&EPA
United States
Environmental Protection
Agency
EPA Region 10
(OEA 095)
910-R-01-004
May 2001
Application of a 1-D Heat
Budget Model to the
Columbia River System
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Application of a 1-D Heat Budget Model to the Columbia River System
APPLICATION
OF A
1-D HEAT BUDGET MODEL
TO THE
COLUMBIA RIVER SYSTEM
John Yearsley
Duane Kama
EPA Region 10
Seattle, Washington
Steve Peene
Brian Watson
Tetra Tech, Inc.
Atlanta, Georgia
EPA-910-R-01-004
May 2001
-------
Executive Summary
In accordance with Section 303 of the Clean Water Act, the states of Oregon and Washington
have identified portions of the main stem of the Columbia River from the International Border (Columbia
River Mile 745.0) to the mouth at Astoria, Oregon and the Snake River from Anatone, Washington
(Snake River Mile 168.0) to its confluence with the Columbia River (Figure 1) as water quality limited.
This designation arises from an analysis of data by the State of Washington's Department of Ecology and
the State of Oregon's Department of Environmental Quality showing these waters do not meet water
quality standards during all or part of the year. Under Section 303 (d) of the Clean Water Act, States are
required to establish Total Maximum Daily Loads for pollutants at a level that implements the applicable
standards for water temperature. The goal of Columbia River Temperature Assessment is to provide
support for the priority-setting phase of the TMDL process by assessing the impacts of the principal
sources of thermal energy. The central product of the temperature assessment was the development of a
mathematical model that predicts temperature along the Columbia River from the Grand Coulee Dam to
the Bonneville Dam and along the Snake River from its confluence with the Grande Ronde River (Snake
River Mile 168) to its confluence with the Columbia.
The mathematical model predicts average daily temperatures, specific to locations along the
lengths of the Rivers, but averaged across the width and depth of the Rivers. Key elements of the model
include the ability to expand the model geographically, an algorithm that quantifies the uncertainty of the
modeled results, and a twenty-one year database of temperature and climate data. The model is based on
the energy budget method and uses an efficient numerical solution technique that simplifies the
characterization of model uncertainty. The energy budget method accounts for the exchange of heat with
the atmosphere and the input of advected thermal energy from major tributaries and points sources.
The temperature assessment includes a summary of a biological study on salmon and the impacts
of temperatures on their various life-stages.
Study Objectives
The objective of this study was to determine, for a given sequence of hydrology and meteorological
conditions, the relative impacts of the operation of dams and reservoirs on the thermal energy budget and
ambient temperature regime of the main stem Columbia and Snake rivers compared to the impact of
thermal input from surface and groundwater inflows. The specific objectives were:
a Estimate the frequency with which daily-average water temperatures in the Columbia and Snake
rivers will exceed the benchmark of 20° C under existing conditions of river management and a
representative record of river hydrology and meteorology
a Estimate the frequency with which daily-average water temperatures in the Columbia and Snake
rivers will exceed the benchmark of 20° C for the unimpounded condition. That is, the condition in
which there are no dams in place below Grand Coulee on the Columbia and on the Snake below
Lewiston, Idaho.
a Estimate the frequency with which daily-average water temperatures in the Columbia and Snake
Rivers will exceed the benchmark of 20° C under existing conditions of river management and with
major tributaries and point sources constrained to maintain temperatures less than 16° C.
a Characterize the uncertainty of these estimates for purposes of ultimately assessing the risks
associated with potential management decisions in the Columbia and Snake rivers.
The benchmark of 20° C was chosen because it is at water temperatures greater than this that adult
salmon are at risk. While the benchmark does represent certain aspects of the physiological requirements
-------
of salmonids, it is not viewed in the Report as a surrogate for water quality criteria or as part of an
ecological risk analysis. The constraint of 16° C on maximum temperatures in the tributaries was based
on the State of Washington's water temperature criterion for tributaries classified as Class A (excellent).
However, the use of the constraint was not meant to imply that tributaries had attained this criterion or
would do so in the future. Rather it was used to evaluate what the relative impact of the tributaries on the
thermal regime of the main stems might be under very favorable conditions.
Model Scenarios
Three scenarios were defined for purposes of achieving the objectives of the assessment. The
scenarios were designed to characterize the temperature regimes under the following conditions:
1. All hydroelectric facilities in the study area in place
2. The Columbia River unimpounded from Grand Coulee Dam to Bonneville and the Snake
River unimpounded from Snake River Mile 168 to the confluence with the Columbia River.
3. All hydroelectric facilities in place and the water temperature of major tributaries constrained
to be equal to or less than contribute water temperatures equal to or less than 16 °C.
A 21-year record of actual meteorological and hydrologic data for the Columbia and Snake rivers
was used to represent the environmental variability of the system for all scenarios and management of
water quantity in the system was assumed to remain the same for all scenarios.
Results
The average frequency of daily-averaged temperature excursions above 20 °C increased
monotonically from 0.0 at Grand Coulee Dam on the Columbia River to 0.16 at Bonneville Dam for the
scenario representing existing conditions (all hydroelectric facilities in place. Corresponding values for
average frequency of excursions for the unimpounded scenario were 0.0 to 0.03 from Grand Coulee Dam
to Bonneville Dam. The average frequency of excursions for the scenario in which tributary temperatures
were constrained to be equal to or less than 16 °C were essentially the same as the scenario for existing
conditions.
For the Snake River, the average frequency of daily-averaged temperature excursions above 20
°C increased from its initial value of 0.16 at Snake River Mile 168 to 0.19 at Ice Harbor Dam for the
scenario representing existing conditions (all hydroelectric facilities in place). The average frequency of
excursions for the unimpounded scenario had an initial value of 0.16 at Snake River Mile 168, decreased
slightly to 0.14 at Lower Granite Dam due to the influence of the Clearwater River, and then increased to
0.15 at Ice Harbor Dam. The average frequency of excursions for the scenario in which tributary
temperatures were constrained to be equal to or less than 16 °C were reduced significantly at Lower
Granite Dam, and only slightly Ice Harbor Dam as a result of the influence of the Clearwater River.
The impact of tributaries on the average frequency of daily-averaged temperature excursions is
related directly to their size relative to the main stem Columbia and Snake rivers. For the geographical
scope included in the analysis, only the Clearwater River in relation to the Snake River and the Snake
River in relation to the Columbia River had a significant impact on the thermal regime of the respective
main stems. The Snake River is the most significant tributary to the Columbia River in terms of its
impact on the temperature regime. The Snake River contributes to increases in the frequency of
temperature excursions above 20 °C for scenarios with dams in place as well as for scenarios for the
unimpounded river. The Clearwater River provides cool water to the Snake and reduces the frequency of
temperature excursions. Constraining the Clearwater River to water temperatures of 16 °C or less results
in significant cooling of the Snake River.
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Conclusions
The following conclusions were drawn from the results:
• Structural changes in Columbia River downstream from Grand Coulee Dam and in the Snake River
from its confluence with the Grande Ronde River to its confluence with the Columbia River near
Pasco, Washington cause an increase in mean frequency of water temperature excursions above a
daily-averaged water temperature of 20 °C relative to the unimpounded river. The structural changes
are a result of the construction and operation of hydroelectric facilities on the Columbia and Snake
rivers in the study area. This conclusion is based on a comparison of the mean frequency of
temperature excursions for the system as presently configured and for the same system in the
unimpounded condition. The unimpounded condition assumes there are no dams on the Columbia
River below Grand Coulee and no dams on the Snake River below Lewiston, Idaho. The uncertainty
in these estimates is approximately of the order of the estimated differences in the results. Improving
both the systems and measurements models could reduce uncertainty. This could include improving
the quality of water temperature observations, increasing the spatial coverage of required
meteorological data and by studying the seasonal variations in certain terms of the heat budget,
particularly the evaporation rate. However, the conclusion that construction and operation of the
hydroelectric facilities have a greater impact on the thermal regime of the Columbia and Snake Rivers
than does thermal input from most major tributaries would not be changed by the reduction in
uncertainty.
• The impact of most advected sources, including tributaries, groundwater and point sources, on the
cross-sectional daily-average water temperature of the main stem Columbia and Snake rivers in the
study area is limited by their relatively small contribution of advected thermal energy. The
exceptions to this are the impacts of the Clearwater River on the cross-sectional daily-average water
temperature of the Snake River and that of the Snake River on the cross-sectional daily-average water
temperature of the Columbia River.
• The objective of the analysis was to assess the relative impact of dams and tributaries on the
temperature regime of the Columbia River from Grand Coulee Dam to Bonneville Dam and Snake
River from its confluence with the Grande Ronde River (River Mile 168) to its confluence with the
Columbia River. The impact of upstream inputs was limited to the characterization of initial
temperature conditions at Grand Coulee Dam on the Columbia River and River Mile 168 on the
Snake River. However, upstream inputs have an important role in the temperature regime of both
rivers. In the Columbia River, construction of Canadian impoundments and the operation of Grand
Coulee Dam have an important role in the temperature of the Columbia River at Grand Coulee Dam.
For the Snake River, initial conditions near Anatone, Washington are such that the mean frequency of
temperature excursions is approximately 0.15. This is due to structural changes to the natural river
upstream from Anatone, Washington as well as to the time the river is exposed to high temperatures
as it crosses the Snake River Plain. A larger geographical scope is needed to assess the basin-wide
impacts of water management in both the Columbia and Snake rivers.
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Contents
CONTENTS
CHAPTER 1: COLUMBIA RIVER SYSTEM AND STUDY OBJECTIVES 1
1.1 INTRODUCTION 1
1.2 GEOGRAPHY, CLIMATE, AND HYDROLOGY OF THE COLUMBIA BASIN 2
Geography 2
Climate 3
Hydrology 3
1.3 WATER RESOURCES DEVELOPMENT WITHIN THE COLUMBIA RIVER BASIN 4
1.4 ROLE OF TEMPERATURE IN WATER QUALITY 5
1.5 IMPACTS OF WATERSHED DEVELOPMENT ON WATER TEMPERATURE 6
1.6 STUDY OBJECTIVES 8
CHAPTER 2: TEMPERATURE MODEL THEORY AND FORMULATION 11
2.1 THERMAL ENERGY BUDGET METHOD AND FORMULATION 11
Base Equations 11
Heat Exchange Across the Air-Water Interface 12
Advected Sources of Thermal Energy 14
2.2 STATE ESTIMATION METHODS 14
2.3 COMPONENTS AND STRUCTURE OF MODEL SYSTEM 20
CHAPTER 3: APPLICATION OF TEMPERATURE MODEL TO COLUMBIA
RIVER SYSTEM 23
3.1 SYSTEM HYDROLOGY BOUNDARIES AND ASSUMPTIONS 23
3.2 TIME AND LENGTH SCALES 25
3.3 RATIONALE FOR APPROACH 26
3.4 MODEL INPUT DATA 26
Water Temperature 26
River Geometry 26
Hydrology 26
Meteorology 28
3.5 PARAMETER ESTIMATION 31
Hydraulic Coefficients 31
Water Balance 32
Heat Flux Across Air-Water Interface 32
Initial Water Temperatures 33
Measurement Bias and Error 33
Systems Model Bias and Error 34
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Application of a 1-D Heat Budget Model to the Columbia River System
3.6 MODEL APPLICATION 42
Scenarios 42
Results 46
CHAPTER 4: MODEL INPUT AND OUTPUT FILES 49
4.1 INPUT FILES 49
Control File 49
Advected Source File 53
Meteorological File 55
4.2 OUTPUT FILES 56
CHAPTER 5: STUDY SUMMARY AND CONCLUSIONS 59
Topics for Further Study 59
REFERENCES 61
APPENDIX A A-l
APPENDIX B B-l
APPENDIX C C-l
APPENDIX D D-l
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Contents
FIGURES
Figure 1 -1. The Columbia and Snake rivers and associated hydroelectric projects in the study area 1
Figure 2-1. Schematic for reverse particle tracking method 19
Figure 2-2. General Model Structure 21
Figure 3-1. Surface elevations in Lake Franklin D. Roosevelt during 1998 24
Figure 3-2. Surface elevations in Lower Granite reservoir during 1998 24
Figure 3-3. Surface elevations in John Day reservoir during 1998 25
Figure 3-4. Simulated and observed water temperatures at Wells Dam for the period 1990-1994 37
Figure 3-5. Simulated and observed water temperatures at Priest Rapids Dam for the period 1990-1994 38
Figure 3-6. Simulated and observed water temperatures at McNary Dam for the period 1990-1994 38
Figure 3-7. Simulated and observed water temperatures at John Day Dam for the period 1990-1994 39
Figure 3-8. Simulated and observed water temperatures at Bonneville Dam for the period 1990-1994 39
Figure 3-9. Simulated and observed water temperatures at Lower Granite Dam for the period 1990-1994 40
Figure 3-10. Simulated and observed water temperatures at Little Goose Dam for the period 1990-1994 40
Figure 3-11. Simulated and observed water temperatures at Lower Monumental Dam for the period
1990-1994 41
Figure 3-12. Simulated and observed water temperatures at Ice Harbor Dam for the period 1990-1994 41
Figure 3-13. Frequency of predicted water temperature excursions in the Columbia River with dams in
place 43
Figure 3-14. Frequency of predicted water temperature excursions in the Snake River with dams in place 44
Figure 3-15. Frequency of predicted water temperature excursions in the Columbia River for the
unimpounded river 44
Figure 3-16. Frequency of predicted water temperature excursions in the Snake River for the
unimpounded river 45
Figure 3-17. Frequency of predicted water temperature excursions in the Columbia River with dams in
place and tributaries equal to or less than 16 °C 45
Figure 3-18. Frequency of predicted water temperature excursions in the Snake River with dams in place
and tributaries equal to or less than 16 °C 46
Figure 4-1. Example control file 50
Figure 4-2. Example advected source file 54
Figure 4-3. Example Meteorological File 55
Figure 4-4. Example output file 57
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Application of a 1-D Heat Budget Model to the Columbia River System
TABLES
Table 1-1. Parameter list for water quality limited segments of the Columbia and Snake River in Washington 2
Table 1-2. Mean annual discharges at selected sites on the main stem Columbia and Snake Rivers 4
Table 1-3. Hydroelectric projects on the main stem Columbia and Snake rivers included in the scope of the
analysis 5
Table 1-4. Summary of temperature preference ranges (°C) for five critical life stages of seven salmonid
species (from Appendix A) 7
Table 1-5. Frequency and average magnitude with which observed temperatures exceed Oregon's and
Washington's water quality criterion at selected locations on the Columbia and Snake rivers. Observed
temperatures are from the total dissolved gas monitoring program (McKenzie and Laenen, 1998) 7
Table 3-1. Sources of advected thermal energy in the Columbia River below Grand Coulee Dam and the
Snake River below its confluence with the Grande Ronde River 23
Table 3-2. Locations of water temperature monitoring sites for major tributaries of the Columbia and Snake
Rivers in the study area 27
Table 3-3. Sources of data for developing the hydraulic characteristics of the Columbia and Snake rivers 27
Table 3-4. U.S. Geological Survey gaging stations for the main stem Columbia and Snake Rivers and their
major tributaries in the study area 27
Table 3-5. First-order meteorological stations used to estimate heat budget parameters for the Columbia and
Snake rivers 29
Table 3-6. Weather stations from the Local Climatological Data Sets included in the parameter estimation
process for heat budget calculations 29
Table 3-7. Selected AGRIMET weather stations in the Columbia Basin maintained by the U.S. Bureau of
Reclamation 29
Table 3-8a. Correlation coefficients and annual average for average daily air temperature collected at
selected first order stations in the Columbia Basin 30
Table 3-8b. Correlation coefficients and annual average for average daily dew point at selected first order
stations in the Columbia Basin 30
Table 3-8c. Correlation coefficients and annual average for average daily sky cover at selected first order
stations in the Columbia Basin 30
Table 3-8d. Correlation coefficients and annual average for average daily wind speed at selected first order
stations in the Columbia Basin 30
Table 3-9. Parameters for estimating input temperatures of main stem and tributaries using nonlinear
regression methods described by Mohseni etal. (1998) 33
Table 3-10. Final configuration of weather stations used to estimate the heat budget terms for the
mathematical model of water temperature in the Columbia and Snake Rivers 35
Table 3-11. Measurement bias, measurement error variance and systems dynamic error variance at
locations of scroll case temperature measurements on the Columbia and Snake Rivers 37
IV
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Chapter 1: Columbia River System and Study Objectives
CHAPTER 1: COLUMBIA RIVER SYSTEM AND STUDY OBJECTIVES
1.1 INTRODUCTION
The objective of the Clean Water Act (as amended by the Water Quality Act of 1987, Public Law 100-4) is to
restore and maintain the chemical, physical, and biological integrity of the Nation's waters. Each state has
developed standards for water quality that are used to judge how well the objectives of the Clean Water Act are
being achieved. The water quality standards consist of the designated beneficial uses of the water and the water
quality criteria necessary for achieving and maintaining the beneficial uses.
Under Section 303 of the Clean Water Act, states must identify waters for which effluent limitations, as
required by Section 301, are not sufficient to implement established water quality standards. Oregon and
Washington have identified portions of the main stem of the Columbia River from the International Border
(Columbia River Mile 745.0) to the mouth at Astoria, Oregon, and the Snake River from Anatone, Washington,
(Snake River Mile 168.9) to its confluence with the Columbia River as water quality limited (Figure 1-1). This
designation arises from an analysis of data (Washington DOE, 1998; Oregon DEQ, 1998) showing these waters
do not meet water quality standards during all or part of the year. Sources that may contribute to impairment of
water quality in these segments of the Columbia and Snake rivers include the following:
Little Lower
Goose Granite
Figure 1-1. The Columbia and Snake rivers and associated hydroelectric projects in the study area.
a Construction of impoundments for hydroelectric facilities and navigational locks, which increase the
time waters of the Columbia and Snake are exposed to high summer temperatures and change the
system's thermal response time.
a Hydrologic modifications to the natural river system to generate electricity, provide irrigation water
for farmlands, and facilitate navigation.
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Application of a 1-D Heat Budget Model to the Columbia River System
a Modifications of the watershed by agriculture and silviculture practices that reduce riparian
vegetation, increase sediment loads, and change stream or river geometry.
a Operation of pulp and paper manufacturing facilities that discharge thermal energy and toxic
substances, particularly dioxin.
After the water quality limited segments have been identified, priorities must be established for attaining
water quality standards based on the severity of the pollution and the beneficial uses of the water body. Water
temperature is one of the most frequently occurring constituents on Oregon's and Washington's lists of water
quality limited segments on the Columbia and Snake rivers. Segments of the Columbia and Snake rivers in the
study area that are water quality limited for water temperature and for which the listing criteria require a Total
Maximum Daily Load (TMDL) are given in Table 1-1.
Table 1 -1. Parameter list for water quality limited segments of the Columbia and Snake River
in Washington
State
OR
OR
OR
OR
WA
WA
WA
WA
WA
Water Body Name
Columbia River
Columbia River
Columbia River
Columbia River
Columbia River
Snake River
Snake River
Columbia River
Franklin D. Roosevelt Lake
River Mile
146.1 -191.5
191.5-215.6
215.6-292.0
292.0-309.3
290.5
139.6-0.0
168.0-139.6
515.6
596.6
Parameter
Temperature
Temperature
Temperature
Temperature
Temperature
Temperature
Temperature
Temperature
Temperature
Action Needed
TMDL
TMDL
TMDL
TMDL
TMDL
TMDL
TMDL
TMDL
TMDL
When setting priorities for attaining established water quality standards for temperature, the first step is to
assess the importance of sources that may significantly affect the thermal energy budget. Changes in the thermal
energy budget of the Snake and Columbia rivers, relative to the natural unregulated river system, are due
primarily to advected thermal energy from point sources, surface water, and ground water, as well as modification
of river geometry and hydraulics due to the construction and operation of hydroelectric facilities. The goal of this
work is to support the priority-setting phase of the TMDL process by assessing the impacts of the principal
sources of thermal energy.
1.2 GEOGRAPHY, CLIMATE, AND HYDROLOGY OF THE COLUMBIA BASIN
Geography
The Columbia River drains more than 259,000 square miles of southeastern British Columbia in Canada and
the states of Idaho, Oregon, Washington, and Wyoming. The Columbia River rises in the Rocky Mountain
Trench and flows more than 400 miles through the rugged, glaciated mountains of southeastern British Columbia
before it reaches the U.S.-Canada border near Castlegar, British Columbia. The Columbia River enters the United
States from the Okanogan Highland Province, a mountainous area of Precambrian-early Paleozoic marine
sediments. The Columbia crosses the western margin of the Columbia Basin—a broad, arid plateau formed by
Miocene lava flows of the Columbia Basalt—and flows south across the state of Washington. Near Pasco,
Washington, and the confluence with the Snake River, the Columbia turns west, forms the border between Oregon
and Washington, and flows more than 300 miles through the Casscade Mountain Range to the Pacific Ocean near
Astoria, Oregon.
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Chapter 1: Columbia River System and Study Objectives
The headwaters of the Snake River are in Jackson Lake in the Teton Mountains of Wyoming at an elevation
of 7,000 feet above sea level. The river flows west across the Snake Plain, which is also a broad, arid plateau
formed by Miocene lava flows of the Columbia Basalt. At the western edge of Idaho, it turns north and flows
through a deeply incised canyon, emerging near Lewiston, Idaho. At Lewiston, the Snake joins the Clearwater
River and flows west through the Palouse Country of eastern Washington, joining the Columbia near Pasco,
Washington. Other major tributaries of the Snake in Idaho include the Bruneau, Owyhee, Boise, Payette, Weiser,
and Salmon rivers.
Although the Snake River is the Columbia's largest tributary, other major tributaries include the Kootenai,
Clark Fork-Pend Oreille, Spokane, Deschutes, and Willamette rivers. The Kootenai lies largely in Canada, but
flows through western Montana, northern Idaho, and back into Canada before entering the Columbia below
Lower Arrow Lake in British Columbia. The Clark Fork-Pend Oreille has its headwaters on the Continental
Divide in Montana, flows through northern Idaho into Pend Oreille Lake and becomes the Pend Oreille River.
The Pend Oreille River flows north into Canada before joining with the Columbia River. Major tributaries of the
Clark Fork are the Flathead, Blackfoot, and Bitteroot rivers. The Spokane River begins in Lake Coeur d'Alene in
Idaho and flows west through eastern Washington, entering the Columbia in Lake Franklin D. Roosevelt (Lake
FDR). Both the Deschutes and Willamette rivers have their headwaters in Oregon; the Deschutes rises in central
Oregon and flows north across lava flows of the Columbia Basalt, while the Willamette begins in the Cascade
Mountains and flows west to the Willamette Valley, then north to join the Columbia near Portland, Oregon.
Climate
The climate of most of the Columbia River drainage is primarily of continental character, with cold winters
and hot, dry summers. Precipitation varies widely, depending primarily on topographic influences. The interior
Columbia Basin and Snake Plain generally receive less than 15 inches of precipitation annually, while annual
precipitation can exceed 100 inches per year in some of the mountainous regions of Canada.
Air temperature also varies considerably, depending on location. Summertime temperatures in the Columbia
Basin and Snake Plain exceed 100 °F (37.8 °C) for extended periods. Temperatures at higher elevations remain
cooler. Winters are cold throughout the basin and heavy snow falls in the mountains. The snowpack accumulates
throughout the winter months as a result of frequent passage of storm systems from the Pacific Ocean. Some of
the snowpack is incorporated into the extensive system of glaciers in the basin; however, between the months of
March and June, depending on elevation, much of the snowpack begins to melt. The resulting hydrograph is
typical of a snowmelt regime.
West of the Cascade Mountains, which includes the lower 150 miles of the Columbia River and all of the
Willamette River, the climate has a more maritime character. Winter air temperatures at lower elevations are
seldom below freezing, and summer air temperatures are seldom above 100 °F (37.8 °C) for long periods.
Average annual precipitation west of the Cascades is more than 40 inches in most areas. Precipitation recorded at
coastal stations is typically higher. Below about 5,000 feet, most of the precipitation falls as rain, with 70 percent
or more falling between October and March.
Hydrology
Although the hydrology of the Columbia River system has been modified by the construction of numerous
hydroelectric, irrigation, flood control, and transportation projects, the hydrograph still has the characteristics of a
snowmelt regime. Streamflows are low during the winter, but increase beginning in spring and early summer as
the snowpack melts. Melting of the winter snowpack generally takes place in May and June, and streamflows
increase until the snowpack can no longer support high flows. Flows then recede gradually during the summer
and are derived from reservoir storage and from ground water recession into the fall and winter.
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Application of a 1-D Heat Budget Model to the Columbia River System
Occasionally, runoff from winter storms augments the base flow and can increase river discharge rapidly.
This is particularly true of the Willamette River, which does not depend on the operation of other reservoirs in the
Columbia River system. Rather, it is influenced more by rain and can reach flood stage even with flood control
available from reservoirs within the Willamette River system.
Mean annual river discharges for key locations on the main stem Columbia and Snake River and selected
tributaries are shown in Table 1-2.
