Calculated Hydrographs for Unsteady 

Research Flows at Selected Sites Along 

the Colorado River Downstream from 

Glen Canyon Dam, Arizona, 1990 and 1991

By Eleanor R. Griffin and Stephen Mark Wiele

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 95 4266

Prepared in cooperation with the 

BUREAU OF RECLAMATION

Boulder, Colorado 

1996
CONTENTS

Page

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

Introduction.............................................................................................^^ 1

Description of the flow model.................................................................................................................... 3

Steady inflow from tributaries............................................................................................................... 5

Unsteady inflow from tributaries.......................................................................................................... 6

Data from streamflow-gaging stations............................................................................................ 6

Data from stage-gaging stations...................................................................................................... 9

Timing of unsteady inflows............................................................................................................. 10

Comparison of model-calculated hydrographs with computed hydrographs............................................. 15

Summary and conclusions .......................................................................................................................... 28

References cited.......................................................................................................................................... 30

FIGURES

1. Hydrograph showing discharge for an unsteady flow release

from Glen Canyon Dam..................................................................................................... 2

2. Map showing locations of streamflow-gaging stations, Colorado River

through Marble and Grand Canyons .................................................................................. 3

3. Graph showing unsteady discharge from the Little Colorado River during

research flow C................................................................................................................... 7

4. Calculated hydrographs and hydrographs determined from stage records and the

stage-discharge relations at streamflow-gaging stations for research flow C.................... 8

5. Graph showing unsteady tributary discharge during research flow E.................................... 9

6 Calculated hydrographs and hydrographs determined from stage records and the

stage-discharge relations at streamflow-gaging stations for research flow E .................... 10

7. Graph showing unsteady tributary discharge during research flow Fl.................................. 11

8. Calculated hydrographs and hydrographs determined from stage records and the

stage-discharge relations at streamflow-gaging stations for research flow Fl................... 12

9. Graph showing stage recorded during research flow C at stage-gaging stations ................... 14

10 16. Calculated hydrographs and hydrographs determined from stage records and the 

stage-discharge relations at streamflow-gaging stations for:

10. Research flow A............................................................................................................. 16

11. Research flow B............................................................................................................. 17

12. Research flow C............................................................................................................. 18

13. Research flow D............................................................................................................. 19

14. Research flow E ............................................................................................................. 20

15. Research flow Fl............................................................................................................ 21

16. Research flow Gl........................................................................................................... 22

Contents ill
FIGURES Continued Page

17 18. Calculated hydrographs and hydrographs determined from stage records and the 

stage-discharge relations at streamflow-gaging stations for:

17. Research flow F2............................................................................................................ 23

18. Research flow G2........................................................................................................... 24

1 9 21. Graphs showing:

19. Calculated and measured rates of discharge increase and decrease

as a function of distance downstream for research flows A-G2 ............................... 25

20. Calculated and measured peak and trough discharges as a function of

distance downstream for research flows A-G2 ......................................................... 27

21. Calculated and measured wave travel time from Glen Canyon Dam and the

model average absolute error for research flows A-G2 ............................................ 29

TABLES

1. Dates and characteristics of the daily releases from Glen Canyon Dam

for the unsteady research flows ................................................................................................. 2

2. Selected locations for calculated hydrographs and distance from Lees Ferry, Arizona.................. 4

3. Gaged tributaries of the Colorado River between Glen Canyon Dam and

Diamond Creek.......................................................................................................................... 5

4. Amount and location of steady inflows used for model hydrograph calculations.......................... 7

5. Stage-gaging stations along the Colorado River between Glen Canyon Dam and

Diamond Creek.......................................................................................................................... 13

6. Average absolute error and percent error of the calculated time for a given 

discharge at five streamflow-gaging stations downstream from 

Glen Canyon Dam..................................................................................................................... 20

CONVERSION FACTORS

Multiply By To obtain

meter (m) 3.281 foot

square meter (m2) 10.76 square foot

kilometer (km) 0.6214 mile

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

IV Contents
Calculated Hydrographs for Unsteady Research 

Flows at Selected Sites Along the Colorado River 

Downstream from Glen Canyon Dam, Arizona, 

1990 and 1991

By Eleanor R. Griffin and Stephen Mark Wiele

Abstract

A one-dimensional model of unsteady discharge waves was applied to research flowr that 

were released from Glen Canyon Dam in support of the Glen Canyon Environmental Studies. 

These research flows extended over periods of 11 days during which the discharge followed 

specific, regular patterns repeated on a daily cycle that were similar to the daily releases for power 

generation. The model was used to produce discharge hydrographs at 38 selected sites in Marble 

and Grand Canyons for each of nine unsteady flows released from the dam in 1990 and 1991. In 

each case, the discharge computed from stage measurements and the associated stage-discharge 

relation at the streamflow-gaging station just below the dam (09379910 Colorado River Hlow 

Glen Canyon Dam) was routed to Diamond Creek, which is 386 kilometers downstream. Steady 

and unsteady tributary inflows downstream from the dam were included in the model calculations.

Steady inflow to the river from tributaries downstream from the dam was determined for each 

case by comparing the steady base flow preceding and following the unsteady flow measured at 

six streamflow-gaging stations between Glen Canyon Dam and Diamond Creek. During three 

flow periods, significant unsteady inflow was received from the Paria River, or the Little Colorado 

River, or both. The amount and timing of unsteady inflow was determined using the discharge 

computed from records of streamflow-gaging stations on the tributaries. Unsteady flow then was 

added to the flow calculated by the model at the appropriate location.

Hydrographs were calculated using the model at 5 streamflow-gaging stations downstream 

from the dam and at 33 beach study sites. Accuracy of model results was evaluated by comparing 

the results to discharge hydrographs computed from the records of the five streamflow-gaging 

stations between Lees Ferry and Lake Mead. Results show that model predictions of wave speed 

and shape agree well with data from the five streamflow-gaging stations.

INTRODUCTION other flows were steady. Several of the research

flows varied between the same maximum and

T ir. j ir.ru i u a minimum discharges but differed in the rates of In 1990 and 1991, twelve research flows were . . , j ,. , ,

i j iv ^ T^ _.r-xi_ increasing and decreasing discharge (ramping released from Glen Canyon Dam in support of the v °

Glen Canyon Environmental Studies (GCES;

table 1). Nine of these flows were unsteady flows, The purpose of the research flows ws to 

which fluctuated between a specified minimum and enable scientists and engineers to study the effects 

maximum discharge on a daily cycle (fig. 1). The of various controlled flow conditions or the

Abst act 1
Table 1 . Dates and characteristics of the daily releases from Glen Canyon Dam for the unsteady research flows

[Discharge was computed from the record of the streamflow-gaging station, 09379910 Colorado River below Glen Canyon Dam. Up-rarrn rate is 

the maximum rate of increase in dam releases on the rising limb of the daily hydrograph, and down-ramp rate is the maximum rate of decrease of 

dam releases on the falling limb]

Periods of releases

Research 

flow From

A............

