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The Threshold Between Braided and Meandering Rivers

John Pitlick and Erich MuellerUniversity of Colorado

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(Schumm, 1985)

Channel Patterns

Sunlight Cr., WY

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Leopold and Wolman, 1957

Original idea

Distinction based on slope:

For the same discharge, braided

rivers tend to have higher slopes

than meandering rivers

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Lewin and Brewer, 2001

Median Grain size (mm)

U  n   i   t   S   t  r  e  a  m   P  o  w  e  r   (   W   /  m   2   )

More recent work

ω  =  ρ  g Q S W

Distinction based on unit streampower:

no difference between braided and

meandering channels

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Rubey, 1952

Recall the basic premise:

Given

•

Discharge, Q

•

•  Grain size, D

Find

•  Width, B

•  Depth, H

•  Velocity, U

•

Slope, S

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Given

•

Channel-forming discharge, Q

•

•  Grain size, D

Find

•  Width, B

•  Depth, H

•  Velocity, U

•

Slope, S

Sediment loads are not measuredin many places

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Given

•

Channel-forming discharge, Q

•

Slope, S

•  Grain size, D

Find

•  Width, B

•  Depth, H

•  Velocity, U

•

•

Assume slope is +/- constantover short time scales

•  Calculate Qs

Alternative formulation

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To calculate sediment loads we need to know:

1. Width, W

2. Grain size, D

3. Shields stress, *

τ *=

τ o

ρ s −  ρ ( )g D

=   HS

(s − 1) D

τ c

*=  threshold for bed load transport

Are there sign. differences in W, D and t* of braided and meandering rivers?

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Width: Braided rivers are much, much wider than single thread rivers

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width vs. discharge

Ashmore and Sauks, 2006

if width ~ Q1.0

unit discharge (UH) and Shields stress,   , would be ~constant

Sunwapta River

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St. Anthony Falls Lab, U. MN

(with J. Pizzuto and J. Marr)

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Shields stress approaches a constant value at bankfull Q

0.05

0.06

0.07

0.08

1.1

1.2

1.3

1.4

1.5

1.6

1.7

0 60 120 180 240 300 360 420 480 540

S

e

d

N

m

b

T

a

p

S

a

Time min)

Y = 0.086*X-0.066

Very useful result!

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Use that result to predict channel geometry sediment loads

1. Channel-forming Shields stress:

H   =  τ b* (ρ s   ρ −1)  D50

S   =

(0.048) (1.65)  D50

U   =  u* 1

κ    ln

11 H

3 D50

⎛

⎝ ⎜

⎞

⎠ ⎟

B  =   Q 2 HU

2. Mean velocity:

3. Continuity:

where Q2 is the 2-year flood

y = 0.40x0.72

1E-01

1E+00

1E+01

1E+02

1E+03

1E+04

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

Drainage Area (km2)

2  -  y  e  a  r

F   l  o  o   d   (  m   3   /  s   )

h

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0.00

0.05

0.10

0.15

0.20

0.0001 0.001 0.01 0.1

θ

B  a  n   k   f  u   l   l

Reach Average Slope

Bankfull     :

Based on measurements at > 200 sites in N. America and Britain

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Mt St Helens

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May 18, 1980 eruption  •  North half of mtn. collapsed largest historic landslide in the world

•  Debris avalanche covered an area of ~60 km2

•  Buried the NF Toutle River under > 100 m of

sediment

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Toutle River continues to erode

through the debris avalanche…

carries the highest sediment loads of

any river in the US

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Field studies, 2006 & 2007

Measure

•  width & depth of active channel

•

average gradient•  grain size of the bed material

97.5

98.0

98.5

99.0

99.5

100.0

100.5

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Distance (m)

E   l  e  v

a  t   i  o  n   (  m   )

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NF 125

Field studies, 2007

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Channel-forming flow?

1

10

100

1000

1 10 100 1000 10000

2  -   Y  e  a  r   F   l  o  o   d   (  m   3   /  s   )

Drainage Area (km2)

Q2 = 0.97*A

0.88

SW Washington

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Strategy (recap)

1. Channel-forming Shields stress:

H   =  τ b* (ρ s   ρ −1)  D50

S   =

(0.048) (1.65)  D50

U   =  u*  1κ    ln 11 H

3 D50

⎛ ⎝ ⎜

⎞ ⎠ ⎟

B  =   Q 2 HU

2. Mean velocity:

3. Channel width:

where Q2 is the 2-year flood

h

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1. Calc. transport rates, q s , for 15 increments of discharge:

2. Weight transport rates byfrequency of discharge, sum

Segura and Pitlick, 2010, WRR

Qs=   Qsii=1

15

∑   f (Qi)

Parker (1979)

qs =  k   1−τ c*

τ *

⎛

⎝ ⎜⎜

⎞

⎠ ⎟ ⎟

4.5

=  k   1− 1φ ⎛

⎝ ⎜⎜

⎞

⎠ ⎟ ⎟

4.5

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10-2

10-1

100

0 20 40 60 80 100 120

Mount St Helens, WA

B  a  n   k   f  u   l   l   B  e

d   L  o  a   d

D   i  s  c   h  a  r  g  e   (  m   3   /  s   )

Bankfull Discharge (m3 /s)

Qs =3.2e-3*Q1.00

R2 = 0.99

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Sunlight Creek, WY

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EF Big Lost R., ID

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10-4

10-3

10-2

10-1

0 5 10 15 20 25

Big Lost River, ID

B  a  n   k   f  u   l   l   B  e

d   L  o  a   d

D   i  s  c   h  a  r  g  e   (  m   3

/  s   )

Bankfull Discharge (m3 /s)

Qs =2.6e-4*Q1.20

R2 = 0.91

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Wheres the threshold?

Big Lost River, WY Toutle River, WA

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10-4

10-3

10-2

10-1

100

0 20 40 60 80 100 120

Toutle: Qs = 0.0030Q^1.0

Big Lost: Qs = 0.00026Q^1.2

B  a  n   k   f  u   l   l   B  e   d   L  o  a   d

D   i  s  c   h  a  r  g  e   (  m

3   /  s   )

Bankfull Discharge (m3 /s)

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Well-sorted surface layer Poorly sorted surface layer

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Conclusions

1.  Effects of sedment supply on channel planform

seem obvious, but we have yet to quantify these effects

2.   Average stresses in braided rivers are not any higher

3. Threshold shear stresses may be lower, hence transportintensities are much higher

4. Linkages between stress and width should be a focus

of future research on braided/meandering transition

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Conditions leading to braiding are partly a function

of the hydrology

Discharges that exceed the threshold for

transport (H = 0.3 m) are quite common

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Grain size:Sunlight Creek, WY

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Shields stress:

0

5

10

15

20

0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

r

e

q

u

e

n

Ratio of Bankfull to Refernce

Mueller et al. 2005

0

2

4

6

8

10

0.00 0.02 0.04 0.06 0.08 0.10 0.12

F     r     e     q     u     e     n     c     y

ref

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Shields stress:

0

5

10

15

20

0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

r

e

q

u

e

n

Ratio of Bankfull to Refernce

Mueller et al. 2005

0

2

4

6

8

10

0.00 0.02 0.04 0.06 0.08 0.10 0.12

F     r     e     q     u     e     n     c     y

ref

LY

FSWR

Braided channels

SW

SU?

TL

SL