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COLUMBIA RIVER THERMAL EFFECTS STUDY
VOLUME II: TEMPERATURE PREDICTION STUDIES
January 1971
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FOREWORD
The Columbia River Thermal Effects Study was undertaken in pur-
suit of the policies and objectives of the Federal Water Pollution
Control Act, particularly as amended by the Federal Water Quality
Act of 1965, which required the establishment of water quality stan-
dards for the protection and enhancement of water quality throughout
the United States. In the process of establishing standards during
the period 1965-1968, the State and Federal water pollution control
agencies recognized water temperatures as an important factor affect-
ing water uses, both directly, as in the case of aquatic life, and
indirectly, as in the synergistic effects of temperature with other
parameters such as dissolved oxygen. In attempting to define temperature
requirements in the standards, however, pollution control authorities
encountered insufficient scientific knowledge and agreement on the
precise limits needed to protect water uses.
The Columbia River Thermal Effects Study was initiated in
July, 1968, in response to the specific problem of two inconsistent
temperature standards adopted for the Columbia River by the
States of Oregon and Washington, which share it as a border. Before
attempting to resolve these inconsistencies, the State and Federal
pollution control agencies could benefit from improved knowledge on
the temperature requirements and tolerances of the Columbia's Pacific
salmon and improved techniques for evaluation and prediction of the
temperature in the Columbia system. The report of the study con-
sists of two volumes. The first concerns the biological effects of
water temperature on Pacific anadromous fish in the Columbia River
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system. The second describes the application of mathematical models
to the Columbia River for prediction of water temperatures.
In the Pacific Northwest, standards were generally required to
protect the economically important Pacific salmon, a cold-water
anadromous species. The upriver runs of Columbia River fish resources
have been reduced and endangered by the physical alteration and blockage
of migration routes by the Nation's largest system of dams and
reservoirs. The quality of the aquatic environment has also been
modified by the discharge of pollutants and impoundment of the river's
flow in a series of reservoir lakes reaching into Canada. Particularly
regarding temperature quality, the Columbia River temperatures have
been both spatially and temporally altered by man's activities and
use of the water resources of the Region.
At about the time standards were established, public and
private electric power interests in the Northwest announced forecasts
of vastly increased power demands. The hydroelectric power potential
of the Northwest is nearly exhausted, and thermal power sources are
planned to meet future needs. This presented further potential for
modification of the thermal regime of the Columbia River system.
Initially, power producers assumed the possibility of using Columbia
River system waters for once-through cooling at thermal power plants.
The prospect, however, of numerous discharges of large quantities of
heated effluents to inland waters has since prompted the Region's
water pollution control agencies to issue policy statements which
require complete offstream cooling for thermal power plants located
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on inland waterways in the Basin. Power planners have accepted this
policy of offstream heat controls throughout the Basin.
Among the remaining environmental problems associated with in-
creased thermal power production is the projected use of the
existing hydroelectric system for power-peaking, with thermal units
providing the baseload, or firm power. The potential water quality
effects of exaggerated flow modification caused by these peaking
operations emphasizes the need to understand the existing thermal
regime of the Columbia River system. The prospects of industrializa-
tion, upon which the power demands are based, hold further potential
for environmental impacts which would require sound standards and
controls.
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CONTENTS
Chapter Page
I INTRODUCTION 1
Purpose 1
Scope 3
Authority 4
II SUMMARY 5
General 5
Conclusions 6
Recommendations 8
III HYDROLOGY, METEOROLOGY, AND GEOGRAPHY OF THE
COLUMBIA RIVER BASIN 9
Geography 9
Stream System 9
Climate 13
Hydrology 14
Water Resource Development 16
IV WATER TEMPERATURE REGIME OF THE COLUMBIA,
SNAKE, AND WILLAMETTE RIVERS 19
The Columbia River in Canada 20
Lake Roosevelt 23
Grand Coulee Dam to Priest Rapids Dam 23
Priest Rapids Dam to the Snake River Confluence. 25
The Snake River Below Brownlee Dam 26
Snake Confluence to Bonneville Dam 27
Bonneville Dam to Astoria 27
The Willamette River 28
V MATHEMATICAL MODELS 29
Deep Reservoir Models 31
Basic Equations and Assumptions 31
Model Verification 33
Data Requirements 34
River-Run Model 35
Basic Equations and Assumptions 35
Model Verification 38
Data Requirements 39
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CONTENTS (Cont.)
Chapter Page
Weakly Stratified Reservoirs 39
Model Verification 40
Data Requirements 40
Estuary Model 41
Basic Equations and Assumptions 41
Model Verification 44
Data Requirements 44
VI OPERATION OF MODEL 47
Temperature Simulation 47
Discussion of Temperature Simulations 51
BIBLIOGRAPHY. . . „ 63
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FIGURES
Number -Title Page
1 Columbia River Basin Map 10
2 Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case I .... 52
3 Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case II. ... 55
4 Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case III ... 57
5 Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case IV. ... 58
6 Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case V .... 60
7 Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case VI. ... 62
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LIST OF TABLES
Table Title Page
1 Mean Discharges at Key Locations for the
Period of Record 15
2 Major Dams and Reservoirs, Columbia River Basin 18
3 Temperature Reporting and Recording Stations on
the Columbia River and Major Tributaries ... 21
4 Monthly Water Temperatures (°F) in the Columbia
River Basin at Selected Stations, Calendar
Year 1967 22
5 Mean (y) and Standard Deviation (a) in Degrees
Fahrenheit for the Difference Between Simulated
and Observed Temperatures at Six Locations on
the Columbia River 50
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INTRODUCTION
Purpose
This report describes the application of the mathematical models
which were adapted to the Columbia River as part of the Columbia River
Thermal Effects Study. The models provide a tool for predicting river
temperatures as a function of flow regulation and point-source thermal
inputs.
The physical, chemical, and biological characteristics of water
are highly dependent on water temperature. Important examples include
the effects of temperature upon: 1) the solubility of gases such as
oxygen and nitrogen; 2) the stages of fish development; 3) the growth
rate of algae; 4) the taste and odor of water; and 5) the density and
stratification of water bodies. Spatial and temporal changes in water
temperature, even though subtle, may disturb the life systems which
have developed under natural conditions. In the Columbia River main-
stem, changes in the natural temperature regime have been noted by
Goebel and Jaske (1967), Davidson (1969), and Moore (1968). The most
significant changes have been in the Columbia River above its con-
fluence with the Snake River. The principal effect has been the
shifting of water temperature maximums so that they occur later in
the year. The resulting temperatures are above the optimums for
salmonids during September and October, according to criteria recom-
mended by the Pacific Northwest Pollution Control Council (1966).
The construction of numerous dams has been attributed as the
primary cause of this change in the temperature regime; the discharge
of cooling water from nuclear power plants on the Hanford Reservation
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in southeastern Washington has also been a contributing factor.
Proposals for additional storage in the Canadian treaty dams, the
construction of a third powerhouse at Grand Coulee Dam, and the
proposed construction of Ben Franklin Dam in the last unimpounded
reach of the river offer potential for further modification of the
river's temperature.
The temperature prediction models described in this report
provide a valuable input for developing a river management system
which considers the effects of reservoir releases on water quality.
The reservoir projects in the Columbia River Basin are operated
primarily for power, flood control, irrigation, and navigation.
The temperature models can be used to evaluate the effects of a
given water management scheme on an important aspect of water quality.
The capability to predict the effect of reservoir release schedules
provides water management agencies the opportunity to influence the
timing and method of withdrawals to minimize adverse temperature
changes in the Columbia River. The models can also be expanded to
include other water quality parameters such as dissolved oxygen and
nitrogen. A water management system which considers water quality
can be a powerful tool in developing release schedules to enhance
the fishery and at the same time optimize flow release for competing
water uses, such as power generation, irrigation, and flood control.
The models can be used as a planning as well as an operational
tool. The capability to forecast the impact of future projects on
water temperature, using advanced techniques for hydrologic forecasting
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and the generation of synthetic weather data has been demonstrated.
In this respect, the mathematical models which have been developed
are sufficiently general so as to be usable in systems other than the
Columbia Basin.
Scope
The Temperature Prediction Study enlarged upon earlier work
performed by the Environmental Protection Agency (EPA) which con-
centrated on the river-run reservoirs of the mid-Columbia. The
scope of the present study has been to adapt, verify, and maintain
an operational system of mathematical models of the Columbia River
from the Canadian border to the river's mouth. The variation in
hydraulic characteristics along the river requires that these models
be capable of predicting temperatures in river-run reservoirs, in
deep reservoirs, and in the estuary. The intent was, insofar as
practicable, to adapt available models to the conditions encountered
in the Columbia River. Under contract with EPA, Water Resources
Engineers, Inc. modified the deep reservoir model they had developed
for application to Columbia Basin Projects. The estuary model,
originally developed by Water Resources Engineers, Inc., was adapted
for use on the Columbia River estuary by the EPA's Coastal Pollution
Research Program, Pacific Northwest Water Laboratory, Corvallis, Oregon.
