Sediment Transport During Three Controlled-Flood 

Experiments on the Colorado River Downstream from 

Glen Canyon Dam, with Implications for EddySandbar Deposition in Grand Canyon National Park

Open-File Report 2010–1128

U.S. Department of the Interior

U.S. Geological Survey
Cover: Nick Voichick (left), Greg Shellenbarger (center), and Steve Jones (right) in the sampling boat at the river-mile 61 study site on 

March 7, 2008, during high, steady discharge during the 2008 controlled-flood experiment (USGS photo by David J. Topping).
Sediment Transport During Three Controlled-Flood 

Experiments on the Colorado River Downstream from 

Glen Canyon Dam, with Implications for EddySandbar Deposition in Grand Canyon National Park 

By David J. Topping, David M. Rubin, Paul E. Grams, Ronald E. Griffiths, Thomas A. Sabol, Nicholas 

Voichick, Robert B. Tusso, Karen M. Vanaman, and Richard R. McDonald 

Open-File Report 2010–1128 

U.S. Department of the Interior 

U.S. Geological Survey 
U.S. Department of the Interior 

KEN SALAZAR, Secretary 

U.S. Geological Survey 

Marcia K. McNutt, Director 

U.S. Geological Survey, Reston, Virginia 2010 

For product and ordering information: 

World Wide Web: http://www.usgs.gov/pubprod 

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its natural and living resources, natural hazards, and the environment: 

World Wide Web: http://www.usgs.gov 

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Suggested citation: 

Topping, D.J., Rubin, D.M., Grams, P.E., Griffiths, R.E., Sabol, T.A., Voichick, N., Tusso, R.B., 

Vanaman, K.M., and McDonald, R.R., 2010, Sediment transport during three controlled-flood 

experiments on the Colorado River downstream from Glen Canyon Dam, with implications for 

eddy-sandbar deposition in Grand Canyon National Park: U.S. Geological Survey Open-File Report 

2010-1128, 111 p. 

Any use of trade, product, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government. 

Although this report is in the public domain, permission must be secured from the individual 

copyright owners to reproduce any copyrighted material contained within this report. 

ii
Contents 

Notation..............................................................................................................................................................................vii

Abstract................................................................................................................................................................................1

Introduction .........................................................................................................................................................................1

Purpose and Scope........................................................................................................................................................5

Theoretical Background................................................................................................................................................5

Acknowledgments........................................................................................................................................................11

Study Sites.........................................................................................................................................................................11

Data.....................................................................................................................................................................................13

Removal of Bias in Data Collected by D-77-Bag-Type Samplers ........................................................................26

Errors ..............................................................................................................................................................................27

Antecedent Conditions for Each Controlled-Flood Experiment (CFE).....................................................................28

Brief Description of Sand-Budgeting Approach.....................................................................................................28

Sand Enrichment in Each Reach Before the 2004 and 2008 CFEs .......................................................................32

Estimation of the Relative Levels of Sand Enrichment Antecedent to the 1996, 2004, and 2008 CFEs..........34

Analysis ..............................................................................................................................................................................35

Data Collected at Each Study Site During Each CFE..............................................................................................35

Data Collected at Each Study Site During All CFEs................................................................................................53

Data Collected During Each CFE at All Study Sites................................................................................................65

Sediment Export Past the Study Sites During the 1996, 2004, and 2008 CFEs....................................................70

Sand Budgeting During the 2004 and 2008 CFEs.....................................................................................................70

Lagrangian Sampling-Program data.........................................................................................................................71

β Analysis...........................................................................................................................................................................79

Values of β at Each Study Site During All CFEs ......................................................................................................84

Estimation of Differences in Reach-Averaged Bed-Sand Area in the Reaches Upstream from Each 

Study Site During Each CFE and Between CFEs .....................................................................................................86

Values of β at All Study Sites During Each CFE ......................................................................................................89

β Analysis of Data Collected During the Lagrangian Sampling Programs, with Estimation of 

Relative Differences in Reach-Averaged Bed-Sand Area Between the 2004 and 2008 CFEs........................92

Size, Known Levels of Sand Enrichment, and Mean Suspended-Sand Concentration in Each 

Reach During the 1996, 2004, and 2008 CFEs ...........................................................................................................97

Conclusions .....................................................................................................................................................................101

References Cited ............................................................................................................................................................103

iii
Figures 

1. Comparison of the flood hydrographs of the 1996, 2004, and 2008 CFEs at the USGS Colorado River 

at Lees Ferry, Arizona gaging station................................................................................................................3 

2. Pre-dam annual and partial-duration flood-frequency analysis for the Colorado River at Lees 

Ferry, Arizona gaging station..............................................................................................................................4 

3. Map showing locations of study sites and reaches between the study sites ..................................................12

4. Hydrographs, suspended-sediment data, and bed-sand data collected at each study site during 

each CFE...............................................................................................................................................................37 

5. Hydrographs, suspended-sediment data, and bed-sand data collected at each study site during 

all three CFEs .......................................................................................................................................................54 

6. Bed-silt and clay data collected at each study site during all three CFEs. .......................................................61 

7. Suspended-sand data collected during each CFE at all study sites...................................................................66 

8. Suspended-sediment data collected in the Lagrangian sampling programs during the 2004 and 

2008 CFEs..............................................................................................................................................................72 

9. Comparison of suspended-sand concentration and grain-size data collected in the Lagrangian 

sampling programs during the 2004 and 2008 CFEs......................................................................................78

10. Influence of changes in reach-averaged bed-sand area on β..........................................................................82 

11. Values of β at each study site during all CFEs ......................................................................................................84 

12. β-based computation of reach-averaged bed-sand area in the reaches upstream from each 

study site during each CFE................................................................................................................................88 

13. Results from β and βA analyses of reach-averaged bed-sand median grain size in the reaches 

upstream from each study site during all CFEs.............................................................................................90 

14. β-based computation of reach-averaged bed-sand area calculated using the suspended-sand 

data from the 2004 and 2008 Lagrangian sampling programs ....................................................................93 

15. Results from β and βA analyses of reach-averaged bed-sand median grain size using the 

suspended-sand data from the 2004 and 2008 Lagrangian sampling programs.....................................95 

16. Ratio of 2008 CFE to 2004 CFE sand conditions from lower Glen Canyon through eastern Grand 

Canyon computed using the suspended-sand data collected at sampling stations common to 

both the 2004 and 2008 Lagrangian sampling programs..............................................................................96

iv
Tables 

1. Inventory of suspended- and bed-sediment data collected during the three CFEs and analyzed in 

this report .............................................................................................................................................................16

2. Sand supply and sand export during the accounting periods antecedent to the 2004 and 2008 CFEs ........33

3. Sand enrichment in each reach during the accounting periods antecedent to the 2004 and 2008 

CFEs.......................................................................................................................................................................33

4. Comparison of discharge and sand supply during the years leading up to each CFE ....................................34 

5. Observed coupled changes in suspended-sand concentration and median grain size through 

each reach during each CFE.............................................................................................................................69 

6. Sand export and silt and clay export past the study sites on the Colorado River during the 1996, 

2004, and 2008 CFEs............................................................................................................................................70 

7. Sand budgets for each reach during the 2004 and 2008 CFE sand-budgeting periods. ..................................71

8. 2008 CFE parameters at each study site normalized by their values during the 2004 CFE and during 

the 1996 CFE .........................................................................................................................................................98

9. Signs of relations between the 2008 CFE parameters normalized by their values during the 2004 

CFE and normalized by their values during the 1996 CFE ..........................................................................100

v
Conversion Factors 

Inch/Pound to SI 

Multiply By To obtain 

Length 

foot (ft) 0.3048 meter (m) 

mile (mi) 1.609 kilometer (km) 

Volume 

ounce, fluid (fl. oz) 0.02957 liter (L) 

pint (pt) 0.4732 liter (L) 

quart (qt) 0.9464 liter (L) 

gallon (gal) 3.785 liter (L) 

Flow rate 

foot per second (ft/s) 0.3048 meter per second (m/s) 

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s) 

Mass 

ounce, avoirdupois (oz) 28.35 gram (g) 

SI to Inch/Pound 

Multiply By To obtain 

Length 

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi) 

Volume 

liter (L) 33.82 ounce, fluid (fl. oz) 

liter (L) 2.113 pint (pt) 

liter (L) 1.057 quart (qt) 

liter (L) 0.2642 gallon (gal) 

Flow rate 

meter per second (m/s) 3.281 foot per second (ft/s) 

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s) 

Mass 

gram (g) 0.03527 ounce, avoirdupois (oz) 

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83). 

vi
Notation 

Ab Fractional bed-sand area 

Ab-ref Reference fractional bed-sand area 

C Suspended-sediment concentration 

CSAND Suspended-sand concentration 

CSILT &CLAY Suspended-silt-and-clay concentration 

Cref Reference concentration of the suspended sand 

D50 Median grain size 

Db Median grain size of the bed sand 

Db-ref Reference median grain size of the bed sand 

Ds Median grain size of the suspended sand 

Ds-ref Reference median grain size of the suspended sand 

J Shear-velocity exponent in equation 1 

K Bed grain-size exponent in equation 1 

L Shear-velocity exponent in equation 6 

M Bed grain-size exponent in equation 6 

nTRANS Number of transits taken by a depth-integrating suspended-sediment sampler at a 

 vertical 

nVERT Number of verticals (that is, sampling stations) in a cross-section 

Q Discharge of water 

u Shear velocity *

β Non-dimensional measure of the reach-averaged bed-surface grain size that interacts 

with the suspended sand in the flow 

vii
viii

βA Version of β corrected for differences in reach-averaged bed-sand area 

δ Factor that needs to be applied to correct CSAND for a change in the median grain size 

of suspended sand over time or space at constant reach-averaged boundary shear 

stress

φ Unit of grain size equal to−log2D where D is grain size in mm 

ρ Density 

τb Boundary shear stress 

τsf Skin-friction component of the boundary shear stress 
Sediment Transport During Three Controlled-Flood 

Experiments on the Colorado River Downstream from 

Glen Canyon Dam, with Implications for EddySandbar Deposition in Grand Canyon National Park 

By David J. Topping, David M. Rubin, Paul E. Grams, Ronald E. Griffiths, Thomas A. Sabol, Nicholas 

Voichick, Robert B. Tusso, Karen M. Vanaman, and Richard R. McDonald 

Abstract 

Three large-scale field experiments were conducted on the Colorado River downstream 

from Glen Canyon Dam in 1996, 2004, and 2008 to evaluate whether artificial (that is, controlled) 

floods released from the dam could be used in conjunction with the sand supplied by downstream 

tributaries to rebuild and sustainably maintain eddy sandbars in the river in Grand Canyon National 

Park. Higher suspended-sand concentrations during a controlled flood will lead to greater eddysandbar deposition rates. During each controlled flood experiment, sediment-transport and bedsediment data were collected to evaluate sediment-supply effects on sandbar deposition. Data 

collection substantially increased in spatial and temporal density with each subsequent experiment. 

The suspended- and bed-sediment data collected during all three controlled-flood experiments are 

presented and analyzed in this report. Analysis of these data indicate that in designing the 

hydrograph of a controlled flood that is optimized for sandbar deposition in a given reach of the 

Colorado River, both the magnitude and the grain size of the sand supply must be considered. 

Because of the opposing physical effects of bed-sand area and bed-sand grain size in regulating 

suspended-sand concentration, larger amounts of coarser sand on the bed can lead to lower 

suspended-sand concentrations, and thus lower rates of sandbar deposition, during a controlled 

flood than can lesser amounts of finer sand on the bed. Although suspended-sand concentrations 

were higher at all study sites during the 2008 controlled-flood experiment (CFE) than during either 

the 1996 or 2004 CFEs, these higher concentrations were likely associated with more sand on the 

bed of the Colorado River in only lower Glen Canyon. More sand was likely present on the bed of 

the river in Grand Canyon during the 1996 CFE than during either the 2004 or 2008 CFEs. The 

question still remains as to whether sandbars can be sustained in the Colorado River in Grand 

Canyon National Park through use of controlled floods in conjunction with typical amounts and 

grain sizes of sand supplied by the tributaries that enter the Colorado River downstream from Glen 

Canyon Dam. 

Introduction 

The 1963 closure and subsequent operation of Glen Canyon Dam has resulted in substantial 

erosion of eddy-sandbar habitats in the Colorado River in Grand Canyon National Park (GCNP). 

1
This has occurred as a result of (1) the dam cutting off approximately 94 percent of the natural sand 

supply at the upstream boundary of GCNP (Andrews, 1991; Topping and others, 2000a; Rubin and 

others, 2002; Wright and others, 2005), (2) dam releases generally exceeding lower seasonal predam discharges where sand accumulation naturally occurred in the channel of the Colorado River 

in GCNP (Topping and others, 2000a, 2003; Rubin and others, 2002; White and others, 2005; 

Wright and others, 2008), and (3) the loss of natural flood flows to redeposit this accumulated sand 

in eddy sandbars (Dolan and others, 1974; Howard and Dolan, 1981; Rubin and others, 1990, 2002; 

Schmidt and Graf, 1990; Schmidt, 1990, 1999; Schmidt and Rubin, 1995; Schmidt and others, 

2004). During the 12-year period from 1996 through 2008, three large-scale field experiments have 

been conducted utilizing controlled floods released from Glen Canyon Dam to test whether it were 

possible to sustainably rebuild and maintain eddy sandbars and associated habitat in the Colorado 

River in GCNP using only the available tributary-supplied sand. These three controlled-flood 

experiments occurred in March-April 1996, November 2004, and March 2008. The 1996 and 2004 

experiments have been referred to in the scientific literature as "controlled floods" or "flood 

experiments" (Rubin and others, 1998; Webb and others, 1999; Hazel and others, 2006; Topping 

and others, 2000b, 2006a), whereas the 2008 experiment has been informally referred to as a "high 

flow." For consistency with the scientific literature and because the peak magnitudes of these 

artificial dam-released floods exceeded the natural pre-dam base flood magnitude of 18,500 ft3

/s 

defined in Topping and others (2003) based on flow-duration analyses, the term "controlled flood 

experiment" (CFE) is used herein to describe all three of these field experiments. 

The hydrograph of the 1996 CFE was different from the hydrographs of the 2004 and 2008 

CFEs. The peak discharge of the 1996 CFE (45,000 ft3

/s) was slightly higher than the peak 

discharges during the 2004 and 2008 CFEs (42,000 to 44,000 ft3

/s depending on reach). This 

difference in peak discharge primarily arose because of maintenance on Glen Canyon Dam during 

the 2004 and 2008 CFEs and to a lesser degree because of lower reservoir levels during the 2004 

and 2008 CFEs. Greater tributary water input, mostly from the Little Colorado River, during the 

2008 CFE helped to reduce the difference in peak discharge between the 1996 and 2008 CFEs in 

downstream reaches. This allowed direct comparison between suspended-sediment data collected 

during the 1996 and 2008 CFEs in downstream reaches (that is, below the mouth of the Little 

Colorado River) without needing to account for the influence of discharge differences on sediment 

transport. As released from Glen Canyon Dam, the duration of the high-, steady-discharge part of 

the flood hydrograph during the 1996 CFE was much longer (~7 days) than during the 2004 and 

2008 CFEs (~60 hours). This difference in flood duration arose because, before the 1996 CFE, sand 

concentrations during the 1996 CFE were expected to be much lower than they actually were (E.D. 

Andrews, U.S. Geological Survey [USGS], oral commun., 1996). Before the 1996 CFE, the only 

available post-dam dataset of sediment-transport during floods consisted of data collected at 

various locations on the Colorado River in Grand Canyon during the 1980s (Garrett and others, 

1993), when suspended-sand concentrations were anomalously low following the large degree of 

bed-sand coarsening during large dam-released floods in 1983-1986 (Topping and others, 2000b, 

2005, 2007a, 2008). These anomalously low concentration data were the data used to design the 

duration of the 1996 CFE hydrograph (E.D. Andrews, USGS, oral commun., 1996). Finally, the 

rising limb of the flood hydrograph during the 1996 CFE was relatively short compared to the more 

gradual rising limbs of the flood hydrographs during the 2004 and 2008 CFEs, and the receding 

limb of the flood hydrograph of the 1996 CFE was longer than those of the 2004 and 2008 CFEs 

(fig. 1). 

2
0

10,000

20,000

30,000

40,000

50,000

1996 

2004

2008

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Q, IN CUBIC 

FEET PER SECOND

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

Figure 1. Comparison of the flood hydrographs of the 1996, 2004, and 2008 CFEs at the USGS gaging 

station on the Colorado River at Lees Ferry, Arizona (station number 09380000). These hydrographs 

were shifted in time such that zero time (indicated by vertical green line) is the beginning of high, 

steady discharge (Q) during each CFE. The Lees Ferry gaging station is located approximately 16 river 

miles downstream from Glen Canyon Dam (see fig. 3 below). 

Although terminology in the nonscientific arena has varied over time in describing these 

events, the 1996, 2004, and 2008 CFEs are technically floods based on the flow-duration and floodfrequency analyses for the pre-dam Colorado River in Topping and others (2003). Flows of 42,000 

to 45,000 ft3

/s were only equaled or exceeded 10.1 to 11.2 percent of the time in the natural predam Colorado River at Lees Ferry, Arizona, near the upstream boundary of GCNP (computed from 

the data for fig. 22A in Topping and others, 2003). Before construction and operation of Glen 

Canyon Dam, floods with peak discharges of 42,000 to 45,000 ft3

/s had a recurrence interval of 1.1 

to 1.2 years on the annual flood series and 0.9 years on the partial-duration flood series (fig. 2). 

Furthermore, the peak discharges of the 1996, 2004, and 2008 CFEs were substantially higher than 

the peak discharges of six1 of the 42 annual snowmelt floods between 1921 and 1962, and only 

slightly lower in peak magnitude than two2 more of these 42 floods. During the post-dam period of 

1963-2000, the recurrence interval associated with floods with peak discharges of 42,000 to 45,000 

ft3/s increased dramatically to about 3 years in the partial-duration series (fig. 37 in Topping and 

others, 2003). This post-dam recurrence interval is somewhat misleading, however, because most 

of the post-dam floods in this discharge range occurred in April-June 1965 during the pulsed dam 

releases informally referred to as "channel-cleaning flows" by engineers (fig. 2C in Grams and 

others, 2007). 

Given the different tributary sand supplies and dam releases antecedent to the 1996, 2004, 

and 2008 CFEs, these three experiments were probably conducted under very different sand-supply 

conditions, and these different sand-supply conditions likely controlled the resultant eddy-sandbar 

responses during these CFEs. Schmidt and others (1993) showed in flume experiments that the 

deposition rate in an eddy sandbar during a flood directly depends on suspended-sand 

concentration. However, as shown below, the relation between the antecedent upstream sand 

supply to a reach in a controlled flood and the concentration of suspended sand in a reach during a 

controlled flood is not straightforward, owing to the physics coupling bed-sand area and bed-sand 

 1

 These six floods were the annual snowmelt floods with peak discharges at Lees Ferry, Arizona, of 25,500 ft3/s in 

1934, 34,300 ft3

/s in 1954, 34,600 ft3/s in 1931, 35,600 ft3/s in 1955, 38,900 ft3/s in 1959, and 40,200 ft3/s in 1961. 2

 These two floods were the annual snowmelt floods with peak discharges at Lees Ferry, Arizona, of 46,800 ft3/s in 

1960 and 47,300 ft3

/s in 1940. 

3
10,000

100,000

0.1 1 10 100

PRE-DAM ANNUAL FLOOD SERIES FROM 

LEES FERRY GAGING STATION RECORD 

PRE-DAM PARTIAL-DURATION FLOOD SERIES FROM 

LEES FERRY GAGING STATION RECORD 

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

RECURRENCE INTERVAL, IN YEARS

1921 FLOOD

1884 FLOOD

500,000

50,000

200,000

20,000

EXPLANATION

 

Figure 2. Pre-dam annual and partial-duration flood-frequency analysis for the Colorado River at Lees 

Ferry, Arizona gaging station. Blue band indicates the 42,000 to 45,000 ft3

/s range in the peak 

discharges of the 1996, 2004, and 2008 CFEs. See figure 3 for the location of the Lees Ferry gaging 

station. After figure 36 in Topping and others (2003). 

grain size to suspended-sand concentration. Designing future controlled floods thus requires 

understanding how the different responses of eddy sandbars observed during these three CFEs were 

related to differences in the suspended-sand concentrations measured during these CFEs, which, in 

turn, were the product of the different sand supplies antecedent to these three CFEs. 

To be a viable tool in rebuilding eddy sandbars in a sustainable manner, controlled floods 

must result in eddy sandbars increasing in overall size over large segments of the Colorado River in 

the study area. Eddy sandbars increase in overall size when the sand deposited in these sandbars is 

derived largely from upstream environments outside of eddies. Controlled floods conducted during 

relatively sand-depleted conditions, such as those that likely existed in upstream reaches during the 

1996 CFE, result in the erosion of upstream eddy sandbars, with an increase in eddy-sandbar size 

only occurring in the most downstream reaches (Hazel and others, 1999; Schmidt, 1999). Repeated 

controlled floods conducted under such sand-depleted conditions would likely lead to the eventual 

erosion of much of the sand from the Colorado River in Grand Canyon, and this is therefore not a 

sustainable strategy for maintaining eddy sandbar size in GCNP (Topping and others, 2006a). 

Subsequent CFEs during 2004 and 2008 were thus conducted to test whether controlled floods 

conducted under greater levels of sand enrichment following large tributary floods and lower dam 

4
releases could result in greater, and potentially sustainable, eddy-sandbar deposition in the 

Colorado River in GCNP (Rubin and others, 2002; Topping and others, 2006a). 

High-resolution sediment-transport and grain-size data are required to evaluate the reachby-reach sand supplies before a CFE, the reach-by-reach sand supplies during a CFE, and the 

downstream patterns of erosion and deposition during a CFE. To meet this need, suspended- and 

bed-sediment data were collected at a number of fixed locations during the 1996, 2004, and 2008 

CFEs, and suspended-sediment data were also collected using a Lagrangian reference frame during 

the 2004 and 2008 CFEs. The 1996 CFE resulted in major advances in the understanding of the 

role of supply limitation in regulating sand transport in the Colorado River in GCNP (Rubin and 

others, 1998, 2002; Topping and others, 1999, 2000a, 2000b, 2005, 2007a, 2008; Rubin and 

Topping, 2001, 2008; Schmidt and others, 2007). Therefore, as a result of this learning, suspendedand bed-sediment data were collected at much higher resolutions during the 2004 and 2008 CFEs 

than during the 1996 CFE. 

Purpose and Scope 

This study was conducted to collect and analyze sediment-transport data to help in the 

evaluation and future design of controlled floods as a possible tool in rebuilding and maintaining 

eddy sandbars in the Colorado River in Grand Canyon National Park. The purpose and scope of 

this report is to present the suspended- and bed-sediment data collected in the Colorado River 

during controlled-flood experiments conducted in 1996, 2004, and 2008 and to analyze those data. 

Theoretical Background 

Previous work has shown that the deposition rate in an eddy sandbar during a flood directly 

depends on suspended-sand concentration (Schmidt and others, 1993). To maximize eddy-sandbar 

deposition, a properly designed controlled flood would therefore maintain the highest suspendedsand concentrations for the longest time possible (at least through the duration of the flood). 

Conducting controlled floods when the sand supply in a river reach of interest is the largest, 

however, will not ensure that suspended-sand concentrations will be sufficiently high to optimize 

eddy-sandbar deposition. Because the boundary shear stress field, bed-sand grain size, bed-sand 

area, and the areal distribution of sand in a reach all interact to regulate suspended-sand transport, 

the highest suspended-sand concentration at a given discharge of water does not necessarily 

correspond to the largest sand supply in a reach. Based on equilibrium suspended-sediment theory 

developed for steady, uniform flow (reviewed by McLean, 1992) for beds entirely composed of 

sand with either narrow or wide lognormal grain-size distributions, and with or without dunes on 

the bed, Rubin and Topping (2001) found that 

C , (1) SAND ∝ u

*

J

Db

K

where CSAND is the time- and spatially averaged suspended-sand concentration, u

* is the spatially 

averaged shear velocity, and Db is the spatially averaged median grain size of the bed sand. 

Depending on the sorting of the bed-sand grain-size distribution and whether dunes were present on 

the bed, Rubin and Topping (2001) found that, for most cases, J equaled 3.5 and K ranged from -

1.5 to -3.0. In the analyses in this report, J is set equal to 3.5 and K is set equal to -2.5. Using these 

values for J and K, and because 

u

* = τ b ρ , (2) 

5
where τb is the spatially averaged boundary shear stress and ρ ≈ 1 g/cm3

 is the density of the 

water/suspended-sediment mixture at typical water temperatures, equation 1 can be rewritten as 

C . (3) SAND ∝τ b

1.8Db−2.5

For steady, uniform flow, and an approximately uniform areal distribution of sand on a gravel bed, 

the fractional area of the bed sand, Ab, ranges from 0 to 1 and exerts an approximately linear 

control on suspended-sand concentration (Topping, 1997; Grams, 2006; Grams and Wilcock, 

2007), thus leading to the following form of equation 3: 

CSAND ∝ Abτ b

1.8Db−2.5

.

 (4) 

For a flat bed composed entirely of sand (that is, a bed without form drag), the reachaveraged skin-friction component of the boundary shear stress, τsf, is equal to τb. As the area of 

sand on a gravel bed decreases, the spatially averaged form drag increases, resulting in a reduction 

of τsf relative to τb. In the absence of form-induced stresses (for example, Giménez-Curto and Lera, 

1996; Nikora and others, 2001; McLean and Nikora, 2006) that may offset this reduction in τsf, the 

spatially averaged near-bed concentration of suspended sand should decrease quasi-linearly as a 

function of τsf (after Topping, 1997). To express this effect, equation 4 may be modified as 

 CSAND ∝ Ab

τ sf

τ b

τ b

1.8Db−2.5 . (5) 

In gravel-bedded rivers where the bed-gravel grain size is very small relative to the flow depth (as 

in most of the Colorado River in the study area except in the riffles and rapids), the reach-averaged 

gravel form-drag component of τb must be much smaller than τb (Wiberg and Smith, 1991; 

Topping, 1997). As a gravel bed becomes buried in sand, dunes will develop on the sand patches 

(Topping, 1997; Rubin and others, 2001) resulting in an additional source of form drag, which may 

become larger than the form drag associated with the gravel (Smith and McLean, 1977; McLean, 

1992, Topping, 1997, McLean and others, 1999; Maddux and others, 2003; Topping and others, 

2007a). As a result of this effect, over these sand patches, the ratio τ sf τ b in equation 5 may range 

from about 0.5 to 1. Because sand patches typically compose a minority of the bed of the Colorado 

River in the study area (Anima and others, 1998; Schmidt and others, 2007; R. Anima, USGS, 

2008, unpublished 1998 and 1999 side-scan sonar data), however, the effect of dune form drag on 

the ratio τ sf τ b in equation 5, when spatially averaged over large parts of the bed, is minimal. The 

ratio τ sf τ b in equation 5 is thus likely equal to approximately 1 at the measurement cross-sections 

in this study and can be excluded from further consideration. 

Using steady, uniform flow suspended-sediment theory, a proportionality similar to that in 

equation 4 can be derived relating the median grain size of the suspended sand to the median grain 

size of the bed sand. Unlike the proportionalities in equations 4 and 5, however, Ab does not enter 

into this new proportionality because it affects the flux of each size class of sediment between the 

bed and the suspended load equally (after Topping, 1997; Topping and others, 2007a). For sand 

beds with either narrow or wide lognormal grain-size distributions, and with or without dunes on 

the bed, Rubin and Topping (2001) found that 

Ds ∝ u

*

L

Db

M , (6) 

where Ds is the spatially averaged median grain size of the suspended sand. Depending on the 

sorting of the bed-sand grain-size distribution and whether dunes were present on the bed, Rubin 

and Topping (2001) found that L ranged from 0.15 to 0.4 and M ranged from 0.5 to 1.0. Based on 

these values and also on the integral constraints that 0.1J = L, and that M - 0.1K = 1 (Rubin and 

6
Topping (2001, 2008), L is set equal to 0.35 and M is set equal to 0.75 in the analyses in this report. 

Substituting equation 2 into equation 6, using these values for L and M, and rearranging yields: 

Ds ∝τ b

0.18Db0.75 . (7) 

Subsequent discussion of the theoretical background and physical assumptions used in the analyses 

in this report are thus based on equations 4 and 7. 

Previous work has shown that suspended-sand transport in the Colorado River in the study 

area varies as a function of both the discharge of water and the upstream supply of sand (Topping 

and others, 2000a, 2000b) and that under typical dam releases, sand transport is regulated equally 

by the discharge of water (through τb) and by the grain-size distribution of the bed sand (Rubin and 

Topping, 2001, 2008). To a lesser degree than these two regulators of sand transport, the reachaveraged bed-sand area also regulates sand transport in the Colorado River (Topping and others, 

2007a). Additionally, changes in how sand is distributed areally within a reach have been observed 

following large changes in discharge (Anima and others, 1998; Topping and others, 2000b; 

Schmidt and others, 2007), and these changes may also influence sand transport. Flow in the 

Colorado River in the study area is typically nonuniform as a result of complicated reach geometry 

(with lateral recirculation eddies, scour holes, and other bed undulations) and sand typically 

composes the minority of the bed (Howard and Dolan, 1981; Schmidt and Graf, 1990; Topping and 

others, 2005, 2008; Hazel and others, 2006). As in any river, the physical interaction between the 

flow and complicated bed topography controls the loci of sand deposition and erosion (for 

example, Nelson and Smith, 1989; Shimizu and others, 1990). Under typical sand-supply 

conditions and dam releases, sand is present mainly in eddy sandbars, along some of the banks, and 

as patches on a bed composed of fluvial gravel, colluvium, and bedrock (Anima and others, 1998; 

Schmidt and others, 2007; R. Anima, USGS, 2008, unpublished 1998 and 1999 side-scan sonar 

data). Sand patches will form in regions on the bed of the Colorado River where convergence 

occurs in τb, and these patches will continue to aggrade and enlarge until either convergence in τb

disappears or the upstream supply of sand becomes insufficient at a given convergence in τb to 

maintain a depositional environment (Topping and others, 2000b). Sand patches will not form in 

regions on the bed where divergence in τb occurs, except in reaches downstream from tributaries 

following large tributary floods that can temporarily overwhelm the bed of the Colorado River with 

sand3

. The regions on the bed where convergence or divergence in τb occurs change location with 

stage, resulting in different bed-sand areas and different areal distributions of sand within a reach at 

different water discharges (Topping and others, 2000b, 2007a). Large increases in sand-patch 

thickness will result in local increases in τb over these patches. Such large changes in sand-patch 

thickness have been observed between repeated bathymetric surveys, but have typically affected 

less than about 20 percent of the bed over the kilometer-long reach scale (USGS Grand Canyon 

Monitoring and Research Center, 2000-2005 unpublished data). Because it is unlikely that τb over 

these patches changes by more than 50 percent as these patches change thickness, typical changes 

in sand-patch thickness will likely result in less than a 10-percent change in the spatially averaged 

τb over the kilometer-long reach scale. 

