TWG Webinar/Conference Call 

June 21, 2010 

Conducting: Paul Grams, GCMRC Convened: 1 p.m. (MDT)

TWG Members/Alternates: 

Mary Barger, WAPA 

Cliff Barrett, UAMPS 

Marianne Crawford, USBR 

Kerry Christensen, Hualapai Tribe 

Jerry Cox, Grand Canyon River Guides 

Bill Davis, CREDA 

Chris Harris, Colorado River Board of California 

Norm Henderson, NPS/GLCA 

Rick Johnson, Grand Canyon Trust 

John Jordan, Federation of Fly Fishers 

Robert King, Utah Division of Water Resources 

Dennis Kubly, USBR 

Bill Stewart, AGFD 

Jason Thiriot, Colorado River Commission/Nevada 

Clayton Palmer, WAPA 

Mike Yeatts, Hopi Tribe

Other Participants: 

Glenn Bennett, USGS/GCMRC 

Jane Bird, Upper Colorado River Commission 

Lori Caramanian, DOI 

Mary Daugherty, USGS/GCMRC 

Paul Grams, USGS/GCMRC 

John Hamill, USGS/GCMRC 

Leslie James, CREDA 

Ted Melis, GCMRC/USGS 

Bruce Moore, Southern Nevada Water Authority 

Jack Schmidt, Utah State University 

Patti Aaron, USBR 

Scott Wright, USGS (Sacramento) 

Webinar Support: Mary Daugherty

Meeting Recorder: Linda Whetton 

Introduction. John said this information request came up through the TWG via a number of different 

avenues, most recently the last TWG meeting where there was a request from a variety of TWG 

members to assess the effects of various different types of dam operations on sediment conservation in 

Marble and Grand Canyon. There was some dialogue with the Secretary’s Designee about the scope of 

the work that GCMRC was going to do and ultimately they were given the go-ahead to provide the 

analysis which should be helpful in forming the TWG’s discussion of the 2011 hydrograph. 

Modeling Results. Scott Wright gave a PowerPoint presentation, “Briefing Subject” (Attachment A) and 

said the Open File Report (Attachment B) would provide more information. He also referenced another 

Open File Report, “An Approach for Modeling Sediment Budgets in Supply-limited Rivers” (Attachment 

C). Since he has talked about the modeling done in several meetings, he would only focus on the results. 

He said two release volumes, the first being 8.23 maf and the reason for doing that was because it has 

been the most common release volume over the last decade so it seemed reasonable to do that. With 

the new equalization guidelines in place, they looked at the April 24-month study, which was the most 

current study they had while they were developing the scenarios to model. At that time the projected 

volume was a 11.0 maf due to the need to do equalization between the two main reservoirs (Lake Powell 

and Lake Mead). They solicited input from the TWG several months ago and compiled the responses 

they received and developed the list of operations: 1 

1. MMLF = Modified Low Fluctuating Flow 

2. SDF = Steady Daily Flows. This operation is the same as MLFF in terms of the monthly 

distribution of the volume but it does not have any daily fluctuations so steady flows for each 

month and then the monthly volume changes through the year. 

3. EMV = Equal Monthly Volume. This is the opposite of #2 where it maintains the MLFF daily 

fluctuations so the flows still fluctuates up and down every day, but the monthly volumes are 

changed so there is an equal volume in each months so getting rid of the MLFF distribution of 

monthly volumes but maintaining the daily fluctuations. 

4. SYR = Steady Year-round Flow. This is a steady flow for the whole year. They’ve looked at 

this before and this is a useful one to do just from the standpoint of providing an upper bound, 

basically as good as you can do for sand conservation with the dam there and providing the 

other scenarios too. 
Glen Canyon Dam Technical Work Group Page 2 

DRAFT Minutes of June 21, 2010, Webinar/Conference Call 

5. SAS = Seasonally Adjusted Steady Flow. For this they used the description of the 1995 EIS 

where it was also analyzed. 

6. IDR = Increased Daily Range and downramp. This was the option A Variation that came from 

the 2006 assessment. It increases the daily range over what is currently allowed by MLFF up 

to 10,000 or 12,000 cfs per day and also increases the downramp rate in certain months up to 

4,000 cfs per hour. 

In 2-5, flows are further constrained to fluctuate MLFF on a daily basis or on a monthly so they all have 

some element of a more steady hydrograph. Number 6 is the lone scenario that increases the degree of 

fluctuation from MLFF. 

Q: I thought there was also a scenario requested that was going to look at pre-ROD? (James) 

A: We had to draw the line somewhere as far as getting to too many scenarios. The one step closer with the 

increased daily range was the interim step towards something with more fluctuations than MLFF. (Grams) 

Q: Just so I understand these, item 6 has more flexibility but all the others are less flexible that current operations, 

correct? (James) 

A: Correct. (Grams) 

Scott said the way they constructed the hydrographs was for MLFF the 8.23 MAF scenario was taken 

directly from the 2006 options that were developed by Reclamation and Western. For the 11.0 MAF, they 

used that information and then for each month looked for a volume that was similar for that month within 

those 30 years of early hydrographs that had been generated and then those were matched up. They 

didn’t match up perfectly so they would just scale them a little bit to get the monthly volume correct. All of 

the hydrographs used were basically derived from those early hydrographs for the 2006 assessment. 

Q: When you say the 2006 assessment, that’s the LTEP analysis that was done? (Johnson) 

A: I don’t think it was considered LTEP. Ted could probably offer a better reason for how that happened but there 

was an assessment of five different scenarios for resource response. I don’t think it was LTEP but was pre-LTEP. 

Is that right, Ted? (Wright) 

R: That was the so-called Science Planning Group (SPG) option assessment. It was released to the TWG in 

October 2006 and preceded the announcement for the so-called LTEP in the Federal Register. (Melis) 

Q: What’s the period of record for the tributary inputs? (Henderson) 

A: For the Paria it goes all the way back to the 1920’s. There is more data in more recent times. As for the Little 

Colorado, we went back to the late 1980’s. For the Paria we ended up using the same period of record as the LCR 

so it’s about 20+ years of record to get the averages. (Wright) 

Scott reviewed the plots for Marble Canyon at 11.0 MAF and 8.23 MAF and then for Eastern Grand 

Canyon at 11.0 MAF and 8.23 MAF. 

Q: Can you give a quick definition of the uncertainty envelope? (Johnson) 

A: We used the same definitions that Topping uses for the mass balance so we varied the tributary inputs by +/- 

10% and we varied the mainstem, the predicted transport rates, for the model in the mainstem by +/- 5%. The 

upper uncertainty would be if the tributary inputs were 10% more than we thought and the mainstem transport was 

5% less so more inputs, less exports that uses the upper bound and vice versa for the lower bound. (Wright) 

Q: Why would you characterize 8.23 MAF as below average annual volumes because in the last 10 years, it’s been 

about 8.0 and for the foreseeable future except if we get some decent inputs? (King) 

A: It depends on how you would define the average for this basin. Certainly that hasn’t been the case over the last 

10 years but if you look at the longer record, the average is between 10.5 – 11 MAF. That’s the number that gets 

used for allocations and the like. (Wright) 

R: It isn’t for allocations. An 8.23 MAF is probably closer to what the average is going to be in the future. (King) 

C: It doesn’t matter too much here for this discussion. That is really important for trying to manage sand in the 

system because less water, which obviously isn’t good for some things, is actually a good thing for sand resources 

in the canyon. Whenever you have average inputs and 8.23 MAF or something around that, that tends to result in 

accumulation in Marble Canyon. (Wright) 

He provided the following summary points: 
Glen Canyon Dam Technical Work Group Page 3 

DRAFT Minutes of June 21, 2010, Webinar/Conference Call 

• Since we don’t know what the 2011 annual volume and tributary inputs will be, the results should 

be viewed in a relative sense (i.e., against each other) 

• SYR consistently ranks 1st in terms of sand retention and provides an upper bound for 

comparison 

• SDF and EMV yield similar results indicating more sand retention than MLFF, EMV is slightly 

better for 11.0 MAF while SDF is slightly better for 8.23 MAF 

• SAS ranks high for 11.0 MAF (2nd or 3rd depending on reach), but ranks 6th for 8.23 MAF. This is 

because the maximum flow (18,000 cfs) is imposed and the same for both volumes. 

• IDR consistently ranks just below MLFF for sand retention. 

Q: Bob Mussetter had wanted to participate in this call but couldn’t, however, one of the questions he has asked in 

the past or a clarification. These are the only two reaches that you guys have looked at and wonder if the modeling 

has the capability to look at the same scenarios for some of the lower reaches? (James) 

A: Not as currently constructed. The reason for that is just a data limitation essentially. The model definitely need 

the data for calibration and we could extend downstream. It’s easy enough to add reaches but that requires data on 

tributary inputs as well as mainstem transport in those reaches. I think Dave Topping is working toward providing 

that information but it’s not something that has happened yet. I don’t think he’s on the call otherwise he could 

update us on where he’s at. I think the mainstem monitoring is coming close to what we need. I’m not sure where 

he is with the tributary work. (Wright) 

C: I appreciate that because I think it’s really to clarify the report is only covering these reaches and not implications 

that it’s for the entire mainstem. (James) 

Q: What portion of the river corridor would this be covering? (Henderson) 

A: It covers from Mile 0 to Mile 88, Lee Ferry to Phantom Ranch. (Wright) 

Q: Have you run any simulations with the HFE thrown in? (Christensen) 

A: No. (Wright) 

Q: Could you run that simulation to calculate the amount of sand augmentation necessary to have a positive benefit 

under all conditions? (King) 

A: Yes, that can be done. The key there would be specifying when it would come in and whether it would be a 

constant trickle or like a slug because that makes a difference in how it ends up getting transported. That would be 

very easy to do. (Wright) 

Q: Does the paper get into the actual numeric comparisons between all the alternatives as far as percentages? 

(Henderson) 

A: Yes. (Wright) 

Q: You said you haven’t done ___ with an HFE but I presume you could do it, right? (Johnson) 

A: You would need to know the hydrograph and then you’d need to know how to redistribute that volume through 

the rest of the year. It’s not as easy as sand augmentation, but it could be done. (Wright) 

Q: At Saguaro Lake you presented the high, low, and average sediment inputs, but you have the inputs coming in 

at different times or was the average input that you showed at Saguaro Lake the same as what you shown here? 

(Johnson) 

A: I think for those we had everything dumping in the first 10 days of the simulation. I didn’t really like that but it 

made more sense to have it distributed using the historical information that we do have. (Wright) 

Q: I’m trying to get a sense of scale here. These volumes, the differences, and the different scenarios – are they 

like totally overwhelmed if you did throw an HFE in there? I mean it wouldn’t really matter given you did an HFE. 

(Christensen) 

A: It would definitely matter. I think for the floods that were conducted in 2004 and 2008 the sand export mass 

during those events – it depends on the event and the site. They were on the order of half a million to 800,000 

metric tons for the 60-hour peak and so the volumes go back to Marble Canyon for 8.23 MAF. You’re talking 

retention of 800,000 up to 1 million and so export during a flood for those conditions would be more than 50% of 

what you retained. (Wright) 

C: And integrating this model with an HFE is part of what we’re talking about is work that would go into the 

development of the HFE protocol. That’s why this was done separately without an HFE but that will be considered. 

(Grams) 

Q: I appreciate that you said this modeling allows a person to make a relative ranking. This operation from a 

sediment budget point of view is better than that operation and it’s better by a lot. I believe that the Bureau can’t 

operate this way because what you’ve presumed here is perfect for knowledge about how much volume is going to 

be released from Glen Canyon Dam and that never happens. I’ve made a couple of suggestions but I’m a little bit at 

a loss to understand the reluctance that you didn’t include in your forecast and modeling. So why aren’t you doing 

that? (Palmer) 
Glen Canyon Dam Technical Work Group Page 4 

DRAFT Minutes of June 21, 2010, Webinar/Conference Call 

A: So the idea would be to somehow change the volumes through the year as you’re going? I see where you’re 

coming from on that. You’re right, the forecast does change through the year but I think for comparing these 

operations, I don’t think that would really make any difference because in the long run if you change the forecast, 

that would change the volumes and the changes would be the same for all the different scenarios that you’re 

looking at. The simplest way to do simulations and rank the scenarios is to assume the forecast is right and run the 

scenarios that way. If you start trying to incorporate the forecast error, 1) it’s not clear to me how you would do that, 

and 2) I don’t think all the extra work that would be required to do that is warranted. I don’t think it would change the 

result in terms of the rankings of the alternatives. I think you could make the same argument about the tributaries. 

We’re using the average tributary inputs. Someone could argue that you have to use every scenario imaginable for 

the tributary inputs and pretty much anything can happen, but to do that would be incredibly complicated from the 

standpoint of doing the simulations and I just don’t think that it would be effecting the bottom line in the results and 

it would just be a lot of work so not much bang for the buck. (Wright) 

Q: This has already been done and you must have looked at the 2006 SPG options report. In that, the forecast was 

included and came out with the monthly volumes that would pertain to this. When you say it’s a lot of work, well, it’s 

already been done. Secondly, I’ve pointed out a couple of times that when you start the year with a presumption of 

8.23 MAF and you end up the year with equalization flows, you actually do things like have equal monthly volumes, 

have greater volumes and therefore greater fluctuations across the four summer months than MLFF does. It seems 

to me that since you end up with greater volumes and greater fluctuations under an equal monthly flow during the 

summertime, that it could easily change the relative ranking of the two. (Palmer) 

Q: That’s if the forecast is off in one direction, but what if it’s off in the other direction? (Wright) 

A: Yes exactly, but stop for just a second. If the forecast is off in one direction, then you’re saying it’s possible but 

the relative ranking of equal monthly volumes vis-á-vis MLFF could change. That’s all I need you to do is 

acknowledge that it’s possible the relative ranking of these operations could change if forecast errors included in 

your analysis. (Palmer) 

C: If you change the volume, then the rankings change. (Wright) 

R: That’s what I’m saying. You’ve retorted to my comment by saying, “look we haven’t done it because we think it 

will be more work and it won’t change relative rankings.” As far as I can tell, it has quite a potential to change 

relative rankings of some of those operational scenarios. (Palmer) 

R: I can’t disagree with that. All I would say is that these are the scenarios that we think are the most probable and 

use the most realistic boundary conditions for the modeling. (Wright) 

C: And you’ve seen several e-mails from me suggesting that if you don’t know whether an 8.23 MAF or an 11 MAF 

at the end of year is going to start out that way in the beginning of the year. It’s easy to do and incorporate the 

monthly volumes and include an error forecast and see that you get hourly hydrological inputs you need to run your 

model. I don’t understand why you don’t use those for the sake of this. (Palmer) 

Q: How many scenarios would you have to run then for forecast error because there could be an infinite number of 

ways that the error could go. (Wright) 