Development of a water temperature measurement and reporting
program was also included to provide a means for verifying the models.
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Authority
The Columbia River Thermal Effects Study (CRTES) was authorized
by the Secretary of the Interior in February, 1968.— In his approval
of the water quality standards for the State of Washington, the
Secretary recognized that the temperature criteria set by the State
for the Columbia River were inconsistent with those set by the State
of Oregon for the same waters. Rather than disapprove the temperature
criteria portion of Washington's standards, the Secretary directed
that the Thermal Effects Study be completed to provide further know-
ledge with which to reconsider the adequacy of temperature criteria
for the Columbia River.
The Northwest Regional Office of the Environmental Protection
Agency was directed to provide leadership in the study. The Tempera-
ture Prediction portion of the CRTES was coordinated through the
Water Supply and Pollution Control Committee of the Pacific Northwest
River Basins Commission.
\J On December 3, 1970, the Presidential Order creating an
independent Environmental Protection Agency took effect. The EPA
incorporates many Federal programs concerning the environment, in-
cluding water pollution control. The Federal Water Quality Adminis-
tration (formerly the Federal Water Pollution Control Administration)
in the Department of Interior was abolished and the water pollution
control responsibilities and authorities of the Secretary of the
Interior were transferred to the Administrator of EPA.
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II. SUMMARY
General
Three numerical models have been adapted to predict temperatures
in the main stem Columbia River, extending 750 miles from the Canadian
border to the mouth of the river at Astoria, Oregon. These three
models facilitate prediction of temperatures in the four hydraulic
regimes which comprise the main stem Columbia in the United States.
The models are:
1. The weakly stratified reservoir model is a more sophisticated
version of the one-dimensional deep reservoir model developed by Water
Resources Engineers, Inc. (Orlob and Selna, 1968). In the weakly
stratified reservoir, the vertical variation of temperature is the
same order of magnitude as the horizontal variation. Lake Roosevelt,
behind Grand Coulee Dam, is a weakly stratified reservoir.
2. The river-run reservoir model was developed by the EPA for
reservoirs which are well-mixed vertically and laterally, but which
have a longtudinal temperature variation. The reservoirs between
Grand Coulee and Bonneville Dams are of this type. This model is also
used for the unimpounded reach of the Columbia River. If averages over
a tidal cycle are sufficient for application, this model can be used
in the estuary as well.
3. The estuary model was adapted by the EPA (Callaway, 1970)
from a model developed by Water Resources Engineers, Inc. for the
San Francisco Bay-Delta region. The Columbia River estuary includes
the river from Bonneville Dam to the mouth at Astoria, Oregon. The
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6
estuary, which is affected by tidal forces, may be stratified
vertically due to the intrusion of high salinity ocean water. In
the Columbia River estuary only the first 25 miles are considered
to be vertically stratified.
The computer software (programming) for the weakly-stratified
reservoir model and the river-run reservoir model, as well as the
necessary hydraulic, hydrologic, and meteorologic data constitutes
the Columbia River temperature model. This model will be used to
simulate and predict daily averaged temperatures on the Columbia
River from the U. S.-Canadian border to the mouth of the river at
Astoria, Oregon. For those cases in which smaller time scales are
important, the estuary model can be used. This would be necessary,
for example, if maximum and minimum temperatures during a tidal cycle
were needed.
Conclusions
From the test runs of the Columbia River temperature prediction
model, the following is concluded:
1. The Columbia River temperature model, consisting of the
weakly-stratified and the river-run reservoir models, has been
verified to simulate river temperatures from the Canadian-U. S. border to
Bonneville Dam. For six simulations with differing input conditions,
the maximum average error was 1.2° F and the maximum standard deviation
was 2.4° F.
2. For a release temperature at Grand Coulee Dam 5° F below the
1967 observed temperature, the temperature at the Snake River confluence
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7
was reduced 3.8° F on the average, and 1.5° F on the average at
Bonneville Dam. However, the amount of temperature reduction
available downstream from Grand Coulee varies considerably with time;
it is smallest in late summer and fall when conditions are most
critical for migrating salmon.
3. The weakly-stratified reservoir model contributed 12 percent
of the total downstream temperature error at the Snake River and 17
percent of the total error at Bonneville Dam. The major error contri-
bution occurs during the time of fall reservoir turnover, when the
prediction capabilities of the weakly-strafitied model are poorest.
4. From April through November, 1967, the heat added to the river
from the Hanford reactor complex raised the simulated water temperature
an average of 2° F at the confluence of the Columbia and Snake Rivers.
5. A more precise simulation of the Columbia River temperature
will require more detailed information on hot water release schedules
from the Hanford complex.
6. The river-run model is adequate for simulating tidally-averaged
temperatures in the Columbia River estuary. The error associated with
the estimate at Bonneville Dam and at Beaver Army Terminal was +0.2° F.
7. The effect of evaporation is most significant from the first
of August to the end of November. Prior to that time the empirical
coefficients in the evaporation equation can vary two orders of
magnitude without significantly affecting the accuracy of temperature
simulation. After the first of August, evaporation begins to play
an important role in heat budget and the determination of the correct
coefficient becomes critical.
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Recommendations
1. The models should be used to evaluate the potential for
temperature control using upriver storage. This could be accom-
plished in conjunction with a program such as the Streamflow Synthesis
and Reservoir Regulation (SSARR) system. The U. S. Army Corps of
Engineers, North Pacific Division, and the National Weather Service,
National Oceanic and Atmospheric Administration, developed this program
which is presently used to operate the hydroelectric projects on the
Columbia.
2. The effects of impoundments in the Columbia River in Canada
and on the main stem Snake River should be incorporated into the
temperature prediction model.
3. High temperature release schedules from the Hanford area
should be made available to better predict the river's thermal regime.
4. The weakly-stratified and river-run reservoir models should
be applied to other river basins for purposes of planning and water
quality control.
5. Continued study of evaporation processes at the air-water
interface would benefit the heat budget approach to temperature
prediction.
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III. HYDROLOGY, METEOROLOGY AND GEOGRAPHY
OF THE COLUMBIA RIVER BASIN
Geography
The Columbia River drains 259,000 square miles in the Pacific
Northwest States of the United States and southeastern British
Columbia in Canada (Figure 1). The area is characterized
by rugged mountain ranges interspersed with valleys and plains.
Stream gradients are generally steep, and mountain torrents which
originate in headwater areas flow quickly down to the valleys
where they join major tributary rivers. The interior Columbia Basin
and Snake Plain are flat, arid, and relatively low plateaus lying
within the surrounding mountain areas. The Columbia and Kootenai
River drainages in Canada are extremely rugged mountain areas,
dotted with glaciers and ice fields in the higher and wetter locations
Along the coastal regions of western Oregon and Washington the
north-south Cascade Range forms an effective barrier between the
interior and the relatively minor coastal sections.
Stream System
The main stem of the Columbia River heads in Canada at Columbia
Lake, British Columbia, and flows north to the Big Bend. Then it
flows south about 130 miles to the Arrow Lakes, through which
the river flows 110 miles to the outlet of the Lower Arrow Lake
near Castlegar, British Columbia. The Columbia River continues its
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FIGURE 1
Columbia River Basin
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12
route generally in a southerly direction to the Canadian border,
traverses the State of Washington through the Columbia Basin,
and finally flows west to form the border between Oregon and Washington.
The slope of the river under natural conditions is fairly steep,
with an average gradient in excess of two feet per mile.
The major tributaries of the Columbia River include the Kootenai,
Clark Fork-Pend Oreille, Spokane, Snake, and Willamette Rivers. The
Kootenai lies largely in Canada, but flows southward in the United
States, making an arc through western Montana and northern Idaho,
and flowing north back into Canada. It flows through Kootenay
Lake, a major natural lake in south-central British Columbia.
The Kootenai River continues west from the outlet of Kootenay
Lake to join the Columbia below Lower Arrow Lake.
The Clark Fork-Pend Oreille system drains a large part of
western Montana. The Clark Fork heads in the Continental Divide and
flows northwest into Idaho where it terminates in Pend Oreille
Lake, another large natural lake in the Columbia River system.
The outflow from Pend Oreille Lake becomes the source of the Pend
Oreille River, which flows north about 75 miles to the Canadian
border. It then flows west about 16 miles to its junction with
the Columbia River. The Flathead, Blackfoot, and Bitterroot Rivers
are all major tributaries of the Clark Fork. Flathead Lake, located
on the Lower Flathead River, is another large body of water which
affects storage and flow of water in the Columbia River system.
