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