Net Transfer of Sediment from Floodplain to Channel on FourU.S. Rivers

J. Wesley Lauer

University of Minnesota

Gary Parker

University of Illinois

Problem

Bank erosion is often considered a source of sediment for stream systems. Rivers, however, must widen infinitely, and their floodplains must be destroyed, if bank erosion represents a net source of sediment to the stream.

Why do so many studies show banks being a net source of material? Are such studies even correct?

How continuous in time and space might we expect the erosion and replenishment processes to be?

Goals of Talk

Present measurements of cut bank erosion rates on long reaches of several U.S. rivers Important for gross cycling of point bar material since

most of what is eroded is replaced immediately in point bars.

Estimate the difference between cut bank erosion and point bar deposition on the same systems Two processes lead to this difference. One is

important for characterizing exchange of fine material between channel and floodplain and has contaminant transport implications.

Emphasize the importance of floodplains in the transport of material downstream through an alluvial valley

What are the exchange processes in a channel-floodplain complex?

Is the sediment load of this river increasing downstream due to bank erosion?

Relation for floodplain sediment balanceConsider the sediment budget of a reach of a river-

floodplain complex containing a meandering river.

/t(Sediment in floodplain) =a) Overbank deposition rate on the floodplain +b) Deposition rate in floodplain lakes (oxbows) –c) Rate of sediment loss to channel by bank erosion

Relation for floodplain sediment balance

Define the following parameters:sv = valley length of reach under considerations = sediment densityb = density of sediment deposit = (1 - p)

= volume rate per unit valley length of overbank deposition

= volume rate per unit valley length of lake (oxbow) filling

= volume rate per unit valley length of (net) bank erosion

vD

v,erosvvbv EFDs)massfloodplain(t/

vF

veros,E

In a graded stream, any net loss of sediment from the floodplain must vanish

Erosion from the floodplain must be balanced by deposition on it:

v,erosvvbv EFDs)massfloodplain(t/

vvv,eros FDE

)massfloodplain(t/

0

Any net source of sediment is from erosion into bluffs, not erosion into the floodplain

Net bank erosion comes in two flavors: shaving and extension

Shaving: the top of the inner point bar tends to be somewhat lower than the opposite eroding cut bank. The difference drives a net erosion of mostly finer (higher) floodplain material into the channel

Note that most of the eroded sediment is recycled in building point bars!

ctHbf

Net bank erosion comes in two flavors: shaving and extension

Extension: as a channel migrates and elongates, it creates an ever-increasing volume of “hole” (channel) in the floodplain. This process of increasing arc length due to migration is balanced by cutoff. The oxbows, however, remain as “holes” until they are filled with sediment.

Note that the surface area of the eroded zone on the outer bank is greater than that of the eroded zone on the inner part of the bank. Extension yields mostly coarser (lower) floodplain sediment to the channel.

Net bank erosion comes in two flavors: shaving and extension

c = migration rate sc = centerline arc lengthHbf = bankfull depth so = outer bank arc lengthBbf = bankfull width si = inner bank arc lengthRc = centerline radius of curvature

ibfobfclocal scHs)H(csE

c

bf

c

bf

bfbflocal R

B

R

B1

HcHE

ds o d

ds c

ds i

R c

ctHbf

c

bfbflocal,E

c

bflocal,S

local,Elocal,Slocal

R

BcHE,

R

BcE

EEE

1

Hbf ct

At the reach-averaged level:

)H(cEEE bfv,Ev,Sv,eros

v,Ev,Svvbv EEFDs)massfloodplain(t/

Hbf ct

The Bogue Chitto River, Louisiana: A typical actively migrating river system

Several processes might result in short term or local net erosion from banks Type 1: Cut bank is higher than point bar

Type 2: Cut bank is longer than point bar

EUB

“Shaving”

“Extension”

An example of typical bank geometry from the Bogue Chitto River, Louisiana

Left Bank (outside of bend) Right Bank (inside of bend)

Flow is near bankfull stage

Since the inner bank is not built to the elevation of the higher outer bank, migration in effect “shaves” off the highest part of the floodplain.

Pearl River, Louisiana/Mississippi, near Bankfull Stage. Vegetation on point bars is submerged while eroding cut banks are exposed. Wild pigs provide scale.