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13
The Snake River drainage is the largest of all Columbia River
tributaries. The Snake River heads in western Wyoming in Yellowstone
National Park and flows west through the arid Snake River plains
of southern Idaho. Then it turns north, forming the boundary
between Oregon and Idaho. The Salmon and Clearwater Rivers join
the Snake River from the east, after which the river emerges into
the Interior Columbia Basin. The Lower Snake River trends in
an arc about 140 miles through southeastern Washington, to join
the Columbia near Pasco, Washington.
Climate
The climate of the Columbia Basin is characterized by cold,
wet winters and generally hot, dry summers. Precipitation varies
widely, depending primarily on topographic influences. The interior
Columbia Basin and Snake Plain generally receive less than 10 inches
per year, but in some of the mountain areas of Canada the annual
precipitation exceeds 100 inches per year. Air temperature also
varies widely with location. In the relatively low Columbia Basin
and Snake Plain, summertime maximums often exceed 100° F for prolonged
periods. In the mountains of Canada temperatures remain cool
during the summer. Winters are generally cold throughout the
basin, and heavy precipitation falls in the form of snow in the
mountain areas. The snowpack accumulates throughout the winter
as the result of frequent passage of storms from the Pacific,
and the snow does not melt appreciably until April or May. Precipitation
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14
is at a maximum during the winter months for the basin as a whole,
but a secondary maximum occurs in June in the Rocky Mountain areas
in the eastern portion of the basin. Winters are cloudy, and
solar radiation is at a minimum, until the arrival of spring.
Solar radiation is at a maximum in June and July, and clear skies
prevail in the plains throughout the summer. Convection activity
in the mountains results in summer build-up of clouds and shower
activity in the afternoons. Occasionally, general storms from
the Pacific invade the northern portions of the basin during the
summer.
Western Oregon and Washington have moderate climates with winter
air temperatures at low elevations seldom below freezing and summer
air temperatures seldom above 100° F for prolonged periods. Average
annual precipitation west of the Cascades is greater than 40 inches
in most areas. Coastal stations are typically much higher; for
example, Astoria, Oregon has an average annual rainfall of 80 inches.
Below 5000 feet, most of this precipitation occurs as rainfall with
70 percent or more occurring between October and March.
Hydrology
Surface runoff in the Columbia River Basin is characterized by
a typical snowmelt regime. Low streamflows prevail during the winter,
and high flows during the spring and early summer, particularly in
the elevated basins. Melting of the winter snowpack accumulation
takes place in May and June, and streamflows rise until the snowpack
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15
can no longer support the high flows. The streamflow recedes
gradually during the summer, and the flows are derived from ground
water recession into the fall and winter seasons. Occasionally,
runoff from winter storms augments the base flow, and significant
rises may occur. With the exception of the Willamette, these rises
are of relatively short duration and are not of the general magnitude
of the rises during the spring snowmelt.
In the Willamette River system, peak flows occur in December,
January, and February, corresponding to the period of heaviest rainfall
in this region. Snowmelt at the higher elevations during May and
June contributes to relatively high runoff during this period.
Mean monthly and mean annual discharges for key locations
on the main stem and tributaries are given in Table 1.
TABLE 1
MEAN DISCHARGES AT KEY LOCATIONS FOR THE PERIOD OF RECORD
Mean Monthly Discharge in cfs
River
Columbia
Kootenai
Clark Fork-
Pend
Oreille
Spokane
Snake
Snake
Willamette
Location
Revelstoke,B.C.
Birchbank,B.C.
Trinidad, Wash.
The Dalles, Ore.
Libby , Montana
Nelson, B .C.
Plains , Montana
Z-Canyon, Idaho
Long Lake, Wash.
Weiser, Idaho
Clarks ton, Wash .
Portland, Ore.
Jan
5,400
19,900
44,900
95,700
3,500
10,100
10,000
14,700
6,900
15,000
29,800
78,100
Apr
13,300
34,900
88,200
201,800
11,200
20,100
19,100
26,900
17,100
27,700
84,500
46,900
Jun
84,800
203,200
318,400
494,700
44,600
89,900
59,300
76,700
11,800
27.400
110,800
20,200
Aug
58,100
102,800
137,300
187,300
10,500
23,200
11,000
17,300
2,100
9.100
19,500
5,200
Oct
17,600
42,400
60,600
99,100
7,100
13,200
9,300
12,400
3,000
13,500
23,400
10,100
Mean
Annual
cfs
33,900
71,000
116,900
195,400
13,600
28,000
19,600
26,900
8,100
17,700
48,900
32,100
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Water Resource Development
The Columbia River and its tributaries are a highly developed
water resource. The only portion of the River which is not impounded
is the reach between Priest Rapids Dam and the confluence of the
Snake River. The 11 main-stem projects, from Grand Coulee to
Bonneville Dam, develop approximately 1,240 feet of the 1,290
feet of hydraulic head in this reach of the Columbia. The completion
of the four Columbia Treaty reservoir projects in Canada and
the United States will result in significant control of flows
in the Upper Columbia and Kootenai River Basins (the Columbia Treaty
between the United States and Canada relates to the Cooperative
development of the Columbia River Basin water resources). Nine
major projects have been completed on the Clark Fork-Fend Oreille
systems, which, with the completion of Boundary Project in the
Lower Clark Fork, will develop a large part of the power potential
in that basin. The Snake River below Weiser, Idaho, is also fast
approaching full development, except for those streams presently
reserved from development in the interest of preservation of fish
and wildlife. The water resources of the Snake River Basin above
Weiser are largely developed in the interest of irrigation, power,
and flood control.
The ownership of the dams in the Columbia River Basin includes
Federal agencies, private power companies, and public utility
districts. The installed capacity of the hydro-electric projects
existing or under construction in the Pacific Northwest is about
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17
20,000,000 kilowatts (kw), of which about one-half is in Federal
projects. Thermal generation of electricity is relatively small
at the present level of development (about 1,200,000 kw of installed
capacity, including 800,000 kw at Hanford) and it is used primarily
to supplement hydro-electric generation in periods of low streamflow.
The dams and reservoirs are multiple purpose, serving the
functions of irrigation, navigation, flood control, preservation of
fish and wildlife, municipal and industrial water supply, and
recreation, as well as hydro-electric power. Irrigation presently
includes providing water for agricultural use to approximately
5,000,000 acres of land; and plans call for an additional 5,000,000
acres to be irrigated in the next 50 years. Slack-water navigation
is planned to extend 330 miles up the Columbia River to Pasco,
Washington, and an additional 140 miles up the Snake River to
Lewiston, Idaho.
Table 2 presents a list of major dams and reservoirs, by
tributaries, which may have an effect upon water temperature studies.
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TABLE 2
MAJOR DAMS AND RESERVOIRS, COLUMBIA RIVER BASIN
S tream
Columbia River
River
Mile
1018.1
780.6
596.6
545.1
516.6
474.5
453.4
415.0
397.1
292.0
215.6
Project Name
Mica
Arrow Lake
Grand Coulee
Chief Joseph
Wells
Rocky Reach
Rock Island
Wanapum
Priest Rapids
McNary
John Day
Owner or Operator
B.C. Hydro Authority
B.C. Hydro Authority
U.S. Bureau of Reclam.
U.S. Corps of Engineers
Douglas County PUD
Chelan County PUD
Chelan County PUD
Grant County PUD
Grant County PUD
U.S. Corps of Engineers
U.S. Corps of Engineers
Status
UC*
UC
C
C
C
C
C
C
C
C
C
Active Stor.
Acre-Feet
12,000,000
7,100,000
5,232,000
Pondage
Pondage
Pondage
Pondage
330,000
170,000
Pondage
500,000
Primary Proj . Function
Power,
Power,
Irrig.
Power,
Power
Power
Power
Power,
Power,
Power,
Power,
Flood Control
Flood Control
, Power, Fl. Con.
Irrigation
Flood Control
Flood Control
Navigation
Navigation,
Flood Control
Kootenay River
Duncan River
So. Fk. Flathead
Flathead River
Clark Fork
Priest River
191.5
146.1
219.9
16.1
8.3
5.2
72.0
208.0
169.7
149.9
44
The Dalles
Bonneville
Libby
Corra Linn
Duncan Lake
Hungry Horse
Kerr (Flathead
Lake)
Thompson Falls
Noxon Rapids
Cabinet Gorge
Priest Lake
*UC-Under Construction
C-Constructed
U.S. Corps of Engineers
U.S. Corps of Engineers
U.S. Corps of Engineers
Consolidated Mining and
Smelting Company
B.C. Hydro Authority
U.S. Bureau of Reclam.
Montana Power Company
Montana Power Company
Washington Water Power
Washington Water Power
Washington Water Power
C
C
UC
C
UC
C
C
C
C
C
C
Pondage
Pondage
4,965,000
817,000
1,400,000
2,982,000
1,219,000
Pondage
231,000
Pondage
72,401
Power,
Power,
Power,
Power,
Power,
Power,
Power,
Power
Power,
Power
Power
Navigation
Navigation
Flood Control
Flood Control
Flood Control
Flood Control
Flood Control
Flood Control
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IV. WATER TEMPERATURE REGIME OF THE
COLUMBIA, SNAKE, AND WILLAMETTE RIVERS
The temperature regime of major streams i,n the Columbia River
Basin has been modified by the construction and operation of numerous
dams and by water uses such as irrigation and power plant cooling.