A: Let’s suppose there is an infinite number and let’s suppose you divided the infinite number of errors into a 

normal distribution and took the upper and lower core tile. At least you’d be able to know whether forecast error 

significantly altered the relative ranking of these operational scenarios for sediment distribution. The way you’re 

doing it now you’re going to leave us with a single conclusion that it’s the core knowledge and people are going to 

take that and say “I see that the relative ranking error for this scenario above or below this other one.” They won’t 

be able to separate a sensitivity analysis which could significantly change a relative ranking. (Palmer) 

R: I disagree with that it would significantly change the relative rankings. (Wright) 

C: This model applies the model to an annual volumes equitably across all the scenarios analyzed. So if you chop 

that up finer, you’re going to get the same results. (Grams) 

R: Not given the information I’ve sent you which shows you that it’s possible to start out the year with a presumption 

about annual volume, use MLFF, and then compare it to equal monthly volume. You’d end up with summer 

releases where the equal monthly volumes actually has greater volumes than MLFF and therefore greater 

fluctuations over a four-month summer period. That’s the period in which you’re getting the Paria inputs and so 

given the way you’ve set up the model, it’s possible that the relative ranking between MLFF and equalized monthly 

volume would change in Marble Canyon. (Palmer) 

C: I think it would be helpful to see something about some scenarios about how the Bureau might distribute monthly 

volumes under a couple different forecast error scenarios because right now it’s pretty much anything. You’re 

saying that anything would be possible. The reality is that 8.23 MAF has been a very, very common release and 

this is targeted towards what I think is the most likely and average condition. (Grams) 

R: 8.23 MAF, for example, was released in 2009 but the Bureau started off with a presumption that 10.5 MAF was 

going to be released and they modified their monthly volumes to accommodate what they thought was going to be 

a higher release year. And the Bureau did this for 10 years under five scenarios for the 2006 report. If you want to 

know how the Bureau would distribute monthly volumes for a 10-year period, including forecast error, you could 
Glen Canyon Dam Technical Work Group Page 5 

DRAFT Minutes of June 21, 2010, Webinar/Conference Call 

look at the 2006 option report which I’ve referred you to. The only reason I keep bringing this up Paul is because it 

was a surprise to everybody when the Bureau prepared the hydrology for the 2006 option report that things like 

seasonally adjusted steady flows and equalized monthly volumes didn’t look anything like that once you 

incorporated the forecast error. (Palmer) 

Q: Scott, you’ve used the average monthly inputs from the Paria and the LCR and obviously that’s not usually how 

it works every year. Usually you get either one or maybe two blips somewhere along that line. Is it just the amount 

of sediment that comes in or is it the timing – will it change the relative merits of this based on when the input 

comes in? (Henderson) 

Q: Can I ask a clarifying question because I have a similar question. I think what Norm is asking and what I want to 

know is does it matter if it all comes in at one time during the month or if it’s spread equally throughout the month? 

Is that right? (Johnson) 

Q: Well, sort of. The way the graph is there are some big months and then there’s some small months and you’re 

basically saying inputs come in every month almost and what I’m saying is that’s not reality. Reality is usually they 

come in – any particular year they’ll come in one time or maybe two times but usually one big impulse or are these 

numbers here, is the base load too or is this the actual pulses that come in? (Henderson) 

A: This illustrates a similar thing to what Clayton is pointing out is that these simulations are not reality. There are 

some assumptions built in to the boundary conditions and so for the tributaries typically such as the Paria, the 

floods happen in a day or two and that’s when all the sand comes in. The bottom line is we don’t know when that’s 

going to happen in 2011. We could do every possible scenario and look at the variability of all the distribution. 

That’s the most vigorous way to do it. The bottom line is that there wasn’t time to do that for this for one thing and I 

just don’t think that is worth all the effort to get these relative comparisons. (Wright) 

Q: Do you think the comparison would basically be the same no matter when the sediment came in? It’s not like 

well I don’t think you should put all the sediment coming in May. We know that doesn’t happen. We’ve got the 

seasonal, the monthly distribution, the way it has happened historically and the difference is that we don’t have – 

we’ve got X amount coming in October. That might come in in one day, but we don’t know what day that will be so 

we’re just distributing over the month. I think it makes sense to do that for simulations like this to keep that simple 

and as long as you’re using the same boundary conditions for all the scenarios that you’re comparing, you get a 

valid comparison between those scenarios. (Wright) 

Q: I was just thinking that in terms of the whole ecosystem approach that we’re going to be looking at at some point 

and knowing the information that came out of the workshop at Saguaro Ranch, the request to do this for the preROD might be really important since they were saying that pre-ROD, that the HBC was doing better and the RBT 

was doing worse. If you wanted the data to work on the full ecosystem approach, it sounds like we should also 

have that run. (Barger) 

A: That’s something that could be done. It’s not going to be in this report. It could be done at a later date I guess. It 

seemed unrealistic to me that those results would be that useful given the current situation but maybe for the 

reasons you outlined it would be worth doing that. (Wright) 

Q: I guess for curiosity I would like to see that, but I would imagine that it’s going to be much worse than any of the 

other alternatives that are here. Is there any way it could be better than any of the alternatives? (Johnson) 

A: I’ll say no. I’d be shocked given the way that’s what built into – the way we did these simulations if we did it 

similarly for a 30 to 30,000 cfs fluctuation. I’m sure that would result in more export than any of these other ones. 

(Wright) 

Q: I was just thinking to have comparable data for whatever they’re looking for on the fish stuff, it might be good to 

have it otherwise you’re just guessing. (Barger) 

Paul asked if there were any more questions. Rick told him that he appreciated all the information that 

GCMRC prepared and that he felt it was really useful. 

Conference Call ended at 2:12 p.m. (MDT) 
Wright, S.A., and Grams, P.E., in press, Evalu

Year 2011 Glen Canyon Dam Flow Release Downstream Sand Storage along the Colo

Geological Survey Open-File Report

USGS-approved, on-line soon

Briefing subject

Attachment A
Approach

Annual release 

volume (2)

Hourly release 

hydrographs (6)

Flow routing 

model

Sand routing 

model

Sa

12 “ba

plus un

Attachment 

A
Sand Routing Model

Wright, S.A., Topping, D.J., Rubin, D.M., and 

press. An approach for modeling sedimensupply-limited rivers, Water Resources R

USGS-approved, accepted by WRR, on

Attachment A
Scenarios Modeled

1) Modified Low Fluctuating Flows (MLFF) 2) Steady Daily Flows (SDF) – No daily fluctu

volumes

3) Equal Monthly Volumes (EMV) – MLFF daily 

volume each month

4) Steady Year Round (SYR) – No daily or mo5) Seasonally Adjusted Steady (SAS) – From 6) Increased Daily Range and Down Ramp (ID

Variation” from 2006 assessment

2 annual volumes: 8.23 MAF and 11.0 (MA

from April 24-month study)

6 daily/monthly release patters:

Attachment A
Annual and monthly vol

0

200400600800

1,0001,2001,400

OCT NOV DEC JAN FEB MAR APR MAY JUN J

MONTHLY RELEASE VOLUME, 

IN THOUSAND ACRE-FEET

11.0 MAF8.23 MAF

Attachment A
MLFF

SDF

EM

Attachment A
Tributary sand input

0

50

100150200250300350400

OCT NOV DEC JAN FEB MAR APR MAY JUN 

MONTHLY AVERAGE SAND LOAD, 

IN THOUSAND METRIC TONS

PariaLittle Colorado

Averages for each month based on histor

Attachment A
Example results plo

Attachment A
Marble Canyon, 11.0 M

-600-400-200

0

200400600

MLFF SDF EMV SYR 

ANNUAL SAND BUDGET, 

IN THOUSAND METRIC TONS

Marble Canyon

EXPLANATION

Base simulations

Uncertainty envelopes

1

Negative

Neutral

Neutral 

Positive

3

4

5

620,000 metric ton difference 

MLFF SDF EMV SYR 

Attachment A
-600

-400-200

0

200400600

MLFF SDF EMV SYR 

ANNUAL SAND BUDGET, 

IN THOUSAND METRIC TONS

Eastern Grand Canyon 

Eastern Grand Canyon, 11.

EXPLANATION

Base simulations

Uncertainty envelopes

1

Negative 

2 4 

5 

Why all negative? LCR inputs Paria, timing of inputs late in 

MLFF SDF EMV SYR 

Negative Negative Negative 230,000 metric ton difference 

Attachment 

A
0

200400600800

100012001400

MLFF SDF EMV SYR 

ANNUAL SAND BUDGET, 

IN THOUSAND METRIC TONS

Marble Canyon 

Marble Canyon, 8.23 M

EXPLANATION

Base simulations

Uncertainty envelopes

1

Positive

2

3

4

MLFF SDF EMV SYR 

Positive Positive Positive 

Why all positive? Below avervolume combined with avera

350,000 metric ton difference 

Attachment 

A
0

200400600800

100012001400

MLFF SDF EMV SYR 

ANNUAL SAND BUDGET, 

IN THOUSAND METRIC TONS

Eastern Grand Canyon 

Eastern Grand Canyon, 8.2

EXPLANATION

Base simulations

Uncertainty envelopes

1 2 3 4 

MLFF SDF EMV SYR 

180,000 metric ton difference 

Positive Positive Positive Positive 

Attachment 

A
Summary

Since we don’t really know what the 2011 anntributary inputs will be, the results should be vsense (i.e. against each other)SYR consistently ranks 1st in terms of sand rete

provides an upper bound for comparisonSDF and EMV yield similar results indicating mthan MLFF. EMV is slightly better for 11.0 MAF slightly better for 8.23 MAF.SAS ranks high for 11.0 MAF (2nd or 3rd depend

ranks 6th for 8.23 MAF. This is because the ma

(18,000 cfs) is imposed and the same for both IDR consistently ranks just below MLFF for san

Attachment 

A
Questions?

Attachment A
MLFF

Attachment A
SDF

Attachment A
EMV

Attachment A
SYR

Attachment A
SAS

Attachment A
United States Department of the Interior

U.S. GEOLOGICAL SURVEY

GnaNo CeNyoN MoNIToRnIG AND R¡SBeRCH CBUTEN.

2255 NoRrH GBvwI Dnrve, MS-5000

FLAGSTAFF, AnzoN¡ 8600 1

520 556-1094 Telephone

520 556-7092 Fax

MEMORANDUM

To: Shane Capron, Chair, Technical Work Group, Glen Canyon Dam Adaptive

Management Program

From: John Hamill, Chief, Grand Canyon Monitoring and Research Center, U.S. Geological

Su.ey, Fragshrf, AZ .-t¿_ t+*._-, ) ]

Date: }i4.ay 17,2010

Subject: Technical Work Group and stakeholder requests for GCMRC to evaluate the effects

of various dam operation scenarios on sediment storage and loss in the Grand Canyon

Beginning February, 2009 andmore recently at the March, 2010 Technical Work Group (TWG)

meeting, members requested that the Grand Canyon Monitoring and Research Center (GCMRC)

use a recently developed sediment transport model to assess the effects of various dam

operations on sediment storage and loss in the Grand Canyon (see attachment). The information

was requested to assist in developing a20Ii hydrograph for Glen Canyon Dam to recommend to

the Adaptive Management Work Group (AMWG).

GCMRC will evaluate several dam operation and hydrologic scenarios and provide a preliminary

report describing the results to the Technical Work Group by June 14,2010. The completion and

dissemination of this report is contingent on final acceptance of the model for publication in the

scientific literature. We expect to receive notification on the status of the publication on or

before }r.4ay 21. Because of the limited time, we will target the model runs to be specif,rcally

applicable to anticipated20Tl hydrology. Thus, we intend to model one sediment input

scenario, two hydrologic scenarios, and six operation scenarios for a total of 12 modeling runs.

The specific conditions are as follows:

Sediment input: Paria and Little Colorado River average annual sand supply

Hydrology: 8.23 maf and 10.8 maf (2011 most probable as of April 8, 2010)

Operations:

A. Modified Low Fluctuating Flows (MLFF) -normal monthly and daily fluctuations

B. MLFF -- normal monthly volumes with steady daily flows,

C. Equalized monthly volumes with normal (MLFF) daily flow fluctuations,

D. Equalized monthly volumes with steady daily flows,

E. Seasonally adjusted steady flows (SASF) as outlined in the 1995 Environmental

Impact Statement, and
F. MLFF with increased (4,000 cfs) down ramp rates (Science Planning Group option

A',).

For model input, we will rely on available hydrographs using either actual hourly hydrographs

from selected past years or artif,icial hourly hydrographs generated in the 2006 Science Planning

Group process.

The GCMRC's sediment staff has longstanding commitments to attend a major conference the

same week of the TWG meeting. Special arangements will be needed if a presentation on the

results of the above analysis is desired.

Please contact me if you have any questions

Attachment

cc TWG

AMWG

Secretary's Designee
Evaluation of Water Year 2011 Glen Canyon Dam Flow 

Release Scenarios on Downstream Sand Storage along the 

Colorado River in Arizona

By Scott A. Wright and Paul E. Grams

 

Open-File Report 2010–1133

U.S. Department of the Interior

U.S. Geological Survey

Attachment B
ii

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:

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Suggested citation:

Wright, S.A., and Grams, P.E., 2010, Evaluation of Water Year 2011 Glen Canyon Dam flow release scenarios on 

downstream sand storage along the Colorado River in Arizona: U.S. Geological Survey Open-File Report 2010-1133, 

19 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.

Attachment B
iii

Contents 

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

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

Purpose and Scope ................................................................................................................................................... 2

Physical Setting ......................................................................................................................................................... 2

Glen Canyon Dam Flow Release Scenarios.................................................................................................................. 3

Modeling Approach.......................................................................................................................................................12

Results..........................................................................................................................................................................13

Summary and Discussion.............................................................................................................................................16

References Cited..........................................................................................................................................................17

Attachment B
iv

Figures 

 

Figure 1. Colorado River below Glen Canyon Dam (GCD)....................................................................................... 3

Figure 2. Monthly release volumes for the two modeled annual release volumes for Modified Low Fluctuating 

Flows (MLFF) operations and major tributary average monthly flow and sand inputs. A, Monthly Glen Canyon Dam 

GCD release volumes. B, Average monthly Paria and Little Colorado River discharges. C, Average monthly Paria and 

Little Colorado River sand loads.................................................................................................................................... 4

Figure 3. Glen Canyon Dam (GCD) flow releases and model results for Modified Low Fluctuating Flow (MLFF) 

operations at 8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget for 

Marble Canyon. C, Modeled sand budget for eastern Grand Canyon. .......................................................................... 6

Figure 4. Glen Canyon Dam (GCD) flow releases and model results for Steady Daily Flow (SDF) operations at 

8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget for Marble Canyon. 

C, Modeled sand budget for eastern Grand Canyon ..................................................................................................... 7

Figure 5. Glen Canyon Dam (GCD) low releases and model results for Equal Monthly Volume (EMV) operations at 

8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget for Marble Canyon. 

C, Modeled sand budget for eastern Grand Canyon ..................................................................................................... 8

Figure 6. Glen Canyon Dam (GCD) flow releases and model results for Steady Year Round (SYR) operations at 

8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget for Marble Canyon. 