 3

 The day after a large flood on the Paria River (located in fig. 3 below) on September 12, 1998 (described in 

Topping and others, 2000b), the downstream bed of the Colorado River was overwhelmed with sand. This resulted in a 

substantial decrease in flow depth across the entire channel. Associated with this change in channel geometry, Froude 

numbers were increased, and upstream-propagating breaking waves were observed over antidunes. In this transient 

situation, the reach-averaged τb was likely substantially increased by the large increase in reach-averaged bed-sand 

thickness and bed-sand area. By September 14, 1998, sand had been eroded from this reach, flow depths had 

increased, and the antidunes were gone. 

7
Although equation 4 was developed for equilibrium suspended-sediment transport under 

steady, uniform flow, it can be applied to the supply-limited suspended-sand transport and 

nonuniform flow conditions that typify the Colorado River in the study area after some key 

physical assumptions. For typical flow conditions in the Colorado River in Marble and Grand 

Canyons, the spatial scale over which suspended sand may equilibrate with the bed ranges from 

about 600 m to well over 1 km (Topping and others, 2007a). Therefore, the following physical 

assumptions are utilized to use the physics described by equations 4 and 7 to allow analysis of the 

suspended-sediment data presented in this report. First, spatial averaging over the kilometer-long 

reach scale is used to relate a given CSAND and Ds in a cross-section to the values of Ab, τb, and Db

averaged over the kilometer-long reach upstream from the measurement cross-section. Second, 

areal heterogeneities in Ab, τb, and Db are assumed to occur over spatial scales much smaller than 

the kilometer-long reach scale. Third, and similar to arguments made in Rubin and Topping (2001) 

based in Einstein and Chien (1953), temporal changes in Ab and Db caused by changes in the 

upstream sand supply are assumed to occur over longer time scales than changes in τb and sand 

transport. These three assumptions together allow use of suspended-sediment theory developed for 

equilibrium suspended-sediment transport under steady, uniform flow in the analysis of suspendedsediment data collected in a river. As a result of these three assumptions, measured values of CSAND

and Ds cannot be used to detect variations on Ab, τb, and Db occurring over less than the kilometerlong reach scale. Finally, because changes in sand-patch thickness do not likely result in substantial 

changes in the reach-averaged value of τb, the reach-averaged τb is only allowed to vary as a 

function of changes in water discharge. The appropriateness of and alternatives to this final 

assumption will be evaluated in a subsequent section of this report. 

For a given discharge of water, therefore, suspended-sand concentration depends strongly 

on the reach-averaged grain-size distribution of the sand on the bed, and to a lesser degree, the 

reach-averaged area of sand on the bed. By equation 4, the reach-averaged grain-size distribution of 

the bed sand exerts a nonlinear control on suspended-sand concentration (Rubin and Topping, 

2001, 2008), whereas the reach-averaged area of sand on the bed exerts an approximately linear 

control on suspended-sand concentration (Grams, 2006; Grams and Wilcock, 2007). In the general 

case, where sand is uniformly distributed on the bed, a factor of 3 decrease in the reach-averaged 

median grain size of the bed will lead to an approximate factor of 10 increase in suspended-sand 

concentration (Topping and others, 2000b); a factor of 3 decrease in the reach-averaged area of 

sand on the bed will lead to an approximate factor of 3 decrease in suspended-sand concentration 

(Topping and others, 2007a). Changes in the reach-averaged bed-sand grain-size distribution will 

lead to changes both in suspended-sand concentration and in the grain-size distribution of the 

suspended sand, whereas changes in the reach-averaged area of sand on the bed will lead to 

changes in only suspended-sand concentration (Topping and others, 2007a). Because of these 

physical effects, a large increase in sand supply to a sand-starved reach under constant discharge 

will lead to an increase in suspended-sand concentration (through a large increase in reachaveraged bed-sand area and possibly a decrease in reach-averaged bed-sand median grain size 

depending on the differences between the antecedent bed-sand grain-size distribution and the grainsize distribution of the newly supplied sand), whereas a much smaller increase in a much finer sand 

supply to this same sand-starved reach under constant discharge will result in a much greater 

increase in suspended-sand concentration (through less of an increase in reach-averaged bed-sand 

area, but a much larger decrease in reach-averaged bed-sand median grain size). Because a greater 

amount of sand was supplied in the first of these two hypothetical scenarios, the supply-driven 

increase in suspended-sand concentration under the first scenario should be longer lived than the 

8
supply-driven larger increase in suspended-sand concentration under the second scenario. 

However, because the sand supply was coarser in the first of these two scenarios, the suspendedsand concentrations under this first scenario could be considerably lower than under the second 

scenario. Therefore, the "best sand supply" to maximize sandbar deposition for a given controlled 

flood is not the largest sand supply, but rather the sand supply composed of a sufficiently large 

volume of sand fine enough to maintain the highest suspended-sand concentrations for the duration 

of the controlled flood. 

In this report, the terms "sand supply" and "sand enrichment" are used to refer to the 

amount, mass or volume, of sand in a given reach of the Colorado River, which for a given 

discharge of water is always positively correlated with bed-sand area and, in most but not all 

instances, negatively correlated with bed-sand median grain size. In the Colorado River in Marble 

and Grand Canyons, negative correlation typically exists between the amount of sand in a reach 

and reach-averaged bed-sand median grain size (that is, more sand equates to a finer bed-sand 

grain-size distribution) because the median grain size of the sand supplied by tributaries is typically 

much finer than the median grain size of the sand on the bed of the river (Topping and others, 

2000b). However, the exact sequence of inputs of new sand from tributaries and various dam 

releases on the Colorado River can negate this negative correlation. For example, Topping and 

others (2005, 2008) showed that, when substantial armoring of bed sand occurs, the surface grain 

size of the bed sand will be positively correlated with the amount of sand in a reach (that is, "more 

sand" is covered by a cap of coarser sand). Furthermore, over a longer period of time, a large input 

of sand from a tributary will be winnowed, such that the correlation between the amount of sand in 

the reach downstream from this tributary and reach-averaged bed-sand median grain size may be 

positively correlated over this longer time period. In other words, the following sequence of events 

is likely in the reach downstream from a large tributary over some period of time given the relative 

magnitudes of a sand input from this tributary and the dam releases in the Colorado River (an 

example of a scenario similar to this exists in figures 13 through 15 in Topping and others, 2000b): 

(1) Initially, the sand in patches on the gravel bed of the Colorado River had an initial median 

grain size of 0.3 mm and composed about 20 percent of the bed. 

(2) A large input of tributary sand occurs, causing the bed-sand area in the reach of the 

Colorado River downstream from this tributary to increase to almost 100 percent and the 

bed-sand median grain size to decrease to about 0.1 mm. 

(3) At some time later, much of the finer fraction of this new input of tributary sand has been 

winnowed from the bed in this reach and transported downstream. 

(4) At a later time, the sand in this reach has coarsened to about 0.4 mm and the reachaveraged bed-sand area has decreased to about 30 percent. Because of the nonlinearity 

between suspended-sand concentration and bed-sand median grain size and the linearity 

between suspended-sand concentration and bed-sand area, winnowing processes will 

likely increase the bed-sand median grain size faster than they will reduce the bed-sand 

area.4

 

(5) For the same discharge of water, the suspended-sand concentration over the final bed state 

would be about a factor of 1.8 lower than that over the initial bed state by only the effect 

of the coarser bed-sand median grain size, and would be about a factor of 1.5 greater than 

that by only the effect of the greater bed-sand area, thus resulting in a net 20 percent 

decrease in suspended-sand concentration between the initial bed state and the final bed 

state. 

 4

 As shown in Topping and others (2007a), bed-sand median grain size dominates over bed-sand area in regulating 

sand transport, and in certain cases the influence of changes in the bed-sand grain-size distribution can completely 

offset the influence of opposing changes in bed-sand area in regulating suspended-sand transport. 

9
Thus, over the time period associated with the above scenario, lower suspended-sand 

concentrations are associated with a larger sand supply. In this case, sand supply is positively 

correlated with reach-averaged bed-sand area and bed-sand median grain size. 

Future design of a controlled flood to maximize eddy-sandbar deposition requires knowing 

the sand-supply and grain-size conditions that gave rise to the suspended-sand concentrations 

observed during the 1996, 2004, and 2008 CFEs. Detailed "mass-balance" sand budgets 

constructed using high-resolution sand-flux data are available for various reaches of the Colorado 

River for the periods antecedent to and during the 2004 and 2008 CFEs, and similar sand budgets 

could be used to design future controlled floods. However, these sand budgets alone cannot be used 

to evaluate differences in the sand supplies between the different controlled floods for two key 

reasons. (1) Data to construct such sand budgets are unavailable for the period antecedent to and 

during the 1996 CFE. (2) Even when it is possible to construct such sand budgets, data collection 

for these budgets began in 2002 and thus do not include pre-2002 "background" sand storage in a 

reach; therefore, these sand budgets cannot compute the entire upstream sand supply in a reach. 

The differences in the sand supplies during the 1996, 2004, and 2008 CFEs can only be determined 

through careful physically based analyses of the suspended-sand data collected during these events. 

Analyses of differences in only suspended-sand concentration between two controlled floods of 

similar discharge will not allow determination of the differences in the upstream sand supply 

between these events. Ideally, analyses must be able to resolve the opposing influences of reachaveraged bed-sand grain size and area on suspended-sand concentration. To explain observed 

coupled changes in suspended-sand concentration and grain size, Rubin and Topping (2001, 2008) 

developed and tested such an analytical technique to back-calculate the required changes in bedsand median grain size for a bed composed of 100 percent sand. Unfortunately, as published, this 

technique does not allow differences in bed-sand area to be evaluated. For reasons described above, 

bed-sand area is one of the most difficult parameters to measure, either directly or in a backcalculated sense from analyses of suspended-sediment data (Topping and others, 2007a), but it is 

the parameter that, at a given discharge of water, is always positively correlated with the upstream 

sand supply. In this report, suspended-sand data will be analyzed using a modified version of the 

Rubin and Topping (2001, 2008) technique to back-calculate the differences in reach-averaged bedsand area between different reaches during the same controlled flood and between identical reaches 

during different controlled floods. 

Even though reach-averaged bed-sand area and upstream sand supply are always positively 

correlated under constant discharge, they are not necessarily positively correlated during large 

increases in discharge nor are they necessarily positively correlated for some time after a large 

reduction in discharge, as a result of the transient effects of sand redistribution on the bed following 

large changes in the discharge of water. Because interactions between the flow field and local 

channel geometry may change with discharge, different regions of the bed can become 

aggradational or degradational as discharge varies (Topping and others, 2000b), resulting in 

different areal distributions of sand on the bed. In the Colorado River in Marble and Grand 

Canyons, the general equilibrium tendency is for sand to be more evenly distributed on the gravel 

bed at higher discharge than at lower discharge. Large increases in discharge tend to result in scour 

of sand from deeper pools and redistribution of this sand over larger parts of the gravel bed. Sidescan sonar data indicate that, in sand-starved reaches of the Colorado River, bed-sand area 

increases during floods as a result of this redistribution process (Anima and others, 1998; Schmidt 

and others, 2007). This process was observed in side-scan sonar data following the 1996 45,000 

ft3

/s CFE and also following a 4-day 31,000 ft3/s powerplant-capacity dam release in September 

10
2000. At high discharge during the 1996 and 2004 CFEs, this sand redistribution process was 

detected to occur over time scales of one to several days through analyses of suspended-sand data 

conducted using a Rouse-mechanics-based model (Topping and others, 2007a). Even as the 

upstream supply of sand decreased during these CFEs, the reach-averaged area of bed sand was 

detected to increase by this transient redistribution process from about 25 percent on day 1 of high, 

steady discharge to about 37 percent on day 6 of high, steady discharge during the 1996 CFE, and 

from about 18 percent on day 1 of high, steady discharge to about 29 percent on day 3 of high, 

steady discharge during the 2004 CFE at the Colorado River near Grand Canyon, Arizona, gaging 

station (see fig. 3 below for the location of this gaging station). At lower discharge after recession 

of these artificial floods, it took longer for the sand to redistribute back to the regions of the bed it 

occupied before these events than it did to expand over larger regions of the bed at higher 

discharge. Before conducting analyses of reach-averaged bed-sand area, it is important to recognize 

the potential pitfalls arising from sand areal redistribution within a reach following large changes in 

discharge. 

Acknowledgments 

Funding for this research was provided by the U.S. Department of the Interior's Glen 

Canyon Dam Adaptive Management Program through the USGS Grand Canyon Monitoring and 

Research Center. Many thought-provoking discussions on this research with Scott Wright, Jack 

Schmidt, Joe Hazel, Matt Kaplinksi, Jim Smith, Jon Nelson, Jim Bennett, Randy Parker, Mark 

Schmeeckle, Amy Draut, Steve Wiele, Tim Randle, Randy Peterson, Ned Andrews, and Peter 

Wilcock are gratefully acknowledged. This report would not be nearly as comprehensive without 

their input over the years. Too many people helped with the collection of the data during these 

three field experiments for them all to be individually acknowledged here. Joe Lyons (Bureau of 

Reclamation), however, was particularly helpful with the collection of the suspended-sediment data 

at the Grand Canyon gaging station in 1996. Ted Melis was instrumental in much of the work 

described in this report and led Lagrangian sampling programs during the 2004 and 2008 CFEs. 

Scott Wright led the data-collection effort at the River-mile 30 study site during the 2004 CFE. Jeff 

Gartner and Neil Ganju helped with the data collection at the River-mile 30 and 61 study sites 

during the 2004 CFE; Chris Magirl and Greg Shellenbarger helped with the data collection at the 

River-mile 30 and 61 study sites during the 2008 CFE. Logistical support for fieldwork on the 

Colorado River in Grand Canyon was provided by OARS during the 1996 CFE and by Humphrey 

Summit Support during the 2004 and 2008 CFEs. Stuart Reeder, Steve Jones, Brent Burger, Scott 

Davis, J.P. Running, and Mark Franke provided expert technical boating support for the suspendedsediment sampling during the 2004 and 2008 CFEs. Thoughtful and insightful reviews of this 

report were provided by Peter Goodwin (University of Idaho) and Kees Sloff (Delft University of 

Technology). 

Study Sites 

During the three CFEs, suspended- and bed-sediment data were collected in cross-sections 

at as many as six study sites along the Colorado River in the study area in lower Glen, Marble, and 

Grand Canyons. These six study sites are: 

(1) the Colorado River at Lees Ferry gaging station (USGS station number 09380000), 

located at the downstream end of Glen Canyon and above the mouth of the Paria River, 

herein referred to as the "River-mile 0" site; 

11
(2) the River-mile 30 sediment station, located at the midpoint of Marble Canyon, herein 

referred to as the "River-mile 30" site; 

(3) the former Colorado River above Little Colorado River near Desert View, Arizona, gaging 

station (09383100), located at the downstream end of Marble Canyon and above the 

mouth of the Little Colorado River, herein referred to as the “River-mile 61” site; 

(4) the Colorado River near Grand Canyon, Arizona gaging station (09402500), herein 

referred to as the “River-mile 87” site; 

(5) the former Colorado River above National Canyon near Supai, Arizona, gaging station 

(09404120), herein referred to as the “River-mile 166” site; and 

(6) the Colorado River above Diamond Creek near Peach Springs, Arizona, gaging station 

(09404200), herein referred to as the “River-mile 225” site (fig. 3). 

By standard convention on the Colorado River in the study area, river miles increase in the 

downstream direction from river mile 0 at the Lees Ferry gaging station. As used in this report, 

lower Glen Canyon extends from Glen Canyon Dam near river mile -16 to the Lees Ferry gaging 

station at river mile 0, Marble Canyon extends from river mile 0 to the mouth of the Little 

Colorado River near river mile 62, and Grand Canyon extends from river mile 62 to the Grand 

Wash Cliffs near river mile 277. The Colorado River in Glen Canyon is within Glen Canyon 

National Recreation Area, whereas the Colorado River in Marble and Grand Canyons is within 

GCNP. The Navajo Indian Reservation borders the Colorado River between river miles -13 and 

Figure 3. Map showing locations of study sites (red circles and labels) and reaches between 

the study sites (green labels); RM is abbreviation for river mile. RM 0 = Colorado River at 

Lees Ferry, Arizona, gaging station; RM 30 = River-mile 30 sediment station; RM 61 = 

former Colorado River above Little Colorado River near Desert View, Arizona, gaging 

station; RM 87 = Colorado River near Grand Canyon, Arizona, gaging station; RM 166 = 

former Colorado River above National Canyon near Supai, Arizona, gaging station; and RM 

225 = Colorado River above Diamond Creek near Peach Springs, Arizona, gaging station. 

LGC = lower Glen Canyon; UMC = upper Marble Canyon; LMC = lower Marble Canyon; 

EGC = eastern Grand Canyon; ECGC = east-central Grand Canyon; WCGC = west-central 

Grand Canyon; and WGC = western Grand Canyon.

12
62, and the Hualapai Indian Reservation borders the Colorado River between river miles 165 and 

273. The six study sites described above divide the Colorado River into seven study reaches: 

(1) lower Glen Canyon (between Glen Canyon Dam and river mile 0), 

(2) upper Marble Canyon (between river miles 0 and 30), 

(3) lower Marble Canyon (between river miles 30 and 61), 

(4) eastern Grand Canyon (between river miles 61 and 87), 

(5) east-central Grand Canyon (between river miles 87 and 166), 

(6) west-central Grand Canyon (between river miles 166 and 225), and 

(7) western Grand Canyon (between river miles 225 and 277). 

These study reaches were chosen for sediment-budgeting purposes; the study sites bounding these 

reaches were chosen on the basis of (1) locations of key sediment-supplying tributaries, (2) 

locations of existing or former USGS gaging stations, and (3) locations where substantial historical 

pre-dam and post-dam sediment-transport data have been collected by the USGS and provide 

context (Howard, 1947; Topping and others, 2000a). 

The closure of Glen Canyon Dam in March 1963 cut off the upstream supply of sediment to 

the Colorado River (U.S. Department of the Interior, 1995; Topping and others, 2000a; Wright and 

others, 2005, 2008). The only suppliers of sand to lower Glen Canyon are now the small tributaries 

that enter the Colorado River below Glen Canyon Dam (Webb and others, 2000; 2001-2009 USGS 

Glen and Marble Canyons lesser tributary stage and sediment-transport data). The present suppliers 

of sand to the Colorado River in Marble and Grand Canyons are now, in decreasing order of 

importance, the Paria River (enters the Colorado River at river mile 1), the Little Colorado River 

(enters the Colorado River near river mile 62), Kanab Creek (enters the Colorado near river mile 

143), Havasu Creek (enters the Colorado River near river mile 157), the small tributaries that enter 

the Colorado River between river miles 1 and 17, and finally all of the other small tributaries that 

enter the Colorado River between river miles 17 and 277 (Garrett and others, 1993; Melis and 

others, 1996; Rote and others, 1997; Topping, 1997; Topping and others, 2000a; Webb and others, 

2000; 1963-1973 USGS sediment-transport data from the Kanab Creek near Fredonia, Arizona, 

gaging station (09403780); 2001-2009 USGS Glen and Marble Canyons lesser tributary stage and 

sediment-transport data). At the upstream boundary of Grand Canyon National Park (located at the 

mouth of the Paria River), the present sand supply to the Colorado River is almost entirely 

contributed by the Paria River and is only about 6 percent of the pre-dam supply (Topping and 

others, 2000a). By river mile 62, below the mouth of the Little Colorado River, the cumulative 

upstream supply of sand to the Colorado River is still only about 12 to 15 percent of the pre-dam 

supply (Topping and others, 2000a; Wright and others, 2005). Because of the relatively small sand 

contributions from the tributaries downstream from this point, the cumulative supply of sand to the 

Colorado River between Glen Canyon Dam and the head of Lake Mead reservoir is likely less than 

about 20 percent of the pre-dam supply. The Colorado River below river mile 236 is within the 

full-pool region of Lake Mead and is affected by the elevation of that reservoir (Smith and others, 

1960). 

Data 

During the 1996 CFE, suspended-sediment data were collected at only four of the six study 

sites using only conventional depth- and point-integrating suspended-sediment samplers, and bedsediment data were collected at only the River-mile 87 study site. During the 2004 CFE, the datacollection program vastly increased in scope and resolution, with suspended-sediment data 

collected at five of the six sites, using not only conventional samplers, but also at higher resolutions 

using ISCO pump samplers, Nortek acoustic-Doppler profilers, and Sequoia Scientific LISST 

13
laser-diffraction instruments (Melis and others, 2003; Topping and others, 2004, 2006a, 2006b, 

2007b). Bed-sediment data were also collected at most of the study sites; no bed-sediment data 

were collected at the River-mile 0 study site because the bed at that site is almost entirely 

composed of cobbles and boulders. The data-collection program increased in scope again during 

the 2008 CFE, with suspended-sediment data collected at all six study sites and bed-sediment data 

collected at all but the River-mile 0 study site. During the 2004 CFE, a Lagrangian sampling 

program was conducted to sample suspended sediment in individual parcels of water between river 

miles 0 and 87 (Topping and others, 2006a). During the 2008 CFE, this effort was expanded and 

two Lagrangian sampling programs were conducted to sample suspended sediment in individual 

parcels of water between river miles 0 and 87 and between river miles 87 and 225. Suspended- and 

bed-sediment data collected during the 1996 CFE have been previously described and/or analyzed 

in Konieczki and others (1997), Rubin and others (1998), Rubin and Topping (2001, 2008), Smith 

(1999), Topping and others (1999, 2000a, 2000b, 2005, 2006a, 2007a, 2008, in press), and Hazel 

and others (2006). Suspended- and bed-sediment data collected during the 2004 CFE have been 

previously described and analyzed in Topping and others (2006a). An inventory of the suspendedand bed-sediment data collected during each CFE and analyzed in this report is provided in table 1. 

At each study site, all suspended- and bed-sediment samples in this study were collected 

using standard USGS methods (described in Edwards and Glysson, 1999; Nolan and others, 2005). 

At most of the study sites, velocity-weighted suspended-sediment data were collected using either 

the Equal Depth Increment (EDI) or Equal Width Increment (EWI) methods. Point suspendedsediment samples were also collected at some of the study sites during the 1996 CFE. The 

suspended-sediment samplers used were: the P-61 and P-61-A1 point-integrating samplers 

(described in Edwards and Glysson, 1999; Federal Interagency Sedimentation Project, [n.d.]a), 

standard rigid-container D-77 depth-integrating samplers (described in Edwards and Glysson, 

1999), D-77-bag-type depth-integrating samplers5

 (described in Szalona, 1982; Wilde and others, 

1998), and D-96 and D-96-A1 depth-integrating samplers (described in Davis, 2001; Federal 

Interagency Sedimentation Project, 2003, [n.d.]b, [n.d.]c). Bed-sediment samplers used were: BM54 bed-material samplers (described in Federal Interagency Sedimentation Project, 1958a; Edwards 

and Glysson, 1999) and pipe dredges. Description of the ISCO 6712 automatic pump samplers used 

in this study is provided in Topping and others (2006b). Data collected by the automatic pump 

samplers were calibrated using the suspended-sediment data collected in the EDI or EWI 

measurement cross-sections. These calibrations were performed for the following size classes of 

sediment: silt and clay, total sand, and each 1/4-φ size class of sand between 0.0625 mm and 0.25 

mm to allow for computation of the median grain size of the suspended sand. Suspended sediment 

becomes more uniformly distributed between the pump intake and the middle of the channel as 

Rouse number decreases. To correct for this effect of increased cross-sectional mixing of the 

coarser sediment size classes in suspension with increased discharge, the calibrations for the data in 

the total sand and 1/4-φ size classes coarser than about 0.088 to 0.125 mm included discharge 

weighting. Methods for processing the acoustic-Doppler-profiler data for suspended-sand 

concentration, suspended-sand median grain size, and suspended-silt-and-clay concentration are 

described in Topping and others (2007b). More complete details on the methods for instrument 

 5

 The configuration of the D-77-bag-type depth-integrating suspended-sediment sampler varies slightly between its 

design in Szalona (1992) and its description in Wilde and others (1998). The configuration of this sampler used in this 

study during the 2004 and 2008 CFEs is that depicted in figure 2-1D in Wilde and others (1998) with the bottle-hole 

configuration depicted in figure 2-2A in Wilde and others (1998). 

14
calibration, data processing, and error analysis for the automatic pump samplers and acousticDoppler profilers are to be published in a forthcoming USGS report. 

Lagrangian sampling programs were conducted during the 2004 and 2008 CFEs to track the 

changes in suspended sediment in individual parcels of water as they traveled downstream through 

Marble and Grand Canyons. Thus, the Lagrangian reference frame used in these sampling 

programs traveled downstream at the mean velocity of the water. Analyses of the data collected 

during these sampling programs allowed determination of longitudinal patterns in: 

(1) reach-scale sand erosion and deposition, 

(2) reach-averaged suspended-sand median grain size, 

(3) reach-scale silt and clay erosion and deposition, 

(4) reach-averaged median grain size of the bed sand through use of Rubin and Topping's 

(2001, 2008) parameter β, 

(5) reach-averaged area of the bed covered by sand through use of a modified form of Rubin 

and Topping's (2001, 2008) parameter β, 

(6) reach-by-reach sand enrichment (by reach-averaged bed-sand median grain size and area) 

before each CFE, and 

(7) reach-by-reach silt and clay enrichment before each CFE. 

Identical sample-collection methods, but different suspended-sediment samplers, were used during 

the 2004 and 2008 Lagrangian sampling programs. During each sampling program, the suspended 

sediment in an individual parcel of water was sampled episodically by the collection of three 

sequential back-to-back, single-vertical, depth-integrated samples in the middle of the channel. 

Because rapids could not be run safely at night, breaks in the sampling program occurred resulting 

in different parcels of water being sampled on different days. These camping breaks resulted in 

backward steps in the Lagrangian reference frame between the different parcels of water. The 

average spacing between the sampling stations in the 2004 and 2008 Lagrangian sampling 

programs between river miles 0 and 87 was approximately 2.5 river miles; where possible, identical 

sampling stations were occupied during each of these programs. The average spacing between the 

sampling stations in the added second 2008 Lagrangian sampling program between river miles 87 

and 225 was approximately 4 river miles. During the 2004 Lagrangian sampling program, data 

were collected using a P-61-A1 point-integrating suspended-sediment sampler operated in the 

upward depth-integrating mode. Because of the mechanical and electrical complexity of this 

sampler, it was difficult to keep the sampler operational during the 2004 sampling program; the 

first P-61-A1 sampler broke after sampling at river mile 24, and the backup P-61-A1 sampler broke 

after sampling at river mile 85. Thus, the simpler D-96-A1 depth-integrating suspended-sediment 

sampler was used to collect data during both 2008 Lagrangian sampling programs. 

During the 2004 CFE, one Lagrangian sampling program was conducted between river 

miles 0 and 87. Travel times for the parcels of water through Marble and Grand Canyons were 

estimated based on the dye studies of Graf (1995, 1997) and Konieczki and others (1997), and the 

well-calibrated step-backwater model of Magirl and others (2008). On the first day of high, steady 

discharge during the 2004 CFE, this program sampled the suspended sediment in one parcel of 

water between river miles 0 and 52; and, on the second day of high, steady discharge, this program 

sampled the suspended sediment in a second parcel of water between river miles 52 and 85 (where 

the backup P-61-A1 suspended-sediment sampler ultimately broke). Owing to the differences in the 

velocity of discharge waves (that is, flood waves) and water based on physical laws (mostly 

conservation of mass), a flood wave travels much faster than the does the water in the Colorado 

River in Marble and Grand Canyons (Wiele, 1996; Wiele and Smith, 1996; Griffin and Wiele, 

1996; Wiele and Griffin, 1998; Wiele and Torizzo, 2003). For example, during the 2008 CFE, the 

first 208 Lagrangian sampling program left the River-mile 0 study site just before the beginning of 

15
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report. 

River-mile 0 study site (09380000, Colorado River at Lees Ferry, Arizona, gaging station) 

Suspended-sediment data collected during the 1996 CFE 

During March 26 through April 6, 1996, a total of 5 five-vertical Equal Discharge Increment (EDI) 

measurements were made from the cableway using a standard rigid-container D-77 depth-integrating 

sampler; of these 5 measurements, only 2 were made during the high, steady-discharge part of the CFE 

hydrograph. 

Bed-sediment data collected during the 1996 CFE 

None 

Suspended-sediment data collected during the 2004 CFE 

During November 19 through 28, 2004, a total of 28 five-vertical EDI measurements were made from the 

cableway using a D-96-A1 depth-integrating sampler. The sampling protocol was to make 4 EDI 

measurements per day from the start of the rising limb to the end of the receding limb of the CFE 

hydrograph. In addition, 4 EDI measurements were made during the two days before the rise of the CFE 

hydrograph, and 4 EDI measurements were made during the two days after the recession of the CFE. 

Bed-sediment data collected during the 2004 CFE 

None 

Suspended-sediment data collected during the 2008 CFE 

During March 4 through 10, 2008, a total of 24 five-vertical EDI measurements were made from the cableway 

using a D-96-A1 depth-integrating sampler. The sampling protocol was to make 4 EDI measurements per 

day from the start of the rising limb to the end of the receding limb of the CFE hydrograph. In addition, 2 

EDI measurements were made during the day before the rise of the CFE hydrograph, and 2 EDI 

measurements were made during the day after the recession of the CFE. 

Bed-sediment data collected during the 2008 CFE 

None 

River-mile 30 study site (River-mile 30 sediment station) 

Suspended-sediment data collected during the 1996 CFE 

None, study site not yet established 

Bed-sediment data collected during the 1996 CFE 

None, study site not yet established 

Suspended-sediment data collected during the 2004 CFE 

During November 18 through 30, 2004, a total of 38 five-vertical Equal Width Increment (EWI) 

measurements were made using a D-77-bag-type depth-integrating sampler deployed from a boat 

positioned under the tagline. The sampling protocol was to make 4 EWI measurements per day from the 

start of the rising limb to the end of the receding limb of the CFE hydrograph. In addition, 4 EWI 

measurements were made during the three days before the rise of the CFE hydrograph, and 14 EWI 

measurements were made during the five days after the recession of the CFE. 

16
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued 

During November 18 through 30, 2004, a total of 128 samples were collected using ISCO 6712 automatic 

pump samplers. From the start of the rising limb to the end of receding limb of the CFE hydrograph, 

these samples were collected every hour. 

During November 18 through 30, 2004, a total of 1,162 suspended-sediment measurements were made using a 

Nortek 1MHz EasyQ sideways-looking acoustic-Doppler profiler. These measurements were made every 

15 minutes, and processed for suspended-sand concentration and suspended-silt-and-clay concentration. 

Bed-sediment data collected during the 2004 CFE 

During November 19 through 30, 2004, a total of 17 bed-sediment measurements were made using a pipe 

dredge deployed from a boat positioned under the tagline. Each of these 17 measurements consisted of 

samples collected at the 3 middle of 5 equally spaced stations in the cross-section under the tagline (these 

5 stations were the centroids of each EWI cell). Only 1 measurement during this period consisted of 

samples at 2 of these 3 stations. The leftmost and rightmost of the 5 stations were not sampled because of 

the presence of large boulders and colluvium on the bed on the sides of the cross-section. The sampling 

protocol was to make 2 of these measurements per day from the start of the rising limb through the end of 

the receding limb of the CFE hydrograph. In addition, 1 measurement was made per day during the two 

days before the rise of the CFE hydrograph, and 1 measurement was made per day during the five days 

after the recession of the CFE. 