Existing thermal characteristics of many streams in the basin,
as well as some historical changes on a few streams, are evidenced
by recorded water temperature data. Since the emphasis on water
temperature observations is relatively new, only a few stations in
the basin have long term daily records. While records of spot ob-
servations at some locations go as far back as 1915, regular
observations did not commence until the 1930's. These early
observations consisted of once daily or twice daily readings. Often
the time of observation was not recorded and it is therefore not
possible to relate the observed temperature to a corresponding point
in the dirunal cycle. In the mid-1940's, the introduction of
recording hydrothermographs in the basin enabled a significant
expansion in systematic water temperature observations. The instruments
needed only periodic servicing and it was possible to locate them
away from populated areas, thus increasing the number of water
temperature stations and also giving them a wider distribution.
By providing a continuous record, information on diurnal as well
as annual variations in stream temperature is obtained.
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20
This coverage has been extended by the Regional Temperature
Reporting Network, a part of the Columbia River Thermal Effects Study
(Schmidt and Cleary, 1969). The stations installed under this program
provide continuous records of temperatures at selected sites. The U.S.
Geological Survey, Battelle Northwest, the U. S. Army Corps of Engineers,
and public utility districts provide temperature monitoring at other
sites. Table 3 shows all the sites on the main stem Columbia at which
temperatures are reported. The U. S. Geological Survey summarizes
and reports most of the temperature data on a weekly, monthly, and
annual basis. Each year they publish a comprehensive report of
the temperature regime of the main stem Columbia, as well as the
Snake River. Table 4 shows monthly water temperatures for calendar
year 1967 at selected stations in the Columbia River Basin.
The Columbia River in Canada
Until October, 1968, when Arrow Lake Dam was completed, the
temperature regime of the Columbia River in Canada was unaltered
from the natural state. Temperature records available prior to
October, 1968, at Trail, B. C. indicate that the annual temperature
range was between 35° and 66° F, with the minimum occurring in
February and the maximum in August.
Future temperatures of the Columbia River in Canada will be
affected by the regulation of Mica and Arrow Lake Dams on the main
stem Columbia, Duncan Dam on Duncan Creek in the Kootenay River Basin,
and Libby Dam on the Kootenai River in Montana. These dams are under
construction and will be completed in 1973.
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TABLE 3
TEMPERATURE REPORTING AND RECORDING STATIONS ON THE COLUMBIA RIVER AND MAJOR TRIBUTARIES
Station
River
River Mile Type of Sensing Devise
(RM)
Owner/Cooperating agency
Harrington Point Columbia 23.5
Beaver Army Terminal Columbia 53.8
Longview, Wash. Columbia 66.0
Kalama, Wash. Columbia 74.8
Columbia City, Ore. Columbia 84.0
St. John Bridge, Ore. Willamette 6.0
Vancouver, Wash. Columbia 106.5
Warrendale, Ore. Columbia 141.0
The Dalles, Ore. Columbia 192.8
Biggs Rapids, Wash. Columbia 208.0
Umatilla Bridge Columbia 290.5
Ice Harbor Dam Snake 9.7
Richland, Wash. Columbia 340.0
Priest Rapids Dam, Wash. Columbia 395.0
Wanapum Dam, Wash. Columbia 415.0
Rock Island Dam, Wash. Columbia 453.4
Rocky Reach Dam Columbia 474.5
Chief Joseph Dam Columbia 545.1
Grand Coulee Dam Columbia 596.0
Little Falls Dam Spokane 30.0
Northport, Wash. Columbia 734.1
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
Punch Tape thermograph
Punch Tape thermograph
Punch Tape thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
7 day chart thermograph
FWQA
PGE/Battelle N. W./USGS
PGE/Battelle N. W./USGS
Clarke & Cowlitz Co. P.U.D./USGS
Corps of Engineers/USGS
FWQA
Corps of Engineers/USGS
AEC/Battelle N. W./USGS
FWQA
AEC/Battelle N. W.
AEC/Battelle N. W.
FWQA
AEC/Battelle N. W.
AEC/Battelle N. W.
FWQA
FWQA
FWQA
FWQA
AEC/Battelle N. W.
FWQA
AEC/Battelle N. W.
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TABLE 4
MONTHLY WATER TEMPERATURES (°F) IN THE COLUMBIA RIVER BASIN
AT SELECTED STATIONS, CALENDAR YEAR 1967 a/
Columbia River at Revelstoke, British Columbia
Columbia River at Trail, British Columbia
Columbia River at Northport, Washington (International Border)
Columbia River below Grand Coulee Dam, Washington
Columbia River below Priest Rapids Dam, Washington
Columbia River above Richland, Washington
Snake River at Brownlee Dam, Idaho
Snake River at Ice Harbor Dam, Washington
Columbia River at Bonneville Dam, Oregon
Willamette River at Salem, Oregon
Columbia River at Beaver Army Terminal, Oregon
Jan.
39
37
45
43
45
40
41
44
45
44
Feb.
38
39
41
42
45
38
40
44
45
44
March
40
41
40
41
44
42
44
45
46
45
April
45
41
42
45
48
48
49
49
50
50
May
49
48
46
50
54
54
53
55
58
56
June
53
54
56
56
61
56
59
July
58
58
58
61
62
68
69
65
69
Aug.
43
64
64
62
65
68
68
75
70
71
72
Sept.
42
62
62
64
64
67
70
71
69
65
70
Oct.
56
55
64
60
61
62
61
61
56
60
Nov.
49
46
57
52
54
51
49
51
53
50
Dec.
32
42
39
48
45
46
43
41
44
44
42
a/ Published monthly by Northwest Water Resources Data Center, Water Resources Division, U. S. Geological Survey
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23
Lake Roosevelt
Lake Roosevelt is the reservoir formed by Grand Coulee Dam. Lake
Roosevelt is approximately 150 miles long, stretching from River Mile
596 to the U.S.-Canadian Border. It has a maximum depth of 350 feet
and, with a total storage capacity of 9,000,000 acre-feet, is the largest
impoundment on the main stem Columbia.
In summer the reservoir becomes stratified. Temperature differences
of 12 to 13° F between top and bottom have been observed during September
(Jaske and Snyder, 1967). In the fall this stratification pattern gives
way to a temperature profile more characteristic of river-run reservoirs;
that is, the longitudinal temperature variation is greater than the
vertical variation.
Grand Coulee Dam to Priest Rapids Dam
The vertical stratification which occurs in the summer and early
fall in Lake Roosevelt has a significant effect on downstream tempera-
tures of the Columbia River. The cool bottom waters are discharged
through the turbines during the summer, resulting in outlet tempera-
tures which are lower than natural river conditions. In the late
summer and fall, when the reservoir begins to overturn, the warmer sur-
face waters begin to affect outflow temperatures, resulting in tempera-
tures which are higher than natural river temperatures. Jaske and
Goebel (1967) have shown that construction of Grand Coulee Dam has
resulted in a phase shift of the water temperature maximums at Rock
Island Dam. The maximum water temperature at Rock Island occurs 30
days later on the average, than it did prior to the construction of
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24
Grand Coulee Dam. Similar results have been obtained by Davidson
(1969) and Sylvester (1963). Figure 5 shows monthly outlet tempera-
ture ranges at Grand Coulee Dam for 1967.
The future thermal effects of Lake Roosevelt will depend upon
three principal factors: the influence of Canadian impoundments on
the thermal regime of Lake Roosevelt; the thermal effect of the third
power house under construction at Grand Coulee Dam; and, perhaps the
most significant factor, the use of selective withdrawals for down-
stream temperature control. Releases can be made from four levels at
Grand Coulee, in addition to the spillway. The third power house is
an important factor because its turbine intakes will be located closer
to the surface of the reservoir than those of the two existing power
houses.
There are six pools between Grand Coulee and Priest Rapids Dam:
Chief Joseph, Wells, Rocky Reach, Rock Island, Wanapum, and Priest
Rapids. Chief Joseph has a maximum depth of 165 feet. Depths of
the remaining five reservoirs range from 54 to 93 feet at their deepest
points.
These six reservoirs do not develop vertical stratification of more
than 1° F and do not have as great an effect upon downstream temperature
as Lake Roosevelt. These reservoirs, however, are wider and deeper
than the natural river and would be expected to alter the temperature
regime. Jaske and Goebel, for example, have concluded that the con-
struction of Chief Joseph Dam has resulted in a three-day delay of the
water temperature maximum at Rock Island Dam (1967). Future temperatures
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25
in this reach of the river will depend primarily upon release
schedules at Grand Coulee Dam.
