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CHAPTER 31 EROSIONAL NARROWING AND WIDENING OF A
CHANNEL AFTER DAM REMOVAL
This chapter was written by Gary Parker,
Alessandro Cantelli and Miguel Wong
View of a sediment control dam on the Amahata
River, Japan. Image courtesy H. Ikeda.
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CONSIDER THE CASE OF THE SUDDEN REMOVAL, BY
DESIGN OR ACCIDENT, OF A DAM FILLED WITH SEDIMENT
Before removal
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REMOVAL OF THE DAM CAUSES A CHANNEL TO INCISE
INTO THE DEPOSIT
After removal
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AS THE CHANNEL INCISES, IT ALSO REMOVES SIDEWALL
MATERIAL
A first treatment of the morphodynamics of this
process was given in Chapter 15.
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EXNER EQUATION OF SEDIMENT CONTINUITY WITH
SIDEWALL EROSION

• The formulation of Chapter 15 is reviewed here.
• Bb channel bottom width, here assumed constant
• b bed elevation
• ?t elevation of top of bank
• Qb volume bedload transport rate
• Ss sidewall slope (constant)
• ?p porosity of the bed deposit
• s streamwise distance
• t time
• Bs width of sidewall zone
• s volume rate of input per unit length
• of sediment from sidewalls

?s gt 0 for a degrading channel, i.e. ??b/?t lt 0
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EXNER EQUATION OF SEDIMENT CONTINUITY INCLUDING
SIDEWALL EROSION contd.
In Chapter 15, the relations of the previous
slide were reduced to obtain the relation
or
That is, when sidewall erosion accompanies
degradation, the sidewall erosion suppresses (but
does not stop) degradation and augments the
downstream rate of increase of bed material load.
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ADAPTATION TO THE PROBLEM OF CHANNEL INCISION
SUBSEQUENT TO DAM REMOVAL THE DREAM MODELS
Cui et al. (in press-a, in press-b) have adapted
the formulation of the previous two slides to
describe the morphodynamics of dam removal.
These are embodied in the DREAM numerical models.
These models have been used to simulate the
morphodynamics subsequent to the removal of
Saeltzer Dam, shown below.
Saeltzer Dam, California before its removal in
2001.
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THE DREAM MODELS
Specify an initial top width Bbt and a minimum
bottom width Bbm. If Bb gt Bbm, the channel
degrades and narrows without eroding its
banks. If Bb Bbm the channel degrades and
erodes its sidewalls without further narrowing.
But Bbm must be user-specified.
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SUMMARY OF THE DREAM FORMULATION
But how does the process really work? Some
results from the experiments of Cantelli et al.
(2004) follow.
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EROSION PROCESS VIEWED FROM DOWNSTREAM
Double-click on the image to see the video clip.
rte-bookdamremfrontview.mpg to run without
relinking, download to same folder as PowerPoint
presentations.
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NOTE THE TRANSIENT PHENOMENON OF EROSIONAL
NARROWING
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EROSION PROCESS VIEWED FROM ABOVE
Double-click on the image to see the video clip.
rte-bookdamremtopview.mpg to run without
relinking, download to same folder as PowerPoint
presentations.
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EVOLUTION OF CENTERLINE PROFILE UPSTREAM (x lt 9
m) AND DOWNSTREAM (x gt 9 m) OF THE DAM
Downstream aggradation
Upstream degradation
Former dam location
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CHANNEL WIDTH EVOLUTION UPSTREAM OF THE DAM
The dam is at x 9 m downstream of sediment feed
point.
Note the pattern of rapid channel narrowing and
degradation, followed by slow channel widening
and degradation. The pattern is strongest near
the dam.
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REGIMES OF EROSIONAL NARROWING AND EROSIONAL
WIDENING
The dam is at x 9 m downstream of sediment feed
point. The cross-section is at x 8.2 m
downstream of the sediment feed point, or 0.8 m
upstream of the dam.
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SUMMARY OF THE PROCESS OF INCISION INTO A
RESERVOIR DEPOSIT
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CAN WE DESCRIBE THE MORPHODYNAMICS OF RAPID
EROSIONAL NARROWING, FOLLOWED BY SLOW EROSIONAL
WIDENING?
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PART OF THE ANSWER COMES FROM ANOTHER SEEMINGLY
UNRELATED SOURCE AN EARTHFLOW IN PAPUA NEW
GUINEA
The earthflow is caused by the dumping of large
amounts of waste rock from the Porgera Gold Mine,
Papua New Guinea.
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THE EARTHFLOW CONSTRICTS THE KAIYA RIVER AGAINST
A VALLEY WALL
The Kaiya River must somehow eat all the
sediment delivered to it by the earthflow.
Kaiya River
earthflow
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THE DELTA OF THE UPSTREAM KAIYA RIVER IS DAMMED
BY THE EARTHFLOW
The delta captures all of the load from upstream,
so downstream the Kaiya River eats only earthflow
sediment
earthflow
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THE EARTHFLOW ELONGATES ALONG THE KAIYA RIVER, SO
MAXIMIZING DIGESTION OF ITS SEDIMENT
A downstream constriction (temporarily?) limits
the propagation of the earthflow.
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THE VIEW FROM THE AIR
Kaiya River
The earthflow encroaches on the river, reducing
width, increasing bed shear stress and increasing
the ability of the river to eat sediment!
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THE BASIS FOR THE SEDIMENT DIGESTER
MODEL (Parker, 2004)

