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TECHNICAL REPORT NO . 1
... ..,.
pr pared lor
THE
OLD WEST REGIONAL
COMMISSON
by j,. WATER RESOURCES DIVISION-----------JULY IQ77
UaroNrANA DEPARTMeNT DF NATURAL R£SOURC£ & coNSCII~AnON
~ ,,
by
Bob Anderson, Assistant Administrator, WRD
Phil Threlkeld, Land Resource Scientist, WRD
Satish Nayak, Systems Analyst, CSD
Hanley Jenkins, Environmental Planner, WRD
TECHNICAL REPORT NO. 1
conducted by the
Water Resources Division
Montana Department of Natural Resources and Conservation
32 S. Ewing
Helena, MT 59601
Bob Anderson, Project Administrator
Dave Lambert, Editor
for the
Old West Regional Commission
228 Hedden Empire Building
Billings, MT 59101
Kenneth A. Blackburn, Project Coordinator
July 1977
1730 K Street, N. W.
Suite 426
The Old West Regional Commission is a Federal-State
partnership designed to solve regional economic
problems and stimulate orderly economic growth in
the states of Montana, Nebraska, North Dakota,
South Dakota and Wyoming. Established in 1972
under the Public Works and Economic Development
Act of 1965, it is one of seven identical commissions
throughout the country engaged in formulating and
carrying out coordinated action plans for regional
economic development.
COMMISSION MEMBERS
State Cochairman
Gov. Thomas L. Jud~e of Montana
Alternate: Dean Hart
Federal Cochairman
George D. McCarthy
State Members
Gov. Edgar J. Herschler of Wyoming
Alternate: Steve F. Freudenthal
Gov. J. James Exon of Nebraska
Alternate: Jon H. Oberg
Gov. Arthur A. Link of North Dakota
Alternate: Woody Gagnon
Gov. Richard F. Kneip of South Dakota
Alternate: Theodore R. Muenster
COMMISSION OFFICES
201 Main Street
Suite D
Washington, D. C. 20006
202/967-3491 Rapid City, South Dakota 57701
605/348-6310
Suite 228
Heddon-Empire Building
Billings, Montana 59101
406/657-6665
ii
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FOREWORD
The Old West Regional Commission wishes to express its appreciation for
this report to the Montana Department of Natural Resources and Conservation,
and more specifically to those Department staff members who participated
directly in the project and in preparation of various reports, to Dr. Kenneth A.
Blackburn of the Commission.staff who coordinated the project, and to the
subcontractors who also participated. The Yellowstone Impact Study was one
of the first major projects funded by the Commission that was directed at
investigating the potential environmental impacts relating to energy develop-
ment. The Commission is pleased to have been a part of this important research.
George D. McCarthy
Federal Cochairman
FIGURES
TABLES
ABBREVIATIONS USED IN THIS REPORT •
PREFACE .••••
The River
The Conflict • • • • • • •
The Study
Acknowledgements • • • • •
INTRODUCTION
Development Projections
Basin Division •
PART I. FUTURE WATER USE PROJECTIONS .
PROJECTIONS OF COAL PRODUCTION FOR ENERGY
Methods •
Previous Projections • • . • •
Energy-Development Alternatives • • •••••• o
Low Level of Development o • • • o • •
Intermediate Level of Development • • • • • • o • o
High Level of Development • • • • • • • • • • • o o •
Summary of Levels of Development • . • • • .
Water Use Associated with Projected Energy Development
PROJECTIONS OF IRRIGATED AGRICULTURE •
Methods • • • • • •
Identification of Irrigable Land •
Calculation of Irrigation Costs .• • • •
Farm Budgets and the Ability to Pay for Irrigation
Irrigation and ~ater Depletion
PROJECTIONS OF MUNICIPAL POPULATION GROWTH
Montana Futures Process • . • •
Economic Calculation . . •
Demographic Calculation
Municipal Population • • . . •
Increased Water Use Associated with
SUMMARY
- i v -
Population Growth .
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PART II. HYDROLOGIC MODELING •
SELECTION DF A WATER MODEL .
Model Varieties • . • . . • • •
The Utah State Model • • • • . • • . •
Streamflow Synthesis and Reservoir
Regulation (SSARR) •••••
HYD-2
SIMYLD-II
. . . . . . . . . . . .
The State Water Planning Model . • • • •
Model Comparison • • • •
ADAPTATION OF THE SWP
How the SWP Model Was Used
Calibration
. . . . . . . . . . . . .
Simulations
Data Preparation
The Annual and Monthly Models .
Annual Model •
Monthly Model • • • • • .
Calibration of the Monthly Model and
Controllable Variables
Calibration Program and New Subroutines •
Subroutine INITIA • • • .
Subroutine EXPORT • • • •
Subroutine SURFAC •••••
Subroutine COMPUT • • • •
SIMQUAL--The Simulation Program •
DEPLET •
SURFAC •
INITIA •
MODIST •
QUALTY .
PRINT • • . •
MEAN ••
SORT and COMPAR
PLOT • •
SIMULATIONS
Types of Simulations
Scenarios • • • • . • •
Area Simulations
. . . . . . . .
The Upper Yellowstone, Clarks,fork Yellowstone,
and Kinsey Area Subbasins • • • •
The Billings Area Subbasin • • • • •
The Bighorn Subbasin • • • • • • • • •
The Mid-Yellowstone Subbasin • • • • .
The Tongue Subbasin • • • • • • . •
The Powder Subbasin • • • •
The Lower Yellowstone Subbasin •
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APPENDIXES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A. Projected Water Requirements in the Yellowstone
River Basin in the year 2000
B. Coefficients and Constants for Subbasin Model Runs •
C. Water Quality Regression Equations .••••
LITERATURE CITED
115
117
127
133
139
1. Yellowstone River Basin . . . . . . . . . . . . .
2. Map of strippable coal in the Yellowstone drainage basin
3. Base, low, intermediate, and high alternative futures
for coal production ••••••
4. Montana futures process simulation-model structure •
5. Labor market areas in Montana
6. Calibration program subroutines . . . . . . . . . . . . . .
7. Simulation program subroutines •.
8. Schematic representation of TDS calculations •
-vii-
7
12
30
56
58
91
94
96
l. Definition of strippable coal . . . . . . . . .
2. Coal production in 1975 and 1980 in the Yellowstone Basin
based on coal sales contracts
3. Stabilized coal production in the Yellowstone River Basin
4. Planned coal production by company, mine and year . . . .
5. Coal production under low-level development,
Yellowstone Basin • • • • • • •
6. Location of coal conversion facilities through the year
2000, low development level, by Yellowstone
River subbasins • • • • • • • • • • • • • • •
. . .
7. Coal ~onnage location by Yellowstone River subbasins, low-level
development 1980, 1985, 2000 ••••••••••••
8. Coal production for consumption-under intermediate-level devel-
opment, Yellowstone Basin •.••••••
9.
10.
Location of coal conversion facilities through year 2000,
intermediate development level, by Yellowstone
River subbasins ••••••••••••••
Coal tonnage location by Yellowstone River subbasins,
intermediate level development, 1980, 1985, 2000
11. Coal production for consumption under high-level development,
Yellowstone Basin • • • • • • • • •
12. Location of coal conversion facilities through the year
2000, high development level~ by Yellowstone
River subbasins •••••.•••••••••
13. Coal tonnage location by Yellowstone River subbasins, high-
level development, 1980, 1985, 2000 . . . .
14. Coal production for consumption under three levels of
development, Yellowstone River Basin,
through the year 2000 . . . . . . . . . .
15. Coal conversion in the Yellowstone Basin in 2000
16. Annual water and coal requirements for coal processes .
-viii-
.
.
.
.
. . . 11
16
17
. . . 18
19
20
21
23
23
24
25
27
28 . . .
29
32
33 . . .
17. Water use in coal m~n~ng and electrical generation by 1980
by Yellowstone River subbasin under various levels of
development • • • • • • • . . • • • • • • • • • • • • . . • 34
18. Water use in coal mining, transportation, and conversion
processes by 1985 by Yellowstone River subbasin under
various levels of development • • • • . • • • . • • . . • • • . 35
19. Water use in coal mining, transportation, and conversion
processes by 2000, by subbasin under various levels
of development . • • • • • • • • . . • • . • 36
20. Land classification specifications by soil or land
characteristics • • • . • . • • • . . • • • • • . • 39
21. Irrigable acreage in Yellowstone River subbasins by lift
and pipe length • • • . • • . . 40
22. Concrete pipeline costs • 43
23. Steel pipeline costs 43
24. Annual water delivery costs
25. Center-pivot irrigation costs
26. Inventory of buildings~ machinery and equipment; investment,
repair, depreciation and taxes for a hypothetical
44
44
320-acre farm . . . . . . . . . . . . . . . . . . . 46
27, Miscellaneous fixed costs for a hypothetical 320-acre farm 47
28. Farm prerequisites (house, garage, well) 47
29. Variable costs per irrigated acre by crop • 48
30. Irrigated-crop production and sales per acre 49
31. Farm budget summary with management allowance 50
32. Cropping patterns by subbasin, 320-acre farm . • . • . • 5'1
33. Costs and returns by subbasin 320-acre farm 53
34. Payment capacity available for pumping 53
35. Maximum pumping distance for various lifts 53
36. Feasibly irrigable acreage by lift and pipeline length,
high-level development . • • • • • . • • • • • • • . • • . . 54
37. The increase in water depletion for irrigated agriculture
by 2000 by subbasin • . • • • . . . • . . • • • . • • 55
38. Permanent, direct energy-related employees in the
Yellowstone basin, 1985 and 2000 .
39. Population simulations for low, medium, and high energy
development • • • . . • • • • . • • • • •
40. Population increases and water depletion in the Yellowstone
River Basin in 1985 and 2000, according to levels
of energy development • • • • • • . • • • • • • •
41. Water requirements by demand source in the Yellowstone
River Basin under three levels of development in 2000
42. Increased water requirements for coal development in the
Yellowstone Basin in 2000 • • • •
43. Model comparison
44. Suggested model evaluation criteria •
45. Model coefficients
46. Percentage by month of TDS returning to streamflow
47. Billings area subbasin water requirements •
48. Outflow of the Billings area subbasin . . .
49. Average out flow and TDS of Billings area subbasin .
50. Bighorn subbasin water requirements . . . .
51. Outflow and TDS of the Bighorn subbasin . . . . . .
52. Mid-Yellowstone subbasin water requirements . .
53. Outflow of the Mid-Yellowstone subbasin . . .
54. Average outflow and TDS of Mid~Yellowstone subbasin •
55. Tongue subbasin water requirements
56. Outflow of the Tongue River subbasin
57. Average outflow and TDS of Tongue subbasin
58. Powder subbasin water requirements
59. Outflow and TDS of the Powder subbasin
60. Lower Yellowstone subbasin water requirements •.
61. Outflow of the lower Yellowstone subbasin ••
62. Average outflow and TDS of the lower Yellowstone subbasin
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. . . .
. . . .
. . . .
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af
af/acre
af/y
b/d
cfs
em
FAA
ft
gal/d/pers
ha 3 hm 3 hm /y
hr
in
kq
km
kwh
lb
LMA
m3
m /sec
M.C.R.
mg/1
mi
millimhos/cm
mmaf
mmcfd
mmt/y
mw
NGPRP
SMSA
SSARR
SWP
t/d
tdh
TDS
USGS
whc
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acre-feet
acre-feet per acre
acre-feet per year
barrels per day
cubic feet per second
centimeter
Federal Aviation Authority
feet
gallons per day per person
hectare
cubic hectometer
cubic hectometers per year
hour
inch
kilogram
kilometer
kilowatt hour
pound
Labor Market Area
meter
cubic meters per second
mean cover rating
milligram per liter
mile
unit of electrical conductivity
per centimeter
million acre-feet
million cubic feet per day
million ton~ per year
megawatts
Northern Great Plains Resource Program
standard metropolitan statistical area
Steamflow Synthesis and Reservoir Regulation
State Water Planning Model
tons per day
total dynamic head
total dissolved salts
United State Geological Survey
water holding capacity
THE RIVER
ihe Yellowstone River Basin of southeastern Montana, nor~hern Wyoming,
and western North Dakota encompasses approximately 180,000 km (71,000 square
miles), 92,200 (35,600) of them in Montana. Montana's portion of the basin
comprises 24 percent of the state's land; where the river crosses the border
into North Dakota, it carries about 8.8 million acre-feet of water per
year, 21 percent of the state's average annual outflow. The mainstem of the
Yellowstone rises in northwestern Wyoming and flows generally northeast to
its confluence with the Missouri River just east of the Montana-North Dakota
border; the river flows through Montana for about 550 of its 680 miles. The
major ·tributaries, the Boulder, Stillwater, Clarks Fork, Bighorn, Tongue,
and Powder rivers, all flow in a northerly direction. The western part of
the basin is part of the middle Rocky Mountains physiographic province;
the eastern section is located in the northern Great Plains (Rocky Mountain
Association of Geologists 1972).
THE CONFLICT
Historically, agriculture has been Montana's most important industry. In
1975 over 40 percent of the primary employment in Montana was provided by
agriculture (Montana Department of Community Affairs 1976). In 1973, a good
year for agriculture, the earnings of labor and proprietors involved in
agricultural production in the fourteen counties that approximate the
Yellowstone Basin were over $141 million, as opposed to $13 million for
mining and $55 million for manufacturing. Cash receipts for Montana's
agricultural products more than doubled fro~ 1968 to 1973. Since that year,
receipts have declined because of unfavorable market conditions; some
improvement may be in sight, however. In 1970, over 75 percent Qf the
Yellowstone Basin's land was in,agricultural use (State Conservation Needs
Committee 1970). Irrigated agriculture is the basin's largest water use,
consw~ing annually about 1.5 million acre-feet (af) of water (Montana DNRC
1977).