Priest Rapids Dam to the Snake River Confluence
Between Priest Rapids Dam and the Snake River confluence, a
distance of 70 miles, the river is unimpounded. It is within this
reach that the Hanford Works discharges high temperature cooling
water from nuclear reactors. The Hanford Works is the largest
identifiable source of advective heat on the Columbia River. No
public information has been released on the discharge temperature or
discharge rates because of classification requirements. However,
Jaske (1969) has reported that from 1965 to 1967 the combined
effects of Hanford and natural heat exchange contributed heat
at the rate of 20,000 megawatts to the river between Priest Rapids
and Richland. Without data on the thermal loadings at the Hanford
Works, no realistic energy budget of the Columbia River downstream
can be obtained.
The future temperature regime of this reach of the river will
depend primarily upon thermal discharges from the Hanford Works.
Other factors influencing the temperature will be upstream reservoir
regulation for temperature control and power peaking and the proposed
Ben Franklin Dam.
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26
The Snake River Below Brownlee Dam
The Snake River has a significant influence upon water temper-
ature in the Columbia River. In August, the month of maximum
temperature, the Snake registers a temperature about 7 F higher
than that of the Columbia River near their confluence. Since the
latter has a discharge of about six times that of the former, the
temperature differential causes an average increase in the temper-
ature of the Columbia River of about 1° F. Changes in the thermal
regime of the Snake River will therefore have an impact on temper-
atures in the Columbia River.
From a temperature standpoint, the lower Snake River is little
affected by conditions above Brownlee Reservoir, and the 350 miles
of the Snake River from the head of Brownlee Pool to the mouth can
be considered as an independent unit. Flow regulation by Brownlee
Reservoir has altered the natural temperature regime which previously
existed at the damsite. The principal modifications have been the
reduction in summer temperatures, the increase in fall temperatures,
and a shift in the period of peak temperature from July to August.
Future temperature of the Snake River in this stretch will de-
pend upon the operation of Hells Canyon Dam, Brownlee Dam, and,
if one is constructed, any high dam in the Middle Snake.
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27
Snake Confluence to Bonneville Dam
The 200-mile reach of the river from the Snake confluence to
Bonneville Dam consists of four pools. These are formed by
McNary, John Day, The Dalles, and Bonneville Dams. The pools are
shallow and temperature surveys indicate they are well-mixed vertically,
typical of river-run reservoirs. Analysis of temperature records
at Bonneville Dam from 1938 to 1966 by Moore (1968) indicates
that upstream dam regulation and water uses have had only a slight
effect on the natural temperature regime at Bonneville Dam.
The future thermal regime of this reach will depend upon
regulation of main stem reservoirs for temperature control and
power peaking, and utilization of Snake River reservoirs for temperature
control and irrigation.
Bonneville Dam to Astoria
The 146-mile reach of the Columbia River below Bonneville Dam
is the only portion of the main stem in the United States which has
no dams and in which none is proposed. In this reach, therefore,
the Columbia River will continue to be a free-flowing stream.
Temperatures in this portion of the river are not presently
influenced significantly by upstream reservoir operations or thermal
loadings, and the prevailing regime can be considered as the natural
temperature regime.
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28
The future temperature regime of this reach will be influenced
by flow regulation at Bonneville Dam for power peaking. Two thermal
power plant sites have been proposed for this reach of the Columbia,
one at Rainier on the Oregon side of the river, and one at Kalama
on the Washington side.
The Willamette River
Peak flows in the Willamette River occur during the winter months
of December, January, and February when the Columbia River is low.
During this period the Willamette River discharge is one-third to one-
half the Columbia River main stem discharge and could, therefore, have
a significant effect upon the Columbia River's temperature. Under
present conditions, however, temperatures of the two rivers at their
confluence are within 2° C of each other during the winter months.
During the summer months the Willamette River temperature may
be as much as 3° C higher than the Columbia, but the average discharge
of the Willamette River is less than 10 percent of the Columbia River.
The future thermal regime of the Willamette will depend upon the
regulation of main stem and tributary reservoirs.
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V. MATHEMATICAL MODELS
In the Columbia River system five types of hydraulic
environments can be recognized:
1. The deep reservoir in which the temperature varies in the
vertical only. Examples of this type on the Columbia River
main stem are the Arrow Lakes in Canada. In addition,
there are numerous such reservoirs on tributary rivers.
Hungry Horse on the South Fork of the Flathead in Montana,
and Detroit Reservoir on the North Santiam in Oregon, are
typical deep reservoirs.
2. The weakly stratified reservoir in which the longitudinal
temperature variations are of the same order as the ver-
tical variation. Lake Roosevelt, behind Grand Coulee Dam,
is a reservoir with these characteristics.
3. River-run reservoirs in which the temperature is uniform
in the vertical, but varies longitudinally. All the reser-
voirs on the main stem Columbia below Grand Coulee can be
classified as river-run reservoirs, although some strati-
fication has been observed in the pool behind Wanapum Dam.
4. The unimpounded reach between Priest Rapids Dam and the
Snake River Confluence.
5. The Columbia River Estuary is that portion of the river
which is influenced by tidal forces, and includes the en-
tire stretch of the river from Bonneville Dam to the mouth.
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30
Three models have been developed for the Columbia River Thermal
Effects Study to simulate temperature in the five hydraulic environments,
These models are based upon numerical solutions to the conservation
laws of physics:
(1) Conservation of momentum
(2) Conservation of energy
(3) Conservation of mass
In their most general form, these mathematical differential
equations are extremely difficult to solve. A general numerical
solution to these equations is, in principle, possible. However,
the development of ADP software and the amount of computer memory
and execution time required make this approach impractical for
a project such as the Columbia River Thermal Effects Study. In
each of the models developed for this study, only those terms
which are important for the transfer of momentum, heat and mass
have been kept. These are determined from experience gained
through laboratory and field experiments. The final test, of
course, is whether or not the particular model is able to simulate
the temperature in the appropriate environment.
The following sections describe the models that have been de-
veloped for the Columbia River Thermal Effects Study and the
testing program conducted to establish their validity.
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31
Deep Reservoir Model
Basic Equators and Assumptions
The method for simulating temperature in deep reservoirs is
based upon a numerical solution of the one-dimensional form of the
energy equation, where the reservoir is divided into horizontal
layers .
pCp AJ + Aj+1 d0. AZj = AJ + Aj+1 h.
where
dt
PCP
pCp {aj+1Aj+1/0.+1 -0.
/>
(4.1)
C = heat capacity of water
p = density of water
= area of upper plane bounding the j element
A. = area of lower plane bounding the j element
h. = change in external solar heat flux per unit of water depth
= coefficient of "effective" diffusivity at the upper boundary
of the j element
AJ = coefficient of "effective" diffusivity at the lower bonndry
of the jth element
AZ = thickness of the jth element
0. = temperature of the j element
-------
32
6-j_ = temperature of inflowing water
Q.. = inflow to the jtn element
60j = outflow from the j^ element
QVO-J = vertical transport through the top boundary of element j.
Q .. = vertical transport through the bottom boundary of element j.
The following assumptions have been made:
1. All heat transfer occurs along the vertical axis.
2. All the heat advected to the reservoir by a fluid inflow
is completely and instantaneously distributed throughout
the horizontal element that receives this inflow.
3. Vertical exchange of heat due to turbulent processes can
be modelled by a Fickian diffusion process. This diffusion
process is characterized by an "effective" diffusion co-
efficient .
4. The level at which an inflowing source enters the reservoir
is determined by finding where in the reservoir the inflow
is neutrally buoyant. Temperature is the only factor used
to determine the density.
5. Vertical distribution of temperature in outflowing water is
determined from the experimental work of Debler (1959) and Craya
(1949) depending upon the nature of the reservoir stratification.
6. The heat budget at the surface can be described by methods
given in Wunderlich and Elder (1968).
7- The geometry of the model consists of finite segments de-
veloped from horizontal slices taken from the prototype.
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33
8. No heat is transferred through the sides or the bottom of
the reservoir.
9. Convective mixing occurs when the temperature gradient is
below a critical value.
Given the initial temperature and time rate of temperature
change, Equation (4.1) is solved numerically to obtain the reservoir
temperature as a function of time and depth.
More specific detail regarding this model can be found in two
publications by Water Resources Engineers, Inc.:
(1) Prediction of Thermal Energy Distribution in
Streams and Reservoirs, prepared for the
Department of Fish and Game, State of California, by
Water Resources Engineers, June 1967.
(2) Mathematical Models for the Prediction of Thermal
Energy Changes in Impoundments, prepared for the
Federal Water Quality Administration by Water
Resources Engineers, December 1969.
Model Verification
Prototype reservoirs which have been used to verify the validity
of this model include: 1) Folsom Reservoir in California; 2) Fontana
Reservoir in North Carolina; 3) Hungry Horse Reservoir in Montana.
