Linking high temporal resolution flux-based sediment budgets with channel change: Establishing morphological meaning to measurements of sediment flux

Christy Leonard 1, David Topping 2, Ronald Griffiths2, and Jack Schmidt1

Department of Watershed Sciences, Utah State Univeristy1,

Grand Canyon Monitoring and Research Center, U.S. Geological Survey2

Christy LeonardDepartment of Watershed Sciences – Utah State University E-mail: christina.leonard@aggiemail.usu.eduhttps://qcnr.usu.edu/wats/colorado_river_studies/

1

EP33D-2437

With continuous measurements of sediment transport and an innovative method to calculate a morphological sediment budget, what more can we infer about river processes?

Area to volume using a Bayesian model: Making the most of little data

Probabilistic approach to account for uncertainty in digitizing and image co-registration

Study Area:

7.1 7.12 7.14 7.16 7.18

Easting 10 5

4.4795

4.48

4.4805

4.481

4.4815

4.482

4.4825

4.483

4.4835

4.484

4.4845

Nor

thin

g

10 6

-8

-6

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-2

0

2

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8

x

7.1 7.12 7.14 7.16 7.18

10 5

4.48

4.481

4.482

4.483

4.484

4.485

10 6

-1

-0.5

0

0.5

1

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2.5

y

Ɛx

Ɛy

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

Area (m 2) 10 4

0

0.05

0.1

0.15

0.2

0.25

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0.35

Prop

ortio

n

Veg Island Deposition

Veg Island Erosion

Channel Boudnary Deposition

Channel Boundary Erosion -1 0 1 2 3 4 5 6 7

Detrended Elevation (m)

0

0.01

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Prob

abilit

y

Bank Elevation

Channel Bed Elevation

Bank Attahced Bar Elevation

In-Channel Bar Elevation

Vegetated Island Elevation

Height(vegetated island) = z(vegetated island) - z(in-channel bar)

Height(bank) = z(bank) - z(channel bed)

Height(bank attached bar) = z(bank attached bar) - z(in-channel bar)

Bayesian Model: Gibbs sampling with 10,000 MCMC stepsz ~ normal(μ,τ) – likelihood distribution

μ ~ normal(0,1x106) – uninformative prior distribution τ ~ gamma(0.01,0.01) – uninformative prior distributionz(i) ~ normal(μ , τ)

Results: Partitioned morphological and flux-based sediment budgets

2014 2015 2016-8

-7

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ons

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Dis

char

ge (m

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-1)

Total Load

2013 2014 2015 2016-3

-2.5

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Met

ric T

ons

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V Fine Sand

Fine Sand

Med Sand

Crs Sand

2011 to 2017

-4 -3 -2 -1 0

Net Volumetric Change (Metric Tons) 10 5

0

0.005

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0.015

0.02

0.025

0.03

Prob

abilit

y

Total Change

Channel Change

Vegetated Island Change

2011 to 2013

-1.5 -1 -0.5 0 0.5 1 1.5

10 6

0

0.01

0.02

0.03

0.04

2013 to 2015

Flux

Bud

get

Upp

er B

ound

s

Low

er B

ound

s

-5 -4 -3 -2 -1 0

10 5

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0.01

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0.042015 to 2017

Flux

Bud

get

Upp

er B

ound

s

Low

er B

ound

s

-4 -3 -2 -1 0

10 5

0

0.005

0.01

0.015

0.02

0.025

0.03

7.126 7.128 7.13 7.132 7.134 7.136 7.138 7.14 7.142 7.144

10 5

4.4796

4.4797

4.4798

4.4799

4.48

4.4801

4.4802

4.4803

10 6

Veg Island Deposition

Veg Island Erosion

Channel Boudnary Deposition

Channel Boundary Erosion

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

Predicted Elevaton for Polygoni (m)

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Pro

babi

lity

Vegetated Island Elevation

In-Channel Bar Elevation

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Predicted Height of Deposition for Polygon i (m)

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babi

lity

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Predicted Volume of Deposition for Polygoni (m

3)

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Pro

babi

lity

0 5000 10000 15000 20000

Predicted Volume of Deposition for All Polygons (m3

)

0

0.005

0.01

0.015

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0.03

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Prob

abilit

y

• Uncertainty was characterized in two components: (1) image co-registration error (Figure 2 A-C) and (2) digitizing error (Figure 2D).

• A spatially continuous error surface of image co-registration error (εx and εy) was created using each tie point’s co-registration error in the X (εx) and Y (εy) direction (Figure 2B).

