HYDRAULIC GEOMETRY OF MOUNTAIN RIVERS

1
HYDRAULIC GEOMETRY OF MOUNTAIN RIVERS Gary
Parker, University of Illinois
Alluvial rivers construct their own channels and
floodplains. Channels and floodplains co-evolve
over time.
Elbow River, Alberta, Canada
Browns Gulch, Montana, USA
2
THE CONCEPT OF BANKFULL DISCHARGE
Let ? denote river stage (water surface
elevation) L and Q denote volume water
discharge L3/T. 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 quantities in brackets denote
dimensions here L length, T time and M
mass.)
Minnesota River and floodplain, USA, during the
record flood of 1965
3
PARAMETERS FOR BANKFULL GEOMETRY

• This lecture characterizes bankfull geometry in
  terms of the following parameters
• Bankfull discharge Qbf in cubic meters per
  second L3/T
• Bankfull channel width Bbf is meters L
• Bankfull cross-sectionally averaged channel
  depth Hbf L
• Down-channel slope S (meters drop per meter
  distance) 1.
• Other parameters are defined in subsequent
  slides.
• Relations for bankfull geometry of the following
  form are often posited

4
BANKFULL PARAMETERS THE RIVER AND ITS FLOODPLAIN
floodplain
An alluvial river constructs its own channel and
floodplain.
channel
At bankfull flow the river is on the verge of
spilling out onto its floodplain.
5
GRAVEL-BED AND SAND-BED RIVERS
Rivers (or more specifically river reaches) can
also be classified according to the
characteristic size of their surface bed
sediment, i.e median size Ds50 or geometric mean
size Dsg. A river with a characteristic size
between 0.0625 and 2 mm can be termed a sand-bed
stream. Two such streams are shown below.
Jamuna (Brahmaputra) River, Bangladesh. Image
courtesy J. Imran.
Fly River, Papua New Guinea.
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GRAVEL-BED AND SAND-BED RIVERS
A river with a characteristic surface size in
excess of 16 mm can be termed a gravel-bed river.
Here the term gravel is used loosely to
encompass cobble- and boulder-bed streams as
well. Three such streams are shown below.
Genessee River, New York, USA.
Raging River, Washington, USA.
Rakaia River, New Zealand
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GRAVEL-BED AND SAND-BED RIVERS
A river with a characteristic surface size
between 2 and 16 mm can be termed transitional in
terms of grain size. Such streams are much less
common than either sand-bed or gravel-bed
streams, but can be found readily enough,
particularly in basins that produce sediment from
weathered granite. An example is shown to the
right.
Hii River, Japan. Image courtesy H. Takebayashi
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GRAVEL-BED AND SAND-BED RIVERS
The diagram to the left shows the frequency of
river reaches with various characteristic grain
sizes within two sets, one from Alberta, Canada
(Kellerhals et al., 1972) and the other from
Japan (Yamamoto, 1994 Fujita et al., 1998).
Note that most rivers can be classified as either
gravel-bed or sand-bed.
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MOUNTAIN RIVERS ALLUVIAL VERSUS BEDROCK
Mountain rivers are generally gravel-bed
rivers. Not all mountain rivers, however, have a
definable bankfull geometry. For example, many
mountain rivers have little alluvium and
considerable amounts of exposed bedrock, and are
thus not free to construct their own geometry.
In addition, some gravel-bed rivers have incised
in recent times, and left their floodplains
abandoned as terraces. Here the following case
is considered alluvial, gravel-bed mountain
streams with definable floodplains.
Wilson Creek, Kentucky, USA a mountain bedrock
stream. Image courtesy A. Parola
10
SINGLE-THREAD VERSUS MULTIPLE-THREAD (BRAIDED)
MOUNTAIN RIVERS
Raging River, Washington, USA a single-thread
gravel-bed river
Sunwapta River, Canada a multiple-thread
(braided) gravel-bed river
The case considered here is that of 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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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.
12
CHARACTERIZING DOWN-CHANNEL SLOPE S
Down-channel bed slope is 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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MORE PARAMETERS USED TO CHARACTERIZE BANKFULL
CHANNEL GEOMETRY OF SINGLE-THREAD GRAVEL-BED
RIVERS
In order to capture as much universality as
possible, it is useful to characterize the
bankfull geometry of alluvial, gravel-bed
mountain streams in dimensionless form. Thus in
addition to the previously-defined
parameters Qbf bankfull discharge L3/T Bbf
bankfull width L Hbf bankfull depth L S
bed slope 1 Ds50 median surface grain size
L the following parameters are added ?
density of water M/L3 ?s material density of
sediment M/L3 R (rs/r 1) sediment
submerged specific gravity ( 1.65 for natural
sediment) 1 g gravitational acceleration
L/T2 ? kinematic viscosity of water L2/T
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DIMENSIONLESS PARAMETERS CHARACTERIZING CHANNEL
BANKFULL GEOMETRY
dimensionless bankfull discharge
dimensionless bankfull depth
dimensionless bankfull width
Down-channel slope S is already dimensionless.
15
MORE DIMENSIONLESS PARAMETERS CHARACTERIZING
CHANNEL BANKFULL GEOMETRY
bankfull Froude number (dimensionless)
(estimate of) bankfull Shields number
(dimensionless)
bankfull Chezy resistance coefficient
(dimensionless)
particle Reynolds number (surrogate for grain
size dimensionless)
width-depth ratio at bankfull flow
(dimensionless)
16
INTERPRETATION OF SOME OF THE DIMENSIONLESS
PARAMETERS
Bankfull flow velocity Ubf Qbf/(HbfBbf)
Bankfull Froude number characterizes a ratio of
momentum force to gravity force. When Froude
number Fr lt 1 the flow is subcritical, or
tranquil when Fr gt 1 the flow is supercritical,
or swift. Here where U and H
are cross-sectionally-averaged flow velocity and
depth, respectively.
The relation can be rewritten as so that a high
value of Czbf implies a low bed resistance.
For the case of steady, uniform (normal) flow,
the bed shear stress ??b is given as ??b ?gHS
where H depth. A dimensionless measure of the
ability of the flow to mobilize sediment is the
Shields number, ? ?b/(?RgD). Here
denotes an estimate of value of ? for bankfull
flow based on a surface median size for D.
Since in most cases g 9.81 m/s2, R ? 1.65 and ?
? 1x10-6 m2/s, Rep50 is a surrogate for median
surface grain size Ds503/2.
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SINGLE-THREAD MOUNTAIN 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 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 in this presentation.
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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 Sv 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 Sv can often be
  considered to be an imposed parameter that the
  river is not free to adjust in short geomorphic
  time.
• The relation between down-channel slope S and
  valley slope Sv is S ? Sv, where ? denotes
  channel sinuosity. Varying the channel sinuosity
  allows for some variation in channel slope S at
  the same valley slope Sv.