The report, Mathematical Models for the Prediction of Thermal Energy
Changes in Impoundments contains the results of a simulation of Hungry
Horse Reservoir as compared with observed values.
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34
Data Requirements
The following data are required as input to the model:
1. Site Characterizations
a. Depth-surface area curve
b. Latitude
c. Longi tude
d. Corrections for sunrise and sunset obstructions
e. Reservoir altitude
2. Hydrologic Data
a. Daily inflow from streams tributary to the reservoir
b. Outflow from reservoir
c. Initial reservoir surface elevation
3. Climatological Data
a. Daily average of cloud cover
b. Daily average of dry-bulb temperature
c. Daily average of wet-bulb temperature
d. Daily average of atmospheric pressure
e. Wind speed at a height of 2 meters above the
water surface.
4. Hydromechanical Data
a. Coefficients for determining effective eddy
diffusivity
b. Light extinction coefficient
c. Critical thermal gradient which determines when
reservoir begins convective mixing
-------
35
5. Water Temperature Data
a. Initial reservoir temperature
b. Initial rate of temperature change in the reservoir
c. Daily average temperature of all inflows
River-Run Model
Basic Equations and Assumptions
This model has been developed to predict temperatures in
regulated river impoundments which have only a small storage
capacity and can be considered well-mixed. The model can be
used in the estuary if it is well-mixed vertically, and if results
in terms of temperatures averaged over a tidal period are sufficient.
The temperature in river-run reservoirs can be predicted from
the one-dimensional energy equation.
pC UdT = ^
dx D (4.2)
where T — the water temperature
U — the longitudinal speed
$ — the flux of heat through the water surface
p — water density
Cp - specific heat capacity of water
D — the average depth of the reservoir
x — longitudinal coordinate
-------
36
The assumptions upon which this model is based are:
(1) The prototype reservoir is thermally well-mixed vertically
and laterally.
(2) Longitudinal diffusion and dispersion can be neglected.
(3) The water surface profile between dams is a function of
longitudinal distance only (water surface profile refers to the shape
of the water surface as seen in a longitudinal section and does not
imply an absolute surface elevation).
(4) Weather data from a representative station is adequate for
describing conditions along the river.
(5) Empirically derived coefficients can be used to evaluate
heat and mass transfer at the air water interface.
(6) The surface heat flux $, composed of the following terms:
$s - net short wave radiation
$a - net atmospheric
$b - net emitted radiation from the water surface
$e - evaporative heat flux
$h - sensible heat conduction
(7) The surface heat flux can be written as a linear function
of the water temperature, T:
$ = AT + B (4.3)
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37
The coefficients A and B are obtained from a least-squares fit
of the surface heat flux-water temperature curve. The rates of
heating/cooling are determined from heat-flux calculations over a
range of water temperatures which would include the expected maxima
and minima. These calculations are based upon the work done by
Wunderlich and Elder (1963).
If the speed, U, and the depth, D, are constant over a reach
equation (4.2) permits a solution of the form:
Ax
T = (To + B/A)e pC DU - B/A (4.4)
where TO is the initial water temperature.
If a heat source is encountered, the contribution is assumed
to be completely mixed with the main stem. The main stem temperature
is:
T = QmTm + QtT
tt
Qm = Qt (4.5)
where Tm, the mainstream temperature just upstream of the tributary
is determined from equation (4.4) and Tt, the tributary temperature,
is input data. Qm and Qt are the main stem and tributary discharges
respectively.
The various parameters in equation (4.4) are updated for each
new reach, daily period, and date. In this way downstream temperatures
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38
are predicted in terms of the linear equation describing the heat
flux, upstream water temperature, average water depth, advected
sources and travel time.
The time of travel of water through each of the reservoirs is
determined from a solution of the continuity equation. Input to
this solution includes backwater curves for each reservoir as a
function of time and cross-sectioned characteristics of the reservoir
at several stations. Stations are spaced such that each reach is 5
to 10 miles long.
The model computes travel times and surface heat flux as
the water moves through the ten projects from Grand Coulee to Bonnevi.lle
Dam. Cumulative travel times and predicted temperatures are reported
at selected points as the water moves downstream.
A complete description of this model, can be found in Working
Paper #65, A Mathematical Model for Predicting Temperature in Rivers
and River-Run Reservoirs published by the Federal Water Quality
Administration, March 1969.
Model Verification
The river-run model has been used to simulate the temperature
of the Columbia River for the periods July 22-31, 1966, August 20-
September 12, 1967, and September 14-19, 1967. The result of these
simulations are discussed in Working Paper #65.
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39
Data Requirements
The following data is required to operate the model:
1. Site Characteristics
a. Cross-sectioned area and water surface width at
regular height intervals for selected river miles.
b. Approximate latitude and longitude of river system.
c. Altitude of reservoir.
2. Hydrologic Data
a. Dam discharge at specified time intervals.
b. Tributary inflows at specified time intervals.
c. Reservoir backwater curves at specified time intervals,
3. Meteorological Data
a. Cloud cover at specified time intervals.
b. Dry bulb temperatures at specified time intervals.
c. Wet bulb temperature at specified time intervals.
d. Atmospheric pressure at specified time intervals.
e. Wind speed at specified time intervals.
4. Water Temperature Data
a. Initial river temperature at specified time intervals.
b. Temperature of tributaries at specified time intervals.
Weakly Stratified Reservoirs
A segmented version of the deep reservoir model developed by
Water Resources Engineers, Inc. was developed to simulate the more
-------
40
complex temperature patterns found in the weakly-stratified prototype,
Lake Roosevelt. The segmentation involved dividing the 150-mile long
reservoir into six reaches. Vertical profiles of the longitudinal
velocity were determined empirically. Inflows to a particular
segment consisted of contributions from tributaries and the upstream
segment.
While this model is not truly a two dimensional model it does
account for longitudinal advection of heat. This is an important
mechanism for heat transfer in Lake Roosevelt and gives rise to the
tilted isotherms observed.
A more detailed description of this model can be found in the
Water Resources Engineers publication, Mathematical Models for the
Prediction of Thermal Energy Changes, prepared for the Federal Water
Quality Administration.
Model Verification
This model has been used to simulate the temperature of Lake
Roosevelt for the period July-October 1967. The results of this
simulation as compared with the observed temperatures are presented
in Mathematical Models for the Prediction of Thermal Energy Changes.
Data Requirements
The data requirements for this model are the same as those
described in the section on the Deep Reservoir Model.
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41
Estuary Model
Basic Equations and Assumptions
The processes governing heat exchange in the estuary are the
same as those in the three reservoir types discussed in the previous
sections. However, in the estuary tidal forces play an important
role in determining the hydrodynamics. As a result, significant
changes in velocities can occur in the estuary over a period of one
tidal cycle. At some points in the estuary a reversal of the flow
occurs on this same time scale. By contrast, in the regulated stretch
of the river, which includes the reservoirs above Bonneville Dam,
time scales associated with significant changes in velocities are
of the order of days or months. To resolve the high-frequency
changes associated with tidal effects, a time-dependent model for
predicting the velocity distribution, as well as the temperature,
is necessary.
Steady-state models have been developed (Thomann, 1963) for
use in estuaries and have proved to be adequate for certain applica-
tions. In cases for which local effects are important, it is
necessary to have the capability for predicting concentrations at
regular intervals during the tidal cycle. For example, the maximum
temperature resulting from a point discharge of heat may be consider-
ably larger than the temperature averaged over a tidal cycle. The
biological studies conducted as part of the Columbia River Thermal
Effects Study illustrate the importance of thermal shock in determining
the mortality rate of anadromous fish. The time-dependent model is
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42
required to evaluate problems such as this.
The estuary model chosen for the Columbia River was originally
developed by Water Resources Engineers, Inc. for the Federal Water
Quality Administration, Southwest Region. It was adapted for use
on the Columbia River estuary by personnel of the Pacific Northwest
Water Laboratory.
The assumptions upon which the model is based are as follows:
1. The estuary is well-mixed vertically.
2. A network of one-dimensional elements with provisions to
branch flows at nodal points gives an adequate represen-
tation of the estuary.
3. The one-dimensional equations can be used along each
branch between node points.
4. Dispersion coefficients can be calculated from empirical
equations (Fischer, 1968) .
5. Surface heat fluxes can be calculated using methods
described by Wunderlich and Elder (1968).
These assumptions lead to the following set of partial differ-
ential equations:
Continuity Equation
jKAu) + B9H = 0
8x at (4.6)
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43
Momentum Equation
3^+u3u.+ g3H_ + Klulu = 0 (4.7)
3t 3x 3x
Energy Equation
Cp {^T + u j)T - _3_ (Dx ^T)} = $ (4.8)
3t 3x 3x 3x
Where:
u is the horizontal velocity
g gravitational potential
H the water depth point
K roughness coefficient
B water surface width
A cross-sectional area
T temperature
Dx dispersion coefficient
x distance between nodes
t time
$ heat sources
Equations (4.6) and (4.7) are converted to finite difference form
and solved by the "leapfrog" method. In the "leapfrog" method,
the initial conditions of velocity and depth are used to compute
velocity from the Equation (4.6); the computed velocity is substi-
tuted in Equation (4.7) to obtain a new depth which is used as the
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44
new initial condition to determine new velocities. The new velocity
is again substituted into the continuity equation and the process
continues.