Replenishment processes should depend on the type of erosion Type 1 (Shaving): Should be balanced by

overbank deposition Type 2 (Extension): Should be balanced by

filling of or migration through the oxbow lakes that eventually form

This talk makes an attempt to measure the relative magnitudes of the shaving and extension erosion processes for the purpose of characterizing their importance in real systems.

The important floodplain exchange processes associated with meander migration:

Mud & Sand (Shaving)

Sand & Mud

Extremely simplified

More realistic

The point is that much of the cohesive material exchange occurs through the shaving process.

Typical Bank, Strickland Typical Bank, Strickland River, Papua New River, Papua New Guinea Guinea

Backpack for scale

Sand

Silts and clays

Point Bar Deposit on Neuse River, Point Bar Deposit on Neuse River, North Carolina is mostly sand but North Carolina is mostly sand but with some layers of silt and clay with some layers of silt and clay mixed in.mixed in.

Measuring the exchange rates

Channel

Lake

Floodplain

At t1 At t2

Conceptual Model of System

Simplified 2-D Representation

Channel + Lake

Floodplain Floodplain

For a graded, non-subsiding valley in which bankfull elevation is not changing over time:

DOEUB

0 CLOLBUB DDEE

ELBDL+C

DO

Net volume

exported from

floodplain

Measurement of Erosion Terms

It would be great to simply subtract two surfaces, but this is not possible Only one topographic survey generally available A few repeatedly surveyed cross sections do not

provide ELB

Instead, estimate rate EUB=dEUB/dt based on bank geometry and local migration rate

Estimate rate ELB using long-term change in channel length, including newly formed lakes

n

iibiiUB LcE

1,

CNewLakeC

LB At

LtLttLE

)()(;

Where are the banks (the border between channel and floodplain)? Outer bank: Easy, since

usually a cut bank on actively migrating streams

Inner bank: Boundary between … Proximal and distal

sources of sediment Lateral and vertical

accretion Presence of material

finer than available on bed of channel (sand vs silt)

Use first break in slope inside vegetation line

Measuring Shaving

Get local migration rates from historic aerial photo analysis

Get bank elevations from LIDAR survey

bUB Lcdt

dE

Rectify a Scanned Rectify a Scanned Aerial Photograph to Aerial Photograph to a Recent Imagea Recent Image

Digitized 1952 BanksDigitized 1952 BanksDigitize Banks Digitize Banks (Vegetation Line) By (Vegetation Line) By HandHand

Centerline Interpolation

Initial

Final

b

a

b

a

Iterate through theta until a = b

where a and b are the shortest distances to the respective curves

from a given point

Interpolated Interpolated CenterlineCenterline

Repeat on Recent Repeat on Recent ImageImage

Modern (1998) aerial Modern (1998) aerial photographphotograph

Measure lateral Measure lateral migration rates at migration rates at evenly spaced evenly spaced intervalsintervals

Correction for Downstream Translating Bends

't

dc ii

Channel Centerline at t

Channel Centerline at t +Δt

di

l

D

tD

lt ', where

The procedure ensures that

the method does not predict

outward migration at downstream

translating bend apices.

An example of the correction procedure

Characterize Bank Elevations Using LIDAR (Light Detection and Ranging) Scanning Airborne Laser/Digital GPS Unit Various returns recorded—useful for removing

vegetation from final DEM, but smoothing also required

Images from Harding, 2000

Sources of Error in LIDAR

Errors in laser rangefinder—generally small Errors in angle of laser—important near

edges, on steep slopes Vegetation Water Post-Processing

Smoothing Vegetation Removal

Result: LIDAR is not good at detecting edges, but we’ll try anyway

Lidar Data Sources

State or Local Floodplain Mapping Projects Louisiana FEMA Project

http://atlas.lsu.edu North Carolina Floodplain Mapping Program

http://www.ncfloodmaps.com Dakota County, MN

Used ungridded data (i.e. bare earth returns) Gridded to 5-m DEM (LA) or 5-ft DEM (NC, MN) Define banks by hand based on point density and

topography, buffer these banks, compute mean elevation from LIDAR in buffered region

Banks as Digitized From Photo

Check Raw LIDAR Point Coverage

Redefine Banks Based on LIDAR Coverage

Check on DEM to Check on DEM to Ensure Banks are at Ensure Banks are at Top of Slope BreakTop of Slope Break

Measure Mean Measure Mean Elevation in Polygons Elevation in Polygons Associated with Each Associated with Each Side of ChannelSide of Channel