23
THE THREE RELATIONS FOR BANKFULL GEOMETRY OF
MOUNTAIN STREAMS
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BANKFULL FROUDE NUMBER VERSUS BED SLOPE
All but one of the streams are in the
Froude-subcritical range (Fr lt 1) at bankfull
flow. This does not mean that supercritical flow
is dynamically impossible in alluvial mountain
streams. Rather, the sediment transport capacity
is typically so high that alluvium cannot usually
be supplied at a fast enough rate. Some braided
streams in glacial outwash have enough sediment
supply to maintain supercritical flow.
Regression of all four data sets
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DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS
SLOPE
The bankfull Chezy resistance coefficient
declines with slope, but is typically in the
range 5 15. Bankfull flow velocity Ubf can be
estimated from measured values of Hbf, S and the
diagram below in accordance with the equation
Regression of all four data sets
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DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS
H/Ds50
Note that Czbf increases weakly with increasing
Hbf/Ds50. A Manning-Strickler resistance
relation implies that Czbf (Hbf/Ds50)1/6, in
which case
Regression of all four data sets
27
BANKFULL SHIELDS NUMBER VERSUS DIMENSIONLESS
DISCHARGE
Gravel-bed streams maintain a bankfull Shields
stress that varies little with dimensionless
discharge, and averages to 0.049.
28
WIDTH-DEPTH RATIO AT BANKFULL FLOW VERSUS
DIMENSIONLESS DISCHARGE
Single-thread mountain gravel-bed streams
maintain width-depth ratios that are typically in
the range 10 60. Note that on the average the
Alberta streams are the widest, and the British
streams the narrowest. This is thought to
reflect a more arid versus a more humid
environment.
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SHIELDS REGIME DIAGRAM
Mountain gravel-bed streams at bankfull flow are
seen to be not far above the threshold for motion
of the surface size Ds50, and well below the
threshold for suspension of the same size.
30
REFERENCES
Charlton, F. G., Brown, P. M. and Benson, R. W. ,
1978, The hydraulic geometry of some gravel
rivers in Britain, Report INT 180, Hydraulics
Research Station, Wallingford, England, 48
p. Fujita, K., K. Yamamoto and Y. Akabori, 1998,
Evolution mechanisms of the longitudinal bed
profiles of major alluvial rivers in Japan and
their implications for profile change prediction,
Transactions, Japan Society of Civil Engineering,
600(II-44) 3750 (in Japanese). Kellerhals, R.,
Neill, C. R. and Bray, D. I., 1972, Hydraulic
and geomorphic characteristics of rivers in
Alberta, River Engineering and Surface Hydrology
Report, Research Council of Alberta, Canada, No.
72-1. Parker, G., Toro-Escobar, C. M., Ramey, M.
and Beck, S., 2003, Effect Of Floodwater
Extraction On Mountain Stream Morphology, J.
Hydraul. Engrg., 129(11), 885-895. 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. Yamamoto, K.,
1994, The Study of Alluvial Rivers, Sankaidou (in
Japanese).
For more information see Gary Parkers e-book 1D
Morphodynamics of Rivers and Turbidity Currents
http//cee.uiuc.edu/people/parkerg/morphodynamics
_e-book.htm