C, Modeled sand budget for eastern Grand Canyon ..................................................................................................... 9

Figure 7. Glen Canyon Dam (GCD) flow releases and model results for Seasonally Adjusted Steady (SAS) 

operations at 8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget for 

Marble Canyon. C, Modeled sand budget for eastern Grand Canyon ......................................................................... 10

Attachment B
v

Figure 8. Glen Canyon Dam (GCD) flow releases and model results for Increased Daily Range and Down Ramp 

(IDR) operations at 8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget 

for Marble Canyon. C, Modeled sand budget for eastern Grand Canyon.................................................................... 11

Figure 9. Modeled annual sand budgets for the 11.0 million acre-foot annual release volume. A, Sand budget for 

Marble Canyon. B, Sand budget for eastern Grand Canyon ....................................................................................... 14

Figure 10. Modeled annual sand budgets for the 8.23 million acre-foot annual release volume. A, Sand budget for 

Marble Canyon. B, Sand budget for eastern Grand Canyon ....................................................................................... 15

Tables 

 

Table 1. Modeled sand budgets for 11.0 million acre-foot annual release volume ................................................ 16

Table 2. Modeled sand budgets for 8.23 million acre-foot annual release volume ................................................ 17

Attachment B
vi

Conversion Factors Inch/Pound to SI

Multiply By To obtain 

acre-foot (acre-ft) 1,233 cubic meter (m3)

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

ton per year (ton/yr) 0.9072 metric ton per year

SI to Inch/Pound 

Multiply By To obtain 

cubic meter (m3) 0.0008107 acre-foot (acre-ft) 

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

metric ton per year 1.102 ton per year (ton/yr) 

Attachment B
Evaluation of Water Year 2011 Glen Canyon Dam Flow 

Release Scenarios on Downstream Sand Storage along 

the Colorado River in Arizona

By Scott A. Wright and Paul E. Grams

Abstract This report describes numerical modeling simulations of sand transport and sand budgets for reaches of the Colorado 

River below Glen Canyon Dam. Two hypothetical Water Year 2011 annual release volumes were each evaluated with six 

hypothetical operational scenarios. The six operational scenarios include the current operation, scenarios with modifications

to the monthly distribution of releases, and scenarios with modifications to daily flow fluctuations. Uncertainties in model 

predictions were evaluated by conducting simulations with error estimates for tributary inputs and mainstem transport rates. 

The modeling results illustrate the dependence of sand transport rates and sand budgets on the annual release volumes as well 

as the within year operating rules. The six operational scenarios were ranked with respect to the predicted annual sand 

budgets for Marble Canyon and eastern Grand Canyon reaches. While the actual WY 2011 annual release volume and levels 

of tributary inputs are unknown, the hypothetical conditions simulated and reported herein provide reasonable comparisons 

between the operational scenarios, in a relative sense, that may be used by decision makers within the Glen Canyon Dam 

Adaptive Management Program.

Introduction Physical characteristics of the riverine ecosystem of the Colorado River in Glen Canyon National Recreation Area and 

Grand Canyon National Park are affected by the existence and operations of Glen Canyon Dam (GCD) upstream (Schmidt 

and Graf, 1990; Wright and others, 2005; Hazel and others, 2006; Grams and others, 2007). The dam has blocked the 

upstream supply of sand and finer sediment since completion in 1963, and dam operations determine the transport capacity 

of the Colorado River, which affects the magnitude of sediment retention along the bed and banks versus the magnitude of 

sediment export downstream to Lake Mead. Sediment that is retained may be stored on the channel bed, along the channel 

margins, or in zones of lateral recirculating flow or eddies (Schmidt, 1990). Sediment within eddies, if deposited by high 

flows that are sufficiently greater than base flow, creates sandbars that are valued as recreational campsites (Kearsley and 

others, 1994), backwater aquatic habitat that may be used by native fish (Valdez and others, 2001), and substrate for riparian 

vegetation (Ralston, 2005). One of the goals of the Glen Canyon Dam Adaptive Management Program (GCDAMP) is to 

manage the dam to promote sand retention and sandbar deposition (Bureau of Reclamation, 2001). Monitoring sediment flux 

and sandbar size provides information on how dam operations have affected sand retention and storage. Numerical modeling 

tools developed and tested with the monitoring data are now available to provide managers with predictions on how future 

dam operations are likely to affect sediment retention and, thereby, sandbar characteristics. 

Results from previous modeling and analyses have varied from predictions of persistent sand erosion (Laursen and 

others, 1976) to likely sand retention (Howard and Dolan, 1981; U.S. Department of the Interior, 1995). Most recently, a 

simplified modeling approach based on assumptions of steady dam releases and a stable suspended sand rating curve 

Attachment B
2

indicated that for these conditions, which would tend to maximize sediment retention, long-term increases in sandbar size 

were possible but not certain (Wright and others, 2008). The uncertainty associated with this model led to the development 

of a more sophisticated semi-empirical model that incorporates unsteady flow and a sand rating curve that shifts in response 

to the sand supply (Wright and others, in press). 

Purpose and Scope 

The purpose of this report is to document the application of the Wright and others (in press) model to a set of 

hypothetical scenarios for potential dam operations (that is, daily and monthly patterns) and annual release volumes in Water 

Year (WY) 2011. Model simulations predict sand export and sand budgets for three reaches, for six different dam operations 

scenarios each applied to two potential WY 2011 annual release volumes (for a total of 12 simulations). The modeled dam 

operation scenarios incorporate variables, such as patterns of daily flow fluctuation and the distribution of monthly release 

volumes. These scenarios derive either from previously implemented dam operations or dam operations proposed by 

members of the GDCAMP. The degree to which each of these scenarios is consistent with the body of legislation, 

agreements, and treaties, collectively known as the “law of the river,” has not been evaluated and is beyond the scope of this 

technical report. Similarly, the annual release volumes that are modeled were chosen because they were considered to be 

most probable at the time this report was prepared (June 2010). Actual release volumes for WY 2011 are subject to change. 

Physical Setting 

The segment of the Colorado River considered for this modeling exercise extends from Lees Ferry, Arizona, 

downstream about 87 miles (fig. 1). Within this segment, the river is divided into three modeling reaches. Upper Marble 

Canyon extends from Lees Ferry to river-mile1 (RM) 30, lower Marble Canyon extends from RM 30 to RM 61, and eastern 

Grand Canyon extends from RM 61 to RM 87. Sand is supplied to the study reach by the Paria River, which is just 

downstream from Lees Ferry, and by the Little Colorado River, which is just downstream from RM 61. Streamflow is 

monitored at each of the reach boundaries (Lees Ferry, RM 30, RM 61, and RM 87), and suspended-sediment concentration 

is monitored at 15-minute intervals at RM 30, RM 61, and RM 87 (Topping and others, 2010). For reporting of results 

herein, the two upstream reaches (upper and lower Marble Canyon) were combined, thus providing information on the entire 

reach between the two major tributaries (Marble Canyon).

 

1 The river-mile convention has long been used as the standard reference system for locations along the Colorado River in 

Grand Canyon and was formalized in 2006 (U.S. Geological Survey, 2006). Lees Ferry is located 15.5 miles downstream 

from Glen Canyon Dam and 1 mile upstream from the mouth of the Paria River.

Attachment B
3

Figure 1. Colorado River below Glen Canyon Dam (GCD). Lees Ferry is designated river-mile (RM) 0 and is 

about 15.5 miles downstream from the dam. RM 30, RM 61, and RM 87 denote model nodes and are labeled 

according to river miles downstream from Lees Ferry. 8-digit numbers denote U.S. Geological Survey gaging 

stations referenced in the text.

Glen Canyon Dam Flow Release Scenarios Six scenarios for GCD hourly release hydrographs were identified through discussions with the GCDAMP Technical 

Work Group. For each of the six hourly release scenarios, two annual release volumes were evaluated, that is, two 

possibilities for the total volume of water to be released in WY 2011 (for a total of 12 simulations). Based on the April 2010 

24-month study from the Bureau of Reclamation (http://www.usbr.gov/uc/water/crsp/studies/24Month_04.pdf, accessed May 

4, 2010), the most probable annual release volume was 11.0 million acre-feet (MAF). For comparative purposes, we also 

evaluated an annual release volume of 8.23 MAF because this volume has been the most common release volume over the 

past decade during multi-year drought conditions (8 of 9 water years from 2001 to 2009, based on data from Lees Ferry, U.S. 

Geological Survey station 09380000). Figure 2A shows the expected pattern of monthly release volumes for current 

operations, known as Modified Low Fluctuating Flows (U.S. Department of the Interior, 1995) for the two annual release 

volumes. The pattern of monthly volumes for 11.0 MAF is based on the April 2010 24-month study, while the pattern for 

8.23 MAF is based on historical data and available synthetic hydrographs, discussed in more detail below:

Attachment B
4

0

200

400

600

800

1,000

1,200

1,400

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP

MONTHLY RELEASE VOLUME, 

IN THOUSAND ACRE-FEET

11.0 MAF

8.23 MAF

A

0

100

200

300

400

500

600

700

800

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP

AVERAGE MONTHLY DISCHARGE, 

IN CUBIC FEET PER SECOND

Paria

Little Colorado

B

0

50

100

150

200

250

300

350

400

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP

AVERAGE MONTHLY SAND LOAD, 

IN THOUSAND METRIC TONS

Paria

Little Colorado

C

Figure 2. Monthly release volumes for the two modeled annual release volumes for Modified Low Fluctuating 

Flows (MLFF) operations and major tributary average monthly flow and sand inputs. A, Monthly Glen Canyon 

Dam release volumes, B, Average monthly Paria and Little Colorado River discharges. C, Average monthly

Paria and Little Colorado River sand loads. MAF, million acre-feet

Attachment B
5

Six operational scenarios were identified for release patterns for a given annual release volume, that is, for how the 

water is distributed on monthly, daily, and hourly bases. For reference, the release hydrographs for each scenario are shown 

as the top panel (A) in figures 3–8; the data sources are discussed in detail below.

1) Modified Low Fluctuating Flows (MLFF) – This is the current operational regime as selected in the 1995 

Environmental Impact Statement and record-of-decision for the operation of Glen Canyon Dam (U.S. Department 

of the Interior, 1995) (fig. 3).

2) Steady Daily Flows (SDF) – This scenario eliminates fluctuations in releases that occur under MLFF on a daily 

basis, but maintains the MLFF pattern of monthly volume releases (fig. 4).

3) Equal Monthly Volumes (EMV) – This scenario maintains the daily fluctuations of MLFF but replaces the pattern 

of monthly volume releases with an equal volume for each month (fig. 5).

4) Steady Year Round (SYR) – This scenario eliminates both daily fluctuations and monthly volume changes resulting 

in a single steady flow all year (fig. 6).

5) Seasonally Adjusted Steady (SAS) – This scenario eliminates daily fluctuations and revises the MLFF monthly 

volumes to a pattern with the highest monthly volumes in May–June and lowest volumes in Aug–Dec (U.S. 

Department of the Interior, 1995) (fig. 7).

6) Increased Daily Range and Down Ramp (IDR) – This scenario increases the MLFF daily ranges in discharge (up to 

12,000 cubic feet per second [cfs] compared with 8,000 cfs) and down ramp rates (up to 4,000 cfs/hr compared with 

1,500 cfs/hr) (fig. 8).

Attachment B
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Figure 3. Glen Canyon Dam (GCD) flow releases and model results for Modified Low Fluctuating Flow (MLFF) 

operations at 8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand 

budget for Marble Canyon. C, Modeled sand budget for eastern Grand Canyon. MAF, million acre-feet. 

Attachment B
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Figure 4. Glen Canyon Dam (GCD) flow releases and model results for Steady Daily Flow (SDF) operations at 

8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget for Marble 

Canyon. C, Modeled sand budget for eastern Grand Canyon. MAF, million acre-feet

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Figure 5. Glen Canyon Dam (GCD) low releases and model results for Equal Monthly Volume (EMV) operations 

at 8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget for 

Marble Canyon. C, Modeled sand budget for eastern Grand Canyon. MAF, million acre-feet

Attachment B
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Figure 6. Glen Canyon Dam (GCD) flow releases and model results for Steady Year Round (SYR) operations at 

8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand budget for Marble 

Canyon. C, Modeled sand budget for eastern Grand Canyon. MAF, million acre-feet

Attachment B
10

Figure 7. Glen Canyon Dam (GCD) flow releases and model results for Seasonally Adjusted Steady (SAS) 

operations at 8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand 

budget for Marble Canyon. C, Modeled sand budget for eastern Grand Canyon. MAF, million acre-feet

Attachment B
11

Figure 8. Glen Canyon Dam (GCD) flow releases and model results for Increased Daily Range and Down Ramp

(IDR) operations at 8.23 and 11.0 MAF annual release volumes. A, GCD hourly hydrograph. B, Modeled sand 

budget for Marble Canyon. C, Modeled sand budget for eastern Grand Canyon. MAF, million acre-feet

Attachment B
12

The modeling simulations required hourly release hydrographs for each operational scenario and annual release 

volume. These were derived primarily from information that was generated in support of an experimental options assessment 

conducted by the Grand Canyon Monitoring and Research Center in 2006 (U.S. Geological Survey, 2006). For the 2006

assessment, hourly release hydrographs were generated by Western Area Power Administration for several operational 

scenarios for three 10-year periods with annual release volumes representative of dry, average, and wet conditions. 

Information from these hydrographs was used to construct the WY 2011 hydrographs for each of the six scenarios as 

follows. For MLFF, the 8.23 MAF hydrograph was taken directly from the hydrographs generated for the 2006 assessment; 

for 11.0 MAF, each month was matched with a similar volume month from the 2006 assessment hydrographs and then scaled 

so that the volumes matched exactly (fig. 3A). The scaling consisted of adjusting all flows in a month by a constant factor; 

typically, a month was available with a volume within about 5 percent of the desired volume such that the need for scaling 

was minimal. For SDF, the monthly volumes are the same as MLFF, but for each month, the MLFF hourly flows were 

averaged to yield a steady flow for each month (fig. 4A). For EMV, the monthly volumes are constant throughout the year 

and the hourly hydrographs were taken from the MLLF month with the volume that most closely matched this constant 

monthly volume (fig. 5A). For SYR, the hydrographs are simply constant flows for the entire year that yield the desired 

annual volumes (fig. 6A). The SAS hydrographs were generated based on information from the 1995 EIS for operation of 

Glen Canyon Dam (U.S. Department of the Interior, 1995); the 8.23 MAF annual release volume hydrograph was based on

the minimum releases provided in the EIS Summary table and the 11.0 MAF annual release volume scales the minimum 

releases in each month to achieve the higher volumes while imposing a maximum release of 18,000 cfs (fig. 7A). Finally, the 

IDR scenario was evaluated in the 2006 assessment as scenario “A Variation” (U.S. Geological Survey, 2006), and the 

hydrographs (fig. 8A) were derived from that analysis in the same manner as the MLFF hydrographs were derived. In 

addition, all release hydrographs incorporate steady flows during the months of September and October as dictated by the 

Final Environmental Assessment for Experimental Releases from Glen Canyon Dam, Arizona, 2008 through 2012 (U.S. 