B............

r

D............

E. ...........

Fl...........

Gl ..........

F2...........

G2..........

10-01-90

01-28-91

12-31-90

05-06-91

09-17-90

07-16-90

07-02 90

07-15-91

07-01-91

To

10-11-90 

02-07-91 

01 10-91

05-16-91 

09-27-90 

07-26-90 

n? i O on

07-26-91 

07 11-91

Maximum 

discharge, In 

cubic meters 

per second

368 

425 

566 

756 

756 

792 

792 

792 

792

Minimum 

discharge, In 

cubic meters 

per second

71 

142 

226 

71 

71 

226 

226 

226 

226

Up-ramp rate, In 

cubic meters per 

second per hour

76.2 

58.4 

73.1 

94.0 

154.9 

90.9 

156.1 

91.7 

149.8

Down-ramp rate, 

In cubic mefers 

per second per 

hour

-65.6 

^6.3

-87.3

140 ")

-126.4 

-88.7 

-88.4 

-91.1 

-91.1

800

^ z 600

o <->liJ

z co

III Lij

*

CO Q]

o 5

400

200

9 10 11 12 13 14 

TIME, IN DAYS FROM APRIL 30, 1991

15 16 17 18

Figure 1. Discharge for an unsteady flow release from Glen Canyon Dam. Hydrograph was computed from the 

record for the streamflow-gaging station, Colorado River below Glen Canyon Dam (09379910), during research 

flow D, May 6, 1991, to May 16, 1991.

downstream environment. These studies were 

concerned with changes in the riparian habitat 

affecting vegetation, fish and wildlife, and changes 

to beach volumes resulting from erosion and 

deposition of sand. Flow information of interest in 

these investigations includes peak and trough 

discharges, rates of discharge increase and 

decrease, and time-of-arrival of the waves at 

downstream locations. The study was conducted

by the U.S. Geological Survey (USGS) 

cooperation with the Bureau of Reclamation.

in

The purpose of this report is to present 

hydrographs calculated using a one-dimensional 

unsteady-flow model for each of nine fluctuating 

GCES research flows released from Glen Canyon 

Dam in 1990 and 1991. The unsteady-flow 

model was used to calculate hydrographs at 5 

streamflow-gaging stations on the Colorado River 

downstream from the dam (fig. 2) and at 33 t?°.ach

2 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 199^-91
study sites (table 2) during the 9 unsteady research 

flows. The model-calculated hydrographs were 

compared with the hydrographs computed from the 

gaging-station records. In addition, an analysis of 

the model results compared to data from the 

streamflow-gaging stations is provided as a 

measure of model accuracy.

DESCRIPTION OF THE FLOW 

MODEL

The one-dimensional unsteady-flow model 

used in this study was developed using data that 

included measured channel cross sections, 

reach-averaged velocities measured by dye tracing,

measurements of stage and the associated 

stage-discharge relations at gaging stations, 

channel slope, and streamflow-gaging station 

information recorded during research flow B 

(January 28, 1991, to February 7, 1991). The 

model is based on large-scale, reach-averaged 

channel properties including a single characteristic 

channel cross section and an average slope 

(0.0015) for the entire 386-kilometer reach from 

Glen Canyon Dam to Diamond Creek. The 

development of the flow model is discussed in 

detail by Wiele and Smith (1995).

Because the model was tailored for the 

Colorado River through Marble and Grand 

Canyons, only discharge hydrographs (discharge as 

a function of time) are required as input. Except

114 111 C

GRAND

CANYON

NATIONAL

PARK

Phantom 

Ranch

35

50 MILES

0 50 KILOMETERS

EXPLANATION 

^ 09404200 STREAMFLOW-GAGING STATION AND NUMBER

Figure 2. Locations of streamflow-gaging stations, Colorado River through Marble and Grand Canyons (modified 

from Graf, 1995).

Description of the Flow Model 3
Table 2. Selected locations for calculated hydrographs (beach study sites) and distance from Lees Ferry, Arizona

[Negative numbers indicate distance upstream from Lees Ferry; positive numbers indicate distance downstream from Lees Ferry. Locat'ons from 

Kaplinski and others, 1995]

Study site name

Hidden Sloughs .....................

3 mile. ....................................

Hot NaNa. .............................

22 mile.............. .....................

Fence Fault ............................

South Canyon ........................

33 mile ...................................

Anasazi Bridge ......................

Eminence Break.... .................

Lower Saddle...... ...................

Dino .......................................

52 mile ...................................

Crash Canyon ........................

Tanner....................................

Grapevine.......... .....................

Cremation ..............................

91 mile...................................

River mile

-6.5 

2.6 

16.4 

21.8 

30.0 

31.6 

33.0 

43.0 

45.0 

47.0 

50.0 

51.5 

62.0 

68.0 

81.0 

87.5 

91.1

Distance, 

in 

kilometers

10

4.2 

26.4 

35.1 

48.3 

50.8 

53.1 

69.2 

72.4 

75.6 

80.5 

82.9 

99.8 

109.4 

130.3 

140.8 

146.6

Study site name

Upper Granite............ ............

104 mile...................... ...........

119 mile..................... ............

122 mile. ................................

Upper Forster..... ....................

Middle Ponchos............ .........

139 mile.................................

145 mile.................................

172 mile.................................

183 mile.................................

194 mile.................................

202 mile.................................

Pumpkin Springs ...................

Middle Gorilla.......................

220 mile.................................

225 mile.................................

River mile

93.0 

103.9 

119.0 

122.2 

122.7 

136.7 

139.0 

145.0 

172.2 

182.8 

194.1 

202.0 

212.9 

219.9 

220.0 

225.0

Dis^nce, 

in 

klloneters

149.6 

167.2 

191.5 

196.6 

197.4 

220.0 

223.7 

233.3 

277.1 

2^4.1 

312.3 

325.0 

3<t2.6 

353.8 

354.0 

3^2.0

during times of major flooding in the tributaries, 

flow is dominated by dam releases. Discharge 

hydrographs at the streamflow-gaging station at 

Colorado River below Glen Canyon Dam 

(09379910; RK 24, RM 15; fig. I) 1 , which were 

computed from stage measurements and the 

associated stage-discharge relation, are used as the 

upstream discharge-boundary condition. The 

streamflow hydrographs at this location typically 

are based on records with a 30-minute sampling 

interval. During research flows D, F2, and G2 

(table 1), however, data were recorded at this 

gaging station in 15-minute time intervals.

IrThe primary units in this paper are metric. Because location on the river commonly is given in river miles (RM) above 

( ) or below (+) Lees Ferry, locations and distances are given 

in river kilometers (RK) and river miles in this paper. The use 

of cubic feet per second for discharge is common and is clearly 

associated with stage at specific points along the river; therefore, discharges are given in cubic meters per second and cubic 

feet per second within the text.

Discharges are interpolated to satisfy the model 

requirement of a 4-minute interval.

Tributary and ground-water contributions to 

the main-stem discharge also must be included in 

model calculations. Procedures for evaluating the 

magnitude and locations of tributary and 

ground-water contributions are described below. 