Validation: Vermillion River, MN

Test measurement of shaving rate Can banks be identified accurately enough

from LIDAR alone? Method: Compare shaving computed using

previous method with shaving computed using Δη from field-surveyed banks

Vermillion Overview

Vermillion Overview Topo

Vermillion RiverMigration Rates

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 500 1000 1500 2000 2500 3000

Down Channel Coordinate (m)

Rig

htw

ard

Mig

rati

on

Ra

te (

m/y

r) DataMoving Average of Absolute Rate over 50 Channel Widths

Mean rate ~0.4 m/yr

Vermillion RiverInner Bank Elevation

256.0

256.5

257.0

257.5

258.0

258.5

259.0

259.5

0 500 1000 1500 2000 2500 3000

Down Channel Coordinate (m)

Ele

va

tio

n o

f A

cc

reti

ng

Ba

nk

(m

)

Lidar

Survey

Moving Average of Survey

Moving Average of Data

Vermillion RiverNet Shaving Erosion

-0.5

0.0

0.5

1.0

1.5

2.0

0 500 1000 1500 2000 2500 3000

Down Channel Coordinate (m)

Ero

sio

n R

ate

(m

³/m

/yr)

Lidar

SurveyMoving Average of Survey

Moving Average of Data

Study Areas Where Both Shaving and Extension Have Been Computed

Validation on Vermillion River, MN

Apply to 3 Southern US Rivers Pearl River,

LA/MS Bogue Chitto

River, LA Neuse River,

NC

Pearl 1:100000 Map

Insert Label Image

Pearl River

Bogue Chitto River

Reach 1Reach 1

Reach 2Reach 2

Reach 3Reach 3

Reach 3Reach 3

Reach 2Reach 2

Reach 1Reach 1

Reach 4Reach 4

Study Areas Where Both Shaving and Extension will be Computed

Validation on Vermillion River, MN

Apply to 3 Southern US Rivers Pearl River,

LA/MS Bogue Chitto

River, LA Neuse River,

NC

Neuse 1:100000

Neuse 1:10000

Neuse River

Computation of Extension Term

Requires Cross Sectional Area Ac

Assume Ac ≈ BH B from photo H from USGS gauge Assumes Ac remains relatively

constant in time

C

NewLakeCCLB A

t

LtLttLE

)()(

Channel Characteristics

Rating Curve for Pearl River at Bogalusa, LAUSGS 02489500

1

10

1 10 100 1000 10000

Flow (m³/s)

Sta

ge

(m)

Typical USGS Rating CurveUsed To Develop Table

Bankfull Characteristics at nearest USGS Gauge Reach Drainage Discharge Depth Width Channel Length

River (State) Area (km²) (m³/s) (m) (m) Slope Sinuosity (km)

Vermillion (MN) 334 10 1.8 11 5.8x10-4 1.8 2.7Pearl (LA/MS) 17030 570 5.5 120 1.9x10-4 1.9 91

Bogue Chitto (LA) 3140 150 3 50 3.9x10-4 1.7 62Neuse (NC) 6970 260 4.8 55 1.7x10-4

1.6 32

Results

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9

Ero

sio

n R

ate

per

Un

it S

trea

m L

eng

th(m

3 /m/y

r)

0

500

1000

1500

2000

Ero

sio

n R

ate

(to

n/k

m/y

r)

Gross Erosion RateChannel ExtensionShaving

Pearl Bogue Chitto Neuse Vermillion30 km 15 km 35 km 11 km 15 km 18 km 29 km 34 km 2.7 km

Extension

Results-Residuals OnlyExtension Shaving

Assume ρb = 1.9 g/cm³

0.00

0.20

0.40

0.60

0.80

1.00

1.20

Reach 1 Reach 2 Reach 3 Reach 4 Reach 1 Reach 2 Reach 3 Reach 1 Reach 1

Ero

sio

n R

ate

per

Un

it S

trea

m L

eng

th(m

3 /m/y

r)

0

500

1000

1500

2000

Ero

sio

n R

ate

(to

n/k

m/y

r)

Channel ExtensionShaving

Pearl Bogue Chitto Neuse Vermillion30 km 15 km 35 km 11 km 15 km 18 km 29 km 34 km 2.7 km

A model for the attenuation of a contaminant by exchange with a clean floodplain

ερb C(x,t)

QsC(x+Δx,t)

QsC(x,t)

ερb Cbank(x,t)

