1

DOWNSTREAM HYDRAULIC DOWNSTREAM HYDRAULIC GEOMETRY GEOMETRY

of of ALLUVIAL RIVERSALLUVIAL RIVERS

Pierre Y. Julien Pierre Y. Julien Colorado State University

New Orleans New Orleans December 2014

Objectives

Discuss the downstream hydraulic geometry of alluvial rivers in terms of:

• Level I – Alluvial river equilibrium

• Level II – Spatial width changes

• Level III – Temporal width changes

I – Alluvial river equilibrium

Objectives: Review the Downstream Hydraulic Geometry (DHG) equations for alluvial rivers

• Define Downstream Hydraulic Geometry

• Review DHG equations

• Compare with field measurements

• Discuss some limitations of DHG

Cross-section geometry

Sand

GravelSilt

Wetted perimeter P

Bankfull widthTop width W

Q = 270 ft /s3

Area A

0 50 100 150 ft

Left bank

Mean flow

depth h

0

2

4

6

10

12

14

Ele

vat

ion

(ft

)

89.5 ft ASL

Flood plain

15 30 45 m

(1 m = 3.28 ft)

A

Q = A V

Width W

Wetted perimeter P

Velocity V1

222

2

2

222

2

Mean flow depthh = A /W

Flood plainW 1

Flood plain

1h = A /W

2

P1

1 1

1V

Q = A V1 1

1A

1

Downstream Hydraulic Geometry

6

Some DHG equations

7

Julien-Wargadalam equations

8

Bankfull width and depth

9

Bankfull velocity and slope

10

Performance of different equations

I – Alluvial river equilibrium

Conclusion:• Downstream Hydraulic Geometry equations provide

very good first order approximations of alluvial river equilibrium conditions.

Limitations of DHG equations

Limitations of the DHG equations include:

• What is the dominant, bankfull or effective discharge?

• What grain size (d50 or d90…) should be used?

• Can DHG equations predict meandering or braiding?

Is it also appropriate to ask:

• Do rivers have constant W, h or S?

• Does equilibrium exist?

Lets discuss further the width changes in space and time

Objectives: illustrate the changes in river widths and explain how river width can decrease

• Illustrate channel width changes in space

• Explain the concept of equivalent channel width

• Show an example on the Rio Grande

II – Spatial width changes

narrow

14

wide

Reach of the Rio Grande, NM

Relationship between channel width and sediment transport

Concept of equivalent widths

The concept of equivalent channel width stems from the decrease in sediment transport with increased channel width:

Hypothesis:

• The channel width of river reaches can be different from the equilibrium channel width from the DHG equations – however, to maintain the same sediment transport level, an increase in channel width requires an increase in channel slope.

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Example on the Rio Grande, NM

From Leon et al. ASCE-JHE 135(4), 2009

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Slope vs width

From Leon et al. ASCE-JHE 135(4), 2009

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Slope vs width-depth ratio

From Leon et al. ASCE-JHE 135(4), 2009

Wider reaches are steeper!

From Leon et al. ASCE-JHE 135(4), 2009

II – Spatial width changes

Conclusion:• Channel widths can be different from equilibrium

conditions, but to satisfy continuity in sediment transport, wider channels require steeper slopes.

Objectives: explain how alluvial river widths change over time

• Illustrate that the channel widths can change with time

• Explain the concept of deviation from equilibrium

• Show and example on the Rio Grande

• Estimate the time scale for river width adjustments

III – Temporal width changes

Temporal Changes in Hydraulic Geometry Rio Grande below Cochiti Dam, NM

Braiding Transition Meandering

1935 1972 1992

From Richard et al. ASCE-JHE 131(11), 2005

Hydraulic Geometry of the Rio Grande

From Richard et al. ASCE-JHE 131(11), 2005

CO-29

1,537

1,538

1,539

1,540

1,541

1,542

0 50 100 150 200 250Distance from left bank reference point (m)

Ele

vatio

n (m

) Sep-71

Sep-74

Oct-82

Nov-86

Aug-95

Aug-9843 km downstream from Cochiti Dam

How do rivers decrease their channel width?