There is another industry in the Yellowstone Basin which, though. it con-
sumes little water now, may require more in the future, and that is the coal
development industry. In 1971, the North Central Power Study (North Central
Power Study Coordinating Committee 1971) identified 42 potential power plant
sites in the five-state (Montana, ~orth and South Dakota, Wyoming, and
Colorado) northern Great Plains region, 21 of them in Montana. These plants,
all to be fired by northern Great Plains coal, would generate 200,000 megawatts
(mw) of electricity, consume 3.4 million acre-feet per year (mmaf/y) of water,
and result in a large population increase. Administrative, economic, legal,
- 1 -
and technological considerations have kept most of these conversion facilities,
identified in the ~orth Central Power Study as necessary for 1980, on the
drawing board or in the courtroom. There is now no chance of their being
completed by that date or even soon after, which will delay and diminish the
economic benefits some basin residents had expected as a result of coal
development. On the other hand, contracts have been signed for the mining
of large amounts of Montana coal, and applications have been approved not
only for new and expanded coal mines but also for Colstrip Units 3 and 4,
twin 700-mw, coal-fired, electric generating plants. And in July 1979 the
U.S. Department of Energy released a study concluding that 36 synthetic fuel
plants could be constructed in Montana; together, they would use 468,000
acre-feet of water annually.
In 1975, over 22 million tons of coal were mined in the state, up from
14 million in 1974, 11 million in 1973, and 1 million in 1969. By 1980, even
if no new contracts are entered, Montana's annual coal production will be
about 35 million tons. Coal reserves, estimated at over 50 billion economically
strippable tons (Montana Energy Advisory Council 1976), pose no serious con-
straint to the levels of development projected by this study, which range
from 186.7 to 462.8 million tons stripped in the basin annually by the year
2000. Strip mining itself involves little use of water. How important the
energy indust~y becomes as a water user in the basin will depend on: 1) how
much of the coal mined in Montana is exported, and by what means, and 2) by
what process and to what end product the remainder is converted within the
state. If conversion follows the patterns projected in this study, the
energy industry will use from 48,350 to 326,740 af of water annually by the
year 2000.
A third consumptive use of water, municipal use, is also bound to
increase as the basin population increases in response to increased employment
opportunities in agriculture and the energy industry.
Can the Yellowstone River satisfy all of these demands for her water?
Perhaps in the mainstem. But the tributary basins, especially the Bighorn,
Tongue, and Powder, have much smaller flows, and it is in those basins that
much of the increased agricultural and industrial water demand is expected.
Some impacts could occur even in the mainstem. What would happen to
water quality after massive depletions? How would a change in water quality
affect existing and future agricultural, industrial, and municipal users?
What would happen to fish, furbearers, and migratory waterfowl that are
dependent on a certain level of instream flow? Would the river be as
attractive a place for recreation after dewatering?
One of the first manifestations of Montana's growing concern for water
in the Yellowstone Basin and elsewhere in the state was the passage of
significant legislation. The Water Use Act of 1973, which, among other
things, mandates the adjudication of all existing water rights and makes
possible the reservation of water for future beneficial use, was followed
by the Water Moratorium Act of 1974, which delayed action on major
applications for Yellowstone Basin water for three years. The moratorium,
by any standard a bold action, was prompted by a steadily increasing rush of
applications and filings for water (mostly for industrial use) which, in two
tributary basins to the Yellowstone, exceeded supply. The DNRC's intention
-2-
during the moratorium was to study the basin's water and related land
resources, as well as existing and future need for the basin's water, so
that the state would be able to proceed wisely with the allocation of that
water. The study which resulted in this series of reports was one of the
fruits of that intention.
THE STUDY
The Yellowstone Impact Study, conducted by the Water Resources Division
of the Montana Department of Natural Resources and Conservation and financed
by the Old West Regional Commission, was designed to evaluate the potential
physical, biological, and water use impacts of water withdrawals and water
development on the middle and lower reaches of the Yellowstone River Basin
in Montana. The study's plan of operation was to project three possible
levels of future agricultural, industrial, and municipal development in the
Yellowstone Basin and the streamflow depletions associated with that develop-
ment. Impacts on river morphology and water quality were then assessed,
and, finally, the impacts of altered streamflow, morphology, and water
quality on such factors as migratory birds, furbearers, recreation, and
existing water users were analyzed.
The study began in the fall of 1974. By its conclusion in December of
1976, the information generated by the study had already been used for a
number of moratorium-related projects--the EIS on reservations of water in
the Yellowstone Basin, for example (Montana DNRC 1976). The study resulted
in a final report summarizeing ~11 aspects of the study and in eleven
specialized technical reports:
Report No. 1
Report No. 2
Report No. 3
Report No. 4
Report No. 5
Report No. 6
Report No. 7
Future Development Projections and Hydrologic Modeling in
the Yellowstone River Basin, Montana.
The Effect of Altered Streamflow on the Hydrology and
Geomorphology of the Yellowstone River Basin, Montana.
The Effect of Altered Streamflow on the Water Quality of
the Yellowstone River Basin, Montana.
The Adequacy of Montana's Regulatory Framework for Water
Quality Control
Aquatic Invertebrates of the Yellowstone River Basin,
Montana.
The Effect of Altered Streamflow on Furbearing Mammals of
the Yellowstone River Basin, Montana.
The Effect of Altered Streamflow on Migratory Birds of the
Yellowstone River Basin, Montana.
-3-
Report No. 8
Report No. 9
Report No. 10
Report No. 11
The Effect of Altered Streamflow on Fish of the
Yellowstone and Tongue Rivers, Montana.
The Effect of Altered Streamflow on Existing Municipal
and Agricultural Users of the Yellowstone River Basin,
1·1ontana.
The Effect of Altered Streamflow on Water-Based Recreation
in the Yellowstone River Basin, Montana.
The Economics of Altered Streamflow in the Yellowstone
River Basin, Montana.
ACKNOWLEDGEMENTS
Bruce Finney, of the Montana Department of Community Affairs, provided
the population projections used in Part I. Derwood Mercer, of the Bureau
of Reclamation, provided the cost information used in projecting farm budgets
in Part I, as well as the equations and cost information used in projecting
pumping cost.
DNRC personnel providing assistance were George Cawlfield, who helped
with the hydrologic modeling reported in Part II and reviewed and revised
Part II; John Jarvie, who also helped with Part II; Glen Smith, who superivsed
the preparation of the irrigable land projections, and Elna Tannehill, who
helped with the economic analysis used in those projections; Gary Fritz,
administrator of DNRC's Water Resources Division, who provided guidance and
review; Mark Nicholson, Ron Schleyer, Shari Meats, Marianne Melton, and Karen
Renne, who performed editing tasks; and Janet Cawlfield, Lynda :~owell, and
Kris Macintyre, typists. Graphics were coordinated and performed by Gary Wolf,
with the assistance of Dan Nelson. The cover was designed and executed by D.C.
Howard.
-4-
DEVELOPMENT PROJECTIONS
The principal objective of the Yellowstone Impact Study was to evaluate
potential environmental impacts resulting from future water development likely
to occur on the Yellowstone River. Achievement of this objective was handi-
capped throughout the study by two inherent problems. First, the Yellowstone,
because it is a free-flowing river, is not controllable. Researchers were
unable to alter the streamflows and observe changes. Thus, all studies had
to be made under the circumstances nature provided, which were less than
ideal for a low-flow study such as this--1975 was a year of record high flows
and 1976 a year of moderate flows.
A second problem, a subject of this report, was the imperfect knowledge
of the magnitude and type of future water developments. The purpose of this
part of the Yellowstone Impact Study was to resolve that problem by projecting
future resource development and economic growth in the basin and the amount
of water that development would require. The material presented in this
report is basic to the entire study; the other ten technical reports project
the types and amounts of impact that would be expected in the Yellowstone
Basin if the water depletions projected in this report were to occur.
If major water developments occur, they are expected to be of two types:
agricultural and energy-industrial. (It was assumed that future agricultural
water use will be for irrigation.) Municipal water use, to be determined
by the two major types of development, will be one order of magnitude less.
Part I of this report projects the amount of development of each of these
three types that might occur in the basin and how much water would be re-
quired. Part II projects, through a computer simulation, what the streamflow
in the Yellowstone River and its major tributaries would be if the projected
amounts of water were withdrawn.
The projections made throughout this report are projections of what might
happen, based on particular assumptions; they are not predictions of what
will happen. The irrigation projections are uncertain because of the unknown
future of many factors, especially crop prices. The energy development pro-
jections are even more uncertain. Although the extent of the coal resource
is well known, the future demand for development of that resource is not,
and no attempt is made in this report to predict future demand for coal.
Rather, a high level of development is defined as the scenario that would
occur if the State of Montana were to actively promote coal development.
Regardless of the rigor of the prediction methodology, it must be based
on numerous assumptions that are plagued with uncertainty. Only one of
these assumptions may turn out to involve the controlling factor, but it is
impossible at this time to identify that factor, let alone the demand's
- 5 -
elasticity to that factor. Rather, this study assumed a "What if •. 7"
approach. If coal development occurs at the high level, what will be the
impacts of that level of development? If they are unacceptable, then the
state can attempt to constrain the development at a lower level through in-
stitutional means. If it is naive to assume that the state can and will
exert such control, then the whole exercise is fruitless.
BASIN DIVISION
To facilitate this study, thi Yellowstone River Basin was divided
into the following nine subbasins :
1) The Upper Yellowstone Subbasin, which consists of the basins of the
Yellowstone mainstem from the Montana-Wyoming border to Laurel
(43B and 43QJ), the Shields River (43A), the Boulder River (43BJ),
Sweet Grass Creek (43BV), and the Stillwater River (43C);
2) The Clarks Fork Yellowstone Subbasin (43D) ;!
3) The Billings Area Subbasin, which consists of the basins of the
Yellowstone River (43Q) and Pryor Creek (43E);
4) The Bighorn Subbasin, which includes the basins of the Bighorn (43P)
and Little Bighorn rivers (430);
5) The Mid-Yellowstone Subbasin, which consists of the basins of
Rosebud Creek (42A) and of the Yellowstone mainstem between the
confluences of the Bighorn and Yellowstone rivers (42KJ);
6) The Tongue Subbasin (42B and 42C);
7) The Kinsey Area Subbasin, the smallest of the nine subbasins con-
sidered in this study, which consists of the basin of the Yellow-
stone mainstem between the confluences of the Tongue and Yellowstone
rivers and the Powder and Yellowstone rivers (42K);
8) The Powder Subbasin, which includes the basins of the Powder (42J)
and Little Powder rivers (42I); and
9) The Lower Yellowstone Subbasin, which consists of the basins of
O'Fallon Creek (42L) and of the Yellowstone mainstem from the
confluence of the Powder and Yellowstone rivers to the Montana-North
Dakota border (42M).
Figure 1 shows the nine subbasins with their boundaries. The subbasins
approximate the basins of the major tributaries of the Yellowstone River,
allowing each of the major tributaries to be modeled for the Yellowstone
Impact Study.
lThe numbers in parentheses correspond to the basin numbers used to indi-
cate hydrologic basins in An Atlas of Water Resources in Montana by Hydrologic
Basins (MWRB 1970).
-6-
YEllowsTONE
CoNTRibuTiNG RiVER
1
2
3
4
5
6
7
8
9
Upper Yellowstone
Clarks Fork Yellowstone
Billings Area
Bighorn
Mid-Yellowstone
Tongue
Kinsey Area
Powder
Lower Yellowstone
0 10 20 u-u-u I
0 10 20
wu------1
YELLOWSTONE
NATIONAL .PARK
40
I
40
I
' )
I
(
RIVER BASIN
BAsiNs
60 80 100 Miles
I I I
60 80 100 Kilometers
I I I
N YELLOWSTONE
RIVER BASIN
GARFIELD
I L-, ROSE . , iS
L-----r.L I COLSTRIP
I ---. --{ e I L
\ ~ ee~
------\-.., ~ cr
' I I ~-:.
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WYOMING
by
Bob Anderson
Phil Threlkeld
Hanley Jenkins
-9-
The low-sulfur coal in southeastern Mbntana currently is in demand. The
increasing world price of oil, decreasing domestic supplies of crude oil and
natural gas, and the goal of United States energy self-sufficiency have
increased the market value of many domestic coal reserves, including
tvlontana's.
Averiet (1974) estimated that coal reserves in Montana might be as
high as 448.6 billion tons of lignite, subbituminous, and bituminous coal.
Estimates by the Bureau of Reclamation (USDI 1972) indicate that approxi-
mately 75 percent of this total lies within 1,000 ft of the surface. The
Montana reserve is part of the vast Fort Union coal region (considered the
world's largest), which contains approximately 40 percent of the United
States coal reserve (Montana Coal Task Force 1973) and underlies parts of
western North Dakota, northwestern South Dakota, northeastern Wyoming,
southeastern Saskatchewan, and eastern Montana.
Strip mining is used to recover these coal reserves. Economically,
underground mining has a weak competitive position in Montana. Compared to
strip mining, capital requirements are higher for underground mining, and
productivity per miner is low. The actual cost of mining is, as a result,
far higher.
In the West, whether a coal deposit is strippable commonly is determined
according to the depth criteria in table 1. Matson (1974) estimated that
42.5 billion tons of strippable coal underlies eastern Montana. Figure 2
locates strippable coal reserves in the Montana portion of the Fort Union
coal region.
Table 1. Definition of strippable coal.
Thickness of Maximum Overburden
Strippable Beds ( ft) Depth ( ft)
0 -10 0 -100
10 -25 0 -150
25 -40 0 -200
more than 40 0 -250
SOURCE: Montana College of Mineral Science
and Technology 1973
-11-
Because of the low cost of strip m1n1ng, use of western coal reserves
for power and fuel is highly profitable for mining companies. There are
three major markets expected to buy Montana coal from the companies:
1) power-plant operators in the South, Midwest, and Pacific Northwest; 2) pro-
ducers of synthetic fuels from coal at mine-mouth conversion facilities, and
3) power-plant operators at mine-mouth plants in Montana. This report does
not attempt to estimate exactly the demand these three markets might generate
for southeastern Montana coal, but postulates certain quantitative increases
in production as the general response to demand for energy.