Control Volume Approach

Where

C = the fraction of sediment in a size class of interest that is contaminated

Cbank = the fraction of contaminant in the eroding banks (assume negligible)

ε = lateral exchange flux with the floodplain, L²/T (i.e shaving rate E per unit channel length)

ρb = sediment bulk density

Qs = the mass sediment transport rate in the grain size of interest

Assume negligible

CQx

C

s

b

The resulting mass conservation model at steady state

xQ

CCs

b exp)0(

bsQ

CQx

C

s

b

represents the distance it takes for contaminant concentration to be cut in half.

represents an e-folding distance for the contaminant concentration, or

bsQx 69.02/1

x1/2 can be computed easily for the shaving rate (assumed to primarily represent fine sediment cycling) or the gross bank erosion rate (assumed to primarily represent bed material cycling). It is a quantitative way of describing the effectiveness of a floodplain at capturing potentially contaminated sediment.

Placing the Results in Context by Computing x1/2

Total suspended sediment load calculations performed on USGS gauge data

Stream Annual SS Load (tons/year) Mean Fraction Sand

Pearl 1.4x106 naBogue Chitto 1.5x105 0.20

Neuse 8x1040.15

Assume 20% Sand for Pearl Assume mud load corresponds with shaving, sand load corresponds

with gross flux

Interaction between channel load and floodplain

1

10

100

1000

10000

100000

Reach 1 Reach 2 Reach 3 Reach 4 Reach 1 Reach 2 Reach 3 Reach 1

Hal

f R

epla

cem

ent

Dis

tan

ce x

1/2 (

km)

bed/bar material

mud

Pearl Bogue Chitto Neuse

30 km 15 km 35 km 11 km 15 km 18 km 29 km 34 km

Take Home Points

Net bank erosion is a small fraction of gross bank erosion Both shaving (upper, finer material) and extension (lower,

coarser material) play a role in setting net bank erosion In a graded stream net erosion can be completely balanced by

floodplain deposition (floodplain and lakes), so that banks need not be a net source of sediment at all.

Valley bluffs, as opposed to banks, can be a net source of sediment

Floodplain exchange distance x1/2 small for sand x1/2 larger for finer material in upper banks, but still on order of

channel length, so floodplain cycling appears important on these rivers

Questions?Questions?

Bogue Chitto River,

Louisiana

Bogue Chitto River,

Louisiana

Results

Pearl River Bogue Chitto River Neuse R. Vermillion R.Reach 1 Reach 2 Reach 3 Reach 4 Reach 1 Reach 2 Reach 3 Reach 1 Reach 1

Δt yr 46 46 46 46 46 46 46 39 16Mean Width m 146 117 60 76 71 54 46 53 11Mean Depth m 5.5 5.5 5.5 5.5 3 3 3 4.8 1.8

Channel Length (at t2) m 30000 15000 35000 10720 15000 17500 29020 33773 2676

Change in channel length from t1 to t2 m 1899 -454 705 227 1420 1152 -870 937 327

New Oxbow Length from t1 to t2 1 m 0 691 0 0 0 0 1758 0 0

Total Channel/Oxbow Length Excavated m 1899 237 705 227 1420 1152 888 937 327Volume Change m³ 1.52E+06 1.53E+05 2.31E+05 9.43E+04 3.02E+05 1.85E+05 1.24E+05 2.38E+05 6.47E+03

Rate of Volume Change m³/yr 33036 3324 5032 2049 6566 4019 2687 6111 405Rate of Volume Change per meter m²/yr 1.10 0.22 0.14 0.19 0.44 0.23 0.09 0.18 0.15Reach Average Shaving per meter m²/yr 0.44 0.07 0.02 0.12 0.40 0.28 0.09 0.16 0.20

Bogue Chitto RiverNet Shaving Erosion

-6

-4

-2

0

2

4

6

0 10000 20000 30000 40000 50000 60000 70000

Down Channel Coordinate (m)

Ero

sio

n R

ate

(m3/

m s

trea

m

len

gth

/yr)

Data

Moving Average over 100 Ch Width

Reach 1 Reach 2 Reach 3

Neuse RiverNet Shaving Erosion

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

0 5000 10000 15000 20000 25000 30000 35000 40000

Down Channel Coordinate (m)

Ero

sio

n R

ate

(m3/

m/y

r)