Suspended-sediment data collected during the 2008 CFE 

During March 3 through 11, 2008, a total of 29 five-vertical EWI measurements were made using a D-96-A1 

depth-integrating sampler and a total of 29 five-vertical EWI measurements were made using a D-77-

bag-type depth-integrating sampler deployed from a boat positioned under the tagline. Measurements 

were made with these two samplers in a sequential back-to-back fashion. These back-to-back sample 

pairs were used with other back-to-back D-96-A1, D-77-bag-type sample pairs collected at this study site 

between February 22, 2007, and January 26, 2008, to develop bias-correction factors for suspendedsediment data collected previously at this study site with the non-isokinetic D-77-bag-type sampler (for 

example, the EWI measurements made at this study site during the 2004 CFE). The sampling protocol 

was to make 4 EWI measurements with each sampler per day from the start of the rising limb to the end 

of the receding limb of the CFE hydrograph. In addition, 3 EWI measurements were made with each 

sampler during the two days before the rise of the CFE hydrograph, and 5 EWI measurements were made 

with each sampler during the three days after the recession of the CFE. 

During March 3 through 11, 2008, a total of 153 samples were collected using ISCO 6712 automatic pump 

samplers. From the start of the rising limb to the end of receding limb of the CFE hydrograph, these 

samples were collected every hour. From 1100 on March 5 through 0600 on March 10, the pump intaketube mount was broken, and the intake tubes were loose in the current. This made the suspended-sand 

data collected by the pumps during 1100 on March 5 through 0600 on March 10 unusable; suspendedsilt-and clay data collected by the pumps during this period were unaffected by this problem, however, 

and could still be used. 

During March 3 through 11, 2008, a total of 940 suspended-sediment measurements were made using a 

Nortek 1MHz and 2MHz EasyQ sideways-looking acoustic-Doppler profiler (both of these instruments 

were used to make each of these 940 measurements). These measurements were made every 15 minutes, 

and processed for suspended-sand concentration, suspended-sand median grain size, and suspended-siltand-clay concentration. During this period, an additional 20 measurements were made using either the 

1MHz or 2MHz instrument, and were processed for only suspended-sand concentration, and suspendedsilt-and-clay concentration. These additional one-instrument measurements were made while the other 

instrument was shut down for downloading. 

17
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued 

Bed-sediment data collected during the 2008 CFE 

During March 3 through 11, 2008, a total of 15 bed-sediment measurements were made using a pipe dredge 

deployed from a boat positioned under the tagline. Each of these 15 measurements consisted of samples 

collected at the 3 middle of 5 equally spaced stations across the cross-section under the tagline (these 5 

stations were the centroids of each EWI cell). The leftmost and rightmost of the 5 stations were not 

sampled because of the presence of large boulders and colluvium on the bed on the sides of the crosssection. The sampling protocol was to make 2 of these measurements per day from the start of the rising 

limb through the end of the receding limb of the CFE hydrograph. In addition, 3 measurements were 

made during the two days before the rise of the CFE hydrograph, and 1 measurement was made per day 

during the two days after the recession of the CFE. 

River-mile 61 study site (09383100, former Colorado River above Little Colorado River near Desert View, 

Arizona, gaging station) 

Suspended-sediment data collected during the 1996 CFE 

During March 27 through April 2, 1996, a total of 3 five-vertical EDI measurements were made from the 

cableway using a standard rigid-container D-77 depth-integrating sampler; all 3 of these measurements 

were made during the high, steady-discharge part of the CFE hydrograph (data published in table 2 of 

Topping and others, 1999). 

Bed-sediment data collected during the 1996 CFE 

None 

Suspended-sediment data collected during the 2004 CFE 

During November 19 through December 4, 2004, a total of 52 five-vertical EWI measurements were made 

using a D-77-bag-type depth-integrating sampler deployed from a boat positioned under the tagline (at 

the former location of the measurement cableway from which data were collected during the 1996 CFE). 

The sampling protocol was to make 4 EWI measurements per day from the start of the rising limb to the 

end of the receding limb of the CFE hydrograph. In addition, 2 EWI measurements were made per day 

during the two days before the rise of the CFE hydrograph and the seven days after the recession of the 

CFE, and 1 final EWI measurement was made on the eighth day after the recession of the CFE. 

During November 19 through December 4, 2004, a total of 191 samples were collected using ISCO 6712 

automatic pump samplers. From the start of the rising limb to the end of receding limb of the CFE 

hydrograph, these samples were collected at least every hour. 

During November 19 through December 4, 2004, a total of 1,486 suspended-sediment measurements were 

made using a Nortek 1MHz EasyQ sideways-looking acoustic-Doppler profiler. These measurements 

were made every 15 minutes, and processed for suspended-sand concentration and suspended-silt-andclay concentration. 

18
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued 

Bed-sediment data collected during the 2004 CFE 

During November 19 through December 4, 2004, a total of 21 bed-sediment measurements were made using a 

pipe dredge deployed from a boat positioned under the tagline. Each of these 21 measurements consisted 

of samples collected at 5 equally spaced stations in the cross-section under the tagline (these 5 stations 

were the centroids of each EWI cell). At least 3 samples had to be collected among the 5 stations to 

constitute a measurement. The sampling protocol was to make 2 of these measurements per day from two 

days before the start of the rising limb through the end of the receding limb of the CFE hydrograph. In 

addition, 1 measurement was made per day during the three days after the recession of the CFE, and 

during December 3 and 4. It became easier to sample the sand and finer sediment on the bed after the 

start of the CFE, and samples at all 5 stations were collected beginning on November 22. Because of the 

predominance of gravel on the bed at the tagline cross-section before the CFE, samples were only 

collected at 3 or 4 of the 5 stations during November 19-21. 

Suspended-sediment data collected during the 2008 CFE 

During March 3 through 12, 2008, a total of 31 five-vertical EWI measurements were made using a D-96-A1 

depth-integrating sampler and a total of 31 five-vertical EWI measurements were made using a D-77-

bag-type depth-integrating sampler deployed from a boat positioned under the tagline. Measurements 

were made with these two samplers in a sequential back-to-back fashion. These back-to-back sample 

pairs were used with other back-to-back D-96-A1, D-77-bag-type sample pairs collected at this study site 

between January 12, 2003, and January 28, 2008, to develop bias-correction factors for suspendedsediment data collected previously at this study site with the non-isokinetic D-77-bag-type sampler (for 

example, the EWI measurements made at this study site during the 2004 CFE). The sampling protocol 

was to make 4 EWI measurements with each sampler per day from the start of the rising limb to the end 

of the receding limb of the CFE hydrograph. In addition, 3 EWI measurements were made with each 

sampler during the two days before the rise of the CFE hydrograph, and 8 EWI measurements were made 

with each sampler during the three days after the recession of the CFE. 

During March 3 through 6, 2008, and during March 10 through 12, 2008, a total of 108 samples were 

collected using ISCO 6712 automatic pump samplers. During the rising limb and during the day after 

recession of the CFE hydrograph, these samples were collected every hour. From 1800 on March 6 

through 1100 on March 10, the pump intake-tube mount was broken, and the intake tubes were pinched 

against a large rock. This made all data collected by the pumps during 1800 on March 6 through 1100 on 

March 10 unusable. 

During March 3 through 12, 2008, a total of 855 suspended-sediment measurements were made using a 

Nortek 1MHz EasyQ and an OTT 2MHz SLD sideways-looking acoustic-Doppler profiler (both of these 

instruments were used to make each of these 855 measurements). These measurements were made every 

15 minutes, and processed for suspended-sand concentration, suspended-sand median grain size, and 

suspended-silt-and-clay concentration. During this period, an additional 100 measurements were made 

using either the 1MHz or 2MHz instrument, and were processed for only suspended-sand concentration 

and suspended-silt-and-clay concentration. Some of these additional one-instrument measurements were 

made while the other instrument was shut down for downloading. Others were made while the mount for 

the OTT 2MHz SLD was shut down for repairs. The mount for the OTT 2MHz SLD broke at 1800 on 

March 6 when the pump intake-tube mount was broken, and the 2MHz OTT SLD became lodged on a 

large rock. Data from the OTT 2MHz SLD could still be used, however, until 1045 on March 9, when the 

water receded below the elevation of the instrument lodged on the rock. The mount for the 2MHz OTT 

SLD was repaired and the instrument was placed back in service at 1045 on March 10. Subsequent 

modifications to this instrument mount should increase its strength during any future CFE. 

19
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued 

Bed-sediment data collected during the 2008 CFE 

During March 3 through 11, 2008, a total of 13 bed-sediment measurements were made using a pipe dredge 

deployed from a boat positioned under the tagline. Each of these 13 measurements consisted of samples 

collected at 5 equally spaced stations in the cross-section under the tagline (these 5 stations were the 

centroids of each EWI cell). At least 3 samples had to be collected among the 5 stations to constitute a 

measurement. The sampling protocol was to make 2 of these measurements per day from two days before 

the start of the rising limb through the end of the receding limb of the CFE hydrograph. In addition, 1 

measurement was made per day during the two days before the rising limb of the CFE, during the first 

day of the rising limb of the CFE, and during the two days after the recession of the CFE. As during the 

2004 CFE, it became easier to sample the sand and finer sediment on the bed after the start of the CFE, 

and samples at all 5 stations were collected beginning on March 6. As during the 2004 CFE, because of 

the predominance of gravel on the bed at the tagline cross-section before the 2008 CFE, samples were 

only collected at 3 of the 5 stations during March 3 and at 4 of the 5 stations on March 5. Samples were 

collected at all 5 stations, however, on March 4. 

River-mile 87 study site (09402500, Colorado River near Grand Canyon, Arizona, gaging station) 

Suspended-sediment data collected during the 1996 CFE 

During March 30 through April 2, 1996, a total of 4 five-vertical EDI measurements were made from the 

cableway using a standard rigid-container D-77 depth-integrating sampler; all 4 of these measurements 

were made during the high, steady-discharge part of the CFE hydrograph (data published in table 2 of 

Topping and others, 1999). 

During March 27 through April 3, 1996, a total of 8 two-vertical EDI measurements were made from the 

cableway using a P-61 point-integrating suspended-sediment sampler deployed in the upward depthintegrating mode (verticals were located at stations at 190 and 290 feet on the cableway); the first 7 of 

these 8 measurements were made one per day during the high, steady-discharge part of the CFE 

hydrograph (inventory of data published in table 3 of Konieczki and others, 1997; data published in table 

2 of Topping and others, 1999; data collected during the individual transits at each vertical in these EDI 

measurements published in Topping and others, in press; positions of the stations at 190 and 290 feet on 

the cableway indicated in figure 5 of Topping and others, 2007a, and figure 2B of Topping and others, in 

press). 

On March 28, 30, and April 2, 1996, 3 point samples were collected at each of 6 elevations in the flow at two 

stations in the cross-section (at 190 and 290 feet on the cableway) using a P-61 point-integrating 

suspended-sediment sampler deployed from the cableway (inventory of data published in table 3 of 

Konieczki and others, 1997; data collected at each elevation in the verticals at the two stations published 

in Topping and others, in press). 

20
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued 

Bed-sediment data collected during the 1996 CFE 

During March 26 through April 3, 1996, a total of 8 bed-sediment measurements were made using a BM-54 

sampler deployed from the cableway (data published in table 1 of Topping and others, 1999). Each of 

these 8 measurements consisted of samples collected at 5 equally spaced stations in the cross-section 

under the cableway (at least 3 samples had to be collected among the 5 stations to constitute a 

measurement). Sampling proved difficult during the 1996 CFE, and only three of the 8 measurements 

consisted of samples collected at all 5 stations. The sampling protocol was to make 1 of these 

measurements per day from the day before the rising limb through the first day of the receding limb of the 

CFE hydrograph. Insufficient samples to constitute a full measurement were collected on March 30 (that 

is, only two samples were collected among the 5 stations on this day). The BM-54 sampler broke after the 

collection of samples at the leftmost and rightmost of the 5 stations on March 31; a third station in the 

middle of the cross-section was sampled on this day using a pipe dredge. The BM-54 sampler was fixed 

prior to sampling on April 1. 

Suspended-sediment data collected during the 2004 CFE 

During November 20 through 30, 2004, a total of 31 five-vertical EDI measurements were made from the 

cableway using either a D-96 or a D-96-A1 depth-integrating sampler. The sampling protocol was to 

make 4 EDI measurements per day from the start of the rising limb to the end of the receding limb of the 

CFE hydrograph (only 3 EDI measurements were actually made during the first day of high, steady 

discharge, however). In addition, 4 EDI measurements were made during the two days before the rise of 

the CFE hydrograph, and 2 EDI measurements were made per day during the four days after the 

recession of the CFE. 

During November 20 through 30, 2004, a total of 163 samples were collected using an ISCO 6712 automatic 

pump sampler. From the day before the start of the rising limb through the day after the end of receding 

limb of the CFE hydrograph, these samples were collected every hour. 

During November 20 through 30, 2004, a total of 713 suspended-sediment measurements were made using 

Nortek 600kHz Aquadopp, 1MHz EasyQ, and 2MHz EasyQ sideways-looking acoustic-Doppler profilers 

(all three instruments were used to make each of these 713 measurements. These measurements were 

made every 15 minutes, and processed for suspended-sand concentration, suspended-sand median grain 

size, and suspended-silt-and-clay concentration. During this period, an additional 217 measurements 

were made using only two of the instruments, and were also processed for suspended-sand concentration, 

suspended-sand median grain size, and suspended-silt-and-clay concentration. During this period, an 

additional 113 measurements were made with only one of the instruments, and were processed for only 

suspended-sand concentration and suspended-silt-and-clay concentration. The measurements made with 

less than all 3 instruments arose because each instrument was episodically shut down for downloading. 

Bed-sediment data collected during the 2004 CFE 

During November 20 through 30, 2004, a total of 20 bed-sediment measurements were made using a BM-54 

sampler deployed from the cableway. Each of these 20 measurements consisted of samples collected at 5 

equally spaced stations in the cross-section under the cableway (at least 3 samples had to be collected 

among the 5 stations to constitute a measurement). Only three of these measurements consisted of 

samples collected at less than all 5 stations. The sampling protocol was to make 2 of these measurements 

per day from the start of the rising limb through the end of the receding limb of the CFE hydrograph. In 

addition, 1 measurement was made per day during the two days before the rise of the CFE hydrograph, 

and 2 measurements were made per day during the four days after the recession of the CFE. 

21
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued 

Suspended-sediment data collected during the 2008 CFE 

During March 4 through 12, 2008, a total of 28 five-vertical and 1 four-vertical EDI measurements were 

made from the cableway using either a D-96 or a D-96-A1 depth-integrating sampler. The sampling 

protocol was to make 4 EDI measurements per day from the start of the rising limb to the end of the 

receding limb of the CFE hydrograph. In addition, 2 EDI measurements were made during the day before 

the rise of the CFE hydrograph (one of these was the four-vertical measurement), and 3 EDI 

measurements were made during the two days after the recession of the CFE. 

During March 4 through 12, 2008, a total of 166 samples were collected using an ISCO 6712 automatic pump 

sampler. From the day before the start of the rising limb through the day after the end of receding limb of 

the CFE hydrograph, these samples were collected every hour. 

During March 4 through 12, 2008, a total of 862 suspended-sediment measurements were made using Nortek 

600kHz Aquadopp, 1MHz EasyQ, and 2MHz EasyQ sideways-looking acoustic-Doppler profilers (all 

three instruments were used to make each of these 862 measurements). These measurements were made 

every 15 minutes, and processed for suspended-sand concentration, suspended-sand median grain size, 

and suspended-silt-and-clay concentration. During this period, only an additional 2 measurements were 

made with only one of the instruments, and were processed for only suspended-sand concentration and 

suspended-silt-and-clay concentration. The 2 measurements made with less than all 3 instruments arose 

because each instrument was episodically shut down for downloading (the instruments were downloaded 

much less frequently at this study site than during the 2004 CFE). 

Bed-sediment data collected during the 2008 CFE 

During March 4 through 12, 2008, a total of 15 bed-sediment measurements were made using a BM-54 

sampler deployed from the cableway. Each of these 15 measurements consisted of samples collected at 5 

equally spaced stations in the cross-section under the cableway (at least 3 samples had to be collected 

among the 5 stations to constitute a measurement). Only one of these measurements consisted of samples 

collected at less than all 5 stations. The sampling protocol was to make 2 of these measurements per day 

from the start of the rising limb through the end of the receding limb of the CFE hydrograph (only 1 

measurement was actually made during the last day of the recession). In addition, 1 measurement was 

made the day before the rise of the CFE hydrograph, and 1 measurement was made per day during the 

two days after the recession of the CFE. 

River-mile 166 study site (09404120, former Colorado River above National Canyon near Supai, Arizona, 

gaging station) 

Suspended-sediment data collected during the 1996 CFE 

On March 28 and 29, 1996, point samples were collected at 7 elevations in the flow at 10 stations in the 

cross-section using a P-61 point-integrating suspended-sediment sampler deployed from the cableway (at 

stations at 175, 195, 210, 230, 245, 260, 275, 290, 310, and 325 feet on the cableway). On March 29, 

1996, an additional depth-integrated sample was collected using a P-61 sampler at the station at 160 feet 

on the cableway. On each day during March 30 through April 2, 1996, point samples were collected at 7 

elevations in the flow at 11 stations in the cross-section (at stations at 160, 175, 195, 210, 230, 245, 260, 

275, 290, 310, and 325 feet on the cableway) using a P-61 point-integrating suspended-sediment sampler 

deployed from the cableway. On these 4 days, additional depth-integrated samples were collected using a 

P-61 sampler at the stations at 145 and 340 feet on the cableway. All samples were analyzed for 

suspended-sand concentration and suspended-silt-and-clay concentration (data published in table 5 of 

Konieczki and others, 1997); grain-size distributions of the suspended sand were analyzed for only those 

samples collected at stations 245 and 325 feet (cross-section averages of these data published in table 2 

of Topping and others, 1999). 

22
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued

Bed-sediment data collected during the 1996 CFE 

None 

Suspended-sediment data collected during the 2004 CFE 

None 

Bed-sediment data collected during the 2004 CFE 

None 

Suspended-sediment data collected during the 2008 CFE 

During March 5 through 13, 2008, a total of 29 five-vertical EWI measurements were made using a D-96-A1 

depth-integrating sampler deployed from a boat positioned under the tagline (at the former location of 

the measurement cableway from which data were collected during the 1996 CFE). The sampling protocol 

was to make 4 EWI measurements per day from the start of the rising limb to the end of the receding limb 

of the CFE hydrograph. In addition, 3 EWI measurements were made during the two days before the rise 

of the CFE hydrograph, and 6 EWI measurements were made during the three days after the recession of 

the CFE. 

During March 6 through 11, 2008, a total of 105 samples were collected using an ISCO 6712 automatic pump 

sampler. From the day before the start of the rising limb through the day after the end of receding limb of 

the CFE hydrograph, these samples were collected every hour (except from 1200 on March 9 through 

1200 on March 10, when the pump sampler was inadvertently not launched). 

During March 5 through 13, 2008, a total of 943 suspended-sediment measurements were made using a 

Nortek 1MHz EasyQ and an OTT 2MHz SLD sideways-looking acoustic-Doppler profiler (both of these 

instruments were used to make each of these 943 measurements). These measurements were made every 

15 minutes, and processed for suspended-sand concentration, suspended-sand median grain size, and 

suspended-silt-and-clay concentration. During this period, an additional 16 measurements were made 

using either the 1MHz or 2MHz instrument, and were processed for only suspended-sand concentration 

and suspended-silt-and-clay concentration. These additional one-instrument measurements were made 

while the other instrument was either shut down for downloading or for repairs to its mount. Both of the 

instruments rotated on their mounts during the CFE, and the data had to be adjusted to compensate for 

this rotation. Both mounts were repaired on March 13. Subsequent modifications to these instrument 

mounts should prevent this rotation in any future CFE. 

Bed-sediment data collected during the 2008 CFE 

During March 5 through 13, 2008, a total of 10 bed-sediment measurements were made using a pipe dredge 

deployed from a boat positioned under the tagline. Each of these 10 measurements consisted of samples 

collected at the 3 middle of 5 equally spaced stations across the cross-section under the tagline (these 5 

stations were the centroids of each EWI cell). The leftmost and rightmost of the 5 stations were not 

sampled because of the presence of large boulders and colluvium on the bed on the sides of the crosssection. The sampling protocol was to make 2 of these measurements per day during the first two days of 

high, steady discharge during the CFE hydrograph. Only 1 measurement per day was made per day 

during March 5, 6, 9-11, and 13. Despite repeated efforts to sample all 3 stations, a sample could only be 

collected at the station in the middle of the river on March 5 because the bed at the tagline cross-section 

was composed mostly of gravel before the rising limb of the CFE. Despite the predominance of gravel on 

the bed, samples at all 3 stations were collected during 7 of the 10 measurements, and samples at 2 of the 

3 stations were collected during 2 of the 10 measurements. 

23
Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued

River-mile 225 study site (09404200, Colorado River above Diamond Creek near Peach Springs, Arizona, gaging 

station) 

Suspended-sediment data collected during the 1996 CFE 

None 

Bed-sediment data collected during the 1996 CFE 

None 

Suspended-sediment data collected during the 2004 CFE 

During November 21 through 30, 2004, a total of 28 five-vertical EDI measurements were made from the 

cableway using either a D-96 or a D-96-A1 depth-integrating sampler. The sampling protocol was to 

make 4 EDI measurements per day from the second day of the rising limb to the end of the receding limb 

of the CFE hydrograph. In addition, 3 EDI measurements were made during the two days before the rise 

of the CFE hydrograph, and 7 EDI measurements were made during the four days after the recession of 

the CFE. 

During November 21 through 30, 2004, a total of 154 samples were collected using an ISCO 6712 automatic 

pump sampler. From the day of the start of the rising limb through the day after the end of receding limb 

of the CFE hydrograph, these samples were collected every hour. 

During November 21 through 30, 2004, a total of 1,056 suspended-sediment measurements were made using a 

Nortek 1MHz sideways-looking acoustic-Doppler profiler. These measurements were made every 15 

minutes, and processed for suspended-sand concentration and suspended-silt-and-clay concentration. 

Bed-sediment data collected during the 2004 CFE 

During November 21 through December 1, 2004, a total of 18 bed-sediment measurements were made using a 

BM-54 sampler deployed from the cableway. Each of these 18 measurements consisted of samples 

collected at 10 equally spaced stations in the cross-section under the cableway (at least 3 samples had to 

be collected among the 10 stations to constitute a measurement). Typically, samples could be collected at 

only 5 of the 10 stations. The sampling protocol was to make 2 of these measurements per day from the 

start of the rising limb through the end of the receding limb of the CFE hydrograph. In addition, 1 

measurement was made per day during the two days before the rise of the CFE hydrograph, and 7 

measurements were made during the four days after the recession of the CFE. 

Suspended-sediment data collected during the 2008 CFE 

During March 5 through 13, 2008, a total of 28 five-vertical EDI measurements were made from the cableway 

using a D-96 depth-integrating sampler. The sampling protocol was to make 4 EDI measurements per 

day from the second day of the rising limb to the end of the receding limb of the CFE hydrograph. In 

addition, 2 EDI measurements were made during the day before the rise of the CFE hydrograph, 2 EDI 

measurements were made during the first day of the rising limb of the CFE hydrograph, and 2 EDI 

measurements were made during the two days after the recession of the CFE. 

24
25

Table 1. Inventory of suspended- and bed-sediment data collected during the three CFEs and 

analyzed in this report.—Continued 

During March 5 through 13, 2008, a total of 163 samples were collected using an ISCO 6712 automatic pump 

sampler. From the day before the start of the rising limb through the day after the end of receding limb of 

the CFE hydrograph, these samples were collected every hour. 

During March 5 through 13, 2008, a total of 864 suspended-sediment measurements were made using a 

Nortek 1MHz and 2MHz EasyQ sideways-looking acoustic-Doppler profiler (both of these instruments 

were used to make each of these 864 measurements). These measurements were made every 15 minutes, 

and processed for suspended-sand concentration, suspended-sand median grain size, and suspended-siltand-clay concentration. 

Bed-sediment data collected during the 2008 CFE 

During March 5 through 13, 2008, a total of 15 bed-sediment measurements were made using a BM-54 

sampler deployed from the cableway. Each of these 15 measurements consisted of samples collected at 5 

equally spaced stations in the cross-section under the cableway (at least 3 samples had to be collected 

among the 5 stations to constitute a measurement). Of these 15 measurements, 11 consisted of samples 

collected at all 5 stations; the remaining 4 of these 15 measurements consisted of samples collected at 4 

of the 5 stations. The sampling protocol was to make 2 of these measurements per day from the start of 

the rising limb through the end of the receding limb of the CFE hydrograph. In addition, 1 measurement 

was made per during the one day before the rise of the CFE hydrograph, and during the two days after 

the recession of the CFE. 

2004 Lagrangian sampling program 

During November 22 and 23, 2004, 3 replicate single-vertical depth-integrated samples were collected at a 

total of 31 sampling stations in the middle of the channel between river miles 0 and 85 by one field crew. 

These samples were collected using a P-61-A1 point-integrating sampler operated in the upward depthintegrating mode deployed from a boat. Two parcels of water were sampled in a Lagrangian reference 

frame in this sampling program. 

2008 Lagrangian sampling programs 

During March 6 through 9, 2008, 3 replicate single-vertical depth-integrated samples were collected at a 

total of 67 sampling stations in the middle of the channel between river miles 0 and 225 by two field 

crews (one sampling between river miles 0 and 87 on March 6 and 7; one sampling between river miles 

87 and 225 on March 7 through 9). These samples were collected using D-96-A1 depth-integrating 

samplers deployed from two boats. Five parcels of water were sampled in a Lagrangian reference frame 

in these sampling programs. 
high, steady discharge and passed the River-mile 30 study site approximately 3 hours after the 

high, steady discharge reached that location. On the second day of sampling, after taking an 11-

hour break in camp at river mile 52, this sampling program passed the River-mile 61 study site 

approximately 19.3 hours after the high, steady discharge arrived at that location and concluded at 

the River-mile 87 study site approximately 22.2 hours after the high, steady discharge arrived at 

that location. 

All suspended-sediment data collected in this study were processed for suspended-sediment 

concentration using standard USGS methods, with sand-sized material being separated from silt 

and clay-sized material by wet sieving using a 0.0625-mm stainless steel sieve (Guy, 1969; Knott 

and others, 1992, 1993). For the 1996 data, grain-size distributions of the material retained on this 

sieve were either measured at 1/4-φ increments through use of a visual accumulation tube (Federal 

Interagency Sedimentation Project, 1957, 1958b) or measured at 1-φ increments by wet sieving6

. 

The visual accumulation tube was calibrated to give results identical to those obtained by dry 

sieving. For the 2004 and 2008 data, grain-size distributions of the material retained on the 0.0625-

mm sieve were measured at 1/4-φ increments through use of a Beckman Coulter LS-100Q Laser 

Diffraction Particle Size Analyzer calibrated using dry sieving. Wet sieving results in some silt and 

clay adhering to the sand retained on the 0.0625 mm sieve. This effect has been observed using 

electron microscopy (Gordon and others, 2001) and has been observed in our laboratory through 

comparison of results from wet and dry sieving. In this study, the amount of silt and clay retained 

with the sand during wet sieving was measured using either the visual accumulation tube or the LS100Q Laser Diffraction Particle Size Analyzer. Silt and clay concentrations were then computed by 

adding the amount of silt and clay retained on the 0.0625-mm sieve during the wet-sieving process 

to the weight of the sediment passing through this sieve. Sand concentrations were computed by 

subtracting the amount of the silt and clay retained on the 0.0625-mm sieve from the weight of the 

material retained on this sieve. This approach removes the negative bias in silt and clay 

concentration and the positive bias in sand concentration observed by Gordon and others (2001). 

The grain-size distributions of the 1996 bed-sediment data were measured through use of dry 

sieving at 1/2-φ increments; the grain-size distributions of the 2004 and 2008 bed-sediment data 

were measured through use of dry sieving at 1/4- φ increments. All dry sieving was conducted 

using standard 8-inch sieves in a Tyler RO-TAP sieve shaker. 

Removal of Bias in Data Collected by D-77-Bag-Type Samplers 

Recent measurements at multiple locations along the Colorado River in Grand Canyon 

indicate that, on average, the D-77-bag-type sampler oversamples suspended silt and clay by about 

5 percent and oversamples suspended sand by about 20 percent relative to the D-96-A1 sampler. 

Among the various sand size classes, the oversampling is positively correlated with grain size. This 

oversampling arises because, although both the D-77-bag-type sampler and D-96-type samplers 

have been shown to sample isokinetically in flumes (Szalona, 1982; Davis, 2001), the D-77-bagtype sampler samples nonisokinetically, at a rate lower than the instantaneous flow velocity, when 

deployed in a river7 (Sabol and others, 2010). This behavior likely arises from backpressure created 

by the bag unfolding too slowly within the sampler cavity (Pickering, 1983). To make suspendedsediment data collected by D-77-bag-type and D-96-A1 samplers equivalent, bias-correction 

 6

 Only the EDI measurements made during the 1996 CFE using a D-77-bag-type depth-integrating sampler were 

processed for sand grain size using wet sieving. 7

 See Federal Interagency Sedimentation Project (1941) for analyses of the effect of nonisokinetic sampling on 

measurements of suspended-sediment concentration for various size classes of sediment. 

26
factors were therefore empirically determined for data collected using a D-77-bag-type sampler. 

These bias-correction factors were determined using sequential back-to-back samples collected 

with D-96-A1 and D-77-bag-type samplers at the River-mile 30, 61, 87, and 225 study sites from 

2003 through 2008. The details of these sampler comparisons with the computed D-77 biascorrection factors for each of these study sites are to be published in a forthcoming USGS report. 

At each study site, the bias-correction factor for each size class was used to convert the suspendedsediment concentration measured by a D-77-bag-type sampler in that size class to be equivalent to 

that measured by a D-96-A1 sampler. For the purposes of this study, the bias in the median grain 

size of the suspended sand measured by a D-77-bag-type sampler was removed by first applying 

the appropriate bias-correction factor to the D-77-measured concentration of sand in each 1/4-φ

size class and then computing the median grain size of the suspended sand. Because the bias in the 

data collected with a D-77-bag-type sampler is caused by the behavior of the bag, this sampling 

bias is not present in the data collected during the 1996 CFE with a standard rigid-container D-77 

depth-integrating sampler. 

Errors 

In this study, errors have only been assigned to suspended-sediment data collected using 

standard depth- or point-integrating suspended-sediment samplers when deployed using the EDI, 

EWI, or point-sampling methods (samplers and methods described in Edwards and Glysson, 1999). 

Evaluation of the errors associated with the calibrated pump measurements and acoustic 

measurements of suspended-sediment concentration and grain size is the subject of ongoing 

research and is to be published in a forthcoming USGS report. The analyses to date suggest that the 

errors associated with these two approaches are only slightly larger than those associated with the 

standard EDI, EWI, or point-sample measurements (Topping and others, 2006b), but because these 

analyses are not yet finalized, no error from these approaches is assigned in this study. 