METHODS
This study develops coal-production projections for energy development
in Montana's portion of the Yellowstone River Basin. Three levels of develop-
ment are postulated for five consuming sectors of the national economy:
household and commercial, industrial, electrical generation, synthetic fuel,
and export for processing or ~onsumption elsewhere. The projections span
the years 1975 through 2000. The intent is not to predict the future but
rather to present alternative futures (levels of development) in coal pro-
duction.
After postulating levels of coal development, the study calculated
industrial wate~ use re~uirements tb aid in determining the potential impacts
of altered streamflows on existing consumers of water and on recreation,
water quality, the ecosystem, and the economy (see reports 2 through 11 in
this series).
PREVIOUS PROJECTIONS
A humber of private-organizations and government agencies have projected
coal production and related economic development in Montana. A few of those
studies are identified below.
1) The Federal Energy Administration's Project Independence Report
(1974) constructed a model of supply and demand for coal in the
Northern Great Plains. Because the assumptions on which the
model is based are unknown, comparison or use of the reported
data is difficult.
2) A Northern Great Plains Resource Program (NGPRP) work group issued a na-
tional report on regional energy considerations in 1974, which
presented a series of coal-development projections for the NGPRP.
Some of those projections are used extensively in this report and
are discussed where applicable. The NGPRP is intergovernmental
and involves the states of the Northern Great Plains region
(Montana, Wyoming, North Dakota, South Dakota, and Nebraska) and
three federal agencies (Environmental Protection Agency, Department
of the Interior, and Department pf Agriculture) with responsibilities
for problems that might arise from coal and energy development in
the region.
-12-
YEllowsTONE RIVER BASIN
STR1ppAblE CoAl REsERVES
Coal Res.erves
SOURCE: Montana College of Science and Technology 1973.
0 10 20 40 60 80 100 Miles
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0 10 20 40 60 80 100 Kilometers
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YELLOWSTONE
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GARFIELD
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3) The Montana University Coal Demand Study (MUCDS) report entitled
Projections of Northern Great Plains Coal.Mining and Energy Con-
version Development 1975-2000 A.D. considered demand for Northern
Great Plains Resource Program coal associated with two primary
facilities--electric generation and synthetic natural gas. The
. MUCDS attempted to (l) identify what factors will influence NGP
coal development, (2) indicate the key variables determining de-
velopment, and (3) establish quantitatively how the levels of
development would be altered .. if th~ variables were to change.
Th~ MUCDS proj~ctions for synthetic natural gas production are
reflected in the projections of the Yellowstone Impact Study.
4) In September 1975, the Missouri River Basin Commission began the
Yellowstone Level B Study, a· two-year planning study to develop
general information on water and related land resources in the
Yellowstone River Basin and adjacent coal areas. The Commission
hired the Harza Engineering Eompany to develop three alternative
coal-mining and energy-conversion levels for the'years 1985 and
2000 reflecting demand and suppl~ of energy nationally and within ·
the Yellowstone Basin.
ENERGY-DEVELOPMENT ALTERNATIVES
This report incorporates many of the aforementioned coal development
estimates to provide a fresh and realistic estimate of potential levels of
coal and energy development in· southeastern Montana and the rest of the
Yellowstone Basin. As with any projection on this subject, predicting the
levels of development is speculation because of the major unknowns--future
demand and cost for coal, and the extent that public policy will allow coal
development to proceed.
Because the number of possible alternative futures is great, this study
chose three-possibilities that might arise from the influences on coal de-
velopment in the Yellowstone River Basin. ·Two of these--low and high levels
of development--were chosen to represent limited development and highly
advanced development of coal resources. An intermediate alternative fills
the gap between the low-lev~l and the advanced-development alternatives.
A fourth and lowest alternative--gradually rising coal production to
1980 and practically stable production thereafter--was examined (see tables
2 and 3),,but it is not considered to be a practical possibility in view
of the pressures tending to encourage coal development in the United States.
Only if alternative sources of energy (such as the sun) or energy conservation
prove·to be more economically attractive than coal conversion is there likely
to be any such leveling off of Montana coal production within a decade.
For this study, a gradual rise in coal production is assumed to be inevitable
in view of existing coal sales contracts signed by six companies operating in
the Yellowstone River Basin.
Alternative levels of development presented here are based on data
from the Montana Energy Advisory Council (1974). Existing data were sup-
plemented and updated in response to more recent production figures. Coal
-15 -
production is given in million short tons (mmt) unless noted otherwise. (A
short ton is equal to 2,000 pounds.)
Table 2 displays estimates of coal production for 1975 and 1980 based
on existing coal sales contracts signed by the six companies. The coal
production tonnages have been reassembled according to two uses: electrical
generation in southeastern Montana and export out of Montana. Most coal
mined in Montana until 1980 under existing contracts will be shipped out
of state for use by Midwestern and Southern utilities in electrical generation.
Table 2. Coal production in 1975 and 1980 in the Yellowstone Basin based on
coal sales contracts (mmt).
Coal for Electrical Generation in Montana
Mining Company 1975 1980
Knife River Coal Co.
(for Sidney plant) 0.32 0.30
Western Energy Co.
(for Corette plant in Billings) 0.50 0.50
Western Energy Co.
(for Colstrip) 0.40 3.20
TOTAL 1.22 4.00
Coal for Export
Western Energy Co. 4.33 10.00
Decker Coal Co. 8.25 13.90
Westmoreland 4.00 6.50
Peabody 3.00 3.00
Shell Oil Co. 8.00
TOTAL 19.58 41.40
-16-
Synthetic-fuel facilities could become part of the Montana stabilized
coal-production alternative in the year 2000. In meeting the gap between
supply and demand for gas, it might be necessary to construct a synthetic
gas plant capable of producing 250 million standard cubic feet per day
(mmcf/d). It would consume approximately 7.6 mmt of coal per year. The
product of stabilized coal production during the remaining years of the
century would be consumed in the five major coal-consuming sectors of the
national economy as indicated in table 3. In this and all other alternatives,
consumption in the household-commercial and industrial sectors is insignifi-
cant after 1975 in comparison with the other consuming sectors.
Table 3. Stabilized coal production in the Yellowstone River Basin
1971 1975a
Consuming Sector (Actual) (Actual) 1980 1985 2000
Household and
Commercial 0.1 0.2 insig. insig. insig.
Industrial 0.1 0.2 insig. insig. insig.
Electrical
Generation 0.8 0.8 4.0 4.0 4.0
Synthetic Fuel 0 0 0 0 7.6
Exports 6.1 21.0 41.4 41.4 41.4
TOTAL 7.1 22.2 45.4 45.4 53.0
a Extrapolated from Montana 01~11C 1976, p. 83, table 5.6.
LOW LEVEL OF DEVELOPMENT
The study assumes that under low-level development coal production will
be limited to meeting Montana demands and supplying existing and planned
delivery contracts. The projections were derived from a combination of data
compiled by the Montana Energy Advisory Council (1974), the Northern Great
Plains Resource Program (1974b), and by companies planning coal production
for export. (Existing data were supplemented or updated since the MEAC
and NGPRP studies in respo~se to more recent production figures as they
became available.)
Table 4 shows coal production planned for export, by three mining com-
panies through the year 2000. These companies have leases for the coal but
are still engaged in planning. Although some contracts are signed, acceptance
of environmental impact statements for the mines and agreements on royalties
are still pending.
Combining this with information on existing sales contracts (table 2)
and coal production forecast by NGPRP (corrected to make it applicable to
-17-
Table 4. Planned coal production by company, mine, and year (mmt)
Production
Company
and Actual Planned
thne 976 1977 1978 1980 1981 1982 1983 1984 1985 2000
SHELL OIL co.a
Youngs Creek 0 0 0 8.0 8.0 8.0 8.0 8.0 8.0 8.0
Tanner Creek 0 0 0 2.0 4.0 4.0 4.0 4.0 8.0 8.0
\~ol f Mountain 0 0 0 2.0 2.0 4.0 4.0 4.0 4.0 8.0
Squirrel Creek 0 0 0 0 0 0 0 0 2.0 8.0
DECKER COAL CO.
East Decker 0 0 2.25 6.6 6.6 6.6 6.6 6.6 6.6 6.6
North Extension 0 0 0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
WESTMORELAND
Crow-Ceded Lands 4.0 4.5 4.5 4.0 4.0 10.0' 10.0 10.0 10.0 15.0
TOTAL 4.0 4.5 6.75 24.6 26.6 34.6 34.6 34.6 40.6 55.6
NOTE: Production shown here is in addition to the existing contracts
tabulated in table 2. Derived from 1975 data, partially updated in 1979.
aThe Shell Oil Company (Ireson 1979) says plans for these mines are
held in abeyance until litigation and negotiation with the Crow Tribe are
complete.
-18 -
the Yellowstone Basin only) yields a complete projection of coal production
to meet low-level consumption demands through the end of the century. It
is presented in table 5.
The Yellowstone Impact Study focused in particular on the years 1980,
1985, and 2000. Under the low-level development assumptions, there would
be 66 mmt mined for export in 1980; 114 mmt in 1985; and 171 mmt mined for
export in 2000.
Electrical generation facilities are projected to consume 4.0 mmt of
coal basin-wide in 1985 and 8.0 mmt in the year 2000. Another 7.6 mmt is
expected to be consumed by the single coal gasification plant envisioned
to be in operation by the end of the century under the assumptions of low-
level development. Table 6 indicates that, through 1985, only the Mid-
Yellowstone Subbasin would have energy conversion facilities. By 2000, the
Tongue Subbasin would have a 500-mw electrical generating plant.
Table 5. Coal production in the Yellowstone Basin under low-level
development (mmt).
1971 1975
1985b Consuming Settor (Actual) (Actual) 1980a
Household-
Commercial 0.1 0.2 insig. insig.
Industrial 0.1 0.2 insig. insig.
Electrical
Generation 0.8 0.8 4.0 4.0
Synthetic Fuels 0 0 0 0
Export from
Montana 6.1 21.0 66.0 114.0
TOTAL 7.1 22.2 69.8 118.0
aExisting contracts and planned exports.
bNGPRP data plus coal exports.
cNGPRP data plus coal exports.
insig.
insig.
8.0
7.6
171.1
186.7
Table 7 shows coal production by subbasin during the rema1n1ng years of
the century under the low-level development projections. The production
figures shown in table 5 thus appear in the basin totals for each of the
consumptive uses shown in the tables--electrical generation, gasification,
production of synthetic crude oil and fertilizer--plus exports. Under the
assumptions of low-level coal development in the Yellowstone Basin, export
of coal by slurry pipeline would play no part in coal exports through the
year 2000.
-19-
Table 6. Location of coal conversion facilities through the year 2000,
low-level development
1000-mw 250-mmdfd 100,000-b/d 2300-t/d
Electric Synthetic Synthetic Fertilizer
Generating Gas Plants Crude Plants Plants
Plants
1980
Mid-Yellowstone 1 0 0 0
All Others 0 0 0 0
TOTAL 1 0 0 0
1985
Mid-Yellowstone 1 0 0 0
All Others 0 0 0 0
TOTAL 1 0 0 0
2000
Tongue 0.5 0 0 0
Mid-Yellowstone 1.5 1 0 0
All Others 0 0 0 0
TOTAL 2 1 0 0
-20-
Table 7. Coal tonnage location by Yellowstone River subbasins, low -level
development, 1980, 1985, 2000 (mmt/y)
Electric
Subbasins Generation Gasification Syncrude Fertilizer Export a Total
1980
Tongue 0 0 0 0 29.7 29.7
Mid-Yellowstone 4.0 0 0 0 23.1 27.1
Powder 0 0 0 0 6.6 6.6
Bighorn 0 0 0 0. 6.6 6.6
TOTAL 4.0 0 0 0 66.0 70.0
1985
Tongue 0 0 0 0 51.3 51.3
Mid-Yellowstone 4.0 0 0 0 39.9 43.9
Powder 0 0 0 0 11.4 11.4
Bighorn 0 0 0 0 11.4 11.4
TOTAL 4.0 0 0 0 114.0 118.0
2000
Tongue 2.0 0 0 0 77 .o 79.0
Mid-Yellowstone 6.0 7.6 0 0 59.9 73.5
Powder 0 0 0 0 17.1 17.1
Bighorn 0 0 0 0 17.1 17.1
TOTAL 8.0 7.6 0 0 171.1 186.7
a All export at the low level of development was assumed to be by unit train
rather than slurry pipeline.
-21 -
INTERMEDIATE LEVEL OF DEVELOPMENT
The study assumes that under intermediate-level development coal
production and energy development will occur midway between the projections
for low and high levels of development. The intermediate level of development
may or may not be the most likely projection and should be regarded simply as
one possibility within the defined range for future coal and energy develop-
ment.
Coal tonnages that would be mined through the end of the century under
assumptions for intermediate-level development are displayed in table B.
The amounts of coal used by the consuming sectors in 1975 are based on data
in table 2 on long-term coal contracts. Each estimate for electrical
generation, synthetic fuel, or export for 1980, 1985, or 2000 in table 8 is
the mean between the low and high levels of development. The study assumes
that under intermediate-level coal development, 20 percent of coal exports
will be by slurry pipeline by the year 2000.
I
Table 9 indicates that under intermediate level development, only the
Mid-Yellowstone Subbasin would have energy conversion facilities in 1980
and 1985. The trend would be toward gradual additions to the mine-mouth
electrical generation capacity of the Mid-Yellowstone Subbasin, with three
1,000-mw generating plants and one 250-mmcf/d synthetic gas plant likely by
the year 2000. By that time, there would also be two 1000-mw electrical
generating plants in the Tongue River subbasin and one in the Powder River
subbasin.