Department of the Interior, 2008).

Modeling Approach The modeling simulations were performed using the Wiele and Smith (1996) model for routing the GCD flow releases

downstream and the Wright and others (in press) model for routing sand and computing sand budgets for the various 

scenarios. The flow model requires release hydrographs and major tributary flow hydrographs as inputs. Streamflows from 

the Paria River (U.S. Geological Survey station 09382000) and Little Colorado River (U.S. Geological Survey station 

09402300) were included using average monthly flows (fig. 2B) for their periods of record. While average monthly tributary 

flows were used for the flow routing, instantaneous tributary flows were used to estimate the tributary sand inputs (methods 

described in detail below, fig. 2C). For each scenario, the hourly release hydrographs described above were routed 

downstream and results were output at RM 30, RM 61, and RM 87 to be used as input to the sand routing model, as 

described below.

The Wright and others (in press) sand routing model computes sand fluxes at the computational nodes shown in 

figure 1 (RM 30, RM 61, and RM 87). The model computes sand concentrations for narrow particle size ranges and includes 

bed sorting algorithms to simulate the fining and winnowing characteristic of sand supply-limited rivers, such as the 

Colorado below Glen Canyon Dam. The sand routing model was calibrated and validated using sand transport monitoring 

data from 2003–2009 as described by Wright and others (in press). Required model inputs are flow hydrographs at the three 

computational nodes as well as time series of sand inputs from the Paria and Little Colorado Rivers (sand transport at the 

upstream boundary, Lees Ferry, is assumed to be zero in the model as per Wright and others, in press). The flow hydrographs 

were provided by the flow model as described above. The tributary inputs were modeled in a similar fashion as for the flow 

routing, that is, average monthly sand loads were used as boundary conditions (fig. 2C). While this approach does not 

incorporate the episodic nature of tributary flooding, it provides the correct long-term seasonal distributions and average 

annual inputs, making it a reasonable approach for comparing alternative flow release scenarios. The average monthly sand 

inputs were derived from long-term records of tributary sand loads provided by the USGS Grand Canyon Monitoring and 

Research Center (David Topping, U.S. Geological Survey, unpub. data). These long-term records were developed using a 

combination of measurements (flow and sediment concentration at the gages cited above, using standard USGS methods) 

and models (Topping, 1997; Topping and others, 2010). The particle size distributions used for the tributaries were the same 

as those used by Wright and others (in press). Finally, the sand routing model requires specification of the initial bed sand 

thicknesses and particle size distribution for each reach. These were specified as the values at the end of the validation 

simulations (March 2009) described by Wright and others (in press) as follows: sand thicknesses equal to 0.45, 0.48, and 

0.56 m and median particle sizes equal to 0.35, 0.32, and 0.30 mm for upper Marble Canyon, lower Marble Canyon, and 

eastern Grand Canyon, respectively. These conditions were chosen because they are the most recent estimates of bed 

conditions in the reaches. It is not possible to know the bed conditions on Oct 1, 2010 (the beginning of the simulations) 

Attachment B
13

because tributary inputs cannot be forecasted accurately. Also, Wright and others (in press) showed that the sand routing 

model is not particularly sensitive to the initial bed conditions for the sensitivity range studied therein.

Uncertainties in the model results were evaluated by conducting simulations with estimated errors incorporated into the 

boundary conditions (tributary inputs) and model calculations (sand transport rates). Following the methods used by Topping 

and others (2010) for constructing error bars for sand budgets based on high-resolution monitoring data, the tributary inputs 

were varied by ±10 percent and the sand transport rates were varied by ±5 percent. That is, for each scenario, two additional 

simulations were performed: 1) tributary inputs increased by 10 percent and sand transport rates decreased by 5 percent, 

providing an upper uncertainty bound; and 2) tributary inputs decreased by 10 percent and sand transport rates increased by 5

percent, providing a lower uncertainty bound. This technique is particularly appropriate here because the sand routing model 

was calibrated to sand transport measurements with comparable error estimates. It is noted that these uncertainty bounds are 

most useful for evaluating whether there is net accumulation or erosion for a given scenario. For comparing scenarios to each 

other, it is important to only compare simulations with the same boundary conditions and model parameters. For example, it 

would not be appropriate to compare one operating scenario with tributary inputs increased by 10% with a different 

operating scenario with tributary inputs decreased by 10%. 

Results The sand routing model predicts sand concentrations at the three computational nodes shown in figure 1 (RM 30, RM

61, RM 87). The sand concentrations were combined with the flows at these locations to compute sand fluxes, and the sand 

fluxes were then used to construct sand budgets for the three reaches bounded by the computational nodes (flux is assumed 

to be zero past Lees Ferry). For this report, the two Marble Canyon reaches were combined for sand budgeting purposes. The 

sand budgets are simply a cumulative accounting of sand inputs to a reach minus sand export from a reach; thus, a positive 

sand budget indicates net sand accumulation within the reach and a negative sand budget indicates net sand erosion within 

the reach. 

The primary results of the simulations are shown in the series of figures 3–8. Each figure represents a different 

operational scenario and consists of three panels. The top panel shows the hourly release hydrographs for the given 

operational scenario for both the 8.23 and the 11.0 MAF annual volumes. The middle panel shows the modeled cumulative 

sand budgets for Marble Canyon, again for 8.23 and 11.0 MAF, including the uncertainty envelopes. The bottom panel 

shows the simulated sand budgets for the eastern Grand Canyon reach.

The model results show some expected trends that are common to most of the operational scenarios. First, the higher 

annual release volume (11.0 MAF) consistently leads to more sand export and thus less sand in the reaches projected at the 

end of WY 2011. The sand budgets are also seen to reflect variations in flow releases (patterns and volumes) and tributary 

inputs throughout the year. For example, the Marble Canyon sand budgets tend toward accumulation during August and 

September when Paria sand inputs are greatest (fig. 2C). An example of the impact of flow volume on the sand budgets is 

apparent in the results for SAS (fig. 7), where it is seen that extended periods of relatively high flows in the spring drive the 

sand budgets substantially in the negative direction (that is, erosion). The dashed lines define the modeling uncertainty 

envelopes and allow for determination of the sign of the sand budget for each scenario at the end of WY 2011 (that is, for 

determination of a positive or negative sand budget, the uncertainty envelope must not span zero).

In order to compare the scenarios more directly, annual sand budgets, including the uncertainty envelopes, were 

computed for each simulation. The annual sand budgets are equivalent to the cumulative sand budgets shown in figures 3–8 

at the end of WY 2011. These results are shown in figures 9 and 10; in these figures, the horizontal lines represent the “base” 

simulations (that is, without uncertainty estimates) and the vertical lines denote the range based on the uncertainty 

simulations. 

Attachment B
14

-600

-400

-200

0

200

400

600

MLFF SDF EMV SYR SAS IDR

ANNUAL SAND BUDGET, 

IN THOUSAND METRIC TONS

Marble Canyon A

-600

-400

-200

0

200

400

600

MLFF SDF EMV SYR SAS IDR

ANNUAL SAND BUDGET, 

IN THOUSAND METRIC TONS

Eastern Grand Canyon B

EXPLANATION

Base simulations

Uncertainty envelopes

Figure 9. Modeled annual sand budgets for the 11.0 million acre-foot annual hydrologic scenario. A, Sand budget 

for Marble Canyon. B, Sand budget for eastern Grand Canyon. Vertical lines denote range based on 

uncertainty simulations.

Attachment B
15

0

200

400

600

800

1000

1200

1400

MLFF SDF EMV SYR SAS IDR

ANNUAL SAND BUDGET, 

IN THOUSAND METRIC TONS

Marble Canyon A

0

200

400

600

800

1000

1200

1400

MLFF SDF EMV SYR SAS IDR

ANNUAL SAND BUDGET, 

IN THOUSAND METRIC TONS

Eastern Grand Canyon B

 

EXPLANATION

Base simulations

Uncertainty envelopes

Figure 10. Modeled annual sand budgets for the 8.23 million acre-foot annual hydrologic scenario. A, Sand budget 

for Marble Canyon. B, Sand budget for eastern Grand Canyon. Vertical lines denote range based on 

uncertainty simulations.

Attachment B
16

For the 11.0 MAF annual release volume for Marble Canyon (fig. 9A), only one scenario, SYR (steady year round 

flows), results in a positive sand budget (that is, an uncertainty envelope entirely above zero indicating net sand 

accumulation). Two scenarios, MLFF and IDR, result in negative sand budgets (that is, uncertainty envelopes entirely below 

zero indicating net sand erosion), and three scenarios, SDF, EMV, and SAS, result in neutral sand budgets (that is, 

uncertainty envelopes span zero). For this release volume in the eastern Grand Canyon reach (fig. 9B), all of the scenarios 

resulted in negative sand budgets based on the model simulations. The differences in the results between the Marble and 

eastern Grand Canyon reaches are primarily due to differences in tributary inputs to each reach. That is, the Paria River 

supplies about 1.23 million metric tons to Marble Canyon, whereas the Little Colorado River supplies about 0.56 million 

metric tons to eastern Grand Canyon. Also, because the Paria inputs are greatest in the months of August and September (fig. 

2C), near the end of the simulations, this sand may not have had sufficient time to move through the Marble Canyon reaches 

and into eastern Grand Canyon. This issue could be avoided in future analyses by conducting modeling simulations over 

multiple water years using a range of annual release volumes in order to evaluate the longer-term response of sand budgets to 

different operational scenarios.

The results for 8.23 MAF (fig. 10) annual volume, when compared to the 11.0 MAF volume results, illustrate the strong 

influence that annual release volume has on the simulated sand budgets. All scenarios resulted in positive sand budgets (that 

is, net accumulation) for Marble and Grand Canyon reaches for an 8.23 MAF annual release volume. This is perhaps not 

surprising given that 8.23 MAF is well below the long-term annual flow volume for the Colorado (10.8 MAF based on the 

period of record for the Colorado River at Lees Ferry, Arizona, U.S. Geological Survey station 09380000) and that average 

annual tributary sand inputs were used in the modeling scenarios. This combination of below average annual release volume

and average tributary sand inputs is conducive to sand accumulation in the reaches below the Paria River (Topping and 

others, 2010). This combination may not be unusual because annual release volumes and tributary inputs tend to be 

uncorrelated since annual volumes are driven by upper basin snowpack conditions, whereas tributary inputs are primarily 

dependent on summer/fall monsoon rainfall. The simulated annual sand budgets for each scenario are compared numerically 

in the following section.

Summary and Discussion The annual sand budget results described in the previous section are summarized in table 1 (11.0 MAF) and table 2 

(8.23 MAF) for both the Marble Canyon and Grand Canyon reaches. For each annual release volume and reach, the 

operational scenarios are ranked 1 through 6 on the basis of the simulated annual sand budgets, with a rank of 1 denoting the

scenario with the most sand in the reach at the end of WY 2011 and a rank of 6 denoting the scenario with the least sand. 

Tables 1 and 2 also report the sign of the sand budget at the end of WY 2011 with consideration of the estimated uncertainty 

envelopes; that is, for a sand budget to be non-neutral (positive or negative), both uncertainty bounds must have the same 

sign. The numbers reported in the tables are for the base simulations (no adjustment for uncertainty), which are the 

appropriate results for comparing the operational scenarios with each other.

Table 1. Modeled sand budgets for 11.0 million acre-foot annual release volume

Rank Scenario Annual sand 

budget (Tmt1) 

Sign (includes 

uncertainty) Rank Scenario Annual sand budget (Tmt) 

Sign (includes 

uncertainty) 

Marble Canyon Grand Canyon

1 SYR +270 Positive 1 SYR -157 Negative

2 SAS +97 Neutral 2 EMV -223 Negative

3 EMV +79 Neutral 3 SAS -249 Negative

4 SDF +8 Neutral 4 SDF -274 Negative

5 MLFF -235 Negative 5 MLFF -354 Negative

6 IDR -349 Negative 6 IDR -391 Negative 1 Tmt – thousand metric tons. 

Attachment B
17

Table 2. Modeled sand budgets for 8.23 million acre-foot annual release volume

Rank Scenario Annual sand 

budget (Tmt) 

Sign (includes 

uncertainty) Rank Scenario Annual sand budget (Tmt) 

Sign (includes 

uncertainty) 

Marble Canyon Grand Canyon

1 SYR +1,032 Positive 1 SYR +248 Positive

2 SDF +945 Positive 2 SDF +208 Positive

3 EMV +919 Positive 3 EMV +200 Positive

4 MLFF +796 Positive 4 MLFF +156 Positive

5 IDR +699 Positive 5 IDR +123 Positive

6 SAS +677 Positive 6 SAS +65 Positive

The first observation from the tables is that the SYR scenario is consistently ranked 1 in terms of the annual sand 

budgets and is the only operation that results in a positive Marble Canyon sand budget for 11.0 MAF (table 1, fig. 9A). This

ranking is an expected result and is consistent with the choice by Wright and others (2008) to evaluate this scenario as the 

optimal flow regime for building and maintaining sandbars below Glen Canyon Dam. The nonlinear relationship between 

sand transport and water discharge (with exponent greater than one) dictates that a steady flow will transport less sand than 

an equivalent-volume fluctuating flow, and thus a steady year round flow yields the least sand export. For the 11.0 MAF 

simulations, the MLFF and IDR operations consistently ranked 5 and 6, owing to the fact that the other four scenarios all 

constrain the MLFF fluctuations to some degree (either monthly variations or daily fluctuations are constrained). MLFF 

ranks higher than IDR because IDR relaxes the MLFF constraints and allows for increased fluctuations and increased down

ramp rates (which allow for longer peaks within each day). The SDF operational scenario ranks 4 for both reaches. The SAS 

and EMV operations rank 2 and 3 and the order is swapped for the two reaches; however, these operations produce quite 

similar results for this annual release volume. 

The results and rankings for the 8.23 MAF annual volume are substantially different from the 11.0 MAF results, the 

only similarity being that SYR is ranked 1 (tables 1, 2). For this annual volume, the SAS operation ranks 6 for both reaches, 

whereas for 11.0 MAF, this operation ranked 2 or 3, depending on the reach. This difference results from the 18,000 cfs 

maximum release imposed by SAS. For all other scenarios, the 11.0 MAF annual volume results in higher peak flows that 

substantially increase sand transport and export rates. MLFF and IDR rank above SAS at positions 4 and 5, again with MLFF 

resulting in more sand in both reaches than IDR. Finally, SDF and EMV yield similar results for 8.23 MAF, with SDF 

ranked 2 and EMV ranked 3 for both reaches.

Finally, it is noted that these simulations should not be considered absolute predictions of the sand budgets below Glen 

Canyon Dam for WY 2011. It is unknown what the actual annual release volume and tributary inputs will be. Also, the initial 

conditions with respect to sand in the reaches are unknown. Rather, these simulations provide realistic estimates of the sand

budgets for the hypothetical initial and boundary conditions simulated, as well as comparisons of the various operational 

scenarios, in a relative sense, that may be used by decision makers within the GCDAMP.