Contributions from these sources were added to the 

flow calculation of the model at the appropriate 

river mile.

Additional inflow from tributaries was 

determined primarily from the records of 

streamflow-gaging stations on the major tributaries 

to the Colorado River downstream from Glen 

Canyon Dam. Data were available from the 

following USGS streamflow-gaging statiors: (A) 

09382000, Paria River at Lees Ferry, Arizona; (B) 

09402000, Little Colorado River near Cameron, 

Arizona; (C) 09403000, Bright Angel Creek near 

Grand Canyon, Arizona; (D) 09403850, Kanab 

Creek above the mouth, near Supai, Arizora; and

4 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 19*vf)-91
(E) 09404115, Havasu Creek above the mouth, 

near Supai, Arizona (table 3 and fig. 2).

Some discrepancies involving the discharge 

computed from the stage record from the gaging 

station, 09379910 Colorado River below Glen 

Canyon Dam, that is used as model input affected 

the calculated hydrographs. During research flows 

A, E, Fl, Gl, F2, and G2, the discharge computed 

for the steady flow preceding the fluctuating flow 

using the stage record from the streamflow-gaging 

station, 09380000 Colorado River at Lees Ferry, 

and the associated stage-discharge relation was 

lower than the discharge computed for the steady 

flow using the record from the gaging station just 

below the dam. The greatest apparent decreases in 

steady discharge between the dam and Lees Ferry 

were recorded during research flows A and E. 

During flows A and E, the steady discharge 

computed from the stage recorded at the gaging 

station below the dam was 150 mVs (5,300 fWs), 

and discharge computed from the stage recorded at 

the gaging station at Lees Ferry was 140 mVs 

(4,950 ftVs), which is a difference of 10 mVs 

(350 fWs). For the remaining research flows, the 

deficit at Lees Ferry was 7 mVs (250 fWs) or less. 

An apparent decrease in the steady discharge was 

recorded only at Lees Ferry.

Another irregularity in the data from the 

gaging station below the dam is in the record for 

research flow Gl. The record shows that the peak

discharge of the fourth wave released from the dam 

had a duration about twice that of the other waves 

during flow Gl. This extended duration is not 

reflected in data from other streamflow-gaging 

station records, and therefore, was assumed to be 

an error in the record from the gaging station 

below the dam. The error does not extend Hyond 

the trough following the fourth wave. Because the 

model was run using the discharge computed from 

the record of the gaging station below the dam as 

the upstream-boundary condition, the error in the 

fourth wave is present in all the calculated 

hydrographs for flow Gl. Attempts were no* made 

to correct this error because it was confined to only 

one of eleven daily waves, and the correction of 

streamflow records in the USGS data base was 

considered outside the scope of this study.

Steady Inflow from Tributaries

Steady inflow to the river from tributaries and 

ground-water sources downstream from tb-^ dam 

can be identified from the steady flows that 

preceded and followed fluctuating flows and from 

the magnitudes of the peaks and troughs of the 

unsteady flows. If inflow is steady, the peaks and 

troughs will have the same magnitude through the 

research-flow period, and the steady main-stem 

flow that follows the fluctuating flow will have the

Table 3. Gaged tributaries of the Colorado River between Glen Canyon Dam and Diamond Creek

Streamflowgaging 

station 

number

09382000

09402000

09403000

Tributary name 

and gaging-statlon 

location

Paria River 

at Lees Ferry, 

Arizona......................

Little Colorado River 

near Cameron, 

Arizona (45 miles 

above mouth).............

Bright Angel Creek 

near Grand Canyon, 

Arizona......... .............

Distance 

downstream 

from Lees Ferry

River Kilommiles eters

1 2

61 98

88 142

Streamflowgaging Tributary name 

station and gaging-station 

number location

Kanab Creek above 

09403850 mouth, near Supai, 

Arizona..................

Havasu Creek

09404115 above mouth, 

near Supai, 

Arizona..................

Distance 

downstr<v*m 

from Lees Ferry

River Kilommlies eters

144 232

157 253

Description of the Row Model 5
same magnitude as the steady flow that precedes 

the fluctuating flow. The magnitude of the steady 

inflow was determined by taking the difference 

between the steady flow recorded at the 

streamflow-gaging station, 09379910 Colorado 

River below Glen Canyon Dam, and discharges 

recorded at five streamflow-gaging stations farther 

downstream from the dam and upstream from Lake 

Mead (fig. 2): (A) 09380000, Colorado River at 

Lees Ferry (RK 0); (B) 09383100, Colorado River 

above the Little Colorado River near Desert View 

(RK 98, RM 61); (C) 09402500, Colorado River 

near Grand Canyon (RK 142, RM 88); (D) 

09404120, Colorado River above National Canyon 

near Supai (RK 267, RM 166); and (E) 09404200, 

Colorado River above Diamond Creek near Peach 

Springs (RK 362, RM 225).

Records from the gaging stations on the 

tributaries (table 3) were first examined to identify 

the sources of additional inflows. Steady inflow 

determined from data recorded at these gaging 

stations was added to the model calculation at the 

location of the mouth of the tributary, in 

kilometers, downstream from Lees Ferry. In some 

cases, the inflow determined from the record at 

these gaging stations did not account for the total 

increase in steady flow. For those cases, the 

remaining difference between the discharge at the 

gaging stations along the Colorado River during 

the steady flow was determined, then added to the 

model at locations of likely sources (for example, 

Tapeats Creek at RK 216 (RM 134) on the 

Colorado River; table 4).

Unsteady Inflow from Tributaries

Data from Streamflow-Gaging Stations

Records of the streamflow-gaging stations 

along the Colorado River show clear evidence of 

unsteady inflow during research flows C, E, and 

Fl. The presence of unsteady inflow is indicated by 

varying peak and trough discharges during the 

research flow. Unsteady inflow data were obtained 

from streamflow-gaging stations on the Paria and 

Little Colorado Rivers, which appear to be the only 

sources of significant unsteady inflow during these 

periods. Records of the other tributary gaging 

stations (table 3) also were checked for unsteady

inflow. The available records, however, indicated 

these tributaries were not significant sources of 

unsteady inflow during any of the research flows. 

The unsteady discharge from the Paria and Little 

Colorado Rivers was added to the model 

calculation for flows C, E, and Fl.

During research flow C, the inflow finm the 

Little Colorado River was greater than 55 mVs 

(I,900ft3/s) for slightly more than 1 day and 

peaked at 76 mVs (2,700 ftVs; fig. 3). Inflow from 

the Little Colorado River during the remainder of 

flow C generally was less than 20 mVs (710 fWs). 