• The channel boundary was moved by the resultant εx + εy vector (Figure 2C).• Digitizing error was characterized for each vertex by randomly sampling a X and Y

coordinate from a normal distribution over 100 iterations (Figure 2D). • 100 realizations of channel boundaries were used to compute a distribution of

planform changes between all time periods (Figure 2E).

A.

B.

100 Pr(Δarea)

X Y

C.D.

E.

Figure 3: Elevations of different geomorphic units extracted from the 2015 detrended LiDAR dataset (Figure 1). In-channel bed elevations were derived using optical bathymetry. Note: the distribution of elevations between 2011 to 2015 were similar, indicating little vertical accretion.

• A Bayesian model was used to predict the depth of erosion or deposition at each polygon for the 100 realization of channel boundaries derived in Figure 2E.

• The final posterior distribution was a combination of all realizations of channel boundaries in Figure 2E and incorporated uncertainty in image co-registration, digitizing, and depth of erosion or deposition (Figure 5).

Figure 6: (A) The morphological sediment budget showed that vegetated islands expanded and the channel boundary eroded in all time periods except 2011 to 2013 . (B) The total load flux-based sand budget was negative for all years, indicating that sand sediment was evacuated from the reach. The partitioned sand budget indicated fine and medium sand grain-size fractions were mostly in a deficit and very fine sand accumulated during high flows in 2014 and 2016.

Does change occur uniformly, or are there hotspots of change?

0.00

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Grain Size (mm)

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% F

iner

Silt

VFine Sand

Fine Sand

Medium Sand

Coarse Sand

VCoarse Sand

Bank

Bank Attached Bar

Vegetated Island

In-channel Bar

Bed Material

-2

-1

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Met

ric T

ons

10 4 2011 to 2013

0.2

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0.9

1 1.2

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2.7

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ons

10 4 2013 to 2015

0.2

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1 1.2

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10 4 2015 to 2017

Distance Downstream of Little Snake Confluence (km)

0.2

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Figure 7: (A) Distance downstream of the Little Snake confluence. (B) Total volumetric change in budget cells between image dates. Generally, areas of erosion were clustered in the upper portion of the reach from 2-2.5 km.

Figure 1: Map showing the study area located near Dinosaur National Monument on the Yampa and Little Snake Rivers. The study area is part of a larger network of USGS-GCMRC acoustic sediment gages that form four flux-based sediment budgets in the region.

Figure 2: Method to characterize and correct for spatially distributed image co-registration error (A,B) while probabilistically accounting for digitizing error (D). Areas of erosion and deposition were calculated by subtracting the channel boundary between two image dates. (E)

Figure 4: (A) Area of vegetated island deposition. (B) Predicted elevation of the vegetated island and in-channel bar from the Bayesian model. (C) Height of deposition. (D) Volume of deposition associated with a single vegetated island.

A. B. C. D.

Figure 5: Example of posterior distribution.

A.

B.

A.

B.

Conclusions Future Work

• Net accumulation of sediment appears to be associated with vegetated island expansion and can be linked to accumulation of very fine sand in the partitioned flux-based sediment budget (Figure 6).

• Vegetated islands are predominately composed of the finest sand grain-size fractions (Figure 9). • The channel narrowed in all river segments from 2011 to 2015 and widened from 2015 to 2017

on the Little Snake River and the Yampa River downstream of the Little Snake (Figure 10). Narrowing appears to be driven by vegetated island expansion that out paces the rate of bank erosion.

• Channel change can be linked to processes of sediment transport when the flux-based budget is partitioned to understand where and why channel change occurs.

Figure 9: Grain size distributions of geomorphic units used in the morphological sediment budget (Figures 6,7). Vegetated islands are composed of the finest sand-size fractions and bed-material is composed of the coarsest sand-size fractions.

• Collect repeat measurements of bed topography to characterize changes in bed elevation through time.

• Spatially characterize the grain size of geomorphic units to link the partitioned flux-based sediment budget with the morphological sediment budget.

• Examine the influence of changes in sediment supply grain size and bed grain size to adjustments in channel form.

2011 2013 2015 201778

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86Little Snake River

2011 2013 2015 2017220.5

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Wid

th (m

)

Yampa River DS Little Snake

2011 2013 2015 2017120

125

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145Yampa River US Little Snake

Figure 10: Channel width through time. Width was calculated by subtracting the vegetated island area from the channel boundary area and dividing by the centerline length.