NCED Stream Restoration Toolbox
The calculator for topographic characteristics
and sediment transport from sand bed surveys
Brandon McElroy
May, 2006 – Version 1.1
The Stream Restoration Toolbox
The Stream Restoration Toolbox consists of current basic research cast into the form of
tools that can be used by practitioners. The details of a tool are presented through a
PowerPoint presentation, augmented by embedded Excel spreadsheets or other commonly
available applications. The toolbox is a vehicle for bringing research findings into practice.
While many tools are being developed by NCED Researchers, the opportunity to contribute
a tool to the Toolbox is open to the community. For more information on how to contribute
please contact Jeff Marr at marrx003@umn.edu.
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Statement of liability and usage
This tool is provided free of charge. Use this tool at your own risk. In offering this tool, the
following entities and persons do not accept any responsibility or liability for the tool’s use by
third parties:
• The National Center for Earth-surface Dynamics;
• The universities and institutions associated with the National Center for Earth-surface
dynamics; and
•The authors of this tool.
Users of this tool assume all responsibility for the tool results and application thereof. The
readers of the information provided by the Web site assume all risks from using the
information provided herein. None of the above-mentioned entities and persons assume
liability or responsibility for damage or injury to persons or property arising from any use of
the tool, information, ideas or instruction contained in the information provided to you.
3
Title Page
Tool Title: The calculator for topographic
characteristics and sediment transport from
sand bed surveys
Tool Author: Brandon McElroy
Author e-mail: bmcelroy@mit.edu
Version: 1.1
Associated files:
1) SandBedCalc.ppt (this file)
2) SandBedCalc.xls
Date: May, 2006
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Outline of this Document
I.
Limitations
A.
Bed material load only, not total load
B.
Requires high data integrity, accurate surveying
C.
Minimum data standards
II.
Motivation
A.
Theoretic
B.
Applied
III.
Schematic Overview
IV.
Introduction to Tool
V.
Theory Behind Tool
A.
Characteristic Height & Length
B.
Sediment Flux from Mass Conservation
C.
Translation and Characteristic Velocity
VI.
Using the Tool
VII
References
5
Warnings on tool limitations
-Estimates of bed geometry and sediment transport produced with this
tool are only snapshots of very dynamic systems and are only
valid for the transport conditions under which bed was surveyed
-Estimates of sediment flux produced with this tool are inherently limited
by the quality of topographic data used to produce them
-Minimum data standards for reliable tool accuracy
-Ten or more characteristic dune lengths in total survey
-Many tens of elevation measurements per characteristic
dune length
-Survey locations repeated within a very small fraction
of characteristic dune length
6
Motivation
THEORETIC
-Characterizing bed topography and sediment transport in sandy systems
is essential for elucidating underlying processes their relations
-Using remote sensing methods, e.g. acoustic doppler, avoids effects of
interfering with systems while collecting data, e.g. sediment traps
APPLIED
-Rates of sediment delivery to deltas are a fundamental part of their
overall sediment budgets
-Understanding effects of sediment loads on ecosystems requires
information on sediment fluxes
-Characterizations of channels for restoration necessitate transport rates
to evaluate the stability of a reach
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Depth [cm]
Tool Overview
Input: 2 or more bed surveys
Position [m]
Calculation based on mass conservation
Output: Characteristic Values of
Dune Height
Dune Length
Bed Translation Velocity
Bed Deformation Rate
Bed Material Sediment Flux
8
Introduction to the tool
Under most conditions, sand bedded rivers transport sediment through
through the propagation of topographic forms. Each sediment grain
moves intermittently such that the bed topography is continually being
recreated. In many sandy systems, there is very little sediment
suspended into the flow and transported very large distances, but in
some instances that style of transport can play a significant role. This
tool does not specifically address that case, rather it is focused on the
sediment that is an active part of the bed.
A low altitude aerial photograph of the N. Loup
River, Nebraska. The clarity of the water is
indicative of the absence of suspended sediment.
The complex bed topography can be seen as
contrasts in color intensity. (from D. Mohrig)
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Theory behind tool
Elevation [cm]
10
5
0
-5
-10
-15
0
5
10
15
20
25
30
Downstream Distance [m]
This profile comes from the photo in the previous slide and depicts well
the complexity of the bed topography. The salient features can,
however, be straightforwardly characterized by statistical measures of
height and length. That is achieved by calculating the variability of
elevations for profile subsets of many different lengths. It is called the
roughness function.
(1)
1
R( L) 
N
N
2
(