Because of the duration and magnitude of this 

inflow, the hydrographs for the Colorado River 

computed from the records of the gaging stations 

near Grand Canyon and above National Canyon 

(fig. 4B and C) show a significant increase in the 

peak and trough discharges of the research flow 

with the inflow from the Little Colorado River. The 

hydrograph computed from the record of the 

gaging station at Lees Ferry shows no evidence of 

unsteady inflow during this period. The timing of 

the increase in peak and trough discharges reflected 

in the records from the gaging stations was useful 

in determining the time of arrival of the inflow 

from the Little Colorado River into the Colorado 

River. The hydrographs computed from the records 

of the gaging station near Grand Canyon were 

useful particularly for inferring the timing of the 

unsteady inflow into the main stem. The method 

used to estimate the timing of the inflow added to 

the model calculation is discussed later in this 

report. Significant inflow from the Paria River or 

other gaged tributaries did not occur during 

research flow C.

The unsteady inflow from the Paria River 

during research flow E consisted of a singH peak 

of short duration (less than half a day) with a 

maximum discharge of about 20 m3/s (71C fWs). 

The unsteady inflow from the Little Cc'orado 

River during research flow E was a series of peaks 

occurring over a 6-day period; one peak was 

greater than 80 mVs (2,800 fWs; fig. 5). Trie flow 

of greatest magnitude on the Little Colorado River 

was about 120 mVs (4,200 fWs). The time of 

arrival of the highest peak at the Colorado River 

during research flow E coincided with the arrival 

of a wave released from the dam. The actual arrival 

of the unsteady inflow from the Little Colorado

6 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 19"VV-91
Table 4. Amount and location of steady inflows used for model hydrograph calculations

[Dashes indicate no data]

Research 

flow

A.......

B.......

Glen Canyon 

Dam to Lees 

Ferry 

(RK -24-0)

0

0

Lees Ferry to Little 

Colorado River 

(RKO-88)

Inflow, in Locacublc tlon, In 

meters river 

per kllomsecond eters

0

6.1 1.6

Little Colorado River 

to near Grand Canyon 

(RK 98-1 42)

Inflow, in Locacubic tlon, in 

meters river 

per kilomsecond eters

6.23 109

2.0 98

Near Grand Canyon to 

above National 

Canyon 

(RK 142-268)

Inflow, in Locacubic tion, In 

meters river 

per kilomsecond eters

32.2 142

1.1 142

Above National 

Canyon to Dlmrcond 

Creek 

(RK 268-a~2)

Inflow, In Locacublc t'~>n, in 

meters river 

per kllomsecond eters

0

B ,, 12.9 288

C1 .......

D ,,

E1 .......

Fl 1 .....

Gl.....

F2......

G2.....

0

0

0

0

0

0

0

0

6.1 1.6

7.36 1.6

4.0 1.6

0

2.83 84

0

0

0

2.0

6.23

5.0

6.37

8.5

12.5

8.5

8.5

98

109

98

109

109

109

98

98

1.1

1.1

1.1

21.5

2.12

8.0

5.0

8.0

0

32.6

18.4

8.0

8.0

4.6

4.6

4.6

4.6

4.6

4.6

142

216

253

142

253

142

216

253

142

142

216

253

142

216

253

142

216

253

12.9

12.9

0

5.5

5.5

0

0

0

6.1

6.1

6.1

6.1

288

319

288

319

...

288

319

288

319

'Unsteady inflows also were added to model calculations for these flows.

80

60

CO

uj'gj 40 

C5 a.

20

56789 

TIME, IN DAYS FROM DECEMBER 31, 1990

10 11 12 13

Figure 3. Unsteady discharge from the Little Colorado River during research flow C. Discharge is computed from 

stage records and the stage-discharge relation developed from stage and discharge measurements at the streamflow-gaging station near Cameron, Arizona.

Description of the How Model 7
56789 

TIME, IN DAYS FROM DECEMBER 31, 1990

10 11 12 13

EXPLANATION

CALCULATED HYDROGRAPH

HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 4. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamflow-gaging stations for research flow C. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River near Grand Canyon (RK 142, RM 88). C, Colorado River above National Canyon near Supai (RK 267, 

RM 166). The streamflow-gaging station records from the remaining gaging stations are either unavailable cr contain 

irregularities suggesting gaging-station malfunction during the flow.

8 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 1990-91
River, therefore, is obscured in the record from the 

gaging station near Grand Canyon (fig. 6).

During research flow Fl, the unsteady inflow 

from the Paria River was again a single peak of 

short duration; the peak was of about 63 mVs 

(2,200 fWs; fig. 7). Two significant flows of short 

duration on the Little Colorado River occurred 

during research flow Fl, which peaked at about 

76 mVs (2,700 ftVs). The effect of this inflow on 

flow in the Colorado River is evident in the hydrographs computed from the records of the 

streamflow-gaging stations near Grand Canyon 

and above National Canyon (fig. 8C and Z>).

Data from Stage-Gaging Stations

More detailed stage records reflecting the 

addition of unsteady inflow were available for 

research flow C from 29 stage-gaging stations 

installed by the USGS along the Colorado River. 

The locations of these stage gages along with other 

stage gages that have no record for flow C are

provided in table 5. The stage gages were installed 

about 8 km apart between Glen Canyon Dam and 

Diamond Creek. Discharge is not measured at 

these sites, and stage-discharge relations have not 

been developed. Plots of the recorded stage and 

time, however, clearly indicate time of arrval of 

peaks and troughs as well as unsteady inflow. 

Although installation and operation of the stage 

gages began in 1990, the first research flow for 

which data generally were available is research 

flow C; therefore, there is no record from the stage 

gages for research flows E and F1.

Examination of the stage-gaging station 

records indicates that unsteady flow was added 

between RK 88 and 113 (RM 55 and 70; fig. 9). 

The mouth of the Little Colorado River is at RK 98 

(RM 61) on the Colorado River. No additional 

unsteady inflow during flow C is indicated by these 

stage-gage records. The gaging station at RK 88 

(RM 55) shows no evidence of additional unsteady 

inflow, but the records from the gaging stations at 

RK 113 (RM 70) and RK 346 (RM 215) show the

17 18 19 20 21 22 23 24 25

TIME, IN DAYS FROM AUGUST 31, 1990

26 27 28 29

Figure 5. Unsteady tributary discharge during research flow E. A, Paria River. B, Little Colorado River.

Description of the Flow Model 9
17 18 19 20 21 22 23 24 25 

TIME, IN DAYS FROM AUGUST 31, 1990

EXPLANATION 

CALCULATED HYDROGRAPH 

HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 6. Calculated hydrographs and hydrographs determined from stage records and the stage-cfischarge 

relations at streamf low-gaging stations for research flow E. A, Colorado River at Lees Ferry (RK 0). 

B, Colorado River near Grand Canyon (RK 142, RM 88). The streamf low-gag ing station records from the remaining 

gaging stations are either unavailable or contain irregularities suggesting gaging-station malfunction during the flow.

well as from the other stage gages in between) 

indicates there was no other significant unsteady 

inflow.

Timing of Unsteady Inflows

The streamflow-gaging station on the Paria 

River (09382000, Paria River at Lees Ferry, 

Arizona) is just above the mouth of the Paria River 

at RK 1.6 on the Colorado River. Inflow from the 

Paria River, therefore, was determined from data 

recorded by this gaging station and added directly 

to the flow calculated by the model 1.6 km 

downstream from Lees Ferry.