Table 10 shows coal production by subbasin during the remaining years
of the century under the intermediate-level development projections The
production figures shown in table 8 appear in the basin-wide totals for each
of the consumptive uses shown in the table--electrical generation, gasifica-
tion, production of synthetic crude oil and fertilizer, and exports. By
the year 2000, under the assumptions of intermediate-level coal development
in the Yellowstone Basin, 20 percent of coal exports would be by slurry
pipeline (see "Export" column, table 10).
HIGH LEVEL OF DEVELOPMENT
The high-level of development estimate shows the extent to which
development of Yellowstone River Basin coal reserves would be pursued if
coal were used to fuel U.S. energy self-sufficiency and if its substitutes--
energy conservation, oil, natural gas, nuclear power, and alternative energy
sources--were unable to supply substantial shares. Table 11 shows coal
production tonnage to meet demand under high-level development.
-22-
Table 8. Coal production in the Yellowstone Basin under the intermediate
level of development (mmt)
1971 1975
Consuming Sector (Actual) (Actual) 1980 1985 ' 2000
Household and
Commercial 0.1 0.2 insig insig insig
Industri<:tl 0.1 0.2 insig insig insig
Electrical
Generation 0.8 0.8 4.0 8.0 24.0
Synthetic Fuel 0 0 0 0 7.6
Exports 6.1 21.0 68.6 154.6 293.2
TOTAL 7.1 22.2 72.6 162.6 324.8
Table 9. Location of coal conversion facilities through the year 2000,
intermediate level of development
1000-mw 1,000-b/d
Electric 250-mmcf/d Synthetic 2,300-t/d
Generating Synthetic Crude Fertilizer
Subbasin Plants Gas Plants Plants Plants
1980
Mid-Yellowstone 1 0 0 0
All others 0 0 0 0
TOTAL 1 0 0 0
1985
Mid-Yellowstone 2 0 0 0
All others 0 0 0 0
TOTAL 2 0 0 0
2000
Tongue 2 0 0 0
Mid-Yellowstone 3 1 0 0
Powder 1 0 0 0
All others 0 0 0 0
TOTAL 6 1 0 0
-23-
Table 10. Coal tonnage location by Yellowstone River subbasin, intermediate level of development, 1980, 1985,
2000 (mmt/y)
Electric Export
Subbasin Generation Gasification Sync rude Fertilizer Rail Slurry Total Total
1980
Tongue 0 0 0 0 30.8 0 30.8 30.8
Mid-Yellowstone 4.0 0 0 0 24.0 0 24.0 28.0
Powder 0 0 0 0 6.9 0 6.9 6.9
Bighorn 0 0 0 0 6.9 0 6.9 6.9
TOTAL 4.0 0 0 0 68.6 0 68.6 72.6
1985
I Tongue 0 0 0 0 69.5 0 69.5 69.5 N
-'==' Mid-Yellowstone 8.0 0 0 0 54.1 0 54.1 62.1 I
Powder 0 0 0 0 15.5 0 15.5 15.5
Bighorn 0 0 0 0 15.5 0 15.5 15.5
TOTAL 8.0 0 0 0 154.6 0 154.6 162.6
2000
Tongue 8.0 0 0 0 105.6 26.4 132.0 140.0
Mid-Yellowstone 12.0 7.6 0 0 73.3 20.5 102.6 122.2
Powder 4.0 0 0 0 23.4 5.9 29.3 33.3
Bighorn 0 0 0 0 23.4 5.9 29.3 29.3
TOTAL 24.0 7.6 0 0 225.7 58.7 293.2 324.8
Table 11. Coal production for consumption under high-level development,
Yellowstone Basin (mmt)
1971 1975
Consuming Sector (Actual) (Actual) 1980 1985 2000
Household and
Commercial 0.1 0.2 insig. insig. insig.
Industrial 0.1 0.2 insig. insig. insig.
Electrical
Generation 0.8 0.8 4.0 8.0 32.0
Synthetic Fuel
gas 0 0 0 0 22.8
crude 0 0 0 0 36.0
fertilizer 0 0 0 0 3.5
Exports 6.1 21.0 71.4 199.1 368.5
TOTAL 7.1 22.2 75.4 207.1 462.8
The 1980 projection of coal production for electrical generation shown
in table 2 is based on· coal production data tabulated by the Montana Energy
Advisory Council (1974). However, the coal export in 1980 is a combination
of the adjusted NGPRP data and recent changes in coal sales contracts. The
1985 projection of coal production for electrical generation is 8.0 mmt,
double the 1980 amount, because it was assumed that Colstrip Units 3 and 4
would be in operation by that date. The projection of coal production for
export in 1985, 199.1 mmt, was derived from NGPRP projections and from a
Missouri River Basin Commission (MRBC) study, Anal sis of Ener Pro·ections
and Implications for Resource Requirements (1976 • High-level coal develop-
ment estimates are based on assumptions that 20 percent of the coal in 1985
will be exported by slurry, increasing total export capacity to 199.1 mmt.
This figure includes coal moving by unit train.
Under high-level development projections for the year 2000, electrical
generation would consume 32.0 mmt of coal. This figure is derived from the
Western States Water Council's (1974) estimation of production of 8,260 mw
of electricity from coal for 1990.
The synthesis of fuel and fertilizer is estimated to require 61.3 mmt
of coal by 2000 under high-level development. Approximately 23 mmt of the
total would go toward synthesis of gas equivalent to the production of three
plants, each with the capacity of 250 million standard cubic feet per day
(mmcfd). The figure was derived from the NGPRP's high-development projection
of demand for substitute natural gas and was modified by MUCDS's findings
concerning the viability of coal gasification.
Because success of technology for the economical production of synthetic
liquid fuel from coal does not appear likely until the late 1990s, high-
level development does not assume the construction of a liquefaction plant
-25 -
until the year 2000. Two such plants are projected. The Stanford Research
Institute (1974) has estimated that one synthetic crude oil facility producing
100,000 barrels of crude per day would require 18 mmt of coal per year.
That amount is more than twice the quantity that would be consumed by a
synthetic natural gas plant of 250 mmcfd capacity.
One fertilizer plant is projected for southeastern Montana by the
year 2000 under high-level development. The present status of technology
makes development possibilities slim. The Koppers' Totzek process seems
to be the most feasible conversion process at this time and would require
a maximum of 3.5 mmt of coal per year to produce 2,300 tons of fertilizer
per day (t/d).
The export of coal in the year 2000 under high-level development is
projected to reach 368.5 mmt. This quantity was derived from the NGPRP's
high-development projection plus a 40 percent increase to account for the
use of slurry pipelines.
Table 12 shows the location by subbasin of the coal-based electrical
generation, synthetic gas, liquefaction, and fertilizer production plants
forecast under the assumptions of high-level development.
Table 13 shows coal production by subbasin during the remalnlng years
of the century under high-level development. The production figures shown
in table 11 appear in the basin-wide totals for each of the consumptive uses
shown in the tables--electrical generation, gasification, production of
synthetic crude oil and fertilizer--plus exports. Under th~ assumpticins of
high-level coal development in the Yellowstone Basin, exports of coal by
slurry pipeline would be 20 percent of coal exports by 1980 and 40 percent
by 2000 (see export column, table 13).
SUMMARY OF LEVELS OF DEVELOPMENT
A gradual rise in coal production to 1980 at least is practically
inevitable based on the demand for coal represented in existing coal sales
contracts. Low-level development projections reflect the existing situation
plus the added demand of planned coal-for-export sales contracts. (The pro-
jected low-level demand for coal is similar to the intermediate coal
development_profile of the Northern Great Plains Resource Program (1974b).)
High-level development is a projection of coal production based on assumptions
about U.S. energy use under a policy of national self-sufficiency and a
reliance on coal rather than energy c~nservation, alternative energy sources,
oil, natural gas, and nuclear power. (An implicit assumption is that the coal
would be produced in western strip mines rather than eastern underground
mines.) Under high-level development, coal production tonnages could reach
the totals indicated in table 14. Intermediate-level development projections·
represent means between the low and high levels of development. As far as
we know, no one of the three development levels is more probable than the
others.
Figure 3 presents a graph of coal production in the Yellowstone River
Basin for the three levels of development during the remaining years of the
-26-
Table 12. Location of coal conversion facilities through the
high-level development
year 2000,
1000-mw 100,000-b/d
Electric 250-mmcf/d Synthetic 2300-t/d
Generating Synthetic Crude Fertilizer
Subbasin Plants Gas Plants Plants Plants
1980
Mid-Yellowstone 1 0 0 0
All others 0 0 0 0
TOTAL 1 0 0 0
1985
Mid-Yellowstone 2 0 0 0
All others 0 0 0 0
TOTAL 2 0 0 0
2000
Tongue 3 1 1 0
Mid-Yellowstone 3 2 1 0
Powder 1 0 0 0
Bighorn 1 0 0 0
Lower Yellowstone 0 0 0 1
TOTAL 8 3 2 1
-27-
Table 13. Coal tonnage location by Yellowstone River subbasins, high-level development, 1980, 1985,
2000 (mmt/y)
Electric Export
Subbasin Generation Gasification Sync rude Fertilizer Rail Slurry Total Total
1980
Tongue 0 0 0 0 32.2 0 32.2 32.2
Mid-Yellowstone 4.0 0 0 0 25.0 0 25.0 29.0
Powder 0 0 0 0 7.1 0 7.1 7.1
Bighorn 0 0 0 0 7.1 0 7.1 7.1
Lower Yellowstone 0 0 0 0 0 0 0 0
TOTAL 4.0 0 0 0 71.4 0 71.4 75.4
1985
I Tongue 0 0 0 0 71.7 17.9 89.6 89.6 N
(X) Mid-Yellowstone 8.0 0 0 0 55.8 13.9 69.7 77.7
Powder 0 0 0 0 15.9 4.0 19.9 19.9
Bighorn 0 0 0 0 15.9 4.0 19.9 19.9
Lower Yellowstone 0 0 0 0 0 0 0 0
TOTAL 8.0 0 0 0 159.3 39.8 199.1 207.1
2000
Tongue 12.0 7.6 18.0 0 99.5 66.3 165.8 203.4
Mid-Yellowstone 12.0 15.2 18.0 0 77.3 51.6 128.9 174.1
Powder 4.0 0 0 0 22.1 14.8 36.9 40.9
Bighorn 4.0 0 0 0 22.1 14.8 36.9 40.9
Lower Yellowstone 0 0 0 3.5 0 0 0 3.5
TOTAL 32.0 22.8 36.0 3.5 221.0 147.5 368.5 462.8
-~------------
Table 14. Coal production for consumption under three levels of development,
Yellowstone River Basin, through the year 2000 (mmt/y)
Consuming Low Intermediate High
Sector Level Level Level
1971 (Actual)
Household and Commercial 0.1 0.1 0.1
Industrial 0.1 0.1 0.1
Electrical Generation 0.8 0.8 0.8
Synthetic Fuel. 0 0 0
Exports 6.1 6.1 6.1
TOTAL 7.1 7.1 7.1
1975 (Actual)
Household and Commercial 0.2 0.2 0.2
Industrial 0.2 0.2 0.2
Electrical Generation 0.8 0.8 0.8
Synthetic Fuel 0 0 0
Exports 21.0 21.0 21.0
TOTAL 22.2 22.2 22.2
1980
Household and Commercial insig. insig. insig.
Industrial insig. insig. insig.
Electrical Generation 4.0 4.0 4.0
Synthetic Fuel 0 0 0
Exports 66.0 68.6 71.4
TOTAL 70.0 72.6 75.4
1985
Household and Commercial insig. insig. insig.
Industrial insig. insig. insig.
Electrical Generation 4.0 8.0 8.0
Synthetic Fuel 0 0 0
Exports 114.0 154.6 199.1
TOTAL 118.0 162.6 207.1
2000
Household and Commercial insig. insig. insig.
Industrial insig. insig. insig.
Electrical Generation 8.0 24.0 32.0
Synthetic Fuel
Gas 7.6 7.6 22.8
Crude 0 0 36.0
Fertilizer 0 0 3.5
Exports 171.1 293.2 368.5
TOTAL 186.7 324.8 462.8
-29-
400
350
300
250
en c:
0
1--... 200 0 ..c.
(/)
c:
0
~
150
100
50
1971 1975 1980 1985
Years
1990 1995
Figure 3. Base, low, intermediate and high alternative
futures for coal production in the Yellowstone River Basin.
-30-
2000
century. It is obvious from the graph that the year 1980 will be a signifi-
cant turning point for questions of public policy associated with coal devel-
opment.
Until 1980, under all three development assumptions, only the Mid-
Yellowstone Subbasin would have energy conversion facilities--the equivalent
of one 1,000-mw power plant. By 1985, under intermediate or high-level
development, the Mid-Yellowstone would have two 1,000-mw power plants.
Table 15 illustrates the situation by the end of the century. With
low-level development, there would be a total of 2000 mw of electrical
generation in the Mid-Yellowstone and Tongue Subbasins, and there would be
one 250-mmcf/d synthetic gas plant in the Mid-Yellowstone. With intermediate-
level development, there would be 6,000 mw of electrical generation facilities:
half of it in the Mid-Yellowstone, 2,000 mw in the Tongue, and 1,000 mw in the
Powder. The Mid-Yellowstone would have one synthetic gas plant.
With high-level development, the addition of a 1,000-mw power plant in
the Bighorn Subbasin would bring to four the total of subbasins with energy
conversion plants. The Tongue Subbasin would have yet another power plant
under high-level development, for a basin total of 3,000 mw, and would
contain a 250-mmcf/d synthetic gas plant and a 100,000-b/d synthetic crude
oil plant as well. The Mid-Yellowstone Subbasin would have one synthetic
crude oil plant and two synthetic gas plants in addition to its power plants.