Errors associated with the standard EDI, EWI, or point-sample measurements are divided 

into field and laboratory components, which are combined in quadrature. The field components of 

these errors consist of both time-averaging and spatial-averaging errors and are computed on the 

basis of Topping and others (in press). From Topping and others (in press), the 95-percentconfidence-interval field error in the EDI- or EWI-measured velocity-weighted suspended-sand 

concentration in a cross-section, in units of percent, is: 

⎛ ⎞ ⎛ ⎞

± + ⎜ ⎟ ⎜

⎜ ⎝ ⎠ ⎝ ⎠

2 2

0.7

12.0 15.4 1.96 %

VERT TRANS VERT n n n

⎟

⎟ , (8) 

the 95-percent-confidence-interval field error in the EDI- or EWI-measured velocity-weighted 

suspended-sand median grain size in a cross-section, in units of percent, is:

⎛ ⎞ ⎛ ⎞

± + ⎜ ⎟ ⎜

⎜ ⎝ ⎠ ⎝ ⎠

2 2

0.7

12.0 2.5 1.96 %

VERT TRANS VERT n n n

⎟

⎟ , (9) 

27
and, the 95-percent-confidence-interval field error in the EDI- or EWI-measured velocity-weighted 

suspended-silt-and-clay concentration in a cross-section, in units of percent, is:

⎛ ⎞ ⎛ ⎞

± + ⎜ ⎟ ⎜

⎜ ⎝ ⎠ ⎝ ⎠

2 2

0.7

0 8.6 1.96 %

VERT TRANS VERT n n n

⎟

⎟

%

%

, (10) 

In equations 8 through 10, nVERT is the number of verticals (that is, sampling stations in a crosssection) and nTRANS is the number of transits at each vertical. In this usage, “one transit” is defined 

as the path a depth-integrating suspended-sediment sampler takes either from the water surface to 

the bed or from the bed to the water surface. Therefore, standard deployment of a depth-integrating 

sampler at a vertical, where the nozzle is open as the sampler is lowered to the bed and 

subsequently raised to the surface, consists of two transits. Because collection of point suspendedsediment samples involves greater time averaging than the collection of depth-integrated 

suspended-sediment samples, the 95-percent-confidence-interval field errors in point-samplemeasured suspended-sand concentration, suspended-sand median grain size, and suspended-siltand-clay concentration in a cross-section consist of only the first of the two terms in equations 8 

through 10. 

The laboratory components of these errors were computed on the basis of the performance 

of different USGS sediment laboratories and the performance of the USGS sediment laboratory at 

the USGS Grand Canyon Monitoring and Research Center in the USGS Branch of Quality Systems 

Sediment Laboratory Quality-Assurance Project (Gordon and Newland, 2000; Gordon and 

others, 2000). Most of the samples in this study were processed at the USGS sediment laboratory at 

the USGS Grand Canyon Monitoring and Research Center. Computations of the laboratory 

components of the errors were based on the 2008-2009 performance of nine different USGS 

laboratories in their analysis of 151 samples for sand concentration and silt and clay concentration. 

These computed errors were found to be consistent with those computed for only the USGS Grand 

Canyon Monitoring and Research Center sediment laboratory over the 2002-2009 span of its 

existence. For both sand concentration and silt and clay concentration, the laboratory processing 

errors decreased with increasing concentration. The 95-percent-confidence-interval laboratoryprocessing error in CSAND used in this report, in units of percent, is: 

±69C−0.5

SAND , (11) 

and the 95-percent-confidence-interval laboratory processing error in silt and clay concentration 

(CSILT&CLAY) used in this report, in units of percent, is: 

±3.9C−0.06

SILT &CLAY . (12) 

Units of concentration used for CSAND and CSILT&CLAY in equations 11 and 12 are in mg/L. In 

comparisons between dry sieving and laser-diffraction measurements, the 95-percent-confidenceinterval laboratory processing error in sand median grain size was found to be approximately ±6 

percent. 

Antecedent Conditions for Each Controlled-Flood Experiment (CFE) 

Brief Description of Sand-Budgeting Approach 

Construction of meaningful sand budgets for reaches of the Colorado River downstream 

from Glen Canyon Dam requires an intensive data-collection effort. Large discharge-independent 

changes in suspended-sand concentration occur over short time scales, of less than one hour, in the 

Colorado River in Marble and Grand Canyons; these changes in concentration are coupled to 

28
changes in suspended-sand grain size and are driven by upstream changes in the sand supply 

associated with changes in bed-sand grain size (Topping and others, 2000a, 2000b, 2007a; Rubin 

and Topping, 2001, 2008). Because of these discharge-independent changes in suspended-sand 

concentration, suspended-sediment data have to be collected at a relatively high resolution (that is, 

at increments of less than an hour) to accurately compute sand loads in Colorado River (Topping 

and others, 2004, 2006b, 2007b). Such accurate loads are needed to compute meaningful sand 

budgets for reaches of the Colorado River downstream from Glen Canyon Dam. To collect 

suspended-sediment data at a sufficiently high resolution, ISCO automatic pump samplers, Sequoia 

Scientific LISST laser-diffraction instruments, and Nortek EasyQ acoustic-Doppler sideways 

looking profilers were installed at the River-mile 30, 61, 87, and 225 study sites in August 2002 

(Melis and others, 2003; Topping and others, 2004, 2006b, 2007b). To provide information on the 

state of the sand budget in central Grand Canyon, this network was expanded to include the Rivermile 166 study site through the installation of the first of two acoustic-Doppler sideways looking 

profilers in March 2007; an automatic pump sampler was also temporarily installed at this study 

site during the 2008 CFE. Sand loads and silt and clay loads were computed for the applicable 

study sites on the Colorado River for the periods leading up to and including each CFE using the 

highest resolution data available (typically 15-minute resolution for the 2004 and 2008 CFEs) and 

the standard USGS methods described in Porterfield (1972). Sand loads were increased by 5 

percent at each study site to include bedload (after Rubin and others, 2001) and the load in the 

"unsampled zone" near the bed that is not sampled by depth-integrating samplers (fig. 1 in Edwards 

and Glysson, 1999) as estimated based on Topping and others (2007a). 

In addition to accurate high-resolution sediment-transport data on the Colorado River, sand 

budgets for reaches of the Colorado River downstream from Glen Canyon Dam must also include 

accurate measurements and/or model estimates of the sand supplied to each reach by tributaries. 

Data collection in these tributaries is difficult because of (1) their remote, ephemeral, and flashy 

nature and (2) the potential of extremely high suspended-sand concentrations during floods; for 

example, one tributary, the Paria River, has some of the highest suspended-sand concentrations in 

the world when it is in flood (Beverage and Culbertson, 1964; Topping, 1997). Most of the 

uncertainty in the reach-scale sand budgets for the Colorado River currently arises from errors in 

computed tributary sand loads during floods. Fortunately, the two most important sand-supplying 

tributaries to the Colorado in Marble and Grand Canyons have a long history of sediment-transport 

data collection by the USGS. These tributaries are the Paria River, where sediment-transport data 

were first collected in October 1947, and the Little Colorado River, where sediment-transport data 

were first collected in July 1931. Substantial gaps in the sediment-transport data collected in these 

tributaries occurred in the 1970s through early 1990s. In response to the need for increased 

information on the sand delivery to the Colorado River from these tributaries to assess management 

strategies for Glen Canyon Dam, the USGS focused more-intensive data-collection activities on 

these two tributaries beginning in the late 1990s. The other sand-supplying tributary with 

substantial historical sediment-transport data is Kanab Creek, where sediment-transport data were 

first collected in December 1963. 

To improve the real-time estimates of sand transport in the Paria River, Topping (1997) 

developed and tested a physically based sediment-transport model coupled to average geomorphic 

and sedimentologic conditions in the channel and floodplains of the Paria River. Support for this 

average modeling approach was provided in Rubin and Topping (2001), who showed that sand 

transport in the largely alluvial Paria River is essentially "flow regulated" with no systematic 

hysteresis in suspended-sand concentration caused by changes in the grain size of the bed sand 

29
during floods. Tests of this model using extensive data from 1947 through 1983 and from a period 

of four large floods in 1997 indicated that this model predicted sand loads within 20 percent of the 

measurements during most floods, and well within 20 percent during the 1997 floods. However, in 

subsequent tests against data collected during large floods in 2003 and 2004, it became clear that 

the differences in the model predictions and measurements of sand loads during individual floods 

could be substantial and biased. Therefore, an approach analogous to the "shifting-control method" 

used to compute discharge in rivers (described in Rantz and others, 1982) was developed to apply 

smoothed time-varying shifts to the model predictions of sand transport to increase the agreement 

between the model-predicted and measured sand transport. This is the approach used in this study 

to compute sand loads in the Paria River. 

A slightly different approach is used to compute sand loads in the more complicated Little 

Colorado River. Most of the sand-transport data in the Little Colorado River is collected at a 

location within the nonalluvial bedrock gorge of this river. Unlike sand transport in the Paria River, 

sand transport in this nonalluvial river is controlled to a measurable degree by changes in the 

upstream supply of sand. Modeling efforts by the USGS to develop more accurate methods for 

computing real-time sand loads in the Little Colorado River are ongoing. Because these models are 

still incomplete, a shifting sand rating curve8

 approach was used in this study that weights the 

"elevation" of the sand rating curve within the "cloud" of sand-concentration data in dischargeconcentration space by the number of measurements within that part of the cloud. Because the 

contributions of sand to the Colorado River from both Kanab and Havasu Creeks are much smaller 

than the sand contributions of the Paria and Little Colorado Rivers, estimates of the sand supplied 

by these other two large tributaries are included with the estimates of the sand supplied by the other 

small tributaries described in the next paragraph. 

The other smaller tributaries, hereafter referred to as the "lesser tributaries," have only very 

limited sediment-transport data and are the most difficult parts of the sand budgeting to constrain. 

The first comprehensive sediment budget for the lesser tributaries to lower Glen and Marble 

Canyons was completed by the Bureau of Reclamation in the late 1950s as part of its planning 

activities for the construction of Marble Canyon Dam (unpublished memoranda from the Denver 

Technical Center files of the Bureau of Reclamation). During the late 1990s, a second sediment 

budget for these tributaries was completed by Webb and others (2000), albeit with large 

uncertainties owing to the small size of the available sediment-transport dataset. To rectify the large 

uncertainties associated with sand loads in the lesser tributaries, downward-looking Campbell 

Scientific SR-50 stage gages and sediment-sampling equipment were installed in 2001 on one key 

lesser tributary in lower Glen Canyon9

 and in 2000 (Schmidt and others, 2007; Griffiths and others, 

2010) and 2001, at six locations on five lesser tributaries in Marble Canyon. Data collected in these 

tributaries suggest that the lesser tributaries in Marble Canyon between river miles 0 and 17 

cumulatively supply, on average, about 10 percent of the sand supplied by the Paria River in a 

given year10. This small percentage arises, not because the concentrations of suspended sand are 

low, but because the durations of floods are much shorter and the peak discharges of floods in these 

tributaries are much smaller in these tributaries than for floods of comparable recurrence interval in 

the Paria River. These data also suggest that the amount of sand supplied by the tributaries 

 8

 A sand rating curve relates the concentration of suspended sand to the discharge of water. 9

 This monitored tributary, Water Holes Canyon, makes up about 23 percent of the total lesser-tributary drainage 

area in this reach. 10 The monitored lesser tributaries between river-miles 0 and 17 cumulatively make up 77 percent of the total 

drainage area of the lesser tributaries in this part of Marble Canyon. 

30
downstream from about river mile 17 is nonzero, but very small11. From suspended-sediment 

samples collected between 2001 and 2009, the ratio of suspended sand to suspended silt and clay in 

floods in the lesser tributaries downstream from river mile 17 is about 1/5. Therefore, in this study: 

(1) the sand loads in the lesser tributaries in lower Glen Canyon are estimated relative to the 

flood activity in the one tributary monitored in that reach, 

(2) the sand loads in the lesser tributaries in upper Marble Canyon are estimated as 10 percent 

of the Paria sand load, 

(3) the cumulative sand loads of the lesser tributaries in lower Marble Canyon are estimated to 

be approximately 20 percent of the measured increase in the silt and clay loads between 

the River-mile 30 and 61 study sites over time scales of years (this assumption is 

consistent with the integral constraint that changes in the silt and clay budget in long 

reaches must equal zero over longer time scales in the Colorado River), 

(4) the timing of the sand inputs from the lesser tributaries in lower Marble Canyon is set 

equal to the timing of the largest increases in silt and clay load between the River-mile 30 

and 61 study sites, and 

(5) the sand loads of the lesser tributaries between each of the River-miles 61 and 87, 87 and 

166, and 166 and 225 study sites are estimated by the same approach outlined in the two 

previous steps. 

In the sand-budget computations in this study, uncertainties were applied that represent the 

largest potential persistent bias in the computed sand loads at each site on the Colorado, Paria, and 

Little Colorado Rivers. These uncertainties include the greatest likely persistent bias in both the 

discharge of water and the concentration of suspended sand. For example, at a given site, if the 

discharge of water were, on average, measured to be 3 percent high because of either 

instrumentation bias or cross-section effects, and the suspended-sand concentration were, on 

average, measured to be 2 percent high, this would result in the computed sand loads being, on 

average, 5 percent high. At some study sites, the uncertainties in the discharge of water and 

suspended-sand concentration are likely positively correlated, whereas, at other sites, these 

uncertainties are likely negatively correlated. Unfortunately, there is no way to know the real 

magnitudes or signs of the biases giving rise to these uncertainties because there is no independent 

measure of either the discharge of water or the concentration of suspended sand. Recent field 

measurements on the Colorado have indicated that EWI measurements at adjacent cross-section 

can systematically disagree by several percent or more over periods of years. Because no net 

aggradation or degradation on this scale can be occurring between these adjacent cross-sections, 

this difference cannot be real and must be included in an estimate of uncertainty. The uncertainty in 

the discharge of water in the Colorado River over months is likely at most several percent, as 

indicated by water balances conducted between the various study sites. The uncertainties associated 

with the sand loads in the tributaries are more poorly constrained than those associated with the 

sand loads in the Colorado River (Topping and others, 2000a). The best way to treat the 

uncertainties in the sand loads is therefore to (1) realize that they cannot be zero, (2) make every 

effort to reduce detected biases in the field, and (3) assign values to the uncertainties that are 

reasonable. The uncertainties chosen for the sand budgets in this study are, therefore, 5 percent for 

the sand loads at the study sites on the Colorado River12, 10 percent for the sand loads in the Paria 

and Little Colorado Rivers13, and 50 percent for the sand loads in the lesser tributaries14, Kanab 

Creek, and Havasu Creek. 

 11 The monitored lesser tributaries between river-miles 17 and 61 cumulatively make up 39 percent of the total 

drainage area of the lesser tributaries in this part of Marble Canyon. 12 This value is identical to the uncertainty used for the Colorado River data in Topping and others (2000a). 

13 This value is half of the uncertainty used for the Paria and Little Colorado River data in Topping and others 

(2000a). 

31
Sand Enrichment in Each Reach Before the 2004 and 2008 CFEs 

Because the 2004 and 2008 CFEs were very different, the sand-budget "accounting periods" 

antecedent to these two experiments were of different durations. In this usage, "accounting period" 

is defined as the period from the zero time at which sand budgeting begins until the beginning of 

the rising limb of a controlled flood. As described in Topping and others (2006a), the 2004 CFE 

was designed to test the hypothesis that a sufficiently large single-season input of sand from the 

Paria River could be retained in the channel of the Colorado River through reduced dam releases 

and then redistributed into sandbars during a relatively short-duration artificial flood released from 

Glen Canyon Dam. In essence, this experiment was a test of experimental option two suggested by 

Rubin and others (2002). Therefore, the accounting period antecedent to the 2004 CFE began at the 

beginning of the sediment-input season on July 1, 2004, (see definition of "sediment year" in 

Topping and others, 2000a) and extended until the start of the rising limb of the November 2004 

controlled-flood release. The design of the 2008 CFE was different from the design of the 2004 

CFE. Hence the accounting period antecedent to the 2008 CFE began upon recession of the 2004 

CFE and extended until the start of the rising limb of the March 2008 controlled-flood release. 

Planning for the 2008 CFE started in response to the extremely large quantity of sand supplied by 

the Paria River in October 2006. During October 2006, a flood with a peak discharge of 5,200 ft3

/s 

on the Paria River was followed one week later by a flood with a peak discharge of 5,300 ft3

/s. A 

flood with a peak discharge in this range has a recurrence interval of about 7 years on the 1923-

1996 Paria River annual-maximum or partial-duration flood series (Topping, 1997). Thus, two 7-

year flood events occurred on the Paria River within about a week. These events together supplied 

about 1.3 million metric tons of sand to the Colorado River. Because other large sand inputs 

occurred from both the Paria and Little Colorado Rivers, and dam releases were relatively low 

between October 2006 and the controlled flood in March 2008, the 2008 CFE became a test of the 

degree of sandbar building that could occur in Marble and Grand Canyons given a much higher 

than average level of sand enrichment in the system. Because the antecedent conditions for the 

2008 CFE are relatively rare, results from the 2008 CFE cannot provide guidance on the degree of 

sandbar building that could occur if controlled floods were conducted relatively frequently with 

more typical sand-enrichment conditions, as suggested in the conclusions of Topping and others 

(2006a). Because the first acoustic-Doppler profiler was not deployed at the River-mile 166 study 

site until March 2007, part way through the accounting period, the level of sand enrichment during 

the accounting period antecedent to the 2008 CFE could only be computed for the two reaches 

between the River-mile 87 and 225 study sites, the east-central and west-central Grand Canyon 

reaches, combined into a single reach. 

The sand supply from the various sources and the sand export past the various study sites during 

the accounting periods antecedent to the 2004 and 2008 CFEs are provided in table 2. Sand 

enrichment in each reach during the accounting periods antecedent to the 2004 and 2008 CFEs is 

provided in table 3. No sand enrichment or depletion can be demonstrated in a reach when the 

propagated uncertainties are larger than the absolute value of the change in sand storage. Finally, it 

is important to note that the "sand enrichment" computed by this sand-budgeting approach does not 

include the "background" sand that was stored in each reach before the antecedent accounting 

periods. The same level of sand enrichment computed by this sand-budgeting approach may result

 14 Because of the almost infinitely greater resolution of the data available upon the completion of this report than 

was available in 2000, this value is considerably less than the factor of 3 uncertainty used for sand transport in the 

lesser tributaries in Topping and others (2000a). 

32
Table 2. Sand supply and sand export during the accounting periods antecedent to the 2004 and 

2008 CFEs. 

Sand inputs from the following sources 

during the accounting periods 

Antecedent 2004 CFE 

sand input with 

uncertainty during the 

accounting period 

(million metric tons) 

Antecedent 2008 CFE 

sand input with 

uncertainty during the 

accounting period 

(million metric tons) 

lower Glen Canyon tributaries Tributaries less active 

than before 2008 CFE, 

thus equating to less sand 

enrichment than before 

2008 CFE 

Tributaries more active 

than before 2004 CFE, 

thus equating to more 

sand enrichment than 

before 2004 CFE

Paria River 0.617±0.062 3.350±0.335 

upper Marble Canyon lesser tributaries 0.062±0.031* 0.335±0.168* 

lower Marble Canyon lesser tributaries 0.044+0.022* 0.096±0.048* 

Little Colorado River 0.180±0.018 3.021±0.302 

eastern Grand Canyon lesser tributaries 0.037±0.019* 0.081±0.041* 

combined east- and west-central 

Grand Canyon tributaries 0.102±0.051* 0.372±0.186* 

Sand export past the following study 

sites during the accounting periods 

Antecedent 2004 CFE 

sand export with 

uncertainty during the 

accounting period 

(million metric tons) 

Antecedent 2008 CFE 

sand export with 

uncertainty during the 

accounting period 

(million metric tons) 

River-mile 30 0.296±0.015 2.490±0.125 

River-mile 61 0.226±0.011 2.051±0.103 

River-mile 87 0.481±0.024 4.317±0.216 

River-mile 225 0.427±0.021 3.586±0.179 

*These values agree within the large error bars of the predictions of Webb and others (2000). 

Table 3. Sand enrichment in each reach during the accounting periods antecedent to the 2004 and 

2008 CFEs. 

[Reaches without demonstrable change in sand storage (that is, propagated uncertainty is much greater than the 

absolute value of net change in sand storage) indicated by red type.] 

Reach Antecedent 2004 CFE sand 

enrichment in reach with 

propagated uncertainty 

during the accounting period 

(million metric tons) 

Antecedent 2008 CFE sand 

enrichment in reach with 

propagated uncertainty 

during the accounting period 

(million metric tons) 

lower Glen Canyon Less than before 

2008 CFE 

More than before 

2004 CFE 

upper Marble Canyon +0.383±0.108 +1.195±0.628 

lower Marble Canyon +0.114±0.048 +0.535±0.276 

eastern Grand Canyon -0.014±0.048 +0.836±0.662 

combined east-central and west-central 

Grand Canyon +0.156±0.096 +0.917±0.395 

33
in very different suspended-sand concentrations and grain sizes during a controlled flood 

depending on both the grain size of the "enriching sand" and if the amount of sand in background 

storage is relatively small or large compared to the level of sand enrichment. 

Estimation of the Relative Levels of Sand Enrichment Antecedent to the 1996, 2004, and 2008 

CFEs 

Unfortunately, during the period antecedent to the 1996 CFE, no sediment-transport 

monitoring program on the Colorado River existed, the sediment-transport monitoring program on 

the two major tributaries (that is, the Paria and Little Colorado Rivers) was less robust, and 

extremely few data existed on sediment-transport in the lesser tributaries. Therefore, a method 

alternative to that presented in the previous section must be used to compare the levels of tributary 

sand enrichment in the Colorado River antecedent to the 1996 CFE relative to those antecedent to 

the 2004 and 2008 CFEs. This simple alternative method uses (1) the same method as above for 

computing the sand supply from the Paria and Little Colorado Rivers during the year leading up to 

each CFE and (2) the sand-transport results from Topping and others (2000a) to evaluate whether it 

is likely that the dam releases during the year leading up to each CFE were likely to retain or export 

tributary-supplied sand in the Colorado River in Marble and Grand Canyons past the River-mile 87 

study site. As shown in table 4, the year antecedent to the 1996 CFE had the conditions least likely 

to result in the accumulation of tributary-supplied sand in the Colorado River between the Rivermile 0 and 87 study sites. This year was characterized by both the highest discharges and the lowest 

sand inputs from the two major tributaries. On the basis of sand-supply information alone, the year 

leading up to the 2008 CFE was the year most likely to result in the accumulation of tributarysupplied sand in the Colorado River in Marble Canyon and eastern Grand Canyon. On the basis of 

discharge alone, the year leading up to the 2004 CFE was only slightly more likely than the year 

leading up to the 2008 CFE to result in the accumulation of tributary-supplied sand in the Colorado 

River in Marble Canyon and eastern Grand Canyon. Therefore, these results, combined with the 

detailed sand-budgeting results in the previous section, suggest that (1) the 1996 CFE was likely 

the least tributary-sand-enriched of any of the three CFEs, (2) the 2008 CFE was by far the most 

tributary-sand-enriched of any of the three CFEs, and (3) the 2004 CFE was in the middle of 

Table 4. Comparison of discharge and sand supply during the years leading up to each CFE. 

[Conditions most likely to be conducive to sand accumulation in the Colorado River upstream from the River-mile 87 

study site are shown in green, conditions least likely to be conducive to sand accumulation are shown in red.] 

Sand supply during year 

leading up to controlled flood 

CFE Median dam release 

during year leading up 

to controlled flood Paria River Little Colorado River 

1996 15,400 ft3/s* ~0.38 million 

metric tons 

~0.04 million 

metric tons 

2004 10,500 ft3/s** ~0.63 million 

metric tons 

~0.19 million 

metric tons 

2008 11,300 ft3/s ~0.92 million 

metric tons 

~1.12 million 

metric tons 

* This discharge would result in either no accumulation of the tributary-supplied sand or net scour of sand already 

stored in the Colorado River during the year prior to the CFE (after Topping and others, 2000a). 

** This discharge is low enough to be within the range in Topping and others (2000a) under which net sand 

accumulation is most likely to occur. 

34
the three CFEs with respect to sand enrichment from tributaries, with the most tributary-sandenriched reach being upper Marble Canyon. Note that the analysis in table 4 has no bearing on 

possible changes in background sand storage in the Colorado River occurring over the multi-year 

periods between the CFEs (for example, decreases in sand storage arising from possible long-term 

scour of sand from the Colorado River in Marble Canyon and eastern Grand Canyon). 

Analysis 

Data Collected at Each Study Site During Each CFE 

Flood hydrographs, and the suspended-sediment and bed-sand data collected at each study 

site during each CFE are presented in figure 4. As first observed by Rubin and others (1998) during 

the 1996 CFE, and subsequently observed during the 2004 and 2008 CFEs, the general tendencies 

at all study sites during the high, steady discharge part of a CFE are: 

(1) the suspended-silt-and-clay concentration decreases over time, indicating depletion of the 

upstream supply of silt and clay, 

(2) the suspended-sand concentration decreases over time, indicating depletion of the 

upstream supply of sand, 

(3) the grain-size distribution of the suspended sand coarsens over time as the upstream 

supply of sand becomes depleted, 

(4) the grain-size distribution of the bed sand coarsens over time as the upstream supply of 

sand becomes depleted, and 

(5) the fraction of the bed sand finer than about 0.125 mm15 decreases over time as the 

upstream supply becomes depleted. 

More analyses focused on comparing the behaviors of the suspended and bed sediment at each 

study site during all three CFEs, and at all study sites during each CFE are provided below. 

Data collection increased substantially, both temporally and spatially, between the 1996 and 

2004 CFEs, with further improvement in data resolution and quality between the 2004 and 2008 

CFEs (fig. 4). During each subsequent CFE, substantial effort was made to increase data resolution 

and reduce error. For example, during the 1996 CFE, only 3 EDI measurements and no bedsediment measurements were made at the River-mile 61 study site, whereas during the 2004 CFE, 

52 EWI measurements, 191 pump samples, 1,486 single-frequency acoustic suspended-sediment 

measurements, and 21 five-station bed-sediment measurements were made at this study site. 

Because of the relatively large degree of sandbar scour in Marble Canyon during the 1996 CFE 

(Schmidt, 1999), the River-mile 30 study site was added before the 2004 CFE to improve spatial 

data resolution within Marble Canyon. To improve data resolution in the western part of Grand 

Canyon, the River-mile 225 study site was also added before the 2004 CFE, although the Rivermile 166 study site was dropped, leading to a decrease in data resolution in the central part of 

Grand Canyon. The biggest single improvement between the 1996 and 2004 CFEs was the 

introduction of the use of single-frequency acoustics to collect 15-minute-resolution suspendedsediment data at the River-miles 30, 61, and 225 study sites and the use of three-frequency 

acoustics to collect 15-minute-resolution suspended-sediment data at the River-mile 87 study site. 

During the 2008 CFE, data were collected at all study sites where data were collected 

during either the 1996 or 2004 CFEs, including the River-mile 166 study site. On the basis of the 

analysis of the errors associated with the use of depth-integrating samplers in Topping and others 

(in press), errors in the EDI and EWI measurements made during the 2008 CFE were reduced by 

 15 This is roughly the fraction of sand finer than the 0.105-0.125 median size of the sand supplied by most 

tributaries 

35
increasing the number of transits at each vertical. The other major improvement between the 2004 

and 2008 CFEs was the addition of two-frequency acoustics at the River-mile 30, 61, 166, and 225 

study sites. This improvement allowed 15-minute-resolution measurements of suspended-sand 

median grain size to be made at the River-mile 30, 61, 87, 166, and 225 study sites; this increase in 

data resolution allowed much better evaluation of the changes in the sand supply at each study site 

during the 2008 CFE than was previously possible. Furthermore, improvements in the 

deployments, both in the mounting of the instruments and through the addition of more 

measurement cells, and improvements in instrument maintenance resulted in a decrease in the noise 

in the acoustic data between the 2004 and 2008 CFEs. One new problem that occurred during the 

2008 CFE and resulted in a decrease in data resolution during the 2008 CFE was the breakage of 

the mounts for the pump intake tubes at the River-mile 30 and 61 study sites. This was a result of 

an oversight in maintenance at these sites before the 2008 CFE. 

The high-resolution acoustic suspended-sediment data are normally used in combination 

with the other suspended-sediment data to compute suspended-silt-and-clay concentration and load, 

suspended-sand concentration and load, and suspended-sand median grain size when the acoustic 

data are in general agreement with the EDI or EWI measurements. However, during both the 2004 

and 2008 CFEs, there are periods when the acoustic data are systematically biased as a result of 

grain-size effects; the acoustic data from these periods are not used. These grain-size related biases 

in concentration are evident in (1) the acoustic measurements of suspended-silt-and-clay 

concentration during most of the 2004 and 2008 CFE hydrographs at all study sites and (2) the 

acoustic measurements of suspended-sand concentration and median grain size during the rising 

limb of the 2004 and 2008 CFEs at the River-mile 30 and 61 study sites (fig. 4). 

Laser-diffraction analyses in the laboratory indicate that suspended silt and clay in the 

Colorado River in Marble and Grand Canyons during periods of normal dam operations (that is, not 

during controlled floods) is dominated by clay-sized particles. These analyses indicate, however, 

that the suspended silt and clay during controlled floods is dominated by silt-sized particles that, as 

shown below, are winnowed from the bed. The data used at all study sites to calibrate 

measurements of acoustic attenuation to the concentrations of suspended silt and clay in the EDI or 

EWI-measurement cross-sections (method described in Topping and others, 2007b) are the claydominated silt-and-clay-concentration data that are more typical of most conditions in the Colorado 

River in Marble and Grand Canyons. By virtue of this approach, the agreement between acoustic 

and physical measurements of suspended-silt-and-clay concentration in the Colorado River during 

normal dam operations tends to be excellent. However, because the relation between silt and clay 

concentration and acoustic attenuation is sensitive to particle size (Urick, 1948; Flammer, 1962), 

and the particle size of the silt and clay during controlled floods is very different from that during 

normal dam operations, the acoustic measurements of silt and clay concentration during controlled 

floods can be less accurate, especially during the rising limbs. Thus, at all study sites, the acoustic 

measurements of suspended silt and clay concentration were excluded from further analyses and 

sediment budgeting during periods of substantial disagreement between these measurements and 

physical measurements (EDI, EWI, or calibrated pump samples) of suspended-silt-and-clay 

concentration. "Substantial disagreement" is defined to be when the acoustic measurements of 

suspended-silt-and-clay concentration lie significantly outside the 95-percent confidence intervals 

associated with the EDI or EWI measurements of suspended-silt-and-clay concentration. 