)
 i L
i 1
R = roughness function [m]
L = profile subset length [m]
N = number of profile subsets of length L
η = bed elevation [m]
ηL = mean bed elevation of subset [m]
i = index of measurements [/]
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Theory behind tool
10
Saturation Length = 190cm
R[cm]
Saturation Height = 3.8cm
1
0.1
1
10
100
1000
L[cm]
Plot of roughness function for profile in previous slide
10000
The roughness plot has 2
distinct regimes. One in which
R is nearly constant and
another in which the slope of
R is nearly constant. The
value of R at large lengths is
the saturation height. The mid
point of the transition to
constant slopes at lower R
occurs at the saturation length.
The saturation height and
length are related
proportionally to a
characteristic height and
length, respectively, by factors
near 1.
H c  2.8H sat
Lc  1.5Lsat
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Elevation [cm]
Theory behind tool
-- Initial Profile
-- Subsequent Profile
Downstream Distance [m]
In the plot above, the 2 profiles were taken at the same location about
half an hour apart, and the gray profile retains much of the form of the
black profile. Specifically the bed has been acted upon in a way that
gives the appearance that it has been both translated in the direction of
sediment transport and that it has been deformed from its initial
configuration. That behavior can be understood within the context of
the conservation of mass of the bed sediment, i.e. Exner’s equation:
qs

  Cb
x
t
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Theory behind tool
Exner’s Equation
qs= sediment flux [m2/s]
x = position along profile [m]
Cb= sediment concentration in bed [/]
η = bed elevation [m]
t = time [s]
qs

  Cb
x
t
By using the chain rule in the right-hand side an equation that can be
directly integrated is obtained. Vc is a characteristic velocity.
qs
 x
 Cb
x
x t
(2)
1
L
 qs  CbVc
L
qs

 Cb
Vc
x
x
1
L

L
This is the equation implemented
in the accompanying Excel file to
calculate sediment transport.
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Theory behind tool
z
qs 0  qsD
Vc

H
x
l
Traditionally, equation 2 has been evaluated for geometrically regular bed
topography, as above, leading to the bedload equation. (Eq. 3; Simons,
et al., 1971) Further, the constant of integration, qs0 had been assumed
zero both for convenience and because is was argued to represent
an otherwise negligibly small amount of transport via suspension.
qs

  Cb
x
t
(3)
qs  qsT  qsD  TRANSLATIVE
qs 
1
l
CbVc (
Hl
2
)  qs 0
FLUX  DEFORMATIVE FLUX
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Theory behind tool
Elevation [cm]
10
5
0
-5
-- Initial Profile
-- Subsequent Profile
-10
-15
0
5
10
15
20
Downstream Distance [m]
This shows the same profiles as before separated by half an hour, but here the
subsequent profile has been shifted backward by the translation length, the
mean distance of bed propagation. It can be quickly seen that certain parts of
the bed changed faster than others. (see red arrows) The deformation is then
measured by the amount of non-overlapping area. The two equations below
distinguish the parts of the total sediment flux, the translative flux and the
deformative flux. Their sum is exactly equation 2.
qsT  C V
1
b c L
 (
1
x
 1  2 )
1
2
qsD  CbVc
1
L

1
2
1  2
x
15
Theory behind tool
Elevation [cm]
10
5
0
-5
-- Initial Profile
-- Subsequent Profile
-10
-15
0
5
10
15
20
Downstream Distance [m]
To determine the translation length, the evolved profile is cross-correlated with
the initial profile. The resulting correlation function has a maximum at the
translation length. The characteristic velocity, Vc is then the length divided by
the time between surveyed profiles.
cross-correlation
function
Correlation value [/]
Cross-correlation plot
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1 0
-0.2
-0.3
-0.4
1
2
3
Shift Distance [m]
4
5
f 

x
t 1
( x) t  2 ( x  shift )