The resulting velocities and water depths are edited and stored
on tape for later use by the temperature model Equation (4.8).
Solution of Equation (4.8), which predicts the temperature as a
function of time, is accomplished by a finite difference scheme
based on an explicit formulation.
A more detailed description of this model can be found in the
Federal Water Quality Administration document, Mathematical Model
of the Columbia River from the Pacific Ocean to Bonneville Dam, by
R. J. Callaway, K. V. Byram, and G. R. Ditsworth, 1969.
Model Verification
Callaway, et al (1970) have described the verification of the
temperature model in the estuary.
Data Requirements
1. Site characteristics
a. cross-sectional area, water surface width, and
distance between nodes.
2. Hydrologic data
a. tributary inflows
b. tidal elevation at estuary mouth
c. Manning coefficients
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45
3. Meteorological data
a. cloud cover at hourly intervals
b. dry-bulb temperature at hourly intervals
c. wet-bulb temperature at hourly intervals
d. atmospheric pressure at hourly intervals
e. wind speed at hourly intervals
4. Water temperature data
a. initial river temperature
b. temperature of tributary inflows
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VI. OPERATION OF MODEL
Temperature Simulation
Six temperature simulations of the combined weakly-stratified
and river-run reservoir models were made using 1967 meteorology,
hydrology and observed water temperature data. The estuary model
was not used in these simulations because of the fact that it is
used on a time scale different from the weakly-stratified and river-
run reservoir models. The testing of the estuary model has been
described by Callaway, et al (1970).
Meteorology from three cities, Spokane, Yakima, and Portland, was
used to represent climatic conditions along the river. Spokane weather
data was used from the Canadian border (river mile 740.0) to Rocky Reach
Dam (river mile 474.5); Yakima weather data was used from Rocky Reach
to Bonneville Dam (river mile 145.0); Portland weather data was used
from Bonneville Dam to the mouth of the Columbia at Astoria.
The purposes of the test program were to:
1. Determine the accuracy of the models for predicting down-
stream temperatures.
2. Determine the effect of cold water releases at Grand Coulee
Dam upon downstream temperatures.
3. Determine the effect of a constant 13,000 megawatt heat source
in the Hanford area.
4. Determine model sensitivity to variations in the constants
governing evaporative and sensible heat flux.
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48
5. Determine how the accuracy of the weakly-stratified model
affects the accuracy of temperature predictions downstream.
To evaluate these problems six conditions were established.
Predicted temperatures were compared with actual temperatures at
various thermograph stations along the Columbia River. The conditions
for the six simulations were as follows:
Case I. 1. 1967 meteorology and hydrology
2. 13,000 mw heat source in the Hanford area
3. temperature at Grand Coulee Dam predicted by weakly-
stratified reservoir model
4. evaporation rate, E=(a+bu) (es-ea), where u is the
wind speed in meters per second, es the saturation
vapor pressure in mb, and ea, the ambient vapor pressure
in mb, was determined with a=0.0 and b=1.0x!09 mb-1.
Predicted temperatures compared with actual temperatures at six
locations are shown in Figure 2. The mean and standard deviation
of the error is shown in Table 5.
Case II. 1. 1967 meteorology and hydrology
2. 13,000 mw heat source in the Eanford area
3. 1967 observed temperatures at Grand Coulee Dam used as
input to the river run reservoir model.
4. evaporation rate determined with a=0.0 and b=1.0x~°
mb-1.
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49
Predicted temperatures compared with observed temperatures at
six locations are shown in Figure 3. The mean and standard deviation
of the error are shown in Table 5.
Case III. 1. 1967 meteorology and hydrology
2. no heat source in the Hanford area
3. 1967 observed temperatures at Grand Coulee Dam used
as input to the river-run reservoir model
_o
4. evaporation rate determined with a=0.0 and b=1.0xlO
mb-1
Predicted temperatures compared with observed temperatures at
six locations are shown in Figure 4. The mean and standard deviation
of the error are shown in Table 5.
Case IV. 1. 1967 meteorology and hydrology
2. 13,000 mw heat source in the Hanford area
3. 1967 observed temperatures at Grand Coulee Dam used as
input to the river-run reservoir model
4. evaporation rate determined with a=0.0 and b-l.OxlO
Predicted temperatures compared with observed temperatures at
six stations are shown in Figure 5. The mean and standard deviation
of the error are shown in Table 5.
Case V. 1. 1967 meteorology and hydrology
2. 13,000 mw heat source in the Hanford area
3. 1967 observed temperatures at Grand Coulee Dam used as
input to the river-run reservoir model
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Table 5
MEAN, (y) AND STANDARD DEVIATION, (a) IN DEGREES FAHRENHEIT FOR THE DIFFERENCE
BETWEEN SIMULATED AND OBSERVED TEMPERATURES AT SIX LOCATIONS ON THE COLUMBIA RIVER.
SIX DIFFERENT CASES OR SIMULATIONS WERE MADE.
Case I Case II Case III Case IV Case V Case VI
y ay ay ay ay ay a
Rocky Reach Dam
Priest Rapids Dam
Confluence of the
Snake River
McNary Dam
-1.2 2.4 -0.1 1.0 -0.1 1.0 1.2 2.3 -5.9 7.7 -4.4 4.5
-1.0 2.2 -0.1 1.1 -0.1 1.1 1.7 3.3 -6.5 8.0 -4.0 4.2
-0.6 2.4 0.1 2.1 -2.1 2.7 2.5 4.7 -6.9 8.2 -3.4 4.1
-0.5 1.7 -0.5 1.3 -1.4 1.8 1.4 2.4 -6.7 7.8 -2.3 2.7
Bonneville Dam -0.3 1.8 -0.3 1.5 -1.0 1.7 2.8 4.4 -8.8 9.8 -1.9 2.6
Beaver Army Terminal 0.8 1.8 0.2 1.5 0.7 1.7 3.7 5.1 -6.0 6.6 -0.7 2.1
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51
—8
4. evaporation rates determined with a=0.0 and b=1.0xlO
Predicted temperatures compared with observed temperatures at
six stations are shown in Figure 6. The mean and standard deviation
of the error are shown in Table 5.
Case VI. 1. 1967 meteorology and hydrology
2. 13,000 mw heat source in the Hanford area
3. 1967 observed temperatures at Grand Coulee Dam minus
5.0° F used as input to the river-run reservoir model
4. evaporation rates determined with a=0.0 and b=1.0xlO~°
Predicted temperatures compared with observed temperature at six
stations are shown in Figure 7. The mean and standard deviation
of the error are shown in Table 5.
Discussion of Temperature Simulations
Case I. The purpose of this simulation was to determine the
accuracy with which the combined weakly-stratified and river^run
reservoir model could simulate water temperature in the Columbia
River. Hydraulic, hydrologic and meteorologic data from 1967 were
used and a constant heat source of 13,000 mw was added in the Hanford
area. The evaporation rate was determined from the equation E=Ca-hbu)
(eg-ea), with a=0.0 and b=1.0xlO~9mb~l. The results of the simulations
at six locations, for the period April 1 to November 30, 1967, are
shown in Figure 2.
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52
ISO 20O 220 240 260 280 300 320 340
GRAND COULEE
16O ISO 20O 220 240 260 280 300 320 340
ROCK ISLAND
160 ISO 200 220 24O 260 280 300 320 340
PRIEST RAPIDS
200 22O 240
SNAKE RIVER
160 ISO 200 22O 240 260 280 300 320 340
BONNEVILLE
DAY 100 120
160 ISO 200 220 240 260 280 300 320 340
BEAVER ARMY TERMINAL
CASE I
-PREDICTED TEMPERATURE
-OBSERVED TEMPERATURE
Figure 2. Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case I.
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53
From June 1 to October 1 the combined models simulate tempera-
tures well. However, the weakly-stratified model anticipates the
fall overturn in Lake Roosevelt by about two weeks and simulated
temperatures at Grand Coulee Dam are considerably lower than observed
temperatures from this time until the first of May.
Comparing the mean error (Table 5) in this simulation with the
mean error for Case II, in which observed temperatures at Grand Coulee
Dam were used as initial conditions, it can be seen that the weakly-
stratified model's contribution to the mean error decreases downstream.
This can be attributed to the fact that any simulated water temper-
atures at Grand Coulee Dam which are not in equilibrium with the cal-
culated atmospheric heating/cooling rates will tend toward equilibrium
as the water proceeds downstream. Therefore, any errors at Grand
Coulee Dam, resulting from the use of the weakly-stratified model,
are essentially in equilibrium with the calculated atmospheric
heating/cooling rates by the time the water parcel reaches McNary Dam.