The Lower Yellowstone Subbasin also would enter the picture with a 2,300-t/d
fertilizer plant. Four subbasins would remain unaffected by direct impacts
of energy facilities under high-level development even in the year 2000;
Upper Yellowstone, Billings Area, Clarks Fork Yellowstone, and Kinsey Area.
WATER USE ASSOCIATED WITH
PROJECTED ENERGY DEVELOPMENT
. Annual water and coal consumption requirements for the conversion
plants envisioned have been calculated (see table 16). Using the water-
use information in table 16 and information on the expected numbers of
energy conversion .facilities in each subbasin, a comprehensive picture of
water use by subbasin for the years 1980, 1985, and 2000 is presented in
tables 17, 18, and 19. The basin-wide totals for all uses in 1980, 1985,
and 2000 are 18,770, 61,995, and 321,175 af/y, respectively, under high-
level development.
-31-
Table 15. Coal Conversion in the Yellowstone Basin in 2000
Electric
Generation SNG Sync rude Fertilizer
Subbasin a (mw) (mmcf /d) (b/d) (t/d)
LOW-LEVEL DEVELOPMENT
Bighorn 0 0 0 0
Mid-Yellowstone 1,500 250 0 0
Tongue 500 0 0 0
Powder 0 0 0 0
Lower Yellowstone 0 0 0 0
TOTAL 2,000 250 0 0
INTERMEDIATE-LEVEL DEVELOPMENT
Bighorn 0 0 0 0
Mid-Yellowstone 3,000 250 0 0
Tongue 2,000 0 0 0
Powder 1,000 0 0 0
Lower Yellowstone 0 0 0 0
TOTAL 6,000 250 0 0
HIGH-LEVEL DEVELOPMENT
Bighorn 1,000 0 0 0
Mid-Yellowstone 3,000 500 100,000 0 Tongue 3,000 250 100,000 0 Powder 1,000 0 0 0 Lower Yellowstone 0 0 0 2,300
TOTAL 8,000 750 200,000 2,300
aThe four subbasins not listed (Upper Yellowstone, Billings Area, Clarks
Fork Yellowstone, and Kinsey Area) are not expected to include sites for coal
conversion facilities.
-32-
Table 16. Annual water and coal requirements for coal processes
Process Water
Thermal-electric generation 15,000 af/y/1,000 mw
Gasification 9,000 af/y/250 mmcf/d
Syncrude 29,000 af/y/100,000 b/d
Fertilizer 13,000 af/y/2,300 t/d
Slurry
Strip Mining
750 af/mmt
50 af/mmt
-33-
Coal
4 mmt/1,000 mw
7.6 mmt/250 mmcf/d
18 mmt/100,000 b/d
3.5 mmt/2,300 t/d
Table 17. Water use in coal mining and electrical generation by 1980 by subbasin
(af/y)
Subbasin a
Tongue
Mid-Yellowstone
Powder
Bighorn
TOTAL
Tongue
Mid-Yellowstone
Powder
Bighorn
TOTAL
Tongue
Mid-Yellowstone
Powder
Bighorn
TOTAL
Elec.
Generation
LOW-LEVEL DEVELOPMENT
0
15,000
0
0
15,000
Strip
Mining
1,490
1,360
330
330
3,510
INTERMEDIATE-LEVEL DEVELOPMENT
0 1,540
15,000 1,400
0 350
0 350
15,000 3,640
HIGH-LEVEL DEVELOPMENT
0 1,610
15,000 1,450
0 360
0 360
15,000 3,780
Total
1,490
16,360
330
330
18,510
1,540
16,400
350
350
18,640
1,610
16,450
360
360
18,780
aFour subbasins (Upper Yellowstone, Billings Area, Clarks Fork Yellowstone,
and Kinsey Area) are not expected to experience water depletion associated with
coal development. The Lower Yellowstone Subbasin would be subject to coal
development only by the year 2000.
-34-
Table 18. Water use in coal mining, transportation and conversion processes by
1985 by subbasin (af/y)
Subbasin a Elec. Total
Generation
Slurr~
Export
Strip
Mining
Tongue
Mid-Yellowstone
Powder
Bighorn
TOTAL
0
15,000
0
0
15,000
LOW-LEVEL DEVELOPMENT
0
0
0
0
0
2,570
2,200
570
570
5,910
2,570
17,200
570
570
20,910
INTERMEDIATE-LEVEL DEVELOPMENT
Tongue 0 0 3,480 3,480
Mid-Yellowstone 30,000 0 3,ll0 33 'llO
Powder 0 0 780 780
Bighorn 0 0 780 780
TOTAL 30,000 0 8,150 38,150
HIGH-LEVEL DEVELOPMENT
Tongue 0 6, 720 4,480 11 '200
Mid-Yellowstone 30,000 10,430 3,890 44,310
Powder 0 1,500 1,000 2,500
Bighorn 0 3,000 1,000 4,000
TOTAL 30,000 21,650 10,370 62,010
aThe four subbasins not shown (Upper Yellowstone, Billings Area, Clarks Fork
Yellowstone and Kinsey Area) are not expected to experience water depletion associa-
tion with coal development. The Lower Yellowstone Subbasin would be subject to coal
development only by the year 2000.
bit is assumed that half of the water for slurry in the Tongue and Powder subbasins
will be from deep ground water, and half fromsurface water. In the Mid-Yellowstone
and Bighorn subbasins, all water for slurry is assumed to come from surface supplies.
-35-
Table 19. Water use in coal m1n1ng, transportation and conversion processes by
2000 by subbasin (af/y)
INCREASE IN DEPLETION
Elec. Gasi fi-Syn-Ferti-Slurryb Strip
Subbasin a Generation cation crude lizer Export Mining Total
LOW-LEVEL DEVELOPMENT
Bighorn 0 0 0 0 0 B60 860
Mid-Yellowstone 22,500 9,000 0 0 0 3,680 35,180
Tongue 7,500 0 0 0 0 3,950 ll ,450
Powder 0 0 0 0 0 860 860
Lower Yeilowstone 0 0 0 0 0 0 0
Total 30,000 9,000 9,350 48,350
INTERMEDIATE-LEVEL DEVELOPMENT
Bighorn 0 0 0 0 4,420 1,470 5,890
Mid-Yellows tone 45,000 9,000 0 0 15,380 6,110 75,490
Tongue 30,000 0 0 0 9,900 7,000 46,900
Powder 15,000 0 0 0 2,210 1,670 18,880
Lower Yellowstone 0 0 0 0 0 0 0
Total 90,000 9,000 31,910 16,250 147,160
HIGH-LEVEL DEVELOPMENT
Bighorn 15,000 0 0 0 ll ,100 2,050 28 '150
Mid-Yellowstone 45,000 18,000 29,000 0 38,700 8,710 139,410
Tongue 45,000 9,000 29,000 0 24,860 10,170 ll8 ,030
Powder 15,000 0 0 0 5,550 2,050 22,600
Lower Yellowstone 0 0 0 13,000 0 0 13,000
Total 120,000 27,000 58,000 13,000 80,210 22,980 321,190
aThe four subbasins not shown (Upper Yellowstone, Billings Area, Clarks Fork
Yellowstone, and Kinsey Area), are not expected to experience water depletion
associated with coal development.
bit is assumed that half of the water from slurry in the Tongue and Powder
subbasins will be from deep ground water and half from surface water. In the Mid-.
Yellowstone and Bighorn subbasins, all water for slurry is assumed to come from
surface supplies.
-36-
The use of irrigated agriculture in the Yellowstone Basin has been
increasing for the past few years, possibly reversing (at least temporarily)
a long-term downward trend. Forecasting the extent of further expansion
of irrigated agriculture to the year 2000 is complicated. General economic
conditions, federal import and export policies, and world eating habits
greatly affect crop prices. Many agricultural products grown in the basin
through irrigation methods are used for the production of beef, which has
a highly variable market. Farmer preferences and peer influences are
significant.but unpredictable in determining whether a farmer will decide
to expand irrigation. Finally, adequate land and an accessible water supply
are necessary. This study considers water and land availability and
economic constraints in projecting the amount of irrigation in the Yellowstone
Basin through the year 2000.
Previous studies of irrigated agriculture illustrate a range of
approaches to these problems. Some of these studies forecast future develop-
ment, and others analyze specific projects or geographical areas for ,
irrigation feasibility. The OBERS Series C projections (U.S. Water Resources
Council 1972) were based on estimates of anticipated supply and demand and
historical trends. However, because irrigated agri~ulture has been
declining until recently, the OBERS study predicted only small increases in
Montana's irrigated acreage to meet anticipated national demand in the year
2020. It became obvious that OBERS study predictions were wrong when the
projections for 2020 were surpassed in 1974. So DNRC developed new pro-
jections based on the OBERS red meat projections (Montana DNRC 1976).
Neither of these studies considered the availability of suitable land or
the economic limitations of irrigated agriculture. The study reported here
takes these factors into account.
The Bureau of Reclamation (USSR 1955, 1959, 1963, 1971, 1972) has
conducted irrigation studies in several areas of the Yellowstone Basin.
Information is available for the Powder, Tongue, and Bighorn rivers, and for
several projects along the mainstem of the Yellowstone. The economic
analysis of these projects was updated for the Yellowstone Level 8 Study.
A single-purpose irrigation study used in its original form (Frederiksen
1976) analyzed additional projects for inclusion in the Level 8 Study. Both
of these studies considered large projects only and either explicitly ar
implicitly assumed_there would be a cooperative effort to build and operate
them. However, recent irrigation development in the basin has occurred
primarily through private development with little or no cooperation among
farmers to coordinate the installation of water-delivery systems; therefore,
this study analyzes irrigation development in the Yellowstone Basin by
postulating a collection of individual developments rather than cooperative
projects.
-37-
t~ETHODS
The objective of this study is to provide agricultural water-demand
projections for a hydrologic model of the Yellowstone River Basin. Data
were gathered and analyzed to provide general information on water demand,
rather than identification of any specific development project. Three
classes of information were used to identify potential water demand: 1) identi-
fication of irrigable land, 2) calculation of irrigation costs, and 3) analysis
of the ability to pay these costs based on farm budgets.
IDENTIFICATION OF IRRIGABLE LAND
By systematically appraising soil, relief, and climate, parcels
of land may be classified based on their suitability for irrigation. Land
classification surveys made by the Water Resources Division, DNRC, were
designed to investigate the theoretical potential of the land in the Yellow-
stone Basin to sustain irrigated farming. The term "irrigable land," as
used here, denotes land with soils, topography, and drainage features
appropriate for irrigation by either ,gravity or sprinkler methods. Such land
is divided into classes on the basis of its relative potential for irrigated
farming. Class 1 irrigable land has potentially high productive value;
class 2 ~irrigable land has intermediate value, and class 3 irrigable land
has the lowest suitability for irrigation among the classes. To perform
the classification process for the Yellowstone River Basin, broad assumptions
were necessary in areas where little soil information was available; conse-
quently, this survey should not be considered adequate for detailed plans.
Table 20 lists the classification criteria.
The land classification survey identified 2,200,000 acres of
irrigable land in the basin. However, the survey considered neither
water availability no.r economic limitations of potential irrigation
systems. For this study, water was considered to be available only from
the Yellowstone River and its four main tributaries in Montana (Clarks Fork,
Bighorn, Tongue, and Powder). Preliminary economic limitations were defined
by using calculations from first drafts of the farm-budgets and water-
delivery analyses. Th~se preliminary calculations helped define potentially
irrigable land as that no more than 3 mi from the river and no more than
450 ft above the river. Hence the total of potentially irrigable land was
reduced to 440,000 acres. That land was divided into categories according
to lift (50-ft increments), and pipeline length (~-mi increments) for each
subbasin (table 21). Irrigation costs were calculated for each category.
CALCULATION OF IRRIGATION COSTS
In this study irrigation costs were divided into water-delivery
costs and water-application costs. Water-delivery cost was defined as the
total cost of pumping water from the river to the point of application.
Water-application cost was defined as the cost of owning and operating a
center-pivot sprinkler system.
-38-
J
·I
.I
'I
I
.:1
I
Table 20. Land classification specifications
Soil or Land
Characteristics
l. Dominant texture of
root zone
2. Depth to clean
sand, gravel and
cobble
3. Hard rock, sandstoBe
or nonsaline shale
4. Textural 11odi fiers c
a. Volume of tillage layer:
Gravel ( -3 in)
Cobble (3-10 in)
b. Stoniness of surfaced
and tillage layer,
stones generally
greater than 12 in
in diameter
c. Rockiness (small out-
crops within soil type)
5. Available waterholding
capacity (to a maximum
depth of 4 ft)
6. Permeability
7. Salinity and/or
alkalinitye
8. Slope
9. \;ater table
drainage
10. Drainage overflo1•
11. Climate
Class 1 -
Only Slight
Limitationsa
Fine sandy loam to
friable clay loam
40 in minimum
60 in minimum
No tillage problem
15 percent
No tillage problem
No tillage problem
Less than 2 percent of
bedrock exposed.
l·lore than 6 in
l·loderately slow--.20 in/
hr to moderate--2.00 in/hr,
may exceed 2 in if suffici-
ent water holding capacity
is maintained--by field
observation of soil texture
and structure
Electrical conductivity not
to exceed 4 millimhos/cm;may
be higher under good leach-
ing and drainage conditions.
Sut not to exceed 8 millim-
hos/cm in top 4 ft
0 to 4 percent
Easily maintained below
5 ft depth during growing
season
:llo overflow
Growing season greater
than 90 days
SOURCE: l-lontana DNRC (unpublished).
CONVERSIONS: ft
in
30.4 em
2. 54 em
Class 2 -
l·loderate
Limitationsa
Loamy sand to
permeable clay
20 in minimum
40 in minimum
l·loderate tillage problem
15-50 percent -~ in
15 percent (3-10 in)
Cultivation not impractical.
