A morphodynamic model to evaluate long-term 

sandbar rebuilding using controlled floods

11/14/2013 ~ 1050 m3/s 11/20/2013 ~ 215 m3/s

Erich R. Mueller1 and Paul E. Grams2

1Department of Geosciences, Southern Utah University

2U.S. Geological Survey, Southwest Biological Science Center, Grand 

Canyon Monitoring and Research Center

9/28/2013 ~ 220 m3/s
Reattachment bars are the focus of the modeling approach

PIC HERE; or diagram here...



Over there, show “fan-eddy” 

diagram, then hydrograph

debris

Reattachment 

Bar

rapid

fan

boat

Separation Bar

Fan-Eddy Complex
Controlled Floods

12/28/2013 ~ 205 m3/s 3/3/2014 ~ 215 m3 1/24/2014 ~ 330 m /s 3/s

9/28/2013 ~ 220 m3/s 11/14/2013 ~ 1050 m3/s 11/20/2013 ~ 215 m3/s

Example sandbar (22-mile) showing sand deposition during the 2013 controlled flood, followed by bar-edge 

erosion and sand re-deposition at lower elevation during post-flood fluctuating flows. 
Background

• Controlled floods have occurred during a period of increasing vegetation 

establishment following the 1980s floods (e.g. Sankey et al., 2015)

• The degree of vegetation encroachment reflects the hydraulics of longer reaches

1984

100 m

1984

100 m

2013

“51-mile”

2013

“22-mile”
Narrower reaches

Larger range in stage Sandbar Groupings

(Mueller et al., 2018)

Wider reaches

Smaller range in stage

High 

Veg

Low 

Veg

Minimal vegetation 

encroachment,

More dynamic

Significant vegetation 

encroachment, 

More Stable

Low Veg

High Veg
A B

204-mile

PC1=3.2

55-mile

PC1=3.5

119-mile

PC1=-0.7

216-mile

PC1=-0.6

C D

Monitoring Site Analog Site Monitoring Site Analog Site

geomorphic reaches

Schmidt and Graf (1990)

A B

C D

width stage

veg area change

Long-term 

monitoring 

sites have 

analogs 

throughout 

the canyon

More of the 

canyon is 

narrow 

(“critical reaches”)
Location of sandbars used to parameterize the model
Morphdynamic Model

Mueller and Grams, 2021
Eddy Exchange and Sandbar Erosion

λλ: Eddy exchange coefficient

- the fraction of the eddy volume exchanged 

with the main channel per second

e: erosion rate parameter

- two models: exponential decay with total 

volume and height/length of exposed bar

Parameters optimized to match the measured data using 

a Nelder-Mead approach

Validated by censoring data from the calibration set
Key model equations 

(after Andrews and Vincent, 2007)

Suspended sand flux into eddy:

qqss,iiii = λλVVeeCCss

SSdd = wwssCCee

Deposition rate in eddy:

λλVVeeCCss=λλVVeeCCoo + wwssCCeeAAee

Mass balance in eddy:

CCee=

CCss+CCoo

2 Linear approximation

SSdd = wwssCCee =

λλhss,aaaaaawwssCCss

λλhss,aaaaaa + wwss

2

Rearrange:

Mass/time

Mass/area

Total flux in = flux out + deposition

Compute volume change using gage data and 

erosion equation

dd dddd

dddd

=

wwssλλhss,aaaaaaCCss

wwss

2 + λλhss,aaaaaa

AAss

1 − φφ − EE

For an “average” bar: 

bars are normalized by their 

maximum measured values 

average average maximum maximum

Sandbar area volume area volume

Location (m2

) (m3) (m2) (m3)

022r 2469 3285 3105 4098

030r 2828 3347 3871 6069

081l 1993 737 2101 1412

084r 959 475 1025 625

119r 3090 3495 3717 5412

122r 4433 3936 5507 5521

137l 3486 2300 3662 3063

145l 880 665 935 1126

213l 2023 2468 2248 4188

average 2462 2301 2908 3502
Input Data (from USGS gage)

Colorado River near 30 mile (09383050)

https://www.gcmrc.gov/discharge_qw_sediment/station/GCDAMP/09383050

Model Results

The model utilized data routinely measured at gages
Model Results: 2002-2019

Mueller and Grams, 2021
Post-hoc Modeling of the 

Controlled Flood Protocol

Mueller and Grams, 2021
Hypothetical Flood Scenarios

flood size and sediment supply both key factors 

2008 Flood:

Measured

Magnitude/

Duration

Sediment Supply/

Concentration

Mueller and Grams, 2021 (15-40% bar size decrease under reduced scenarios)
2021-2022 Scenarios

Using the Wright et al. (2010) model for sediment concentration

Preliminary data, do not cite
2021-2022 Scenarios overpredicts underpredicts

Measured data is more variable in the early period, likely related to the timing of surveys

Preliminary data, do not cite
Anticipated low release volumes lead to continued erosion (in the model)

May need to re-parameterize if flows or bar conditions (i.e. vegetation) 

are considerably different than calibration period

Preliminary data, do not cite
Re-calibrated model (2015-2020) improves the fit to the more recent data

~33% 

increase

Both erosion and eddy exchange parameters were slightly lower than in the original model

Preliminary data, do not cite
Sandbar Timelapse (courtesy of Ryan Lima)
Conclusions

- The model is simple, but is physically-based and captures major changes in bar size

- Model input utilizes the high-resolution sediment concentration data at gages

- Provides a useful tool for rapid scenario modeling because it is based on extensive measured data 

(flow and sediment conditions; sandbar surveys)

- Simple erosion models likely miss important processes, some of which (vegetation, mass failure) 

can be difficult to quantify

Future Work

- Couple sandbar model with hydropower generation model

- Explore better approaches to erosion modeling

- Incorporate effects of vegetation on stabilizing portions of bars
Acknowledgements

This work was supported by the Glen Canyon Adaptive Management Program.

Many scientists, field technicians, and boat operators assisted in data collection 

during more than two decades of monitoring, including Matt Kaplinski, Joe 

Hazel, Keith Kohl, Jack Schmidt, Rob Ross, Bob Tusso, Dan Buscombe, Tom 

Gushue, Katie Chapman and many more.