t 1
( x)
2
x
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Using the tool: step-by-step details
1- Preparing your data (in a separate spreadsheet)
The first step in using this tool is to ensure that your data is formatted
appropriately for the excel macro. Following these guidelines will do just that.
- All data should conform to these units
lengths, depths/heights: meters [m]
time: hours [hr] (e.g. 1 hour 15 minutes = 1.25)
- If data are in other units, convert them into the above units
- Use this convention:
depth measurements (i.e. water surface as datum) are negative numbers
height measurements (i.e. datum below sediment bed) are positive numbers
- Profiles should have similar extents. Prior to using data, delete any portions
of profiles that do not overlap in space.
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Using the tool: step-by-step details
2- Importing your data
After completing step 1, copy data into the DataInput sheet as shown below.
- All profiles must be defined at the same positions for the analysis. To that
end, the original profiles can be resampled in the ‘DataInput’ page.
Resampling is accomplished after the analysis positions are created.
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Using the tool: step-by-step details
2- Importing your data (continued)
- Analysis positions (brown column) are calculated from 3 parameters: starting
position, position spacing, and final position. The starting position is arbitrary,
the spacing should be the average distance between survey measurements,
and the final position is determined by the following formula
final position = start position + (spacing * total survey points)
- In this case there are 1550 point
measurements spaced 2cm
apart, and the start position was
set to zero for convenience.
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Using the tool: step-by-step details
2- Importing your data (continued)
- After creating the analysis positions, copy a profile into the light blue columns
labeled ‘Input’ for resampling. The dark blue columns labeled ‘Output’ will
then contain a resampled profile (i.e. values of profile interpolated at analysis
positions). The ‘Output’ column should be copied to the ‘DataAnalysis’ sheet.
- The positions should be copied once into the far left column in the
‘DataAnalysis’ sheet as shown below. Thereafter, only the ‘depth’ data is
needed. For the remaining profiles, simply copy each new profile into the next
column in ‘DataAnalysis’ sheet after resampling.
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Using the tool: examples
-In the example show here, 3 profiles each
containing 1550 point measurements were
used to calculate bed material flux over a
35 minute interval. The characterization
of the bed and its deformation is reported
in the upper left corner.
-Height --> characteristic height
-Length --> characteristic length
-Velocity --> characteristic velocity
-Deformation Flux --> percent magnitude of
total sediment flux (i.e. 100*Qsd/Qs)
-Bed Material Flux --> total volumetric flux
of sediment per unit width
21
References
Simons, D. B., Richardson, E. V., and Nordin, C. F., Jr. (1965). “Bedload
equation for ripples and dunes,” U.S. Geological Survey Professional
Paper 462-H.
++++
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Disclaimer Notice
The information on this site is subject to a disclaimer notice. Thank you for visiting the National
Center for Earth Dynamics Web site and reviewing our disclaimer notice. The Web site is for
informational purposes only and is not intended to provide specific commercial, legal or other
professional advice. It is provided to you solely for your own personal use and not for purposes
of distribution, public display, or any other uses by you in any form or manner whatsoever. The
information on this Web site is offered on an “as is” basis without warranty. The readers of the
information assume all risks from using the information provided herein.
This tool is provided free of charge. Use this tool at your own risk. In offering this tool, the following
entities and persons do not accept any responsibility or liability for the tool’s use by third parties:
• The National Center for Earth-surface Dynamics;
• The universities and institutions associated with the National Center for Earth-surface dynamics; and
•The authors of this tool.
Users of this tool assume all responsibility for the tool results and application thereof. The readers of the
information provided by the web site assume all risks from using the information provided herein. None of
the above-mentioned entities and persons assume liability or responsibility for damage or injury to
persons or property arising from any use of the tool, information, ideas or instruction contained in the
information provided to you.
23
Want more information?
For more information on this tool or the NCED Stream
Restoration Toolbox please contact the author of this tool,
Brandon McElroy, or the NCED Stream Restoration
Project Manager, Jeff Marr at marrx003@umn.edu
National Center for Earth-surface Dynamics
2 3rd Ave SE,
Minneapolis, MN 55414
612.624.4606
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