Stones 12 in diameter occupy
0.01 to 0.1 percent of the
surface, and 0.15 to 1.5
cubic yards/acre-foot
2 percent of surface may have
bedrock exposed.
l·lore than 4 in
Slow--.06 in/hr to moderately
rapid--2.00 to 6.30 in/hr--
by field observation of soil
texture and str11cturc.
Electrical conductivity not
to exceed 8 millimhos/cm;
except under good leaching
and drainage conditions. Host
horizons will have less than
8 millimhos/cm.
Less than 8 percent
Practical to maintain below
40 in de-pth most of the time
in growing season (requires
drainage)
Free of overflow in grm•ing
season
Growing season greater than
90 days
Class 3 -
Severe
Limitations"
Loamy sand to clay (sands
with su ffic.i ent 1'/IIC. can
be included)
10 in minimum
30 in minimum
Severe tillage problem
-50 percent -3 in
15-50 percent 3-10 in
Cultivation impractical
unless cleared. Stones
12 in diameter; occupy
0.1 to 3 percent of the
surface, and 1.5 to 50
cubic yds/acrc-fool.
2 to 10 percent surface
may have bedrock exposed.
l·lore than 2 in
Very slow--less lhan .06
in/hr only in thin layers.
To rapid--greater than
6.30 in/hr if upper 4 ft.
of soil has sufficient
water holding capacity--by
field observation of soil
texture and structure.
Electrical conductivity
not to exceed 0 millimhos/
em in top 2 ft. Lower
l1orizons may l1e hiqher under
good leaching and drainage
conditions, but not to
exceed 15 millimhos/cm.
15 percent (sprinkler irri-
4ation on slopes more than
8 percent)
Can maintain below 20 in
most of the growing
season.
Ovnrflow may be hazard to
crops in 2 or 3 of 10 yrs
Growing season may be less
than 90 days
aAny one deficiency below the limits of a class is cause for downgrading to next lower class. h10 or more such
deficiencies may cause downgrading two classes if judgment indicates they arc additive. Combinations of less-severe
deficiencies may or may not effect a change in ·class.
bSoils known to be underlain by saline shale at depths as shallow as 60 in are excluded from Closs l through 3.
cln areas where the planned agricultural use is of demonstrated suitability, any modifier can he rated irrignhle
for special uses not requiring tillage.
dFor detailed description see USDA, 1951 Soil Survey 1-innual, pp. 217 'lnd 220.
eSlight or moderate salinity or alkalinity may exclude soils from Classes 1 through 3 if associated with a slow-permeable
substratum, or saline shale, or both. If leaching is not practical, u soil may be excluded from irriguhle clAss if ex-
changeable sodium is greater than 3.0 millequivalents per 100 grams and/or if sodium absorption ratio is greater than 12
millequivalcnts per 100 grams, in any so.il with cation-exchange capacity less than 25 millequivalento per 100 grams.
-39-
Table 21. Irrigable acreage by lift (fl), pipeline length (mi) and subbasin
in Yellowstone River Basin
Lift
Pipe
length 50 100 150 200 250 300 )50 400 450 Total
UPPER YELLOWSTONE SUBBASIN
.5 JB,076 1,014 39,090
1.0 1,404 3,962 1,601 6,967
1.5 670 1,235 J, 252 l,OB7 6,244
2.0 2,391 1,533 2,649 3,613 10 ,1B6
2.5 0
3.0 0
Total JB,076 5,479 1,235 3,252 0 5,495 0 4,250 4,700 62,4B7
CLARKS FORK YELLmiSTONE SUBBASIN
.5 2,160 392 766 442 3, 760
1.0 203 203
1.5 4'i6 3,432 2,157 6,025
2.0 1,006 1,006
2.5 3 '715 J. 715
3.0 B91 B91
Total 2,160 595 1,442 766 3. 715 4,765 0 2,157 0 15,600
BILLINGS AREA SUB BAS IN
.5 3 ,JOB J ,324 329 2,147 222 9,330
1.0 347 71 B,OB4 1,305 1,254 447 11,50B
1.5 110 3, 549 5B5 442 B7B 5,564
2.0 165 99B 27B 2,325 3,766
2.5 446 446
3.0 11B 662 780
Total 3,765 3,67B 11,962 4,037 1,440 2,354 27B 3,21B 662 Jl, 394
BIGHORN SUBOASIN
.5 4,47B 1,309 5, 7B7
1.0 1,60B 3,451 949 1,054 7,062
1.5 2,191 2,191
2.0 1 ,431 7BJ JB4 2. 59B
2.5 l,JB7 5Bl 1,96B
3.0 3,734 1,159 4,B93
Total 6,U~6 I ,Vl~ ~,UU4 L,~~6 u J~4 u u u l4,49~
I~ID-YELLOI1STONE SUBBASIN
.5 16,000 1,691 17,691
1.0 3,180 4 ,J5B 4,616 2,B02 297 15' 253
1.5 4,004 2,270 4,522 309 2,071 13,176
2.0 B20 257 2,693 6,6Bl ),353 1,149 14,953
2.5 42B 3,534 4 ,B51 B,B13
3.0 1 979 2 459 1 5JB 5 976
lola! 20,000 l0,7JB 9,2BB D,2B7 B,l72 B,76B J,609 0 0 75,B62
KINSEY AREA SUBBASIN
• 5 J,24B l,lBO 4,42B
1.0 539 539
1.5 JOB 2,035 731 3,074
2.0 464 546 1,405 2,415
2.5 0
J.O 0
Total 3,556 2,499 549 l,lBO 0 1,277 1,405 0 0 10,456
TONGUE SUBBASIN
.5 21,947 0 21,947
1.0 0
1.5 9BJ 1,004 1,9B7
2.0 0
2.5 529 529
3.0 0
Total 21,947 0 0 9BJ 1,004 529 0 0 24,463
POWDER SUBBASIN
• 5 74.224 74,224
1.0 9Bl 9Bl
1.5 993 1,2BB 2,2Bl
2.0 2,612 2,612
2.5 6,B72 6,B72
J.O 904 27 040 27 944
Total 75.205 0 0 u 995 J,900 I, 776 Ll ,040 0 114,914
l011ER YELlOWSTONE SUBBASIN
.5 23,677 l,B04 1, 775 27,256
1.0 .l,B13 4,992 4,BB7 11 ,692
1.5 2. 599 792 JB6 12,JB9 16,166
2.0 805 4,B07 2,120 1,603 564 537 290 10.726
2.5 350 5,101 5,451
).0 96) 355 1 )41 6 56) 9 222
Total 25,490 11,163 7,374 3,211 1,603 564 l,B7B 29.230 0 00.513
-40-
Water Delivery Costs
The cost of deliveri~g water to the farm depends on the lift, distance,
and amount of water delivered. Because of the large size of the study area
and limitations of data, plans could not be tailored fa~ individual farm
sizes, irrigation layouts, and soils data. Therefore, several assumptions
and generalizations were made.
A hypothetical 320 acre farm was used as the basis for all calculations.
Water would be diverted at the rate of 1 cfs/50 acres (6.4 cfs/farm). Crop
water requirements were set at 2.84 acre-feet/acre, including a 65 percent
irrigation efficiency factor (USDA 1974). Therefore, the annual water re-
quirement for the 320-acre farm would be 908 acre-feet. We assumed that the
pumps would be electric and would require 1,717 hours of operation per year.
The cost of electricity was assumed to be $.01/kWh.
Using the foregoing assumptions, a computer program was used to calculate
the annual cost of delivering water to the farm. All equations and cost
factors were provided by the U.S. Bureau of Reclamation (USBR), and were
updated to January 1976 prices.
The initial investment for vertical pumps was determined from the equation:
c = (QI)(6.10TDH + 600)
where: c = cost of pumps ($)
Q = flow rate (6.4 cfs)
I = Cost index factor (2.09)
TDH = Total dynamic head
Total dynamic head equals static lift plus friction loss. Static
lift was divided into 50-ft increments from 50 to 450 ft, and friction loss
was computed using the Chezy-Manning formula with a roughness coefficient of
n = 0.010.
where: v = velocity (6.4cfs/area of pipe)
n = Mannings coefficient (0.010)
L = pipe length
R = hydraulic raidus (pire diameter/4)
The total investment in pumps, housing, electrical panels, and installa-
tion was assumed to be four times the cost of the pumps (USBR cost analyses).
The initial cost of the pipe was provided by the USBR (tables 22 and 23),
and excavation costs were determined from the equation:
-41-
Excavation cost = 3 WDL/27
where: W = width (twice the pipe diameter in ft)
D = depth (6 ft plus pipe diameter)
L = pipe length
Annual investment costs were obtained by amortizing the initial invest-
ment of pumps and pipe over 10 years at 10% interest, using a capital re-
covery factor of 0.16275.
Annual operation costs were calculated from the equation:
Operation cost= (1.8Q"47 )(TDH)"46 (T/168)"34 (1.2W +I ) c w
where: Q = flow rate (6.4 cfs)
TDH = total dynamic head
T = operation time (1,717 hours)
W = workers wages ($5.83/hour) c
I = costs index factor (1.87) c
Maintenance costs were calculated .from the equation:
Maintenance cost = (2Q·11 )(TDH)"41 (af)"43 (0.49W + I ) c w
where: Q = flow rate (6.4 cfs)
TDH = total dynamic head
af = water pumped (908 acre-feet/year)
W = workers wages ($5.83/hour) c
I = cost index (1.87) w
Finally, electricity costs were calculated from the equation:
C = (UQT)(TDH)/8.8E
where: U = electricity cost/k~vh ($.01/k~~h)
Q = flow rate (6.4 cfs)
T = time of operation (1,717 hours)
TDH = total dynamic head
E = pump efficiency factor (.7)
-42-
The total annual costs of operation, maintenance, and electricity
were added to the amortized cost of the pumps and pipe. All calculations
were repeated for each pipe size, and the most economical system was
selected. ·Water delivery costs were then calculated for each lift and dis-
tance category, and are displayed in table 24.
Table 22. Concrete pipe costs ( $/ft)
Diameter (in)
Head
(ft) 12 18 24 30
50 8.94 14.72 21.26 28.34
100 9.27 15.26 22.89 30.52
150 9.59 16.35 23.98 32.70
200 10.79 18.53 27.25 37.06
Table 23. Steel pipe costs ($/ft)
Diameter (in)
Head
( ft) 12 18 24 30 36 42 48
50 10.90 21.80 32.70 43.60 57.77 70.85 87.20
100 14.17 25.07 35.97 46.87 61.04 78.48 93.74
150 18.53 29.43 40.33 51.23 65.40 81.75 102.46
200 25.07 35.97 46.87 57.77 80.66 100.28 123.17
300 38.15 49.05 59.95 70.85 91.56 112.27 143.88
350 45.78 56.68 67.58 78.48 99.19 118.81 154.78
400 49.05 59.95 70.85 81.75 102.46 134.07 164.59
450 56.68 67.58 78.48 89.38 110.01 143.88 176.58
-43-
Table 24. Annual water-delivery costs ($/acre)
Elevation
Length
(mi) 50 100 150 200 250 300 350 400
0.5 55 68 79 105 116 136 147 167
1.0 79 93 133 144 168 184 207 223
1.5 103 117 172 202 213 250 261 299
2.0 128 142 212 247 258 304 315 362
2.5 152 167 251 292 303 358 369 424
3.0 176 192 291 337 348 412 423 487
a Steel pipe is unsuitable for these pressures.
Water Application Costs
Water application costs were derived from information provided by
Montana State University (Montana State University 1969).
-
450
178
247
310
373 a
a
Table 25 itemizes the cost of owning and operating one center-pivot
sprinkler system. Changes that were made in the CES data to make the costs
compatible with farm budget estimates are included under the column labeled
NOTES. The initial cost of all equipment was amortized over 10 years at 10
percent interest (Capitol Recovery Factor = 0.16275) and added to the annual
operating costs. The data then were indexed to December 1975 prices (Water
Resources Council unpublished) to yield an annual cost of $66/acre.
Initial investment
Annual payment
~1aintenance
Electricity
Labor
Taxes
Insurance
TOTAL
per acre
Table 25. Center-pivot irrigation costs
Costs
$48,022
7,816
158
652
175
768
288
9,857
66
-44-
Notes
10% over 10 years
0.33% of investment
65,180 kWh/yr ® 1 mill/kWh
$2.50/hr, 70 hrs/yr
160 mills on 10% of investment
.6% of investment
148 irrigated acres
FARM BUDGETS AND THE ABILITY TO PAY FOR IRRIGATION
The potential for expanding irrigated land, of course, depends heavily
on returns that can be expected on the investment. For each subbasin,farm
budgets were prepared reflecting local cropping patterns. The budgets in-
cluded the specific costs and returns associated with irrigated-crop pro-
duction, plus generalized farm costs such as investment, maintenance, and
repair of buildings and fences. Because the budgets included all costs
associated with an irrigated farm (except water delivery and application).
including payments to th~ fa~mer for his labor, management, and investment,
profit after sale of the irrigated crops was assumed to he available to pay
for irrigation.
Historical records (Montana Department of Agricultura 1946-74) were used
to develop cropping patterns for each subbasin. All crops produced in each
area were placed into one of four categories. Sugar beets represented all
high-value cash crops such as beets or dry beans. Barley represented the
grain crops, alfalfa represented all hay, and corn silage represented silage
crops including ~nsiled hay and beet tops.
All calculations were based on the hypothetical 320-acre farm because
data were readily available from the USBR for that siz~ of operation. The
farmstead, roads, ditrhes, and wasteland accounted for 18 acres (5.6 percent);
the remaining 302 acres were assumed to be available for crop production.
Far convenience, costs and revenues were divided into four categories: fixed
costs, variable costs, revenues, and perquisites.