1.3 WA TER RESOURCES DEVELOPMENT WITHIN THE COLUMBIA RIVER BASIN
The Columbia River and its tributaries have been developed to a high degree. The only segment of the
Columbia River above Bonneville Dam that remains unimpounded is the Hanford Reach between Priest Rapids
Dam (Columbia River Mile 397.1) and the confluence with the Snake River (Columbia River Mile 324.3). The
11 main stem hydroelectric projects in the United States (Table 1-3), from Grand Coulee Dam to Bonneville Dam,
develop approximately 1,240 feet of the 1,290 feet of hydraulic head available in this segment of the Columbia
River main stem. Hydroelectric and flow control projects on the main stem of the Columbia River and its
tributaries in Canada have resulted in significant control of flow in the Upper Columbia and Kootenai River
Basins. The Snake River is also nearly fully developed, with 19 dams on the main stem and a number of
impoundments on its tributaries.
Table 1-2. Mean annual discharges at selected sites on the main stem Columbia and Snake Rivers
Station Name
Snake River near Anatone, Washington
Tucannon near Starbuck, Washington
Palouse River near Hooper, Washington
Snake River below Ice Harbor Dam
Columbia River at the International Boundary
Columbia River at Grand Coulee
Columbia River at Bridgeport, Washington
Okanogan River at Malott, Washington
Methow River near Pateros, Washington
Columbia River below Wells Dam
Columbia River at Rocky Reach Dam
Wenatchee River at Monitor, Washington
Columbia River below Rock Island Dam
Crab Creek near Moses Lake, Washington
Columbia River below Priest Rapids Dam
Walla Walla River at Touchet, Washington
John Day River at McDonald Ferry, Oregon
Deschutes River at Moody, near Biggs, Oregon
Columbia River at the Dalles
Gage#
13334300
13344500
13351000
13353000
12399500
12436500
12438000
12447200
12449950
12450700
12453700
12462500
12462600
12467000
12472800
14018500
14048000
14103000
14105700
Station
Latitude
46°05'50"
46°30'20"
46°15'02"
46°15'02"
49° OO'OS"
47° 57'56"
48° 00'24"
48° 16' 53"
48° 04' 39"
47° 56'48"
47° 31 '28"
47° 29' 58"
47°19'57"
47° 11' 22"
46° 37'44"
46° 01 '40"
45° 35' 16"
45° 37' 20"
45° 36'27"
Location
Longitude
116°58'36"
118°03'55
118°52'55
118°52'55"
117°37'42"
118°58'54"
119°39'51"
11 9° 42' 12"
11 9° 59' 02"
11 9° 51 '56"
120°18'04"
120° 25' 24"
120°04'48"
11 9° 15' 53"
11 9° 51 '49"
11 8° 43' 43"
120° 24 30"
120° 54 54"
121°10'20"
Period of
Record
1958-1995
1914-1996
1898-1996
1913-1992
1938-1996
1923-1996
1952-1993
1965-1996
1959-1996
1968-1996
1961-1996
1962-1996
1961-1996
1942-1996
1918-1996
1951-1996
1904-1996
1907-1996
1878-1996
Average Flow
(cfs)
34800
176
588
53400
99200
108200
110200
3050
1560
109400
113200
3250
116300
63
118400
568
2080
5800
191000
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Chapter 1: Columbia River System and Study Objectives
Table 1-3. Hydroelectric projects on the main stem Columbia and Snake rivers
included in the scope of the analysis
Project
Grand Coulee
Chief Joseph
Wells
Rocky Reach
Rock Island
Wanapum
Priest Rapids
McNary
John Day
The Dalles
Bonneville
Lower Granite
Little Goose
Lower Monumental
Ice Harbor
River
Mile
596.6
545.1
515.8
473.7
453.4
415.8
397.1
292.0
215.6
191.5
146.1
107.5
70.3
41.6
9.7
Start of
Operation
1942
1961
1967
1961
1933
1963
1961
1957
1971
1960
1938
1975
1970
1969
1962
Generating
Capacity
(megawatts)
6,494
2,069
774
1,347
622
1,038
907
980
2,160
1,780
1,050
810
810
810
603
Storage
Capacity
(1000s acre-feet)
8,290
588
281
440
132
710
231
1,295
2,294
311
761
474
541
351
400
These dams and reservoirs serve many purposes, including irrigation, navigation, flood control, municipal and
industrial water supply, recreation, and hydroelectric power generation. There are approximately 7 million acres
of irrigated farmlands in the Columbia River Basin, including 3.3 million acres in Idaho, 0.4 million acres in
Montana, 1.9 million acres in Washington, and 1.3 million acres in Oregon (Bonneville Power Administration et
al., 1994). The system has the capacity for generating more than 20,000 megawatts of hydroelectric energy, and
slack-water navigation now extends more than 460 river miles from the mouth at Astoria, Oregon, to Lewiston,
Idaho.
In the United States, federal agencies, private power companies, and public utility districts own the dams in
the Columbia River Basin. The Columbia Treaty between the United States and Canada governs transboundary
issues related to the operation of dams and reservoirs on the Columbia River system in Canada.
1.4 ROLE OF TEMPERA TURE IN WA TER QUALITY
For the Columbia and Snake rivers in Washington, Chapter 173-201A-030 (2) (b) of the Washington
Administrative Code (WAC) defines characteristics uses as the following:
(i) Water supply (domestic, industrial, agricultural).
(ii) Stock watering.
(iii)Fish and shellfish:
Salmonid migration, rearing, spawning, and harvesting.
Other fish migration, rearing, spawning, and harvesting.
(iv) Wildlife habitat.
-------
Application of a 1-D Heat Budget Model to the Columbia River System
(v) Recreation (primary contact recreation, sport fishing, boating, and aesthetic enjoyment).
(vi) Commerce and navigation.
The characteristic uses for the segments of the Columbia River in Oregon, as defined in the Oregon
Administrative Rules (OAR) Chapter 340-041, are similar to those of Washington.
Water quality in the main stem Columbia and Snake rivers is sufficient to protect many of these beneficial
uses. An important exception is that of salmonid migration, rearing, spawning, and harvesting. According to the
Independent Scientific Group (1996), 200 distinct anadromous stocks returned several million adult salmon and
steelhead to the Columbia River prior to development of the basin. Of these stocks, 69 have been identified as
extinct and 75 others are at risk of extinction in various parts of the basin. The Independent Scientific Group
concluded that the "development of the Columbia River for hydropower, irrigation, navigation and other purposes
has led to a reduction in both the quantity and quality of salmon habitat, and most critical, a disruption in the
continuum of that habitat."
Water temperature is an important water quality component of habitat for salmon and other cold water
organisms in the Columbia and Snake rivers. The criterion for water temperature (Chapter 173-201A WAC and
Chapter 340-041 OAR) in the main stem Columbia River from the mouth to Priest Rapids Dam (R.M. 397.1) and
Snake River from the mouth to its confluence with the Clearwater River (R.M. 139.3) is that temperature shall not
exceed 20 °C (60 °F) due to human activities. For the Columbia River from Priest Rapids Dam (R.M. 397.1) to
Grand Coulee Dam (R.M. 596.6), the criterion for water temperature is that the temperature shall not exceed 18
°C (64.4 °F) due to human activities.
These criteria were developed specifically to protect cold-water aquatic life, including salmon and steelhead,
in the Columbia and Snake rivers. Salmonids evolved to take advantage of the natural cold, freshwater
environments of the Pacific Northwest. Temperature directly governs their metabolic rate and directly influences
their life history. Natural or anthropogenic fluctuations in water temperature can induce a wide array of
behavioral and physiological responses in these fish. These fluctuations may lead to impaired functioning of the
individual and decreased viability at the organism, population, and species level. Feeding, growth, resistance to
disease, successful reproduction, sufficient activity for competition and predator avoidance, and successful
migrations are all necessary for survival.
Temperature preferences for five critical life stages of the salmonids found in the Columbia River system are
listed in Table 1-4. Appendix A contains more detailed information on the preference ranges and effects of
temperature on these fish. Additional information can be obtained from two recent EPA-sponsored reports: (1) A
Review and Synthesis of Effects of Alterations to the Water Temperature Regime on Freshwater Life Stages of
Salmonids, with Special Reference to Chinook Salmon (1999) by Dale A. McCullough, and (2) Perspectives on
Temperature in the Pacific Northwest's Fresh Waters (1999) by Charles C. Coutant.
1.5 IMPACTS OF WATERSHED DEVELOPMENT ON WATER TEMPERATURE
Once the water quality limited segments have been identified, Section 303 (d) of the Clean Water Act requires
that each state establish a priority ranking determining the severity of the pollution and the uses of the water. One
of the first steps is to assess the problems associated with a given water quality parameter. The purpose of an
assessment is to identify the sources for the water quality parameter of concern.
-------
Chapter 1: Columbia River System and Study Objectives
Table 1-4. Summary of temperature preference ranges (°C) for five critical life stages of seven
salmonid species (from Appendix A)
Adult
Migration
°C
Spring Chinook
Salmon
Summer Chinook
Salmon
Fall Chinook
Salmon
Sockeye
Salmon
Coho Salmon
Chum Salmon
Steelhead/
Rainbow Trout
Cutthroat Trout
Bull Trout
3.3-
13.9
10.6-
7.2-
7.2-
8.3-
10-
13.3
-20
19.4
15.6
15.6
15.6
13
NA
10-
12
Spawning
°C
5.
5.
6
6
5.6
6.1
10.
10.
5.6
10
4
7.
7.
3
4.
6.
<
.6
.4
2
2
.9
4
1
=9
4
-14.4
-12.8
-14.4
-18
-12.8
-16.7
-13.9
-12.2
-9.4
-12.8
-12.8
-9.4
-12.8
-17.2
-10
-10
Incubation
°C
5-
4.5
5-
10-
10-
5-
4.4
4.4
4-
4.4
5.6
14.4
-12.8
14.4
-12.8
-16.7
14.4
-13.5
-13.3
-6.5
-13.3
-11.1
NA
2
4
-4
-6
Rearing
°C
10-
10-
10-
12-
10-
12-
11.2-
11.8-
10-
11.2-
7.3-
9.5-
12.8
14.8
12.8
-14
12.8
-14
-14.6
-14.6
12.8
-14.6
14.6
12.9
4 - 4.5 fry
4 - 10 juv
Smoltification
Out-migration
°C
3.3-12
NA
4.5-15
2-10
12-15.
NA
< 12
NA
NA
.2
.5
5
NA - Not available
The listing of water temperature by Oregon and Washington is based on analysis of data collected by state
and federal agencies. These agencies include the Oregon Department of Environmental Quality (DEQ), the
Washington State Department of Ecology (DOE) and the U.S. Army Corps of Engineers (USAGE). An analysis
of long-term records the USAGE collected as part of the total dissolved gas monitoring study (McKenzie and
Laenen, 1998) shows the frequency with which water temperatures have exceeded the water quality criterion at
various locations on the Columbia and Snake rivers (Table 1-5).
Table 1-5. Frequency and average magnitude with which observed temperatures exceed
Oregon's and Washington's water quality criterion at selected locations on the Columbia
and Snake rivers. Observed temperatures are from the total dissolved gas monitoring
program (McKenzie and Laenen, 1998)
Exceeds Water Quality Criterion
Location
Lower Granite Dam
Little Goose Dam
Lower Monumental Dam
Ice Harbor Dam
Wells Dam
Priest Rapids Dam
McNary Dam
John Day Dam
Bonneville Dam
Frequency
0.15
0.15
0.18
0.18
0.10
0.18
0.17
0.15
0.14
Magnitude
2.04
2.49
2.10
2.35
0.87
1.61
1.65
1.65
1.39
Record Length
5/30/88-9/17/96
5/30/88-9/16/96
5/29/88-9/17/96
5/29/88-9/23/96
4/18/93-9/2/97
4/28/88-12/31/97
4/2/85-12/31/97
4/17/84-9/16/97
4/3/86-11/2/97
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Application of a 1-D Heat Budget Model to the Columbia River System
Previous studies of the Columbia and Snake rivers (Davidson, 1964; Jaske and Synoground, 1970; Moore,
1969; Independent Scientific Group1, 1996) have identified the construction and operation of hydroelectric
facilities as having a major impact on the thermal regime of the Columbia and Snake rivers. Jaske and
Synoground (1970) concluded that the construction of river-run reservoirs on the main stem of the Columbia
River caused no significant changes in the average annual water temperature, but that the operation of Lake FDR,
the reservoir behind Grand Coulee Dam, delayed the time of the peak summer temperature in the Columbia River
at Rock Island Dam by about 30 days. Moore (1969) found that both Lake FDR and Brownlee Reservoir on the
Snake River caused cooling in the spring and summer and warming in fall and winter. The Independent Scientific
Group (1996) concluded that "mainstem reservoirs in the Snake and Columbia rivers have created shallow, slowly
moving reaches of shorelines where solar heating has raised temperature of salmon rearing habitat above tolerable
levels" and that changes in the thermal energy budget associated with the hydropower system in the Columbia and
Snake rivers have resulted in conditions that are suboptimal or clearly detrimental for salmonids.
Surface and groundwater flows tributary to the Snake and Columbia rivers are also sources of advected
thermal energy that have the potential for modifying the thermal energy budget of the main stem. Moore (1969)
studied the impact of the Clearwater and Salmon rivers on the main stem Snake and the Kootenai and Pend
Oreille rivers on the Columbia during 1967 and 1968. He found that the Clearwater and Salmon rivers cooled the
Snake River during some of this period, but at no time did they produce a warming effect. Viewing the Snake as
a tributary to the Columbia, Moore (1969) and Jaske and Synoground (1970) concluded that the advected thermal
energy from the Snake River increased the temperature of Columbia River during the summer. Moore (1969)
estimated that the maximum temperature increase was of the order of 1 °C during 1967 and 1968, while Jaske and
Synoground (1970) estimated the annual thermal energy contribution of the Snake River to the Columbia River to
be on the order of 4,000 megawatts. The Independent Scientific Group (1996) discusses temperature in the
tributaries primarily as it relates to habitat in individual tributaries. The group concludes that high temperatures in
the late summer and fall are detrimental to both juvenile and adult salmon in the main stem and tributaries, but
does not discuss the impact of the tributaries on the thermal energy budget of the main stem.
The only significant permitted point source discharge of thermal energy to the Columbia and Snake rivers in
the study area (Figure 1-1) is the Potlatch Corporation discharge to the Snake River at Snake River Mile 139 near
the confluence of the Snake and the Clearwater rivers. The Potlatch facilities discharge approximately 130
megawatts of thermal energy to the Snake River. The Hanford Project discharged as much as 23,000 megawatts
of thermal energy and had significant impacts on the temperature of the Columbia River (Jaske and Synoground,
1970; Moore 1969; Yearsley, 1969). However, this discharge was discontinued in the 1970s.
1.6 STUDY OBJECTIVES
For the segments of the main stem Columbia and Snake rivers included in the study area (Figure 1-1), the
impacts of watershed development on the thermal energy budget are associated with the operation of dams and
reservoirs and advected energy from tributaries, ground water, and point sources. The objective of this study is to
determine, for a given sequence of hydrology and meteorological conditions, the relative impacts of the operation
of dams and reservoirs on the thermal energy budget of the main stem Columbia and Snake rivers compared to the
impact of thermal input from surface and ground water inflows. The specific objectives are to do the following:
a Estimate the frequency with which daily average water temperatures in the Columbia and Snake
rivers will exceed the benchmark of 20 °C (68 °F) under existing conditions of river management and
a representative record of river hydrology and meteorology.
1 The Independent Scientific Group comprised nine experts in fishery sciences commissioned by the Northwest Power Planning Council to
(1) perform an independent review of the science underlying salmon and steelhead recovery efforts and Columbia River Basin ecosystem
health, and (2) develop a conceptual foundation that could form the basis for program measures and basinwide fish and wildlife
management.
8
-------
Chapter 1: Columbia River System and Study Objectives
a Estimate the frequency with which daily average water temperatures in the Columbia and Snake
rivers will exceed the benchmark of 20 °C (68 °F) with all dams on the Columbia River below Grand
Coulee Dam in place and for the unimpounded condition with no dams in place below Grand Coulee
on the Columbia and on the Snake below Lewiston, Idaho.
a Estimate the frequency with which daily average water temperatures in the Columbia and Snake
Rivers will exceed the benchmark of 20 °C (68 °F) under existing conditions of river management and
with major tributaries and point sources constrained to maintain temperatures less than 16 °C (60.8
°F).
a Characterize the uncertainty of these estimates for purposes of ultimately assessing the risks
associated with potential management decisions in the Columbia and Snake rivers.
The benchmark of 20 °C (68 °F) was chosen because adult salmon are at risk when water temperatures are
warmer. For example, Karr et al. (1998), used 20 °C (68 °F) as a benchmark, representing it as an upper incipient
lethal water temperature for migrating salmon and steelhead. Based on a literature review, Karr et al. (1998)
determined that 20 °C (68 °F) is the point where the zone of lower resistance starts for immigrating adult salmon
and steelhead. Results from the Columbia River Thermal Effects study reported by Bonneville Power
Administration et. al. (1994) show that 20 °C (68 °F) is the water temperature where the zone of lower resistance
starts for immigrating adult salmon and steelhead. At water temperatures higher than 21.1 °C (70 °F), salmonids
are in a lethal range where the time it takes to kill the fish declines rapidly. More detailed information on
temperature requirements for several species of salmonids is contained in Appendix A.
Although the benchmark does represent certain aspects of the physiological requirements of salmonids, this
report does not view it as a surrogate for water quality criteria or as part of an ecological risk analysis.
Washington's water quality standard is based on an instantaneous value. An ecological risk analysis would have
to consider both the timing and magnitude of temperature changes. Although these issues are not specifically
considered in this assessment, they may be included in future analyses of water temperature in the Columbia and
Snake rivers.
The constraint of 16 °C (60.8 °F) on maximum temperatures in the tributaries was based on Washington's
water temperature criterion for tributaries classified as Class A (excellent). The use of the constraint, however,
was not meant to imply that tributaries had attained this criterion or would do so in the future; rather, it was used
to evaluate what the relative impact of the tributaries on the thermal regime of the main stems might be under very
favorable conditions.
A one-dimensional mathematical model of the thermal energy budget that simulates daily average water
temperature under conditions of gradually varied flow is used to address the specific objectives described above.
Models of this type have been used to assess water temperature in the Columbia River system for a number of
important environmental analyses. The Federal Water Pollution Control Administration (Yearsley, 1969)
developed and applied a one-dimensional thermal energy budget model to the Columbia River as part of the
Columbia River Thermal Effects Study. The Bonneville Power Administration et al. (1994) used HEC-5Q, a one-
dimensional water quality model, to provide the temperature assessment for the System Operation Review, and
Normandeau Associates (1999) used a one-dimensional model to assess water quality conditions in the Lower
Snake River for the U.S. Army Corps of Engineers.
A one-dimensional model of daily average temperatures is appropriate for answering basic questions on how
watershed development effects water temperature. Important issues associated with water temperature in the
main stem Columbia and Snake Rivers for which this type of model is not appropriate include the following:
a Instantaneous temperatures: The water quality standards for the Columbia and Snake rivers in both
Oregon and Washington are written in terms of instantaneous temperatures. The model used for this
analysis does not simulate instantaneous water temperatures. Therefore, the model results cannot be
-------
Application of a 1-D Heat Budget Model to the Columbia River System
compared directly to the criteria for water temperature established by the water quality standards of
Oregon and Washington.
Lateral and vertical variations in water temperature: The thermal energy budget model simulates the
daily, cross-sectional averaged temperature. Important spatial dimensions of the lotic ecosystem
(Independent Scientific Group, 1996) are the riverine (longitudinal), riparian (lateral) and hyporheic
(vertical habitat below the river channel). Development of the hydropower system has caused
significant changes to the thermal regimes in all these dimensions. The one-dimensional thermal
energy budget model results can be used only to characterize the water temperatures in the riverine or
longitudinal dimension of habitat. The model results correspond approximately to the state variable,
"thalweg temperature," used by the Independent Scientific Group (1996).
Unsteady flow: The model uses the methods of gradually varied flow to characterize river hydraulics.
The gradually varied flow model may not be appropriate for highly transient flow conditions such as
storm or very rapid snowmelt events.
Strong longitudinal temperature gradients: The model assumes that dispersion and longitudinal
turbulent diffusion can be neglected. Diffusion-like processes will be important when
> 1
where
Kx = coefficient of longitudinal dispersion or eddy diffusivity
U = river speed in the longitudinal direction
L = a characteristic longitudinal distance
Longitudinal dispersion is generally of great importance for one -dimensional models. Experimental
values of the longitudinal dispersion coefficient in rivers and estuaries, reported in Fischer et al.
(1979), vary from approximately 30 feet2/second to 15,000 feet2/second in rivers and from 100
feet2/second to 15,000 feet2/second in estuaries. Assuming the largest value of the dispersion
coefficient (15,000 feet2/second) and a river velocity of 1.0 foot /second implies a characteristic
length of approximately 3 miles. To analyze conditions in the Snake and Columbia rivers when
strong cross-sectionally averaged longitudinal gradients were important and scales on the order of 3
to 10 miles were of interest, it would be necessary to consider including diffusion-like processes in
the model. The analysis described in this report did not include any impacts with scales of less than 3
to 10 miles.
10
-------
Chapter 2: Temperature Model Theory and Formulation
CHAPTER 2: TEMPERATURE MODEL THEORY AND FORMULATION
2.1 THERMAL ENERGY BUDGET METHOD AND FORMULATION
Base Equations
The thermal energy budget method is a useful concept for simulating temperatures in aquatic environments.
Concern about the impact of reservoir operations on water temperature and aquatic ecosystems motivated early
applications of the method (Burt, 1958; Delay and Seaders, 1966; Raphael, 1962; Edinger et al., 1974). Prior to
the passage of the Clean Water Act, numerous studies of Electric Power Industry thermal discharges were also
performed using the energy budget method (Edinger et al., 1974). Brown (1969, 1970) applied the method to
simulating stream temperature increases resulting from the removal of riparian vegetation during logging
operations. Recent applications of the energy budget method have focused on water quality planning issues
related to reservoir operations (Cole and Buchak, 1995; Normandeau Associates, 1999), watershed management
(Bonneville Power Administration et al., 1994, Foreman et al., 1997; Risley, 1997; Rishel et al., 1982; Sinokrot
and Stefan, 1993) and fisheries habitat enhancement (Bartholow, 1989; Theurer et al., 1984).
Thermal energy budget models for aquatic ecosystems are developed either in an Eulerian frame of reference,
in which the reference system is fixed in space and through which the water flows, or a Lagrangian frame of
reference, in which the reference system moves with the fluid. The one-dimensional thermal energy model for
estimating the state variable, water temperature, stated in terms of the Eulerian viewpoint and assuming there is
no longitudinal dispersion is as follows:
„ . 5T _ 5(QT) ,, _
PCPAX—+ PCp^-^= wxHnet+Sadv + WT
where
A = the density of water, kg/meter3
Cp = the specific heat capacity of water, kcal/deg C/kg
Ax = the cross-sectional area of the river at the distance, x, meter2
T = the true water temperature, °C
Q = the river flow rate, meterVsecond
wx = the width of the river at the distance, x, meters
Hnet= the heat flux at the air-water interface, kcal/meterVsecond
Sadv = the heat advected from tributaries and point sources, kcal/meter/second
WT = a random water temperature forcing function, ~N(0, EQ(t))
x = the longitudinal distance along the axis of the river, meters
t = time
In the Lagrangian frame of reference, the systems model for estimating the water temperature, using the
energy budget method and assuming no longitudinal dispersion, is given by
11
-------
Application of a 1-D Heat Budget Model to the Columbia River System
P CPAX — = wxHnet + Sadv + WT
where the symbols are as previously defined.
Equations 1 and 2 are the state-space system equations for water temperature in the Eulerian and Lagrangian
frames of reference, respectively. Water temperature measurements also provide an estimate of the system state.
