Transcript Slide 1

Net Transfer of Sediment from
Floodplain to Channel on Four
U.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
balance
Consider the sediment budget of a reach of a riverfloodplain 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 consideration
s = sediment density
b = density of sediment deposit = (1 - p)

= volume rate per unit valley length of overbank
D
v
deposition
= volume rate per unit valley length of lake
Fv
(oxbow) filling
E eros,v
= volume rate per unit valley length of (net) bank
erosion
  F  E
 / t( floodplainmass)  sv b D
v
v
eros ,v 
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:
  F  E
 / t( floodplainmass)  sv b D
v
v
eros ,v 
 / t( floodplainmass)  0 
E
 D  F
eros ,v
Any net source of
sediment is from erosion
into bluffs, not erosion
into the floodplain
v
v
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


Hbf
ct
Note that most of the eroded sediment is recycled in building point
bars!
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 length
Hbf = bankfull depth
so = outer bank arc length
Bbf = bankfull width
si = inner bank arc length
Rc = centerline radius of curvature
ds i
E s  c( H   )s  cH s
local
c
bf
 
E local  cH bf 
 H bf
o
bf
i
B  B 

 1  bf   bf 
Rc  Rc 

ds c
d
Rc
E local  E S ,local  E E ,local
B
 B 
E S ,local  c 1  bf  , E E ,local  cH bf bf
Rc 
Rc


Hbf
Hbf
ct
ct
ds o
At the reach-averaged level:
E eros ,v  E S ,v  E E ,v  c( H bf   )
  F  E  E 
 / t( floodplainmass)  sv b D
v
v
S ,v
E ,v

Hbf
ct
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
EUB
“Shaving”
 Type 2: Cut bank is longer than point bar
“Extension”
An example of typical bank geometry
from the Bogue Chitto River, Louisiana
Flow is near bankfull stage
Left Bank (outside of bend)
Right Bank (inside of bend)
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:
Extremely simplified
More realistic
Mud & Sand (Shaving)
Sand
& Mud
The point is that much of the cohesive material exchange occurs
through the shaving process.
Backpack
for scale
Typical Bank, Strickland
River, Papua New
Guinea
Silts and clays
Sand
Point Bar Deposit on Neuse River,
North Carolina is mostly sand but
with some layers of silt and clay
mixed in.
Measuring the exchange rates
Conceptual Model of System
At t1
Floodplain
Channel
Lake
At t2
Simplified 2-D Representation
Floodplain
Channel
+ Lake
Floodplain
For a graded, non-subsiding valley in which
bankfull elevation is not changing over time:
Net volume
exported from  EUB  ELB  DO  DLC  0
floodplain
EUB
DO
DL+C
DO
ELB
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
EUB   ci i Lb ,i
i 1
;

LC (t  t )  L(t )  LNewLake 

ELB 
AC
t
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
dEUB
 cLb
dt
 Get local migration rates from historic aerial
photo analysis
 Get bank elevations from LIDAR survey
Rectify a Scanned
Aerial Photograph to
a Recent Image
Digitized
1952 Banks
Digitize Banks
(Vegetation Line) By
Hand
Centerline Interpolation
a
a
b


Initial
b
Final
Iterate through theta until a = b
where a and b are the shortest distances to the respective curves
from a given point
Interpolated
Centerline
Repeat on Recent
Image
Modern (1998) aerial
photograph
Measure lateral
migration rates at
evenly spaced
intervals
Correction for Downstream
Translating Bends
Channel
Centerline at
t
D
l
di
Channel
Centerline at
t +Δt
di
ci 
t '
, where
l
t '  t
D
An example of the
correction procedure
The procedure ensures that
the method does not predict
outward migration at downstream
translating bend apices.
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
Ensure Banks are at
Top of Slope Break
Measure Mean
Elevation in Polygons
Associated with Each
Side 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 River
Migration Rates
Rightward Migration Rate (m/yr)
1.5
Moving Average of
Absolute Rate over
50 Channel Widths
Data
1.0
0.5
0.0
-0.5
-1.0
Mean rate ~0.4 m/yr
-1.5
0
500
1000
1500
2000
Down Channel Coordinate (m)
2500
3000
Vermillion River
Inner Bank Elevation
Elevation of Accreting Bank (m)
259.5
259.0
Moving Average of
Survey
258.5
Lidar
Survey
258.0
257.5
257.0
Moving Average
of Data
256.5
256.0
0
500
1000
1500
2000
Down Channel Coordinate (m)
2500
3000
Vermillion River
Net Shaving Erosion
Erosion Rate (m³/m/yr)
2.0
1.5
Lidar
Survey
Moving Average
of Survey
1.0
0.5
0.0
Moving Average
of Data
-0.5
0
500
1000
1500
2000
Down Channel Coordinate (m)
2500
3000
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
Pearl
River
Reach 1
Insert Label Image
Reach 2
Bogue
Chitto
River
Reach 3
Reach 1
Reach 2
Reach 3
Reach 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