• The earthflow narrows the channel, so increasing
  the sidewall shear stress and the ability of the
  river flow to erode away the delivered material.
• The earthflow elongates parallel to the channel
  until it is of sufficient length to be digested
  completely by the river.
• This is a case of depositional narrowing!!!

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GEOMETRY
H flow depth n transverse coordinate nb Bb
position of bank toe Bw width of wetted
bank nw Bb Bw position of top of wetted
bank Ss slope of sidewall (const.) ?b
elevation of bed volume sediment input per
unit streamwise width from earthflow

• The river flow is into the page.
• The channel cross-section is assumed to be
  trapezoidal.
• H/Bb ltlt 1.
• Streamwise shear stress on the bed region
  ?bsb constant in n
• Streamwise shear stress on the submerged bank
  region ?bss ??bsb constant
• in n, ? lt 1.
• The flow is approximated using the normal flow
  assumption.

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EXNER EQUATION OF SEDIMENT BALANCE ON THE BED
REGION
Local form of Exner where qbs and qbn are the
streamwise and transverse volume bedload
transport rates per unit width. Integrate on bed
region with qbs qbss, qbn 0
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EXNER EQUATION OF SEDIMENT BALANCE ON WETTED BANK
REGION
Integrate local form of Exner on wetted bank
region with region with qbs qbss for nb lt n lt
nb Bw qbn - at n nt where q denotes
the volume rate of supply of sediment per unit
length from the earthflow Geometric
relation Result
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EQUATION FOR EVOLUTION OF BOTTOM WIDTH
Eliminate ??b/?t between
and
to obtain
Note that there are two evolution equations for
two quantities, channel bottom elevation ?b and
channel bottom width Bb. To close the relations
we need to have forms for qbsb, qbss and .
The parameter is specified by the motion of
the earthflow.
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FLOW HYDRAULICS
Flow momentum balance where S streamwise slope
and Bw H/Ss, Flow mass balance Manning-St
rickler resistance relation
Here ks roughness height, D grain size, nk
o(1) constant. Reduce under the condition H/Bs
ltlt 1 to get
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Shields number on bed region where R (?s/?
- 1) ? 1.65. Shields number on bank
region Streamwise volume bedload transport
rate per unit width on bed and bank regions is
qbsb and qbss, respectively where ??s 11.2 and
?c denotes a critical Shields stress,
BEDLOAD TRANSPORT CLOSURE RELATIONS
(Parker, 1979 fit to relation of Einstein, 1950).
Transverse volume bedload transport rate per
unit width on the sidewall region is qbns, where
?n is an order-one constant and from Parker and
Andrews (1986),
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SUMMARY OF THE SEDIMENT DIGESTER
Equation for evolution of bed elevation
Equation for evolution of bottom width
The earthflow encroaches on the channel
Hydraulic relations
Sediment transport relations
As the channel narrows the Shields number
increases
A higher Shields number gives higher local
streamwise and transverse sediment transport
rates.
Higher local streamwise and transverse sediment
transport rates counteract channel narrowing
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EQUILIBRIUM CHANNEL
Equilibrium channels that transport bedload
without eroding their banks can be created in the
laboratory (Parker, 1979). The image below shows
such a channel (after the water has been turned
off). The image is from experiments conducted by
J. Pitlick and J. Marr at St. Anthony Falls
Laboratoty, University of Minnesota.
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EQUILIBRIUM CHANNEL SOLUTION
As long as ? lt 1, the formulation allows for an
equilibrium channel without widening or narrowing
as a special case (without input from an
earthflow).
Choose bed shear stress so that bank shear stress
critical value
Streamwise sediment transport on wetted bank
region 0
Transverse sediment transport on wetted bank
region 0
Total bedload transport rate
Three equations if any two of Qw, S, H, Qb and
Bb are specified, the other three can be
computed!!
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ADAPTATION OF THE SEDIMENT DIGESTER FOR EROSIONAL
NARROWING

• As the channel incises, it leaves exposed
  sidewalls below a top surface ?t.
• Sidewall sediment is eroded freely into the
  channel, without the
• external forcing of the sediment digester.
• Bb now denotes channel bottom half-width
• Bs denotes the sidewall width of one side
  from channel bottom to top
• surface.
• The channel is assumed to be symmetric, as
  illustrated below.

