The Gravel River Bankfull Discharge Estimator

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A tool from the NCED Stream Restoration Toolbox
The Gravel River Bankfull Discharge
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 Discharge Estimator
This tool consists of an equation to estimate
bankfull discharge in an undisturbed (reference)
reach of a single-thread, mobile-bed gravel-bed
stream from measured channel characteristics. Rive
r bankfull discharge is a key parameter for
estimating channel geometry. A knowledge of
bankfull discharge is necessary for the
evaluation and implementation of many river
restoration projects. The best way to measure
bankfull discharge is from a stage-discharge
relation. Bankfull discharge is often estimated
in terms of a flood of a given recurrence
frequency (e.g. 2-year flood, or a flood with a
peak flow that has a 50 probability of occurring
in a given year Williams, 1978). In some cases,
however, the information necessary to estimate
bankfull discharge from a stage-discharge
relation or from flood hydrology may not be
available. The tool presented here provides an
alternative estimator.
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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 allows estimation of bankfull
  discharge of a single- thread gravel-bed river
  with a definable floodplain that actively moves
  the gravel on its bed from time to time.
  Bankfull discharge is estimated from measured
  bankfull channel characteristics.

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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, as described in this
  tool.

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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 tool presented here cannot be used to
estimate bankfull discharge from bankfull channel
characteristics if a) there is no floodplain or
b) the channel is so disturbed that it is no
longer interacting morphologically with its
floodplain.
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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 21-27) 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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DATA BASE FOR THE TOOL

• The bankfull discharge predictor presented here
  was developed by Parker (2004) from the following
  data base for gravel-bed streams.
• 16 stream reaches flowing from the Rocky
  Mountains in Alberta, Canada (Kellerhals et al.,
  1972)
• 23 mountain stream reaches in Idaho (Parker et
  al., 2003)
• 23 upland stream reaches 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.
• The predictor was further tested with a set of 11
  reaches in Maryland/ Pennsylvania, USA
  (McCandless, 2003) and 62 reaches of British
  streams (Hey and Thorne, 1986).

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RANGE OF PARAMETERS USED TO DEVELOP THE TOOL
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 define
the range of applicability of the tool.
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THE TOOL
The tool consists of the following relation.
Where g the acceleration of gravity (9.81
meters/second2 or 32.2 feet/second2),
That is, if Bbf, Hbf, S and Ds50 can be
determined from field measurements, Qbf can be
estimated from the above relation. The tool is
implemented as an Excel spreadsheet in the next
slide.
Caution use the relation subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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IMPLEMENTATION OF THE TOOL
Stop the slide show and double-click the Excel
spreadsheet to activate it. If you type in the
indicated input parameters in the indicated
units, Qbf is computed as output.
Caution use the relation subject to the caveats
of Slides 5, 6, 7, 8 and 14!
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ACCURACY OF THE TOOL
The plot shows the values of Qbf predicted by the
tool versus the reported (observed) values for
the data set used to develop the tool. In 93 of
all reaches the predicted value is between half
and twice the reported value.
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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.
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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. Hey, R. D. and Thorne, C. R. 1986
Stable channel with mobile gravel bed. Journal
of Hydraulic Engineering, 112(8),
671-689. 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.
32
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. McCandless, T. L.,
2003, Maryland Stream Survey Bankfull Discharge
and Channel Characteristics of Streams in the
Allegheny Plateau and the Valley and Ridge
Hydrologic Regions. Report CBFO-S03-01, U.S. Fish
and Wildlife Service, Chesapeake Bay Field
Office, May, 33 p. 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.
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REFERENCES contd.
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.