References Cited Bureau of Reclamation, 2001, Strategic plan, Glen Canyon Dam Adaptive Management Program: Glen Canyon Dam 

Adaptive Management Work Group, 53 p., accessed on December 31, 2009, at 

http://www.usbr.gov/uc/rm/amp/pdfs/sp_final.pdf. 

Grams, P.E., Schmidt, J.C., and Topping, D.J., 2007, The rate and pattern of bed incision and bank adjustment on the 

Colorado River in Glen Canyon downstream from Glen Canyon Dam, 1956-2000: Geological Society of America, v. 119, 

no. 5-6, doi: 10.1130/B25969.1, p. 556–575, accessed on February 12, 2010, at 

http://gsabulletin.gsapubs.org/content/119/5-6/556.abstract. 

Hazel, J.E., Jr., Topping, D.J., Schmidt, J.C., and Kaplinski, M., 2006, Influence of a dam on fine-sediment storage in a 

canyon river: Journal of Geophysical Research, v. 111, no. F010252004JF000193, doi: 10.1029/2004JF000193, p. 1–16, 

accessed on December 28, 2009, at http://www.agu.org/journals/jf/jf0601//2004JF000193.pdf.

Attachment B
18

Howard, A., and Dolan, R., 1981, Geomorphology of the Colorado River in Grand Canyon: Journal of Geology, v. 89, no. 3, 

p. 269–298, accessed on February 18, 2010, at http://www.jstor.org/pss/30078299. 

Kearsley, L.H., Schmidt, J.C., and Warren, K.D., 1994, Effects of Glen Canyon Dam on Colorado River sand deposits used 

as campsites in Grand Canyon National Park, USA: Regulated Rivers, v. 9, p. 137–149. 

Laursen, E., Ince, S., and Pollack, J., 1976, On sediment transport through the Grand Canyon, in Federal Interagency 

Sediment Conference, 3d, Denver, Colo., March 22–25, 1976, Proceedings: p. 4-76 to 74-87.

Ralston, B.E., 2005, Riparian vegetation and associated wildlife, in Gloss, S.P., Lovich, J.E., and Melis, T.S., eds., The state 

of the Colorado River ecosystem in Grand Canyon: U.S. Geological Survey Circular 1282, 103-121 p., accessed on May 

10, 2010, at http://pubs.usgs.gov/circ/1282/.

Schmidt, J.C., 1990, Recirculating flow and sedimentation in the Colorado River in Grand Canyon, Arizona: Journal of 

Geology, v. 98, no. 5, doi: 10.1086/629435, p. 709–724, accessed on December 10, 2009, at 

http://www.journals.uchicago.edu/doi/abs/10.1086/629435. 

Schmidt, J.C., and Graf, J.B., 1990, Aggradation and degradation of alluvial sand deposits, 1965–1986, Colorado River, 

Grand Canyon National Park, Arizona: U.S. Geological Survey Professional Paper 1493, 74 p.

Topping, D.J., 1997, Physics of flow, sediment transport, hydraulic geometry, and channel geomorphic adjustment during 

flash floods in an ephemeral river, the Paria River, Utah and Arizona: University of Washington, Ph.D. thesis, 406 p.

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. 

U.S. Department of the Interior, 1995, Operation of Glen Canyon Dam-final Environmental Impact Statement, Colorado 

River Storage Project, Coconino County, Arizona: Salt Lake City, Utah, Bureau of Reclamation, Upper Colorado 

Regional Office, 337 p.. 

U.S. Department of the Interior, 2008, Final environmental assessment for experimental releases from Glen Canyon Dam, 

Arizona, 2008 through 2012, accessed May 21, 2010, at http://www.usbr.gov/uc/envdocs/ea/gc/2008hfe/GCD-finalEA2-

29-08.pdf

U.S. Geological Survey, 2006, Assessment of the estimated effects of four experimental options on resources below Glen 

Canyon Dam: Grand Canyon Monitoring and Research Center, submitted to U.S. Department of the Interior, Glen Canyon 

Dam Adaptive Management Program, 44 p., accessed on March 22, 2010, at 

http://www.usbr.gov/uc/rm/amp/amwg/mtgs/06dec05/Attach_09a.pdf. 

Valdez, R.A., Hoffnagle, T.L., McIvor, C.C., McKinney, T., and Leibfried, W.C., 2001, Effects of a test flood on the fishes 

of the Colorado River in Grand Canyon, Arizona: Ecological Applications, v. 11, no. 3, p. 686–700.

Wiele, S. M., and Smith J. D., 1996, A reach-averaged model of diurnal discharge wave propagation down the Colorado 

River through the Grand Canyon: Water Resources Research, v. 32, no. 5, p. 1375–1386.

Wright, S.A., Melis, T.S., Topping, D.J., and Rubin, D.M., 2005, Influence of Glen Canyon Dam operations on downstream 

sand resources of the Colorado River in Grand Canyon, in Gloss, S.P., Lovich, J.E., and Melis, T.S., eds., The state of the 

Colorado River ecosystem in Grand Canyon: U.S. Geological Survey Circular 1282, 17-31 p., accessed on May 10, 2010, 

at http://pubs.usgs.gov/circ/1282/. 

Wright, S.A., Schmidt, J.C., Melis, T.S., Topping, D.J. and Rubin, D.M. 2008, Is there enough sand? Evaluating the fate of 

Grand Canyon sandbars: GSA Today, v. 18, no. 8, p. 4–10. 

Wright, S.A., Topping, D.J., Rubin, D.M., and Melis, T.S., in press, An approach for modeling sediment budgets in supplylimited rivers: Water Resources Research.

 

Attachment B
IDR

Attachment A
An approach for modeling sediment budgets in supply-limited 

rivers 

Scott A. Wright1, David J. Topping2, David M. Rubin3, Theodore S. Melis2

1

 U.S. Geological Survey, California Water Science Center, Sacramento CA 

2

 U.S. Geological Survey, Grand Canyon Monitoring and Research Center, Flagstaff AZ 

3 U.S. Geological Survey, Pacific Science Center, Santa Cruz CA 

ABSTRACT 

 Reliable predictions of sediment transport and river morphology in response to variations in 

natural and human-induced drivers are necessary for river engineering and management. Because 

engineering and management applications may span a wide range of space and time scales, a broad 

spectrum of modeling approaches has been developed, ranging from suspended-sediment “rating 

curves” to complex three-dimensional morphodynamic models. Suspended-sediment rating curves 

are an attractive approach for evaluating changes in multi-year sediment budgets resulting from 

changes in flow regimes because they are simple to implement, computationally efficient, and the 

empirical parameters can be estimated from quantities that are commonly measured in the field (i.e. 

suspended-sediment concentration and water discharge). However, the standard rating-curve 

approach assumes a unique suspended-sediment concentration for a given water discharge. This 

assumption is not valid in rivers where sediment supply varies enough to cause changes in particle 

size or changes in areal coverage of sediment on the bed; both of these changes cause variations in 

suspended-sediment concentration for a given water discharge. More complex numerical models of 

hydraulics and morphodynamics have been developed to address such physical changes of the bed. 

This additional complexity comes at a cost in terms of computations as well as the type and amount 

1
of data required for model set-up, calibration, and testing. Moreover, application of the resulting 

sediment-transport models may require observations of bed-sediment boundary conditions that 

require extensive (and expensive) observations or, alternatively, require the use of an additional 

model (subject to its own errors) merely to predict the bed-sediment boundary conditions for use by 

the transport model. In this paper, we present a hybrid approach that combines aspects of the ratingcurve method and the more complex morphodynamic models. Our primary objective was to 

develop an approach complex enough to capture the processes related to sediment-supply limitation, 

but simple enough to allow for rapid calculations of multi-year sediment budgets. The approach 

relies on empirical relations between suspended-sediment concentration and discharge, but on a 

particle-size specific basis, and also tracks and incorporates the particle-size distribution of the bed 

sediment. We have applied this approach to the Colorado River below Glen Canyon Dam, a reach 

that is particularly suited to such an approach because it is substantially sediment supply-limited 

such that transport rates are strongly dependent on both water discharge and sediment supply. The 

results confirm the ability of the approach to simulate the effects of supply limitation, including 

periods of accumulation and bed fining as well as erosion and bed coarsening, using a very simple 

formulation. Though more empirical in nature than standard one-dimensional morphodynamic 

models, this alternative approach is attractive because its simplicity allows for rapid evaluation of 

multi-year sediment budgets under a range of flow regimes and sediment-supply conditions, and 

also because it requires substantially less data for model set-up and use. 

INTRODUCTION 

 It is often important to engineers, geomorphologists, and resource managers to simulate 

changes in fluvial sediment budgets resulting from changes in driving forces, such as climate, dam 

operations, land-use changes, etc. Humans have had a dramatic impact on the world’s river systems 

in terms of water storage and flow regulation (Nilsson et al., 2005) as well as sediment transport and 

2
budgets (Syvitski et al., 2005). Because sediment provides the physical framework for aquatic 

ecosystems, management of aquatic resources requires the ability to simulate changes in sediment 

budgets resulting from natural and anthropogenic influences. 

 In response to this need, substantial research and development has been conducted in the 

area of fluvial sediment-transport modeling. The wide range of space and time scales of interest has 

led to a range of modeling approaches, from simple empirical concentration-discharge relations (i.e. 

sediment rating curves, see e.g., ASCE, 1975) to complex multi-dimensional morphodynamic 

models. Suspended-sediment rating curves assume a unique relation between suspended-sediment 

concentration (or flux) and water discharge and have thus often been used to evaluate changes in 

flow regimes. Multi-dimensional morphodynamic models solve some form of the Navier-Stokes 

equations for the fluid and mass conservation for the sediment, sometimes for a range of particle 

sizes. Because of their simplicity, rating curves can be applied over large space and time scales, 

whereas multi-dimensional models are typically limited in the scale of application by computation 

times and data requirements. Between these two bookends lies an array of one-dimensional, 

pseudo-one-dimensional, and two-dimensional morphodynamic models, including several “generaluse” codes such as HEC-RAS (Corps of Engineers), SRH-1D and 2D (Bureau of Reclamation), 

MIKE-11 and 21 (Danish Hydraulics Institute), and SOBEK (Delft Hydraulics), as well as codes 

developed for specific research applications (e.g. Rahuel et al., 1989, van Niekerk et al., 1992, Hoey 

and Ferguson, 1994, Wright and Parker, 2005, among many others). Even within this family of 

models there is a wide range of complexity, such as equilibrium versus non-equilibrium transport, 

uniform sediment versus multiple particle sizes, steady versus unsteady flow, etc. The general use 

codes typically attempt to include all of these various options in order to be applicable to a range of 

study areas and conditions. Recently, Ronco et al. (2009) presented criterion for simplification of 

3
the standard one-dimensional models, based on the assumption of uniform flow, in order to 

facilitate long-term simulations for rivers where minimal topographic information is available. 

 Sediment rating curves are an attractive approach for evaluating long-term sediment budgets 

resulting from changes in flow regimes because they are very simple, easy to implement 

computationally, and the empirical parameters can be estimated from quantities that are frequently 

measured in the field (suspended-sediment concentration and water discharge). However, an 

implicit assumption in this approach is that sediment transport is always in equilibrium with 

sediment supply, i.e., that the particle-size distribution of sediment on the bed of the river is not 

changing (or that it is uniquely correlated with discharge). Rubin and Topping (2001, 2008) 

presented an approach for evaluating this assumption for sand-bedded rivers and suspended-sand 

transport, and showed that the bed particle size is often measurably important and sometimes as 

important as water discharge in regulating suspended-sand transport. Changes in bed particle-size 

distribution can be accounted for with multiple-size numerical formulations (e.g. Parker et al., 

2000); however, this comes at the cost of significant additional complexity, not only in terms of the 

model formulation but also in terms of the boundary and initial conditions that must be specified. 

For example, multiple-size morphodynamic models require information on bed particle-size 

distributions (i.e. the surface “active” layer and the underlying substrate) and sediment flux by 

particle size for calibration and testing. The methods of Ronco et al. (2009) can potentially 

overcome the limitations of the rating curve approach by incorporating multiple size classes. 

However, the primary assumption in their approach, i.e. uniform flow, is not suitable to our study 

site because the releases from Glen Canyon Dam are highly unsteady, on a daily basis, due to 

hydroelectric power demand. Where a model requires additional knowledge of sediment boundary 

conditions, either additional data must be collected, or another model must be used to predict the 

4
sediment-boundary conditions; this extra modeling step can introduce error, even before the 

sediment-transport model is implemented. 

 Because of the limitations of the available methods, we have developed and tested an 

alternative approach that combines aspects of several modeling methods. The approach uses 

empirically based rating curves, but in contrast to the standard approach, they are formulated on a 

particle-size specific basis. This allows for calculations of the particle-size distribution on the bed 

within a given reach by applying mass conservation by grain size (i.e., the Exner equation), albeit in 

a substantially simplified manner. Thus, the rating curves can respond to changes in sediment 

supply with a formulation that is quite simple, computationally efficient, and easy to implement. 

The model is spatially discretized over long reaches (~ 50 km) as opposed to attempting to 

characterize the details of channel complexity. Herein, we present the details of this modeling 

approach and its application to the Colorado River below Glen Canyon Dam. We do not argue that 

the empirical parameters developed for the Colorado River have general applicability; rather, they 

are site-specific. However, the general modeling approach for accounting for changes in sediment 

supply in order to evaluate long-term changes in sediment budgets should have general 

applicability, particularly below dams where the flow regime and sediment supply are often 

dramatically altered (e.g. Schmidt and Wilcock, 2008). 

 We chose to develop this alternative approach as opposed to applying standard onedimensional morphodynamic modeling for several reasons. First, our approach is much simpler and 

thus more computationally efficient than typical one-dimensional models. Increases in computer 

power have made this less of an issue, and we acknowledge that standard 1D models can be applied 

to long reaches over multi-year time periods, but computational efficiency is still an advantage 

when considering a large number of alternative modeling scenarios with highly variable boundary 

conditions. Second, and probably more important, standard 1D models require information that is 

5
not readily available for our study site, namely detailed cross-sections and information on the spatial 

distribution of sand thickness and bed particle-size distributions (longitudinally). Our study site is a 

pool-rapid system with very complex channel geometry; attempting to model erosion and 

deposition within this complicated channel geometry is a difficult task, and likely not necessary for 

modeling multi-year sediment budgets over long reaches. Finally, our modeling approach builds on 

a previously developed unsteady discharge-routing model (Wiele and Smith, 1996) that also uses 

reach-averaging to deal with this complexity. This previously developed model can provide the 

required flows at the computational nodes and thus circumvent the need to model anew the detailed 

hydraulics, including critical-flow transitions that occur in rapids along the Colorado River in our 

study site. 