The observation model for water temperature at the kth time interval is given by (Gelb et al., 1974)
Zk = HkTk + vk (3)
where
Zk = the measured value of the water temperature, °C
Hk = the measurement matrix,
vk = the measurement error, ~N(0, ER)
ER = the variance of the measurement error, vk
Heat Exchange Across the Air-Water Interface
Heat exchange across the air-water interface is generally the major source of thermal energy for lakes, rivers,
and reservoirs. As is the case for the applications described above, this study assumes the net exchange of
thermal energy, Hnet, across the air-water interface can be described by
Hnet = (Hs - Hrs) + (Ha - Hra) +/- Hevap +/- Hcond - Hback (4)
where
Hnet = Net heat exchange across the air-water interface, kcal/meter2/second
Hs = Shortwave solar radiation, kcal/meter2/second
Hrs = Reflected shortwave solar radiation, kcal/meter2/second
Ha = Longwave atmospheric radiation, kcal/meter2/second
Hra = Reflected atmospheric radiation, kcal/meter2/second
Evaporative heat flux, kcal/meter2/second
Conductive heat flux, kcal/meter2/second
Hback = Blackbody radiation from the water surface, kcal/meterVsecond
The specific form for each of the terms in the heat budget formulation (Equation 4), as used in this and most
other studies involving the energy budget method, is based on a compilation of heat budget studies by Wunderlich
and Gras (1967). Chapra (1997) and Bowie et al. (1985) also have comprehensive discussions of each of the
terms in Equation 4 adapted from Wunderlich and Gras (1967). From the work of Wunderlich and Gras (1967),
individual elements of the heat budget are given by
12
-------
Chapter 2: Temperature Model Theory and Formulation
Shortwave (Solar) Radiation
(Hs-Hrs)= F(M,*,Dy) (5)
where
M = the latitude of the site
* = the declination of the sun at the site
Dy = the day of the year
Longwave (Atmospheric) Radiation
(Ha-Hra)= (1-Var)1.23x10-16(1.0 + 0.17C2)(TDB + 273.)6 (6)
where
Var = reflectivity of the water surface for atmospheric radiation, ~ 0.03
C = cloud cover, decimal fraction
TDB = dry bulb temperature, °C
Evaporative Heat Flux
Hevap = A 8 Ev W (e0 - ea) (7)
where
A = water density, kg/meter3
8 = latent heat of vaporization , kcal/kg
Ev = empirical constant, mb"1
W = wind speed, meters/second
e0 = saturation vapor pressure at the temperature of the water surface, mb
ea = vapor pressure of the air near the water surface, mb
Conductive Heat Flux
Hpi a | ra
cond - r
e0-eaj 1013.3 (8)
where
RB = an empirical constant, 0.66
pa = atmospheric pressure, mb
13
-------
Application of a 1-D Heat Budget Model to the Columbia River System
Black Body (Water Surface) Radiation
Hback = 0.97
-------
Chapter 2: Temperature Model Theory and Formulation
and data requirements are substantial. The available literature revealed no applications of this programming
package that solve the inverse problem for surface water models.
Many studies do not even attempt to quantify the adequacy of the calibration process. For example, the
criteria used in the calibration process for a mathematical model of temperature and biological productivity in the
Lower Snake River (Normandeau Associates, 1999) were that "the output reproduced general patterns and long
term averages of observed data or knowledge."
In the second step, "validation" or "verification," output from the calibrated model is compared to
observations from an independent data set. The degree to which the simulations and observations agree is
subjected to some form of hypothesis testing to determine model "validity." While goodness-of-fit criteria have
been proposed by some (Bartholow, 1989; van der Heijde, 1990), many studies use qualitative statements to
support the conclusion that the model has been validated. The study of the Lower Snake River referenced above
concludes the verification process by simply stating that "the calibrated model predicts correct seasonal warming,
maximum temperatures, and fall cooling." In another example of the calibration/verification paradigm, the
Bonneville Power Administration et al. (1994) relied on a water quality model, HEC5Q, of the Columbia River to
evaluate complex system operations strategies and provide support for an environmental analysis required by the
National Environmental Policy Act (NEPA). Although the report of the model studies invokes the terms
"calibration" and "verification," no quantitative tests or results are provided. In the case of the water temperature
simulations, the report simply states, "The model has been shown to adequately represent the thermal responses
throughout the river system for summer months . . . . "
These examples typify the lack of rigor and consistency associated with the calibration/verification paradigm.
While calibration/verification is still considered standard practice in surface water quality modeling, there has
been some effort devoted to address the lack of rigor and inconsistencies in the traditional approaches. Matalas
and Maddock (1976), for example, observed that
"Calibration implies that for the parameters of the identified model, one has control over the degree of
accuracy in a particular estimation. Verification implies that the identified calibrated model, tested under
controlled conditions, mimics the physical system of interest and therefore the identified calibrated
verified model is to be accepted.
The words identification, calibration and verification are misleading because of their connotation of
greater understanding of and control over the physical processes than actually exists. " (emphasis added)
Bartholow (1989) has an excellent discussion of these issues with regard to temperature models for surface
water. Oreskes et al. (1994) noted the philosophical problems associated with attempting to verify or validate
deterministic earth science models.
The techniques of state estimation avoid many of the philosophical difficulties associated with traditional
modeling approaches by assuming the state estimates are random variables and that there is error associated with
both the systems model and the measurement model. The methods of state estimation formulate the problem in
terms of a process or systems model (Equation 1 or 2) and a measurement model (Equation 3).
The systems model (Equations 1 and 2) includes both deterministic and probabilistic components. The
deterministic component of the systems model is based on the known laws of physics, chemistry, and biology. In
this case, the systems model is based on scientific and empirical knowledge of the thermal energy budget. The
probabilistic component represents the uncertainty in the systems model. Depending on the nature of the
problem, the uncertainty can be due to level of spatial or temporal aggregation, model structure, parameter
estimation and input variability. The detail with which previous studies have treated systems uncertainty in water
quality or quantity studies ranges from the very basic (Moore et al., 1976) to the very complex (Rajaram and
Georgakakos, 1987).
15
-------
Application of a 1-D Heat Budget Model to the Columbia River System
The measurement model (Equation 3) reflects the fact that estimating the state of a system with some form of
measuring device cannot be done without some uncertainty. This uncertainty arises from inherent error in the
measurement device, sampling error and mapping of point observations to block observations. The matrix, Hk,
describes which state variables or combinations of state variables are being sampled at time, k, and can also
include instrument calibration factors or transformations.
State estimation methods combine the estimates from the systems model (Equation 1 or 2) and the
measurement model (Equation 3), when measurements are available, to obtain an optimal estimate of the system
state. As described by Gelb et al. (1974), there are three types of state estimation problems based on the time of
the estimate compared to that of the last measurement of the system state. When the state estimate precedes the
last measurement, it is a smoothing problem; when it coincides with the last measurement it is filtering; and when
it occurs after the last measurement it is prediction. The Kalman filter (Gelb et al., 1974; Schweppe, 1973) gives
an unbiased, minimum squared error estimate of the system state for the filtering and prediction problems when
all parameters in Equation 1 or 2 and Equation 3 are known. For the filtering problem, the Kalman filter
combines the state estimates from the systems model and the measurement model. The two estimates are
combined using a weighting factor determined by the relative uncertainty of the systems model compared to the
uncertainty of the observation model. The weighting factor, the Kalman gain matrix, Kk, is derived by
constraining the error in the estimate to be unbiased and to have a minimum mean square error.
For linear systems, the complete Kalman filter algorithm is
Systems Model: J_k = fk-1 Ik-1 + wk-i wk~N(0,SQ) (10)
Measurement Model: J_k = H^ + y^ Vk~N(0, SR) (11)
System Extrapolation: J_k(-) = fk-i Ik-i(+) (12)
Error Covariance
Extrapolation: Pk(-) = fk.! Pk.1(+)fk.1 + SQ (13)
State Estimate Update: J_k(+) = J_k(-) + Kk[zk - Hk Tk(-)] (14)
Error Covariance Update: Pk(+) = [I - Kk Hk] Pk(-) (15)
Kalman Gain Matrix: Kk = Pk(-)HkT[Hk Pk(-)HkT + SR]-1 (16)
Innovations Sequence: vk = zk-HkTk(-) (17)
where (-) denotes values at time, k, prior to filtering; (+) denotes values at time, k, after filtering; and fkis the
systems matrix.
The filter equations (Equations 10 to 17) are used for the prediction problem as well. However, in the
prediction problem, the Kalman gain matrix, Kk, is zero because there are no observations available. In this case,
only the systems model provides an estimate of the state. However, an additional feature of the Kalman filter is
that it provides an estimate of the error covariance (Equation 13) for both the filter and the prediction problems.
The innovations sequence (Equation 17) provides a quantitative measure for parameter estimation. The
innovations sequence is simply the difference between the system extrapolation (Equation 12) and the actual
measurement, zk. If one is thinking in terms of the traditional approach to model development, the innovations
sequence is superficially similar to comparing the simulated state estimates with the measured state estimates.
Formally, it is different in that the system extrapolation is a function of the previous measurements; the
innovations sequence incorporates aspects of both the systems error and the measurement error. When the filter is
optimal, the innovations sequence is unbiased and uncorrelated in time. That is,
16
-------
Chapter 2: Temperature Model Theory and Formulation
E{vk} = 0
and
E{viVjT} = 0, for i>j
where E is the expectation operator. When the innovations sequence satisfies these criteria, it means all the
deterministic information has been extracted from the systems model. When the model parameters are unknown,
the innovations sequence can be used as way of finding a parameter set that provides optimal estimates. That is,
the model parameters can be adjusted until the criteria given above are satisfied.
Although state estimation techniques provide the basis for dealing with issues of model and measurement
uncertainty in a more rational and consistent manner than do the traditional deterministic modeling methods, there
have been relatively few applications of state estimation techniques in the field of surface water modeling.
Lettenmaier (1975), Moore (1973), Moore et al. (1976), and Dandy and Moore (1979) used state estimation
methods to evaluate strategies for designing surface water quality monitoring systems. Lettenmaier and Burges
(1976) provided a tutorial on state estimation for application to measurement system design, model building and
assessment, and data extension. Koivo and Phillips (1976) used state estimation techniques to show how one
could obtain optimal estimates of DO, BOD, and stream parameters for a dynamic water quality model. Beck and
Young (1976) studied the use of the Extended Kalman Filter (EKF) for purposes of system identification of DO-
BOD model structure. Bowles and Grenney (1978) incorporated sequential EKF's into a surface water quality
model to estimate nonpoint source loadings over a 36.4-mile stretch of the Jordan River in Utah.
These examples represent some of the efforts researchers made to apply or to demonstrate how to apply state
estimate methods to surface water quality modeling. Their limited success in encouraging wider use of the
methods could be due to a number of factors. The methods appear somewhat complex, even though the most
common technique, the Kalman filter, is a close relative of linear regression using the method of least squares.
The structures of models for many surface water state variables, particularly the biological constituents, cannot
always be well defined; in such cases the use of state estimation techniques may not be entirely satisfactory (Beck
and Young, 1976). Solving the inverse problem for surface water quality model problems can also be technically
difficult. The inverse problem can carry data-gathering burdens that are not compatible with the time and capital
resources available to natural resource and regulatory agencies. Water temperature, given the state of the art, is
one state variable for which the techniques of state estimation are well suited. It is simple and comparatively
inexpensive to gather water temperature data. In addition, there is general agreement among researchers
regarding the structure of the thermal energy budget model. Algorithms for estimating rates of energy transfer for
the various components of the energy budget have also been well developed. Therefore, state estimation methods
were developed to make estimates of the system state and its uncertainty for water temperature in the Columbia
and Snake river main stems.
To obtain an estimate of the water temperature from the systems model, it is first necessary to decide whether
to implement the solution method with a Lagrangian point of view or with an Eulerian point of view. Given the
spatial and temporal complexity of the natural environment, most mathematical models using the thermal energy
budget method are developed in the Eulerian frame of reference. The Eulerian frame of reference is a more
intuitive way of viewing changes in concentrations simply because most measuring devices are fixed at a specific
location rather than moving with the water. It is also less difficult to incorporate spatial complexity into the
Eulerian framework, and, therefore, easier to add more spatial dimensions as well as more complex spatial
processes such as dispersion and turbulent diffusion.
Most systems models using the Eulerian framework solve Equation 1 with either finite difference (Brown and
Barnwell, 1987; Cole and Buchak, 1995; Sinokrotand Stefan, 1993; Smith, 1978) or finite element methods
(Baca and Arnett, 1976). These models have generally proved valuable for simulating water temperatures in a
variety of aquatic environments. However, it is well known that solutions to equations of the type characterized
17
-------
Application of a 1-D Heat Budget Model to the Columbia River System
by Equation (1), using finite difference or finite element techniques, are subject to stability and accuracy problems
(e.g., O'Neill, 1981). For water quality models, stability problems are generally not as serious as accuracy
problems. When a solution becomes unstable, it is usually obvious and can generally be eliminated by reducing
the time step. Accuracy problems are more pervasive and often subtle. Of particular concern to developers of
finite difference and finite element methods are problems, commonly characterized as numerical dispersion,
associated with the propagation of phenomena with short wavelengths. Numerical dispersion is most evident in
the propagation of sharp spatial gradients when advection dominates the system. The resulting simulations can
have spurious damping of high frequencies or oscillations. They are caused by differences between the rate at
which the numerical scheme propagates the solution in space and the rate at which the solution would be
propagated in space by the natural system.
Solution techniques based on the Lagrangian point of view (Jobson, 1981) avoid the accuracy problems
associated with Eulerian methods but lack the computational convenience of a fixed grid. However, efficient
accurate solution methods have been proposed which combine some of the virtues of each point of view (Cheng
et al., 1984; Yeh, 1990; Zhang et al., 1993). In these hybrid Eulerian-Lagrangian methods, advective processes
are treated with a Lagrangian formulation. Diffusion or dispersion processes, if present, are treated with an
Eulerian formulation. With many of the hybrid methods, the need to satisfy the Courant criterion
U At/Ax < 1
can be relaxed. In addition, the application of state estimation techniques, as discussed below, is greatly
simplified. Hybrid methods do not always eliminate numerical dispersion. However, Yeh (1990) found that the
use of hybrid methods with single-step reverse particle tracking (SRPT) was definitely superior to the Eulerian
method using upwind method. Zhang et al. (1993) found that hybrid methods using SRPT introduced some
numerical dispersion, but that a modified form of SRPT eliminated the numerical dispersion. Cheng et al. (1984)
reported that when linear interpolation was used with hybrid solution techniques, numerical dispersion was
similar to that of upwind methods. Cheng et al. (1984) were able to eliminate numerical dispersion from the
hybrid method by using second-order Lagrangian polynomial interpolation.
The mixed Eulerian-Lagrangian method using reverse particle tracking was chosen as the solution technique for
simulating water temperature in the Columbia River system for the following reasons:
a It reduces the state-estimation (filtering and prediction) problem to one of a single state variable
rather than one requiring a state variable for each finite difference or finite element grid point.
a It is relatively easy to avoid instabilities in the solution when the Courant stability criterion is
exceeded.
a It provides the flexibility to expand the scope of model to include diffusion-like processes and/or
more spatial dimensions.
a Although the method does not completely eliminate numerical dispersion, the results of studies
described previously show that the method's ability to propagate high frequencies is generally
superior to Eulerian methods. Tests of three numerical schemes showed that reverse particle tracking
propagated high frequencies more accurately than both WQRRS and QUAL2E (Appendix B). These
schemes are (1) reverse particle tracking, the numerical method used in this report; (2) the numerical
method used by WQRRS, a water quality model commonly used by the U.S. Army Corps of
Engineers (Smith, 1978; Normandeau Associates, 1999); and (3) QUAL2E (Brown and Barnwell,
1987).
The mixed Eulerian-Lagrangian method uses the concept of reverse particle tracking to implement the
Lagrangian step. The river system is divided into N segments, not necessarily of the same spatial dimensions.
Within each segment, however, the geometric properties of the river system are assumed to be constant during a
18
-------
Chapter 2: Temperature Model Theory and Formulation
given time step. Water temperature values are recorded only on the boundaries between segments. As an
example of the method, consider Segment J (Figure 2-1). At the end of a computational time step, t = tk+i a
particle at the downstream end of the Segment J is flagged. The flagged particle is tracked backward in time
upstream until its position at the beginning of the time step, t = tk, is located. The location of a particle tracked in
this manner will, in general, not be precisely on a segment boundary, where water temperatures are stored by the
computational scheme. Therefore, it is necessary to determine the water temperature of the particle at the
beginning of the time by interpolating between the points where water temperatures are recorded. In the solution
technique used in this study, this is accomplished with a second-order polynomial using Lagrangian interpolation
(Press et al., 1986). Once the location of the particle and its initial water temperature are determined for the
beginning of the time step, the particle is followed back downstream to its location at the end of the time step (the
downstream end of Segment J). The change in water temperature for the particle during this time step is
estimated using Equation 2.
r t=tk
Particle J
k
Figure 2-1. Schematic for reverse particle tracking method.
The information required for obtaining a solution to Equation 2 using reverse particle tracking includes
a River width as a function of longitudinal distance during the time step.
a Cross-sectional area as a function of longitudinal distance during the time step.
a River velocity as a function of longitudinal distance during the time step.
a Net heat exchange as a function of longitudinal distance during the time step.
The hydraulic characteristics of the unimpounded reaches of the river system are estimated from power
equations relating mean velocity, area, and width (Leopold and Maddock, 1953). That is,
U=AUQ
Bu
Ax = Aa Q
Ba
Wx = Aw Q
Bw
(18)
(19)
(20)
19
-------
Application of a 1-D Heat Budget Model to the Columbia River System
where
U = the river velocity, feet/second
Ax = the cross-sectional area, feet2
Q = the river flow, cfs
Wx = the river width, feet
The coefficients, Au, Bu, Aa, Ba, Bu, Aw, and Bw, are estimated by simulating river hydraulics conditions under
various flow conditions using the methods of steady gradually varied flow (USACE-HEC, 1995). The gradually
varied flow method gives estimates of the average longitudinal velocity, U, the average water depth, D, and the
river width, Wx, as a function of river flow. The coefficients are determined by fitting Equations (18)-(20) to the
resulting estimates using the method of least squares.
For the impounded reaches, the water surface elevation is assumed to remain constant, such that the depth and
width remain constant at any cross-section and the velocity, U, is simply
U = Q/(WX*D) (21)
Exchange of thermal energy across the air-water interface is estimated from Equation (4) using formulations
for components of the heat budget as described by Water Resources Engineers (1968).
2.3 COMPONENTS AND STRUCTURE OF MODEL SYSTEM
Based on the theoretical formulations discussed in Section 2.2, a heat budget model has been developed that
projects the temperature conditions for a water body within a one-dimensional framework. The model projects
the temperature under a specified set of heat flux conditions from atmospheric sources, upstream boundaries, and
adjacent tributary inflows. The model projects the temperature and provides evaluation and adjustment to the
model uncertainty using the Kalman filter described previously. A detailed description of the model application
to the Columbia River is presented in Chapter 3.
Figure 2-2 presents a general flow chart of the model system developed. Inputs include the system geometry,
the heat flux across the air-water interface, the tributary inflows, and the model hydraulic parameters.
As this is a heat budget model, the hydraulic parameters must be determined a priori to the simulation. This is
done through application of another model or methodology that provides the coefficients for input to the model.
These then become model input conditions rather than parts of the overall simulation. The specifics of the
hydraulic parameters are presented in detail for the Columbia River application in Section 3.5.
The tributary inflows and the heat flux across the air-water interface are the other input parameters for the
model. These are prescribed as time series for the period of simulation. The tributary information required is the
flow rate and temperature as a function of time. The heat budget information required is the input to the six terms
listed in Equation 4.
Using these inputs, the model solves the system model equation for each model segment using the mixed
Eulerian-Lagrangian approach and redefines the interim system state based upon the inputs over the prescribed
time period.
20
-------
Chapter 2: Temperature Model Theory and Formulation
Model Inputs
Waterbody Geometry
Hydraulic Parameters
Tributary Inflow Data
Air-Water Interface Heat Flux
Data
Flow Logic
Define Model Reaches
Define Model Segments
Define Initial Conditions
Step Forward to Calculate
Tk+1
Define Filtered Tk+1
Output Corrected Results
Figure 2-2. General Model Structure.
21
-------
Application of a 1-D Heat Budget Model to the Columbia River System
22
-------
Chapter 3: Application of Temperature Model to Columbia River System
CHAPTER 3: APPLICATION OF TEMPERATURE MODEL TO COLUMBIA
RIVER SYSTEM
3.1 SYSTEM HYDROLOGY BOUNDARIES AND ASSUMPTIONS
The boundaries of the Columbia River system for the assessment of water temperature include the Columbia
River from the International Boundary (River Mile 745.0) to Bonneville Dam (River Mile 145.5) and the Snake
River near Anatone, Washington (River Mile 168.9) to its confluence with the Columbia River near Pasco,
Washington. With the exception of Grand Coulee Dam and its impounded waters, Lake Franklin D. Roosevelt
(FDR), all the hydroelectric projects on these segments of the Columbia and Snake rivers have limited storage
capacity and are operated as run-of-the-river reservoirs. Because of its large storage capacity (Table 1-3), Lake
FDR is used for flood control as well as providing water for irrigation and generation of hydroelectric power.
Typical reservoir elevations for Lake FDR show substantial annual variation (Figure 3-1).
Table 3-1. Sources of advected thermal energy in the Columbia River below Grand Coulee
Dam and the Snake River below its confluence with the Grande Ronde River
Source
Location
Clearwater River
Potlatch Corporation
Tucannon River
Palouse River
Lower Snake River Groundwater
Okanogan River
Methow River
Chelan River
Crab Creek
Yakima River
Walla Walla River
John Day River
Deschutes River
Upper Columbia River Groundwater
Lower Columbia River Groundwater
Snake R.M. 140.0
Snake R.M. 139.8
Snake R.M. 62.2
Snake R.M 59.5
Snake R.M. 168.0-R.M. 0.0
Columbia R.M. 533.5
Columbia R.M. 523.9
Columbia R.M. 503.3
Columbia R.M.410.8
Columbia R.M.335.2
Columbia R.M. 314.6
Columbia R.M. 218.0
Columbia R.M. 204.1
Columbia R.M. 596.0 - R.M. 292.0
Columbia R.M. 292.0 - R.M. 146.1
Run-of-the-river reservoirs are those for which reservoir elevation is kept more or less constant; water coming
into the reservoir is passed directly through the reservoir. Typical run-of-the-river reservoirs are Lower Granite
Reservoir and John Day Reservoir, the two largest run-of-the-river reservoirs on the Snake and Columbia rivers.
Surface elevations for these two reservoirs during 1998 are shown in Figures 3-2 and 3-3, respectively.
The differences between the run-of-the-river reservoirs and Lake FDR, with respect to both their modes of
operation and storage capacity, give rise to differences in their respective thermal regimes. For the run-of-the-
river reservoirs, the spatial variability of temperature within a cross section perpendicular to the direction of flow
is generally less than 1 °C (McKenzie and Laenen, 1998) except near the forebay of some dams. In Lake FDR,
vertical variations in water temperature of up to 5 °C have been observed at various locations along the
longitudinal axis of the reservoir. Because of this difference in the thermal regimes, the run-of-the-river projects
23
-------
Application of a 1-D Heat Budget Model to the Columbia River System
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Figure 3-1. Surface elevations in Lake Franklin D. Roosevelt during 1998.
can be modeled as systems with variability in the longitudinal direction only. Lake FDR, however, is treated as a
system with both vertical and longitudinal spatial variability using the water quality modeling system CEQUAL-
W2 (Cole and Buchak, 1995). The assessment of water temperature in Lake FDR will be described in a later
study.
740
738
£ 736
I 734
§732
730 J
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Figure 3-2. Surface elevations in Lower Granite reservoir during 1998.
24
-------
Chapter 3: Application of Temperature Model to Columbia River System
270 i
> 268 ]
£2
a 266
o
I 264
260
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Figure 3-3. Surface elevations in John Day reservoir during 1998.
This report describes the development and application of a one-dimensional thermal energy model for the run-
of-the-river reservoirs. The system boundaries for the model of the run-of-the-river segments are the main stems
of the Columbia River from the tailwaters of Grand Coulee Dam (Columbia River Mile 596.6) to Bonneville Dam
(Columbia River Mile 145.5) and the Snake River from its confluence with the Grande Ronde River (Snake River
Mile 168.7) to its confluence with the Columbia River near Pasco, Washington (Snake River Mile 0.0). Advected
thermal energy from ground water, point sources, and major tributaries (Table 3-1) to these segments are treated
as inputs to the main stem rivers in this analysis.
3.2 TIME AND LENGTH SCALES
To accomplish the management objectives of the analysis, it is necessary to simulate daily average water
temperatures as a function of longitudinal distance in the Columbia and Snake rivers. This establishes an
approximate lower limit on system time scales and on data requirements. Stability and accuracy issues associated
with solutions to Equation 2 can impose a requirement of even smaller time increments to obtain reliable
solutions. However, the simulated results for time scales less man a day are valuable only in terms of their
contribution to the solution accuracy. Because the time scale of the input data is equal to or greater than one day,
there is no physical significance to higher-frequency output associated with the need to obtain a stable solution.
In an effort to include the environmental variability due to hydrology and meteorology, the largest time scales
are on the order of two decades. The time scales are constrained by the hydrologic data available for the
Columbia River system under existing management. Existing management in this case means operation of the
system after the construction of the last hydroelectric project, Lower Granite Dam and Reservoir, completed in
1975. The simulation time scale, therefore, is 1975 to 1995.
The length scales for the analysis are determined by a number of factors. These factors include the availability
of geometric data, spatial variability in the river geometry, and computational stability and accuracy. Data
availability often provides the most severe constraint; however, there are ample data for describing river geometry
in both the Columbia and Snake rivers within the boundaries of this analysis. The primary factor determining the
length scale of this analysis is the need to achieve stable, accurate solutions. Length scales are such that the time
it takes a parcel of water to traverse a given computational segment is always equal to or less than 1 day. For the
Columbia and Snake rivers, this results in length scales on the order of 1 to 10 miles.