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INTEGRAL SEDIMENT BALANCE FOR THE BED AND
SIDEWALL REGIONS
On the bed region, integrate Exner from n 0 to
n nb Bb to get On the sidewall region,
integrate Exner from n nb to n nt under the
conditions that streamwise sediment transport
vanishes over any region not covered with water,
and transverse sediment transport vanishes at n
nt
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INTEGRATION FOR SIDEWALL REGION
Upon integration it is found that or reducing
with sediment balance for the bed region,
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INTEGRAL SEDIMENT BALANCE SIDEWALL REGION
For the minute neglect the indicated
terms The equation can then be rewritten in
the form As the channel degrades i.e. ??b/?t
lt 0, sidewall material is delivered to the
channel. Erosional narrowing, i.e. ?Bb/?t lt 0
suppresses the delivery of sidewall material to
the channel.
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INTEGRAL SEDIMENT BALANCE SIDEWALL REGION contd.
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INTERPRETATION OF TERMS IN RELATION FOR EVOLUTION
OF HALF-WIDTH
This term causes narrowing whenever sediment
transport is increasing in the streamwise
direction. But this is exactly what we expect
immediately upstream of a dam just after removal
downward concave long profile!
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REDUCTION FOR CRITICAL CONDITION FOR INCEPTION OF
EROSIONAL NARROWING
Where NS and NB are order-one parameters,
Narrows if slope increases downstream
Widens
Either way
At point of width minimum ?Bb/?s 0
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REDUCTION FOR CRITICAL CONDITION FOR INCEPTION OF
EROSIONAL NARROWING contd.
Where Ns and Nb are order-one parameters,
After some reduction, where M is another
order-one parameter. That is, erosional
narrowing can be expected if the long profile of
the river is sufficiently downward concave,
precisely the condition to be expected
immediately after dam removal!
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NUMERICAL MODELING OF THE MORPHODYNAMICS OF
EROSIONAL NARROWING AND WIDENING
Wong et al. (2004) used the formulation given in
this chapter to numerically model one of the
experiments of Cantelli et al. (2004). The code
will eventually be made available in this e-book.
Meanwhile, some numerical results are given in
the next two slides. The reasonable agreement
was obtained with a minimum of parameter fitting.

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COMPARISON OF NUMERICAL MODEL WITH EXP. 5 OF
CANTELLI et al. (2004) EVOLUTION OF LONG PROFILE
Calculated and measured long profile 1200 seconds
after commencement of experiment.
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COMPARISON OF NUMERICAL MODEL WITH EXP. 5 OF
CANTELLI et al. (2004) EVOLUTION OF CHANNEL WIDTH
Calculated and measured water surface width 0.9 m
upstream of original position of dam.
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REFERENCES FOR CHAPTER 31
Cantelli, C. Paola and G. Parker, 2004,
Experiments on upstream-migrating erosional
narrowing and widening of an incisional channel
caused by dam removal, Water Resources Research,
40(3), doi10.1029/2003WR002940. Cui, ,Y.,
Parker, G., Braudrick, C., Dietrich, W. E. and
Cluer, B., in press-a, Dam Removal Express
Assessment Models (DREAM). Part 1 Model
development and validation, Journal of Hydraulic
Research, preprint downloadable at
http//cee.uiuc.edu/people/parkerg/preprints.htm
. Cui, Y., Braudrick, C., Dietrich, W.E., Cluer,
B., and Parker, G, in press-b, Dam Removal
Express Assessment Models (DREAM). Part 2 Sample
runs/sensitivity tests, Journal of Hydraulic
Research, preprint downloadable at
http//cee.uiuc.edu/people/parkerg/preprints.htm
. Einstein, H. A., 1950, The Bed-load Function
for Sediment Transportation in Open Channel
Flows, Technical Bulletin 1026, U.S. Dept. of
the Army, Soil Conservation Service. Parker, G.,
1979, Hydraulic geometry of active gravel rivers,
Journal of Hydraulic Engineering, 105(9),
1185-1201. Parker, G., 2004, The sediment
digester, Internal Memorandum 117, St. Anthony
Falls Laboratory, University of Minnesota, 17 p,
downloadable at http//cee.uiuc.edu/people/parker
g/reports.htm . Wong, M., Cantelli, A., Paola, C.
and Parker, G., 2004, Erosional narrowing after
dam removal theory and numerical model,
Proceedings, ASCE World Water and Environmental
Resources 2004 Congress, Salt Lake City, June
27-July 1, 10 p., reprint available at
http//cee.uiuc.edu/people/parkerg/conference_repr
ints.htm .