STUDY SITE 

 The modeling approach described in the next section was developed as part of our ongoing 

work on the Colorado River below Glen Canyon Dam (fig. 1). The construction of Glen Canyon 

Dam in the early 1960s substantially reduced 1) the supply of sand to Grand Canyon by trapping 

most of it in the upstream reservoir (Topping et al., 2000a), and 2) the capacity of the river to 

transport sand by reducing large flood peaks (Topping et al., 2003). In addition, although operation 

of the dam reduced the magnitude and frequency of floods during which most of the natural sand 

transport occurred in the Colorado River in Grand Canyon, dam operations have actually increased 

the duration of moderate discharges that can transport substantial amounts of sand (Topping et al., 

2003). The post-dam flow regime is illustrated in fig. 2 which shows the study period to which the 

model was applied (top, Sep-2002 through Mar-2009), several weeks of daily fluctuating flows 

including a transition between months when the release volume typically changes (middle), and an 

example of a “controlled flood” where flows above powerplant capacity are released with the 

primary goal of rebuilding eroded sandbars (bottom, see e.g. Schmidt, 1999). For a complete review 

6
of pre- and post-dam flow regimes refer to Topping et al. (2003). Note that we use the English unit 

for water discharge, cubic feet per second or cfs, herein because of its common use and acceptance 

within the Colorado River scientific, management, and recreational community. 

 Several attempts have been made at generalizing the post-dam sand budget in Grand 

Canyon, i.e., whether there is long-term erosion or accumulation in the various reaches below the 

major tributaries. The answer to this question has important implications for the sustainability of 

sand deposits in Marble and Grand Canyons (fig. 1), typically referred to as “eddy-sandbars” 

because they tend to form in recirculating eddies downstream from tributary debris fans (Schmidt, 

1990). Eddy-sandbars are considered a valued resource within the Glen Canyon Dam Adaptive 

Management Program (GCDAMP), a federal advisory committee established to advise the 

Secretary of the Interior on operations of Glen Canyon Dam (U.S. Department of the Interior, 

1996), for a variety of reasons: they are a fundamental element of the pre-dam riverscape; they 

provide areas for recreational use by river runners and hikers; they provide low-velocity, warm 

water habitat for potential use by juvenile native fish; they are the substrate for riparian vegetation; 

and they are a source of sand for upslope wind-driven transport that may help protect archeological 

resources (Draut and Rubin, 2007). The numerous studies of the post-dam sand budget have come 

to conflicting results about long-term erosion versus accumulation. However, recent work indicates 

that eddy-sandbars have been substantially eroded since construction of the dam and that this 

erosion has not been abated by enactment of the Record-of-Decision (ROD) operation of Glen 

Canyon Dam in the mid-1990s (U.S. Department of Interior, 1995, U.S. Department of Interior, 

1996) which constrained the allowable daily hydropower fluctuations. 

 The approach presented herein was designed specifically to bridge the gap between 

approaches that have previously been used to evaluate the post-dam sand budget. Randle and 

Pemberton (1987) used suspended-sand rating curves developed by Pemberton (1987) as the basis 

7
for the sand budgets used in development of the ROD, but it has subsequently been shown by 

Topping et al. (1999, 2000a) that sand transport rates are strongly dependent on tributary sand 

supply as well as water discharge. This dependence is illustrated in fig. 3 which shows changes in 

the relation between suspended-sand concentration and water discharge resulting from a flood on 

the Paria River (the first major tributary downstream from the dam) in October 2006 that delivered 

substantial quantities of sand directly to upper Marble Canyon (data are described in detail in a 

subsequent section). It is seen that sand concentrations (for a given discharge) are much greater 

during the tributary flooding and remain significantly higher than pre-flood levels after the tributary 

flooding recedes, indicating sand accumulation and fining of the bed sediment. Over time, this fine 

sediment is subsequently winnowed from the bed and concentrations decrease. 

 In addition to the rating curve model of Randle and Pemberton (1987), a variety of more 

complex numerical models have been developed and applied as well, including multi-dimensional 

models of specific eddy-sandbar sites (Wiele et al., 1996, 1999, Wiele, 1998, Wiele and Torizzo, 

2005) and a pseudo-one-dimensional, reach-averaged, multiple-particle size, sand-routing model 

(Wiele et al., 2007). While the Wiele et al. (2007) model has the potential for application to multiyear time scales, its complexity in terms of initial and boundary conditions dictate that it is more 

suitable to event-scale (e.g. weeks to months) applications. In contrast, the approach described 

herein was developed specifically to reduce the required input data and number of tunable 

parameters to facilitate multi-year simulations of sand flux, and thus help address the primary 

sediment-related question identified by program scientists at a knowledge assessment workshop 

held in July 2005 (Melis et al., 2006): “Is there a ‘flow-only’ (non-sediment augmentation) 

operation that will restore and maintain eddy-sandbar habitats over decadal time scales?” 

8
MODELING APPROACH 

 Because our approach was developed with a specific application in mind, there were several 

overarching goals guiding its development, as follows: 

1) The model should reproduce the basic processes of sand accumulation and fining of the bed 

during and immediately after tributary flooding, followed by erosion and bed coarsening 

during tributary quiescence (see fig. 3). 

2) The model should be simple enough to allow for multi-year simulations, potentially in a 

Monte Carlo framework to account for variability in hydrology and tributary sediment supply. 

3) The number of adjustable empirical model parameters should be as few as possible and, along 

with the initial/boundary conditions, be readily specifiable from available data sources and 

ongoing monitoring programs. 

 Our approach is similar to more standard formulations in that it relies on a relation between 

hydraulic variables (e.g. depth, velocity, shear stress, discharge) and sediment transport rate, and 

sediment mass conservation for computing erosion, deposition, and bed particle-size distributions. 

A large number of “transport relations” have been proposed over the past half century, for bed load, 

suspended load, and combined total load (e.g. ASCE, 1975, Yang, 1996), and most “general-use” 

morphodynamic models allow the user a choice between various relations. Most of the relations are 

formulated in terms of power-laws between transport rate, bed shear stress, and particle size, some 

with additional complexity to account for phenomena such as hiding and exposure. Our approach 

differs from the general-use models in that, instead of choosing an available transport relation, we 

have developed empirical rating-curve-type relations specific to the Colorado River below Glen 

Canyon Dam, as described below. 

9
 Rubin and Topping (2001, 2008) applied the transport relation formulation of McLean 

(1992) to a wide range of hydraulic conditions and particle size distributions and found that the 

results could be adequately generalized into the following form: 

K

b

J   DuC (1)

where C is suspended-sediment concentration, is shear velocity, Db is the median bed particle 

diameter, and J and K are empirical coefficients. For conditions with and without dunes and for 

wide and narrow bed particle size distributions, Rubin and Topping (2001) found that J ranges from 

3.5 to 5.0, and K ranges from -1.5 to -3.0. Application of eq. 1 on a site-specific basis requires 

estimation of the constant of proportionality and a model for shear velocity. The longitudinal shear 

velocity field in a pool-rapid system such as our study site can be quite complex, and we argue that 

the spatial variability is less important than changes with discharge for modeling broad-scale 

sediment budgets. Thus, we have assumed that shear velocity can be approximated as a power-law 

function of discharge. While this assumption is clearly not strictly correct, it is a reasonable 

approximation that facilitates achieving our stated goals. We also note that for steady, uniform flow, 

shear velocity goes as the square root of the depth-slope product, and at-a-station hydraulic 

geometry (e.g. Leopold and Maddock, 1953) suggests that this quantity can often be characterized 

by a power-law with discharge. Applying this assumption to eq. 1 and writing in terms of individual 

particle sizes (necessary for bed composition calculations as described below) yields: 

u

K

i

L  bii DAQFC (2)

where Q is water discharge, i denotes individual particle sizes, is the fraction of particle size i in 

the bed sediment ( ), and A is an empirical, site-specific constant (discussed further in the 

next section). Note that eq. 2 is a more general form of the classical sediment rating curve, the 

difference being that bed particle-size distributions are used to compute concentrations for 

Fbi

  1 Fb i

10
individual sizes (as opposed to for all particle sizes lumped together). To apply eq. 2, A, L, and K

must be estimated empirically on a site-specific basis; the advantage is that A and L can be 

estimated from measurements of concentration and discharge, two quantities that are routinely 

measured on many rivers. The parameter K is more difficult to specify, as discussed in the next 

section, but it should fall between -1.5 and -3.0 as per Rubin and Topping (2001). 

 Application of eq. 2 requires a method for computing changes in the bed-sediment particlesize distribution (i.e. ), and this is indeed the mechanism for simulating bed fining and 

coarsening in response to changing sediment supply, as outlined in modeling goal #2. For this we 

apply the active layer form of the Exner equation for bed sediment mass conservation (e.g. Parker et 

al., 2000), in a slightly simplified form. For our study site, which is a bedrock controlled canyon 

river, it is reasonable to approximate the mobile bed sediment, i.e. the active layer, as a relatively 

thin layer of sand overlying bedrock; this assumption is supported by data presented in the 

following section. Also, underwater video and time-lapse side-scan sonar movies (Rubin and Carter, 

2006) of the bed of the river within our study sites indicates the presence of sand-starved dunes (i.e. 

with gravel in the troughs) which further supports the assumption of complete mixing of the sand 

layer (though we note that complete sand “equilibrium” dunes and thick sand deposits in eddies 

without dunes also exist, such that complete mixing is an approximation). By assuming that the 

substrate (i.e. bedrock, gravel, cobble) is non-erodible and that the sand layer thickness (Hs) is 

equivalent to the active layer thickness (i.e. it is completely mixed and available to the flow), the 

Exner equation reduces to: 

Fbi

 

x

Q

t

H

B s s

p 

   1  (3)

   

x

Q FH

t

B si

p bis 

  

 1  (4)

where CQQ , , Q , B is channel width, and s   CC i  isiQC  p is bed porosity. Note that eq. 3 

is the result of integrating eq. 4 over the entire bed-sediment particle-size distribution since 

11
  1 Fbi and  . This formulation provides significant simplification over the standard 

Exner equation because it circumvents the need to keep track of substrate layering and associated 

size distributions. 

 QQ ssi

 The non-erodible substrate (bedrock, gravel, cobble) substrate limits transport from a reach, 

in a given time step, to the amount of sediment in the reach plus what comes into the reach during 

that time step (by grain size). Thus, if the potential transport rate of a size i is greater than what’s 

available for transport, the reach becomes exhausted of that size such that  0 and Fbi Ci  0 . It is 

well known that patches of river contain little or no sand (e.g. rapids, gravel bars). One way to 

account for this is with a “bed-sand area” correction factor in transport relations (i.e. eq. 2, see for 

example Topping et al., 2007b), however, this requires information on the area of the bed that is 

covered in sand and how these areas are distributed with respect to bed shear stress, as well as a 

mechanism for simulating changes presumably based on local hydraulics and sediment supply. 

Because our modeling approach does not incorporate the necessary local hydraulics, we have not 

attempted to include this effect. The bed sand area is effectively lumped into the “catch all” 

coefficient A in eq. 2, and thus remains constant for our simulations. Instead, we focus on 

accounting for changes in bed particle-size distribution, which has been shown to exert greater 

control on transport rates than bed sand area (Topping et al., 2007b). 

 The set of eq. 2-4 constitutes a model for , , and , so long as water discharge can be 

estimated or modeled independently. The boundary conditions are at the upstream boundary 

and major tributaries; required initial conditions are and for each reach. The final 

approximation of our modeling approach is that we apply the formulation to relatively long reaches, 

as opposed to attempting to discretize the river into short segments. This assumption sacrifices the 

ability to accurately model short-duration, localized, changes in concentration and bed particle-size 

Ci Hs

Hs

Fbi

Fbi

Qsi

12
distributions, such as that shown during the Paria River flood peak (squares) in fig. 3. That is, the 

spatial averaging will tend to “smooth out” these short duration effects while capturing the reach 

scale effects that have greater influence on the long term flux. However, it circumvents the need for 

detailed information on sand thickness and bed particle size within the reaches; instead, these 

parameters are lumped into reach-averages. Also, the empirical nature of eq. 1 dictates that it should 

only be applied at locations where data are available to estimate the empirical parameters (A, L, K). 

To this end, we applied the formulation to three reaches bracketed by sites where suspended-sand 

concentration, grain size, and water discharge are monitored. The three modeling reaches are shown 

geographically in fig. 1 and schematically in fig. 4 and are defined as follows: 1) upper Marble 

Canyon (UMC), from Lees Ferry/Paria River confluence to RM30; 2) lower Marble Canyon 

(LMC), from RM30 to RM61/Little Colorado River confluence; and 3) eastern Grand Canyon 

(EGC), from RM61/Little Colorado River confluence to RM87. For the model applications 

described herein upwind finite differences were used to solve eq. 3-4, with the following 

specifications: 15-minute time step, 20 particle sizes spaced logarithmically between 0.0625 – 2 

mm, B  80 m, and p  4.0 . While it is well known that channel width varies, for example, 

between pool and rapid, and by reach, and with discharge, these variations in channel width are 

relatively small in the study area and the use of a constant width is consistent with our reachaveraged approach. The implication is that variability in sand storage resulting from variability in 

channel width is not modeled. The following section describes specification of the remaining model 

parameters and initial/boundary conditions. 

ESTIMATION OF MODEL PARAMETERS 

 Application of the modeling approach requires specification of the coefficients in eq. 2, the 

initial sand thickness and bed material composition, and the incoming sediment flux (by particle 

13
size) from the Paria and Little Colorado Rivers (the primary tributaries), as well as estimates of 

water discharge at RM30, RM61, and RM87 (where fluxes are calculated). For the Colorado River 

below Glen Canyon Dam, a program of extensive suspended-sediment transport, bed material, and 

bathymetric surveying has been ongoing in various forms since approximately 1999, with previous 

periods of intensive monitoring as well including pre-dam years and during the high flows of the 

mid-1980s. One of the goals of this monitoring program is to construct reach-based sand budgets 

that are used to determine the timing of controlled flood releases from GCD for the purposes of 

rebuilding sandbars (Wright et al., 2005, Topping et al., 2006a). This monitoring program has 

provided the data necessary to implement the modeling approach, namely measurements of 1) 

suspended-sand concentration and water discharge at multiple sites, 2) tributary sand inputs, 3) sand 

thickness on the bed, and 4) bed particle size. 

 The time period of available high-resolution sand transport data extends from Sep-2002 

through Mar-2009. For purposes of model calibration and validation, this period was split roughly 

equally into two parts. The calibration period was from Sep-2002 through Mar-2006, and the 

validation period was from Apr-2006 through Mar-2009. Each period contains episodes of 

substantial tributary inputs from the Paria and Little Colorado Rivers, a range of fluctuating releases 

from Glen Canyon Dam, and a controlled flood release. The primary calibration parameter is the 

coefficient A in eq. 2; the calibration and validation procedure is described in detail below following 

definition of the boundary and initial conditions. 