The streamflow-gaging station providing the 

best available record for flow in the Little 

Colorado River during the research flows is 

09402000, Little Colorado River near Cnneron, 

Arizona, about 72 km (45 mi) above the mouth of 

the Little Colorado River. The hydrograph 

computed from the stage recorded at this gaging 

station was shifted in time to account for tin travel 

time between the gaging station and the mouth of 

the Little Colorado River. The time shift used was 

the time shift that gave the best match of the 

hydrograph calculated by the model at RM 88 with 

the hydrograph derived from the data recorded by 

the gaging station near Grand Canyon (09^02500, 

Colorado River near Grand Canyon, Arizona).

10 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 1990-91
o

8111 

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111 o.

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2 

o 

en^ 

o

2

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tr

17 18 19 20 21 22 23 24 25 26 27 28 

TIME, IN DAYS FROM JUNE 30, 1990

Figure?. Unsteady tributary discharge during research flow F1. A, Paria River. B, Little Colorado River.

the gaging station near Grand Canyon (09402500, 

Colorado River near Grand Canyon, Arizona).

An initial estimate of 7 hours was made for 

the travel time of the flow between the gaging 

station near Cameron and the mouth of the Little 

Colorado River. This estimate was selected as an 

initial estimate on the basis of the timing of the 

flow peak recorded at the gaging station near 

Cameron and the time of arrival of the unsteady 

flow peak at the gaging station on the Colorado 

River near Grand Canyon. The travel time of the 

wave released from the dam between the gaging 

station on the Colorado River above the Little 

Colorado River, near Desert View, Arizona 

(09383100) and the gaging station near Grand 

Canyon was subtracted from the total travel time of 

the Little Colorado River flow peak between the 

gaging stations near Cameron and Grand Canyon.

The difference in time between the arrival of 

the flow peak at the gaging station near Cameron 

and the arrival of the wave peak on the Colorado 

River, which included the Little Colorado River

inflow, at the gaging station on the Colorado River 

near Grand Canyon was about 12 hours during 

research flows C and Fl. The travel time of the 

research flow wave on the Colorado River between 

the gaging stations above the Little Colorado River 

and near Grand Canyon was about 5 hours during 

research flows C, E, and Fl. The travel time for the 

flow peak between the gaging station near 

Cameron and the mouth of the Little Colorado 

River, therefore, was about 7 hours. The model was 

run with the unsteady flow from the Little 

Colorado River added at RK 98 (RM 61) with a 

+7-hour time shift of the discharge of the Little 

Colorado River computed from the recorded stage 

and the stage-discharge relation at the gaging 

station near Cameron.

A comparison of the model-calculated 

hydrograph at the gaging station near Grand 

X^anyon with the hydrograph computed frcTi the 

recorded stage and stage-discharge relation at that 

location showed that the +7-hour time shift did not 

result in an accurate representation of the t:me of

Description of the Row Mc4el 11
UJ

co 

a:

UJ

a.

co 

a:

UJ

o 

CD

o 

o

UJ

o 

a:

o 

co 

o

800

600 -

400 -

200

18 19 20 21 22 23 24 25 

TIME, IN DAYS FROM JUNE 30, 1990

26 27 28 29

EXPLANATION 

CALCULATED HYDROGRAPH 

HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 8. Calculated hydrographs and hydrographs determined from stage records and the stage-dscharge 

relations at streamflow-gaging stations for research flow F1. A, Colorado River at Lees Ferry (RK 0). 

B, Colorado River above Little Colorado River near Desert View (RK 98, RM 61). C, Colorado River near Grand 

Canyon (RK 142, RM 88). D, Colorado River above National Canyon near Supai (RK 267, RM 166). The record 

from the streamflow-gaging station above Diamond Creek during this period was unavailable.

12 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 1990-91
Table 5. Stage-gaging stations along the Colorado River between Glen Canyon Dam and Diamond Creek

[RM, river miles upstream or downstream from Lees Ferry]

U.S. Geological 

Survey 

gaglngstatlon 

number

09379965

09383003

09383006

09383009

09383035

09383040

09383050

09383060

09383070

09383075

09383080

09383090

09402350

09402490

09402430

09402460

09403020

09403030

09403035

09403040

09403045

09403060

09403065

09403100

Stagegage 

name

R20(M)2

R2(XM)3

R200-04

R2(XM)5

R200-06

R200-07

R2(XM)8

R200-09

R200-10

R200-11

R200-12

R200-13

R200-14

R200-15

R200-16

R200-17

R200-18

R200-18A

R200-18B

R200-19

R200-19A

R200-20

R200-20A

R200-21

Location

6.5 miles above Lees Ferry

At RM 5 below 5 Mile Wash

At RM 1 0 below 1 0 Mile Rock

At RM 15 below Sheer Wall Rapid

At RM 20 above North Canyon Rapid

At RM 25 below 24 Mile Rapid

At RM 30 below 29 Mile Rapid

At RM 35 below Nautiloid Canyon

At RM 40 at tramway site

At RM 45 below President Harding 

Rapid

At RM 50 below 50 Mile Camp

At RM 55 above Kwagunt Rapid

At RM 65 above Lava Canyon Rapid

At RM 70 below Basalt Canyon

At RM 65 above Hance Rapid

At RM 80 above Grapevine Rapid

At RM 90 above Horn Rapid

At RM 93 above Granite Rapid

At RM 93.5 below Granite Rapid

At RM 95 above Hermit Rapid

At RM 95.5 below Hermit Rapid

At RM 98 above Crystal Rapid

At RM 98.5 below Crystal Rapid

At RM 1 05 below Ruby Rapid

U.S. Geological 

Survey 

gaglngstatlon 

number

09403150

09403170

09403200

09403250

09403300

09403350

09403400

09403860

09403870

09403880

09404117

09404119

09404130

09404135

09404140

09404145

09404150

09404155

09404165

09404170

09404180

09404185

09404190

Stagegage 

name

R200-22

R200-23

R200-24

R200-25

R200-26

R200-27

R200-28

R200-29

R200-30

R200-31

R200-32

R200-32A

R200-33

R200-34

R200-35

R200-36

R200-37

R200-38

R200-39

R200-40

R200-41

R20(M2

R200-43

Location

At RM 1 1 0 below 1 1 0 Mile Rapid

At RM 1 1 5 below Garnet Canyon

At RM 120 above Blacktail Rapid

At RM 125 above Fossil Rapid

At RM 131 above Deubendorflf Rapid

At RM 135 above Granite Narrows

At RM 140 below 140 Mile Canyon

At RM 145 above Olo Canyor

At RM 1 50 above Upset Rapid

At RM 1 55 below Sinyala Rapd

At RM 160, 3 miles below Ha^asu 

Creek

At RM 165.5 above National Canyon

At RM 1 70 above Stairway Canyon

At RM 1 75 below Cove Canyon

At RM 179 above Lava Falls Rapid

At RM 185 above 185 Mile Rapid

At RM 190, 2 miles below Wl "tmore 

Rapid

At RM 195 below 194 Mile Canyon

At RM 200 below Parashant Wash

At RM 205 above 205 Mile Rapid

At RM 210 below Granite Par^

At RM 2 1 5 above Three Sprin <*s 

Canyon

At RM 220 above 220 Mile Canyon

Description of the Row Mc4el 13
LU

a

4 '-

56789 

TIME, IN DAYS FROM DECEMBER 31, 1990

10 11 12 13

Figures. Stage recorded during research flow C at stage-gaging stations. A, R200-13 (RK 88, RM 55). E, R200- 