 Although typically excellent, the agreement between the acoustic measurements and physical 

measurements of suspended-sand concentration and median grain size can also be quite poor 

during periods of highly anomalous grain size. Such periods typically lasted less than 12 hours and 

36
occurred during parts of the rising limbs of 2004 and 2008 CFEs only at the River-mile 30 and 61 

study sites (figs. 4D-E, G-H). No such periods of substantial disagreement were observed anywhere 

downstream from these sites during either CFE. Owing to the effects of particle attenuation and 

backscatter on acoustic data of different frequencies (for example, Flammer, 1962; Thorne and 

Campbell, 1992; Thorne and others, 1993; Thorne and Hanes, 2002), high concentrations of 

suspended sand with an anomalously fine grain size may result in acoustic measurements of 

suspended-sand concentration that are too high or too low, depending on the frequency at which the 

acoustic measurements are made. During the 2004 CFE, acoustic measurements of suspended-sand 

concentration were only made at the River-mile 30 and 61 study sites with 1 MHz acousticDoppler profilers. Upon fining of the suspended sand during the initial part of the rising limb at 

these study sites, the acoustic measurements of suspended-sand concentration began to 

underpredict the physical measurements of suspended-sand concentration. This problem reoccurred 

at these two study sites, but in an opposing sense, during the 2008 CFE. During the 2008 CFE, 

acoustic measurements of suspended-sand concentration were made at these study sites using a 

two-frequency approach employing both 1 MHz and 2 MHz acoustic-Doppler profilers. Upon 

much greater fining of the suspended sand during the initial part of the rising limb of the 2008 CFE 

due to extreme fining of the bed sand16 at these study sites, the two-frequency acoustic 

measurements of suspended-sand concentration began to overpredict the physical measurements of 

suspended-sand concentration. Associated with this overprediction of suspended-sand 

concentration was an underprediction of the median grain size of the suspended sand. Therefore, 

the acoustic measurements of suspended-sand concentration and grain size were excluded from the 

further analyses and sediment budgeting presented in this report during the periods of substantial 

 

Figure 4 (next pages). Hydrographs, suspended-sediment data, and bed-sand data collected at each 

study site during each CFE. Solid green vertical lines indicate the beginning and end of the high, 

steady discharge part of a controlled flood at a given site; dashed green vertical lines indicate the 

beginning of the rising limb and end of receding limb of a controlled flood at a given site. Error bars 

for the EDI, EWI, or point suspended-sediment concentration and grain-size data indicate the 95-

percent confidence interval associated with these measurements (incorporating the field and 

laboratory errors described above). Error bars for the bed-sediment data are one standard error, 

indicating the 67-percent confidence interval associated with the mean value of the median grain size 

or < 0.125-mm sand fraction among the stations sampled across the cross-section in each bedsediment measurement. Q is water discharge, CSAND is the velocity-weighted concentration of 

suspended sand in the cross-section, CSILT&CLAY is the velocity-weighted concentration of suspended 

silt and clay in the cross-section, and D50 is either the median grain-size of the bed sand or the 

velocity-weighted median grain size of the suspended sand in the cross-section. Hydrograph and data 

collected at (A) the River-mile 0 study site during the 1996 CFE; (B) the River-mile 0 study site 

during the 2004 CFE; (C) the River-mile 0 study site during the 2008 CFE; (D) the River-mile 30 

study site during the 2004 CFE; (E) the River-mile 30 study site during the 2008 CFE; (F) the Rivermile 61 study site during the 1996 CFE; (G) the River-mile 61 study site during the 2004 CFE; (H) 

the River-mile 61 study site during the 2008 CFE; (I) the River-mile 87 study site during the 1996 

CFE; (J) the River-mile 87 study site during the 2004 CFE; (K) the River-mile 87 study site during 

the 2008 CFE; (L) the River-mile 166 study site during the 1996 CFE; (M) the River-mile 166 study 

site during the 2004 CFE; (N) the River-mile 225 study site during the 2004 CFE; and (O) the Rivermile 225 study site during the 2008 CFE. 

 16 The bed sand fined by a factor of two, from a median size of about 0.3 mm to an extremely fine value of 0.15 

mm, during the initial part of the rising limb of the 2008 CFE. This degree of fining has never before been observed 

during the rising limb of any flood in the Colorado River in Marble or Grand Canyons. The only time this degree of 

bed fining has been observed was in uppermost Marble Canyon in September 1998 immediately following two large 

floods on the Paria River (Topping and others, 2000b). 

37
A 1996 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 0 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

50

100

150

200

250

300

EDI 

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

EDI 

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

1

2

3

4

5

6

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

NO BED-SEDIMENT SAMPLES COLLECTED

0

20

40

60

80

100

EDI 

3/25/19963/26/19963/27/19963/28/19963/29/19963/30/19963/31/1996

4/1/19964/2/19964/3/19964/4/19964/5/19964/6/1996

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

 

38
B 2004 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 0 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

50

100

150

200

250

300

EDI 

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

EDI 

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

1

2

3

4

5

6

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

NO BED-SEDIMENT SAMPLES COLLECTED

0

20

40

60

80

100

EDI 

11/20/200411/21/200411/22/200411/23/200411/24/200411/25/200411/26/2004

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

39
C 2008 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 0 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

50

100

150

200

250

300

EDI 

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

EDI 

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

1

2

3

4

5

6

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

NO BED-SEDIMENT SAMPLES COLLECTED

0

20

40

60

80

100

EDI 

3/4/20083/5/20083/6/20083/7/20083/8/20083/9/2008

3/10/2008

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

40
D 2004 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 30 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EWI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

PUMP 

EWI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

1

2

3

4

5

6

D

50

% < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EWI

11/20/200411/21/200411/22/200411/23/200411/24/200411/25/200411/26/2004

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

41
E 2008 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 30 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EWI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

ACOUSTIC 

PUMP

EWI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

5

10

15

20

25

30

D

50

% < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EWI

3/4/20083/5/20083/6/20083/7/20083/8/20083/9/2008

3/10/2008

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

42
F 1996 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 61 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

EDI 

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

EDI 

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

10

20

30

40

50

60

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

NO BED-SEDIMENT SAMPLES COLLECTED

0

1,000

2,000

3,000

4,000

5,000

6,000

EDI 

3/25/19963/26/19963/27/19963/28/19963/29/19963/30/19963/31/1996

4/1/19964/2/19964/3/19964/4/19964/5/19964/6/1996

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

43
G 2004 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 61 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EWI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

PUMP 

EWI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

10

20

30

40

50

60

D

50 % < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EWI

11/20/200411/21/200411/22/200411/23/200411/24/200411/25/200411/26/200411/27/2004

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

44
H 2008 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 61 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EWI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

ACOUSTIC 

PUMP

EWI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

10

20

30

40

50

60

D

50 % < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EWI

3/4/20083/5/20083/6/20083/7/20083/8/20083/9/2008

3/10/20083/11/2008

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

45
I 1996 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 87 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

EDI

EDI (P-61 at 2 verticals) 

POINT-SAMPLE MEAN 

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

EDI

EDI (P-61 at 2 verticals) 

SUSPENDED-SAND

POINT-SAMPLE MEAN D50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

1

2

3

4

5

6

D

50

% < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

EDI

EDI (P-61 at 2 verticals) 

POINT-SAMPLE MEAN 

3/25/19963/26/19963/27/19963/28/19963/29/19963/30/19963/31/1996

4/1/19964/2/19964/3/19964/4/19964/5/19964/6/1996

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

46
J 2004 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 87 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EDI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

ACOUSTIC 

PUMP

EDI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

1

2

3

4

5

6

D

50

% < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EDI

11/20/200411/21/200411/22/200411/23/200411/24/200411/25/200411/26/200411/27/2004

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

47
K 2008 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 87 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EDI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

ACOUSTIC 

PUMP

EDI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

2

4

6

8

10

12

14

D

50

% < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EDI

3/4/20083/5/20083/6/20083/7/20083/8/20083/9/2008

3/10/20083/11/2008

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

48
L 1996 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 166 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

POINT-SAMPLE MEAN 

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

POINT-SAMPLE MEAN 

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

2

4

6

8

10

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

NO BED-SEDIMENT SAMPLES COLLECTED

0

1,000

2,000

3,000

4,000

5,000

6,000

POINT-SAMPLE MEAN 

3/25/19963/26/19963/27/19963/28/19963/29/19963/30/19963/31/1996

4/1/19964/2/19964/3/19964/4/19964/5/19964/6/1996

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

49
M 2008 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 166 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EWI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

ACOUSTIC 

PUMP

EWI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

2

4

6

8

10

D

50

% < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EWI

3/5/20083/6/20083/7/20083/8/20083/9/2008

3/10/20083/11/2008

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

50
N 2004 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 225 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EDI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

PUMP 

EDI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

5

10

15

20

D

50 % < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EDI

11/21/200411/22/200411/23/200411/24/200411/25/200411/26/200411/27/200411/28/2004

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

51
O 2008 CONTROLLED-FLOOD EXPERIMENT RIVER-MILE 225 

0

10,000

20,000

30,000

40,000

50,000

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

ACOUSTIC 

PUMP

EDI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

ACOUSTIC 

PUMP

EDI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

5

10

15

20

D

50 % < 0.125 mm 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

ACOUSTIC 

PUMP

EDI

3/5/20083/6/20083/7/20083/8/20083/9/2008

3/10/20083/11/20083/12/2008

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DATE

Figure 4. — Continued.

52
disagreement between these measurements and physical measurements of suspended-sand 

concentration and grain size at only the River-mile 30 and 61 study sites during the rising limbs of 

the 2004 and 2008 CFEs (figs. 4D-E, G-H). Again, "substantial disagreement" is defined to be 

when the acoustic measurements of suspended-sand concentration and median grain size lie 

significantly outside the 95-percent confidence intervals associated with the EDI or EWI 

measurements of suspended-sand concentration and median grain size. 

Data Collected at Each Study Site During All CFEs 

Comparisons of the data collected at each study site during all three CFEs are provided in 

figures 5 and 6. Although differences in the upstream sediment supplies at the study sites during 

each CFE resulted in very different concentrations and grain sizes, similar processes were observed 

during each CFE at the study sites where data collection was at a sufficiently high temporal 

resolution. The following processes were observed in the suspended sediment during the rising 

limb of the 2004 and 2008 CFEs at the sites with 15-minute data resolution. Although these 

processes likely also occurred at all study sites during the 1996 CFE and at the River-mile 0 study 

site during all CFEs, limited data resolution prevented making such inferences. 

 (1) At each study site during the 2004 and 2008 CFE, suspended-sand concentration 

increased with the initial increase in the discharge of water during the rising limb. 

Associated with this increase in suspended-sand sand concentration is a decrease in the 

median grain size of the suspended sand. 

(2) In Marble Canyon at the River-mile 30 and 61 study sites during the 2004 and 2008 CFEs, 

two peaks in suspended-sand concentration occurred during the rising limb. The first of 

these peaks coincided with the minimum median grain size of the suspended sand. This 

occurred at a water discharge of approximately 20,000 ft3

/s (a dam release slightly higher 

than any discharge during the antecedent accounting periods for each CFE). During both 

the 2004 and 2008 CFEs, this initial peak in suspended-sand concentration was more 

pronounced at the River-mile 61 study site than at the River-mile 30 study site. Following 

this initial peak in concentration coupled to the minimum median grain size, the median 

grain size of the suspended sand increased as the discharge continued to increase. During 

this second part of the rising limb, suspended-sand concentration first decreased and then 

increased, all while the median grain size of the suspended sand increased. 

(3) No initial peak in suspended sand concentration is evident in the data collected at the 

River-mile 87, 166, and 225 study sites in Grand Canyon during either the 2004 or 2008 

CFE. However, after the initial increase in suspended-sand concentration associated with 

the decrease in suspended-sand median grain size, suspended-sand concentration and 

median grain size both increased through the remainder of the rising limb as discharge 

increased from about 20,000 ft3

/s to 42,000 ft3/s. 

(4) Peak suspended-sand concentration generally occurred at all study sites either at or just 

before the attainment of peak discharge. At the River-mile 30 and 61 study sites, this was 

the second peak in suspended-sand concentration. 

(5) At each study site during the 2004 and 2008 CFE, suspended-silt-and-clay concentration 

increased with the initial increase in the discharge of water during the rising limb. Peak 

silt and clay concentration generally coincided with the above-described minimum in 

suspended-sand median grain size (and at a discharge of about 20,000 ft3

/s). Following 

this peak in concentration, suspended-silt-and-clay concentration decreased during the 

remainder of the rising limb. 

The following processes were typically, but not always, observed in the bed sediment during the 

rising limb of each CFEs at each study site. 

(1) The median grain size of the bed sand decreased, sometimes associated with a substantial 

increase in the fraction of the bed sand composed of sand finer than 0.125 mm. 

53
(2) Silt and clay was winnowed from the bed. This winnowed silt and clay was likely the 

source of the peak in suspended-silt-and-clay concentration during the initial part of the 

rising limb. 

The following processes were observed in the suspended- and bed-sediment at all study sites 

during the high, steady discharge part of all CFEs. These processes have been previously described 

in Rubin and others (1998), Topping and others (1999, 2000a, 2000b, 2005, 2006a, 2007a, 2008), 

Rubin and Topping (2001, 2008), Schmidt and others (2007). 

(1) Suspended-sand concentration decreased over time. 

(2) Suspended-sand median grain size increased over time. 

(3) Suspended-silt-and-clay concentration continued to decrease over time. 

(4) The median grain size of the bed sand increased. This was typically associated with a 

substantial decrease in the fraction of the bed sand composed of sand finer than 0.125 

mm. 

(5) The amount of silt and clay in the bed either continued to decrease or remained constant at 

extremely low levels. 

Although similar suspended- and bed-sediment processes were observed at the various 

study sites during the three CFEs, suspended-sand concentrations and grain sizes were very 

different among the different study sites during the three CFEs, owing to very different upstream 

supplies of sand. For a given discharge of water, the dominant nonlinear controller of suspendedsand concentration is the reach-averaged grain size of the sand on the bed, and the secondary linear 

controller of suspended-sand concentration is the reach-averaged area of the sand on the bed 

(summarized in Topping and others, 2007a). Owing to this boundary condition, the same 

concentration of sand in suspension can be supported by coarser bed sand covering a large fraction 

of the bed in a reach or by finer bed sand covering a small fraction of the bed in a reach. By this 

logic, it is evident that increasing levels of sand enrichment could be associated with decreasing 

concentrations of suspended sand if the "enriching sand" covers more of the bed in a reach as its 

grain size progressively coarsens (however unlikely this scenario might be). In addition, when one 

also incorporates the complexities in relating reach-averaged bed-sand area and grain size to the 

upstream sand supply reviewed in the "Theoretical Background" section of this report, it becomes 

Figure 5 (next pages). Hydrographs, suspended-sediment data, and bed-sand data collected at each 

study site during all three CFEs. Hydrographs and sediment data were shifted in time such that zero 

time (indicated by the leftmost vertical green line) is the beginning of high, steady discharge (Q) 

during each CFE. Right vertical green line indicates the end of the high, steady discharge part of the 

2004 and 2008 controlled floods at a given site; note that data collected during the 1996 CFE to the 

right of the right green line cannot be compared to data collected during the 2004 and 2008 CFEs 

because of the much greater duration of high, steady discharge during the 1996 CFE. Data collected 

after day 5 of high, steady discharge during the 1996 CFE not shown. Error bars for the EDI, EWI, or 

mean point suspended-sediment concentration and grain-size data indicate the 95-percent confidence 

interval associated with these measurements (incorporating the field and laboratory errors described in 

the text). Error bars for the bed-sediment data are one standard error, indicating the 67-percent 

confidence interval associated with the mean value of the median grain size or < 0.125-mm sand 

fraction among the stations sampled across the cross-section in each bed-sediment measurement. Q is 

water discharge, CSAND is the velocity-weighted concentration of suspended sand in the cross-section, 

CSILT&CLAY is the velocity-weighted concentration of suspended silt and clay in the cross-section, and 

D50 is the median grain size of the bed sand or the velocity-weighted median grain size of the 

suspended sand in the cross-section. Hydrograph and data collected at (A) the River-mile 0 study site 

during the 1996, 2004, and 2008 CFEs; (B) the River-mile 30 study site during the 2004 and 2008 

CFEs; (C) the River-mile 61 study site during the 1996, 2004, and 2008 CFEs; (D) the River-mile 87 

study site during the 1996, 2004, and 2008 CFEs; (E) the River-mile 166 study site during the 1996 

and 2008 CFEs; and (F) the River-mile 225 study site during the 2004 and 2008 CFEs. 

54
A ALL CONTROLLED-FLOOD EXPERIMENTS RIVER-MILE 0 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

1996 

2004

2008

Q, IN CUBIC 

FEET PER SECOND

0

50

100

150

200

250

300

1996 EDI

2004 EDI 

2008 EDI CSAND, IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1996 EDI 

2004 EDI 

2008 EDI 

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

10

20

30

40

50

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

NO BED-SEDIMENT SAMPLES COLLECTED

0

10

20

30

40

50

1996 EDI 

2004 EDI 

2008 EDI 

-2 -1 0 1 2 3 4 5

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

55
B ALL CONTROLLED-FLOOD EXPERIMENTS RIVER-MILE 30 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

2004 

2008 

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

2004 ACOUSTIC 

2004 PUMP

2004 EWI

2008 ACOUSTIC

2008 PUMP

2008 EWI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

2004 PUMP

2004 EWI

2008 ACOUSTIC 

2008 PUMP

2008 EWI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

10

20

30

40

50

2004

2008

2004

2008 

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

D

50

% < 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

2004 ACOUSTIC 

2004 PUMP

2004 EWI

2008 ACOUSTIC 

2008 PUMP

2008 EWI

-2 -1 0 1 2 3 4 5

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

Figure 5. — Continued.

56
C ALL CONTROLLED-FLOOD EXPERIMENTS RIVER-MILE 61 STUDY SITE 

0

10,000

20,000

30,000

40,000

50,000

1996 

2004 

2008

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

1996 EDI 

2004 ACOUSTIC 

2004 PUMP

2004 EWI

2008 ACOUSTIC 

2008 PUMP

2008 EWI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1996 EDI 

2004 PUMP

2004 EWI 

2008 ACOUSTIC 

2008 PUMP

2008 EWI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

10

20

30

40

50

60

2004

2008

2004

2008

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

D

50

% < 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

1996 EDI

2004 ACOUSTIC 

2004 PUMP

2004 EWI

2008 ACOUSTIC 

2008 PUMP

2008 EWI

-2 -1 0 1 2 3 4 5

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

Figure 5. — Continued.

57
D ALL CONTROLLED-FLOOD EXPERIMENTS RIVER-MILE 87 STUDY SITE

0

10,000

20,000

30,000

40,000

50,000

1996

2004

2008 

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

1996 EDI (5 verts.) 

1996 EDI (2 verts.) 

1996 POINT SAMP. 

2004 ACOUSTIC

2004 PUMP

2004 EDI

2008 ACOUSTIC

2008 PUMP

2008 EDI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

1996 EDI (5 verts.) 

1996 EDI (2 verts.)

1996 POINT SAMP. 

2004 ACOUSTIC

2004 PUMP

2004 EDI

2008 ACOUSTIC

2008 PUMP

2008 EDI 

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

2

4

6

8

10

12

14

1996

2004

2008

1996

2004

2008

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

D

50

% < 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

1996 EDI (5 verts.) 

1996 EDI (2 verts.)

1996 POINT SAMP. 

2004 ACOUSTIC

2004 PUMP

2004 EDI

2008 ACOUSTIC

2008 PUMP

2008 EDI

-2 -1 0 1 2 3 4 5

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

Figure 5. — Continued.

58
E ALL CONTROLLED-FLOOD EXPERIMENTS RIVER-MILE 166 STUDY SITE

0

10,000

20,000

30,000

40,000

50,000

1996 

2008 

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

1996 POINT SAMP. 

2008 ACOUSTIC

2008 PUMP

2008 EWI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1996 POINT SAMP. 

2008 ACOUSTIC

2008 PUMP

2008 EWI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

2

4

6

8

10

2008 

BED-SAND

2008 

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

D

50

% < 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

1996 POINT SAMP. 

2008 ACOUSTIC

2008 PUMP

2008 EWI

-2 -1 0 1 2 3 4 5

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

Figure 5. — Continued.

59
F ALL CONTROLLED-FLOOD EXPERIMENTS RIVER-MILE 225 STUDY SITE

0

10,000

20,000

30,000

40,000

50,000

2004 

2008 

Q, IN CUBIC 

FEET PER SECOND

0

1,000

2,000

3,000

4,000

5,000

2004 ACOUSTIC 

2004 PUMP

2004 EDI

2008 ACOUSTIC

2008 PUMP

2008 EDI

CSAND,

IN MILLIGRAMS PER LITER

0.08

0.10

0.12

0.14

0.16

0.18

0.20

2004 PUMP

2004 EDI

2008 ACOUSTIC 

2008 PUMP

2008 EDI

SUSPENDED-SAND

D

50, IN MILLIMETERS

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0

5

10

15

20

2004

2008

2004

2008

BED-SAND

D

50, IN MILLIMETERS

PERCENT BED SAND

FINER THAN 0.125 mm

D

50

% < 0.125 mm

0

1,000

2,000

3,000

4,000

5,000

6,000

2004 ACOUSTIC 

2004 PUMP

2004 EDI

2008 ACOUSTIC 

2008 PUMP

2008 EDI

-2 -1 0 1 2 3 4 5

CSILT & CLAY,

IN MILLIGRAMS PER LITER

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

Figure 5. — Continued.

60
61

apparent that estimating differences in the upstream sand supply from suspended- or bed-sediment 

data is a nontrivial exercise that requires coupled analyses of sediment load, concentration, and 

grain size, with consideration of whether differences in the upstream sand supply could be causing 

differences in the reach-averaged τb. These more complicated analyses are pursued later in this 

report. 

Before conducting these more complicated analyses, it is informative to first evaluate the 

differences in upstream sediment supply between the three CFEs through ranking of the data 

collected at each study site in figures 5 and 6 in terms of concentration and grain size. When 

ranking these data, it is important to realize that, by definition, the suspended-sediment data are 

more representative of the bed-sediment conditions in the reach upstream from a measurement 

cross-section than are bed-sediment data collected only at that measurement cross-section. At a 

given discharge of water, that is, reach-averaged τb, differences in the grain-size distribution of the 

sand in suspension can only be explained by changes in the grain-size distribution of the sand on 

the bed upstream, with the reach-averaged grain size of the sand on the bed and in suspension being 

proportional (equation 7). The spatial scale over which suspended sand equilibrates with the bed 

sand ranges from about 600 m to well over 1 km under typical flow conditions in the Colorado 

River in the study area (Topping and others, 2007a). Therefore, a proper analysis of the grain-size 

distribution of the suspended sand will provide a more representative sample of the grain-size 

distribution of the bed sand in the reach upstream from a measurement cross-section than does only 

bed-sediment measurements made only at the measurement cross-section (Rubin and Topping, 

2001, 2008). For example, the apparent inconsistency at the River-mile 30 study site between the 

coarser suspended sand during the 2008 CFE than during the 2004 CFE and finer bed sand during 

the 2008 CFE than during the 2004 CFE can be explained by the bed-sand data at the measurement 

cross-section being less representative of the bed-sand grain-size distribution in the reach upstream 

from this study site than are the suspended-sand data. 

An alternative explanation to this inconsistency could be that, because more sand was 

present on the bed upstream from the River-mile 30 study site (table 3), thus resulting in thicker 

sand patches over much of the bed, the reach-averaged τb upstream from the River-mile 30 study 

site could have been higher during the 2008 CFE than during the 2004 CFE. This difference in 

reach-averaged τb would result in coarser suspended sand during the 2008 CFE than during the 

2004 CFE, with bed sand that was finer during the 2008 CFE than during the 2004 CFE. This 

alternative explanation can be illustrated by moving along a path from the origin up and slightly 

left of the "Db = constant" line in figure 3B in Rubin and Topping (2001), with the origin 

representing conditions during the 2004 CFE. Moving along such a path results in an increase in 

reach-averaged τb, a decrease in reach-averaged median grain size of the bed sand, an increase in 

suspended-sand concentration, and an increase in the median grain size of the suspended sand 

Figure 6 (next page). Bed silt and clay data collected at each study site during all three CFEs. Data 

were shifted in time such that zero time (indicated by the leftmost vertical solid green line) is the 

beginning of high, steady discharge during each CFE. Right vertical green line indicates the end of 

the high, steady discharge part of the 2004 and 2008 controlled floods at a given site. As in figure 5, 

data collected after day 5 of high, steady discharge during the 1996 CFE not shown. Vertical dashed 

green line indicates beginning of rising limb of 2008 CFE at each study site. Silt and clay were 

winnowed from the bed at most study sites during the rising limbs of the CFEs. Error bars for the 

bed-sediment data are one standard error, indicating the 67-percent confidence interval associated 

with the mean value of the silt and clay fraction among the stations sampled across the cross-section 

in each bed-sediment measurement.
0.0

0.5

1.0

1.5

2004 

2008 

PERCENT OF FINE BED 

SEDIMENT COMPOSED

OF SILT AND CLAY

RIVER-MILE 30

0

5

10

15

20

25

30

2004 

2008

PERCENT OF FINE BED 

SEDIMENT COMPOSED

OF SILT AND CLAY

RIVER-MILE 61

0.0

0.5

1.0

1.5

1996 

2004 

2008 

PERCENT OF FINE BED 

SEDIMENT COMPOSED

OF SILT AND CLAY

RIVER-MILE 87

0.0

0.2

0.4

0.6

0.8

1.0

1.2

2008 

PERCENT OF FINE BED 

SEDIMENT COMPOSED

OF SILT AND CLAY

RIVER-MILE 166

0

1

2

3

4

5

6

2004 

2008 

-2 -1 0 1 2 3 4 5

PERCENT OF FINE BED 

SEDIMENT COMPOSED

OF SILT AND CLAY

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

RIVER-MILE 225

62
between the 2004 and 2008 CFEs. Whether such a path is physically realistic for this River-mile 30 

study-site example can be evaluated by: 

(1) setting constant coefficients of proportionality for equations 4 and 7 at the River-mile 30 

measurement cross-section between the 2004 and 2008 CFEs, 

(2) converting the proportionalities in equations 4 and 7 to equations relating the ratios of C, 

Ab, τb, Db, and Ds at this cross-section between the 2004 and 2008 CFEs, 

(3) substituting the values of C, Db, and Ds measured at the measurement cross-section during 

the first day of steady, high discharge during the 2004 and 2008 CFEs, 

(4) solving for values of reach-averaged τb and Ab, and 

(5) determining whether these values of reach-averaged τb and Ab are realistic. 

When using conditions during the 2004 CFE as the reference conditions, equation 4 can be 

rewritten in terms of ratios as: 

( )

( )

( )

( )

( )

( )

( )

( )

τ

τ

−

⎛ ⎞⎛ ⎞ ⎛

= ⎜ ⎟⎜ ⎟ ⎜

⎝ ⎠⎝ ⎠ ⎝

1.8 2.5

2008 2008 2008 2008

2004 2004 2004 2004

SAND b b b

SAND b b b

CA D

CA D

⎞

⎟

⎟

⎠

, (13) 

where the subscripts "2008" refer to conditions during the 2008 CFE and the subscripts "2004" 

refer to conditions during the 2004 CFE. Similarly, equation 7 can be rewritten in terms of ratios 

as: 

( )

( )

( )

( )

( )

( )

τ

τ

⎛ ⎞⎛

= ⎜ ⎟⎜

⎝ ⎠⎝

0.18 0.75

2008 2008 2008

2004 2004 2004

sb b

sb b

D D

D D

⎞

⎟

⎟

⎠

. (14) 

Using EWI and bed-sediment measurements made on the first day of steady, high discharge at the 

River-mile 30 study site during both CFEs, the following values of the ratios are obtained: 

( ) CSAND 2008

( ) CSAND 2004

= 1.4 , 

( ) Ds 2008

( ) Ds 2004

= 1.2 , and (Db )2008

( ) Db 2004

= 0.86 . Inserting these values into equations 13 and 

14 and rearranging yields: ( )

( )

τ

τ

⎛ ⎞ ⎜ ⎟ =

⎝ ⎠

2008

2004

5.2 b

b

, and ( )

( )

⎛ ⎞ ⎜ ⎟ =

⎝ ⎠

2008

2004

0.049 b

b

A

A . 

These ratios of reach-averaged τb and Ab are physically unrealistic, given that the maximum 

likely 2008 to 2004 ratio in reach-averaged τb associated with changes in sand thickness on the bed 

should be about 1.1 based on the "Theoretical Background" section of this report, and a more likely 

2008 to 2004 ratio in reach-averaged Ab should be greater than 1 based on the much greater sand 

enrichment in upper Marble Canyon antecedent to the 2008 CFE than antecedent to the 2004 CFE 

(table 3). Support for an approximate 10-percent increase in reach-averaged τb and constant water 

discharge between the 2004 and 2008 CFEs is provided by acoustic-Doppler-current-profiler 

velocity measurements made at 5 stations across the measurement cross-section at the River-mile 

30 study site during both CFEs. These measurements indicate that the mean velocity through the 

measurement cross-section was on average 6 percent greater at steady, high discharge during the 

2008 CFE than it was during the 2004 CFE. This increase in mean velocity was, in fact, associated 

with a decrease in cross-sectional area at the measurement cross-section arising from greater sand 

thickness on the bed. Because mean velocity is proportional to τb

2

, this suggests that the 2008 to 

2004 ratio in reach-averaged τb associated with the increase in sand thickness on the bed should, in 

fact, be about 1.1. Inserting this value and the measured (Ds )2008

( ) Ds 2004

= 1.2 into equation 14 and 

63
rearranging to solve for a more plausible reach-averaged value of (Db )2008

( ) Db 2004

 yields ( ) Db 2008

( ) Db 2004

= 1.2 , 

not the above value of ( ) Db 2008

( ) Db 2004

= 0.86 that is based on bed-sediment measurements made at only 

the one cross-section where suspended-sediment measurements were made. Furthermore, inserting 

values of ( ) CSAND 2008

( ) CSAND 2004

= 1.4 , 

( ) Db 2008

( ) Db 2004

= 1.2 , and 

τ( b )2008

τ( )b 2004

= 1.1into equation 13 and rearranging to 

solve for a more likely 2008 to 2004 ratio in reach-averaged Ab yields ( )

( )

⎛ ⎞ ⎜ ⎟ =

⎝ ⎠

2008

2004

1.9 b

b

A

A

. For 

comparison, inserting values of ( ) CSAND 2008

( ) CSAND 2004

= 1.4 , 

(Db )2008

( ) Db 2004

= 1.2 , and 

τ( b )2008

τ( )b 2004

= 1into equation 13 

and rearranging to solve for a 2008 to 2004 ratio in reach-averaged Ab that is computed by 

excluding the effects of changes in bed-sand thickness on reach-averaged τb (as done in the 

analyses later in this report) yields ( )

( )

⎛ ⎞ ⎜ ⎟ =

⎝ ⎠

2008

2004

2.2 b

b

A

A . Therefore (1) as suggested above, the apparent 

suspended- and bed-sand grain-size inconsistency at the River-mile 30 study site between the 2004 

and 2008 CFEs can best be explained by the bed-sand data at the measurement cross-section being 

less representative of the bed-sand grain-size distribution in the reach upstream from this study site 

than are the suspended-sand data, and (2) changes in reach-averaged τb arising from reach-averaged 

changes in bed-sand thickness may play an important role in regulating suspended-sand 

concentration and median grain size: however, exclusion of this role will likely result in only an 

approximate 16-percent error in reach-averaged bed-sand area estimated from suspended-sediment 

data. 

With the notable exception of the suspended- and bed-sand grain-size inconsistency at only 

the River-mile 30 study site, the general results from the simple comparative analyses in figures 5 

and 6 are: 

(1) Average suspended-sand concentrations at each study site during the 2008 CFE were as 

high as or higher than during all other CFEs. 

(2) Except at the River-mile 87 study site, average suspended-sand concentrations at each 

study site during the 1996 CFE were as low as or lower than during all other CFEs. 