Boundary conditions

 The main boundary condition requirements are size-specific sand fluxes from the major 

tributaries, the Paria and Little Colorado Rivers. Mainstem sand transport at Lees Ferry was 

assumed to be zero because the reach between the dam and Lees Ferry is substantially sanddepleted (Grams et al., 2007) such that measured concentrations at Lees Ferry are typically very 

14
low. For the Paria River, a U.S. Geological Survey (USGS) gage is located near the confluence with 

the Colorado River (09382000 Paria River at Lees Ferry, AZ) where water discharge and 

suspended-sediment concentration and particle-size measurements are made, primarily during 

floods, using standard USGS techniques (http://pubs.usgs.gov/twri/). The water discharge record is 

then used to estimate suspended-sand transport using both the suspended-sediment data and the 

model developed by Topping (1997). Because sand transport in the largely alluvial Paria River is 

essentially "flow regulated" with no systematic hysteresis in suspended-sand concentration during 

floods, a reach-averaged coupled flow and sediment transport approach is used. For the Little 

Colorado River, data from two USGS gages (09402000 Little Colorado River near Cameron, AZ, 

and 09402300 Little Colorado River above mouth near Desert View, AZ) were used to estimate 

sand transport rates using time-weighted suspended-sand rating curves. Daily mean water discharge 

and total cumulative sand flux for these two tributaries for the study period are shown in fig. 5. The 

tributary sand particle-size distributions were estimated by averaging the distributions from the 

available samples, and it was found that log-normal distributions (φ-scale) with 1.0 mm and D50 

 g  8.1 for the Paria and 2.0 the Little Colorado fit the data very well ( and D50  g are median 

diameter and geometric standard deviation, respectively). There are numerous ungaged tributaries 

entering the Colorado River along the study reach in addition to the Paria and Little Colorado 

Rivers. Recent monitoring data (not shown) indicate that ungaged inputs to upper Marble Canyon 

are about 10% of Paria inputs and are significantly larger than ungaged inputs to lower Marble 

Canyon and eastern Grand Canyon. Thus, for modeling purposes we increased inputs to UMC by 

10% and neglected the ungaged inputs to the LMC and EGC reaches. We note that these estimates 

are different from (somewhat less than but within the error bars) those published by Webb et al. 

(2000); we chose to use the more recent estimates because they are based on direct measurements of 

15
suspended-sediment transport whereas the Webb et al. (2000) estimates were made using indirect 

methods. 

 Water-discharge time series must also be specified at the downstream end of each reach (i.e. 

at RM30, RM61, RM87) for application of eq. 2. For the modeling period, discharge was estimated 

at each site from 15-minute stage measurements and stage-discharge relations based on episodic 

discharge measurements. For modeling potential future scenarios, the water discharges could be 

routed downstream from the dam to the computational sites using the model of Wiele and Smith 

(1996). 

Initial conditions

 Solution of eq. 3-4 requires specification of the initial sand thickness and initial bed particlesize distribution, for each of the three reaches. To estimate these quantities, we used data from 

reach-based monitoring program implemented from 2000 – 2005. This program consisted of remote 

sensing, ground surveys, and bathymetric surveys (Kaplinski et al., 2009, Hazel et al., 2008) and 

bed particle-size measurements (using digital photographic techniques, Rubin, 2004, Rubin et al., 

2007) for several 3-5 km reaches between Lees Ferry and RM87. The reach surveys closest in time 

to the beginning of the modeling period were conducted in May 2002. Thus, we averaged the 

available May 2002 sand thickness and particle-size data (M. Breedlove, Grand Canyon Monitoring 

and Research Center, written communication) within each modeling reach resulting in thicknesses 

of 0.4, 0.5, and 0.5 m and mean particle sizes of 0.4, 0.3, and 0.3 mm for UMC, LMC, and EGC, 

respectively. The sand thicknesses were estimated by differencing the maximum and minimum 

surfaces in sandy areas and thus represent the amount of erosion and accumulation that took place 

during the monitoring period. The digital photographic technique provides a mean particle size of 

the bed surface only; the initial size distributions were estimated by assuming log-normal 

16
distributions with  g  2.0 (estimated from available grab samples from the gage locations). The 

initial conditions are summarized in table 1. 

Transport relation parameters

 Three parameters (A, L, and K) must be specified to apply eq. 2, on a site-specific basis. We 

estimated these parameters using the high-resolution (every 15 minutes) suspended-sediment 

monitoring data from the three monitoring sites. This monitoring program uses a combination of 

standard USGS techniques and “surrogate” technologies, including laser diffraction and 

hydroacoustic scattering. These techniques are described in detail elsewhere (Melis et al., 2003, 

Topping et al., 2004, 2006b, 2007a), and the data are available on-line at 

http://www.gcmrc.gov/products/other_data/. Figure 6 shows suspended-sand concentration versus 

water discharge for the study period (Sep-2002 to Mar-2009) for the three monitoring sites. These 

data further illustrate the range in sand concentration for a given discharge due to changes in the 

upstream supply. Also shown in fig. 6 are power-law curves based on our empirical estimates of the 

discharge exponents (L in eq. 2); the data indicate a break in the curve for each site at about 25,000 

cfs (Randle and Pemberton, 1987, also noted this break), and we have incorporated this break by 

using two sets of exponents. The exponents were estimated by power-law curve fitting to the rising 

and falling limbs of the high flow releases conducted in 2004 and 2008. This approach was used 

because these periods encompass nearly the full range of discharge over the study period, and are 

also of short duration (< 1 day) such that the effects of changes in supply should be relatively small. 

The exponents, for above and below 25,000 cfs, are given in table 1. We chose to estimate L based 

on total sand concentration, as opposed to using particle-size specific concentrations, because this 

latter approach would require a priori knowledge of the exponent K (discussed further below). The 

exponents for below 25,000 cfs are likely greater than what would be expected for uniform flow 

over a spatially-constant bed particle-size distribution. Under this assumption, the exponents should 

17
be approximately 2 assuming shear velocity goes as the square root of discharge which is a 

reasonable assumption for our gage locations. This is the result of the complex organization of bed 

shear stress and bed particle-sizes in the pool-rapid system of the Colorado River (for example, as 

flow goes up it accesses finer particle sizes along the channel margins and in eddies). 

 The particle size exponent in eq. 2 (K) is more difficult to estimate empirically because it 

requires data on reach-averaged particle size distributions and particle-size-specific transport rates. 

However, Rubin and Topping (2001) reported a range of computed exponents of -1.5 to -3.0, thus 

providing a range of reasonable values. We conducted exploratory simulations and evaluated the 

results, particularly in terms of the degree of bed fining and coarsening that occurred for a given Kvalue. It was found that a value on the high end of the reasonable range was necessary to achieve 

the degree of fining and coarsening that has been observed (particularly during the high flow 

releases), and thus we chose a value of K   0.3 . It is perhaps not surprising that an exponent that 

tends to accentuate particle size dependence is necessary, given the reach-averaged nature of the 

model and assumption of complete mixing of the bed sediment. 

 There are several options for estimating the remaining coefficient in eq. 2, the 

proportionality constant A. Because the ultimate goal of our modeling is to predict multi-year sand 

budgets for the individual reaches, we chose to calibrate A at each gage location in order to match 

the measured total sand flux from the reach over the calibration time period, Sep-2002 through Mar2006. These computations proceeded in a downstream direction, whereby trial-and-error was used 

for A until the total sand flux from the reach matched the measured sand flux to within <1%. The 

resulting A coefficients are given in table 1. The form of eq. 1 and its empirical nature dictate that 

the coefficients are not dimensionless and are a combination of various units to different powers. 

The values of A given in table 1 are such that, when applied to eq. 2 with Q in m3

/s and Di in m, the 

resulting Ci is a volumetric concentration. Finally, the fact that A is such a small number is simply 

18
the result of the units used in its determination; concentration is linearly related to A (eq. 2) and it 

thus has a direct influence on modeled sand fluxes. 

ANALYSIS AND DISCUSSION OF RESULTS 

 Several measures can be used to evaluate the model’s performance, during both the 

calibration and validation time periods. Because the model was calibrated to match the total sand 

flux from each reach over the calibration period (through specification of A), it is appropriate to 

evaluate how well the model predictions agree with the measurements over shorter time scales 

within the calibration period. The validation time period provides an independent test of the model 

calibration. In particular, as stated in our overall modeling goals, the model should be able to 

simulate sand accumulation and bed fining in response to tributary flooding, followed by erosion 

and coarsening. Both the calibration and validation periods contain episodes of sand accumulation 

and bed fining, followed by high flow releases wherein substantial coarsening occurred. Substantial 

tributary flooding and sand inputs occurred during fall 2004, winter 2005, fall 2006, and fall 2007 

(fig. 3). High flow releases occurred in Nov-2004 and Mar-2008 (fig. 2). 

 An initial test of model performance is a comparison of the total sand flux at each 

monitoring site during the validation period, since the model was calibrated to match the total fluxes 

during the calibration period. Table 2 shows percent differences between modeled and measured 

fluxes over the validation period. The differences are 11%, 0.70%, and -4.6% for RM30, RM61, 

and RM87, respectively. Though the model over-estimates the flux at RM30 by 11%, it is a 

substantial improvement over a stable sand rating curve which under-estimates this flux by 37% 

because it cannot incorporate bed fining due to large Paria River flooding in Oct-2006. A variety of 

reasons could explain the model over-estimates for this reach, including the various model 

simplifications as well as uncertainty in the tributary inputs (which control the degree of bed 

fining). The measured and modeled cumulative sand fluxes for the entire study period for each of 

19
the three monitoring sites are shown in fig. 7 (note that the calibration procedure forces these to 

match at the end of the calibration period). The measurement uncertainty has been estimated to be 

±5% as per Topping et al. (2000a) and this envelope is included in fig. 7. 

Monthly sand flux and annual sand budgets

 Water discharge varies substantially on a monthly basis below Glen Canyon Dam in order to 

meet hydroelectricity demand; that is, release volumes are highest in the summer and winter when 

demand is highest and lowest in spring and fall. Thus, a potential application of the model would be 

to compare monthly sand flux for a range of release volumes. To this end, measured and modeled 

monthly sand fluxes for the three sites are compared in fig. 8 for both calibration and validation 

periods. While the model captures the general behavior well, there is substantial variability and 

some indication of model over-estimation at the lowest fluxes particularly at RM87. The modeled 

and measured monthly fluxes are compared numerically in table 2, where R is the ratio of modeled 

to measured monthly flux. In table 2, values for the validation period are shown in parentheses 

alongside those for the calibration period, for comparison. A very high percentage (~90%) of the 

modeled monthly fluxes are within a factor of 2 of the measurements, for both calibration and 

validation time periods. The percentage of modeled fluxes within a factor of 1.5 of the measured 

values ranges from 56% (RM61) to 79% (RM30) for the calibration period (the agreement at RM30 

and RM87 is generally better than at RM61). The agreement during the calibration period is 

generally slightly better than during the validation period, as expected, though there in a couple 

instances the agreement is better during the validation period. It is again seen that the model is 

superior to the stable sand rating curve approach, as expected. 

 One of the main goals outlined for the model is the ability to simulate the sand budget over 

annual to decadal time scales. To this end, fig. 9 compares the measured and modeled annual sand 

budgets for each of the three reaches. The sand budget is defined as the sand inputs to the reach 

20
minus the sand export (fig. 4), i.e. the annual change in storage on a mass basis. The model proves 

capable of reproducing periods of substantial accumulation as well as erosion (during both 

calibration and validation time periods), an important test for the model. The modeled sand budgets 

are primarily a test of the modeled annual sand fluxes, since inputs are a specified boundary 

condition. Table 2 summarizes the ratios of measured to modeled annual sand flux (R) for the three 

sites; the median ratios are near one and all years have ratios within a factor of 1.5. 

Accumulation/fining and erosion/coarsening

 The monthly and annual comparisons, in particular the comparison with a stable sand rating 

curve approach, indicate that the model is capable of simulating sequences of sand accumulation 

and bed fining followed by erosion and bed coarsening. This is further illustrated in fig. 10 which 

shows the modeled sand thickness (top), median bed particle size ( , middle) and cumulative 

sand budget (bottom) for the upper Marble Canyon reach. The figure also contains available 

measurements of sand thickness and bed , as well as the measured cumulative sand budget (data 

sources are described in the previous section). Several examples of accumulation and fining 

followed by erosion and coarsening are apparent. The most significant accumulation and fining 

occurred during Paria River flooding in October 2006 (see fig. 2), which resulted in more than 

 metric tons of sand accumulation in the reach (fig. 10 bottom). The model simulation 

indicates a 25 cm increase in sand thickness and corresponding decrease in bed from about 

0.40 to 0.25 mm (no measurements of sand thickness or bed are available for this time period). 

For time periods with available sand thickness and bed measurements (2002 – 2004), the 

model is in agreement in terms of the overall trends but not in terms of the magnitudes (fig. 10 top, 

middle). The measurements exhibit greater variability, particularly in the period leading up to and 

following the Nov-2004 high flow release. The measurements indicate greater accumulation and 

D50

D50

6 101

D50

D50

D50

21
fining followed by greater erosion and coarsening than the model. This could be due to the fact that 

the measurement reaches constitute only a small percentage of the entire reach (and thus may 

represent the overall trend but not the magnitude), or could be a result of the reach-averaging and 

assumption of complete mixing of the bed sand layer (which tends to smooth out rapid changes). 

Likely, it is a combination of these and other factors. It is also noteworthy that sand thickness (fig. 

10 top) and bed D50 (fig. 10 middle) are near mirror images of each other. This is a direct result of 

the assumption of complete bed mixing, which dictates that processes such as erosion through a 

coarse surface layer into finer material are precluded. However, the model does not impose a unique 

relation between sand thickness and bed-sand D50. For example, two tributary inputs of the same 

magnitude and particle-size distribution, without any coarsening in between, will result in different 

degrees of bed fining because the new tributary sand is mixing with a progressively finer bed (i.e. 

the 2nd tributary flood would result in the same increase in sand thickness as the 1st flood, but 

proportionately less fining since it’s mixing with an initially finer bed). 

 The controlled flood releases in Nov-2004 (during the calibration period) and Mar-2008 

(during the validation period) provide excellent tests of the model’s ability to simulate sand erosion 

and coarsening of the bed. Though these releases are designed to facilitate deposition in 

recirculating eddies and associated sandbars, they necessarily export significant amounts of sand 

from the system and substantially coarsen the bed of the river (Topping et al., 1999, 2006a) over a 

short period of time (days). Coarsening of the bed during the flood peak is reflected in decreasing 

suspended-sand concentrations while water discharge is constant, indicating winnowing of the 

finest sizes leaving behind the coarser sizes that are less transportable. This effect is illustrated in 

fig. 11 which shows measured and modeled suspended-sand concentrations for the three sites for 

the two high flow releases that occurred during the study period. Note that all panels have the same 

y-axis scale which illustrates the differences in sand supply preceding the events and the models’ 

22
ability to simulate these differences. In general, the model does a very good job of simulating the 

coarsening of the bed and resulting decrease in suspended-sand concentration during the flow peak 

(the Mar-2008 hydrograph is shown in fig. 2; the Nov-2004 hydrograph was nearly identical). There 

is a general tendency, however, for the model to under-estimate the concentrations on the rising 

limb of the hydrograph, as well as the peak concentration. One possible explanation for this is the 

inability of the model to account for variations in bed particle size with elevation within the 

channel; i.e. bed-sand particle size tends to be coarsest in deeper parts of the channel and finest in 

higher elevation deposits such as eddy sandbars (Topping et al., 2005). This structure is to some 

degree embedded in the rating curve exponents; however it is not treated explicitly in the modeled 

particle size distribtions and would require a significantly more complex formulation. Several other 

explanations are possible as well, such as unsteady transport process, local hydraulics (particularly 

in eddies), breaking of “armor layers” that release finer sand, among others. 