Any errors in the simulation at that point would be due to incorrect
atmospheric heating/cooling rates, imprecise knowledge of heated dis-
charges, and errors in predicting the travel time of water parcels.
Case II. The purpose of this simulation was to determine how
effectively the river-run model could be used to simulate daily-
averaged temperatures from Grand Coulee Dam to the mouth of the
Columbia River at Astoria, Oregon. Conditions for this simulation
were the same as in Case I, except that the observed temperature
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54
at Grand Coulee Dam were used as initial conditions. Simulated
temperatures were compared with observed temperatures at six locations
and the results are shown in Figure 3.
From Table 5 it can be seen that the difference between simulated
and observed temperatures at Rock Island and Priest Rapid Dams each
show a mean of -0.1° F, and a standard deviation of 1.0° F and 1.1° F,
respectively. At the confluence of the Snake River, below the Hanford Area,
the mean difference between simulated and observed is still small,
-0.1° F, but the standard deviation, 2.1° F, has increased 100 percent
from upstream values. This result implies that while 13,000 megawatts
may be a good average value for the heat input due to Hanford, deviation
from this value makes it difficult to simulate temperatures accurately
on a short-term basis. However, as in the case of the weakly-stratified
model, errors introduced due to imprecise knowledge of the Hanford
discharge, are attenuated as the simulation proceeds downstream.
Comparison of this simulation with Cases IV and V, which are
identical, except for the coefficients used to calculate the evapora-
—Q —1
tion rate, indicate that the values a = 0.0 and b = 1.0xlOmb,
in the equation, E = (a + bu) (eg-ea) gives the best results. This
corresponds closely to the value found in the Lake Hefner Study (1954),
where the values a = 0.0 and b = 1.16 x 10~^ mb~ were obtained.
Case III. The purpose of this simulation was to estimate the
average temperature increase resulting from the introduction of
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55
140 160 180 200 220 240 260 280 300 320 340
GRAND COULEE
140 160 180 200 220 240 260 280 300 320 340
ROCK ISLAND
140 160 180 200 220 240 260 280 300 320 340
PRIEST RAPIDS
140 160 180 200 220 240 260 280 300 320 340
SNAKE RIVER
140 160 180 200 220 240 260 280 300 320 340
BONNE VILLE
DAY' 100 120 140 160 180 200 220 240 260 280 300 320 34O
BEAVER ARMY TERMINAL
CASE II
-PREDICTED TEMPERATURE
-OBSERVED TEMPERATURE
Figure 3. Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case II.
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56
heated water at Hanford. The conditions for this simulation were
identical to those of Case II, except that no heat was added to the
river at Hanford. The results of the simulation compared with ob-
served temperatures at six locations on the Columbia River are shown
in Figure 4.
The estimated average increase in 1967, at the confluence of the
Columbia and Snake Rivers from April 1 to November 30 was 2.2° F;
at McNary Dam 1.1° F; at Bonneville Dam 0.7° F, and at the Beaver
Army Terminal -0.1°F. The error associated with the estimate at the
Snake River was ± 0.5° F; at McNary Dam, Bonneville Dam, and the
Beaver Army Terminal the error was ± 0.2° F.
Case IV. The purpose of this simulation was to determine how
sensitive the river-run model was to lowering the evaporation rate
by an order of magnitude, as compared to the results obtained in the
Lake Hefner Study (1954). Conditions for this simulation were
identical to those of Case II, except that the coefficients in the
equation for determining the evaporation rate, E = Ca + bu) Ces~ea)>
were a = 0.0 and b = 1.0 x 10 mb~ . Simulated temperatures are
compared with observed temperatures in Figure 5.
The results of this simulation indicate that, on the average,
simulated temperatures are higher than the observed temperatures. The
mean difference varies from a minimum of +1.2 F at Rock Island to a
maximum of 3.7° F at the Beaver Army Terminal.
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57
140 160 180 ZOO 220 240 260 280 300 320 340
GRAND COULEE
140 160 ISO 200 220 240 260 28O 300 320 340
ROCK ISLAND
ISO 20O 220 24O 260
PRIEST RAPIDS
140 160 180 200 220 240 260 280 300 32O 340
SNAKE RIVER
140 160 ISO 200 220 240 260 280 300 320 340
BONNE VI LLE
DAY 100 120 140 160 180 200 220 240 260 280 300 320 340
BEAVER ARMY TERMINAL
CASE m
-PREDICTED TEMPERATURE
-OBSERVED TEMPERATURE
Figure 4. Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case III.
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58
DAY 100 120 I4O 160 ISO 200 220 240 260 280 300 320 340
GRAND COULEE
180 200 220 240 260 28O 300 320 34O
ROCK ISLAND
140 160 180 200 220 240 260 280 300 320 340
PRIEST RAPIDS
140 160 180 200 220 240 260 280 30O 320 340
SNAKE RIVER
140 160 180 2OO 220 240 260 280 300 320 340
BONNE VI LLE
DAY 100 120 I4O 160 ISO 200 220 240 260 280 30O 32O 340
BEAVER ARMY TERMINAL
CASE IV
-PREDICTED TEMPERATURE
-OBSERVED TEMPERATURE
Figure 5. Simulated and Actual Temperatures (1967 in the
Columbia River at Six Locations, Case IV.
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59
It is interesting to note that during the warming part of the
cycle, from the first of April to the end of August, the error
introduced by decreasing the evaporation rate is small. The major
contribution to the difference between simulated and observed
occurs after the first of September when water temperatures are
decreasing.
Case V. The purpose of this simulation was to determine how
sensitive the river-run model was to increasing the evaporation rate,
compared to results obtained in the Lake Hefner Study (1954). In
this simulation the coefficients in the evaporation equation were
_0 1
a = 0.0 and b=1.0xlO°mb. Results at six locations are shown
in Figure 6.
The increased heat loss resulted in simulated temperatures
substantially lower than observed temperatures at all locations.
The average difference between simulated and observed was a mini-
mum at Rock Island Dam, -5.9° F, and a maximum at Bonneville Dam,
-8.0° F.
Once again, the simulation appeared to be more sensitve to the
evaporation rate during the period when water temperatures were
decreasing.
Case VI. The purpose of this simulation was to determine how
far downstream the effects of cold water releases at Grand Coulee
Dam could be observed. The conditions for this simulation were
identical to those of Case II, except that the observed temperatures
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60
120 140 160
ISO ZOO 22O 24O 260 28O 300 32O 340
GRAND COULEE
140 160 180 200 22O 240 260 280 300 320 34O
ROCK ISLAND
ISO 200 220 240 260
PRIEST RAPIDS
280 300 320 34O
140 160 ISO 200 220 24O 260 28O 300 320 340
SNAKE RIVER
140 160 ISO 200 220 240 26O 28O 300 320 340
BONNE VILLE
DAY 100 120
140 160 ISO 20O 220 240 260 280 300 320 34O
BEAVER ARMY TERMINAL
CASE TZ.
-PREDICTED TEMPERATURE
-OBSERVED TEMPERATURE
Figure 6. Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case V.
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61
at Grand Coulee Dam were arbitrarily reduced 5° F. The amount
of temperature control available from the natural stratification of
Lake Roosevelt varies considerably during the season and this test
was not meant to imply that 5° F temperature control could always
be obtained. However, developments in the future, such as use of
Canadian storage may increase the amount of temperature control.
Importantly, this simulation provides some idea of the benefits which
might be obtained by decreasing water temperature at Grand
Coulee Dam during the entire season. Simulated temperatures com-
pared to observed temperatures at six locations are shown in
Figure 7.
The results of the simulation indicate that on the average 84
percent of the cold water released at Grand Coulee Dam is available
at Rock Island, 78 percent at Priest Rapids, 70 percent at the Snake
confluence, 36 percent at McNary, 32 percent at Bonneville, and 18
percent at the Beaver Army Terminal. As can be seen from the graphs,
the amount varies with the season. During the period of increasing
water temperatures, the amount of benefit available from the cold
water releases at Grand Coulee is greater than during the period
of decreasing temperatures.
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62
DAY— 100 120 140 160 180 200 220 240 260 280 300 320 340
GRAND COULEE
180 200 220 240 260 280 300 320 340
ROCK ISLAND
ISO 2OO 220 24O 260
PRIEST RAPIDS
140 160 180 200 220 240 26O 280 300 320 340
SNAKE RIVER
140 160 ISO 200 220 240 260 280 300 320 34O
BONNEVILLE
40
DAY 100 I2O
140 160 180 20O 220 240 260 280 3OO 320 340
BEAVER ARMY TERMINAL
CASE
-PREDICTED TEMPERATURE
-OBSERVED TEMPERATURE
Figure 7. Simulated and Actual Temperatures (1967) in the
Columbia River at Six Locations, Case VI.
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