the valley
(essentially straight) ? 1. Gravel-bed rivers
tend to have sinuosities ranging from about 1.2
to 1.8, with lower values generally at higher
slopes. The relation between downchannel slope S
and down-valley slope Sv is given as
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SINGLE-THREAD GRAVEL-BED RIVERS HAVE CONSISTENT
BANKFULL GEOMETRIES!

• This is illustrated here using data from four
  sources
• 16 streams flowing from the Rocky Mountains in
  Alberta, Canada (Kellerhals et al., 1972)
• 23 mountain streams in Idaho (Parker et al.,
  2003)
• 23 upland streams in Britain (mostly Wales)
  (Charlton et al. 1978)
• 10 reaches along the upper Colorado River,
  Colorado (Pitlick and Cress, 2002) (Each reach
  represents an average of several subreaches.)
• The original data for Qbf, Bbf, Hbf, S and Ds50
  for each reach can be found in the companion
  Excel file, ToolboxGravelBankfullData.xls.

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RANGE OF PARAMETERS
Among all four sets of data, the range of
parameters is as given below Bankfull discharge
Qbf (in meters3/sec) 2.7 5440 Bankfull width
Bbf (in meters) 5.24 280 Bankfull depth Hbf
(in meters) 0.25 6.95 Channel
slope S 0.00034 0.031 Surface median
size Ds50 (in mm) 27 167 These ranges
approximate the range of applicability of the
relations presented in this tool.
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DIMENSIONLESS PARAMETERS
The universality of bankfull characteristics of
single-thread gravel-bed rivers is expressed with
the use of dimensionless parameters.
Dimensionless bankfull depth, width and discharge
are defined as
where g denotes the acceleration of
gravity. These parameters can be computed in
either SI or English. When using SI units, Hbf,
Bbf and Ds50 should be in meters (convert Ds50
from mm), Qbf should be in cubic meters per
second, and g should take a value of 9.81
meters/sec2. When using English units, Hbf, Bbf
and Ds50 should be in feet (convert Ds50 from
mm), Qbf should be in cubic feet per second, and
g should take a value of 32.2 ft/sec2. Note
that down-channel bed slope S is already
dimensionless (meter drop per meter distance or
feet drop per feet distance).
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WHAT THE DATA SAY
The four data sets tell a consistent story of
bankfull channel characteristics.
Dimensionless width
Dimensionless depth
Down-channel bed slope
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REGRESSION RELATIONS FOR BANKFULL CHANNEL
CHARACTERISTICS
To a high degree of approximation,
S
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WHY DOES THE RELATION FOR SLOPE SHOW THE MOST
SCATTER?
S
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WHY DOES THE RELATION FOR SLOPE SHOW THE MOST
SCATTER?

• Rivers can readjust their bankfull depths and
  widths over short geomorphic time, e.g. hundreds
  to thousands of years.
• Readjusting river valley slope involves moving
  large amounts of sediment over long reaches, and
  typically requires long geomorphic time (tens of
  thousands of years or more).
• As a result, valley slope can often be
  considered to be an imposed parameter that the
  river is not free to adjust in short geomorphic
  time. This concept should be used in most river
  restoration projects.
• Varying the channel sinuosity ? allows for some
  variation in channel slope S at the same valley
  slope Sv.