SENSITIVITY ANALYSIS 

 Because of the simplified and empirical nature of the modeling approach, it is instructive to 

evaluate the sensitivity of the model results to the various model parameters that must be specified, 

include boundary and initial conditions. To this end, we conducted a suite of simulations with the 

following parameters varied by ±10%: 1) tributary sand loads (Paria and Little Colorado); 2) 

tributary sand D50; 3) initial sand thickness on the bed (Hs); 4) initial bed D50; 5) rating curve 

coefficient (A in eq. 2); 6) discharge exponent (L in eq. 2); 7) bed-sand particle-size exponent (K in 

eq. 2), and 8) channel width (B). The choice of ±10% is arbitrary to some degree and does not 

necessarily represent uncertainty in the various parameter (the uncertainty is unknown). Rather, the 

±10% is simply a reasonable perturbation to impose on the model in order to study its sensitivity. 

Imposing the same relative perturbation for all parameters allows for evaluation of the relative 

23
sensitivity to each parameter and can thus provide guidance on, for example, which parameters 

warrant further study and measurements. 

 Model sensitivity was evaluated by comparing the sand flux at each gage for the ±10% runs 

with that of the calibrated model (total flux over the simulation period (Sep-2002 though Mar2009). While each parameter influences the model in different and complex ways, comparison of 

total fluxes is the simplest, most direct, and most relevant method because simulation of multi-year 

sand flux is the primary objective of the model. The results are displayed in figure 12, in terms of 

percent differences between the sensitivity runs and the calibrated model, for the three gage 

locations. From the figure it is immediately apparent that the rating-curve exponents (L and K in eq. 

2) exert, by far, the greatest control on the model results. The ±10% perturbation introduced in these 

exponents results in differences in total flux at the gages ranging from ~50-100%, depending on the 

site. In contrast, all other parameters yield differences that are less than the ±10% perturbation. 

Tributary loads, tributary D50, initial bed D50, and the rating coefficient (A) all yield differences in 

the 3-7% range, while initial sand thickness and channel width had almost no effect on the results 

(differences <0.5%). 

 It is perhaps not surprising that the exponents exert such strong influence, given that they are 

substantially greater than one resulting in a highly non-linear response in sand concentration with 

changes in discharge and particle size. This sensitivity supports our approach of directly calibrating 

the rating coefficient A to match measured loads; without this type of calibration large differences in 

loads could easily occur. It is also instructive for sediment-transport modeling in general, because 

any model must incorporate a similar sediment-transport formula whereby concentration or flux is 

dependent on hydraulic variables (and particle size) in a highly non-linear way (for example, the 

Rouse equation with a near-bed concentration predictor). Thus, some calibration of concentration or 

24
flux (directly or through shear-stress partitioning) is likely always necessary for sediment-transport 

modeling of this type. 

LIMITATIONS OF THE APPROACH 

 The modeling approach that we have developed and applied is empirical in nature and 

substantially simplified with respect to the physical processes known to govern sediment transport 

in the study reach. The empiricism and simplifications were necessary to meet the primary goal of 

the modeling, i.e. the ability to simulate the long-term (decadal scale) sand budget for the reach with 

only one adjustable calibration parameter. The consequences of the simplifications have been noted 

throughout this article, but warrant summary here so that potential users of this approach have a 

clear understanding of the limitations, as follows: 

• Though the approach should have general applicability to supply-limited rivers, and 

particularly those where complete bed mixing is a reasonable approximation, the model 

coefficients (table 1) are specific to the study reach and thus do not have general applicability. 

• The model integrates the pool-rapid-eddy morphology over long reaches, and thus should not 

be expected to capture the specific effects of this morphology on sediment transport. For 

example, the model cannot discriminate between sand on the main channel bed and sand within 

eddy-sandbars. 

• The model does not account for changes in the area of sand covering the bed at a given time. 

This phenomenon is essentially lumped in the calibration of the rating curve coefficient A. 

Thus, application of the model to conditions where large changes in bed sand area might be 

expected (e.g. long-term substantial accumulation) must be viewed with some caution. 

• Though the model uses a short (15-min) time step in order to capture the sub-daily variability 

in flow, it should not be expected to capture rapid changes in bed particle size and suspendedsand concentration, for example during tributary flooding (e.g. fig. 3). The use of long reaches 

25
and assumption of complete mixing of the bed sediment tends to “smooth out” these rapid 

changes. To capture the type of short-term response shown in fig. 3 (squares), an unsteady, 

advection-dispersion approach for suspended-sediment would likely be required. 

• The model cannot capture variability in particle size as a function of elevation within the 

channel that is known to exist, i.e. the river bed is coarser in the deeper main channel than in 

shallower eddy environments. The model lumps all sand deposits into a single pool (for each 

reach) that is completely mixed. 

• The model cannot simulate a scenario where a coarse surface layer temporarily precludes 

access to a finer substrate. This is thought to have happened following the extremely high 

flows of the mid-1980s, after which transport rates gradually increased for a given discharge 

despite a likely negative sand budget. This behavior was presumably a result of morphologic 

adjustments of eddy-sandbars following the high flows (Topping et al., 2005). The assumption 

of completely mixed bed sediment precludes simulation of this behavior. 

 Because of these limitations, we consider the modeling approach as one that should be used 

in concert with an ongoing monitoring program allowing for ongoing evaluation of the calibration 

parameter A. Indeed, the empirical nature of the transport relation requires at least some monitoring 

data in order to specify the model parameters. The model, as with almost all models, was designed 

with the intent to forecast future conditions for various hydrological and management scenarios. 

However, because of the empirical nature and inherent limitations, the approach and results should 

be routinely evaluated and adjusted as necessary as new data become available. Ideally, this is the 

approach that should be taken with all simulation models, but it is particularly important for the 

approach described here. 

26
CONCLUSIONS 

 The modeling approach described herein represents a compromise between a desire for 

model simplicity, in order to limit input data requirements as well as facilitate multi-year 

simulations of a large number of scenarios, and the need to capture a fundamental mechanism 

controlling transport rates in the study reach, i.e. supply-driven changes in bed particle size and 

suspended-sediment concentration. In the spectrum of sediment-transport models, it lies between 

suspended-sediment rating curves and standard one-dimensional, multiple-particle-size, 

morphodynamic models. The approach was formulated specifically for sand supply-limited 

conditions, in particular the conditions along the Colorado River below Glen Canyon Dam where 

the relation between suspended-sand concentration and water discharge strongly depends on sand 

supply from tributaries downstream from the dam. A primary objective of the modeling approach 

was the ability to simulate multi-year sediment budgets, perhaps in a Monte Carlo framework to 

account for variability in hydrology and tributary sediment supply. Achieving this objective 

required various simplifications and empiricism, as summarized in the previous section. The 

proposed formulation certainly achieved this objective as the approximately 7-year simulations 

described herein took only ~30 seconds on a standard desktop computer. 

 The model was applied to the reach of the Colorado River below Glen Canyon Dam for the 

period Sep-2002 through Mar-2009. The model was calibrated such that the total sand flux from 

each of the three modeling reaches matched the measured total flux during the calibration time 

period (i.e. the first 3.5 years of the simulation). Comparisons between measured and modeled 

monthly sand fluxes and annual sand budgets showed the model capable of simulating the 

variability in sand flux resulting from discharge variability as well as changes in sand supply. 

Model comparisons to data were generally comparable during the calibration and validation time 

periods. Comparisons of measured and modeled bed sand thickness and bed confirmed the D50

27
models’ ability to simulate accumulation of sand accompanied by bed fining during and 

immediately following tributary flooding, followed by erosion and bed coarsening during tributary 

quiescence. Comparisons of measured and modeled suspended-sand concentrations during the high 

flow releases in Nov-2004 and Mar-2008 indicate that the model can adequately simulate bed 

coarsening during the peak flows, but tends to under-estimate suspended-sand concentration on the 

rising limb of the high flow hydrograph. The model was also shown to provide significant 

improvement over a stable suspended-sand rating curve approach for our study site, as expected. 

Analysis of model sensitivity to input parameters illustrated strong dependencies on the rating curve 

exponents (discharge and particle size), thus providing support for our procedure of direct 

calibration of the rating curve coefficient to match measured loads. Finally, these comparisons 

provide confidence in application of the model to forecast future conditions under various dam 

operation scenarios, for example to estimate how much accumulation or erosion might occur for a 

given dam operation and tributary supply. This information could then potentially be used to plan 

future high flow releases designed to rebuild sandbars. 

 As formulated, the modeling approach should have general applicability to supply-limited 

rivers, particularly those where the assumption of complete bed mixing is appropriate such as many 

rivers flowing through bedrock canyons. However, the empirical model parameters (i.e. table 1) are 

not expected to have general applicability, but must rather be estimated on a site-specific basis. 

Thus, this type of approach can only be applied to river reaches where sufficient data are available 

to estimate the model parameters. Also, given the simplified and empirical nature of the approach, 

applications will be most successful if conducted within the context of an ongoing monitoring 

program so that the results can be evaluated on a regular basis and, if necessary, the formulation can 

be modified to account for new findings related to sand transport processes within the river. 

28
REFERENCES 

ASCE (1975). Sedimentation Engineering, V.A. Vanoni, ed., New York. 

Draut, A.E. and Rubin, D.R., 2007. The Role of Aeolian Sediment in the Preservation of 

Archaeological Sites in the Colorado River Corridor, Grand Canyon, Arizona: Final Report on 

Research Activities, 2003–2006, U.S. Geological Survey Open-File Report 2007-1001. 

Grams, P.E., Schmidt, J.C., Topping, D.J., 2007, The rate and pattern of bed incision and bank 

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Table 1 – Initial conditions for the reaches and model parameters at the computation/monitoring 

sites. 

UMC/RM30 LMC/RM61 EGC/RM87 

Initial Hs (m) 0.4 0.5 0.5 

Initial (mm), D50  g 0.4, 2.0 0.3, 2.0 0.3, 2.0 

L, below 25,000 cfs 3.7 4.0 3.7 

L, above 25,000 cfs 1.7 1.7 1.3 

K -3.0 -3.0 -3.0 

A1 26 103.4   27 102.6   26 101.6  

1

 coefficients yield Ci as a volumetric concentration for Q in m3/s and Di in m (see eq. 2) 

Table 2 – Model-result statistics for the fluxes at the computation/monitoring sites. 

RM30 RM61 RM87 RM30 stable 

% difference in total sand flux, 

validation period 11% 0.70% -4.6% -37% 

Monthly flux statistics (n = 43 months for calibration, 36 months for validation) 

median R 1.03 (1.23)1 1.15 (1.34) 1.17 (1.08) 0.89 (0.64) 

 % of months with 0.5<R<2 93 (100) 88 (86) 98 (97) 86 (67) 

% of months with 0.67<R<1.5 79 (72) 56 (61) 74 (67) 56 (42) 

Annual flux statistics (n = 7 years) 

median R 0.90 0.94 1.0 N/A 

range in R 0.69 – 1.15 0.71 – 1.24 0.84 – 1.11 N/A 

1

 first value is calibration, value in parentheses is validation 

33
Figure 1 – Colorado River below Glen Canyon Dam. Lees Ferry is designated river-mile 0 and is 

about 15 miles downstream from Glen Canyon Dam. RM30, RM61, and RM87 denote locations of 

monitoring sites and are labeled according to river miles downstream from Lees Ferry (i.e. RM30 is 

approximately thirty river miles downstream). The Paria and Little Colorado Rivers are the primary 

sand-supplying tributaries. 

Figure 2 – Examples of the flow regime below Glen Canyon Dam. Top: Sep-2002 through Mar2009, which is the entire period of model application. Middle: Daily fluctuating flows in the spring 

and summer of 2006. Bottom: Controlled flood release hydrograph from March 2008. 

Figure 3 – Left: Suspended-sand concentration versus water discharge for the RM30 gage (all data - 

gray dots) and for three days before (circles), during (squares), and after (triangles) Paria River 

flooding during October 2006. Right: Paria River daily mean discharge showing the dates of the 

highlighted data. 

Figure 4 – Schematic diagram of the three modeling reaches indicating sand inputs and export from 

each reach. UMC, LMC, and EGC refer to upper Marble Canyon, lower Marble Canyon, and 

eastern Grand Canyon, respectively (see fig. 1). 

Figure 5 – Top panels: Daily mean discharge for the Paria (left) and Little Colorado (right) rivers 

during the study period. Bottom panels: Cumulative sand fluxes into the mainstem Colorado River. 

Tmt denotes thousand metric tons. X-axis ticks are at the beginning of each water year (Oct-1). 

Figure 6 – Suspended-sand concentration versus water discharge as measured at the 3 monitoring 

sites between Sep-2002 and Mar-2009, and relations derived from eq. 2 with the exponents given in 

table 1. 

Figure 7 – Comparison of measured and modeled cumulative sand fluxes at the 3 monitoring sites 

for the entire modeling period (calibration and validation). Measured fluxes are shown as an 

envelope with ±5% uncertainty (Topping et al., 2000a). For RM30, the model results using a stable 

rating curve are also shown. 

Figure 8 – Comparison of measured and modeled monthly sand fluxes at the 3 monitoring sites 

(RM30 – top, RM61 – middle, RM87 – bottom) for the calibration and validation periods, line 

indicates perfect agreement. Statistics are given in table 1. 

Figure 9 – Comparison of measured and modeled annual sand budgets for the three reaches. The 

annual sand budget is defined as sand inputs minus export from the reach (based on water year), i.e. 

the change in storage on a mass basis. 

Figure 10 – Time series of measured and modeled sand thickness (top), bed median particle size 

(middle), and cumulative sand budget (bottom) for the upper Marble Canyon (UMC) reach. Data 

sources are described in the text 

Figure 11 – Comparison of measured (circles) and modeled (solid black lines) suspended-sand 

concentration at the three monitoring sites during high flow releases in Nov-2004 (during 

calibration period) and Mar-2008 (during validation period). The high flow hydrographs are shown 

light solid lines in each panel. 

34
35

Figure 12 – Results of model sensitivity analyses for the three gage sites. The y-axis portrays the 

percent difference between the given scenario and the fully calibrated model, for variations in each 

parameter of ±10%.