LC (t  t )  LC (t )  LNewLake 

ELB 
AC
t
 Requires Cross Sectional Area Ac
 Assume Ac ≈ BH
 B from photo
 H from USGS gauge
 Assumes Ac remains relatively
constant in time
Channel Characteristics
Bankfull Characteristics at nearest USGS Gauge
Reach
Drainage Discharge Depth Width Channel
Length
River (State)
Area (km²)
(m³/s)
(m)
(m)
Slope Sinuosity
(km)
5.8x10-4
Vermillion (MN)
334
10
1.8
11
1.8
2.7
1.9x10-4
Pearl (LA/MS)
17030
570
5.5
120
1.9
91
-4
3.9x10
Bogue Chitto (LA)
3140
150
3
50
1.7
62
1.7x10-4
Neuse (NC)
6970
260
4.8
55
1.6
32
Rating Curve for Pearl River at Bogalusa, LA
USGS 02489500
Typical USGS Rating Curve
Used To Develop Table
Stage (m)
10
1
1
10
100
Flow (m³/s)
1000
10000
Results
7
2000
6
Gross Erosion Rate
Channel Extension
Shaving
5
1500
4
1000
3
2
500
1
0
0
1
30 km
2
15 km
3
35 km
Pearl
4
11 km
5
15 km
6
18 km
7
29 km
Bogue Chitto
8
34 km
9
2.7 km
Neuse Vermillion
Erosion Rate (ton/km/yr)
Erosion Rate per Unit Stream Length(m3/m/yr)
Extension
Extension
Shaving
1.20
2000
1.00
Assume ρb = 1.9 g/cm³
0.80
1500
0.60
Channel Extension
Shaving
1000
0.40
500
0.20
0.00
0
Reach 1 Reach 2 Reach 3 Reach 4 Reach 1 Reach 2 Reach 3 Reach 1 Reach 1
30 km 15 km 35 km 11 km 15 km 18 km 29 km 34 km 2.7 km
Pearl
Bogue Chitto
Neuse Vermillion
Erosion Rate (ton/km/yr)
Erosion Rate per Unit Stream Length(m3/m/yr)
Results-Residuals Only
A model for the attenuation of a contaminant by
exchange with a clean floodplain
Control Volume
Approach
ερb C(x,t)
ερb Cbank(x,t)
Assume negligible
QsC(x+Δx,t)
QsC(x,t)
C
 b

C
x
Qs
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
The resulting mass conservation model
at steady state
C
 b