25
-------
Application of a 1-D Heat Budget Model to the Columbia River System
3.3 RATIONALE FOR APPROACH
Idealizing the largest part of the Snake and Columbia River system in terms of a one-dimensional model is
based on the assumption that the primary processes affecting the thermal energy budget are advection and the
transfer of thermal energy across the air-water interface. This assumption is in keeping with the management
objective of providing a primary temperature assessment for the water quality planning process as required by
Section 303(d) of the Clean Water Act. Based on previous work in the Columbia and Snake rivers (Raphael,
1962; Yearsley, 1969; Jaske and Synoground, 1970), a model of this type should capture the major features of
water temperature impacts in this system. As described above, a number of other temperature assessments of the
Columbia and Snake rivers (Bonneville Power Administration et al., 1994; Normandeau Associates, 1999) are
based on one-dimensional models of the thermal energy budget. The mixed Lagrangian-Eulerian scheme for
handling advection was chosen based on studies such as those done by Yeh (1990) and Zhang et al. (1993).
3.4 MODEL INPUT DA TA
Water Temperature
The extensive water temperature data records for the Columbia and Snake rivers have been assembled and
reviewed for quality by McKenzie and Laenen (1998). In addition, McKenzie and Laenen (1998) organized the
data in electronic formats for rapid analysis. The results of their work provide a water temperature data set for the
Columbia and Snake rivers, which can be used to describe uncertainty in the temperature model. The data quality
analysis performed by McKenzie and Laenen (1998) provides a basis for characterizing the uncertainty associated
with the measurements.
McKenzie and Laenen (1998) compiled data for the main stem Columbia and Snake rivers. Temperature data
for the tributaries included in the analysis were obtained from observations made by the Idaho Power Company,
Washington State Department of Ecology (DOE) and the U.S. Geological Survey (USGS). The location of
monitoring locations, period of record, and frequency of analysis are shown in Table 3-2.
River Geometry
River geometry is needed to characterize the hydraulic properties of the river as a function of flow and time.
The basic information required is elevation of the river channel above mean sea level at a sufficient number of
cross sections so as to adequately describe water depth, water width, and velocity as a function of river flow. A
number of sources, described in Table 3-3, were used to obtain the data needed.
Hydrology
River hydrology data for the main stem Columbia and Snake rivers, as well as the major tributaries, were
obtained from the records maintained by the U.S. Geological Survey. Gaging stations used in the study are shown
in Table 3-4. Estimates of groundwater return flow were obtained from Hansen et al. (1994).
26
-------
Chapter 3: Application of Temperature Model to Columbia River System
Table 3-2. Locations of water temperature monitoring sites for
Columbia and Snake Rivers in the study area
Station Name
Clearwater River
at Spalding
Tucannon River
at Powers
Palouse River
at Hooper
Okanogan River
at Malott
Methow River
at Pateros
Chelan River
at Chelan
Crab Creek
near Beverly
Yakima River
at Kiona
John Day River
at Highway 206
Deschutes River
at Deschutes Park
Agency
U.S. Geological
Survey
Washington
DOE
Washington
DOE
Washington
DOE
Washington
DOE
Washington
DOE
Washington
DOE
Washington
DOE
Oregon DEQ
Oregon DEQ
Station
Number
13342500
35B060
34A070
49A070
48A070
47A070
41A070
37A090
404065
402081
Station
Latitude
46°26'55"
46°32'18"
46°45'33"
48°16'53"
48°04'29"
47°50'23"
47°11'23"
46°15'13"
45°28'37"
45°37'40"
major tributaries of the
Location
Longitude
116°49'35"
118°09'18"
118°08'49"
119°42'12"
119°57'20"
120°01'11"
119°15'54"
119°28'37"
120°28'07"
120°54'13"
Period of
Record
1911-1996
10/17/73-
09/02/96
07/30/59 -
09/02/96
11/17/66-
09/10/96
07/29/59 -
09/10/96
07/20/60 -
09/14/94
10/24/61 -
09/05/94
03/20/68 -
09/09/96
02/11/73-
12/04/97
07/16/62-
12/01/97
Table 3-3. Sources of data for developing the hydraulic characteristics of the
Columbia and Snake rivers
River
Segment
Data Source
Columbia River: Grand Coulee Dam to
Confluence with the Snake River
Columbia River Thermal Effects cross-
sectional data (Yearsley, 1969)
Snake River: Lewiston, Idaho to Confluence U.S. Army Corps of Engineers (Walla Walla
with the Columbia River District) HEC-6 cross-sectional data
Columbia River: Confluence with the Snake
River to Bonneville Dam
NOAA Navigation Charts
Table 3-4. U.S. Geological Survey gaging stations for the main stem Columbia and Snake Rivers
and their major tributaries in the study area
Station Location Drainage Average Gage Datum
Station Period of Area Annual Flow (feet above
Station Name Number Latitude Longitude Record (mi2) (cfs) MSL)
27
-------
Application of a 1-D Heat Budget Model to the Columbia River System
Station Name
Snake River at
Anatone, WA
Clearwater
River at
Spalding, ID
Tucannon
River near
Starbuck, WA
Palouse River
at Hooper, WA
Columbia
River at Grand
Coulee, WA
Okanogan
River at Malott,
WA
Methow River
at Pateros, WA
Chelan River
at Chelan, WA
Crab Creek
near Beverly,
WA
Yakima River
at Kiona, WA
Walla Walla
River at
Touchet, WA
John Day
River at
McDonald
Ferry, OR
Deschutes
River at
Moody, OR
Station -
Number
13334300
13342500
13344500
13351000
12436500
12447200
12449950
12452500
12472600
12510500
14018500
14048000
14103000
Station
Latitude
46°05'50"
46°26'55"
46°39'20"
46°45'31"
47°57'56"
48°37'57"
48°04'39"
47°50'05"
46°49'48"
46°15'13"
46°01'40"
45°35'16"
45°37'20"
Location
Longitude
116°58'36"
116°49'35"
118°03'55"
118°05'52"
118°58'54"
119°42'12"
119°59'02"
120°00'43"
119°49'48"
119°28'37"
118°43'43"
120°24'30"
120°54'05"
Period of
Record
1958-1995
1911-1996
1915-1992
1898-1994
1923-1995
1966-1994
1959-1994
1904-1993
1951-1994
1906-1994
1951-1996
1905-1994
1898-1994
Drainage Average Gage Datum
Area Annual Flow (feet above
(mi2) (cfs) MSL)
92960 35100 807.
9570 15200 4360.
431 175 730.
2500 580 1041.
74700 107200 900.
8080 3000 784.
1772 1550 900.
924 2090
4840 200 500.
5615 3600 454.
1657 570 405.
7580 2080 392.
10500 5800 168.
Meteorology
Meteorological data, including solar radiation, barometric pressure, cloud cover, wind speed, air temperature
(dry-bulb), and relative humidity, are required for the thermal energy budget calculations. First order weather
stations in the Columbia Basin maintained by the Weather Service and for which data are archived in the National
28
-------
Chapter 3: Application of Temperature Model to Columbia River System
Climatological Data Center (NCDC) include Lewiston, Idaho; Spokane, Washington; and Yakima, Washington.
Data are available for these locations at 3-hour intervals from the NCDC SAMSON data sets. The period of
record for each of these stations is shown in Table 3-5.
Table 3-5. First-order meteorological stations used to estimate heat budget parameters for
the Columbia and Snake rivers
Station Name
Lewiston, Idaho
Pendleton,
Oregon
Spokane,
Washington
Yakima,
Washington
WBAN#
24149
24155
24157
24243
Period of
Record
01/01/1948-
12/31/1997
01/01/1948-
12/31/1997
01/01/1948-
12/31/1997
01/01/1948-
12/31/1997
Latitude
46°23'00"
45° 41 '00"
47°38'00"
46° 34' 00"
Longitude
11 7° 01 '00"
11 8° 51 '00"
117°32'00"
120°23'00"
Station Elev
(feet above MSL)
1436
1482
2356
1064
Stations with maximum and minimum daily air temperatures are more numerous and are included in the
NCDC Local Climatological Data Sets. The selected stations in the Columbia Basin selected are shown in Table
3-6.
Table 3-6. Weatherstations from the Local Climatological Data Sets included in the
parameter estimation process for heat budget calculations
Station Name
Connell
Coulee Dam
The Dalles
Pullman
Richland
Wenatchee
Station #
1690
1767
8407
6789
7015
9074
Latitude
46°45'37
47°57'00
45°36'00"
46°45'37"
46°23'00"
47°25'00"
Longitude
117°10'10"
119°00'00"
121°12'00"
117°10'10"
117°01'00"
120°19'00"
Station
Elevation
1020.
1700.
102
2545
373
640
Period of Record
11/01/1960-12/31/1997
06/01/1948-12/31/1997
07/01/1948-12/31/1997
10/21/1940-12/31/1997
06/01/1948-12/31/1997
02/08/1877-12/31/1997
The U.S. Bureau of Reclamation maintains a network of agricultural weather stations called AgriMet stations.
These stations report daily averages for all of the necessary meteorological data except cloud cover. They also
report daily average solar radiation. Selected stations from the AgriMet network are shown in Table 3-7.
Table 3-7. Selected AGRIMET weather stations in the Columbia Basin maintained by the
U.S. Bureau of Reclamation
Station ID
GERW
GOLW
HERO
LEGW
ODSW
Station Name
George
Goldendale
Hermiston
Legrow
Odessa
State
WA
WA
OR
WA
WA
Elevation
1150
1680
600
580
1650
Latitude
47° 02' 38"
45° 48' 43"
45° 47' 56"
46° 12' 19"
47° 18' 32"
Longitude
11 9° 38' 32"
120° 49' 28"
11 9° 31 '46"
11 8° 56' 10"
11 8° 52' 43"
Install Data
5/14/86
11/27/91
5/17/83
7/17/86
4/24/84
29
-------
Application of a 1-D Heat Budget Model to the Columbia River System
An analysis of a 24-year record (January 1, 1972, to December 31, 1995) for the four NCDC SAMSON
weather stations showed a high degree of correlation between stations for dry bulb and dew point temperature
(Table 3-8). Average annual air temperatures showed more variability among the stations than did dew point.
Cloud cover was correlated, though not to the same degree as dry bulb and dew point temperature. Mean annual
cloud cover in Yakima differed substantially from that of the other three SAMSON stations in the Columbia
Basin. As expected, wind speed showed a much lower correlation among stations as well as more variability in
the mean annual value.
Table 3-8a. Correlation coefficients and annual average for average daily air temperature
collected at selected first order stations in the Columbia Basin
Lewiston
Lewiston
Pendleton
Spokane
Yakima
1.000
Annual Average 11.6°C
Pendleton
0.977
1.000
11.2°C
Spokane
0.985
0.976
1.000
8.6 °C
Yakima
0.969
0.966
0.975
1.000
10.1 °C
Table 3-8b. Correlation coefficients and annual average for average daily dew point at
selected first order stations in the Columbia Basin
Lewiston Pendleton
Lewiston
Pendleton
Spokane
Yakima
1.000 0.932
1.000
Annual Average 2.4 °C 2.0 °C
Spokane
0.937
0.916
1.000
1.0 °C
Yakima
0.894
0.899
0.919
1.000
1.5°C
Table 3-8c. Correlation coefficients and annual average for average daily sky cover at
selected first order stations in the Columbia Basin
Lewiston
Lewiston
Pendleton
Spokane
Yakima
1.000
Annual Average 64.1%
Pendleton
0.851
1.000
59.0%
Spokane
0.837
0.790
1.000
61.5%
Yakima
0.712
0.830
0.784
1.000
54.9%
Table 3-8d. Correlation coefficients and annual average for average daily wind speed
at selected first order stations in the Columbia Basin
Lewiston
Lewiston
1.000
Pendleton
0.500
Spokane
0.540
Yakima
0.390
-------
Chapter 3: Application of Temperature Model to Columbia River System
Pendleton
Spokane
Yakima
Annual Average
1.000 0.560
1.000
2.86 m/s 3.79 m/s 3.97 m/s
0.0.560
0.530
1.000
3.20 m/s
3.5 PARAMETER ESTIMATION
The parameter estimation process addresses both the deterministic and probabilistic parameters in the model.
The deterministic elements include the source term, fk, and, implicitly, the travel times of parcels in the
Lagrangian reference system. The components of the heat budget (Equation 4) and the advected thermal inputs
from tributaries and groundwater compose the source terms. The parameters required to determine the travel
times are derived from an analysis of the system hydraulics. It should be noted these parameters are not really
deterministic; rather, they are random variables. For the purposes of this analysis, the composite error resulting
from variability in the so-called deterministic parameters is included in the error term, w^, in Equation 10. Given
this assumption, the probabilistic parameters are the means and variances of the error terms for the measurement
model and the systems model.
In this study, the parameter estimation process is implemented in three steps. In the first step, the
deterministic parameters are estimated, ideally, from first principles or, as is more often the case, from available
research. Next, the estimated deterministic parameters are adjusted until the simulated results from the systems
model are approximately unbiased. The systems model is unbiased if the mean of the innovation vector is small,
where the innovation vector is the difference between time-updated simulations from the systems model and the
actual measurements (Van Geer et al., 1991). Assuming the actual measurement bias and their variances are
known, the final step in the parameter estimation process is to estimate the variance, FQ, of the systems model.
Hydraulic Coefficients
As described previously, the hydraulic properties of each unimpounded river segment are estimated from
relationships of the type given in Equations 18 to 20. Because a primary objective of the study is to assess the
impact of impoundments, it was necessary to estimate these coefficients for two states of the system: one with
dams in place and one without dams. For the case in which the dams were in place, the results from the USAGE
HEC-5Q model of the Columbia and Snake rivers were provided by Nancy Yun of the USAGE North Pacific
Division Office. They are given in Tables C-l and C-2, Appendix C. The only unimpounded reach under the
present configuration is the Hanford Reach. The coefficients in Equations 18 to 20 for the Hanford Reach are
given in Table C-3, Appendix C.
For the unimpounded conditions, geometric properties of the Columbia and Snake rivers, obtained from the
sources given in Table 3-3, were used as input data to HEC-RAS (USACE-HEC, 1995), the steady gradually
varied flow model developed by the U.S. Army Corps of Engineer's Hydrologic Engineering Center. Surface
elevations of the Columbia and Snake rivers were estimated for flows of 150,000, 250,000, and 500,000 cfs in the
Columbia River and 60,000, 120,000, and 240,000 cfs in the Snake River. For each of these flows, the average
water depth, surface width, and velocity at selected locations were used to estimate the coefficients in Equations
18 to 20 using the methods of least squares. The coefficients obtained in this manner are given in Table C-4 and
C-5, Appendix C.
31
-------
Application of a 1-D Heat Budget Model to the Columbia River System
Water Balance
The daily flow at any location in either river was determined from the sum of estimated ground water return
flow (Hansen et al., 1994) and the daily gaged flow of the main stem headwaters and the tributaries upstream
from the location. This assumes the following:
a Information regarding flow changes is transmitted instantaneously to locations downstream.
a Tributary sources other than those shown in Table 3-1 are negligible.
a The river gradient is sufficiently high such that the slope terms dominate (Henderson, 1966).
Heat Flux Across Air-Water Interface
The variables in the meteorological input file (* .HOT) were either directly measured or calculated from daily
averaged data. These variables were then used to quantify the heat flux terms used in the energy budget method.
The variables in the meteorological input file were determined as follows:
a Net Solar Radiation - calculated using equation (5)
a Net Atmospheric Radiation - calculated using Equation 6
a Dry-Bulb Temperature - directly measured
a Wind Speed - directly measured
a Factor for Bowen Ratio (psychrometric constant) - calculated using the following equation:
RB = (Ca P) / (0.622 8) (22)
where
ca = heat capacity of air, cal/g/C, 0.24;
P = pressure at sea level, mb, 1013.3;
A, = latent heat of vaporization, cal/g;
A, = 597.3 - (0.564 Td); and (23)
Td = dry-bulb temperature, degrees Celsius
a Vapor Pressure - was calculated using the following equation
ea = 6.11 EXP (17.27 Tdew) / (237.3 + Tdew) (24)
where,
Tdew = dew-point temperature, degrees Celsius
Photo Period - this variable is not used in this model.
32
-------
Chapter 3: Application of Temperature Model to Columbia River System
Initial Water Temperatures
Bail}' water temperatures are not always available for the locations used as initial conditions on the tributaries
(Table 3-1) of the Columbia and Snake. For most stations, long-term sampling with a period of two to four weeks
provides sufficient data to synthesize stream temperatures using air temperature. In their study of 584 USGS
stream gaging stations within the contiguous United States, Mohseni et al. (1998) used a nonlinear model of the
following type to synthesize water temperatures:
a -
where
Ts
Ta
1 + ey(P-Ta)
the weekly stream temperature
the weekly air temperature from a nearby weather station and
(25)
V, 3, (, and JJL are determined by regressing the observed water temperature data on the air temperature
data by minimizing the squared error with the downhill simplex method (Nelder and Mead, 1965).
Separate functions of the type defined in Equation 25 are used to describe the rising limbs and the falling
limbs of the annual water temperature cycle in each of the tributaries. Mohseni et al. (1998) concluded that the
method was accurate and reliable at 89 percent of the streams. Mohseni et al. (1998) also found that the method
gave good results even when the air temperature measurements were not in proximity to the stream gaging
locations.
The parameters obtained forthe tributaries following the method of Mohseni et al. (1998), for both rising and
falling limbs, at each of the input locations, are given in Table 3-9.
For the initial water temperatures on the main stem Columbia River, scroll case and total dissolved gas data
from Chief Joseph Dam were combined to provide a long-term record. On the Snake River, the USGS data from
the monitoring site at Anatone, Washington, was combined with data collected by Idaho Power Company and the
Columbia River Intertribal Fish Commission to fonii a long-term record.
Measurement Bias and Error
The analysis of water temperature in the Columbia and Snake rivers by McKenzie and Laenen (1998)
provides the basis for an initial estimate of the probabilistic parameters of the measurement model (Equation (3)).
The data reviewed by McKenzie and Laenen (1998) were obtained from scroll case measurements and
Table 3-9. Parameters for estimating input temperatures of main stem and tributaries
using nonlinear regression methods described by Mohseni et al. (1998)
River
Methow River
Walla Walla River
Clearwater River
Weather Station
Wenatchee
Yakima
Lewiston
Week for Rising Limb
Week for Falling Limb
1
30
1
30
1
30
Tmax
22
22
29
29
24
24
P
14.4976
12.9058
12.7334
11.6612
16.2527
13.00
Y
0.2007
0.1787
0.1763
0.1615
0.2250
0.1800
H
0.5576
0.4964
0.4897
0.4485
0.6251
0.500
-------
Application of a 1-D Heat Budget Model to the Columbia River System
River
Chelan River
Crab Creek
Deschutes River
John Day River
Okanogan River
Palouse River
Tucannon River
Wenatchee River
Yakima River
Weather Station
Wenatchee
Wenatchee
Yakima
Lewiston
Wenatchee
Yakima
Lewiston
Wenatchee
Yakima
Week for Rising Limb
Week for Falling Limb
1
30
1
30
1
30
1
32
1
30
1
30
1
32
1
30
1
30
I max
26
26
26
26
24
24
29
29
26
26
28
28
22
22
23
23
28
28
P
13.0000
8.3590
11.2747
11.4084
10.5902
8.0669
13
12.3896
15.4810
13.3483
14.2740
14.7654
12.2640
11.3405
16.5413
12.5088
12.7321
11.9158
Y
0.1800
0.1157
0.1561
0.1580
0.1466
0.1117
0.1800
0.1715
0.2144
0.1848
0.1976
0.2044
0.1698
0.1570
0.2290
0.1732
0.1763
0.165
H
0.500
0.3215
0.4336
0.4388
0.4073
0.3103
0.5000
0.4765
0.5954
0.5134
0.5490
0.5679
0.4717
0.4362
0.6362
0.4811
0.4897
0.4583
measurements made in conjunction with total dissolved gas monitoring. The scroll case measurement reflects the
temperature of the water as it enters the generating turbine and is measured by reading the level of a mercury
thermometer. The total dissolved gas monitoring program uses a temperature probe located in the forebay of each
of the dams usually at a depth of 15 feet or more.
The quality, bias, and variability of these data vary considerably from site to site. For the scroll case data,
McKenzie and Laenen (1998) report frequent "stepping" of the data. Stepping is characterized by periods of
several days when the reported temperature is constant. Scroll case temperatures are measured by visual
observations from mercury thermometers and recorded manually, usually on a daily basis. McKenzie and Laenen
(1998) suggest that the measurement method might have contributed to the "stepping" and that the stepping might
have been due to the frequency with which scroll case temperatures were measured and reported in the past.
The variation in data quality makes the task of quantifying measurement bias and error a difficult one.
McKenzie and Laenen (1998) report bias in the measurements as high as 2.0 °C and variability as high as 2.0 °C
at certain sites and during certain periods of the year. However, at most sites and for recent data (post-1990), bias
is in the range of 0.0-1.5 °C and variability is generally less than 1.0 °C.
Systems Model Bias and Error
The approach to estimating the probabilistic parameters for the systems model (Equation 2) follows that of
Van Geer et al. (1991). Initial estimates of deterministic parameters are obtained from some combination of first
principles and existing research. These parameters include the heat transfer across the air-water interface,
advected thermal energy from tributaries and point sources and hydraulic properties of the river system.
Adjustments are made to certain parameters until the mean of the innovations vector (Equation 17) is small.
34
-------
Chapter 3: Application of Temperature Model to Columbia River System
The parameters selected for adjustment are constrained by assuming that any error in the basic heat transfer
components (Equations 5 to 9), the advected energy from tributaries, and the hydraulic computations can be
aggregated into the systems model error, rQ(t). Given these constraints, what remains to be adjusted is the choice
of meteorological stations used to estimate the basic heat transfer components and the evaporation rate. This
formulation of the evaporation was obtained from the comprehensive energy budget of Lake Hefner in Oklahoma
(Marciano and Harbeck, 1952) and has been shown to perform satisfactorily for other water bodies (Bowie et al.,
1985). However, there is uncertainty in the empirical constant, EV (Kohler, 1954; Bowie et al., 1985). There is
also uncertainty and variability associated with the meteorological variables, wind speed, W, and vapor pressure,
ea. The uncertainty in the meteorological variables, as discussed below, is primarily a result of the assumption in
this study that wind speed and vapor pressure can be treated as regional phenomena. The approach used in this
report has been to assume the meteorological variables can be obtained from the NCDC SAMSON data sets and
treat the empirical constant, EV, as a parameter that can be estimated during the process described above.
The choice of appropriate meteorological stations for estimating the heat budget at the spatial scale of this
analysis must take into account regional variations in weather under the constraint of a limited number of stations
with complete data. The problem is not unique to this study. The analysis of systems operations in the Columbia
Basin (Bonneville Power Administration et al., 1994) used the data from three weather stations (Boise, Idaho;
Lewiston, Idaho; and Spokane, Washington) to develop the heat budget for the Columbia, Snake, and Clearwater
rivers. These data were used to describe surface heat exchange from and including Brownlee Reservoir on the
Snake to the confluence with the Columbia; the Clearwater River from and including Dworshak Reservoir and the
Columbia River from the International Border to Bonneville Dam. A study of thermal energy in the Hells Canyon
complex by Idaho Power Company (Harrison et al., 1999) used the combined meteorological data from Parma,
Idaho, and Prairie City, Oregon, to predict water temperatures in Brownlee Reservoir from approximately Snake
River Mile 335 to Snake River Mile 285. Parma is approximately 50 miles from Brownlee Reservoir, while
Prairie City is approximately 100 miles from Brownlee Reservoir.
As shown in Table 3-8, there are strong regional correlations among certain meteorological variables in the
Columbia Basin, particularly air temperature, dew point, and cloud cover. Regional correlations for wind speed
are not as strong because of the influence of topography. There is some regional variation in the climate as
reflected in the annual average values (Table 3-8). Data from two classes of meteorological stations are available
to estimate these components, as described previously. Some Surface Airways (SAMSON) stations report the
complete suite of meteorological variables. There is extensive coverage of daily maximum and minimum air
temperatures from the Local Climatological Data (LCD). Data from the SAMSON stations were used to expand
the spatial coverage for heat budget analysis. This was accomplished by assuming mat wind speed, cloud cover,
relative humidity, and barometric pressure are large-scale phenomena and that air temperature is more of a local
phenomenon. Several LCD stations were augmented with SAMSON data in this way to provide more spatial
coverage of the surface heat transfer. Meteorological data were assigned to river segments based on a qualitative
assessment of local meteorology. A number of combinations of stations were evaluated in an effort to achieve
unbiased simulations. The final configuration of stations and the values of the empirical constant, EV, for each
river segment are given in Table 3-10.
Table 3-10. Final configuration of weather stations used to estimate the heat budget terms
for the mathematical model of water temperature in the Columbia and Snake Rivers.