(3) Average suspended-sand median grain size at and and downstream from the River-mile 61 

study site during the 2008 CFE was as fine as or finer than during all other CFEs. At the 

River-mile 0 study site, average suspended-sand median grain size was finest during the 

1996 CFE, and at the River-mile 30 study site, average suspended-sand median grain size 

was finest during the 2004 CFE. 

(4) Though not necessarily representative of the grain size of the bed sand in the reaches 

upstream from these cross-sections, the bed sand at the measurement cross-sections 

during the 2008 CFE was as fine as or finer than that during the 2004 CFE. Most of the 

difference in the bed-sand grain-size distribution between these two CFEs was during the 

rising limb, when the bed during the 2008 CFE was considerably finer than during the 

2004 CFE. 

(5) At the one measurement cross-section where bed-sediment data were collected during all 

three CFEs, at the River-mile 87 study site, the bed sand during the 2008 CFE was 

64
slightly finer than that during both the 1996 and 2004 CFEs. Bed-sand median grain size 

was similar at this study site during the 1996 and 2004 CFEs. 

(6) Except at the River-mile 30 study site, where suspended-silt-and-clay concentrations were 

higher during the 2004 CFE than during the 2008 CFE, average suspended-silt-and-clay 

concentrations during the 2008 CFE were as high as or higher than during all other CFEs. 

(7) There was typically more silt and clay present in the bed sediment before the 2008 CFE 

than there was before the 2004 CFE or 1996 CFE. 

Data Collected During Each CFE at All Study Sites 

Comparison of the suspended-sand data collected during each CFE at all study sites is 

provided in figure 7. 

Averaged over the 1996 CFE, suspended-sand concentration increased between the Rivermile 0 and 87 study sites and then remained constant between the River-mile 87 and 166 study 

sites. As the concentration of suspended sand increased between the River-mile 0 and 87 study 

sites, suspended-sand median grain size coarsened. Suspended-sand median grain size then fined 

between the River-mile 87 and 166 study sites while suspended-sand concentration remained 

constant. 

Averaged over the 2004 CFE, suspended-sand concentration increased the most between 

the River-mile 0 and 30 study sites. Between the River-mile 30 and 61 study sites, suspended-sand 

concentration again increased, but to a lesser degree, and then remained approximately constant 

between the River-mile 61 and 225 study sites. However, suspended-sand concentration during the 

rising limb at the River-mile 87 study site was greater than at either the River-mile 61 or 225 study 

sites. Suspended-sand median grain size was coarsest at the River-mile 0 study site and finest at the 

River-mile 30 study site. Between the River-mile 30 and 87 study sites, suspended-sand median 

grain size coarsened; between the River-mile 87 and 225 study sites, suspended-sand median grain 

size fined to be approximately equal to that at the River-mile 61 study site. Suspended-sand 

median grain size was anomalously coarse during the rising limb at the River-mile 61 study site, 

nearly as coarse as at the River-mile 0 study site. 

Averaged over the 2008 CFE, suspended-sand concentration increased the most between 

the River-mile 0 and 30 study sites, as it did during the 2004 CFE. Similarly, during the 2008 CFE, 

suspended-sand concentration increased between the River-mile 30 and 61 study sites, as it did 

during the 2004 CFE. In contrast to the 2004 CFE, however, suspended-sand concentrations 

continued to increase between the River-mile 61 and 87 study sites over the entire flood 

hydrograph, not just during the rising limb. Downstream from the River-mile 87 study site, 

suspended-sand concentration decreased between the River-mile 87 and 166 study sites, mostly 

during the rising limb; suspended-sand concentration then remained approximately constant 

between the River-mile 166 and 225 study sites, although at a level greater than at the River-mile 

61 study site. Suspended-sand median grain size was coarsest at the River-mile 30 study site and 

finest at the River-mile 166 study site; in contrast, during the 2004 CFE, suspended-sand median 

grain size was finest at the River-mile 30 study site. Suspended-sand median grain size coarsened 

between the River-mile 0 and 30 study sites and then fined between the River-mile 30 and 166 

study sites. Suspended-sand median grain size then coarsened, but only slightly between the Rivermile 166 and 225 study sites. 

These observations encompass almost every possible coupled change in suspended-sand 

concentration and grain size through a reach (table 5). The following coupled changes in 

suspended-sand concentration and grain size have been observed during a CFE through the long 

65
A 

0

1,000

2,000

3,000

4,000

5,000

RM 0 EDI

RM 61 EDI

RM 87 EDI (5 verts.) 

RM 87 EDI (2 verts.) 

RM 87 POINT

RM 166 POINT

CSAND,

IN MILLIGRAMS PER LITER

1996

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.20

0.21

0.22

0.23

0.24

0.25

0.26

RM 0 EDI

RM 61 EDI

RM 87 EDI (5 verts.) 

RM 87 EDI (2 verts.) 

RM 87 POINT

RM 166 POINT

-2 -1 0 1 2 3 4 5 6 7 8 9 10

SUSPENDED-SAND D

50, IN MILLIMETERS

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

Figure 7. Suspended-sand data collected during each CFE at all study sites. Upper graphs, 

suspended-sand concentration; lower graphs, suspended-sand median grain size. Data were shifted in 

time such that zero time (indicated by the leftmost vertical solid green line) is the beginning of high, 

steady discharge during each CFE. Right vertical green line indicates the end of the high, steady 

discharge part of the 1996, 2004, and 2008 controlled floods at a given site. Error bars for the EDI, 

EWI, or mean point suspended-sediment concentration and grain-size data indicate the 95-percent 

confidence interval associated with these measurements (incorporating the field and laboratory 

errors described above). A, 1996 CFE. B, 2004 CFE. C, 2008 CFE.

66
B

 

Figure 7. — Continued.

67
C

Figure 7. — Continued.

68
reaches between the study sites: 

(1) concentration increase with coarsening, 

(2) concentration increase with no change in grain size, 

(3) concentration increase with fining, 

(4) concentration decrease with fining, 

(5) no change in concentration with fining, and 

(6) no change in concentration with coarsening. 

Of these six different coupled changes in concentration and median grain size, numbers 1, 2, and 6 

require a longitudinal increase in bed-sand area in the downstream direction through a reach (at 

assumed constant reach-averaged τb), numbers 4 and 5 require a longitudinal decrease in bed-sand 

area in the downstream direction through a reach, and only number 3 requires a longitudinal 

decrease in bed-sand median grain size in the downstream direction through a reach. Interestingly, 

only the following two coupled changes in suspended-sand concentration and median grain size 

have not yet been observed during a CFE through the long reaches between the study sites: (1) 

concentration decrease with coarsening and (2) concentration decrease with no change in median 

grain size. As shown below, however, these last two coupled changes in concentration and median 

grain size have been observed over shorter reaches than those between the study sites in the 

suspended-sand data collected during the 2004 and 2008 Lagrangian sampling programs. 

Therefore, any possible coupled change in suspended-sand concentration and median grain size is 

possible in the downstream direction through a reach of the Colorado River during a CFE, 

depending on the details of the longitudinal distribution of the upstream sand supply (for example, 

downstream changes in reach-averaged bed-sand area and median grain size) and the details of the 

longitudinal distribution of the reach-averaged τb antecedent to the CFE. 

 

Table 5. Observed coupled changes in suspended-sand concentration and median grain size 

through each reach during each CFE. 

Reach 1996 CFE 2004 CFE 2008 CFE 

upper Marble Canyon Concentration 

increase with fining 

Concentration 

increase with 

coarsening 

lower Marble Canyon 

Concentration 

increase with slight 

coarsening Concentration 

increase with 

coarsening 

Concentration 

increase with fining 

eastern Grand Canyon Concentration 

increase with 

coarsening 

Slight rising limb 

concentration 

increase then no 

concentration change 

with coarsening 

Concentration 

increase with no 

change in median 

grain size 

east-central Grand Canyon No change in 

concentration with 

fining 

Slight concentration 

decrease with fining 

west-central Grand Canyon No data 

No net change in 

concentration with 

fining (opposing 

concentration 

changes on rising and 

receding limbs) 

No change in 

concentration with 

coarsening 

69
Sediment Export Past the Study Sites During the 1996, 2004, and 2008 CFEs 

Using the same approach used to compute sand export in table 2, sand export and silt and 

clay export past the various study sites during the 1996, 2004, and 2008 CFEs are provided in table 

6. As in table 2, uncertainties are 5 percent for the sand loads at the study sites on the Colorado 

River. Uncertainties used for the silt and clay loads are 2 percent. Loads during each CFE are 

computed from the beginning of the rising limb through the recession. At each study site, sand 

loads during the 1996 CFE are typically as large as or larger than those during the 2004 and 2008 

CFEs because of the much greater duration of high, steady discharge during the 1996 CFE. 

Table 6. Sand export and silt and clay export past the study sites on the Colorado River during the 

1996, 2004, and 2008 CFEs. 

Study site Sand export with 

uncertainty during the 

1996 CFE 

(million metric tons) 

Sand export with 

uncertainty during the 

2004 CFE 

(million metric tons) 

Sand export with 

uncertainty during the 

2008 CFE 

(million metric tons) 

River-mile 0 0.06±0.003 0.020±0.001 0.048±0.002 

River-mile 30 no data 0.476±0.024 0.651±0.033 

River-mile 61 0.84±0.04 0.657±0.033 0.879±0.044 

River-mile 87 1.52±0.08 0.622±0.031 1.197±0.060 

River-mile 166 1.54+0.08 no data 1.076±0.054 

River-mile 225 no data 0.689±0.034 1.055±0.053 

Study site Silt and clay export 

with uncertainty during 

the 1996 CFE 

(million metric tons) 

Silt and clay export with 

uncertainty during the 

2004 CFE 

(million metric tons) 

Silt and clay export with 

uncertainty during the 

2008 CFE 

(million metric tons) 

River-mile 0 0.01±0.0002 0.004±0.0001 0.010±0.0002 

River-mile 30 no data 0.177±0.004 0.109±0.002 

River-mile 61 0.14±0.002 0.278±0.006 0.236±0.005 

River-mile 87 0.24±0.005 0.489±0.010 0.464±0.009 

River-mile 166 0.22±0.004 no data 0.715±0.014 

River-mile 225 no data 0.646±0.013 0.866±0.017 

Sand Budgeting During the 2004 and 2008 CFEs 

Employing the same approach used to compute the mass-balance sand budgets during the 

accounting periods antecedent to the 2004 and 2008 CFEs in table 3, sand budgets for the periods 

from the beginning of the accounting periods antecedent to each CFE through the recession of each 

of the 2004 and 2008 CFEs are provided in table 7. For simplicity, this extended sand-budgeting 

period is herein referred to as the CFE sand-budgeting period. These sand budgets were computed 

using the data in tables 3 and 6, with propagated uncertainty. As in table 3, no sand enrichment or 

depletion can be demonstrated in a reach when the propagated uncertainties are much larger than 

the absolute value of the change in sand storage during the CFE sand-budgeting period; in table 7 

this threshold uncertainty value is arbitrarily set equal to a factor of 1.5 times the absolute value of 

70
Table 7. Sand budgets for each reach during the 2004 and 2008 CFE sand-budgeting periods. 

[Reaches without demonstrable change in sand storage (that is, propagated uncertainty is much greater than the 

absolute value of net change in sand storage) indicated by red type. Reaches with likely but not necessarily positive net 

change in sand storage (that is, propagated uncertainty is only slightly greater than positive value of net change in sand 

storage) shown in black type. Reaches with demonstrable positive change in sand storage (that is, propagated 

uncertainty is less than positive value of net change in sand storage) indicated by green type. No reaches can be 

demonstrated to have negative net change in sand storage during the sand-budgeting periods for either CFE.]

Reach Net change in sand 

storage during 2004 CFE 

sand-budgeting period 

with propagated 

uncertainty 

(million metric tons) 

Net change in sand 

storage during 2008 CFE 

sand-budgeting period 

with propagated 

uncertainty 

(million metric tons) 

upper Marble Canyon -0.073±0.133 +0.592±0.663 

lower Marble Canyon -0.067±0.105 +0.307±0.353 

eastern Grand Canyon +0.021±0.112 +0.518±0.766 

combined east-central and west-central 

Grand Canyon 

+0.089±0.161 +1.059±0.508 

the change in sand storage. As one measure of the sustainability of a given controlled-flood design 

in building sandbars, the sand budget for the accounting period antecedent to a controlled flood 

through the recession of that controlled flood should not be negative. In other words, a controlled 

flood should not be demonstrated to have exported more sand from a reach than was supplied to 

that reach during the period leading up to the controlled flood. If a controlled flood can be shown to 

have exported more sand from a reach than was supplied to it during the period leading up to that 

controlled flood, then that particular controlled-flood design scoured sand from “background 

storage” in that reach and cannot be used to sustainably rebuild sandbars; this scenario is likely 

what happened during the 1996 CFE in Marble Canyon, based on Schmidt (1999). As shown in 

table 7, in all reaches where sand budgets could be computed for the 2004 CFE, no demonstrable 

change in sand storage occurred in any reach during the 2004 CFE sand-budgeting period because 

the uncertainties were much larger than absolute values of change in sand storage. In contrast, 

during the much more sand-enriched 2008 CFE, the sand budgets in the upstream three reaches 

(upper Marble, lower Marble, and Grand Canyons) were likely but not necessarily positive during 

the 2008 CFE sand-budgeting period. The sand budgets in these three reaches were likely but not 

necessarily positive because the changes in sand storage were all positive, but the uncertainties 

were slightly larger than the changes in sand storage. Only in one reach and only during the 2008 

CFE was a sand budget demonstrably positive, in the combined east- and west-central Grand 

Canyon reach located between the River-mile 87 and 225 study sites. 

Lagrangian Sampling-Program data 

Suspended-sediment data collected during the 2004 and 2008 Lagrangian sampling 

programs are presented in figure 8, with each sampled parcel of water indicated by a different 

color. Also shown are the EDI, EWI, or calibrated pump measurements made at the study sites in 

close temporal proximity to the Lagrangian data in each parcel of water. Agreement is excellent 

between all Lagrangian and study-site suspended-sediment data except during the sampling of 

water parcel 5 near the River-mile 225 study site during the 2008 CFE. Although agreement is 

71
good between the Lagrangian data and data collected at this study site with respect to suspendedsand median grain size and suspended-silt-and-clay concentration, agreement is poor between 

Lagrangian data and data collected at this study site with respect to suspended-sand concentration. 

Analysis of the Lagrangian data collected during the 2004 and 2008 CFEs allows 

identification of reaches of net sediment erosion or deposition, as well as identification of reaches 

of net change in suspended-sand median grain size. This analysis is possible by virtue of 

conservation of mass between the bed and the water column, and by the assumption that the spatial 

patterns in the suspended sediment observed in a sampled parcel of water are similar to spatial 

patterns in suspended sediment in other parcels of water traveling through the same reach at 

different times during a CFE. This assumption is most justified in cases where the flood duration is 

relatively short, as in the cases of the 2004 and 2008 CFEs, and in cases where step changes in 

concentration and grain size are relatively small during backward or forward steps in the 

Lagrangian reference frame. Because the discharge of water is constant during the high, steady 

discharge parts of the CFEs, an increase in the suspended-sediment concentration in a parcel of 

water traveling downstream through a reach indicates a net flux of sediment from the bed to the 

water column in this reach, that is, erosion of sediment in this reach. Likewise, a decrease in the 

suspended-sediment concentration in a parcel of water traveling downstream through a reach 

indicates a net flux of sediment from the water column to the bed in this reach, that is, deposition of 

sediment in this reach. 

During the 2004 CFE, analysis of the Lagrangian data between river miles 0 and 85 

indicates that net sand erosion occurred between river miles 0 and 24 in Marble Canyon, net sand 

deposition occurred between river miles 24 and 52 in Marble Canyon, and net sand erosion 

occurred between river miles 52 and 85 in Marble and eastern Grand Canyons (fig. 8A). The 

suspended sand quickly coarsened between river miles 0 and 1 (reaching its maximum value), fined 

between river miles 1 and 10 (reaching its minimum value), and then coarsened gradually between 

river miles 10 and 85 (fig. 8A). Net erosion of silt and clay occurred between river miles 0 and 85 

(fig. 8B). The downward step in silt and clay concentration between water parcels 1 and 2 in fig. 8B

does not represent net deposition of silt and clay overnight while the sampling program was in 

camp and merely reflect a backward step in the Lagrangian reference frame associated with 

Figure 8 (next pages). Suspended-sediment measurements made during the Lagrangian sampling 

programs during the 2004 and 2008 CFEs. Data collected in different parcels of water are indicated 

by different colors. Also shown are the EDI, EWI, or calibrated-pump suspended-sediment data 

collected in closest temporal proximity to the Lagrangian suspended-sediment data in each parcel of 

water. Step changes between the data collected in the various parcels of water arise from referenceframe effects (see text for discussion). Error bars for the Lagrangian data are one standard error, 

indicating the 67-percent confidence interval associated with the mean values of these data among 

the three replicate single-vertical depth-integrated suspended-sediment samples collected at each 

sampling station. As in previous figures, error bars for the EDI and EWI suspended-sediment 

concentration and grain-size data indicate the 95-percent confidence interval associated with these 

measurements (incorporating the field and laboratory errors described above). A, Suspended-sand 

concentration and median grain size measured during the 2004 Lagrangian sampling program. B, 

Suspended-silt-and-clay concentration measured during the 2004 Lagrangian sampling program. C, 

Suspended-sand concentration and median grain size measured during the 2008 Lagrangian 

sampling program. The reason a calibrated pump measurement is used for comparison with the 

Lagrangian data collected in water parcel 3 is that no EDI measurement was made at the River-mile 

87 study site until several hours after the Lagrangian sampling program passed this study site. D, 

Suspended-silt-and-clay concentration measured during the 2008 Lagrangian sampling program.

72
A

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 50 100 150 200 250

PARCEL 1 (11-22-2004)

PARCEL 2 (11-23-2004)

PARCEL 1 EDI OR EWI MEASUREMENTS 

PARCEL 2 EWI MEASUREMENT

CSAND, IN MILLIGRAMS PER LITER

RIVER MILE

EXPLANATION

NET SAND

EROSION

NET SAND

DEPOSITION

NET SAND

EROSION

LAGRANGIAN DATA STUDY-SITE DATA

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.20

0 50 100 150 200 250

SUSPENDED-SAND D

50, IN MILLIMETERS

RIVER MILE

NET SAND COARSENING

NET SAND

COARSENING

NET SAND FINING

73
B

0

500

1,000

1,500

0 50 100 150 200 250

PARCEL 1 (11-22-2004)

PARCEL 2 (11-23-2004)

PARCEL 1 EDI OR EWI MEASUREMENTS

PARCEL 2 EWI MEASUREMENT

CSILT & CLAY, IN MILLIGRAMS PER LITER

RIVER MILE

EXPLANATION

LAGRANGIAN DATA STUDY-SITE DATA

Figure 8. — Continued.

74
C

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 50 100 150 200 250

PARCEL 1 (3-6-2008)

PARCEL 2 (3-7-2008)

PARCEL 3 (3-7-2008)

PARCEL 4 (3-8-2008)

PARCEL 5 (3-9-2008)

PARCEL 1 EDI OR EWI MEASUREMENTS

PARCEL 2 EDI OR EWI MEASUREMENTS 

PARCEL 3 PUMP MEASUREMENT

PARCEL 4 EWI MEASUREMENT

PARCEL 5 EDI MEASUREMENT

CSAND, IN MILLIGRAMS PER LITER

RIVER MILE

EXPLANATION

NET SAND

EROSION

NET SAND

DEPOSITION

NET SAND

DEPOSITION

NET SAND

EROSION

NO NET CHANGE 

IN SAND STORAGE

LAGRANGIAN DATA STUDY-SITE DATA

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.20

0 50 100 150 200 250

SUSPENDED-SAND D

50, IN MILLIMETERS

RIVER MILE

NET SAND COARSENING

NET SAND

FINING

SLIGHT 

NET SAND

COARSENING

NET SAND

COARSENING

SLIGHT 

NET SAND

COARSENING

NET SAND FINING

NET SAND FINING

Figure 8. — Continued.

75
D 

0

500

1,000

1,500

0 50 100 150 200 250

PARCEL 1 (3-6-2008)

PARCEL 2 (3-7-2008)

PARCEL 3 (3-7-2008)

PARCEL 4 (3-8-2008)

PARCEL 5 (3-9-2008)

PARCEL 1 EDI OR EWI MEASUREMENTS

PARCEL 2 EDI OR EWI MEASUREMENTS 

PARCEL 3 PUMP MEASUREMENT

PARCEL 4 EWI MEASUREMENT

PARCEL 5 EDI MEASUREMENT

CSILT & CLAY, IN MILLIGRAMS PER LITER

RIVER MILE

EXPLANATION

LAGRANGIAN DATA STUDY-SITE DATA

Figure 8. — Continued.

76
switching from water parcel 1 to 2. Note that this step change is much larger than and opposite in 

sign to the associated step changes in suspended-sand concentration and median grain size between 

these two water parcels in figure 8A. 

During the 2008 CFE, analysis of the Lagrangian data between river miles 0 and 225 

indicates that net sand erosion occurred between river miles 0 and 24 in Marble Canyon 

(identically as during the 2004 CFE), net sand deposition occurred between river miles 24 and 47 

in Marble Canyon (very similar to what happened during the 2004 CFE), net sand erosion occurred 

between river miles 47 and 105 in Marble and eastern Grand Canyons, net sand deposition 

occurred between river miles 105 and 179 in Grand Canyon, and no net change in sand storage 

occurred between river miles 179 and 225 in Grand Canyon (fig. 8C). As during the 2004 CFE, the 

suspended sand quickly coarsened between river miles 0 and 2.5, reaching its maximum value (fig. 

8C). However, downstream from river mile 2.5, the longitudinal patterns in suspended-sand median 

grain size were far more complicated during the 2008 CFE than during the 2004 CFE. Although the 

suspended sand fined dramatically between river mile 2.5 and 8 (similarly as during the 2004 

CFE), the suspended sand then coarsened substantially between river miles 8 and 13.5 before fining 

to its minimum value near river mile 42. Thus, the longitudinal patterns in suspended-sand median 

grain size were very different in upper Marble Canyon between the 2004 and 2008 CFEs. 

Downstream from river mile 47, however, the longitudinal patterns in suspended-sand median 

grain size were similar (at least through the end of the 2004 Lagrangian sampling program near 

river mile 85). During the 2008 CFE, suspended-sand median grain size was characterized by three 

long reaches of gradual coarsening (between river miles 47 and 91, 100 and 150, and 171 and 225) 

separated by two short reaches of abrupt fining (between river miles 91 and 100, and 150 and 171). 

It is important to note that these two prominent downward steps in suspended-sand median grain 

size are real because they do not coincide with breaks in camp between the different sampled 

parcels of water (that is, they are not a result of backward steps in the Lagrangian reference frame). 

As during the 2004 CFE, net erosion of silt and clay occurred during the 2008 CFE over the entire 

reach sampled. During the 2008 CFE, this was the reach from river mile 0 to 225 (fig. 8D). The 

upward and downward steps in sand concentration and silt and clay concentration between the 

water parcels in figures 8C and 8D are merely reference-frame effects. The downward steps in sand 

concentration and silt and clay concentration between water parcels 1 and 2, and between 3, 4, and 

5 arise from the decrease in sand concentration and silt and clay concentration over time during the 

2008 CFE at all locations along the Colorado River (that is, backward steps in the Lagrangian 

reference frame associated with switching between these different parcels of water). The upward 

step in sand concentration and silt and clay concentration between parcels 2 and 3 is an artifact of 

these two water parcels being sampled simultaneously by two field crews17 (that is, a forward step 

in the Lagrangian reference frame associated with switching from water parcel 2 to 3). Thus, this 

upward step also arises from the decrease in sand concentration and silt and clay concentration over 

time during the 2008 CFE at all locations along the Colorado River. 

Direct comparison of the Lagrangian data collected during the 2004 and 2008 CFEs shows 

the similarity in Marble and eastern Grand Canyons in the longitudinal patterns in suspended-sand 

concentration and the large differences in Marble Canyon in the longitudinal patterns in suspendedsand median grain size between the two CFEs (fig. 9). The peaks and troughs in suspended-sand 

concentration occurred at essentially the same locations in Marble and eastern Grand Canyons 

 17 Water parcel 3 was sampled beginning at the River-mile 87 study site in the morning on March 7, whereas water 

parcel 2 was sampled ending at the River-mile 87 study site in the afternoon of March 7. 

77
0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

-10 0 10 20 30 40 50 60 70 80 90

2004 CFE PARCEL 1

2004 CFE PARCEL 2

2008 CFE PARCEL 1 

2008 CFE PARCEL 2

CSAND, IN MILLIGRAMS PER LITER

RIVER MILE

EXPLANATION

UPPER 

MARBLE 

CANYON

LOWER 

MARBLE 

CANYON

EASTERN

GRAND

CANYON

LOWER 

GLEN CANYON

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.20

-10 0 10 20 30 40 50 60 70 80 90

SUSPENDED-SAND D

50, IN MILLIMETERS

RIVER MILE

EASTERN

GRAND

CANYON

LOWER 

MARBLE 

CANYON

UPPER 

MARBLE 

CANYON

LOWER 

GLEN CANYON

Figure 9. Comparison of suspended-sand concentration and grain size measured in the Lagrangian 

sampling programs during the 2004 and 2008 CFEs. Data collected in different parcels of water are 

indicated by different colors. Step changes between the data collected in the various parcels of water 

arise from reference-frame effects (see text for discussion). Error bars for the Lagrangian data are 

one standard error, indicating the 67-percent confidence interval associated with the mean values of 

these data among the three replicate single-vertical depth-integrated suspended-sediment samples 

collected at each sampling station. 

78
during these two CFEs, thus indicating similar longitudinal patterns of net sand erosion and 

deposition. However, the magnitudes of the differences between the peaks and troughs in 

suspended-sand concentration are much larger during the 2008 CFE than during the 2004 CFE, 

with much higher suspended-sand concentrations during the 2008 CFE. This indicates that, 

although the locations of net sand erosion and deposition were similar, the magnitudes of the net 

sand erosion or deposition in these locations were much larger during the 2008 CFE than during 

the 2004 CFE. Between about river miles 2 and 50, the longitudinal patterns in and the 

magnitudes of the suspended-sand median grain size were very different during the two CFEs. In 

general, the suspended sand was much coarser during the 2008 CFE than during the 2004 CFE 

over most of this reach, except between about river miles 40 and 50 where it was finer during the 

2008 CFE than during the 2004 CFE. Downstream from river mile 50, the suspended-sand 

median grain size was essentially identical during the two CFEs. It is informative to examine the 

data in figure 9, keeping in mind the previous reviews and analyses of the influences of reachaveraged τb, reach-averaged bed-sand median grain size, and reach-averaged bed-sand area on 

suspended-sand concentration and median grain size. Given that the likely maximum difference 

in reach-averaged τb at steady, high discharge between the two CFEs is only about 10 percent18

at any individual Lagrangian sampling station, the only realistic physical mechanism that ca

explain the larger suspended-sand concentrations associated with either equivalent or larger 

suspended-sand median grain size between the two CFEs is greater reach-averaged bed-sand area 

(that is, a larger amount of sand of equal or greater median grain size on the bed). Thus, during 

the 2008 CFE, much more sand had to be present on the bed than during the 2004 CFE between 

river miles 14 and 35 and between river mile 51 and at least 85. This observation will be 

explored further in more sophisticated physically based analyses later in this report. 

n 

 

β Analysis 

Physical suspension processes in a river provide a more representative "sample" of the 

average bed sedimentologic conditions upstream from a measurement cross-section than do bedsediment measurements made only at that single cross-section (Rubin and others, 2001). For 

typical flow conditions in the Colorado River in Marble and Grand Canyons, the spatial scale 

over which suspended sand equilibrates with the bed ranges from about 600 m to well over 1 km 

(Topping and others, 2007a). Therefore, an appropriate analysis of the suspended-sand data can 

yield information on changes in the reach-averaged grain size of the sand on the surface of the 

channel bed, banks, and eddy sandbars upstream from the suspended-sand measurement location 

in exactly the proportion these environments are "sampled" by the suspended sand. Rubin and 

Topping (2001, 2008) developed such a technique to analyze suspended-sediment data based on 

theory and tested this technique against data from flumes and rivers. Their parameter “β” is a 

nondimensional measure of the average bed-surface grain size that interacts with the suspended 

18 As previously discussed, a substantial change in sand-patch thickness over 20 percent of the bed in a 

kilometer-long reach would likely result in an approximate 10-percent difference in reach-averaged τb at constant 

water discharge. Although differences greater than 10 percent in reach-averaged τb at constant discharge may have 

occurred in certain individual reaches between the two CFEs, such greater differences would require substantial 

changes in sand-patch thickness over more of the bed than are suggested by available bathymetric and bed-textural 

data. Therefore, a 10-percent difference in reach-averaged τb at constant discharge is deemed the likely maximum 

for typical reaches. 

79
sand at a given flow condition. The parameter β was derived for beds composed of 100 percent 

sand, and uses the concentration and grain size of the sand in suspension to compute the spatially 

averaged upstream grain size of the sand on the bed. The definition of β is given as 

β = Db

Db−ref

, (15) 

where Db is the spatially averaged median grain size of the bed-surface sand at an instant in time 

and Db-ref is the reference median grain size of the sand on the bed surface. For broad and narrow 

log-normal bed-sand grain-size distributions and for cases with and without dunes on the bed, 

Rubin and Topping (2001, 2008) found that 

β

−

−

⎛ ⎞⎛

= ⎜ ⎟⎜

⎝ ⎠⎝

0.1

SAND s

ref s ref

C D

C D

⎞

⎟

⎟

⎠

, (16) 

where CSAND is the concentration of suspended sand observed during a single measurement, Cref

is the reference concentration of sand in suspension, Ds is the median grain size of suspended 

sand observed during a single measurement, and Ds-ref is the reference median grain size of sand 

in suspension. This result was computed using the suspended-sediment theory reviewed by 

McLean (1992). The reference concentration and median grain sizes in the denominators of 

equations 15 and 16 can be set equal to the average concentration and median grain sizes over 

any specified time interval. 

For the same reasons that a proper physically based analysis of the suspended sand can 

provide a more representative and physically meaningful sample of the reach-averaged bed-sand 

grain-size distribution in the reach upstream from a measurement cross-section, a similar analysis 

of the suspended sand could provide a more physically meaningful measure of the reachaveraged area of the sand on the bed that is interacting with the flow and in equilibrium with the 

suspended sand at the given measurement location. In addition, such an analysis could actually 

provide a better relative measure of the bed-sand area than any other approach. For example, 

side-scan sonar data have been used extensively to estimate bed-sand area in the Colorado River 

in lower Glen, Marble, and Grand Canyons (Anima and others, 1998; Schmidt and others, 2007). 