Fixed Costs
Fixed costs included those incurred regardle~s of the acreage planted to
a particular crop. Depreciation, repair, taxes, and investment are all fixed
co~ts; they are listed in table 26. Depreciation was calculated on all
buildings, machinery~and equipment using a 6.5 percent sinking fund factor
over the expected life of the item. Repair costs were assumed to be 2 percent
of the value of buildings and improvements, and 2.5 percent on machinery and
equipment. A 7.1 percent return was calculated on all investments.
Taxes were assumed to be levied against 30 percent of the assessed value
on land and buildings and 20 percent on machinery and equipment. The assess-
ed value of an acre of irrigated land was assumed to be $48.00. Buildings
and improvements were assumed to be assessed at 40 percent, and machinery
and equipment at 50 percent of their average values. The mill levy in the
Yellowstone Basin was assumed to average 160 mills.
Depreciation and repair costs for automobiles and trucks, based on
mileage estimates, are shown in table 27. Fixed costs for insurance,
telephone, and electricity also are included in table 27.
-45-
Table 26. Inventory of buildings, machinery and equipment; investment, repair,
depreciation, and taxes for a hypothetical 320-acre farm
t~arket Annual Annual Expected Annual Annual
Item Value Investment Repairs Life (yrs) Depreciation Tax
Land $ 80,000 $ 5,680 $ 737
House 22,200 1,576 $444 50 $65 426
Garage 2,200 158 44 40 13 42
Granary 1,665 ll8 33 20 43 32
Shop 1,665 ll8 33 20 43 32
Fuel Tanks 444 32 9 20 12 9
Well 888 63 18 30 10 17
Plow 1,332 95 33 12 77 21
Disk . 1,554 llO 39 15 64 25
Harrow 355 25 7 20 9 6
Sugar Beet 7,082 503 177 12 408 ll3
Equip.
Drill 1,554 llO 39 20 40 25
Planter 1,787 127 45 15 74 26
Cultivator 1,415 100 35 12 81 23
Loader 1,132 80 28 12 65 18
Wagon 666 47 17 15 28 11
Sprayer 710 50 18 15 29 11
Baler 3,885 276 97 10 288 62
\Hndrow 3,996 284 100 10 296 64
Auger 699 50 17 15 29 11
Small tools 311 22 8 5 55 5
Trucks 9,435 670 a a a 151
Auto 3,885 276 a a a 62
Tractors 7,215 512 b b b 115
TOTAL $ll,082 $1,241 $1,729 $2,047
~Depreciation and repair costs are computed in table 27.
Depreciation and repair costs are computed in table 29.
-46-
Table 27. Miscellaneous fixed costs for a hypothetical 320-acre farm
Item Amount Used Rate Cost ($)
DEPRECIATION & REPAIR
Auto
Truck (~ T)
Truck ( 2 T)
INSURANCE
Buildings
Vehicles
TELEPHONE
ELECTRICITY
TOTAL
Perquisites
4,000 mi
5,000 mi
3,500 mi
$32,634
$ .14/mi
$ .14/mi
$ .28/mi
$10.80/$1,000
560
700
980
352
165
90
210
$3,057
Farmers receive certain benefits (perquisites) living on the farm. A
nonfarm person usually pays the cost of owning and maintaining a house, but
on a farm such items are part of the economic enterprise. The farmer--not
the farm enterprise--theoretically reaps the benefit from the farm's invest-
ment in them. Table 28 lists these farm perquisites.
Technically, perquisites are items of revenue not available for capital
investment; as such, they are subtracted from fixed costs.
Table 28. Farm perquisites (house, garage, well)
Item Perquisite value ($)
Depreciation 88
Investment 1,797
Repairs 506
Taxes 486
Insurance 273
TOTAL $3,150
-47-
/
Table 29. Variable costs per irrigated acre by crop
Amount Cost/Unit Total Cost
Item Used ($) ($)
SUGAR BEETS
Fertilizer: N. 100.8 lbs 0.22 22.18
P205 43.3. lbs 0.16 6.93 2
Labor: Family 8.4 hrs 2.25 18.90
Hired 11.7 hrs 2.50 29.25
Tractor 7.1 hrs 2.78 19.74
Seed 2.5 hrs 2.78 6.95
Custom Harvest 23.31 23.31
Ensiled Tops 10.5 tons 1.30 13.65
TOTAL 140.91
CORN SILAGE
Fertilizer: N2 110.4 lbs 0.22 24.29
P205 59.0 lbs 0.16 9.44
Labor: Family 6.0 hrs 2.25 13.50
Hired 4.1 hrs 2.50 10.25
Tractor 3.4 hrs 2. 78 9.45
Seed 0.5 bu 25.00 12.50
Silage Storage 21 tons 1.30 27.30
TOTAL 106.73
ALFALFA
Fertilizer: N2 0
P205 48.0 lbs 0.16 7.68
Labor: Family 5.4 hrs 2.25 12.15
Hired 2.8 hrs 2.50 7.00
Tractor 4.1 hrs 2.78 11.40
Seed 3.0 lbs 1.86 5.58
Twine 5 tons hay 0.61 3.05
TOTAL 46.86
BARLEY
Fertilizer: N2 65.4 lbs 0.22 14.39
P205 38.1 lbs 0.16 6.09
Labor: Family 3.2 hrs 2.25 7.20
Hired 0
Tractor 2.0 hrs 2.78 5.56
Seed 2.0 bu 3.70 7.40
Weed Spray 1.15 1.15
Custom Combine 7.70 7.70
TOTAL 49.49
-48-
Variable Costs
In addition to the fixed costs associated with the farm enterprise,many costs,
such as fertilizer, seed, labor, and tractor use, vary with the crop type
and acreage grown. Table 29 lists these variable costs per acre for a
hypothetical farm. All costs were tailored to a specific crop and an
anticipated yield under irrigation. Fertilizer use was based on the amount
needed to produce the expected yield. Tractor costs were included as variable
costs primarily because of the format of available data.
Revenues
Table 30 lists irrigated-crop production and sales per acre. Expected
yields assume better-than-average management skills and reflect amounts of
labor, fertilizer, and chemical sprays used to ensure good crop growth.
Sales prices were based on Water Resources Council price standards (U.S.
Water Resources Council 1975). Prices for silage (corn and beet tops) were
based on Water Resources Council hay prices and adjusted to reflect nutrient
content.
Table 30. Irrigated-crop production and sales per acre
Crop Yield Sales Price/Unit Total Revenue
per acre
Sugar Beets
Beets 21 tons $34.97 $734
Tops 10.5 tons 18.73 197
CROP TOTAL 931
Corn Silage 21 tons 18.73 393
Al fa! fa 5 tons 44.59 223
Barley
Grain 74 bushels 1.90 140
Straw 16 tons 2.68 43
CROP TOTAL 183
An allowance for the farmer's management skills was included in all
budgets. This allowance amounted to 10 percent of·the net profit, and was
calculated by reducing the absolute value of all costs and profits by 10
percent. Table 31 summarizes all costs and returns and calculates the
management allowance.
-49-
Table 31. Farm budget summary with management allowance
Management Net
Item $Value Allowance ($) Value ($)
Investment -ll '082 1,108 -9,974
Repairs -1,241 124 -1 'll7
Depreciation -1,729 173 -1,556
Taxes -2,047 205 -1,842
Miscellaneous -3,057 306 -2,751
Perquisites + 3,150 315 +2,835
Fixed Costs & Perquisites -14,405
Variable Costs (per acre)
Sugar beets -141 14 -127
Corn Silage -107 ll -96
Alfa1 fa -47 5 -42
Barley -49 5 -44
Variable Returns (per acre)
Sugar beets +931 93 +838
Corn Silage +393 39 +354
Alfalfa + 223 22 +201
Barley +183 18 +165
-50-
Irrigation Feasibility
The farm budgets prepared for each subbasin were based on cropping
patterns listed in table 32. Variable costs and revenues were multiplied by
the acres of each irrigated crop and combin~d with fixed costs of farming
(except for the cost of water application systems) to obtain the figures shown
in table 33. Then irrigation payment capacities were calculated per acre, and
application-system costs (listed in table 25 as $66/acre) were subtracted from
that amount to determine the landowner's capacity to pay for water-delivery
systems (table 34). This per acre capacity to pay for pumping was compared
with pumping costs per acre to determine the maximum pumping distance for
each subbasin (table 35). Finally, the pumping distances were compared with
the 440,000 acres of potentially irrigable land in the basin (table 21) to
determine the total feasibly irrigable acreage. Table 36 displays the results
in acres by subbasin--237,472 acres basin-wide; approximately 80 percent is
within .5 mi of the water source and less than 50 feet above it.
Table 32. Cropping patterns by subbasin, 320-acre farm
Cropping Pattern (acres)
Subbasin Farmstead Grain Hay Silage Cash Crop
Upper Yellowstone 18 51 239 3 9
Clarks Fork 18 51 239 3 9
Billings Area 18 88 121 24 69
Bighorn 18 79 169 9 45
Mid-Yellowstone 18 73 178 9 42
Tongue 57 196 15 33
Kinsey Area 18 54 184 24 39
Powder 18 36 217 18 30
Lower Yellowstone 18 88 115 30 69
IRRIGATION AND WATER DEPLETION
To allocate the 237,480 acres of feasibly irrigable acreage to the
three development levels, we assumed that the low level of development would
irrigate one-third of that figure, the intermediate level two-thirds, and the
high level all 237,480 acres.
Under assumptions of this study, annual irrigation-water requirements
for the feasibly irrigable acreage in each subbasin would be constant at 906
af/farm, or 3.0 af/acre ~ssuming 3Q2 acres under irrigation. It is further
assumed that one-third of the water withdrawn for application to crops
eventually finds its way back to the rivers. Hence, net water depletion from
irrigation development is assumed to be 2.0 af/acre. Development is assumed
to rise steadily to completion in the year 2000.
Low-level development of basin farmland--irrigating a total of one-third
of the feasibly irrigable acreage in each subbasin--would deplete 158,000
af/y to water 79,160 acres (see table 37).
-51-
Intermediate-level development would irrigate a total of 158,310 acres
and deplete the basin's water supply by over 316,000 af/y.
High-level development would irrigate the entire 237,480 acres of
feasibly irrigable land and cause depletion of nearly 475,000 af/y.
-52-
Table 33. Costs and returns by subbasin, 320-acre farm
Variable Costs and Returns ($) Payment
Cost($) Grain Hay Silaae Cash Crop Cap a-
Subbasin Fixed Cost Return Cost Return Cost Return Cost Return city ($)
Upper Yellowstone 14,405 2,224 8,415 10,038 48,039 288 1,062 1,143 7,542 36,960
Clarks Fork 14,405 2,224 8,415 10,038 48,039 288 1,062 1,143 7,542 36,960
Billings Area 14,405 3,872 14,520 5,082 24,321 2,304 8,496 8,763 57,822 70,733
Bighorn 14,405 3,476 13,035 7,098 33,969 864 3,186 5,715 37,710 56,342
Mid-Yellowstone 14,405 3,212 12,045 7,476 35,778 864 3,186 5,334 35,196 54,914
Tongue 14,405 2,508 9,405 8,232 39,396 1,440 5,310 4 ' 191 27 '6 54 50,989
Kinsey Area 14,405 2,376 8,910 7 '728 36,984 2,304 8,496 4,953 32,682 55,306
Powder 14,405 1,584 5,940 9,ll4 43,617 1 '728 6,372 3,810 25,140 50,428
Lower Yellowstone 14,405 3,872 14,520 4,830 23,115 2,880 10,620 8,763 57,822 71,327
Table 34. Payment capacity available for pumping (per acre)
Irrigation Payment Capacity
Payment Sprinkler for
Basin Capacity Cost Pumping
Upper Yellowstone $ 122 66 $ 56
Clarks Fork 122 66 56
Billings Area 234 66 168
Bighorn 187 66 121
t1id-Yellowstone 182 66 ll6
Tongue 2169 66 103
Kinsey Area 183 66 117
Powder 167 66 101
Lower Yellowstone 236 66 170
Table 35. ~1aximum pumping distance (mi)
Subbasin Lift (ft)
50 100 150 200 250 300 350 400
Upper Yellowstone 0.5
Clarks Fork 0.5
Billings Area 2.5 2.5 1.0 1.0 1.0 0.5 0.5 0.5
Bighorn 1.5 1.5 0.5 0.5 0.5
Mid-Yellowstone 1.5 1.0 0.5 0.5 0.5
Tongue 1.5 1.0 0.5
Kinsey Area 1.5 1.0 0.5 0.5 0.5
Powder 1.0 1.0 0.5
Lower Yellowstone 2.5 2.5 1.0 1.0 1.0 0.5 0.5 0.5
-53-
Table 36. Feasibly irrigable acreage by lift and pipeline
length, high level of development (acres)
Lift (ft)
Pipeline
length (mi) 0-50 50-100 100-150 150-200 200-250 250-300 Total
UPPER YELLOWSTONE SUBBASIN
0 .5 38,076 0 0 0 0 0 38,075
CLARKS fORK SUBBASIN
0 • 5 2,160 0 0 0 0 0 2,160
BILLINGS AREA SUBBASIN
0 -• 5 3,308 3,324 329 2,147 0 222 9,330
. 5 -1.0 347 71 8,084 1,305 0 0 9,807
1.0 -1. 5 110 0 0 0 0 0 110
1.5 -2.0 0 165 0 0 0 0 165
TOTAL 3,765 3,560 8,413 3,452 0 222 19,412
BIGHORN SUBBASIN
0 .5 4,478 0 1,309 0 0 0 5,787
• 5 -1.0 1,608 3,451 0 0 0 0 5,059
1.0 -1.5 0 2 191 0 0 0 0 2,191
TOTAL 6,086 5,642 1,309 0 0 0 13,037
MID-YELLOWSTONE SUBBASIN
0 .5 16,000 1,691 0 0 0 0
.5 -1.0 3,180 4,358 0 0 0 0
TOTAL 19,180 6,049 0 0 0 0
TONGUE SUBBASIN
0 • 5 21,947 0 0 0 0 0 21,947
KINSEY AREA SUBBASIN
0 • 5 3,248 0 0 l,lBO 0 0 4,42B
• 5 -1.0 0 0 0 0 0 0 0
1.0 -1.5 308 0 0 0 0 0 308
TOTAL 3,556 0 0 1,180 0 0 4,736
PO\'/DER RIVER SUBBASIN
0 .5 74,224 0 0 0 0 0 74,224
.5 -1.0 981 0 0 0 0 0 981
TOTAL 75,205 0 0 0 0 0 7 5' 205
LmiER YELLmiSTONE SUBBASIN
0 -.5 23,677 1,804 1 '775 0 0 0 27,256
• 5 -1.0 1,813 4,992 100 0 0 0 6,905
1.0 -1. 5 0 2,599 0 0 0 0 ' 2,599
1.5-2.0 0 805 0 0 0 0 805
2.0 -2.5 0 105 0 0 0 0 105
TOTAL 25,490 10,305 1,875 0 0 0 37,670
BASIN SUMMARY
0 -.5 187,118 6,819 3,413 3,327 0 222 200,899
. 5 -1.0 7,929 12,872 8,184 1,305 0 0 30,290
1.0 -1. 5 418 4,790 0 0 0 0 5,208
1. 5 -2.0 0 970 0 0 0 0 970
2.0 -2.5 0 105 0 0 0 0 105
TOTAL 195,465 25,556 11' 597 4,632 0 222 237,472
NOTE: This table should not be considered an exhaustive listing of all feasibly
irrigable acreage in the Yellowstone Basin; it includes only the acreage identified
as feasibly irrigable according to the geographic and economic constraints explained
in this report.