Evaporation Coefficient
Weather Station Station Type (mb'1) River Segments
Lewiston, Idaho SAMSON 1.45x10"9 Snake River from Lewiston,
Idaho to the Confluence with
the Columbia
Wenatchee, Washington LCD 1.55x10"9 Columbia River from Grand
Coulee Dam to Rock Island
Dam
Yakima, Washington SAMSON 1.40x10'9 Columbia River from Rock
35
-------
Application of a 1-D Heat Budget Model to the Columbia River System
Richland, Washington
LCD
1.10x10"
Island Dam to the Confluence
with the Snake
Columbia River from the
confluence with the Snake to
Bonneville Dam
Using the parameters estimated above, estimates of the system model error variance, FQ(t), are obtained by
adjusting the estimated variance until the theoretical variance for the innovations vector is approximately equal to
the sample variance (Mehra, 1972). The theoretical variance is given by (Kailath, 1968)
E{vkvkT} = H Pk(-) HT + S
and the sample variance, S, by
(26)
S = —
>'kvk
(27)
This is an iterative process because the innovations vector is a function of the deterministic parameters and
the probabilistic parameters. In addition, there are bias and error in the observations (McKenzie and Laenen,
1998), as described previously. The systems model error estimate was obtained by first finding a set of
meteorological stations, which provided good (in a qualitative sense) agreement. This was followed by an
adjustment of measurement bias and error for the total dissolved gas temperature data, within the range estimated
by McKenzie and Laenen (1998). The final values for systems model variance, EQ, and measurement error and
bias are given in Table 3-11.
After completing the parameter estimation process for both the deterministic and probabilistic parameters, the
systems model was run in the predictive mode. That is, the measurements were not used to update the state
estimate. Running the model in the predictive mode provides a way of comparing state estimates from the
systems model with the state estimates from the measurement model in a manner similar to the traditional
approaches using the calibration and verification paradigm. The output from these simulations is shown in
Figures 3-4 through 3-12. Various statistics that can be used to assess model performance are given in Appendix
D.
-------
Chapter 3: Application of Temperature Model to Columbia River System
Table 3-11. Measurement bias, measurement error variance and systems dynamic error variance
at locations of scroll case temperature measurements on the Columbia and Snake Rivers
Location of Measurement
Lower Granite Dam
Little Goose Dam
Lower Monumental Dam
Ice Harbor Dam
Rock Island Dam
Priest Rapids Dam
McNary Dam
The Dalles Dam
Bonneville Dam
Measurement Bias
(°c)
0.0
0.0
0.0
0.0
0.5
0.0
1.0
1.0
1.5
Error
Measurement
°c2
0.50
0.50
0.50
0.5
0.50
0.50
0.50
0.50
0.50
Variance
Systems Dynamics
°c2
0.008
0.008
0.008
0.008
0.008
0.008
0.008
0.008
0.008
1990
*
Simulated
Scroll Case
Total Dissolved Gas
1992 1993
Time - Years
1994
Figure 3-4. Simulated and observed water temperatures at Wells Dam for the period 1990-1994.
37
-------
Application of a 1-D Heat Budget Model to the Columbia River System
o
O!
I
15
10
1990
1991
1992
1993
Simulated
Scroll Case
Total Dissolved Gas
Time -Years
1994
1995
Figure 3-5. Simulated and observed water temperatures at Priest Rapids Dam for the period 1990-1994.
30 r-r-r
o>
0>
•o
25
20
15
IJ
a.
10
1990
1991
Simulated
Total Dissolved Gas
1992 1993
Time -Years
1994
1995
Figure 3-6. Simulated and observed water temperatures at McNary Dam for the period 1990-1994.
-------
Chapter 3: Application of Temperature Model to Columbia River System
1990
1991
Simulated
•> Scroll Caie
• Total Dissolved Gas
1992 1993
Time -Years
1994
1995
Figure 3-7. Simulated and observed water temperatures at John Day Dam for the period 1990-1994.
1990
1991
1992
1993
1994
1995
Simulated
Scroll Case
Total Dissolved Gai
Time -Years
Figure 3-8. Simulated and observed water temperatures at Bonneville Dam for the period 1990-1994.
-------
Application of a 1-D Heat Budget Model to the Columbia River System
1990
1991
Simulated
• Scroll Case
• Total Dissolved Ga
1992 1993
Time -Years
1994
1995
Figure 3-9. Simulated and observed water temperatures at Lower Granite Dam for the period 1990-1994.
1990
1991
Simulated
Scroll Cue
Total Dissolved Gas
1992 1993
Time -Years
1994
1995
Figure 3-10. Simulated and observed water temperatures at Little Goose Dam for the period 1990-1994.
40
-------
Chapter 3: Application of Temperature Model to Columbia River System
30
25 -
20 -
£ 15
a.
10 -
1990
1991
Simulated
Scroll Case
Total Dissolved Gai
1992 1993
Time -Years
1994
1995
Figure 3-11. Simulated and observed water temperatures at Lower Monumental Dam for the period
1990-1994.
1990
1991
*
Simulated
Scroll Case
Total Dissolved Gas
1992 1993
Time -Years
1994
Figure 3-12. Simulated and observed water temperatures at Ice Harbor Dam for the period 1990-1994.
41
-------
Application of a 1-D Heat Budget Model to the Columbia River System
3.6 MODEL AP PLICA TION
Scenarios
The objectives of this study are to assess the relative contribution of impoundments and tributary inputs to
changes in the thermal regime of the Columbia and Snake rivers. To capture the environmental variability in
hydrology and meteorology, the 21-year record of stream flows and weather data from 1975 to 1995 is used to
characterize river hydraulics and surface heat transfer rates. Most tributary temperatures are developed from local
air temperatures using the relationship given by Equation 25 and air temperature data for the same 21-year period.
The period from 1975 to 1995 was chosen to represent a period of relatively consistent management of the
hydroelectric system. This assumption was based on the fact that it includes the period for which all the dams that
are presently installed have been in operation. However, the assumption is confounded to a degree by the change
in operation of Dworshak Dam beginning in the summer of 1992. Selective withdrawal of cold water at
Dworshak Dam, beginning in 1992, has led to modifications in the temperature regime of the Snake River (Karr
et al., 1998). For the period 1992-1995, measured temperatures at Dworshak Dam and at Orofino, Idaho, were
used to account for the effects of selective withdrawal at Dworshak Dam.
The assessment of impacts to the thermal regime of the Columbia and Snake River is based on the following
three scenarios:
Scenario 1 This scenario includes the existing configuration of dams, hydrology, and meteorology from 1975
to 1995 and tributary temperatures estimated from the 21-year meteorologic record using
Equation 25.
Scenario 2 This scenario assumes the Columbia River downstream from Grand Coulee and the Snake River
downstream from Lewiston, Idaho, are unimpounded and that hydrology, meteorology, and
tributary temperatures are the same as Scenario 1.
Scenario 3 This scenario assumes the existing configuration of dams, with hydrology and meteorology for
the period 1975 to 1995. Tributary input temperatures are estimated from the 21-year
meteorologic record using Equation 25, but are not allowed to exceed 16 °C (60.8 °F).
For each of these scenarios, daily average water temperatures are simulated and the mean, mean plus one
standard deviation, and the mean minus one standard deviation of the simulated water temperatures are compared
to the benchmark, 20 °C (68 °F). Temperature excursions are defined for the three conditions as follows:
T;X = Tiim -20 for nim >20
= 0 for Tiim < 20
where
Tsim = the simulated daily average water temperature - one standard deviation
Tsim = the simulated daily average water temperature
T?m = the simulated daily average water temperature + one standard deviation
The average annual duration, or frequency, fgx, of temperature excursions is estimated as the number of days
in excess of the benchmark compared to the total number of days in the simulation. That is,
42
-------
Chapter 3: Application of Temperature Model to Columbia River System
where
N
= 1
for T;X > 20
for
< 20.
N
= total number of days simulated
The standard deviation for these simulations is computed with the Kalman filter (Equations 10 to 17) in the
prediction mode. In the prediction mode, the measurement matrix, H, is set to zero. This means the Kalman gain,
K, is always zero and the variance propagation is a result of updating by the systems model only:
V — f D f T , v
Ak - Tk-1 rk-1 Tk-1 + LQ
where the (+) and (-) convention has been dropped since mere is no updating based on the observations.
The frequencies of temperature excursions for each scenario as a function of Columbia and Snake River Mile
are shown in Figures 3-13 to 3-18. The error bars in each of the plots represent the frequencies estimated with the
simulated means plus one standard deviation and the simulated means minus one standard deviation.
0.25
>• 0.15 H
0.10 -
0.05 -
0.00
-I ^
Grand Wells Rock Priest McNary John Bonneville
Coulee Island Rapids Day
Figure 3-13. Frequency of predicted water temperature excursions in the Columbia River with
dams in place.
43
-------
Application of a 1-D Heat Budget Model to the Columbia River System
0.25
E
<1>
"
0.20 -
0.15 -
0.10 -
0.05 -
0.00
*
A
Le wist on Lower Little Lower Ice
Granite Goose Monumental Harbor
Figure 3-14. Frequency of predicted water temperature excursions in the Snake River with dams in place.
0.25
0.20 -
> 0.15-1
c
£ 0.10 -
0.05 -
0.00
^ * 4-
Grand Wells Rock Priest McNary John Bonneville
Coulee Island Rapids Day
Figure 3-15. Frequency of predicted water temperature excursions in the Columbia River for the
unimpounded river.
44
-------
Chapter 3: Application of Temperature Model to Columbia River System
0.25
0.20 -
o 0.15 -
c
0.10 -
0.05 -
0.00
Lewiston Lower Little Lower Ice
Granite Goose Monumental Harbor
Figure 3-16. Frequency of predicted water temperature excursions in the Snake River for the
unimpounded river.
0.25
0.20 -
> 0.15 J
E
0.10 -I
0.05 -
0.00
T A
•
Grand Wells Rock Priest McNary John Bonneville
Coulee Island Rapids Day
Figure 3-17. Frequency of predicted water temperature excursions in the Columbia River with dams in
place and tributaries equal to or less than 16 °C.
45
-------
Application of a 1-D Heat Budget Model to the Columbia River System
0.25
-------
Chapter 3: Application of Temperature Model to Columbia River System
Scenario 1, so that the frequencies of temperature excursion associated with the mean simulation plus one
standard deviation are approximately 0.04 greater than that of the simulation. The increase in the uncertainty of
the estimate for the river in the unimpounded scenario is due to the change in system dynamics associated with
shallower depths and higher velocities. In spite of the increase in uncertainty, the difference in Scenarios 1 and 2
at those sites downstream from the confluence of the Snake River are clearly outside the bands defined by one
standard deviation of the state estimates. In a qualitative sense, these differences are significant; that is, the
unimpounded Columbia River has significantly fewer temperature excursions than does the impounded river. For
the purposes of this assessment, however, no attempt has been made to evaluate the significance in terms of
impact on the ecosystem.
The frequency properties of Scenario 3, for which tributary temperatures are constrained to be always less
than 16 °C, are similar to Scenario 1 on the Columbia River upstream of its confluence with the Snake. The
combined average annual flows of advected sources in this segment (Table 3-1) are less than 10 percent of
average annual flow of the Columbia River at Grand Coulee Dam. The impact of these sources on the thermal
energy budget of the main stem Columbia is, therefore, small. The 16 °C constraint was not applied to the Snake
River and the warming effect of the Snake River on the Columbia is evident in the increase in the frequency of
excursions between Priest Rapids Dam and McNary Dam. The net result being that frequency of excursions is
not significantly different between Scenarios 1 and 3.
In the Snake River, with dams in place (Figure 3-14), the mean frequency of temperature excursions is
relatively high (0.15) at the starting point (Snake River Miles 168.0), drops slightly due to the influence of the
Clearwater River, then increases to 0.19 between there and Ice Harbor Dam (Snake River Miles 9.0). Because the
Snake is a smaller river, it responds more rapidly to changes in systems dynamics. This, in turn, leads to larger
uncertainty in the estimates as reflected in increased ranges of both frequency and magnitude of excursions. For
the unimpounded case (Figure 3-16), the analysis predicts that the mean frequency of temperature excursions at
Ice Harbor is approximately the same as the initial point near Anatone, Washington. The Clearwater River has a
noticeable impact on water temperatures of the Snake River as shown by the reduction in the mean frequencies of
temperature excursions for Scenarios 2 and 3 at Lower Granite Dam compared to the initial conditions for the
Snake River at Anatone, Washington.
The wider bands of uncertainty reduce the significance of the results for the Snake River scenarios in the
estimated frequency and magnitude of temperature excursions. At Lower Granite Dam, the differences in the
three scenarios are small and within the uncertainty bands defined by one standard deviation of the state
estimates. The qualitative level of significance in differences between Scenarios 1 and 2 increases downstream.
At Ice Harbor Dam, the mean values of the frequency estimates for Scenario 2 are outside the uncertainty bands
defined by one standard deviation of the state estimates of Scenario 1. Differences between Scenarios 1 and 3 are
significant only at Lower Granite, where the impact of lower temperatures in the Clearwater River is still
important.
Changes in cross-sectional daily average water temperature between initial conditions and some downstream
point in rivers are due to (1) meteorology (wind speed, air temperature, cloud cover, air moisture content), (2)
river depth, and (3) travel time between the two points. The meteorology determines the maximum temperature
the water body can achieve; the depth and certain components of meteorology determine the rate at which the
water body exchanges heat with the atmosphere; and the travel time determines the importance of initial
conditions.
Some limits on the cross-sectional daily average water temperature in rivers can be estimated by defining the
equilibrium temperature as the temperature a body of water would reach after very long exposure to a specific set
of meteorological conditions. For a river moving with an infinitely high speed, the cross-sectional daily average
water temperature at some downstream point will be exactly the same as the initial conditions. The meteorology
would have no effect on cross-sectional daily average water temperature for this case. A water body at rest (no
velocity) under constant meteorological conditions would eventually reach the equilibrium temperature
47
-------
Application of a 1-D Heat Budget Model to the Columbia River System
determined by wind speed, air temperature, cloud cover, and air moisture content. The water depth and certain
components of the meteorology would determine the time it takes to reach the equilibrium temperature.
The impact of structural changes on the cross-sectional daily average water temperature river system, such as
the construction and operation of dams and reservoirs, is determined by the relative importance of the three
factors described above. The results for Scenarios 1 and 2 imply that the structural changes associated with
construction and operation of hydroelectric facilities on the Columbia and Snake rivers have led to changes in the
travel times that are sufficient to modify the temperature regimes of these rivers.
The impact of advected sources such as tributaries and point discharges on the cross-sectional daily average
water temperature of the main stem Columbia and Snake rivers is determined by the ratio of advected energy from
the source (pCpQadvTadv) to the advected energy of the main stem (pCpQmamTmam). Contribution of thermal energy
of most of the advected sources (Table 9) is small due to the magnitude of their flow compared to the main stems.
The Clearwater River does have a significant cooling effect on the cross-sectional daily average water
temperature of the Snake River. In addition, the Snake River has a significant warming effect on the cross-
sectional daily average water temperature of the Columbia River.
48
-------
Chapter 4: Model Input and Output Files
CHAPTER 4: MODEL INPUT AND OUTPUT FILES
4.1 IN PUT FILES
The Columbia River Temperature model requires three types of input files: the control file, advected source
file, and meteorological file. The main input file, or control file, contains general model and reach information
and lists which weather station files the model will use. The advected source file contains daily flow and
temperature values for the main reaches as well as all the tributary inputs. The meteorological file contains data
about each weather station that is used in the model.
The input files are divided into sections. Each section pertains to a general group of data. The sections are as
follows:
Control File
Section 1 - General Model Information
Section 2 - Reach Information
Section 3 - Weather Station (Meteorological) File Names
Advected Source File
Section 4 - Input File Information for Advected Source File
Meteorological File
Section 5 - Input File Information for Meteorological File
Each section is made up of one or more records. A record contains data for a specific portion of that section.
Each record is then defined by one or more lines of data. A detailed description of the input data structure for the
input files follows.
Control File
An example of a control file is shown in Figure 4-1.
Section 1 (General Model Information)
Record 10 (General Model Information)
Line 1 advected source file name (i.e., crtass.adv)
Name of file that contains advected thermal energy data (flow and temperature)
for main river stems and tributaries. In this model, there are three main river
stems (Clearwater River, Snake River, and Columbia River) and 12 tributaries.
Line 2 model description
Description of Temperature Model
Line 3 model title
Temperature Model Title
Line 4 model start date, model end date
Date that model will begin and end computations. Format for each date is
YYYYMMDD.
49
-------
Application of a 1-D Heat Budget Model to the Columbia River System
RIO
RIO
RIO
RIO
RIO
RIO
R20.
R20.
R21.
R21.
R21.
R21.
R22.
R22.
R22.
R22.
R22.
R22.
i*********** INPUT FILE - CRTES.INP - FOR RBM10 ***************
i*********** SECTION 1 - GENERAL MODEL INFORMATION ***************
.LI crtass.adv
.L2 Reverse Particle Tracking Model-Existing Conditions-add Clearwater R
.L3 Columbia River Temperature Assessment Project - EPA Region 10
,L4 19750101 19951231 2
.L5 Number of reaches
. L6 3
i*********** SECTION 2 - REACH INFORMATION ***************
i*********** REACH 1 - CLEARWATER RIVER ***************
.LI Clearwater River 4 5
,L2 40.0 30.0 20.0 10.0 5.0
R20.
R20.
R21.
R21.
R21.
R21.
R22.
R22.
R22.
R22.
R22.
R22.
R24.
R24.
R24.
R24.
R24.
R24.
LI Abv NF Confluence RIVER
L2 23000
L3 4.1693 0.693 56.765
L4 End of Segment #A
LI Blw NF Confluence 1 RIVER
L2 30 3 0 1 0
L3 4.053 0.693 56.234
L4 Tributary Inflows
L5 NF Clearwater R INFclr
L6 End of Segment #B
*********** REACH 2 - SNAKE RIVER
LI Snake River 49
L2 168. 107. 70.5 41.7 10.1
LI Hells Canyon Reach RIVER
L2 93000
L3 4.222 0.693 57.005
L4 End of Segment #A
42 .0 40.6 980.0000.
0.233
40.6 11.9 900.
0.233
40.1 9640.0
168.7150.0 812.0000.
0.233
.LI Hells Canyon Reach RIVER
. L2 2 3 0 1 1
,L3 4.169 0.693 56.764
.L4 Tributary Inflows
.L5 Clearwater R. 2clear
.L6 End of Segment #C
144.0140.0 760.
0.233
140.1 9640.0
RSRVR
R20.
R20.
R21.
R21.
R21.
R21.
R24.
R24.
R24.
R24.
R24.
R24.
R22.
R22.
R22.
R22.
R22.
R22.
R23.
R23.
R23.
R23.
.LI Lower Granite Resrvr
. L2 2 3 0 1 0
,L3 20825. 597.4
.L4 Tributary Inflows
.L5 Potlatch Corp Spotlt
.L6 End of Segment #1
i*********** REACH 3 - COLUMBIA RIVER *
.LI Columbia River 56
,L2 516. 474. 397. 292. 216. 192. 146.
140.0137.3 746.
2.7 Volume (acre-feet) and Area (acres) in Seg 1
139.5
.LI Head of Chief Joseph
. L2 1 1 0 0 0
,L3 2.6338 0.7352 18.
. L4 End of Segment #1
.LI Wells Reservoir #1 R
. L2 1 1 0 1 0
,L3 33809.6 1571.
. L4 Tributary Inflow
. L5 Okanogan River 6okngn
. L6 End of Segment #13
RIVER
596.1593.31000.
SRVR 539.2533.3 803.
5.9 Volume (acre-feet) and Area (acres) in Seg 1
533.3 8340.0
RIVER
.LI Hanford Reach #13
. L2 1 2 0 1 2
,L3 94.4921 0.5597 1585.1760
.L4 Tributary Inflow
.L5 Snake River 12 sna 324.0
.L6 End of Segment #41
329.4324.0 450. 0.0 0.0
0.1194
109000.
165.7145.5 82. 0.0 0.0
Volume (acre-feet) and Area (acres) in Seg 2
R30
R30
R30
R30
.LI Bonneville Reservoir RSRVR
. L2 7 4 0 0 0
,L3 285538. 9072. 20.2
.L4 End of Segment #56
i*********** SECTION 3 - WEATHER STATION FILES AND EVAPORATION COEFFICIENTS
.LI wnatchee.hot 1.55e-9
.LI yakima.hot 1.40e-9
.LI lewiston.hot 1.45e-9
.LI richland.hot 1.10e-9
Figure 4-1. Example control file.
50
-------
Chapter 4: Model Input and Output Files
Line 5 comment line
Line 6 number of reaches
This is the number of river reaches that are being modeled. In this model there
are three river reaches (Clearwater River, Snake River, and Columbia River).
Section 2 (Reach Information)
Record 20 (Reach Description)
Line 1 reach name, number of segments in reach, number of plots to be sent to output file
Line 2 location of plots with respect to River Mile
Record 21 (River Segment with no tributary inflow)
Line 1 segment name, segment type, beginning mile location of segment, ending mile location
of segment, elevation
Line 2 number of computational elements per segmentation, weather file to be used, headwaters
number, number of entering tributaries, reach number if the tributary is one for which
temperatures are simulated
There can be a maximum of 600 computational elements per reach. The reach
number of the tributary in this case (no tributary inflow) should be zero.
Line 3 a area, b area, a width, b width
These are the hydraulic coefficients determined for each reach.
Line 4 end of record
Record 22 (River Segment with tributary inflow)
Line 1 segment name, segment type, beginning mile location of segment, ending mile location
of segment, elevation
Line 2 number of computational elements per segment, weather file to be used, headwaters
number, number of entering tributaries, reach number if the tributary is one for which
temperatures are simulated
There can be a maximum of 600 computational elements per reach. The
tributary numbering system is tricky, particularly if the tributary is one that is
being simulated. The number appearing on this line is the REACH NUMBER of
the tributary, while the number appearing on line 5 below is the ORDINAL
NUMBER for the tributary. As an example, the Snake River (REACH 2) is a
tributary to the Columbia and is the 12th tributary in the order of tributaries.
Therefore, to specify the Snake as a tributary, one would enter a "2" on line 2,
and a "12" on line 5, below. The order in which simulated tributaries occur is
also important. The main requirement is that tributaries must be simulated
before the reach to which they are tributary is simulated.
Line 3 a area, b area, a width, b width
These are the hydraulic coefficients determined for each reach.
Line 4 comment line
51
-------
Application of a 1-D Heat Budget Model to the Columbia River System
Line 5 tributary name, designated tributary number (ordinal number), abbreviated tributary
name, river mile at which tributary connects to main segment, square miles of the
watershed associated with the tributary
The square miles of the watershed associated with the tributary is not used in the
program at this point.
Line 6 end of record
Record 23 (Reservoir Segment with no tributary inflow)
Line 1 segment name, segment type, beginning mile location of segment, ending mile location
of segment, elevation
Line 2 number of computational elements per segmentation, weather file to be used, headwaters
number, number of entering tributaries, reach number if the tributary is one for which
temperatures are simulated
There can be a maximum of 600 computational elements per reach. The reach
number of the tributary in this case (no tributary inflow) should be zero.
Line 3 reservoir volume, reservoir area, delta x
Line 4 end of record
Record 24 (Reservoir Segment with tributary inflow)
Line 1 segment name, segment type, beginning mile location of segment, ending mile location
of segment, elevation
Line 2 number of computational elements per segment, weather file to be used, headwaters
number, number of entering tributaries, reach number if the tributary is one for which
temperatures are simulated
There can be a maximum of 600 computational elements per reach. The
tributary numbering system is tricky, particularly if the tributary is one that is
being simulated. The number appearing on this line is the REACH NUMBER of
the tributary, while the number appearing on line 5 below is the ORDINAL
NUMBER for the tributary. As an example, the Snake River (REACH 2) is a
tributary to the Columbia and is the 12th tributary in the order of tributaries.
Therefore, to specify the Snake as a tributary, one would enter a "2" on line 2,
and a "12" on line 5, below. The order in which simulated tributaries occur is
also important. The main requirement is that tributaries must be simulated
before the reach to which they are tributary is simulated.
Line 3 reservoir volume, reservoir area, delta x
Line 4 comment line
Line 5 tributary name, designated tributary number (ordinal number), abbreviated tributary
name, river mile at which tributary connects to main segment, square miles of the
watershed associated with the tributary
The square mileage of the watershed associated with the tributary is not used in
the program at this point.
Line 6 end of record
52
-------
Chapter 4: Model Input and Output Files
Section 3 (Weather Station (Meteorological) File Names)
Record 30 (Weather Station File Name Information)
Line 1 weather station file name, evaporation coefficient
Advected Source File
An example of an advected source file is shown in Figure 4-2.
Section 4 (Input File Information for Advected Source File)
Record 40 (Input File Information for Advected Source File)
Line 1 model start date, model end date
Record 41 (Advected Source Data for Each Julian Day)
Line 1 year, Julian day, flow for Clearwater River (cfs), water temperature for Clearwater River (deg-C),
flow for Snake River (cfs), water temperature for Snake River (deg-C), flow for Columbia River
(cfs), water temperature for Columbia River (deg-C)
Line 2 NF of Clearwater River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Line 3 Potlatch Corp: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Line 4 Tucannon River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Line 5 Palouse River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Line 6 Okanogan River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Line 7 Methow River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Line 8 Chelan River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Line 9 Wenatchee River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
-------
Application of a 1-D Heat Budget Model to the Columbia River System
*** SECTION 4 - INPUT
19750101 19951231
1975 1 1150.
1 2890.0 6.6
3 62 .2 33.0
4 138.0 3.4
5 174.0 4.2
6 894.0 2.0
7 320.0 2.5
8 2190.0 2.6
9 1250.0 6.4
10 30.0 3.2
11 2860.0 4.1
13 494.0 4.3
14 451.0 4.8
15 6560.0 4.6
1975 2 1140.