15 (RK 113, RM 70). C, R200-42 (RK 346, RM 215). R200-42 is the stage-gaging station farthest downstream 

from the dam that recorded data during research flow C.

arrival of the unsteady flow peak at the gaging 

station near Grand Canyon. An estimate of the 

additional time delay required to obtain a better 

match between the two hydrographs then was 

made and added to the adjusted flow data from the 

gaging station at Little Colorado River near 

Cameron. The time shift that achieved the best 

match in each case was +9.12 hours. This 

adjustment is based on single flow events in the 

Little Colorado River during research flows C and

Fl that had peak discharges of about 76 mVs 

(2,700 ftVs).

The same adjustment (+9.12 hours) was 

applied to the data from the gaging station near 

Cameron for research flow E because the record 

from the gaging station near Grand Canyon does 

not clearly indicate the arrival of the flow peak 

from the Little Colorado River during flow E. The 

+9.12 hours, therefore, was the best estimate that 

could be made of the necessary time shift for 

research flow E. The addition of the unsteady

14 Calculated Hydrographs for Unsteady Research Rows, Colorado River Downstream from Glen Canyon Dam, 1990-91
discharge from the Paria and Little Colorado 

Rivers to the model calculations for reach flows C, 

E, and Fl resulted in good agreement between the 

calculated hydrographs and the hydrographs 

computed from the stage record at the downstream 

gaging stations as shown in figures 4, 6, and 8, 

respectively.

COMPARISON OF MODELCALCULATED HYDROGRAPHS 

WITH COMPUTED HYDROGRAPHS

The hydrographs calculated by the model and 

hydrographs computed from the data recorded by 

the streamflow-gaging stations are shown in 

figs. 10-18 for the first four days of research flows 

A, B, C, D, E, Fl, Gl, F2, and G2, respectively. 

The hydrographs calculated for the 5 streamflowgaging stations and 33 beach study sites for each of 

the 9 unsteady research flows also are available in 

electronic form through the USGS. Information 

concerning how to access the hydrographs can be 

obtained by contacting the District Chief, Water 

Resources Division, Tucson, Arizona.

An analysis of model results was performed 

by comparing data from the five streamflowgaging stations along the Colorado River with the 

model-calculated results. Wave characteristics that 

were compared included rate of increase and 

decrease of discharge, peak and trough discharges, 

and wave travel time (determined by tracking the 

advance of the wave trough) as functions of 

distance downstream. Also, the average absolute 

error of the wave travel time over 90 percent of the 

wave, excluding just the peaks and troughs, was 

calculated as a measure of model accuracy over 

most of the wave (table 6). Periods with only 

steady inflow were used to compare model results 

with hydrographs computed from gaging-station 

records for research flows that had unsteady 

inflows (C, E, and Fl).

In some cases, gaging-station records were 

unavailable, and in other cases, the records 

contained irregularities that appear to be caused by 

gaging-station malfunction during part of all of the 

research flow. These records, therefore, were not 

used in the analysis of model results. Cases where 

records were missing or may be in error are noted

in table 6. For research flow E, data are available 

only from the gaging stations at Lees Ferry and 

Grand Canyon. Estimates of inflow added to the 

model calculation and the analysis of the research 

flows are based on the available records.

Before the calculated hydrographs were 

compared to the hydrographs computed from the 

streamflow data from the gaging stations above 

National Canyon and Diamond Creek, a correction 

was applied to this streamflow data to ensure that 

mass was conserved between the gaging stations. 

A detailed discussion of the reasons for applying 

this correction and its development is provided by 

Wiele and Smith (1995). In the calculation^ made 

for this report, this correction was appMed to 

discharge computed from data recorded at these 

gaging stations during each of the flows except for 

the data from the gaging station above National 

Canyon for research flows Fl and Gl. A correction 

of the data from the gaging station above National 

Canyon was not necessary for research flows Fl 

and Gl. Flows Fl and Gl are the only research 

flows in 1990 for which a gaging-station record for 

National Canyon is available.

The first test of the ability of the model to 

predict accurately the evolution of the wa^e as it 

travels downstream is a comparison of the rates of 

increase and decrease in discharge calculated by 

the model with the rates determined from the 

gaging-station records. These rates are measures of 

the wave shape and reflect the steepening of the 

rising limb of the wave as it moves downstream 

after its release from the dam. The model 

accurately predicts the rates of decrease in 

discharge (negative values) compared to tH rates 

calculated from each of the hydrographs derived 

from gaging-station records (fig. 19). The model, 

however, tends to produce a higher rate of increase 

in discharge than the rates calculated from 

stage-discharge relations and the stage records at 

the gaging stations between the dam and the 

gaging station near Grand Canyon for some of the 

flows.

The second test used to evaluate the model 

results is a comparison of the peak and trough 

discharges calculated by the model with the 

discharges computed from the gaging-station 

records as a function of distance upstream and 

downstream from Lees Ferry (fig. 20). For the

Comparison of Model-Calculated Hydrographs with Computed Hydrognohs 15
o o

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cc

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500

400

300

200

100

456 

TIME, IN DAYS FROM SEPTEMBER 30, 1990

EXPLANATION

CALCULATED HYDROGRAPH

HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 10. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamflow-gaging stations for research flow A. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River above Little Colorado River near Desert View (RK 98, RM 61). C, Colorado River near Grand Canyon 

(RK 142, RM 88). D, Colorado River above Diamond Creek near Peach Springs (RK 362, RM 225). No record was 

available for the gage above National Canyon near Supai (RK 267, RM 166) during flow A. The hydrographs are 

positioned to show the rise of the first wave following the steady flow.

16 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Darr 1990-91
Ill

CO 

DC 

111 

Q.

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n: 

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30 31 32 33 

TIME, IN DAYS FROM DECEMBER 31, 1990

CALCULATED HYDROGRAPH

EXPLANATION 

....... HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 11. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relattons at streamf low-gag ing stations for research flow B. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River above Little Colorado River near Desert View (RK 98, RM 61). C, Colorado River near Grand Canyon 

(RK 142, RM 88). D, Colorado River above National Canyon near Supai (RK 267, RM 166). E, Colorado River 

above Diamond Creek near Peach Springs (RK 362, RM 225). The hydrographs are positioned to show tr ? rise of 

the first wave following the steady flow, with the exception of B where the streamflow record is incomplete.

