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 Fv (oxbow) filling E eros,v = volume rate per unit valley length of (net) bank erosion / t( floodplain mass ) sv b D v Fv E 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: / t( floodplain mass ) sv b D v Fv E eros ,v / t( floodplain mass ) 0 E D F eros ,v v Any net source of sediment is from erosion into bluffs, not erosion into the floodplain 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 ct 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 ct ct ds o At the reach-averaged level: E eros,v E S ,v E E ,v c( H bf ) / t( floodplain mass ) sv b D v Fv E S ,v E E ,v 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 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 DLC 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 EUB 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 cLb 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 Q̂ 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