1 4990.0 5.6
3 62 .2 33.0
4 136.0 3.5
5 167.0 3.9
6 866 .0 1.9
7 330.0 2.3
8 2180.0 2.6
9 1180.0 5.3
10 29.0 3.3
11 2750.0 3.9
13 482.0 4.1
14 416.0 4.6
15 6560.0 4.6
1975 3 1430.
1 7090.0 4.8
3 62 .2 33.0
4 136.0 3.5
5 172.0 3.7
6 793.0 1.8
7 330.0 2.1
8 2180.0 2.6
9 1160.0 4.5
10 28.0 3.4
11 2700.0 3.7
13 462.0 3.9
14 451.0 4.5
15 6490.0 4.5
1975 4 1500.
1 7070.0 4.2
3 62 .2 33.0
4 167.0 3.6
5 282.0 3.5
6 932.0 1.7
7 340.0 2.0
8 2180.0 2.6
9 1160.0 3.8
10 30.0 3.5
11 2730.0 3.6
13 482.0 3.7
14 375.0 4.4
15 6560.0 4.5
Line 10 Crab Creek:
Line 1 1 Yakima River:
Line 12 Walla Walla:
FILE INFORMATION FOR ADVECTED SOURCE DATA ***
6.6 24000. 3.9 95300. 6.2
5.6 23000. 3.6 94700. 5.7
4.8 25000. 3.3 93000. 5.3
4.2 26800. 3.3 104000. 5.5
Figure 4-2. Example advected source file.
Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Line 13 John Day River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
54
-------
Chapter 4: Model Input and Output Files
Line 14 Deschutes River: Ordinal number of tributary, flow (cfs),
water temperature (degrees Celsius)
Meteorological File
An example of a meteorological file is shown in Figure 4-3.
***** SECTION 5 - INPUT FILE INFORMATION FOR METEOROLOGICAL FILE *****
YAKIMA AIR TERMINAL
1 2000.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
01556
00917
01056
01472
01500
01444
01000
01194
01000
01833
00972
01194
01000
00972
01278
01194
01222
01944
01306
01889
01917
01000
01111
00944
01167
02111
02306
01528
01500
01306
01444
01389
01389
01389
01500
01528
01639
02222
01639
02389
02833
01944
01556
02250
02944
01556
03194
02750
01472
01472
02694
03306
02472
02861
03639
0.05185
0.04683
0.05717
0.05598
0.05373
0.05612
0.05278
0.05350
0.05152
0.04228
0.04945
0.04960
0.05516
0.05800
0.06001
0.05885
0.05940
0.05614
0.05137
0.05849
0.04951
0.05606
0.05710
0.05991
0.05907
0.05234
0.04568
0.05235
0.04988
0.05191
0.05375
0.05646
0.05536
0.05835
0.05561
0.05304
0.05381
0.05130
0.05296
0.04909
0.04934
0.06050
0.06309
0.05747
0.05142
0.05005
0.04922
0.05098
0.05966
0.05984
0.05153
0.05173
0.05581
0.05922
0.05435
47.
1
_3
1
1
1
1
-2
1
_3
_7
-7
-6
-2
0
1
0
1
5
-0
6
-1
-0
1
2
1
0
-4
_3
-4
_4
_3
-1
_1
0
-0
-2
-3
_4
_3
-5
_1
4
6
4
1
_3
-0
0
1
3
1
1
2
3
4
16667
38889
38889
11111
38889
11111
83333
27778
33333
94444
00000
61111
11111
16667
72222
83333
38889
77778
33333
66667
11111
11111
44444
55556
00000
11111
16667
94444
77778
83333
27778
05556
94444
44444
72222
61111
22222
11111
94444
61111
72222
22222
16667
22222
61111
22222
72222
27778
72222
00000
33333
16667
22222
00000
27778
121. 19750101 19951231
2
2
2
4
3
2
2
5
3
2
2
2
1
0
2
0
2
3
2
3
2
2
1
1
1
1
3
1
2
3
2
2
1
1
4
4
3
1
2
2
2
3
5
3
4
2
2
2
1
3
6
3
2
2
2
90580
14582
32464
20223
48695
63757
19052
72218
21873
59286
54816
14582
29643
89409
10111
75998
32464
48695
14582
53166
27993
01170
78818
87759
34114
92230
08461
56466
19052
17402
95050
59286
92230
87759
78339
96220
08461
56466
72698
50345
86109
79989
81159
08461
24693
50345
59286
63757
38584
17402
39275
57636
41405
63757
81639
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
65531
65250
65545
65527
65545
65527
65284
65538
65253
64971
65029
65052
65328
65469
65565
65510
65545
65818
65438
65873
65390
65452
65548
65617
65520
65465
65202
65216
65165
65161
65257
65393
65339
65486
65414
65298
65260
65205
65216
65114
65352
65721
65842
65721
65558
65260
65414
65476
65565
65645
65541
65531
65596
65645
65724
4
3
5
4
5
4
4
4
3
2
2
2
4
5
5
5
5
7
5
5
4
4
5
6
6
4
3
3
3
3
3
4
4
5
4
3
3
3
2
3
3
5
7
5
3
3
3
4
5
6
3
3
4
5
5
62069
87065
06278
89787
77268
85739
23095
50621
47740
80806
74667
82048
41275
54193
29756
34127
89121
05872
04190
04190
05583
97972
61028
23463
18451
54409
17492
61468
38847
40315
53783
64001
23095
14707
28478
16112
49242
56839
69842
16112
55308
40743
31533
79621
98760
70885
92039
19540
12588
46463
72475
25886
64001
27583
21110
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
05000
Figure 4-3. Example Meteorological File.
Section 5 (Input File Information for Meteorological File)
Record 50 (Input File Information for Meteorological File)
Line 1 weather station name
55
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Application of a 1-D Heat Budget Model to the Columbia River System
Line 2 nwpd, elevation of weather station, latitude of weather station, longitude of weather
station, start date of weather station data, end date of weather station data
Record 51 (Weather Data for Each Day)
Line 1 Julian day, net solar radiation, Net atmospheric radiation, dry bulb temperature, wind
speed, factor for Bowen ratio, vapor pressure at given air temperature, photo period
Photo period is not used in this model
4.2 OUTPUT FILES
An output file will be generated for each reach in the model. The number of output files is therefore specified
in Record 10, Line 6. Data in the output file consist of daily average temperature and the standard deviation at
each specified location. The number of sections within a reach to output data is located in Record 20, Line 1.
The location of the output data, in river mile, is indicated in Record 20, Line 2. All output files contain the same
format. An example of an output file is shown in Figure 4-4.
Column 1 of the output file is the decimal date out to three digits. The output from each station is then listed
as three columns with the first column being the segment number, the second column being the standard deviation
of the temperature in Deg C, and the third column being the absolute temperature in Deg C.
56
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Chapter 4: Model Input and Output Files
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
004 3 0 0.007
006
009
012
015
017
020
023
026
028
031
034
037
039
042
045
048
050
053
056
059
061
064
067
069
072
075
078
080
083
086
089
091
094
097
1975.1
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
102
105
108
111
113
116
119
121
124
127
130
132
135
138
141
143
146
149
152
154
157
160
3 5
3 4
3 4
3 3
3 3
3 2
3 2
3
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 2
3 3
3 2
3 2
3 1
3 2
3
3 2
3 1
3 0
3 1
3 1
3 1
3
3
3 1
3 1
3 1
3
3 0
3 0
3 0
3 0
3 0
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3
3 2
3 2
3
3 2
3
6
2
8
4
9
7
2
8
6
5
7
6
5
5
4
9
3
8
5
1
3
1
7
6
2
3
2
1
1
4
3
2
1
9
9
9
9
9
1
4
6
7
6
4
4
5
5
7
4
7
7
2
4
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.031
.028
.028
.031
.084
.083
.028
.069
.125
.147
.166
.028
.182
0.34
.301
.222
0.1
.468
.313
.335
.133
.156
.372
.482
.144
.428
.425
.323
.152
.124
.104
0.28
.372
.229
0.22
.207
.133
.302
.199
.192
.043
.169
.183
.189
.161
.167
.252
.144
0.1
.027
.175
.097
.036
.133
.209
.157
.124
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
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14
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14
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14
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14
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14
14
14
14
14
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14
5
4
4
3
3
2
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
5
1
8
3
8
6
8
7
3
2
7
7
5
5
5
4
2
8
5
1
3
1
7
6
2
3
2
7
7
4
3
2
1
8
7
7
8
7
1
5
7
8
6
4
4
5
5
8
4
7
7
1
5
2
2
5
0.007
0.13
0.092
0.095
0.103
0.132
0.129
0.098
0.113
0.136
0.142
0.096
0.096
0.162
0.23
0.19
0.151
0.112
0.226
0.162
0.182
0.113
0.125
0.222
0.329
0.116
0.24
0.247
0.18
0.128
0.12
0.12
0.188
0.205
0.154
0.16
0.16
0.136
0.199
0.154
0.164
0.105
0.145
0.148
0.157
0.147
0.15
0.216
0.145
0.125
0.099
0.151
0.125
0.105
0.128
0.175
0.152
0.132
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
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24
4
4
3
3
2
2
1
1
1
1
1
1
2
4
2
2
1
2
2
i
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
0
9
3
4
7
3
8
6
7
6
1
1
7
7
5
5
6
1
2
8
5
1
3
2
7
7
2
2
2
5
5
4
3
2
1
8
6
6
8
6
1
5
8
9
7
4
4
5
5
8
3
7
7
2
6
3
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.007
.227
.147
.154
.174
.229
.225
.161
.193
.239
.252
.136
.159
.295
.425
.339
.264
.186
.388
0.27
.309
.184
.205
.386
.576
.188
.417
.446
.319
0.22
.206
.207
0.34
.371
.271
.284
.285
.238
.363
.273
.294
.177
.255
.262
.278
.259
.264
.393
.256
.217
.164
.268
.218
.177
.223
.315
.268
.231
Figure 4-4. Example output file.
57
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Application of a 1-D Heat Budget Model to the Columbia River System
58
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Chapter 5: Study Summary and Conclusions
CHAPTER 5: STUDY SUMMARY AND CONCLUSIONS
The results of the analysis lead to the following conclusions:
• Structural changes in Columbia River downstream from Grand Coulee Dam and in the Snake River
from its confluence with the Grande Ronde River to its confluence with the Columbia River near
Pasco, Washington, cause an increase in mean frequency of water temperature excursions above a
daily average water temperature of 20 °C. The structural changes are a result of the construction and
operation of hydroelectric facilities on the Columbia and Snake rivers in the study area. This
conclusion is based on a comparison of the mean frequency of temperature excursions for the system
as presently configured and for the same system in the unimpounded condition. The unimpounded
condition assumes there are no dams on the Columbia River below Grand Coulee and no dams on the
Snake River below Lewiston, Idaho. The uncertainty in these estimates is approximately of the order
of the estimated differences in the results, however. Improving both the systems and measurements
models could reduce uncertainty. Actions could include improving the quality of water temperature
observations, increasing the spatial coverage of required meteorological data, and studying the
seasonal variations in certain terms of the heat budget, particularly the evaporation rate. The
reduction in uncertainty would not affect the basic result that structural differences in the system due
to the construction and operation of hydroelectric facilities have a greater impact on the temperature
regime than does the thermal input from all of the major tributaries other than the Clearwater River.
• Most advected sources, including tributaries, groundwater and point sources, contribute a relatively
small amount of advected thermal energy to of the main stem Columbia and Snake rivers in the study
area. Their impact on the cross-sectional daily average water temperature is limited. The exceptions
are the impact of the Clearwater River on the cross-sectional daily average water temperature of the
Snake River and that of the Snake River on the cross-sectional daily average water temperature of the
Columbia River.
• The objective of the analysis was to assess the relative impact of dams and tributaries on the
temperature regime of the Columbia and Snake rivers. The impact of upstream inputs was limited to
the characterization of initial temperature conditions at Grand Coulee Dam on the Columbia River
and River Mile 168 on the Snake River. However, upstream inputs have an important role in the
temperature regime of both rivers. In the Columbia River, construction of Canadian impoundments
and the operation of Grand Coulee Dam affect the temperature of the Columbia River at Grand
Coulee Dam, although the frequency of excursions are small at this location. For the Snake River,
initial conditions near Anatone, Washington, are such that the mean frequency of temperature
excursions is approximately 0.15. This is due to structural changes to the natural river upstream from
Anatone, and to the river's exposure to high temperatures as it crosses the Snake River Plain. A
larger geographical scope is needed to assess the impacts of water management in both the Columbia
and Snake rivers.
Topics for Further Study
The results of this assessment lead to the conclusion that the construction and operation of dams on the
Columbia River downstream from Grand Coulee Dam and on the Snake River downstream from Lewiston, Idaho,
have a greater impact on the thermal regime of these rivers than do the thermal inputs form most of the tributaries.
However, in the case of the Snake River, the significance of this conclusion is reduced by uncertainty in the
mathematical model. Use of the model as a decision-making tool would require additional efforts to reduce this
uncertainty. Elements of the model where reduction in uncertainty would be of benefit include the following:
59
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Application of a 1-D Heat Budget Model to the Columbia River System
• Heat budget - The choice of meteorological stations to characterize the energy budget was done
subjectively, to achieve good (in a qualitative sense) agreement between simulated values and
observations. The analysis would benefit from additional studies of the effect of local climatology,
particularly wind speed.
• River hydraulics - Particle displacement speeds and system geometry were based on the assumption
that gradually varied, steady-state flow methods were appropriate. This assumption is reasonable for
the scenarios for which the dams are in place and less so for the river without dams. The
uncertainties associated with rapidly changing flows are likely to be greatest during the spring and
early summer snowmelt periods. It is less likely they will be important during the critical late
summer and early fall periods when flows are low and reasonably steady.
• Initial water temperatures - Initial conditions for water temperature of both main stem and tributaries
were estimated by synthesizing a record with data from various sources. The error introduced as a
result is greatest for the main stem temperatures, since the results of the analysis show that the
tributaries have little impact on the average temperatures of the Columbia and Snake rivers. The error
introduced in the main strem estimates will decrease in the downstream direction.
• Filter - The estimation of the systems model error is based on the assumption the filter is optimal.
The filter is optimal if the innovations sequence is a zero mean, Gaussian white noise process. Tests
for optimality of the filter have been described by Mehra (1970). These tests were not performed on
the water temperature innovations sequence due to the number of missing data points, but a visual
inspection of the 30-day averages of the innovations sequence suggest the results are autocorrelated.
This correction could be a result of structural errors in the model, as described above, or could be
related to observation bias and error reported by McKenzie and Laenen (1998).
• Water temperature data - The water temperature monitoring program on the Columbia and Snake
rivers has produced a large volume of data; however, the quality of the data is sometimes
questionable. The analysis of water temperature issues on the Columbia and Snake rivers would
benefit greatly from a comprehensive plan for measuring water temperatures.
60
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References
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65
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Acknowledgements
This report was prepared as part of the problem assessment for a Total Maximum Daily Load
(TMDL) for water temperature in the Snake and Columbia rivers. The authors acknowledge the
administrative support provided by Mary Lou Soscia, Patricia Cirone, and Richard Parkin of EPA
Region 10. Richard Parkin, Dan Opalski and George Abel of EPA Region 10 provided critical
colleague reviews of the original report as did Stuart McKenzie. The peer reviewers, Scott Wells
of Portland State University and David Wegner of Ecosystem Management International
provided insightful comments that we believe have improved the report.
-------
Appendix A
Summary of Temperature Preference Ranges and Effects for Life Stages of
Seven Species of Salmon and Trout
-------
Appendix A
The information in this appendix was taken from a review of the State of Oregon standard for water temperature
completed by Cara Berman, U.S. Environmental Protection Agency Region 10, on September 3, 1998.
Definitions (from McCullough 1999):
Optimum: The optimum temperature range provides for feeding activity, normal physiological response, and
normal behavior. The optimum range is slightly wider than the growth range.
Preferred: The preferred temperature range is that which the organism most frequently inhabits when allowed to
freely select temperatures in a thermal gradient. The final temperature preferendum is a preference made within
24 hours in a thermal gradient and is independent of acclimation temperature.
Lethal loading: Increased burden on metabolism that controls growth and activity. Lethal loading stress occurs
over long periods (Brett et al. 1958).
Upper incipient lethal temperature: An exposure temperature, given a previous acclimation to a constant
temperature, that 50 % of the fish can tolerate for 7 days. The ultimate upper incipient lethal temperature is
the point where further increases in acclimation temperature results in no increase in temperature tolerated.
Upper lethal temperature: The temperature at which survival of atest group is 50 % in a 10 minute exposure,
given a prior acclimation temperatures within the tolerance zone.
I. Sockeye Salmon
Adult migration:
Spawning:
Incubation:
Rearing:
7.2-15.6°C (Bell 1986, Spence etal. 1996)
10°C adult sockeye lost 7.5 % body weight and had visible fat reserves, at 16.2°C
they lost 12 % of their body weight and visible fat reserves were essentially
depleted. Females with developing eggs lost more body weight than males;
adverse gonadal development in females (Bouck et al. 1975)
21°C migration inhibition (Beschta et al. 1987 from Major and Mighell 1966).
Above 21°C rising or stable temperatures blocked entry offish from the
Columbia River into the Okanagan River, WA; falling temperatures allowed
migration to resume.
10.6-12.2°C (Bell 1986, Spence etal. 1996)
4.4-13.5°C (Combs 1965)
4.4-13.3°C (Bell 1986, Spence etal. 1996)
10°C (Dept of Fisheries Canada, International Pacific Salmon Fisheries
Commission 1952)
> 12.8°C severe mortality (Dept of Fisheries Canada, International Pacific
Salmon Fisheries Commission 1952; Combs 1965)
10-12.8°C(Bell 1986)
10.6°C (Huntsman 1942, Burgner 1991)
10.6-12.8°C (Coutant 1977)
14.5°C (Coutant 1977, Ferguson 1958, Huntsman 1942)
12-14°C (Brett 1952)
11.2-14.6°C preferred (Beschta et al. 1987)
15°C optimum (Beschta et al. 1987)
A-1
-------
Appendix A
Physiological optimum:
Smolt out-migration:
Terminates smolt
out-migration:
15°C (Brett etal. 1958)
2-10°C(Spenceetal. 1996)
12-14°C (Brett etal. 1958)
II. Spring Chinook Salmon:
Adult migration:
Spawning:
Incubation:
Rearing:
Adult holding:
Smoltiflcation and
Out-migration:
Optimum production:
Maximum growth:
Lethal:
Sublethal:
3.3-13.3°C (Bell 1986, Bjornn and Reiser 1991, Spence et al. 1996)
21°C migration block (Temperature Subcommittee, DEQ 1995)
5.6-14.4°C (Olson and Foster 1955)
5.6-13.9°C (Bell 1986, Spence etal. 1996)
5.6-12.8°C (Temperature Subcommittee, DEQ 1995)
5-14.4°C (Bell 1986, Spence et al. 1996)
4.5-12.8°C (Temperature Subcommittee, DEQ 1995)
11.7°C (Coutant 1977, Ferguson 1958, Huntsman 1942)
10-12.8°C(Bell 1986)
10-14.8°C (Temperature Subcommittee, DEQ 1995)
8-12.5°C (Temperature Subcommittee, DEQ 1995)
13-15.5°C pronounced mortality (Temperature Subcommittee, DEQ 1995)
6-14°C optimal pre-spawning brood stock survival, maturation, and spawning
(Marine 1992)
3.3-12.2°C (Temperature Subcommittee, DEQ 1995)
18.3°C smolt lethal loading stress (Temperature Subcommittee, DEQ 1995)
10°C (Temperature Subcommittee, DEQ 1995)
14.8°C (Temperature Subcommittee, DEQ 1995)
18-21°C (Marine 1992)
17.5°C - upper sub-lethal to lethal range (Berman 1990)
15-17°C (Marine 1992, Berman 1990)
Summer Chinook Salmon:
Adult Migration:
Spawning:
Incubation:
13.9-20°C (Bell 1986, Spence et al 1996)
5.6-14.4°C (Olson and Foster 1955)
6.1-18.0°C (Olson and Foster 1955)
5.6-13.9°C (Spence et al. 1996)
5.0-14.4°C (Spence et al. 1996)
A-2
-------
Appendix A
Rearing: 11.7°C (Coutant 1977; Ferguson 1958; Huntsman 1942)
10.0-12.8°C (Bell 1986)
IV. Fall Chinook Salmon:
Adult migration: 10.6-19.4°C (Bell 1986, Spence et al. 1996)
Spawning: 10-12.8°C (Bell 1986)
10-16.7°C (Olson and Foster 1955)
5.6-13.9°C (Spence etal. 1996)
Incubation: 10-12.8°C (Bell 1986)
10-16.7°C (Olson and Foster 1955)
10-12°C (Heming 1982, Neitzel and Becker 1985, Garling and Masterson 1985)
5-14.4°C (Spence etal. 1996)
> 12°C alevins substantial reduction in survival (Ringler and Hall 1975)
> 15.6°C mortality (Smith et al.1983)
Rearing: 12-14°C (Bell 1986)
Smoltification: 4.5-15.5°C typical migration (Spence et al. 1996)
ATPase Activity - 8°C and 13°C allow increased activity over a 6 week period, at
18°C ATPase activity decreases over the same time period - inhibitory effect of
water temperature on gill Na-K ATPase activity (Sauter unpublished data)
V. Chinook Salmon (general): Final Temperature Preferendum
Adult: 17.3°C (Coutant 1977)
Yearling: 11.7°C (Ferguson 1958, Huntsman 1942)
Spawning: 5.6-13.9°C (Bjornn and Reiser, 1991)
5.6-10.6°C(Bell 1986)
5.6-12.8°C (Temperature Subcommittee, DEQ 1995)
15.5°C causes spawning inhibition
Incubation: 5-14.4°C (Bjornn and Reiser 1991)
13°C (Bell 1986)
> 12.5°C increases egg mortality and inhibits alevin development - produces only
50 % egg survival (California Department Water Resources 1988)
Rearing: 10-15.6°C maximum productivity (Brett 1952)
12-14°C preferred range (Brett 1952)
7.3°C-14.6°C preferred range (Beschta et al. 1987)
12.2°C optimum (Beschta et al. 1987)
> 12.8°C first feeding fry do not develop normally
> 15.5°C disease increases mortality (Temperature Subcommittee, DEQ 1995)
Smoltification: < 12.2°C for all salmonids (California Department Water Resources 1988)
18-21°C sub-lethal and lethal loading stress (Brett 1952)
A-3
-------
Appendix A
Independent Scientific Group (1996): Chinook salmon and other salmon species are not markedly different in
their requirements.
Adult migration and spawning: optimum 10°C, with range about 8 to 13°C; stressful >15.6°C; lethal 21°C
Incubation: optimum <10°C with range about 8 to 12°C; stressful >13.3°C; lethal >15.6°C
Juvenile rearing: optimum 15°C with range about 12 to 17°C; stressful >18.3°C; lethal 25°C
National Marine Fisheries Service (1996):
Chinook habitat assessment: 10 to!3.9°C for properly functioning; 14 to!5.5°C at risk for spawning; and 14
to!7.5°C at risk for rearing and migration.
VI. Steel head Trout:
Adult migration:
Upper incipient
lethal temperature:
Spawning:
10-13°C general preferred (Bjornn and Reiser 1991)
21°C migration inhibition (Beschta et al. 1987)
21-22°C(Hicks 1998)
3.9-9.4° C (Bell 1986, Spence et al. 1996)
4.4-12.8°C (Swift 1976)
Rainbow trout brood fish must be held at water temperatures below 13.3°C and
preferably not above 12.2°C for a period of 2 to 6 months before spawning to
produce eggs of good quality (Smith et al. 1983)
Incubation: 5.6-11.1°C (Hicks 1998)
Preferred Temperatures Rearing:
summer run 10-12.8°C (Bell 1986)
10-12.8°C(Bell 1986)
10-14.4°C (Bell 1986)
winter run
fall run
spring run
Smoltiftcation:
VII. Coho Salmon:
Adult migration:
Spawning:
10-12.8°C(Bell 1986)
7.3-14.6°C preferred (Beschta et al. 1987)
10°C optimum (Beschta et al. 1987)
11-12.2°C from 7.2°C resulted in cessation of downstream movement (Hicks
1998)
<12°C (Hicks 1998)
7.2-15.6°C (Reiser and Bjornn 1979, Brett 1952)
4.4_9.4°C (Reiser and Bjornn 1979, Brett 1952)
A-4
-------
Appendix A
Incubation:
Incubation (cont.):
Lower lethal:
Upper lethal:
Rearing:
Smoltiftcation:
Optimum Cruising
Speed:
10-12.8°C(Bell 1986)
7.2-12.8°C (Hicks 1998)
4.4-13.3°C (Reiser and Bjornn 1979, Brett 1952)
10-12.8°C(Bell 1986)
8-9°C (Sakh 1984)
4-6.5°C(Dong 1981)
Egg mortality approx. 14°C (Reiser and Bjornn 1979, Brett 1952)
>12°C increased mortality (Allen 1957 in Murray and McPhail 1988)
>11°C increased mortality (Murray and McPhail 1988)
1.3-10.9°C produced best survival rates of eggs and alevins (Tang et al. 1987)
2-8°C optimum range (Tang et al. 1987)
0.6-1.3°C (Dong 1981)
12.5-14.5°C (Dong 1981), University of Washington
10.9-12.5°C (Dong 1981), Dungeness River, WA
11.8-14.6°C (Reiser and Bjornn 1979, Brett 1952)
11.4°C(Coutantl977)
12-14°C (Bell 1986)
Cessation of growth >20.3°C (Temperature Subcommittee, DEQ 1995, Reiser
and Bjornn 1979, Brett 1952)
11.8-14.6°C, preferred (Beschta et al. 1987)
25.8°C, upper lethal (Beschta et al. 1987)
12-15.5°C (Brett etal. 1958)
2.5-13.3°C observed migration, most fish migrate before temperatures reach 11-
12°C (Spence et al. 1996)
20°C Under yearling and yearling approach velocities above dams exceeding 1.0
foot/second creates a problem in safeguarding under yearlings. Capacity to stem
such a current for greater than one hour is limited to 18.5-21.5°C (Brett etal.