However, these data are complicated to work with because (1) they require highly sophisticated 

data collection, (2) identification of bed sand in the sonar data is highly interpretive, and it is 

difficult to distinguish flat sand beds from flat beds composed of fine gravel, and (3) it is 

impossible to identify sand interstitial to cobbles and boulders on the bed (this could be most of 

the sand in some reaches). Multibeam sonar data have also been extensively collected with a 

secondary goal of measuring bed-sand area (Kaplinski and others, 2009), but these data have the 

same associated problems as the side-scan-sonar data. Video transects have also been collected 

with the goal of identifying bed-sediment type (for example, Anima and others, 1998), and 

although these data involve the least interpretation, it is only possible to map small parts of the 

bed with the video-transect technique. Thus, as with the reach-averaged bed-sand grain-size 

distribution, it is perhaps best to let the physics of suspended-sand transport provide a 

measurement of the reach-averaged area of the sand on the bed. This new analysis builds strongly 

on the work of Rubin and Topping (2001) and extends their work for conditions of constant 

reach-averaged τb. 

The analysis described below is the simplest possible suspended-sediment analysis for 

detecting changes in reach-averaged bed-sand area and neglects several potentially important 

physical effects. Although this approach will not likely provide an absolute measurement of the 

reach-averaged bed-sand area, it at least provides a measure of reach-averaged bed-sand area that 

80
is coupled to the sand transport. As shown below, such an approach is possible for detecting 

differences in reach-averaged bed-sand area upstream from the same measurement cross-section 

between or over periods of constant reach-averaged τb. In addition, such an approach can also be 

used to detect differences in reach-averaged bed-sand area upstream from different measurement 

cross-sections between or over periods of similar water discharge as long as the reach-averaged 

τb at these different cross-sections is similar. Finally, this approach can be used to area-correct 

the computations made using equation 16 such that they take into account the influence of 

changes in bed-sand area on the β estimates of bed-sand median grain size. 

As stated previously, at constant reach-averaged τb, differences in the grain-size 

distribution of the sand in suspension at a given cross-section can only be explained by changes 

in the reach-averaged grain-size distribution of the sand on the bed upstream. Under conditions 

of constant reach-averaged τb, reach-averaged bed- and suspended-sand median grain size are 

positively correlated (equation 7), reach-averaged bed-sand median grain size and suspendedsand concentration are negatively correlated when reach-averaged bed-sand area is constant 

(equation 4), reach-averaged bed-sand area and suspended-sand concentration are positively 

correlated for constant reach-averaged bed-sand median grain size (equation 4), and reachaveraged bed-sand area and suspended-sand median grain size are uncorrelated (equation 7). 

Thus, under conditions of constant reach-averaged τb, the only mechanism that can explain a 

change in suspended-sand concentration without a change in suspended-sand median grain size is 

a change in reach-averaged bed-sand area. Because the influence of reach-averaged bed-sand 

area on suspended-sand concentration is typically much smaller than is the influence of reachaveraged bed-sand median grain size, the formulation of β in equation 16 provides a reasonably 

good estimate of reach-averaged bed-sand median grain size upstream from a measurement 

cross-section when changes in reach-averaged bed-sand area are either small or change 

systematically with water discharge or reach-averaged τb (as during rising limb of floods in the 

Colorado River in Marble and Grand Canyons). However, this formulation can result in 

substantial error in the estimates of reach-averaged bed-sand median grain size in situations 

where reach-averaged bed-sand area changes are larger than about a factor of 10. This is the case, 

when one uses equation 16 to compute β in a spatial sense to compare reach-averaged bed-sand 

median grain size over the entire length of the Colorado River in lower Glen, Marble, and Grand 

Canyons, a reach over which large changes occur in the upstream sand supply and, therefore, 

reach-averaged bed-sand area. 

Sensitivity of β in equation 16 to changes in reach-averaged bed-sand area at constant 

reach-averaged τb can be evaluated by holding both grain-size terms in equation 16 constant, 

holding the reference concentration term in the denominator constant, and by varying only the 

concentration term in the numerator to account for changes in reach-averaged bed-sand area 

relative to the initial reach-averaged bed-sand area associated with β = 1. This is justified based 

on the reasoning of Topping and others (2007a), who argued, on the basis of the flume 

experiments of Grams (2006) and Grams and Wilcock (2007), that the depth-averaged 

suspended-sand concentration scaled approximately linearly with changes in reach-averaged bedsand area such that, for the same flow and grain-size conditions, a reach-averaged bed-sand area 

of 50 percent would result in a depth-averaged suspended-sand concentration that is 

approximately 50 percent of the depth-averaged suspended-sand concentration associated with a 

reach-averaged bed-sand area of 100 percent. For example, if for a reach-averaged bed-sand area 

of 100 percent, the concentration term in the numerator of equation 16 were 1,000 mg/L, this 

concentration term would decrease to 750 mg/L for a reach-averaged bed-sand area of 75 

81
percent, 500 mg/L for a bed-sand area of reach-averaged bed-sand area of 50 percent, and 100 

mg/L for a reach-averaged bed-sand area of 10 percent. As discussed in detail in Topping and 

others (2007a) and above, this is perhaps an oversimplification of the problem, but it does 

provide insight into the effects of changes in reach-averaged bed-sand area on β. Results from 

this sensitivity analysis are shown in figure 10. As shown in figure 10, a factor of 2 change in 

reach-averaged bed-sand area at constant reach-averaged τb only results in a change in β of 7 

percent, as previously suggested by Rubin and Topping (2001). 

Relative differences in reach-averaged bed-sand area between two times or locations of 

constant reach-averaged τb can be computed by solving a modified version of equation 16, where 

the suspended-sand data collected over a specified time interval at only one time or location are 

used to compute the reference terms, Cref and Ds-ref, in the denominator. Hereafter, the term 

"reference condition" is used to define the specified time interval at the one time or location over 

 

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0.1 1 10

β

REACH-AVERAGED Ab NORMALIZED TO 

INITIAL REACH-AVERAGED Ab

 ASSOCIATED WITH β = 1

+7% CHANGE 

IN β

-7% CHANGE

IN β

Figure 10. Influence of changes in reach-averaged bed-sand area, Ab, on β. Horizontal solid line 

indicates initial value of β associated with initial reach-averaged Ab and a given reach-averaged 

bed-sand median grain size; vertical solid line indicates initial reach-averaged Ab normalized by 

itself. Blue band encompasses region within a factor of 2 change in reach-averaged Ab relative to 

this initial value. Red curve is computed by holding bed- and suspended-sand median grain size 

and reach-averaged τb constant and changing suspended-sand concentration by only changing 

reach-averaged Ab. Factor of 2 changes in reach-averaged Ab are associated with only ±7 percent 

changes in β, as indicated by the intersection of the red curve with the edges of the blue band. 

82
which these reference terms are computed. Based on the results from the sensitivity analysis in 

figure 10, a more-general form of equation 16 that incorporates effects of variable reachaveraged Ab is 

β β

−

− −

⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎛ ⎞ = = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠

0.1 0.1 0.1

b SAND sb

A

b ref ref s ref b ref

A C DA

A C DA −

, (17) 

where βA is the reach-averaged Db normalized by reach-averaged Db-ref for variable reachaveraged Ab. Using the same convention as in equation 16, Ab-ref is the reference reach-averaged 

Ab (averaged over the same time interval as Cref and Ds-ref). As with the original β-approach 

derived by Rubin and Topping (2001, 2008), which computes a reach-averaged bed-sand median 

grain size normalized by the reference reach-averaged bed-sand median grain size, this new βAapproach does not directly compute reach-averaged bed-sand area but can, for conditions of 

constant or near-constant reach-averaged τb, compute a reach-averaged bed-sand area normalized 

by the reference reach-averaged bed-sand area. Therefore, because reach-averaged bed-sand area 

is correlated with upstream sand supply, this approach can compute relative differences in the 

upstream sand supply during two time periods at the same location or between two different 

locations, but cannot compute the actual upstream sand supply. This new βA-approach does 

provide guidance, however, on (1) the accuracy of the previously presented sand budgets in 

estimating changes in the total upstream sand supply to the reaches (including changes in 

background sand storage) antecedent to the 2004 and 2008 CFEs and (2) the utility of using only 

the simple analyses in the previous sections of coupled changes in suspended-sand concentration 

and grain-size between different CFEs and between different reaches during the same CFE to 

infer relative differences in upstream sand supply. 

Solving equation 17 requires a reduction in the number of unknown quantities from 2 to 

1. As written, the unknown quantities in equation 17 are βA and the ratio 

−

⎛ ⎞ ⎜

⎜

⎝ ⎠

b

b ref

A

A ⎟

⎟. Because 

reach-averaged bed-sand area is treated independently of both reach-averaged bed-sand median 

grain size and suspended-sand median grain size, it is possible to solve equation 17 for the ratio 

−

⎛ ⎞ ⎜

⎜

⎝ ⎠

b

b ref

A

A ⎟

⎟ by setting βA = 1, replacing Ds with Ds-ref, and then modifying CSAND to account for the 

difference between Ds and Ds-ref. At constant reach-averaged τb, (Rubin and 

Topping, 2001). Therefore, the factor used to modify CSAND to account for the difference between 

Ds and Ds-ref can be written as 

CSAND ∝ Ds

−2

δ

−

− ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

2

s ref

s

D

D . (18) 

After making the appropriate substitutions and rearrangements, equation 17 becomes 

δ

−

⎛ ⎞⎛ ⎜ ⎟⎜ =

⎝ ⎠⎝

b SA

b ref ref

A C

A C

⎞

⎟

⎟

⎠

ND . (19) 

Again, as with β as a measure of reach-averaged bed-sand median grain size, this measure of 

bed-sand area is only appropriate in a reach-averaged sense over the kilometer-long reach scales 

over which suspended sand equilibrates with bed-sediment conditions in the Colorado River in 

83
84

the study area (Topping and others, 2007a). Unlike β, however, which can be applied for 

conditions of changing reach-averaged τb, this measure of bed-sand area requires constant or 

near-constant reach-averaged τb to result in reasonably accurate estimates of differences in reachaveraged bed-sand area. 

By virtue of the relative insensitivity of β to changes in reach-averaged bed-sand area 

(fig. 10), β computed using equation 16 can be used directly as an indicator of changes in reachaveraged bed-sand median grain size when changes in reach-averaged bed-sand area are less than 

about a factor of 2 (fig. 10). However, when greater changes in reach-averaged bed-sand area 

occur, substantial error can be introduced into β-estimated reach-averaged bed-sand median grain 

size. For example, when reach-averaged bed-sand area decreases by a factor of 5 at a constant 

reach-averaged bed-sand median grain size, β computed by equation 16 will be 17 percent too 

high, and when reach-averaged bed-sand area increases by a factor of 5 at a constant reachaveraged bed-sand median grain size, β computed by equation 16 will be 15 percent too low. 

This effect can be corrected for by using equation 17 to solve for βA, when reach-averaged τb can 

be assumed to be constant to within about 10 or 20 percent. 

Values of β at Each Study Site During All CFEs 

Values of β computed using standard β analysis (conducted using equation 16) of the 

suspended-sand data collected at each study site during all three CFEs are shown in figure 11. At 

each study site, the reference condition was set equal to days -2 through 5 of the 2008 CFE (that is, 

the 7-day period from 2 days before the beginning of high, steady discharge to 5 days after the 

beginning of high, steady discharge during the 2008 CFE). This data-collection period 

encompassed the entire flood hydrograph for the 2004 and 2008 CFEs. Because data were only 

collected at every study site during the 2008 CFE and were collected with the most consistent 

methods during the 2008 CFE, this approach allowed better direct comparison of β values between 

the different CFEs. Only the best (that is, lowest error) physical measurements of suspended-sand 

concentration and grain size were used in this analysis, that is, only data collected using the EDI, 

EWI, or point-sampling methods. 

 The tendency at each site is for β to decrease during the rising limb of each CFE and then 

subsequently increase, continuing to increase even after recession of each CFE. Because changes in 

reach-averaged bed-sand median grain size dominate over changes in reach-averaged bed-sand 

area on influencing β, these changes in β most likely arise from fining of the bed and then 

subsequent coarsening of the bed upstream from the measurement cross-sections. These same 

patterns were typically observed in the bed-sediment data collected at only the measurement crosssections (figs. 4 and 5). The amount of bed fining during the rising limbs varies from site to 

Figure 11 (next page). Values of β at each study site during all CFEs. At each study site, data were 

shifted in time such that zero time is the beginning of high, steady discharge during each CFE. 

Except at the River-mile 30 study site, β was as fine or finer during the 2008 CFE than during the 

other two CFEs. β generally fined during the rising limb of each CFE and then subsequently 

coarsened. Solid green vertical lines indicate the beginning and end of high, steady discharge at each 

study site during the 2008 CFE. Dashed green vertical lines indicate the beginning of the rising limb 

and end of the recession at each study site during the 2008 CFE. Solid pink vertical lines indicate the 

end of high, steady discharge at each study site during the 1996 CFE. Beginning of high, steady 

discharge during the 1996 CFE indicated at each study site by the leftmost solid vertical green line.
0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1996 EDI 

2004 EDI 

2008 EDI

β

RIVER-MILE 0

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2004 EWI 

2008 EWI 

β

RIVER-MILE 30

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1996 EDI 

2004 EWI 

2008 EWI 

β

RIVER-MILE 61

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1996 EDI, POINT

2004 EDI

2008 EDI

β

RIVER-MILE 87

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1996 POINT 

2008 EWI

β

RIVER-MILE 166

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2004 EDI 

2008 EDI

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8

β

RIVER-MILE 225

DAYS AFTER BEGINNING OF HIGH, STEADY DISCHARGE

85
site during each CFE, but the bed coarsening follows similar patterns at each study site during at 

least the 2004 and 2008 CFEs. Bed coarsening during the 1996 CFE likely follows different 

patterns from those during the 2004 and 2008 CFEs at some sites because of the much longer 

duration of the 1996 CFE. 

Values of β were generally smaller during the 2008 CFE than during the 1996 and 

2004 CFEs downstream from upper Marble Canyon. From the River-mile 61 study site 

through the River-mile 225 study sites, β was smaller during the 2008 CFE at each study 

site than during the 1996 and 2004 CFEs. At the River-mile 0 study site, β was 

approximately equal during the 1996 and 2008 CFEs, but smaller during both of these 

CFEs than during the 2004 CFE. At the River-mile 30 study site, β was smaller during the 

2004 CFE than during the 2008 CFE. These relative differences in β between the CFEs at 

each study site only disagree with relative differences in bed-sediment data between the 

CFEs at the River-mile 30 study site. Thus, as already discussed, the response of the bedsand median grain size at the measurement cross-section at the River-mile 30 study site 

was likely not representative of that in the kilometer-long reach upstream. Except at the 

River-mile 0 study site, β during the 1996 CFE tended to be larger than during the 2004 

and 2008 CFEs at all other sites where data were collected in 1996. 

Because reach-averaged bed-sand median grain size dominates over reach-averaged bedsand area in influencing β, these analyses indicate that, with the exception of at the River-mile 30 

study site, substantial parts of the bed upstream from the measurement cross-sections were finest 

during the 2008 CFE and were coarsest during the 1996 CFE. These results do not necessarily 

track with the known levels of enrichment in the upstream sand supply computed from sand 

budgeting nor do they necessarily agree with inferred levels of enrichment in the upstream sand 

supply estimated from the simple coupled analyses of suspended-sand concentration and grain size 

in the previous sections of this report. For example, both the sand budgeting and the simple 

coupled analyses of suspended-sand concentration and grain size suggest that upper Marble 

Canyon was more enriched with respect to sand before the 2008 CFE than it was before the 2004 

CFE. Results from the β analysis, in contrast, indicate that, at least upstream from the River-mile 

30 study site, the reach-averaged median grain size of the bed sand in this reach was consistently 

finer during the 2004 CFE than it was during the 2008 CFE. This will be addressed further below 

in β analysis of the data from the Lagrangian sampling programs. As shown in the "Theoretical 

Background" section of this report, reach-averaged bed-sand median grain size and upstream sand 

supply may be typically negatively correlated, but this relation is not required. This is pursued 

further in the next few analyses. 

Estimation of Differences in Reach-Averaged Bed-Sand Area in the Reaches Upstream 

from Each Study Site During Each CFE and Between CFEs 

To compute the relative differences in reach-averaged bed-sand area in the reaches 

upstream from each study site, the EDI, EWI, and point-sample data collected at each site were 

reanalyzed using the approach outlined in equations 17 through 19. To proceed with this analysis, 

reach-averaged τb was assumed to be constant among the various study sites. Although this 

assumption may not be valid at low discharges, it is likely valid in the discharge range from 42,000 

to 45,000 ft3

/s on the basis of the analysis of pre-dam suspended-sand data collected at the Rivermile 0 and 87 study sites (the two of the six study sites that are most different from each other) in 

Topping and others (2000a). This analysis will allow better relations to be developed between 

86
upstream sand supply, reach-averaged bed-sand median grain size, reach-averaged bed-sand area, 

and suspended-sand concentration during CFEs. Because of the complexities outlined in the 

"Theoretical Background" section of this report in regard to (1) the different relations between 

upstream sand supply and reach-averaged bed-sand area at very different discharges of water and 

(2) the transient effects of sand redistribution on the bed on reach-averaged bed-sand area 

following large changes in discharge, back-calculated changes in reach-averaged bed-sand area 

could only be computed using suspended-sand data collected during the first day of a CFE at 

similar discharge (that is, the only data that could be analyzed were those collected at the same 

relative time after a large discharge change has occurred during a CFE). This approach avoided 

effects that could result in apparent negative correlations between upstream sand supply and bedsand area. To proceed with this analysis, suspended-sand concentrations and median grain sizes 

were first averaged over the first day of high, steady discharge at each study site during each CFE. 

For these analyses, the reference condition was set equal to the first day of high, steady discharge 

at the River-mile 87 study site during the 2008 CFE, with Cref set equal to 2,740 mg/L and Ds-ref set 

equal to 0.125 mm in equations 18 and 19. The ratio 

−

⎛ ⎞ ⎜

⎜

⎝ ⎠

b

b ref

A

A ⎟

⎟

 was then computed at each study site 

using the "first-day" averaged suspended-sediment concentrations and median grain size and these 

values of Cref and Ds-ref. By this approach, the ratio 

−

⎛ ⎞ ⎜ ⎟ = ⎜ ⎟ ⎝ ⎠

1 b

b ref

A

A for the River-mile 87 study site 

during the first day of high, steady discharge during the 2008 CFE, and Αb-ref became the reachaveraged bed-sand area in the kilometer-long reach upstream from the River-mile 87 study site 

during the first day of high, steady discharge during the 2008 CFE. This allowed direct comparison 

between the reach-averaged bed-sand areas computed for all reaches upstream from each study site 

during any one CFE and between all CFEs. 

By this analysis, reach-averaged bed-sand area during the 2008 CFE increased between the 

River-mile 0 and 30 study sites, then decreased slightly between the River-mile 30 and 61 study 

sites, and then increased to its maximum value at the River-mile 87 study site. Downstream from 

the River-mile 87 study site, reach-averaged bed-sand area gradually decreased to be slightly less 

at the River-mile 225 study site than it was at the River-mile 30 study site (fig. 12). Thus, the 

reaches with likely greatest upstream sand supply during the 2008 CFE were eastern and eastcentral Grand Canyon. During the 2004 CFE, reach-averaged bed-sand area increased more 

gradually between the River-mile 0 and 87 study sites than during the 2008 CFE and then remained 

essentially constant between the River-mile 87 and 225 study sites. The greatest increase in reachaveraged bed-sand area during both the 2004 and 2008 CFEs occurred between the River-mile 0 

and 30 study sites in upper Marble Canyon, although this increase was much less during the 2004 

CFE than during the 2008 CFE. This is consistent with the previously presented mass-balance 

sand-budgeting results that showed that upper Marble Canyon had the greatest enrichment in the 

upstream sand supply during the sand-budgeting accounting periods antecedent to both the 2004 

and 2008 CFEs. During the 1996 CFE, reach-averaged bed-sand area increased between the Rivermile 0 and 87 study sites, and then decreased between the River-mile 87 and 166 study sites. As in 

the 2004 and 2008 CFEs, the greatest increase in reach-averaged bed-sand area during the 1996 

CFE occurred in Marble Canyon. However, in contrast to the 2004 and 2008 CFEs, the increase in 

reach-averaged bed-sand area in eastern Grand Canyon (between the River-mile 61 and 87 study 

sites) was as large as that within Marble Canyon. This large increase in reach-averaged bed-sand 

87
0.0

0.5

1.0

1.5

2.0

0 50 100 150 200 250

1996 

2004 

2008 

Ab / Ab-rel

RIVER MILE

UPPER MARBLE 

CANYON

LOWER GLEN CANYON

LOWER MARBLE 

CANYON

EASTERN

GRAND

CANYON

EAST-CENTRAL

GRAND

CANYON

WEST-CENTRAL

GRAND

CANYON

WESTERN

GRAND CANYON

0

10

20

30

40

Ab , IN PERCENT

Figure 12. β-based computation of reach-averaged bed-sand area in the kilometer-long reaches 

upstream from each study site during each CFE. Study reaches are indicated, separated by vertical 

dashed lines. 

area in eastern Grand Canyon could have been the legacy of the coarse tail of the extremely large 

inputs of sand that occurred from the Little Colorado River during January-March 1993 (Wiele and 

others, 1996; Topping and others, 2000b). Although much of these sand inputs from the Little 

Colorado River were likely exported downstream from this reach before the 1996 CFE because of 

the relatively large dam releases between the 1993 and the 1996 CFE, it is likely that part of the 

coarse tail of these extremely large sand inputs was still in eastern Grand Canyon during the 1996 

CFE (Topping and others, 2000b). 

Throughout lower Glen, Marble, and Grand Canyons, reach-averaged bed-sand area was 

likely greater during the 2008 CFE than it was during the 2004 CFE (fig. 12). However, in only 

lower Glen Canyon was reach-averaged bed-sand area likely greater during the 2008 CFE than it 

was during the 1996 CFE. Reach-averaged bed sand area was likely about equal during the 1996 

and 2008 CFEs in lower Marble Canyon (upstream from the River-mile 61 study site) and reachaveraged bed-sand area was likely greater during the 1996 CFE than it was during the 2008 CFE in 

much of Grand Canyon (upstream from the River-mile 87 and 166 study sites). Reach-averaged 

bed-sand area during the 2004 CFE was likely less than that during the 2008 CFE in all reaches 

and it was likely less than that during the 1996 CFE in all reaches except lower Glen Canyon. 

Because no suspended-sand data were collected at the River-mile 30 study site during the 1996 

CFE, it is impossible to compare reach-averaged bed-sand area in upper Marble Canyon between 

the 1996 CFE and the 2004 and 2008 CFEs. Among the three CFEs, the minimum and maximum 

values of reach-averaged bed-sand area both likely occurred during the 1996 CFE, with the 

minimum value occurring in lower Glen Canyon (upstream from the River-mile 0 study site) and 

the maximum value occurring in eastern Grand Canyon (upstream from the River-mile 87 study 

site). 

88
Combination of the results from this analysis with modeling results from Topping and 

others (2007a) allows conversion of the relative values of reach-averaged bed-sand area, 

−

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

b

b ref

A

A , 

to approximate fractional values of reach-averaged bed-sand area, Ab (fig. 12). Using a more 

sophisticated physically based suspended-sediment model than the simple β-based analysis in this 

section of this report, Topping and others (2007a) computed that the reach-averaged bed-sand area 

in the kilometer-long reach upstream from the River-mile 87 study site during day 1 of high, steady 

discharge during the 1996 CFE was approximately 25 percent, and during day 1 of high, steady 

discharge during the 2004 CFE it was approximately 18 percent. The difference between these two 

numbers is a factor of 1.4. For comparison, by the simple β-based analysis in this report, the 

difference in reach-averaged bed-sand area at the River-mile 87 study site between days 1 of the 

1996 and 2004 CFEs is only somewhat larger at a factor of 1.8. Because these differences are 

similar (1.8 is only 29 percent larger than 1.4) whereas the approaches used to arrive at these 

differences are very different in complexity (yet still physically based), this result lends further 

support to the utility of using simple β-based analysis to estimate relative differences in reachaveraged bed-sand area. Best-fit between the two approaches was achieved by setting Ab-ref(the 

reach-averaged fractional bed-sand area during the reference condition) equal to 20 percent. When 

making conclusions based on values of Ab computed by this approach, it is important to remember 

that these values of Ab are not unweighted, linear geometric spatial averages, but rather are 

estimates of the fractional bed-sand area in a reach weighted by how the suspended sediment 

interacts with (that is, "samples") the bed sand over kilometer-long reaches at assumed constant 

reach-averaged τb. Therefore, these values of Ab are perhaps best used, not as an exact measure of 

the percentage of sand on the bed in a reach, but rather in a relative sense in evaluations of (1) how 

the relative amount of sand on the bed changes longitudinally over long reaches or (2) how the 

relative amount of sand on the bed in a reach differs between CFEs. 

Values of β at All Study Sites During Each CFE 

To compute the relative differences in reach-averaged bed-sand median grain size in the 

reaches upstream from each study site, the EDI, EWI, and point-sample data collected at each site 

during day 1 of high, steady discharge were analyzed using both a standard β analysis as described 

by equation 16 and a “sand-area-corrected” βA analysis as described by equation 17 using the 

values of 

−

⎛ ⎞ ⎜

⎜

⎝ ⎠

b

b ref

A

A ⎟

⎟

 computed in the previous analysis and presented in figure 12. To proceed with 

this analysis, as in the previous analysis, suspended-sand concentrations and suspended-sand 

median grain sizes were first averaged over the first day of high, steady discharge at each study site 

during each CFE. For this analysis, as in the previous analysis, the reference condition was set 

equal to the first day of high, steady discharge at the River-mile 87 study site during the 2008 CFE. 

β and βA values were then computed using the "first-day" averaged suspended-sediment 

concentrations and median grain size, and these reference-condition values of Cref and Ds-ref. By 

this approach, both β = βA = 1 for the River-mile 87 study site during the first day of high, steady 

discharge during the 2008 CFE. This allowed direct comparison of reach-averaged bed-sand 

median grain size in all reaches upstream from each study site during any one CFE and between all 

CFEs. Results from this analysis with comparisons with the mean bed-sand median grain sizes 

89
measured at the measurement cross-sections at each site during day 1 of high, steady discharge 

during each CFE are shown in figure 13. These comparisons indicate general good agreement at 

the 95-percent confidence interval between βA and the mean bed-sand median grain sizes 

measured at the cross-sections at all study sites during all CFEs when the reference reach-averaged 

median grain size of the bed-sand, Db-ref, is set equal to a reach-averaged bed-sand median grain 

size of 0.32 mm. 

This analysis indicates that the greatest enrichment of the upstream sand supply in a reach 

antecedent to a CFE is not uniquely related to reach-averaged bed-sand median grain size and can 

be associated with either the finest or coarsest bed sand in any reach during that CFE. During the 

2008 CFE, reach-averaged bed-sand median grain size increased slightly between the River-mile 0 

and 30 study sites, then generally decreased in the downstream direction between the River-mile 30 

and 166 study sites, and then increased slightly between the River-mile 166 and 225 study sites 

(fig. 13A). Thus, during the 2008 CFE, the finest reach-averaged bed sand was present in east- and 

west-central Grand Canyon, and the coarsest reach-averaged bed sand was present in upper Marble 

Canyon. Note that upper Marble Canyon was the reach with the greatest sand enrichment during 

the mass-balance sand-budgeting accounting period antecedent to the 2008. Thus, during the 2008 

CFE, the greatest enrichment in the upstream sand supply was associated with the reach with the 

coarsest reach-averaged bed sand. During the 2004 CFE, reach-averaged bed-sand median grain 

size decreased in the downstream direction between the River-mile 0 and 30 study sites, then 

increased slightly between the River-mile 30 and 61 study sites, and then remained essentially 

constant between the River-mile 61 and 225 study sites (fig. 13B). Thus, during the 2004 CFE, the 

finest reach-averaged bed sand was present in upper Marble Canyon, with coarser and similar 

reach-averaged bed sand present everywhere else. Note that, as during the 2008 CFE, upper Marble 

Canyon was also the reach with the greatest sand enrichment during the mass-balance sandbudgeting accounting period antecedent to the 2004. Thus, during the 2004 CFE, the greatest 

enrichment in the upstream sand supply was associated with the reach with the finest reachaveraged bed sand. During the 1996 CFE, reach-averaged bed-sand median grain size increased 

between the River-mile 0 and 61 study sites, increased slightly between the River-mile 61 and 87 

study sites, and then decreased between the River-mile 87 and 166 study sites (fig. 13C). Thus, 

during the 1996 CFE, the finest reach-averaged bed sand was present in lower Glen Canyon and 

east-central Grand Canyon, and the coarsest reach-averaged bed sand was present in eastern Grand 

Canyon. 

Reach-averaged bed-sand median grain size was typically finest during the 2008 CFE and 

typically coarsest during the 1996 CFE (fig. 13D). Reach-averaged bed sand was likely coarser at 

the River-mile 61 and 87 study sites during the 1996 CFE than it was at any other site during the 

1996 CFE, and coarser than it was at any site during the 2004 and 2008 CFEs. Except at the Rivermile 0 and 30 study sites, reach-averaged bed-sand median grain size was finest at all study sites 

Figure 13 (next page). Results from β and βA analyses of reach-averaged bed-sand median grain 

size in the kilometer-long reaches upstream from each study site during all CFEs. β = βA = 1 is 

equivalent to reach-averaged bed-sand D50 = 0.32 mm at all study sites during all CFEs. Error bars 

indicate the 95-percent confidence interval in the mean median grain size of the bed sand measured 

at the measurement cross-section at each study site on day 1 of high, steady discharge during each 

CFE. Study reaches are indicated, separated by vertical dashed lines. Comparison of β, βA , and 

bed-sand D50 (A) during the 2008 CFE, (B) during the 2004 CFE, and (C) during the 1996 CFE. D, 

Comparison of βA or bed-sand D50 at each study site during all CFEs. 