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THE TOOL CONSISTS OF THREE RELATIONS
Caution use these relations subject to the
caveats of Slides 5, 6, 7, 8 and 14!
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TOOL IMPLEMENTATION BANKFULL GEOMETRY PREDICTED
FROM THE REGRESSION RELATIONS
Stop the slide show and double-click to activate
the Excel spreadsheet. The spreadsheet is then
live you can change input as you please.
Caution use the relations subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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A WORKED EXAMPLE OF RIVER RESTORATION
A reach of river had the following
characteristics before intervention. Qbf 600
m3/s (2-year flood) Bbf 96 m Hbf 2.9 m S
0.00015 Ds50 46 mm A dam was constructed on
the reach. As a result all flood flows were cut
off, and the channel was turned into a threshold
channel. As part of a river restoration scheme,
annual flooding is to be restored using
controlled reservoir releases. No gravel is to
be fed in immediately downstream of the dam, so
that reach will remain a threshold channel.
Gravel of similar size to that which prevailed in
the channel enters the stream at the first major
tributary. The effective 2-year recurrence flood
of the restoration scheme is 220 m3/s. Compute
the bankfull characteristics of the restored
mobile-bed channel downstream of the first
tributary.
Caution use the relations subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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WORKED EXAMPLE contd.
In this example, the original bankfull discharge
was 600 m3/s. The intervention of a dam cut off
all flood flows. The restoration scheme brings
back a 2-year flood of 220 m3/s. Using this
value as the new bankfull discharge, it is
apparent that the channel must shrink to fit it.
That is, both bankfull width Bbf and bankfull
depth Hbf must reduce over time to fit the
reduced bankfull discharge. In nature, this is
accomplished by means of sediment deposition,
augmented by vegetal encroachment. In time, a
smaller but morphologically (and presumably
ecologically) healthy channel should evolve.
This natural process may take decades or
centuries. A river restoration scheme can speed
the evolution to this new state by partially
pre-installing the new channel.
Caution use the relations subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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CALCULATIONS FOR THE ORIGINAL CHANNEL
Stop the slide show and double-click to activate
the Excel spreadsheet. The spreadsheet is then
live you can change input as you please.
Caution use the relations subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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COMPARISON BETWEEN THE OBSERVED ORIGINAL CHANNEL
AND THAT COMPUTED FROM THE REGRESSION RELATIONS
The values predicted from the regression
relations are similar to the observed values, at
least within the scatter of the data used to
determine them.
Caution use the relations subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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CALCULATIONS FOR RESTORATION SCHEME
Double-click to activate the Excel
spreadsheet. The spreadsheet is live you can
change input as you please.
Caution use the relations subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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BANKFULL CHARACTERISTICS OF THE RESTORED CHANNEL
Caution use the relations subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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BANKFULL CHARACTERISTICS OF THE RESTORED CHANNEL
contd.
The restored bankfull channel should have 63 of
the original width and 68 of the original depth.
These percentages should be applied to the
values for the original channel (rather than
those predicted from the regression relations) if
they are known. It may take decades or centuries
for the new channel to evolve on its own channel
modification can help speed the evolution to the
new dimensions by providing a head start.
Caution use the relations subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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SINUOSITY OF THE RESTORED CHANNEL
Valley slope Sv is assumed to be constant. As a
result, the relation between sinuosity and slope
is where the subscripts o and ar denote
original and after restoration. The numbers
in the above table give Thus the restored
channel should be somewhat less sinuous than the
original channel before intervention.
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FURTHER CAVEATS

• It is not possible to restore a stream in a
  meaningful way by supplying it with a discharge
  that is constant the year round. Channel and
  floodplain formation, cleaning of the gravel bed
  and renewal of the riparian ecosystem all require
  both flood and low flows.
• A restored flood regimen should not consist of
  only a very brief spike. The restored flood
  hydrograph should have a duration that is at
  least somewhat similar to the original one before
  intervention. If the flood hydrograph is too
  short it will be insufficient to a) overturn the
  gravel and b) rip out excessive encroaching
  vegetation.
• The flood regimen should not be restored without
  a gravel supply. If the gravel supply of the
  first major tributary downstream of a dam is
  insufficient, or too fine, it may be necessary to
  feed gravel in addition to restoring flood flows.
  A threshold channel will develop or be
  maintained on any reach that has no gravel
  supply.