1958)
Final Temperature Preferendum:
Adult:
Upper lethal:
Preferred
temperature:
VIII. Chum salmon:
11.4°C (Coutant 1977) Laboratory
16.6°C (Coutant 1977) L. Michigan
26°C, incipient lethal temperature (Brett 1952)
Acclimation was 20°C, 50 % mortality in 1,000 min.
25°C (Temperature Subcommittee, DEQ 1995)
12-14°C, temperatures >15°C were avoided (Brett 1952)
Adult migration:
8.3-15.6°C (Bjornn and Reiser 1991)
A-5
-------
Appendix A
Spawning:
Incubation:
Rearing:
7.2-12.8°C (Bjornn and Reiser 1991)
8°C (Beacham and Murray 1985)
4.4-13.3°C (Bjornn and Reiser 1991)
6-10°C, maximum efficiency for conversion of yolk to tissue (Beacham and
Murray 1985)
12°C, alevin mortality occurred 1-3 days after hatch (Beacham and Murray 1985)
14.1°C (Coutant 1977, Ferguson 1958, Huntsman 1942)
10-12.8°C(Bell 1986)
11.2-14.6°C, preferred (Beschta et al. 1987)
12-14°C, preferred (Brett 1952)
13.5°C, optimum (Beschta et al. 1987)
25.8°C, upper lethal (Beschta et al. 1987)
Final temperature preferendum:
Under yearling: 14.1°C (Coutant 1977) Laboratory
Yearling:
Smoltiflcation:
Upper lethal:
IX. Cutthroat trout:
Adult migration.
Adult Holding:
Spawning:
Incubation:
Rearing:
Smoltiflcation:
X. Bull trout:
Migration:
14.1°C (Ferguson 1958) Laboratory
14.1°C (Huntsman 1942) Laboratory
Information not available
25.4°C, incipient lethal temperature (Brett 1952)
Acclimation was 20°C, 50 % mortality in 1,000 min.
Information not available
18-22.8°C upper lethal temperature range (Kruzic 1998)
Smith et al. (1983), west-slope cutthroat trout: Females held in fluctuating
temperatures (2-10°C) had significantly better eggs than those held at a constant
10°C. Elevated temperatures experienced by mature females affected subsequent
viability and survival of embryos.
6.1-17.2°C (Beschta etal. 1987, Bell 1986)
Information not available
10°C (Bell 1986)
9.5-12.9°C, preferred (Beschta et al. 1987)
23°C, upper lethal (Beschta et al. 1987)
22.8°C, upper lethal (Bell 1986)
Information not available
10-12°C (EPA 1997, DEQ 1995)
A-6
-------
Appendix A
Spawning:
Incubation:
Rearing:
Adult resident:
Competition:
<9-10°C, initiate spawning, MT (Temperature Subcommittee, DEQ 1995)
<9°C, initiate spawning, B.C. (Spence et al. 1996, Temperature Subcommittee,
DEQ 1995, Pratt 1992)
4.5°C, Metolius River, Oregon (Spence et al. 1996, Temperature Subcommittee,
DEQ 1995)
4-10°C (Temperature Subcommittee, DEQ 1995)
5-6.5°C, peak spawning activities (EPA 1997)
8-10°C, 0-20 % survived to hatch, B.C. (Temperature Subcommittee, DEQ 1995)
6°C, 60-90 % survived to hatch, B.C. (Temperature Subcommittee, DEQ 1995)
2-4°C, 80-95 % survived to hatch, B.C. (Temperature Subcommittee, DEQ 1995)
4-6°C, MT (Temperature Subcommittee, DEQ 1995)
1-6°C (Temperature Subcommittee, DEQ 1995)
2-6°C (Spence et al. 1996)
4°C optimal temperature for growth, B.C. (Temperature Subcommittee, DEQ
1995)
4.5°C, Metolius River, Oregon (Temperature Subcommittee, DEQ 1995)
4-4.5°C, optimum fry growth (Temperature Subcommittee, DEQ 1995)
4-10°C, optimum juvenile growth (Temperature Subcommittee, DEQ 1995)
<10°C, Metolius River (EPA 1997)
>14°C is a thermal barrier in closely related arctic char (Pratt 1992)
19°C, no bull trout were observed, MT (Temperature Subcommittee, DEQ 1995)
15-18°C, bull trout were present, MT (Temperature Subcommittee, DEQ 1995)
<16°C, bull trout present, John Day Basin, OR (Temperature Subcommittee,
DEQ 1995)
<12°C, highest densities of bull trout, MT (Temperature Subcommittee, DEQ
1995)
9-13°C, adult preference (Temperature Subcommittee, DEQ 1995)
Less than or equal to 12°C, highest adult density (Temperature Subcommittee,
DEQ 1995)
4-18°C, adults present (Temperature Subcommittee, DEQ 1995)
<15°C vertical distribution in lakes (Pratt 1992)
12°C, Metolius River, reach susceptible to brook trout invasion (EPA 1997)
A-7
-------
Appendix A
Appendix A References
Bell, M. 1986. Fisheries Handbook. Chapter 11.
Beacham, T.D. and C.B. Murray. 1985. Effect of female size, egg size, and water temperature on developmental
biology of chum salmon (Oncorhynchus keta) from the Nitinat River, British Columbia. Can. J. Fish. Aquat.
Sci. 42:1755-1765.
Berman, C.H. 1990. Effect of elevated holding temperatures on adult spring chinook salmon reproductive
success. MS Thesis. University of Washington, Seattle.
Beschta, R.L., R.E. Bilby, G.W. Brown, L.B. Holtby, T.D. Hofstra. 1987. Stream Temperature and aquatic
habitat: fisheries and forestry interactions, pp. 191-232. In E.O. Salo and T.W. Cundy (editors) Streamside
Management: Forestry and Fishery Interactions, Institute of Forest Resources, University of Washington.
Contribution No. 57.
Bjornn, T.C. and D.W. Reiser. 1991. Habitat requirements of salmonids in streams. In: Influences of Forest and
Rangeland Management on Salmonid Fishes and Their Habitats. American Fisheries Society Spec. Pub.
19:83-138.
Bouck, G.R., G.A. Chapman, P.W. Schneider, and D.G. Stevens. 1975. Effects of holding temperatures on
reproductive development in adult sockeye salmon (Oncorhynchus nerkd). In: 26th Annual Northwest Fish
Culture Conference. Editor J.R. Donaldson, pp.24-40.
Brett, J.R. 1952. Temperature tolerance in young Pacific salmon, Genus Oncorhynchus. J. Fish. Res. Bd. Can.
9:265-323.
Brett, J. R., M. Hollands, and D.F. Alderdice. 1958. The effect of temperature on the cruising speed of young
sockeye and coho salmon. J. Fish. Res. Bd. Can. 32: 485-491.
Burgner, R.L. 1991. Life history of sockeye salmon, pp 3-117. In C. Groot and L. Margolis (editors) Pacific
Salmon Life Histories.
California Department of Water Resources. 1988. Water temperature effects on chinook salmon (Oncorhynchus
tshawytschd) with emphasis on the Sacramento River: A literature review. Northern District Office Report.
Red Bluff, CA 42 pp.
Combs, B. D. 1965. Effect of temperature on the development of salmon eggs. Prog. Fish-Cult. 27: 134-137.
Coutant, C.C. 1977. Compilation of temperature preference data. J. Fish. Res. Bd. Can. 34:739-745.
Coutant, C.C. 1999. Perspectives on temperature in the Pacific North west's fresh waters. Oak Ridge National
Laboratory, Environ. Sci. div. Pub. No. 4849 108 pp.
Department of Fisheries of Canada and the International Pacific Salmon Fisheries Commission. 1952. Report on
the fisheries problem created by the development of power in the Nechako-Kemano-Nanika river systems,
Supplement #1, Temperature changes in the Nechako River and their effects on the salmon population. 42 pp.
Dong, J.N. 1981. Thermal tolerance and rate of development of coho salmon embryos. Master's thesis.
University of Washington.
A-8
-------
Appendix A
EPA. 1997. Administrative record, water quality standards for Idaho; final rule (see specific temperature criteria
for bull trout in Idaho Streams: technical basis, notes, and issues). 40 CFR Part 131, July 31, 1997.
Ferguson, R.G. 1958. The preferred temperature of fish and their midsummer distribution in temperate lakes and
streams. J. Fish. Res. Bd. Can. 15:607-624.
Garling, D.L. and M. Masterson. 1985. Survival of Lake Michigan chinook salmon eggs and fry incubated at
three temperatures. Prog. Fish-Cult. 47:63-66.
Heming, T. A. 1982. Effects of temperature on utilization of yolk by chinook salmon (Oncorhynchus
tshawytschd) eggs and alevins. Can. J. Fish. Aquat. Sci. 39:184-190.
Hicks, M. 1998. Preliminary review draft discussion paper: Supplementary appendix: Evaluating standards for
protecting aquatic life in Washington's surface water quality standards. Washington Department of Ecology,
Water Quality Program.
Huntsman, A.G. 1942. Death of salmon and trout with high temperatures. J. Fish. Res. Bd. Can. 5:485-501.
Independent Scientific Group. 1996. Return to the river: restoration of salmonid fishes in the Columbia River
ecosystem.
Kruzic, L.M. 1998. Ecology of juvenile coho salmon within the upper South Umpqua River basin, Oregon. MS
Thesis. University of Idaho.
Major, R.L. and J.L. Mighell. 1966. Influence of Rocky Reach Dam and the temperature of the Okanogan River
on the upstream migration of sockeye salmon. U.S. Fish and Wildlife Service Fishery Bulletin 66: 131-147.
Marine, K. R. 1992. A background investigation and review of the effects of elevated water temperature on
reproductive performance of adult chinook salmon. Department of Wildlife and Fisheries Biology,
University of California, Davis.
McCullough, D.A. 1999. A review and synthesis of effects of alterations to the water temperature regime on
freshwater life stages of salmonids, with special reference to chinook salmon. Prepare for U.S. EPA Region
10, Seattle, WA 279 pp.
Murray, C.B. and J.D. McPhail. 1988. Effect of incubation temperature on the development of five species of
Pacific salmon (Oncorhynchus) embryos and alevins. Can. J. Zool. 66:266-273.
National Marine Fisheries Service. 1996. Making ESA determinations of effect for individual or grouped actions
at the watershed scale. NW Regional Office, Portland, OR.
Neitzel, D.A. and C.D. Becker. 1985. Tolerance of eggs, embryos, and alevins of chinook salmon to temperature
changes and reduced humidity in dewatered redds. Trans. Am. Fish. Soc. 114:267-273.
Olson, P.A. and R.F. Foster. 1955. Temperature tolerance of eggs and young of Columbia River chinook
salmon. Trans. Am. Fish. Soc. 85:203-207.
Pratt, K.L. 1992. A review of bull trout life history. Proceedings of the Gearhart Mountain Bull Trout Workshop,
Oregon Chapter of the American Fisheries Society.
Reiser, D.W. and T.C. Bjornn. 1979. Habitat requirements of anadromous salmonids. Gen. Tech. Rep. PNW-96.
USDA Forest Service, Pacific NW Forest and Range Exper. Station. Portland, OR 54 pp.
A-9
-------
Appendix A
Ringler, N.H. and J.D. Hall. 1975. Effects of logging on water temperature and dissolved oxygen in spawning
beds. Trans. Am. Fish. Soc. 104:111-121.
Sakh. 1984. Egg incubation in coho salmon as a function of water temperature. Rybn. Khoz. 10:21-22.
Sauter, S. Unpublished data. Columbia River Research Laboratory, Biological Resources Division, USGS.
Smith, C.E, W.P. Dwyer, and R.G. Piper. 1983. Effect of water temperature on egg quality of cutthroat trout.
Prog. Fish Cult. 45:176-178.
Spence, B.C, G.A. Lomnicky, R.M. Hughes, R.P. Novitzki. 1996. An ecosystem approach to salmonid
conservation. TR-4501-96-6057. ManTech Environmental Research Services Corp., Corvallis, OR.
Swift, C.H. III. 1976. Estimation of stream discharges preferred by steelhead trout for spawning and rearing in
western Washington. 50 pp.
Tang, J., M.D. Bryant, and E.L. Brannon. 1987. Effect of temperature extremes on the mortality and
development rates of coho salmon embryos and alevins. Prog. Fish Cult. 49:167-174.
Temperature Subcommittee, Technical Advisory and Policy Advisory Committees. 1995. Temperature 1992-
1994 Water Quality Standard Review, Final Issue Paper. Oregon Department of Environmental Quality.
A-10
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Appendix B
Source Code Tests
-------
Appendix B
The source code for the numerical solution to Equation (2), incorporating reverse particle tracking, was tested
against a number of benchmark cases for which the solution was exactly known. In addition, the simulations for
these benchmark cases using reverse particle tracking were compared with simulations using the numerical
schemes from two widely-applied water quality modeling packages, Water Quality for River-Reservoir Systems
(WQRRS) (Smith, 1978) and QUAL2E (Brown and Barnwell, 1987).
NUMERICAL METHODS
Reverse Particle Tracking
Reverse particle tracking, the numerical method used in this study, is a mixed Eulerian-Lagrangian scheme.
As described by Zhang et al (1993), the state variable is simulated in the advection step by sending a fictitious
particle from each node, j (Figure 5), backward to the point,
tk=i
x;=Xi- fu*dt (B.1)
rjV
where,
u* = velocity encountered by the particle while moving fromx'jto Xj.
WQRRS
The numerical method used in WQRRS is a finite difference Eulerian scheme that begins with the mass
balance equation for a state variable, T, stated in matrix form as
[V]{TJ=[S]{T}+{P} (B.2)
where,
[V] = matrix with element volumes on the diagonal and zeroes elsewhere,
vector of the rates of change of T in each element,
[S] = Matrix of coefficients multiplies the state variable, T,
{T} = Vector of the state variable in each segment,
[P] = Vector of constant terms for each segment.
B-1
-------
Appendix B
Equation (B.2) is solved numerically by assuming
Tt+At = Tt+f (Tt+Tt+At) (B.3)
This leads to the following solution
where,
At
[s*] = M - f [s]
{>*} = [S]{B}+{P}
B = Tt + fit
QUAL2E
QUAL2E (Brown and Barnwell, 1987) uses an upstream, implicit method to solve the finite difference
equation for a state variable, T
Tk+1-Tk QjTk+1-Qj_1Tk;1
J L = ._!_J J J-1 +riTk+1 +P: (B.5)
At Vj J J J ^ '
where,
QJ = flow out of the jth element,
Vj = volume of the jth element,
PJ = first order rate constant,
PJ = internal sources in the jth element.
Equation (B.5) does not include a term for longitudinal dispersion, as does the more general form of the
equation found in the QUAL2E documentation (Brown and Barnwell, 1987).
TEST CASES
Test Case A
Test Case A is based on an idealized river system 100 miles long divided into 100 equal segments. The
longitudinal speed of the water is one mile/day. The boundary condition at x=0 for the state variable, T, is kept
constant at 20 units and decays according to a first-order loss rate, K = 0.20. In a Lagrangian frame of reference,
B-2
-------
Appendix B
= -KT
dt
and in an Eulerian frame of reference
(B.6)
where,
+U = -KT
at dx
U = (constant) longitudinal speed of the water.
(B.7)
The solutions to Test Case A, obtained with reverse particle tracking, WQRRS and QUAL2E are shown in
Figure B-l.
.,
1
o 10
0 •
\
\
%.
~iiffl&fittof&l&nto*IX»ZK*z»I*.+*+**.***.*^***x**-.~l~.~tt:
0 5 10 15 20 25 30 35 40 45 5
Time - Days
—A- RBKH10
- ••- QUAL2E
— • — WQRRS
^^Exact
>
0
Figure B-1. Steady state flow and boundary condition - First order decay
Test Case B
The geometry and hydrology for this case are the same as for Test Case A above. The boundary for the state
variable, T, is varied according to
T(x = 0) = 10 + 10sin(2jit/P0)
where,
PO = 10,20,50, 100 days
The results from the various numerical schemes are shown in Figures B-2 - B-5.
B-3
-------
Appendix B
70
90 110
Time - Days
130
150
Figure B-2. Harmonic boundary condition with period = 10 days
70
90 110 130
Time - Days
150
Figure B-3. Harmonic boundary condition with period = 20 days
8-4
-------
Appendix B
70
90 110
Time - Days
130
150
Figure B-4. Harmonic boundary condition with period = 50 days
70
90 110
Time - Days
130
150
Figure B-5. Harmonic boundary condition with period = 100 days
8-5
-------
Appendix B
Test Case C
Test Case C uses the same geometry and hydrology as the previous two test cases. The boundary condition at
X = 0 is defined as
T(t,x=0) = 20 u.,(t)
Where,
u_i(t) = the generalized function such that
Results of simulations are shown in Figure B-6.
T(t,x=0)= 0 fort<0,
T(t,x=0)= 1 fort>0.
70
90 110
Time - Days
130
150
Figure B-6. Step function boundary condition
Test Case D
Test Case D is similar in all respects to Test Case B, with the exception that the segments used to describe the
system are unequal and the periods associated with the harmonic functions describing the boundary conditions are
Po = 5, 10, 20, 50 days.
Segment 1 (the most upstream segment) is 0.5 miles in length, Segment 2 is 1.0 miles in length, Segment 3 is 1.5
miles in length, Segment 4 is 0.5 miles in length, Segment 5 is 1.0 miles in length, Segment 7 is 1.5 miles in
length, the pattern repeating in this way for the entire length of the idealized system. The simulation results for
this case are shown in Figures B-7 - B-10.
B-6
-------
Appendix B
Time - Days
Figure B-7. Harmonic boundary condition with period = 5 days and unequal segment volumes
Time - Days
Figure B-8. Harmonic boundary condition with period = 10 days and unequal segment volumes
B-7
-------
Appendix B
Time - Days
Figure B-9. Harmonic boundary condition with period = 20 days and unequal segment volumes
Time - Days
Figure B-10. Harmonic boundary condition with period = 50 days and unequal segment volumes
8-8
-------
Appendix B
Test Case E
Test Case E is developed from solutions to the linearized form of the thermal energy budget equation
(Edinger et al, 1974). In Lagrangian form,
= K(Tequil-T) (B.8)
And in Eulerian form,
9T
dt ' dx
!L. +U^- = K(Tequil-T) (B.9)
where,
K = a first-order rate constant which is a function of meteorological parameters and water depth,
Tgquii = water temperature at which there is no heat transfer across the the air-water interface,
= TA sin (2 n t/ PA) + Tavg.
The Laplace transform gives the following solution
T(t) = T0 (t) + KTA [COS,((D(t'T)) (co e'KT - co cos (cor) + K sin (cor))
co +K^
Sin (C0(t- T)
oo2+K2
+ —, .., (-K e'KT + K cos (cor) + cosin(coi)] + Tavg (1-e'KT) (B.10)
where,
TO = boundary condition at x = 0
= AT0sin (2nt/P0) + T0avg,
co = 2H/PA,
T = x/U.
Simulations were done for specific cases in which
AT0 = 10,
Toavg = 10,
TA = 10,
Tavg = 15,
PA = 360,
P0 = 5, 10,20,50,
B-9
-------
Appendix B
x/U = 5.
The results are shown in Figures B-l 1 - B-14.
70
90 110
Time - Days
130
150
Figure B-11a. Harmonic boundary condition with period = 5 days and equal segment volumes. RBM10
compared to exact solution
70
90 110
Time - Days
130
150
Figure B-11b. Harmonic boundary condition with period = 5 days and equal segment volumes. QUAL2E
compared to exact solution
B-10
-------
Appendix B
70
90 110
Time - Days
130
150
Figure B-11c. Harmonic boundary condition with period = 5 days and equal segment volumes. WQRRS
compared to exact solution
-<--RBM10
Exact
70
90 110
Time - Days
130
150
Figure B-12a. Harmonic boundary condition with period = 10 days and equal segment volumes. RBM10
compared to exact solution
B-11
-------
Appendix B
70
90 110
Time - Days
130
150
Figure B-12b. Harmonic boundary condition with period = 10 days and equal segment volumes. QUAL2E
compared to exact solution
70
90 110
Time - Days
130
150
Figure B-12c. Harmonic boundary condition with period = 10 days and equal segment volumes. WQRRS
compared to exact solution
B-12
-------
Appendix B
70
90 110
Time - Days
130
150
Figure B-13a. Harmonic boundary condition with period = 20 days and equal segment volumes. RBM10
compared to exact solution
70
90 110
Time - Days
130
150
Figure B-13b. Harmonic boundary condition with period = 20 days and equal segment volumes. QUAL2E
compared to exact solution
B-13
-------
Appendix B
70
90 110
Time - Days
130
150
Figure B-13c. Harmonic boundary condition with period = 20 days and equal segment volumes. WQRRS
compared to exact solution
70
90 110
Time - Days
130
150
Figure B-14a. Harmonic boundary condition with period = 50 days and equal segment volumes. RBM10
compared to exact solution
B-14
-------
Appendix B
70
90 110
Time - Days
130
150
Figure B-14b. Harmonic boundary condition with period = 50 days and equal segment volumes. QUAL2E
compared to exact solution
25
20
o 15
ra
.fc
o 10
O
50
70
90 110
Time - Days
130
150
Figure B-14c. Harmonic boundary condition with period = 50 days and equal segment volumes. WQRRS
compared to exact solution
B-15
-------
Appendix B
DISCUSSION
For the Test Case A, the steady-state problem with a first-order decay constant, K (Figure B. 1), all three
methods differ slightly from the exact solution. This error is a function of the ratio of the integration time step to
the time constant (1/K). Reducing this ratio will also reduce the errors in all simulations.
Test Cases B - E provide indications of model performance in propagating high frequencies when advection
is important. The reverse particle tracking method gives nearly exact solutions when the Courant number, U
Ax/At, is equal to one (Test Cases, B, C, and E). For the case when the Courant number is not always equal to one
(Test Case D), reverse particle begins to show the effects of numerical dispersion when the period, P0 = 10 or
lower.
Numerical dispersion is evident in simulations using WQRRS and QUAL2E for all test conditions including
those where the Courant number is equal to one. In Test Cases B, C and D, the effects of numerical dispersion on
amplitudes are severe when the period, P0 = 20 or lower. WQRRS has somewhat better high-frequency response
than QUAL2E, however. Both amplitude and phase of QUAL2E and WQRRS simulations are affected in Test
Case E.
B-16
-------
Appendix C
GEOMETRIC AND HYDRAULIC PROPERTIES OF THE COLUMBIA AND
SNAKE RIVERS FOR EXISTING CONDITIONS AND FOR UNIMPOUNDED
CONDITIONS
-------
Appendix C
Table C-1. Surface elevation, volume and surface area of run-of-the-river reservoir segments in the Snake
River from Lewiston, Idaho to Ice Harbor Dam.