90
A

0.5

1.0

1.5

2.0

0.16

0.20

0.24

0.28

0.32

0.36

0.40

0.44

0.48

0.52

0.56

0.60

0.64

0 50 100 150 200 250 ββ AD50

β OR β A

BED-SAND D

50, IN MILLIMETERS

RIVER MILE

2008

WEST-CENTRAL

GRAND

CANYON

WESTERN

GRAND CANYON

EAST-CENTRAL

GRAND

CANYON

EASTERN

GRAND

CANYON

LOWER

MARBLE 

CANYON

UPPER

MARBLE 

CANYON

LOWER GLEN CANYON

B

0.5

1.0

1.5

2.0

0.16

0.20

0.24

0.28

0.32

0.36

0.40

0.44

0.48

0.52

0.56

0.60

0.64

0 50 100 150 200 250 ββ ΑD50

β OR β A

BED-SAND D

50, IN MILLIMETERS

RIVER MILE

2004

WEST-CENTRAL

GRAND

CANYON

WESTERN

GRAND CANYON

EAST-CENTRAL

GRAND

CANYON

EASTERN

GRAND

CANYON

LOWER

MARBLE 

CANYON

UPPER

MARBLE 

CANYON

LOWER GLEN CANYON

C

0.5

1.0

1.5

2.0

0.16

0.20

0.24

0.28

0.32

0.36

0.40

0.44

0.48

0.52

0.56

0.60

0.64

0 50 100 150 200 250 ββ ΑD50

β OR β A

BED-SAND D

50, IN MILLIMETERS

RIVER MILE

1996

WEST-CENTRAL

GRAND

CANYON

WESTERN

GRAND CANYON

EAST-CENTRAL

GRAND

CANYON

EASTERN

GRAND

CANYON

LOWER

MARBLE 

CANYON

UPPER

MARBLE 

CANYON

LOWER GLEN CANYON

91
D

 

0.5

1.0

1.5

2.0

0.16

0.20

0.24

0.28

0.32

0.36

0.40

0.44

0.48

0.52

0.56

0.60

0.64

0 50 100 150 200 250

1996

2004 

2008 

β A

BED-SAND D

50, IN MILLIMETERS

RIVER MILE

WEST-CENTRAL

GRAND

CANYON

WESTERN

GRAND CANYON

EAST-CENTRAL

GRAND

CANYON

EASTERN

GRAND

CANYON

LOWER

MARBLE 

CANYON

UPPER

MARBLE 

CANYON

LOWER GLEN CANYON

Figure 13. — Continued.

during the 2008 CFE; and, except at the River-mile 0 study site, the reach-averaged bed-sand 

median grain size was coarsest at all study sites during the 1996 CFE. Among all study sites during 

all three CFEs, reach-averaged bed-sand median grain size was finest at the River-mile 30 study 

site during the 2004 CFE and coarsest at the River-mile 87 study site during the 1996 CFE. Except 

in upper Marble Canyon, reach-averaged bed-sand median grain size was generally intermediate 

during the 2004 CFE relative to during the 1996 and 2008 CFEs. At the River-mile 0 study site, 

reach-averaged bed-sand median grain size was coarsest during the 2008 CFE and finest during the 

1996 CFE. Because monitoring data indicate that greater enrichment of the upstream sand supply 

in lower Glen Canyon occurred before the 2008 CFE than before the 2004 CFE, and the reachaveraged bed-sand median grain size at the River-mile 0 study site was coarser during the 2008 

CFE than during the 2004 CFE, lower Glen Canyon during the 2004 and 2008 CFEs is another 

example of how coarser reach-averaged bed sand can be associated with a greater upstream sand 

supply. 

β Analysis of Data Collected During the Lagrangian Sampling Programs, with Estimation of 

Relative Differences in Reach-Averaged Bed-Sand Area Between the 2004 and 2008 CFEs 

To provide a more complete estimate of the longitudinal distribution of bed-sand median 

grain size and bed-sand area during the 2004 and 2008 CFEs, the data collected in the Lagrangian 

sampling programs were analyzed using both standard β analyses and “sand-area-corrected” βA

analyses. To be consistent with the previous analyses, the reference condition was set equal to the 

first day of high, steady discharge at the River-mile 87 study site during the 2008 CFE, with Cref set 

equal to 2,740 mg/L, Ds-ref set equal to 0.125 mm, and Ab-ref set equal to 0.2 in equations 17 through 

19. This also allowed ultimate conversion of βA to the reach-averaged D50 of the bed sand by 

multiplying βA by 0.32 mm (the best-fit D50 value for Db-ref determined by the previous analysis). 

As in the previous analyses, constant (or, at least, near-constant) reach-averaged τb is assumed at 

92
constant water discharge among the different sampling stations to allow computation of 

−

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

b

b ref

A

A , 

Ab, and βA. Because discharge was constant among all of these sampled stations, and the variability 

in flow depth and depth-averaged velocity at and among these sampled stations was reasonably 

small, reach-averaged values of τb at the same sampling station during the 2004 and 2008 CFEs and 

among the various sampled stations during each CFE were deemed similar enough to proceed with 

this analysis. 

Results from this analysis indicate that, except in parts of uppermost Marble Canyon and a 

short section of lower Marble Canyon, reach-averaged bed-sand area was considerably greater 

throughout Marble Canyon and all of eastern Grand Canyon during day 1 of the 2008 CFE than it 

was during day 1 of the 2004 CFE (fig. 14). The results from this analysis also generally agree with 

the values of reach-averaged bed-sand area computed in the prior analysis at only the study sites, 

but also illustrate that the longitudinal variability in reach-averaged bed-sand area is likely much 

greater than is captured by the analysis of reach-averaged bed-sand area at only the study sites. The 

longitudinal density of information on reach-averaged bed-sand area is, of course, much greater in 

the analyses of the Lagrangian data than in the analyses of only the data from the study sites. 

During the day 1 of the 2008 CFE, reach-averaged bed-sand area likely increased substantially in 

the downstream direction from only a few percent at river mile 0 to its highest value of 

approximately 29 percent at river mile 17. With the exception of between river miles 40 and 47, 

where a local minimum occurred in computed reach-averaged bed-sand area, during the 2008 CFE 

reach-averaged bed-sand area likely generally increased downstream from river mile 17 to about 

river mile 93, where it attained its second highest value of about 26 percent. It then decreased, 

0.0

0.5

1.0

1.5

2.0

0 50 100 150 200 250

2004 LAGRANGIAN 

2008 LAGRANGIAN

2004 STUDY SITES 

2008 STUDY SITES

Ab / Ab-rel

RIVER MILE

UPPER

MARBLE 

CANYON

LOWER GLEN CANYON

LOWER

MARBLE 

CANYON

EASTERN

GRAND

CANYON

EAST-CENTRAL

GRAND

CANYON

WEST-CENTRAL

GRAND

CANYON

WESTERN

GRAND CANYON

Ab , IN PERCENT

0

40

30

20

10

Figure 14. β-based computation of reach-averaged bed-sand area calculated using the suspendedsand data from the 2004 and 2008 Lagrangian sampling programs. Values of reach-averaged bedsand area from figure 12 computed using the data from the study sites shown for comparison. Study 

reaches are indicated, separated by vertical dashed lines. 

93
with large longitudinal variability, to about 12 to 16 percent at river mile 225. Again, as discussed 

in the previous analysis of reach-averaged bed-sand area at the study sites, it is important to 

remember that these computed values of Ab are not unweighted, linear geometric spatial averages, 

but rather are estimates of the fractional bed-sand area in a reach weighted by how the suspended 

sediment physically samples the bed sand over kilometer-long reaches at assumed constant reachaveraged τb. 

Computations of reach-averaged bed-sand area during the 2004 CFE are more limited 

because the Lagrangian sampling program did not extend downstream from river mile 85. During 

day 1 of the 2004 CFE, reach-averaged bed-sand area likely increased in the downstream direction 

from river mile 0, as during the 2008 CFE, but attained a value of only about 10 percent at river 

mile 2. Reach-averaged bed-sand area then remained essentially constant during the 2004 CFE 

until river mile 39, where it began to decrease to a low of about 6 percent near river mile 50. It then 

began to gradually increase, reaching a high value of about 15 percent at the River-mile 87 study 

site. Because no suspended-sand data were collected between the River-mile 87 and 225study sites 

during the 2004 CFE, it is impossible to compute reach-averaged bed-sand area between these 

study sites with any certainty during the 2004 CFE. However, because the computed reachaveraged bed-sand area at the River-mile 225 study site during the 2004 CFE is also only 15 

percent, and very little sand was supplied by tributaries to the reach between the River-mile 87 and 

225 study sites during the sand-budgeting accounting period antecedent to the 2004 CFE, it is 

unlikely that reach-averaged bed-sand area was greater than about 15 percent in east- and westcentral Grand Canyon during the 2004 CFE. The computations of reach-averaged bed-sand areas in 

figure 13B combined with the relatively large magnitude of the tributary sand inputs during the 

sand-budgeting accounting period antecedent to the 2008 CFE suggests that, given the present 

tributary sand supply and dam releases in the Colorado River downstream from Glen Canyon Dam, 

reach-averaged bed-sand area over long reaches probably does not typically exceed about 30 

percent, even under highly sand-enriched conditions. This result is also consistent with the results 

in Topping and others (2007a) that show that only under pre-dam sand supply and discharge 

conditions were values of reach-averaged bed-sand area likely to greatly exceed 30 percent, during 

the annual period of sand accumulation in Marble and Grand Canyons under the lower discharges 

that preceded the rising limb of the annual snowmelt flood (Topping and others, 2000a). 

As in the β-based analysis of data at the study sites, the agreement between β and D50 is 

improved when β is corrected for bed-sand-area effects (fig. 15). Interestingly, βA computed using 

the Lagrangian data agrees better with the bed-sand D50 at the study-site measurement crosssections than does βA computed using the study-site data. This analysis indicates that during day 1 

of the 2008 CFE, reach-averaged median grain size of the bed sand likely coarsened in the 

downstream direction from about 0.32 mm at river mile 0 to about 0.52 mm at river mile 2.5. With 

some downstream longitudinal variation (with a pronounced local minimum near river mile 8), the 

reach-averaged median grain size of the bed sand likely then fined to about 0.25 mm near river 

mile 42. Downstream from this location, the reach-averaged median grain size of the bed-sand 

likely coarsened slightly to about 0.35 mm near river miles 87 to 93. It then fined abruptly (the first 

of two pronounced downward steps in grain size), reaching a value of about 0.30 mm near river 

mile 98 before coarsening slightly to about 0.33 mm near river miles 140 to 150. A second abrupt 

decrease in grain size occurred between river miles 150 and 157. Downstream from river mile 157, 

the reach-averaged median grain size of the bed sand remained approximately constant, varying 

only between about 0.29 and 0.32 mm. It is important to note that these downward steps in 

94
A

0.5

1.0

1.5

2.0

0.16

0.20

0.24

0.28

0.32

0.36

0.40

0.44

0.48

0.52

0.56

0.60

0.64

0 50 100 150 200 250

LAGRANGIAN β

LAGRANGIAN β A

STUDY-SITE β A

D

50

 AT STUDY SITES

β OR 

β A

BED-SAND D

50, IN MILLIMETERS

RIVER MILE

2008

WEST-CENTRAL

GRAND

CANYON

WESTERN

GRAND CANYON

EAST-CENTRAL

GRAND

CANYON

EASTERN

GRAND

CANYON

LOWER MARBLE 

CANYON

UPPER

MARBLE 

CANYON

LOWER GLEN CANYON

B

0.5

1.0

1.5

2.0

0.16

0.20

0.24

0.28

0.32

0.36

0.40

0.44

0.48

0.52

0.56

0.60

0.64

0 50 100 150 200 250

LAGRANGIAN β

LAGRANGIAN β A

STUDY-SITE β A

D

50

 AT STUDY SITES

β OR 

β A

BED-SAND D

50, IN MILLIMETERS

RIVER MILE

2004

WEST-CENTRAL

GRAND

CANYON

WESTERN

GRAND CANYON

EAST-CENTRAL

GRAND

CANYON

EASTERN

GRAND

CANYON

LOWER MARBLE 

CANYON

UPPER

MARBLE 

CANYON

LOWER GLEN CANYON

Figure 15. Results from β and βA analyses of reach-averaged bed-sand median grain size using the 

suspended-sand data from the 2004 and 2008 Lagrangian sampling programs. Values of β and βA

computed using the data from the study sites, and bed-sand D50 measured at the study sites from 

figure 13 shown for comparison. As in figure 13, βA = 1 is equivalent to reach-averaged bed-sand 

D50 = 0.32 mm. Error bars indicate the 95-percent confidence interval in the mean median grain size 

of the bed sand measured at the measurement cross-section at each study site on day 1 of high, 

steady discharge during each CFE. Study reaches are indicated, separated by vertical dashed lines. 

Comparison of β, βA , and bed-sand D50 (A) during the 2008 CFE and (B) during the 2004 CFE. 

95
computed bed-sand median grain size do not coincide with the sampling breaks between the 

different parcels of water sampled during the 2008 CFE. The downstream longitudinal pattern in 

reach-averaged bed-sand median grain size was quite different during day 1 of the 2004 CFE. 

During the 2004 CFE, as during the 2008 CFE, reach-averaged bed-sand median grain size 

coarsened abruptly from about 0.32 mm at river mile 0 to about 0.53 mm near river mile 1.5. In 

contrast to the 2008 CFE, however, reach-averaged bed-sand median grain size during the 2004 

CFE fined substantially and quickly downstream from river mile 1.5, reaching the minimum value 

of about 0.27 mm between river miles 5 and 10. During the 2004 CFE, reach-averaged bed-sand 

median grain size then likely coarsened at an almost constant rate between river miles 10 and 87, 

reaching a value of about 0.35 mm at the River-mile 87 study site. 

Substantial differences in computed reach-averaged bed-sand area and bed-sand median 

grain size are evident within lower Glen, Marble, and eastern Grand Canyons between the 2004 

and 2008 CFEs (fig. 16). Except at only 3 of the Lagrangian sampling stations common to both the 

2004 and 2008 CFEs, there was likely considerably more sand present on the bed during the 

2008CFE than during the 2004 CFE. Computed reach-averaged bed-sand area during the 2008 CFE 

was about a factor of 3 greater than during the 2004 CFE at river mile 0 at the downstream 

terminus of lower Glen Canyon. Near river mile 17, there was likely also a factor of 3 more sand 

on the bed during the 2008 CFE than during the 2004 CFE. Between river miles 23 and 85, there 

was likely on average about 50 percent more sand on the bed during the 2008 CFE than during the 

2004 CFE. Between river miles 2 and 36, the reach-averaged bed-sand median grain size was 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

-10 0 10 20 30 40 50 60 70 80 90

BED-SAND D

50

 RATIO

BED-SAND AREA RATIO 

SUSPENDED-SAND 

CONCENTRATION RATIO 

RATIO OF 2008 TO 2004 

SAND CONDITIONS

RIVER MILE

UPPER MARBLE 

CANYON

LOWER GLEN CANYON

LOWER MARBLE 

CANYON

EASTERN

GRAND CANYON

Figure 16. Ratio of 2008 CFE to 2004 CFE sand conditions from lower Glen Canyon through 

eastern Grand Canyon computed using the suspended-sand data collected at sampling stations 

common to both the 2004 and 2008 Lagrangian sampling programs. Horizontal green line indicates a 

ratio of one, that is, the line of zero change in sand conditions between the two CFEs. Shown are the 

ratios for reach-averaged bed-sand median grain size, reach-averaged bed-sand area, and suspendedsand concentration. Values plotting above the green line are greater during the 2008 CFE than during 

the 2004 CFE, whereas values plotting below the green line are greater during the 2004 CFE than 

during the 2008 CFE. 

96
generally finer during the 2004 CFE than it was during the 2008 CFE, whereas between about river 

miles 39 and 80, the reach-averaged bed-sand median grain size was approximately equal during 

the 2004 and 2008 CFEs. At the downstream terminus of lower Glen Canyon at river mile 0, reachaveraged bed-sand median grain size was likely also approximately equal between the two CFEs. 

As discussed at length above, reach-averaged bed-sand median grain size dominates over reachaveraged bed-sand area in regulating suspended-sand concentration. Thus, in reaches where the bed 

was much finer during the 2004 CFE than during the 2008 CFE and where reach-averaged bedsand area was only slightly less during the 2004 CFE than during the 2008 CFE, suspended-sand 

concentration was typically greater during the 2004 CFE than during the 2008 CFE (mostly in 

uppermost Marble Canyon between river miles 2 and 12). At all other locations, suspended-sand 

concentration was much greater during the 2008 CFE than during the 2004 CFE because reachaveraged bed-sand area was likely much greater during the 2008 CFE than during the 2004 CFE, 

and reach-averaged bed-sand median grain size was not that different between the two CFEs. 

Comparison of Computed Reach-Averaged Bed-Sand Area, Reach-Averaged Bed-Sand 

Grain Size, Known Levels of Sand Enrichment, and Mean Suspended-Sand Concentration 

in Each Reach During the 1996, 2004, and 2008 CFEs 

To provide guidance in the design of possible future controlled floods, and to provide 

guidance on possible improvements to monitoring the status of sediment resources in and along the 

Colorado River in GCNP, it is informative to compare reach-averaged bed-sand area, reachaveraged bed-sand median grain size, measured levels of sand enrichment, and observed 

suspended-sand concentrations during the three CFEs. Because sandbar-deposition rate depends 

strongly on suspended-sand concentration (for example, Schmidt and others, 1993), and suspendedsand concentration at constant discharge depends on bed-sand grain size and area, future controlled 

floods may be viable as management tools for sustainably rebuilding sandbars only if these floods 

can be designed to maintain the highest possible concentrations of suspended sand for specific 

different antecedent sand-supply conditions. This final analysis will provide some guidance for that 

effort. The parameters compared at each study site between the 1996, 2004, and 2008 CFEs in this 

analysis are: (1) EDI, EWI, and point-sample-measured suspended-sand concentration averaged 

over the last few hours of the rising limb and the entire high, steady discharge part of the flood 

hydrograph19 (figs. 4, 5, 7); (2) sand enrichment20 computed for each CFE by combining the 

antecedent sand enrichment values for each reach (table 3) with the measured sand loads entering 

the upstream end of each reach during the CFE (table 6); (3) reach-averaged bed-sand area 

computed using the study-site β-based analysis in figure 12; and (4) reach-averaged bed-sand 

median grain size computed using the sand-area-corrected study-site β analysis in figure 13. 

Because the magnitudes of these parameters differed greatly among the various study sites during 

the three CFEs, these parameters were normalized by their values during the 2004 CFE for the 

comparison between the 2004 and 2008 CFEs, and they were normalized by their values during the 

1996 CFE for the comparison between the 1996 and 2008 CFEs. This nondimensionalization 

allowed better comparison of these parameters among the study sites by removing the effect of 

 19 Because the duration of high, steady discharge during the 1996 CFE was much longer than during the 2004 and 

2008 CFEs, only the suspended-sand concentrations measured over the first 3 days of high, steady discharge during the 

1996 CFE were averaged for this comparative analysis. 20 Note that data needed to compute sand enrichment were not collected before the 1996 CFE. 

97
different reach lengths between study sites. These four dimensionless parameters are compared in 

table 8. 

Table 8. 2008 CFE parameters at each study site normalized by their values during the 2004 CFE and 

during the 1996 CFE. 

Study site and 2008 CFE parameters normalized by their values during the 2004 CFE 

associated upstream 

reach 

Suspended-sand 

concentration 

Sand enrichment Reach-averaged bedsand area Reach-averaged bedsand median grain 

size 

River-mile 0 

(lower Glen Canyon) 

2.2 Positive number of 

unknown magnitude 

2.1 0.96 

River-mile 30 

(upper Marble 

Canyon ) 

1.3 3.1 2.1 

(large enough to 

offset opposing effect 

on concentration of 

coarsening bed-sand 

grain size) 

1.28 

(coarsening should 

cause decrease in 

suspended-sand 

concentration)

River-mile 61 

(lower Marble 

Canyon) 

1.5 2.0 1.3 0.95 

River-mile 87 

(eastern Grand 

Canyon) 

1.6 2.7 1.3 0.95 

River-mile 225 

(combined east- and 

west-central Grand 

Canyon) 

1.6 2.7 1.1 0.85 

Study site and 2008 CFE parameters normalized by their values during the 1996 CFE 

associated upstream 

reach 

Suspended-sand 

concentration 

Sand enrichment Reach-averaged bedsand area Reach-averaged bedsand median grain 

size 

River-mile 0 

(lower Glen Canyon) 

1.7 No data 2.7 

(large enough to 

offset opposing effect 

on concentration of 

coarsening bed-sand 

grain size) 

1.07 

(coarsening should 

cause decrease in 

suspended-sand 

concentration) 

River-mile 61 

(combined upper and 

lower Marble 

Canyon) 

1.7 No data 1.0 0.82 

River-mile 87 

(eastern Grand 

Canyon) 

1.3 No data 0.7 

(not large enough to 

offset opposing effect 

on concentration of 

fining bed-sand grain 

size) 

0.84 

River-mile 166 

(east-central Grand 

Canyon) 

1.2 No data 0.9 

(not large enough to 

offset opposing effect 

on concentration of 

fining bed-sand grain 

size) 

0.77 

98
Predictions of eddy-sandbar deposition rates in a reach during a controlled flood require 

predictions of suspended-sand concentration. Such predictions require (1) knowledge of either the 

antecedent sand enrichment or reach-averaged bed-sand area and (2) knowledge of the reachaveraged bed-sand median grain size. Comparison of the dimensionless parameters in table 8 

indicates that measured sand enrichment and reach-averaged bed-sand area are always positively 

correlated, as expected at constant discharge. Because measured sand enrichment and reachaveraged bed-sand area are always positively correlated at constant discharge (table 9), reachaveraged bed-sand area is the best proxy for sand enrichment when the data needed to compute 

sand enrichment by mass-balance sand budgeting are unavailable, for example, before the 1996 

CFE. Reach-averaged bed-sand median grain size is a less reliable proxy for sand enrichment 

because reach-averaged bed-sand median grain size and area are negatively correlated in only 5 out 

of 9 cases (table 9). Correlations between these three parameters and suspended-sand 

concentration, however, are more complicated. As shown in tables 8 and 9, greater reach-averaged 

bed-sand area (and therefore likely greater sand enrichment) can coincide with lower suspendedsand concentration when the reach-averaged bed-sand median grain size is coarse, for example in 

Grand Canyon upstream from the River-mile 87 and 166 study sites during the 1996 CFE (figs. 5, 

12, 13). This is because reach-averaged bed-sand median grain size exerts a stronger nonlinear 

control on suspended-sand concentration than does reach-averaged bed-sand area. 

It is possible to have situations where greater sand enrichment leads to larger amounts of 

coarser sand in a reach, for example, in eastern Grand Canyon during the 1996 CFE and in upper 

Marble Canyon during the 2008 CFE. These situations are most likely to reoccur in these two 

reaches because they are located immediately downstream from the two largest sand-supplying 

tributaries. As already discussed, at some finite time interval after a large tributary sand-supplying 

event, the finer sand will be winnowed from the bed in the reach downstream from the tributary, 

leaving only the coarse tail of the grain-size distribution of sand supplied during this tributary flood 

to be mixed with the bed sand that existed in this reach before the tributary flood. In the coarse-bed, 

greater-bed-sand-area cases during the 1996 CFE, the sand that covered more of the bed in eastern 

and east-central Grand Canyon was too coarse to result in higher suspended-sand concentrations at 

the River-mile 87 and 166 study sites than during the two subsequent CFEs (figs. 5, 12, 13). Thus, 

it was possible for lesser amounts of finer sand on the bed to result in suspended-sand 

concentrations at the River-mile 87 and 166 study sites that were higher during the 2008 CFE than 

during the 1996 CFE (fig. 5). In the coarse-bed, greater-bed-sand-area cases during the 2008 CFE, 

the sand that covered more of the bed in upper Marble Canyon was not too coarse to result in lower 

suspended-sand concentrations than during the 2004 CFE (figs. 5, 12, 13). Thus, during the 2008 

CFE in upper Marble Canyon, the effect on suspended-sand concentration arising from more than 3 

times greater reach-averaged bed-sand area relative to during the 2004 CFE (fig. 16) was enough to 

overcome the opposing effect on suspended-sand concentration arising from coarser bed sand (figs. 

5, 12, 15). 

Therefore, in the design of future controlled floods, knowing just total "sand enrichment" in 

each reach of the Colorado River in lower Glen, Marble, and Grand Canyons is not enough to 

ensure sufficiently high suspended-sand concentrations to result in high eddy-sandbar deposition 

rates during a controlled flood; one must also know the relative grain size of the bed sand in each 

reach. This is important because if suspended-sand concentrations are not high enough during a 

controlled flood, eddy sandbars either will not gain sand or, in the worst-case scenario, will erode, 

as observed during the 1996 CFE in Marble Canyon (Hazel and others, 1999; Schmidt, 1999; 

Topping and others, 2006a). The sand-transport monitoring program maintained by the USGS on 

99
Table 9. Signs of relations between the 2008 CFE parameters normalized by 

their values during the 2004 CFE and normalized by their values during the 1996 

CFE. 

[Parameter states that opposed larger suspended-sand concentration during the 2008 CFE than 

during the 2004 CFE or during the 2008 CFE than during the 1996 CFE indicated by red type. 

Parameter states that promoted larger suspended-sand concentration during the 2008 CFE than 

during the 2004 CFE or during the 2008 CFE than during the 1996 CFE indicated by green 

type. Identical signs in adjacent columns indicate positive correlation between parameters in 

these columns.]

Sign of relation between normalized suspended-sand concentration 

during 2004 and 2008 CFEs and each of the following 

Study site 

Normalized sand 

enrichment 

Normalized reachaveraged bed-sand 

area 

Normalized reachaveraged bed-sand 

median grain size 

River-mile 0 + + - 

River-mile 30 + + (dominates over 

bed-sand grain size 

in this case)

+ (opposes bed-sand 

area!!!) 

River-mile 61 + + - 

River-mile 87 + + - 

River-mile 225 + + - 

Sign of relation between normalized suspended-sand concentration 

during 1996 and 2008 CFEs and each of the following

Study site 

Normalized sand 

enrichment 

Normalized reachaveraged bed-sand 

area 

Normalized reachaveraged bed-sand 

median grain size 

River-mile 0 No data + (dominates over 

bed-sand grain size 

in this case)

+ (opposes bed-sand 

area!!!)

River-mile 61 No data + - 

River-mile 87 No data - (opposes bed-sand 

grain size!!!)

- (dominates over 

bed-sand area in this 

case)

River-mile 166 No data - (opposes bed-sand 

grain size!!!)

- (dominates over 

bed-sand area in this 

case)

the Colorado River in Grand Canyon National Park measures suspended-sand concentration and 

grain size every 15 minutes at the River-mile 30, 61, 87, 166, and 225 study sites. In addition to 

being used to compute sand enrichment, these data can be analyzed using the β-based analyses 

described in this report to provide information on reach-averaged bed-sand median grain size in 

each reach. Thus, information on sand enrichment and reach-averaged bed-sand median grain size 

(the two parameters most needed to predict suspended-sand concentrations during a controlled 

flood) can be provided to managers for optimized design of future controlled floods to most 

efficiently rebuild eddy sandbars. 

Finally, the analyses in this report suggest that post-1996 dam operations may be resulting 

in net scour of sand from Grand Canyon. Although suspended-sand concentrations were higher at 

all study sites during the 2008 CFE than during either the 1996 or 2004 CFEs, these higher 

100
concentrations were not necessarily associated with greatest sand enrichment occurring during the 

2008 CFE. Although (1) more sand was likely present on the bed during the 2008 CFE in lower 

Glen Canyon than during either the 1996 or 2004 CFE and (2) more sand was likely present on the 

bed during the 2008 CFE in Marble and Grand Canyons than during the 2004 CFE, equal or lesser 

amounts of sand were likely present on the bed during the 2008 CFE in lower Marble Canyon and 

much of Grand Canyon than during the 1996 CFE. Among the three CFEs, the greatest level of 

sand enrichment in lower Glen Canyon occurred during the 2008 CFE, and this was a result of the 

combination of the largest tributary sand inputs and second-lowest dam releases occurring 

antecedent to the 2008 CFE. Among the three CFEs, however, more sand was likely present on the 

bed in Grand Canyon during the 1996 CFE than during either the 2004 or 2008 CFE. Therefore, 

among the three CFEs, the greatest level of sand enrichment in Grand Canyon occurred during the 

1996 CFE, and this was a result of either (1) a temporary increase in the amount of sand on the bed 

following the extremely large inputs of sand to this reach during the January-March 1993 Little 

Colorado River floods, or (2) long-term scour of sand from this reach during dam operations. Thus, 

although the analyses in this report can provide guidance in the design of future controlled floods, 

further experimentation (with controlled floods and intervening dam releases) and monitoring are 

required to evaluate whether controlled floods can utilize the existing tributary sand supply to 

rebuild eddy-sandbars in a sustainable manner, or if dam operations with or without controlled 

floods will result in long-term scour of sand from the Colorado River in GCNP. 

Conclusions 

The major conclusions from this study are as follows. 

1. Although suspended-sand concentrations were higher at all study sites during the 

2008 CFE than during either the 1996 or 2004 CFE, these higher concentrations 

were only associated with more sand on the bed of the Colorado River in lower Glen 

Canyon. More sand was likely present on the bed of the river in Grand Canyon 

during the 1996 CFE than during either the 2004 or 2008 CFE. It remains unclear as 

to whether ongoing dam operations are resulting in long-term net scour of sand from 

Grand Canyon. 

2. Nothing observed in the sediment-transport data collected during the 2008 CFE 

refuted any of the conclusions in Topping and others (2006a). In their analysis of 

sediment-transport and bar data collected during the 1996 and 2004 CFEs, Topping 

and others (2006a) concluded that 

results from the 1996 controlled-flood experiment indicate that, during sediment-depleted 

conditions, sand deposited at higher elevations in downstream eddy sandbars is derived from the 

lower-elevation parts of upstream sandbars. Thus, controlled floods conducted under these 

conditions result in decreases in total eddy-sandbar area and volume (especially in Marble 

Canyon). 

They also concluded that compared to the 2004 CFE, 

in future controlled floods, more sand is required to achieve increases in the total area and 

volume of eddy sandbars throughout all of Marble and Grand Canyons. Annual tributary inputs 

of sand much larger than one million metric tons occur, but are relatively rare. Therefore, “more 

sand” could be achieved directly by augmentation from sand trapped in the reservoir impounded 

by Glen Canyon Dam or perhaps indirectly by following each large tributary input of sand with 

short-duration controlled floods. Frequent short-duration controlled floods under sand-enriched 

conditions could result in the downstream propagation (into the downstream half of Marble 

101
Canyon and into Grand Canyon) of the gains in total eddy-sandbar area and volume observed in 

the upstream half of Marble Canyon during the 2004 controlled-flood experiment. 

The relatively high level of sand enrichment from tributaries antecedent to the 2008 

CFE is not a frequent occurrence. Therefore, the 2008 CFE could not address the 

key question implied in the last two sentences of the conclusions excerpted from 

Topping and others (2006a), that is, whether sandbars can be sustainably rebuilt in 

the Colorado River in Grand Canyon National Park through use of controlled floods 

with more typical levels of sand enrichment. The answer to this question remains 

unknown and will require future experimentation and monitoring. 

3. Although the 2008 CFE did not answer this key question, it did allow collection of 

the most comprehensive sediment-transport dataset collected during a controlled 

flood to date, and thus helped provide answers to key process-related questions. 

Analysis of the suspended- and bed-sediment data collected during the 1996, 2004, 

and 2008 CFEs indicates that, although greater levels of antecedent sand enrichment 

generally lead to higher suspended-sand concentrations during a controlled flood, 

this is not always the case by virtue of the opposing physical effects of reachaveraged bed-sand grain size and area in regulating suspended-sand concentration. 

Greater levels of sand enrichment will lead to greater reach-averaged bed-sand area, 

but will not always lead to finer reach-averaged bed-sand grain size. Because the 

reach-averaged bed-sand grain-size distribution exerts an opposing and stronger 

nonlinear control on suspended-sand concentration than does reach-averaged bedsand area, greater levels of sand enrichment can produce lower suspended-sand 

concentrations during a controlled flood than can lower levels of sand enrichment 

when a smaller area of the bed is covered by finer sand. Larger suspended-sand 

concentrations during a controlled flood are required to produce higher eddysandbar deposition rates. Therefore, design of controlled floods for optimal sandbar 

deposition in the Colorado River in Grand Canyon National Park should not be 

based only on threshold levels of sand enrichment, but also on reach-averaged bedsand median grain size. The analyses present in this report suggest that reachaveraged bed-sand median grain size could be estimated before future controlled 

floods using β. A lesser amount of finer sand on the bed could easily result in higher 

eddy-sandbar deposition rates during a controlled flood than could a larger amount 

of coarser sand on the bed. 

102
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Implications for Eddy-Sandbar Deposition in Grand Canyon National Park—Open-File Report 2010–1128