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APPENDIX SEDIMENT SIZE DISTRIBUTIONS IN
GRAVEL-BED STREAMS
Armored surface
Implementation of the regression relations
requires a knowledge of the median size of the
surface armor Ds50. This value must be
determined by sampling the bed. In order to
characterize the bed sediment of the stream the
surface and substrate should be sampled
separately. The results of sampling are plotted
in terms of percent finer versus grain size (mm)
as illustrated below.
substrate
Bed sediment of the River Wharfe, U.K., showing a
pronounced surface armor. Photo courtesy D.
Powell.
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WOLMAN COUNT OF SURFACE SEDIMENT
The simplest way to sample a gravel bed surface
is by means of a Wolman count (Wolman, 1954).
The gravel surface is paced, and at set intervals
a particle next to the toe of ones foot is
sampled. The sampling should be chosen so as to
capture the spatial variation in bed texture.
Grain size is characterized in terms of the
b-axis of a grain (middle axis as measured with a
caliper) or the size of the smallest square
through which the grain will fit. A series grain
size ranges is set for estimating the grain size
distribution. In analyzing a Wolman sample, it
is necessary to determine the number of grains in
each range. These numbers are used to determine
the grain size distribution. A sample
calculation is given in the live spreadsheet of
the next slide. Wolman sampling is not practical
for sand-sized or smaller grains. More
specifically, grains finer than about 4 mm should
not be included in a sample. It should be
understood that this method misses the finer
grains in the surface.
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GRAIN SIZE DISTRIBUTION FROM WOLMAN COUNT
The live spreadsheet to the right shows a worked
example for a Wolman count. Stop the slide show
and double-click to activate it. It is customary
to plot grain size on a logarithmic scale when
presenting grain size distributions.
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KLINGEMAN SAMPLE OF SURFACE SEDIMENT
The methodology for a Klingeman sample of the
surface sediment is outlined in Klingeman et al.
(1979). A circular patch of sediment is
specified on the bed. The largest grain that
shows any exposure on the bed surface is located
and removed. All of the bed material (including
sand) is then sampled down to the level of the
bottom of the hole created by removing the
largest grain. The resulting sample is analyzed
by mass (weight) rather than number. A Klingeman
sample captures the sand as well as the gravel in
the surface layer. Sampling is, however, more
laborious than that required for a Wolman sample.
In addition, several Klingeman samples at
different locations may be needed to characterize
the spatial variability of the surface sediment.
A sample calculation is given in the live
spreadsheet of the next page.
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KLINGEMAN SAMPLE OF SURFACE SEDIMENT contd.
The live spreadsheet to the right shows a worked
example for a Klingeman sample. Stop the slide
show and double-click to activate it.
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BULK SAMPLE OF SUBSTRATE
The substrate may be sampled in bulk. The
surface layer is first carefully stripped off
down to the depth of the bottom of the largest
particle exposed on the surface. A bulk sample
(e.g. cubical) volume of substrate is then
excavated. According to the guidelines of Church
et al. (1987), the mass (weight) of the sample
should be at least 100 times the mass (weight) of
the largest grain contained in the sample.
Several such samples may be needed to
characterize the spatial variability of the
substrate. The sample is analyzed in terms of
mass (weight) rather than number.
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MEDIAN SIZE
It is useful to characterize a sample in terms of
its median size D50, i.e. the size for which 50
of the material is finer. To do this, find the
grain sizes D1 and D2 such that the percentage
content F1 is the highest value below 50 and the
percentage content F2 is the lowest percentage
above 50. The median size D50 is then estimated
by log-linear interpolation as For example, in
the Klingeman sample of slide 13 D1 32 mm, F1
45.24, D2 64 mm and F2 59.52. The
calculation of D50 is illustrated in terms of the
live spreadsheet below. Stop the slide show and
double-click to activate it.
45
REFERENCES
Charlton, F. G., Brown, P. M. and R. W. Benson
1978 The hydraulic geometry of some gravel
rivers in Britain. Report INT 180, Hydraulics
Research Station, Wallingford, England, 48 p.
Church, M. A., D. G. McLean and J. F. Wolcott
1987 River bed gravels sampling and analysis.
In Sediment Transport in Gravel-bed Rivers,
Thorne, C. R., J. C. Bathurst, and R. D. Hey,
eds., John Wiley Sons, 43-79. Dietrich, W. E.,
J. W. Kirchner, H. Ikeda and F. Iseya 1989
Sediment supply and the development of the
coarse surface layer in gravel-bedded
rivers. Nature, 340, 215-217. Ferguson, R. I.
1987 Hydraulic and sedimentary controls of
channel pattern. In Rivers Environment and
Process, K. Richards. ed., Blackwell, Oxford,
129-158. Kellerhals, R., Neill, C. R. and D. I.
Bray 1972 Hydraulic and geomorphic
characteristics of rivers in Alberta. River
Engineering and Surface Hydrology Report,
Research Council of Alberta, Canada, No. 72-1.
46
REFERENCES contd.
Klingeman, P. C., C. J. Chaquette, and S. B.
Hammond 1979 Bed Material Characteristics
near Oak Creek Sediment Transport Research
Facilities, 1978-1979. Oak Creek Sediment
Transport Report No. BM3, Water Resources
Research Institute, Oregon State University,
Corvallis, Oregon, June. Parker, G.,
Toro-Escobar, C. M., Ramey, M. and S. Beck 2003
The effect of floodwater extraction on the
morphology of mountain streams. Journal of
Hydraulic Engineering, 129(11). Parker, G. 2004
Quasi-universal relations for bankfull hydraulic
geometry of single- thread gravel-bed rivers .
In preparation. Pitlick, J. and R. Cress 2002
Downstream changes in the channel of a large
gravel bed river. Water Resources Research
38(10), 1216, doi10.1029/2001WR000898,
2002. Williams, G. P. 1978 Bankfull discharge
of rivers. Water Resources Research, 14,
1141-1154. Wolman, M.G. 1954. A method of
sampling coarse river bed material. Trans. Am.
Geophys. Union, 35, 951956.