Comparison of Model-Calculated Hydrographs with Computed Hydrographs 17
234 

TIME, IN DAYS FROM DECEMBER 31, 1990

EXPLANATION

- CALCULATED HYDROGRAPH

 HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 12. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamflow-gaging stations for research flow C. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River near Grand Canyon (RK 142, RM 88). C, Colorado River above National Canyon near Supai (PK 267, 

RM 166). The records from the remaining gaging stations are either unavailable or contain irregularit; 3s that 

indicate gaging-station malfunction during the flow. The hydrographs are positioned to show the rise of the first wave 

following the steady flow.

research flows with unsteady inflow, periods with 

only steady inflow were chosen for the 

comparison. The waves released from the dam 

spread as they move downstream and caused the 

peak discharge to decrease and the trough 

discharge to increase. The increase in trough 

discharge is a result of the repeated wave release. 

Steady tributary inflows cause step increases in 

peak and trough discharges (fig. 20).

In most cases, the peak and trough discharges 

calculated by the model agree well with the

discharges computed from the gaging-station 

records. The two cases with the largest deviations 

between the calculated discharge and the discharge 

computed from the gaging-station record are; at the 

gaging stations near Grand Canyon (RK 142) 

during research flow E and above National Canyon 

(RK 267) during research flow G2. In both cases, 

the difference is in the magnitude of the peak 

discharge calculated by the model and the peak 

discharge computed from the gaging-station 

record, and the difference is less than 10 percent of

18 Calculated Hydrographs for Unsteady Research Rows, Colorado River Downstream from Glen Canyon Dam, 1990-91
o 

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9 10 11 

TIME, IN DAYS FROM APRIL 30, 1991

12

CALCULATED HYDROGRAPH

EXPLANATION 

........ HYDROGRAPH FROM STREAMFLOW-GAGING STATION?

Figure 13. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamflow-gaging stations for research flow D. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River above Little Colorado River near Desert View (RK 98, RM 61). C, Colorado River near Grand Canyon 

(RK142, RM 88). D, Colorado River above National Canyon near Supai (RK 267, RM 166). E, Colorrdo River 

above Diamond Creek near Peach Springs (RK 362, RM 225). The hydrographs are positioned to show the rise of 

the first wave following the steady flow.

Comparison of Model-Calculated Hydrographs with Computed Hydrogrnhs 19
19 20 21 

TIME, IN DAYS FROM AUGUST 31, 1990

22

EXPLANATION 

CALCULATED HYDROGRAPH 

HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 14. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamflow-gaging stations for research flow E. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River near Grand Canyon (RK 142, RM 88). The records from the remaining gaging stations either are unavailable 

or contain irregularities that indicate gaging-station malfunction during the flow. The hydrographs are posifoned to 

show the rise of the first wave following the steady flow.

Table 6. Average absolute error and percent error of the calculated time for a given discharge at five 

streamflow-gaging stations downstream from Glen Canyon Dam

[Numbers in parentheses are percent error and were calculated by dividing the average absolute error, in hours, by the travel time of the fi-st trough 

from Glen Canyon Dam to the gaging-station location, in hours, and multiplying by 100. Dashes indicate that gaging-station records are 

unavailable or may be in error]

Gaging-station 

location

Lees Ferry..............

Above the Little 

Colorado River......

Near Grand 

Canyon ................ ..

Above National 

Canyon ....... ...........

Above Diamond 

Creek.....................

Distance 

downstream from 

Lees Ferry, 

In river 

kilometers

0

98 

142 

267 

362

Average absolute error, in hours, for specified research flow

A

0.53 

(9.0)

1.10 

(4.9)

.36 

(1.3)

1.71 

(3.1)

B

0.31 

(4.1)

1.38 

(6.7)

.82 

(2.8)

1.6 

(3.7)

1.24 

(2.2)

C

0.35 

(6.4)

1.18 

(5.0)

.78 

(2.1)

D

0.23 

(4.8)

1.38 

(6.8)

1.24 

(4.9)

.82 

(2.2)

.86 

(1.8)

E

0.33 

(4.1)

.98 

(3.6)

F1

0.30 

(5.5)

1.76 

(8.3)

1.29 

(5.0)

.48 

(1.2)

G1

0.38 

(4.2)

1.96 

(8.8)

1.51 

(5.5)

.36 

(-9)

F2

0.36 

(5.5)

1.69 

(8.6)

1.56 

(6.4)

.43 

(1.2)

2.01 

(4.2)

G2

0.36 

(5.5)

1.69 

(9.2)

1.56 

(6.8)

.43 

(1.2)

2.01 

(4.4)

20 Calculated Hydrographs for Unsteady Research Rows, Colorado River Downstream from Glen Canyon Dam, 1990-91
18 19 20 

TIME, IN DAYS FROM JUNE 30, 1990

21

EXPLANATION

CALCULATED HYDROGRAPH

HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 15. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamflow-gaging stations for research flow F1. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River above Little Colorado River near Desert View (RK 98, RM 61). C, Colorado River near Granc1 Canyon 

(RK 142, RM 88). D, Colorado River above National Canyon near Supai (RK 267, RM 166). The record from the 

streamflow-gaging station above Diamond Creek during this flow was unavailable. The hydrographs are positioned 

to show the rise of the first wave following the steady flow.

Comparison of Model-Calculated Hydrographs with Computed Hydrographs 21
456 

TIME, IN DAYS FROM JUNE 30, 1990

EXPLANATION

CALCULATED HYDROGRAPH

HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 16. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamf low-gaging stations for research flow G1. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River above Little Colorado River near Desert View (RK 98, RM 61). C, Colorado River near Grand Canyon 

(RK 142, RM 88). D, Colorado River above National Canyon near Supai (RK 267, RM 166). The record from the 

streamftaw-gaging station above Diamond Creek during this flow was unavailable. The hydrographs are positioned 

to show the rise of the first wave following the steady flow.

22 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Danr 1990-91
1,000 r

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16 17 18 19 

TIME, IN DAYS FROM JUNE 30, 1991

EXPLANATION

CALCULATED HYDROGRAPH

HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 17. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamflow-gaging stations for research flow F2. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River above Little Colorado River near Desert View (RK 98, RM 61). C, Colorado River near Granc1 Canyon 

(RK 142, RM 88). D, Colorado River above National Canyon near Supai (RK 267, RM 166). The hydrographs are 

positioned to show the rise of the first wave following the steady flow.

Comparison of Model-Calculated Hydrographs with Computed Hydrographs 23
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345 

TIME, IN DAYS FROM JUNE 30, 1991

CALCULATED HYDROGRAPH

EXPLANATION 

 ....... HYDROGRAPH FROM STREAMFLOW-GAGING STATIONS

Figure 18. Calculated hydrographs and hydrographs determined from stage records and the stage-discharge 

relations at streamflow-gaging stations for research flow G2. A, Colorado River at Lees Ferry (RK 0). B, Colorado 

River above Little Colorado River near Desert View (RK 98, RM 61). C, Colorado River near Grand Canyon 

(RK142, RM 88). D, Colorado River above National Canyon near Supai (RK 267, RM 166). E, Colorado River 

above Diamond Creek near Peach Springs (RK 362, RM 225). The hydrographs are positioned to show the rise of 

the first wave following the steady flow.