C
x
Qs
Qs
 b
 b 
C  C (0) exp  
x 
 Qs 
represents an e-folding distance for the
contaminant concentration, or
x1/ 2  0.69
Qs
represents the distance it takes for
 b contaminant concentration to be cut in half.
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
Pearl
Bogue Chitto
Neuse
Annual SS Load (tons/year)
1.4x106
1.5x105
4
8x10
Mean Fraction Sand
na
0.20
0.15
 Assume 20% Sand for Pearl
 Assume mud load corresponds with shaving,
sand load corresponds with gross flux
Interaction between channel load and
floodplain
Half Replacement Distance x1/2 (km)
100000
10000
bed/bar material
mud
1000
100
10
1
Reach 1 Reach 2 Reach 3 Reach 4 Reach 1 Reach 2 Reach 3 Reach 1
30 km
15 km
35 km
11 km
15 km
18 km
29 km
34 km
Pearl
Bogue Chitto
Neuse
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?
Bogue Chitto
River,
Louisiana
Bogue Chitto
River,
Louisiana
Results
Δt
Mean Width
Mean Depth
Channel Length (at t2)
yr
m
m
m
Change in channel length from t1 to t2
m
1
Pearl River
Reach 1
Reach 2
46
46
146
117
5.5
5.5
30000
15000
1899
New Oxbow Length from t1 to t2
m
0
Total Channel/Oxbow Length Excavated m
1899
Volume Change m³
1.52E+06
Rate of Volume Change m³/yr
33036
Rate of Volume Change per meter m²/yr
1.10
Reach Average Shaving per meter m²/yr
0.44
-454
Reach 3
46
60
5.5
35000
Reach 4
46
76
5.5
10720
705
227
691
0
0
237
705
227
1.53E+05 2.31E+05 9.43E+04
3324
5032
2049
0.22
0.14
0.19
0.07
0.02
0.12
Bogue Chitto River
Reach 1
Reach 2
46
46
71
54
3
3
15000
17500
Reach 3
46
46
3
29020
Neuse R.
Reach 1
39
53
4.8
33773
Vermillion R.
Reach 1
16
11
1.8
2676
1420
1152
-870
937
327
0
1420
3.02E+05
6566
0.44
0.40
0
1152
1.85E+05
4019
0.23
0.28
1758
888
1.24E+05
2687
0.09
0.09
0
937
2.38E+05
6111
0.18
0.16
0
327
6.47E+03
405
0.15
0.20
Bogue Chitto River
Net Shaving Erosion
6
Reach 1
Reach 2
Reach 3
Erosion Rate (m3/m stream
length/yr)
4
2
0
-2
Data
Moving Average over 100 Ch Width
-4
-6
0
10000
20000
30000
40000
50000
Down Channel Coordinate (m)
60000
70000
Neuse River
Net Shaving Erosion
3.00
Erosion Rate (m3/m/yr)
2.00
1.00
0.00
-1.00
Data
-2.00
Moving Average over 100 Channel Widths
-3.00
0
5000
10000
15000
20000
25000
Down Channel Coordinate (m)
30000
35000
40000
Pearl River
Net Shaving Erosion
6
Reach 1
Erosion Rate (m3/m/yr)
5
Reach 3
Reach 2
Reach 4
4
3
2
1
0
-1
Data
-2
Moving Average over 100 Channel Widths
-3
-4
0
10000
20000
30000
40000
50000
60000
70000
Down Channel Coordinate (m)
80000
90000
100000
Vermillion River
Channel Width
30
Channel Width (m)
25
20
15
10
Data
5
Moving Average over 50
Channel Widths
0
0
500
1000
1500
2000
Down Channel Coordinate (m)
2500
3000
Pearl 1:250000
Pearl River
Channel Width
300
Channel Width (m)
250
200
150
100
50
0
0
10000
20000
30000
40000
50000
60000
70000
Down Channel Coordinate (m)
80000
90000
100000
Pearl River
Bankfull Elevation
Elevation of Accreting Bank (m)
35
30
25
20
15
10
5
0
0
10000
20000
30000
40000
50000
60000
70000
Down Channel Coordinate (m)
80000
90000
100000
Pearl River
Migration Rates
Rightward Migration Rate (m/yr)
8
Reach 1
Reach 3
Reach 2
Reach 4
6
4
2
0
Data
-2
Absolute Value
-4
Moving Average over 50 Widths of Absolute
Rate
-6
-8
0
10000
20000
30000
40000
50000
60000
70000
Down Channel Coordinate (m)
80000
90000
100000
Bogue Chitto River
Channel Width
140
Channel Width (m)
120
100
80
60
40
20
0
0
10000
20000
30000
40000
50000
Down Channel Coordinate (m)
60000
70000
Bogue Chitto River
Bankfull Elevation
Elevation of Accreting Bank (m)
40
35
30
25
20
15
10
5
0
0
10000
20000
30000
40000
50000
Down Channel Coordinate (m)
60000
70000
Bogue Chitto River
Migration Rates
4
Rightward Migration Rate (m/yr)
Reach 1
Reach 2
Reach 3
3
2
1
0
-1
Data
-2
Absolute Value
-3
Moving Average of Absolute Rate over 50
Widths
-4
0
10000
20000
30000
40000
50000
Down Channel Coordinate (m)
60000
70000
Neuse River
Channel Width
120
Channel Width (m)
100
80
60
40
20
0
0
5000
10000
15000
20000
25000
Down Channel Coordinate (m)
30000
35000
40000
Neuse River
Bankfull Elevation
Elevation of Accreting Bank (m)
14.00
Bad Data
12.00
10.00
8.00
6.00
4.00
2.00
0.00
0
5000
10000
15000
20000
25000
Down Channel Coordinate (m)
30000
35000
40000
Neuse River
Migration Rates
Rightward Migration Rate (m/yr)
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
Data
-0.6
Absolute Value
-0.8
Moving Average over 50 Widths of Absolute
Rate
-1.0
0
5000
10000
15000
20000
25000
Down Channel Coordinate (m)
30000
35000
40000
Vegetation Removal (From Puget
Sound Lidar Consortium)
If the channel bankfull elevation is not changing in time:
S valley  OD  E1  VC  L 
OD
1
Qs,in  Qs,out t  Avalley
1   p 
E1
OD
Assume Channel Can Adjust to
Constant Bankfull Shields Stress
Dimensionless Discharge vs. Bankfull
Shields Stress
1.E+01
1.E+00
bf 50
Grav Brit
Grav Alta
Sand Mult
Sand Sing
Grav Ida
1.E-01
1.E-02
1.E-03
1.E+02
1.E+04
1.E+06
1.E+08
1.E+10
1.E+12
1.E+14
ˆ
Q
Implies Channel Maintains Constant Cross
Sectional Area if Qbf, D, Cf remain Constant
Floodplain Transfer Categories
E1
F2
OD3
F4
OD1
DE
E2
OD2
C2
F1
F3
FP1
FP2
B1
S1
B2
“Shaving” will be used
synonymously with E1
S2
C1
B3
Resulting Generalize Conservation
Equation
Svalley  DO  F2  EUB  C2  F4  VC  L 
DO
DO
F2
C2
1
Qs,in  Qs,out t  Avalley
1   p 
EUB
F4
DO
2-D Representation of Floodplain
FP
Lake
Floodplain
Channel
Floodplain
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