Data

Moving Average over 100 Channel Widths

Pearl RiverNet Shaving Erosion

-4

-3

-2

-1

0

1

2

3

4

5

6

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

Down Channel Coordinate (m)

Ero

sio

n R

ate

(m3/

m/y

r)

Data

Moving Average over 100 Channel Widths

Reach 1 Reach 2 Reach 3 Reach 4

Vermillion RiverChannel Width

0

5

10

15

20

25

30

0 500 1000 1500 2000 2500 3000

Down Channel Coordinate (m)

Ch

an

ne

l W

idth

(m

)

Data

Moving Average over 50Channel Widths

Pearl 1:250000

Pearl RiverChannel Width

0

50

100

150

200

250

300

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

Down Channel Coordinate (m)

Ch

ann

el W

idth

(m

)

Pearl RiverBankfull Elevation

0

5

10

15

20

25

30

35

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

Down Channel Coordinate (m)

Ele

va

tio

n o

f A

cc

reti

ng

Ba

nk

(m

)

Pearl RiverMigration Rates

-8

-6

-4

-2

0

2

4

6

8

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

Down Channel Coordinate (m)

Rig

htw

ard

Mig

rati

on

Rat

e (m

/yr)

Data

Absolute Value

Moving Average over 50 Widths of AbsoluteRate

Reach 1 Reach 2 Reach 3 Reach 4

Bogue Chitto RiverChannel Width

0

20

40

60

80

100

120

140

0 10000 20000 30000 40000 50000 60000 70000

Down Channel Coordinate (m)

Ch

an

ne

l Wid

th (

m)

Bogue Chitto RiverBankfull Elevation

0

5

10

15

20

25

30

35

40

0 10000 20000 30000 40000 50000 60000 70000

Down Channel Coordinate (m)

Ele

va

tio

n o

f A

cc

reti

ng

Ba

nk

(m

)

Bogue Chitto RiverMigration Rates

-4

-3

-2

-1

0

1

2

3

4

0 10000 20000 30000 40000 50000 60000 70000

Down Channel Coordinate (m)

Rig

htw

ard

Mig

rati

on

Rat

e (m

/yr)

Data

Absolute Value

Moving Average of Absolute Rate over 50Widths

Reach 1 Reach 2 Reach 3

Neuse RiverChannel Width

0

20

40

60

80

100

120

0 5000 10000 15000 20000 25000 30000 35000 40000

Down Channel Coordinate (m)

Ch

ann

el W

idth

(m

)

Neuse RiverBankfull Elevation

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0 5000 10000 15000 20000 25000 30000 35000 40000

Down Channel Coordinate (m)

Ele

va

tio

n o

f A

cc

reti

ng

Ba

nk

(m

) Bad Data

Neuse RiverMigration Rates

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000 30000 35000 40000

Down Channel Coordinate (m)

Rig

htw

ard

Mig

rati

on

Rat

e (m

/yr)

Data

Absolute Value

Moving Average over 50 Widths of AbsoluteRate

Vegetation Removal (From Puget Sound Lidar Consortium)

ODOD E1

If the channel bankfull elevation is not changing in time:

valleyoutsinsp

LCvalley AtQQVEODS

,,1 1

1

Assume Channel Can Adjust to Constant Bankfull Shields Stress

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14

Grav BritGrav AltaSand MultSand SingGrav Ida

Q̂

50bf

Dimensionless Discharge vs. Bankfull Shields Stress

Implies Channel Maintains Constant Cross Sectional Area if Qbf, D, Cf remain Constant

Floodplain Transfer Categories

OD1OD2

FP1FP2

B1

B2 B3

OD3F2

F1

F3 C1

C2

S1

S2

E1

E2F4

DE

“Shaving” will be used synonymously with E1

Resulting Generalize Conservation Equation

valleyoutsinsp

LCUBOvalley AtQQVFCEFDS

,,422 1

1

DO

DOF2

C2EUB

F4

DO

2-D Representation of Floodplain

Lake ChannelFloodplain FloodplainFP

Other assumptions

Channel extends continuously, so instantaneous extension rate is same as long-term rate, which is easily measured

Cross-sectional area conserved Computation of Shaving Transfer E1:

E1 = Σ(ηouter- ηinner)cLouter

Units L3/T Computation of Extension Transfer ∆VC+L/ ∆ t:

∆VC+L=[(Lc(t+ ∆t)+Lcutoff) – Lc(t)]Ac

Units L3/T