24 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dan, 1990-91
CHANGE INDISCHARGE PETIME, CUBIC METERSSECOND HOUR

100 

4

50 

0 

-50 

100

100 

50 { 

0

100

100 

<

0

100< 

0

-100 

< 

-200 

250 

200 

4 

100

0 

-100

2

Lees Ferry

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1 1 1 1 1 1 1 1 I 1 1 1 1 1

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RESEARCH FLOW A ~

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RESEARCH FLOW E \

75 175 275 37 

LOCATION, IN KILOMETERS FROM LEES FERRY

EXPLANATION

{ :: , : -:-: : ] UPSTREAM FROM LEES FERRY 

I | DOWNSTREAM FROM LEES FERRY

 r.Ai r.i n ATPn RATP nr nisr.MAnriP iwr:npA<?p

 CALCULATED RATE OF DISCHARGE DECREASE

 MEASURED RATE OF DISCHARGE INCREASE

O MEASURED RATE OF DISCHARGE DECREASE

Figure 19. Calculated and measured rates of discharge increase (positive values) and decrease (negative values) 

as a function of distance downstream for research flows A-G2. The rates were determined from the middle 90 

percent of the wave height.

Comparison of Model-Calculated Hydrographs with Computed Hydrographs 25
200 p

Lees Ferry

DC

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-200

25 0 75 175 275 

LOCATION, IN KILOMETERS FROM LEES FERRY

375

Figure 19. Continued.

the peak discharge computed from the gagingstation record.

Finally, the model prediction of the wave 

travel time after its release from the dam to each of 

the five streamflow-gaging stations is compared to 

the travel time of the wave as recorded at the 

gaging stations. The travel time was determined by 

taldng the difference between the time of release of 

the lowest point of the first trough from the dam (as 

recorded by the gaging station just below the dam) 

and the arrival time of the same point at each of the 

gaging stations farther downstream. The model 

results agree well with the travel times obtained 

from the available gaging-station records (fig. 21).

The average absolute error in the computed 

arrival time of the wave over the wave period also 

was calculated for each flow at each gaging station 

(fig. 21 and table 6). This value indicates the 

accuracy with which the model predicts the arrival 

of a complete wave. The average absolute error is 

calculated by (1) summing the difference between 

the calculated time for a given discharge on a 

nondimensionalized hydrograph and the corresponding time on a hydrograph derived from stage 

records at the gaging station over a 24-hour period 

and (2) dividing by the number of sampler (The 

upper and lower 5 percent of the wave was not 

used in this calculation). The normalized discharge

26 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 1990-91
Lees Ferry

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RESEARCH FLOW E j

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25 0 75 175 275 375 

LOCATION, IN KILOMETERS FROM LEES FERRY

EXPLANATION 

UPSTREAM FROM LEES FERRY 

______ DOWNSTREAM FROM LEES FERRY

 CALCULATED PEAK DISCHARGE

 CALCULATED TROUGH DISCHARGE 

 MEASURED PEAK DISCHARGE 

O MEASURED TROUGH DISCHARGE 

4 STEADY TRIBUTARY INFLOW

Figure 20. Calculated and measured peak and trough discharges as a function of distance downstream for 

research flows A-G2.

Comparison of Model-Calculated Hydrographs with Computed Hydrographs 27
1,000

Lees Ferry

T

800<t»

600

400

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RESEARCH FLOW F1

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25 0 75 175 275 

LOCATION. IN KILOMETERS FROM LEES FERRY

375

Figure 20. Continued.

was used to avoid dependence on stage-discharge 

relations (Wiele and Smith, 1995).

SUMMARY AND CONCLUSIONS

Hydrographs have been calculated at 5 

streamflow-gaging stations and the 33 beach-study 

sites on the Colorado River for each of 9 unsteady 

releases from Glen Canyon Dam. The results of the 

model have been compared to the hydrographs 

computed from recorded stage and the associated 

stage-discharge relations developed for each of the 

five gaging stations where records are available.

These comparisons show that the model accurately 

predicts the changes in the shape of the wave as it 

moves downstream, as well as the decrease in peak 

discharge and increase in trough discharge 

resulting from the wave spreading as it moves 

downstream. The agreement in the peak and trough 

discharges between the model-calculated hydrographs and hydrographs computed from the 

streamflow-gaging stations records also indicates 

steady and unsteady inflows were accurately 

added. The greatest average absolute error in the 

model-calculated wave travel time was 2.01 hours 

at the streamflow-gaging station above Diamond 

Creek for research flows F2 and G2. This error was

28 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 1990-91
Lees Ferry

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cc

8

60

50

40

30

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75 175 275 

LOCATION, IN KILOMETERS FROM LEES FERRY

375

 

O

EXPLANATION 

UPSTREAM FROM LEES FE RRY 

DOWNSTREAM FROM LEES FERRY 

CALCULATED WAVE TRAVEL TIME 

MEASURED WAVE TRAVEL TIME 

MODEL AVERAGE ABSOLUTE ERROR

Figure 21. Calculated and measured wave travel time from Glen Canyon Dam, and the model average absolute 

error for research flows A-G2.

Summary and Conclusions 29
Lees Ferry

25 0 75 175 275 

LOCATION, IN KILOMETERS FROM LEES FERRY

375

Figure 21. Continued.

less than 5 percent of the total time (about 47 

hours) for the wave to travel 386 km downstream 

from Glen Canyon Dam to Diamond Creek. The 

hydrographs calculated by the one-dimensional 

unsteady flow model, therefore, are in good 

agreement with the hydrographs computed from 

gaging-station records.

REFERENCES CITED

Graf, J.B., 1995, Measured and predicted velocity and 

longitudinal dispersion at steady and unsteady flow, 

Colorado River, Glen Canyon Dam to Lake Mead:

American Water Resources Association, Water 

Resources Bulletin, v. 31, no. 2, p. 265-281.

Kaplinski, M., Hazel, I.E., Jr., Beus, S.S., 1995, Monitoring 

the effects of interim flows from Glen Canyon Dam 

on sand bars in the Colorado River corridor, Grand 

Canyon National Park, Arizona Final report: 

Flagstaff, Arizona, Northern Arizona University Final 

Report to the National Park Service, Cooperative 

Agreement No. CA8022-8-0002, 62 p. [in press]

Wiele, S.M., and Smith, J.D., 1995, A reach-averaged 

model of diurnal discharge wave propagation down 

the Colorado River through the Grand Canyon: 

American Geophysical Union, Water Resources 

Research, [in press]

30 Calculated Hydrographs for Unsteady Research Flows, Colorado River Downstream from Glen Canyon Dam, 1990-91