Beginning River Mile
140.0
137.3
134.6
131.9
129.2
126.5
123.8
121.1
118.4
116.3
114.3
112.3
110.1
107.9
104.5
101.0
97.6
94.1
90.7
87.4
84.0
81.5
78.9
76.6
74.2
70.8
67.5
64.2
60.9
57.6
54.2
50.7
47.1
44.6
42.0
38.3
34.7
31.0
27.4
23.7
21.1
18.5
16.0
13.9
11.8
Ending River Mile
137.3
134.6
131.9
129.2
126.5
123.8
121.1
118.4
116.3
114.3
112.3
110.1
107.9
104.5
101.0
97.6
94.1
90.7
87.4
84.0
81.5
78.9
76.6
74.2
70.8
67.5
64.2
60.9
57.6
54.2
50.7
47.1
44.6
42.0
38.3
34.7
31.0
27.4
23.7
21.1
18.5
16.0
13.9
11.8
9.7
Elevation
(feet abv MSL)
746
746
746
746
746
746
746
746
746
746
746
746
746
646
646
646
646
646
646
646
646
646
646
646
646
548
548
548
548
548
548
548
548
548
446
446
446
446
446
446
446
446
446
446
446
Volume
(acre-feet)
20825.0
20825.0
20825.0
20825.0
20825.0
35044.0
35044.0
35044.0
38586.0
38586.0
38586.0
57027.0
57027.0
20883.2
20883.2
20883.2
20883.2
20883.2
50635.0
50635.0
56622.0
56622.0
55658.0
55658.0
75002.0
25614.6
25614.6
25614.6
25614.6
25614.6
51914.0
53397.0
57812.0
60125.0
25571.6
25571.6
25571.6
25571.6
25571.6
44783.3
44783.3
44783.3
40202.7
40202.7
40202.7
Area
(acres)
597
597
597
597
597
558
558
558
524
524
524
718
718
580
580
580
580
580
905
905
814
814
727
728
956
518
518
518
518
518
717
738
735
764
752
752
752
752
752
772
772
772
574
574
574
C-1
-------
Appendix C
Table C-2. Surface elevation, volume and surface area of run-of-the-river reservoir segments on the
Columbia River between Grand Coulee Dam and Bonneville Dam
Beginning River Mile
590.0
584.9
579.9
574.8
569.8
564.7
559.7
554.8
549.9
545.1
539.2
533.3
527.4
521.5
515.6
505.1
494.7
484.3
480.8
477.3
473.7
466.9
460.1
453.4
424.2
415.8
324.0
314.4
301.1
292.0
273.3
265.0
256.6
249.1
243.7
236.3
229.1
222.3
215.6
191.5
165.7
Ending River Mile
584.9
579.9
574.8
569.8
564.7
559.7
554.8
549.9
545.1
539.2
533.3
527.4
521.5
515.6
505.1
494.7
484.3
480.8
477.3
473.7
466.9
460.1
453.4
424.2
415.8
397.1
314.4
301.1
292.0
273.3
265.0
256.6
249.1
243.7
236.3
229.1
222.3
215.6
191.5
165.7
145.5
Elevation
(feet abv MSL)
978
978
978
978
978
978
978
978
978
803
803
803
803
803
719
719
719
719
719
719
619
619
619
580
580
491
357
357
357
276
276
276
276
276
276
276
276
276
182
82
82
Volume
(acre-feet)
46717.0
46717.0
46717.0
46717.0
46717.0
46717.0
91643.0
91643.0
91643.0
33809.6
33809.6
33809.6
33809.6
33809.6
52658.0
52658.0
52658.0
52604.0
52604.0
52604.0
42688.0
42688.0
42688.0
173964.0
157110.0
184014.0
217147.0
209010.0
250113.0
206635.0
227752.0
235460.0
214530.0
213204.0
241671.0
292632.0
295188.0
286356.0
299532.0
284148.0
285538.0
Area
(acres)
734
734
734
734
734
734
459
459
459
1571
1571
1571
1571
1571
1731
1731
1731
1092
1092
1092
997
997
997
7728
5094
7014
9724
5176
4323
8712
9325
5771
4184
3533
3348
3711
4068
3175
8567
8387
9072
C-2
-------
Appendix C
Table C-3. Surface elevation and parameters for equations 14 and 15 describing the hydraulics of the
Hanford Reach of the Columbia River.
Beginning River
Mile
397.1
392.4
386.7
382.1
377.4
371.6
364.4
358.3
353.6
346.3
339.5
333.6
329.4
Ending River
Mile
392.4
386.7
382.1
377.4
371.6
364.4
358.3
353.6
346.3
339.5
333.6
329.4
324.0
Elevation
(feet abv MSL)
450
450
450
450
450
450
450
450
450
450
450
450
450
Aa
16.0994
10.4826
5.1545
35.6628
21.0634
29.5736
16.1049
14.0921
41.4013
1.4800
60.2303
26.2448
94.4921
Ba
0.6010
0.6491
0.6966
0.5364
0.6032
0.5646
0.6030
0.6336
0.5346
0.8018
0.5596
0.6340
0.5597
\
99.5337
46.1598
10.8665
798.8506
292.7820
374.7002
91.6599
82.1749
940.1158
1.0554
664.3698
129.2020
1585.1760
Bw
0.2170
0.2990
0.3940
0.0730
0.1990
0.1290
0.2060
0.2670
0.0690
0.6050
0.1190
0.2680
0.1190
C-3
-------
Appendix C
Table C-4. Surface elevation and parameters for equations 14 and 15 describing the hydraulics of the
Snake River with dams removed
Beginning
River Mile
139.3
135.1
130.0
124.9
120.5
114.9
111.2
105.0
100.0
95.0
90.0
85.0
80.0
75.0
70.0
65.0
64.1
60.0
55.0
50.0
45.2
39.6
34.7
29.7
24.9
20.5
15.0
10.1
5.1
Ending
River Mile
135.1
130.0
124.9
120.5
114.9
111.2
105.0
100.0
95.0
90.0
85.0
80.0
75.0
70.0
65.0
64.1
60.0
55.0
50.0
45.2
39.6
34.7
29.7
24.9
20.5
15.0
10.1
5.1
0.0
Elevation
(feet abv MSL)
727
714
700
683
675
657
650
634
616
604
591
578
564
550
536
519
519
497
484
470
456
440
426
413
401
389
371
356
344
Aa
1.3734
0.2497
4.5948
13.1143
65.4102
0.4202
86.6362
3.6130
0.4122
33.1126
11.5359
15.8938
2.8035
0.0371
34.9564
13.6486
13.6486
2.8014
12.9094
5.7302
11.7427
0.8356
12.8951
10.0577
99.3539
1336.7927
7.3970
14.7118
3.1882
Ba
0.8395
0.9333
0.6862
0.6076
0.4679
0.8997
0.4700
0.7320
0.8931
0.5367
0.6274
0.6009
0.7458
1.0999
0.5409
0.6047
0.6047
0.7103
0.6103
0.6849
0.6265
0.8345
0.6176
0.6458
0.4457
0.2308
0.6552
0.6003
0.7395
\
1219.8387
46.2064
33.9653
183.1265
31.1958
27.1063
495.2805
20.2729
153.2817
482.9053
411.3987
546.5048
949.4666
21.1241
41.3614
262.7923
262.7923
1.7944
274.3042
625.4147
675.5304
674.6927
561.4941
215.5004
144.4178
217.4554
528.2647
738.0669
236.7204
Bw
0.0527
0.2693
0.268
0.1204
0.2663
0.3282
0.0575
0.3588
0.1676
0.0617
0.0815
0.0624
0.0317
0.3705
0.2837
0.1151
0.1151
0.5102
0.1084
0.0585
0.0599
0.0508
0.0676
0.1681
0.1517
0.0779
0.0806
0.0397
0.1704
C-4
-------
Appendix C
Table C-5. Surface elevation and parameters for equations
Columbia River with dams removed
Beginning
River Mile
596.1
593.0
590.0
582.3
574.6
568.0
560.5
556.1
550.5
543.5
536.0
528.5
524.1
521.0
516.6
513.5
509.6
504.0
496.7
489.3
481.0
474.5
472.8
465.3
461.1
456.9
452.1
447.2
441.3
435.8
427.5
419.2
415.0
412.2
409.5
407.1
403.1
397.1
392.4
386.7
382.1
377.4
371.6
364.4
358.3
Ending River
Mile
593.3
590.0
582.3
574.6
568.0
560.5
556.1
550.5
543.5
536.0
528.5
524.1
521.0
516.6
513.5
509.6
504.0
496.7
489.3
481.0
474.5
472.8
465.3
461.1
456.9
452.1
447.2
441.3
435.8
427.5
419.2
415.0
412.2
409.5
407.1
403.1
397.3
392.4
386.7
382.1
377.4
371.6
364.4
358.3
353.6
Elevation
(feet abv
MSL)
1000
980
957
950
942
931
923
915
875
795
787
773
761
755
742
740
737
727
716
702
682
645
638
622
596
591
550
541
533
529
523
514
490
472
468
459
454
450
450
450
450
450
450
450
450
A°
2.6338
2.6338
0.7270
8.0662
0.7307
3.0785
78.9803
13.6134
0.9457
241.4499
3.6436
3.6436
4.3695
21.8397
8.9346
8.9346
50.0570
0.6773
30.0809
2.1101
4.5249
18.5590
18.5590
98.3723
98.3723
46.2149
19.1734
9.3458
34.7602
177.3813
116.7612
116.7612
304.7172
304.7172
71.4189
71.4189
93.4202
16.0994
10.4826
5.1545
35.6628
21.0634
29.5736
16.1049
14.0921
B°
0.7352
0.7352
0.8120
0.6987
0.8405
0.7268
0.4911
0.5940
0.7627
0.3980
0.7084
0.7084
0.7015
0.5685
0.6667
0.6667
0.5268
0.8267
0.5715
0.7502
0.7103
0.6002
0.6002
0.4602
0.4602
0.4941
0.5999
0.6566
0.5667
0.4614
0.5084
0.5084
0.3970
0.3970
0.5197
0.5197
0.5409
0.6010
0.6491
0.6966
0.5364
0.6032
0.5646
0.6030
0.6336
14 and 15 describing the hydraulics of the
A.
18.0219
18.0219
71.3679
1099.0507
33.2019
41.2264
106.4525
77.8754
28.1202
569.5330
37.3599
37.3599
30.4070
62.3113
204.5063
204.5063
373.5261
1.3620
141.8256
24.0741
29.2092
381.3065
381.3065
601.2292
601.2292
52.8461
97.9604
249.7985
650.6808
1239.7894
2121.0964
2121.0964
481.3450
481.3450
589.8682
589.8682
434.8807
99.5337
46.1598
10.8665
798.8506
292.7820
374.7002
91.6599
82.1749
Bw
0.3374
0.3374
0.223
0.0508
0.2845
0.2468
0.1716
0.1894
0.2858
0.045
0.2799
0.2799
0.3061
0.2475
0.1391
0.1391
0.0727
0.5177
0.1773
0.3206
0.3209
0.1018
0.1018
0.0486
0.0486
0.1974
0.2138
0.1548
0.087
0.0537
0.0471
0.0471
0.1025
0.1025
0.1286
0.1286
0.1681
0.2172
0.299
0.3948
0.0731
0.1991
0.1297
0.2066
0.2678
C-5
-------
Appendix C
Table C-5 (continued). Surface elevation and parameters for equations 14 and 15 describing the
hydraulics of the Columbia River with dams removed
Beginning
River Mile
353.6
346.3
339.5
333.6
329.4
324.0
319.0
315.0
310.0
305.0
300.0
295.0
290.0
285.0
280.0
275.0
270.0
265.0
260.0
255.0
250.0
245.0
240.0
235.0
230.0
225.0
220.0
215.0
210.0
205.0
200.0
195.0
190.0
185.0
180.0
175.0
170.0
165.0
160.0
155.0
150.0
146.1
Ending
River Mile
346.3
339.5
333.6
329.4
324.0
319.0
315.0
310.0
305.0
300.0
295.0
290.0
285.0
280.0
275.0
270.0
265.0
260.0
255.0
250.0
245.0
240.0
235.0
230.0
225.0
220.0
215.0
210.0
205.0
200.0
195.0
190.0
185.0
180.0
175.0
170.0
165.0
160.0
155.0
150.0
146.1
140.0
Elevation
(feet abv
MSL)
450
450
450
450
450
319
319
311
304
298
290
279
267
260
256
244
237
230
224
221
216
212
209
206
199
181
176
164
160
148
140
137
76
75
73
72
69
65
62
59
48
24
Aa
41.4013
1.4800
60.2303
26.2448
94.4921
8.1919
8.1919
8.1919
3.6979
0.1471
0.3042
5.5772
7.3793
1.2465
222.7504
1.0377
0.2465
12.4667
0.2303
22.1718
10.2468
0.0527
12.0935
524.6108
1.6655
3.5737
1878.4895
7.9771
27.2777
41.1050
41.1050
2244.5522
0.9950
5.2198
1800.4440
227.3922
27.8419
21.0582
21.0582
2.7886
2.7886
0.3407
Ba
0.5346
0.8018
0.5596
0.6340
0.5597
0.6777
0.6777
0.6777
0.7577
0.9998
0.9383
0.7054
0.6946
0.8363
0.4407
0.8121
0.9716
0.6535
0.9490
0.6173
0.6940
1.0805
0.6696
0.3843
0.7684
0.7293
0.2832
0.6813
0.5970
0.5813
0.5813
0.2914
0.8306
0.7354
0.3021
0.4594
0.6190
0.6312
0.6312
0.7433
0.7433
0.8362
A,
940.1158
1.0554
664.3698
129.2020
1585.1760
15.5388
15.5388
15.5388
4.8827
50.1033
32.7658
16.3420
20.1463
184.3870
2.3317
0.6808
7.7394
161.5547
21.5631
88.7304
178.6500
19.4272
71.3909
935.8895
476.1715
260.5219
1367.9987
141.3714
634.6995
9.0817
9.0817
680.3396
58.5292
745.1066
106.4071
121.2100
574.8106
959.7112
959.7112
302.9572
302.9572
1.1586
Bw
0.0693
0.605
0.1195
0.2683
0.1194
0.4047
0.4047
0.4047
0.5124
0.3363
0.3662
0.4116
0.3881
0.2182
0.5328
0.6399
0.5002
0.2115
0.3816
0.2695
0.2291
0.3972
0.2919
0.07
0.1207
0.1704
0.0409
0.2097
0.105
0.4604
0.4604
0.095
0.2722
0.0994
0.2303
0.2483
0.1414
0.1039
0.1039
0.1456
0.1456
0.5184
C-6
-------
Appendix D
Statistical Analysis Of Simulation Results
-------
Appendix D
The statistical analyses were performed in this study to quantify levels of uncertainty associated with
simulation results. Means and standard deviations of the difference between observed and simulated temperatures
were computed for the entire simulation period and for each two-month period for the duration of the simulation
(01/01/1990 - 12/31/1994). The results are given in Tables D-l through D-9. An analysis of the regression of
observed results on simulated results was also performed. In the regression analysis, the linear relationship is
constrained to pass through the origin of the coordinates at (X=0, Y=0) as shown in Figures D-l through D-9.
The results of the regression are shown Table D-10.
Certain statistics are also generated as part of the parameter estimation process. These include the theoretical
and sample variance of the innovations process Figures D-10 through D-18 and the innovations process (Equation
12) (Figures D-l9 through D-27).
When reviewing these statistics it is important to keep in mind that the means and standard deviations of the
difference between observed and simulated are based on state estimates using the model in the prediction mode.
That is, the state estimates from the model do not depend on prior observations. The statistics generated by the
parameter estimation process are a result of using the model in the filtering mode. This means that the
innovations sequence, the difference between observed and the systems update prior to filtering, is a function of
previous observations and state estimates. In addition, the parameter estimation process attempts to estimates the
bias in the observations.
D-1
-------
Appendix D
Table D-1. Mean and standard deviation of the difference between observed and simulated temperatures
at Wells Dam (Columbia River Mile 515.6) for the period 1990-1994. Observed data are from the total
dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—) indicate
limited (N<10) data for computing statistics
Time Period Mean Difference Standard Deviation of Difference
January-February
March-April -0.028 0.510
May-June 0.035 0.802
July-August -0.136 0.529
September-October 0.494 0.488
November-December
Entire Year 0.009 0.677
Table D-2. Mean and standard deviation of the difference between observed and simulated temperatures
at Priest Rapids Dam (Columbia River Mile 397.1) for the period 1990-1994. Observed data are from the
total dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—)
indicate limited (N<10) data for computing statistics
Time Period
January-February
March-April
May-June
July-August
September-October
November-December
Entire Year
Mean Difference
—
0.320
-0.623
-0.499
0.855
—
-0.277
Standard Deviation of Difference
—
0.999
0.895
0.880
0.433
-
1.012
Table D-3. Mean and standard deviation of the difference between observed and simulated temperatures
at McNary Dam (Columbia River Mile 292.0) for the period 1990-1994. Observed data are from the total
dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—) indicate
limited (N<10) data for computing statistics
Time Period Mean Difference Standard Deviation of Difference
January-February
March-April 0.940 0.929
May-June 0.749 1.194
July-August 0.884 1.335
September-October 1.653 1.027
November-December
Entire Year 0.983 1.236
D-2
-------
Appendix D
Table D-4. Mean and standard deviation of the difference between observed and simulated temperatures
at John Day Dam (Columbia River Mile 215.6) for the period 1990-1994. Observed data are from the total
dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—) indicate
limited (N<10) data for computing statistics
Time Period Mean Difference Standard Deviation of Difference
January-February 0.580 1.309
March-April 1.273 0.730
May-June 0.283 0.924
July-August 0.288 0.986
September-October 0.9425 0.646
November-December
Entire Year 0.560 1.021
Table D-5. Mean and standard deviation of the difference between observed and simulated temperatures
at Bonneville Dam (Columbia River Mile 215.6) for the period 1990-1994. Observed data are from the total
dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—) indicate
limited (N<10) data for computing statistics
Time Period
January-February
March-April
May-June
July-August
September-October
November-December
Entire Year
Mean Difference
—
0.909
0.413
-0.382
0.524
—
0.241
Standard Deviation of Difference
—
1.002
1.248
1.423
0.868
—
1.306
Table D-6. Mean and standard deviation of the difference between observed and simulated temperatures
at Bonneville Dam (Columbia River Mile 215.6) for the period 1990-1994. Observed data are from the total
dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—) indicate
limited (N<10) data for computing statistics
Time Period Mean Difference Standard Deviation of Difference
January-February
March-April 0.909 1.002
May-June 0.413 1.248
July-August -0.382 1.423
September-October 0.524 0.868
November-December
Entire Year 0.241 1.306
D-3
-------
Appendix D
Table D-7. Mean and standard deviation of the difference between observed and simulated temperatures
at Lower Granite Dam (Snake River Mile 107.5) for the period 1990-1994. Observed data are from the total
dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—) indicate
limited (N<10) data for computing statistics
Time Period
January-February
March-April
May-June
July-August
September-October
November-December
Entire Year
Mean Difference
—
1.052
-0.040
1.136
0.409
-0.133
0.588
Standard Deviation of Difference
—
1.388
1.363
1.120
1.076
0.203
1.320
Table D-7. Mean and standard deviation of the difference between observed and simulated temperatures
at Little Goose Dam (Snake River Mile 70.3) for the period 1990-1994. Observed data are from the total
dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes ( — ) indicate
limited (N<10) data for computing statistics
Time Period
January-February
March-April
May-June
July-August
September-October
November-December
Entire Year
Mean Difference
—
1.086
-0.196
0.131
-0.228
—
0.048
Standard Deviation of Difference
—
1.144
1.167
1.532
1.436
—
1.420
Table D-8. Mean and standard deviation of the difference between observed and simulated temperatures
at Lower Monumental Dam (Snake River Mile 41.6) for the period 1990-1994. Observed data are from the
total dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—)
indicate limited (N<10) data for computing statistics
Time Period Mean Difference Standard Deviation of Difference
January-February
March-April 1.543 0.900
May-June 0.027 0.884
July-August -0.067 1.269
September-October -0.036 0.933
November-December
Entire Year 0.124 1.187
D-4
-------
Appendix D
Table D-9. Mean and standard deviation of the difference between observed and simulated temperatures
at Ice Harbor Dam (Columbia River Mile 9.7) for the period 1990-1994. Observed data are from the total
dissolved gas monitoring locations in the forebay of the dam at a depth of 15 feet. Dashes (—) indicate
limited (N<10) data for computing statistics
Time Period
January-February
March-April
May-June
July-August
September-October
November-December
Entire Year
Mean Difference
—
1.784
0.155
0.192
0.625
—
0.407
Standard Deviation of Difference
—
1.021
0.888
1.190
1.093
—
1.202
Table D-10. Slope of line and R2 for regression of observed temperature data on simulated results in the
Columbia and Snake rivers for the period 1990-1994. Regression was constrained to force the straight
line to pass through the origin (X (simulated)=0, Y (observed)=0).
Measurement Site Slope of Line R2
Wells Dam 0.995 0.973
Priest Rapids Dam 0.999 0.940
McNary Dam 1.004 0.929
John Day Dam 0.995 0.976
Bonnevile Dam 0.995 0.904
Lower Granite Dam 1.005 0.931
Little Goose Dam 0.997 0.907
Lower Monumental Dam 0.992 0.923
Ice Harbor Dam 0.998 0.929
D-5
-------
Appendix D
2.5
2.0 -
6
1.5 -
£ 1.0 i
0.5 -
0.0
1990
1991
1992
1993
1994
1995
O Sample Variance
f Theoretical Variance
Time -Years
Figure D-10. Theoretical and sample variance of innovations sequence at Wells Dam -1990-1995
D-6
-------
Appendix D
2.5
2.0 -
-------
Appendix D
2.5
2.C
O
O)
4>
TJ
8
1.5 -
1.0 -
0.5 -
0.0
O
1990
1991
1992 1993
Time -Years
1994
1995
O Sample Variance
• Theoretical Variance
Figure D-12. Theoretical and sample variance of innovations sequence at McNary Dam -1990-1995
D-8
-------
Appendix D
2.5
2.0 -
CM
6
O)
1.5 -
« 1.0
0.5 -
0.0
o
1990
1991
1992
1993
1994
1995
O Sample Variance
» Theoretical Variance
Time -Years
Figure D-13. Theoretical and sample variance of innovations sequence at John Day Dam -1990-1995
D-9
-------
Appendix D
CN
<
O
0)
O
2.5
2.0 -
1.5 -
1.0 -
0.5 -
0.0
1990
1991
1992
1993
1994
1995
Q Sample Variance
• Theoretical Variance
Time -Years
Figure D-14. Theoretical and sample variance of innovations sequence at Bonneville Dam -1990-1995
D-10
-------
Appendix D
2.5
2.0
t^ ir-
6 1-5^
D)
TJ
i
-------
Appendix D
2.5
2.0 -
1.5 -
O
Cfl
i
01
U
« 1.0
0.5 -
0.0
1990
1991
1992 1993
—i Time -Years
1994
1995
O Sample Variance
• Theoretical Variance
Figure D-16. Theoretical and sample variance of innovations sequence at Little Goose Dam -1990-1995
D-12
-------
Appendix D
2.5
2.0 -
O
I
|
1.5 -
1.0 -
0.5 -
e
9
o
1990
1991
1992 1993
Time -Years
1995
O Sample Variance
• Theoretical Variance
Figure D-17.
Theoretical and sample variance of innovations sequence at Lower Monumental Dam -1990-1995
D-13
-------
Appendix D
3.0
2.5 -
2.0 -
O)
0>
(J
1.5 -
1.0 -
0.5 -
0.0
o
1990
1991
1992
1993
1994
1995
O Sample Variance
T Theoretical Variance
Time -Years
Figure D-18. Theoretical and sample variance of innovations sequence at Ice Harbor Dam -1990-1995
D-14
-------
Appendix D
3 -
2 -
o
o)
•o
cr
CO
w
o
1
o
c
n
U -
i
-2 -
-3 -
-4
t
i
i
1990
1991
1992 1993
Time -Years
1994
1995
Figure D-19. Innovations sequence for Wells Dam -1990-1995
D-15
-------
Appendix D
3
2 -
o
o)
g
m
m
CO
s
o
c
n
U -
-1 -
-2 -
-3 -
-A
T
1 :
1^
1990 1991 1992 1993
Time -Years
1994
1995
Figure D-20. Innovations sequence for Priest Rapids Dam -1990-1995
D-16
-------
Appendix D
3 -
2 -
o
O)
o>
TJ
nnovations Sequence
i
— o
-2 -
-A
1990 1991 1992 1993
Time -Years
1994
1995
Figure D-21. Innovations sequence for McNary Dam -1990-1995
D-17
-------
Appendix D
o
o)
4)
•O
0>
y
4
3 -
2 -
1 -
0 -
o
1 -1
o
c
-2 -
-3 -
-4
1990 1991 1992 1993
Time -Years
1994
1995
Figure D-22. Innovations sequence for John Day Dam -1990-1995
D-18
-------
Appendix D
4 -
S 2
4>
I
I 0
-A -
-6
i
1990 1991 1992 1993
Time -Years
1994
1995
Figure D-23. Innovations sequence for Bonneville Dam -1990-1995
D-19
-------
Appendix D
I
to
c
o
3 -
2 -
1 -
0 -
>
o
i -1
-2
-3 -
1990 1991
1992 1993
Time -Years
1994 1995
Figure D-24. Innovations sequence at Lower Granite Dam -1990-1994
D-20
-------
Appendix D
4 -
O
O) 2
o>
TJ
I
0 -
O
E -2
-4 -
-6
1990
1991
1992 1993
Time -Years
1994
1995
Figure D-25. Innovations sequence for Little Goose Dam -1990-1995
D-21
-------
Appendix D
5 -
4 -
3 -
2 -
o
TJ
i
U
c
? °
10
i -1
-2 -
-3 -
-4 -
-5 -
-6
1990
1991
1992 1993
Time -Years
1994
1995
Figure D-26. Innovations sequence for Lower Monumental Dam -1990-1995
D-22
-------
Appendix D
6 -
O
o> 4
3
S" 2
ui
O
c 0
-2 -
-4
I
1990
1991
1992 1993
Time -Years
1994
1995
Figure D-27. Innovations sequence for Ice Harbor Dam -1990-1995
D-23
------- |