1971 1971

1998 1998

Rio Grande – note the channel width changes 1996-2009

1996

26

Rio Grande

2005

27

Rio Grande

2006

28

Rio Grande

2009

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Temporal width changes

Hypotheses:

1. The alluvial channel width gradually adjusts towards the equilibrium width.

2. The annual change in channel width is proportional to the deviation from equilibrium, measured as the difference between the current channel width and the equilibrium channel width.

0

50

100

150

200

250

300

350

400

0 100 200 300 400

Measured Active Channel Width (m)

Ca

lcu

late

d E

xpe

cte

d C

ha

nn

el W

idth

(m

) Ju

lien

-Wa

rga

da

lam

(1

99

5)

19181935194919621972198519922001

19182001

Hypothesis 1. Channel widths change towards equilibrium

Hypothesis 2. Width changes are proportional to the deviation from equilibrium

equilibrium

Changes in active channel width Rio Grande, NM (after Richard et al., 2005)

Reach No.Reach No. kk11 kk11WWee WWe e (m)(m) RR22

EntireEntire 0.02910.0291 1.65811.6581 7575 0.420.42

11 0.02710.0271 1.06071.0607 3939 0.180.18

22 0.03130.0313 3.16153.1615 101101 0.570.57

33 0.04370.0437 3.70703.7070 8585 0.580.58

Sub-reach 1, y = -0.0271x + 1.0607

R2 = 0.1799

Sub-reach 2, y = -0.0313x + 3.1615

R2 = 0.5729

Sub-reach 3, y = -0.0437x + 3.707

R2 = 0.581

- 25

- 20

- 15

- 10

- 5

0

5

10

0 100 200 300 400 500 600Active Channel Width (m)

Change in A

ctive C

hannel W

idth

(m

/year)

.

Sub- reach 1Sub- reach 2Sub- reach 3Linear (Sub- reach 1)Linear (Sub- reach 2)Linear (Sub- reach 3)

)(1 eWWkdt

dW

Change in active channel width

equilibrium

Deviation from equilibrium

Entire reach

R2 = 0.97

0

50

100

150

200

250

300

350

1980 1990 2000 2010 2020 2030 2040 2050

Time (year)

Active c

hannel w

idth

(m

)

.

MeasuredEquilibrium WidthExpon. (predicted)Expon. (Measured)

Prediction of Active Channel Widthby Exponential equation (after Richard et al., 2005)

tke0e

1e)W(WWW

Equilibrium width

half adjustment

Half adjustmentTime scale 0.7/k1

Conclusions:• Channel widths gradually change toward equilibrium

• The annual width change is proportional to the difference between the actual width and the equilibrium width

• The time required to reach equilibrium is asymptotic, but half the width adjustment can be reached in 0.7/k years, with for instance k ~ 0.025-0.045 on the Rio Grande.

III – Temporal width changes

Conclusions

I - Downstream Hydraulic Geometry equations• Give very good first order approximations of alluvial river equilibrium

II - Spatial changes in channel widths• Channel widths can differ from equilibrium channel widths, and wider reaches

require steeper slopes

III - Temporal changes in channel widths• Channel widths gradually change toward equilibrium at a rate proportional to

the difference between the actual width and the equilibrium width

• The time required to reach equilibrium is asymptotic, but half the width adjustment can be reached in 0.7/k years, and k ~ 0.035 on the Rio Grande

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J. Wargadalam, CSU and DID IndonesiaG. Richard, CSU and Mesa State University

C. Leon, CSU and RTIU. Ji, Y.H. Shin and K.Y. Park, CSU and K-WATER

D.C. Baird, R. Padilla and J. Aubuchon, USBRJ.S. Lee, Hanbat University

So many others…

Acknowledgments

ByenByen Mersi !Mersi !