-54-
Table 37. The increase in water depletion for irrigated agriculture by
2000 by subbasin
Acreage Increase in
Subbasin Increase Depletion (af/y)
HIGH LEVEL OF DEVELOPMENT
Upper Yellowstone 38,080 76,160
Clarks Fork 2,160 4,320
Billings Area 19,410 38,820
Bighorn 13,040 26,080
Mid-Yellowstone 25,230 50,460
Tongue 21,950 43,900
Kinsey Area 4,740 9,480
Powder 75,200 150,400
Lower Yellowstone 37,670 75,340
TOTAL 237,480 474,960
INTERMEDIATE LEVEL OF DEVELOPMENT
BASIN TOTAL 158,320 316,640
LOW LEVEL OF DEVELOPMENT
BASIN TOTAL 79,160 158,320
NOTE: The numbers of irrigated acres at the low and intermediate
levels of development are not shown by subbasin; however, those numbers
are one-third and two-thirds, respectively, of the acres shown for each
subbasin at the high level of development.
-55-
Communities in southeastern Montana will demand more water if population
increases accompany energy development. (Municipal population growth in
the Yellowstone River Basin presumably would be unaffected by agricultural
development, such as expanded irrigation.) The method used to project popu-
lation increases due to energy development relied on the Montana Futures
Process (MFP), developed by the Montana Department of Community Affairs. MFP
simulates projected economic and demographic conditions. The economic calcula-
tion combines economic bases and several assumptions to simulate employment
levels by industrial sectors in labor market areas (LMAS). The demographic
calculation simulates population levels from a combination of the simulated
labor-force participation rates.
MONTANA FUTURES PROCESS
Although MFP can be used to estimate population levels for the 14 Labor
Market Areas (LMAS), it is not designed to project population changes at
the municipal level. The estimated labor-market population levels therefore
had to be allocated among municipalities and communities in each labor market.
This allocation was made according to informed judgments concerning likely
spatial development of the new population based on historical trade patterns
in each labor market area.
MFP combines trends in employment and economic exports to avoid simulation
of the effects of external economic changes while accounting for the region's
population and employment baselines. The direct and indirect effects on
employment of hypothesized developments are merged with long-term employment
trends to yield simulated employment levels. These simulated employment
levels are transformed into simulated population levels using employment and
population multipliers assumed in the demographic calculation. The structure
of the system is depicted in figure 4.
Hypothesized
development~
Montana I/0 Simulated Demographic Simulated
Model __ ....,.employment ___. submodel ______..population
/ level level
Employment
base trends
Figure 4. Montana Futures Process simulation-model structure.
-56-
ECONOMIC CALCULATION
The economic calculation is based on employment trends of twenty-eight
employment sectors (two for each LMA) at the state and LMA levels (figure 5).
the LMA data were produced by grouping county employment data from 1969 to
1973 (U.S. Department of Commerce 1975) at the LMA level. Because of the
short length of this series at the LMA level, the longer 1963-74 state-level
series (Montana Department of Labor and Industry 1975) was used to produce
long-term projections for the LMAs.
The economic calculation relied on secondary data (U.S. Department of
Commerce 1972, 1974, 1975a, 1975b) to analyze employment linkages (through
an input-output model) in the state. Because this project was concerned with
employment changes rather than industrial output changes, the input-output
(I/0) matrix, which is usually formulated in terms of outputs, was transformed
into employment terms. This transformation was based on output and employment
ratios for Montana weighted by productivity projections from the Bureau of
Labor Statistics (U.S. Department of Labor 1975).
Because the I/0 matrix was constructed at the state level, it was
necessary to allocate state-wide employment changes associated with a
specific energy development level to 14 LMAs. The allocation of secondary
employment (i.e., jobs resulting from the economic impact of jobs directly
related to energy development) generally was based on the change in base
activity. In other words, secondary employment was allocated to the LMA where
the primary employment would occur, except for financial service and trade
employment, which was partially allocated to one or more LMAs by taking into
account distance from marketing centers and historical trade patterns.
After the effects on employment of projected development levels were
calculated and allocated to the LMAs, employment changes contingent on
levels of energy development were merged with existing Montana employment
trends by sector. The total employment estimations that resulted represented a
simulated employment level for each LMA. Thus each si~ulated employment level repre-
sents the sum of existing employment trends in each LMA plus the employment
changes that would be associated with levels of energy development.
DEMOGRAPHIC CALCULATION
Multiplying a simulated employment level by the commonly used employment-
population multiplier produces a simulated population level. The employment-
population multipliers chosen here are keyed to LMA population data and range
from 2.1 to 2.4, but all converge gradually to 2.0 by the year 2000. The
convergence is consistent with a 25-percent increase projected over the next
25 years in the labor-force participation rate. The overall effect of a change
in the participation rate would be to dampen employment-related migration,
because employment opportunities would be absorbed internally. Because of
this, the population multiplier assumed to apply in the future by MFP is,
in general, lower than that which exists now.
-57-
I
(.]1 co
I
Figure 5. Labor market areas in Montana.
'··-··-------' ""?··-··
)
----------------·-r-··---------J·--------·-·;·-----------
. . I
··-------~---·-··-·· --:·-___ .. -.. T .. -.. --·--!
· r 1 • I ·1 . I ')
c-~
LINCOLN,
N
KALISPE!LL rj
0
0
f
<
>" ~RAVALLI
,/·
( .
'"\ . .1 ·./
G L A c I E R ! T 0 0 L E ! HAVRE LMA
SHELBY! LMA ! H I L L !
O
r·-·--t.,,... I ~
L IBERTY •
·---. .J "'1...-, I.--...
~-
L A I N E
i , DANIELS~HERIOAN:
'v A L L E yl-~-----~ !
,) ~ 0 [ GLASGOW l-MA L-----,
.J •ROOSEVELT: , ~ I
PHILLIPSr ·-·---·t. ,_ ___ --1
T E T 0 N
LMA-Labor market area
SMSA-Standard metropolitan statistical area
MUNICIPAL POPULATION
To estimate municipal water needs associated with hypothesized levels
of energy development, it was necessary to allocate population increases in
each LMA among affected municipalities. Because the MFP is not designed
to simulate municipal population changes, additional information was re-
quired to translate LMA employment and population changes to the city level.
During this study, therefore, considerable attention was given to infor-
mation on the likely spatial development pattern. The pattern was then
compared with the distribution of existing settlement.
Specifically, the economic activities associated with projected levels
of development were disaggregated into subbasins, and we assumed that workers
hired for jobs directly related to energy development would live in towns
near each development area. A worker directly hired for work in any given
energy development was assumed to head a household of 2.5 persons in the town
closest to the energy development. The secondary population of workers
generated by the primary activity was allocated among the towns of the region
on the basis of past trade patterns in each basin. The total effect foreseen
by the MFP for each town therefore includes the workers directly related to
energy development, their families, and service sector population resulting
from the new population in that town and other towns in its market area.
The data in table 38 were derived from this study's assumptions of
energy-development levels and from employment information from Freudenthal
et al. (1974). After the direct-worker requirements were further refined
according to subbasins, these requirements were put into the MFP model.
The MFP model produced the total population for the indicated municipalities
under conditions of low, medium, and high energy development, and the results
are shown in table 39.
INCREASED WATER USE
ASSOCIATED WITH POPULATION GROWTH
Table 40 summarizes the projected population increase (from table 39) for
all subbasins of the Yellowstone Basin for 1985 and 2000 and lists the result-
ing increases in water depletion under three levels of energy development.
-59-
Table 38. Permanent, direct energy-related employees in the Yellowstone
Basin, 1985 and 2000
Subbasin 1985 2000
Mining Conversion Transportation Mining Conversion Transportation
TONGUE
Low 972 0 164 1687 0 283
Intermediate 1544 0 120 2087 360 346
High 2060 0 238 5148 2890 523
ROSEBUD
Low 778 180 109 1298 1210 165
Intermediate 1200 360 158 2688 1390 320
High 1600· 360 188 4000 3740 280
POWDER
Low 220 0 21 411 0 69
Intermediate 343 0 58 757 180 101
High 458 0 55 1140 180 154
BIGHORN
Low 220 0 21 411 0 69
Intermediate 343 0 58 757 0 124
High 458 0 55 1140 180 161
-60-
I
0"1 -I
Table 39. Population simulations for low, medium and high energy development
1970a 1985 2000
Low Medium , High Low Medium
Ashland 531 847 986 2,127 2,379 3,423
Billings 63 '729 79,472 79,872 80,197 94,999 95,533
Birney 13 91 129 129 60 70
Broadus 799 1,568 1,988 3,158 4,138 6,096
Busby 300 831 877 1,011 1,160 1,038
Colstrip 200 2,231 3,606 4,455 5,044 5,824
Forsyth 1,873 3,372 4,195 4,640 5,189 5,664
Glendive 6,441 7,168 7,168 7,168 8,341 8,341
Hardin 2,733 4,016 4,377 5,977 4,783 5,458
Lame Deer 650 934 944 2,337 1,062 1,012
Lodge Grass 806 885 939 977 1,090 1,215
Miles City 9,023 11,596 12,100 12,955 15,890 16,641
Sidney 4,551 5,120 5,120 5,120 6,032 6,032
aBaseline populations for Billings, Sidney, and Glendive are based on 1975 estimates.
High
7,236
98,294
137
10,692
2,036
15,107
10,249
8 '713
7,094
1,442
1,462
20,254
6,404
Table 40. Population increases and water depletiona increases from municipal
water use in the Yellowstone River Basin in 1985 and 2000
Level of
Development
Low
Intermediate
High
Low
Intermediate
High
Population
Increase
1985
26,482
30,652
38,602
2000
56,860
62,940
94,150
Increase in
Depletion (af/y)
2,970
3,430
4,320
5,880
6,960
10,620
aDepletion is assumed to be 100 gal per person rounded to the
nearest 10 acre-feet.
-62-
The preceding sections present assumptions and methods used to estimate
water requirements in the Yellowstone River Basin to meet the demands of
energy development, irrigation, and municipal growth during the remaining
years of the century. Three levels of development were considered.
Table 41 summarizes the water demands arising from the activities
assumed for each level of development by the year 2000. Table 42 itemizes the
energy-development activities and associated water demands that appear in
table 41. Appendix A details the demands of energy, irrigation, and municipal
growth month by month that year in each of the subbasins.
The projections shown in table 41 are the first step in estimating the
impact of potential development on the Yellowstone Basin. Part II of this
report contains the second step--calculation of how the streamflow in the
basin would be affected by such development. In turn, these streamflow
calculations helped define the physical, biological, and economic effects of
water consumption in the Yellowstone River Basin contained in the other
reports of this series.
-63-
I m
~
I
Table 41. Water requirements by demand source in the Yellowstone Basin in 2000
Irrigation Municipal Energy a
Level of
develop-Acreage Associated Population Associated Associated
ment Increase Depletion (af/y) Increase Depletion (af/y) Depletion (af /y)
Low 79,160 158,320 56,860 5,880 48,350
Intermediate 158,320 316,640 62,940 6,960 147.160
High 237,480 474,960 94,150 10,620 321,190
aDetails of water requirements for energy use are in table 42.
bThis total assumes that the same level of development occurs in all categories of
consumption.
Total In-
crease inb
Depletion
(a f /y)
212,550
470,760
806,770
I
0'1
(J'1
I
Level of
Development
Low
Intermediate
High
Low
Intermediate
High
Low ! Intermediate
High I
*
Table 42. Increased water requirements for coal development in the Yellowstone
Basin in 2000
'
Coal Development Activity
Electric Gasi fi-Ferti-Strip
Generation cation Sync rude lizer Export Mining
COAL MINED (mmt/y)
8.0 7.6 0.0 0.0 171.1
24.0 7.6 o.o 0.0 293.2
32.0 22.8 36.0 3.5 368.5
CONVERSION PRODUCTION
2000 mw 250 mmcfd 0 b/d 0 t/d
6000 mw 250 mmcfd 0 b/d 0 tid
8000 mw 750 mmcfd 200,000 b/d 2300 t/d
WATER CONSUMPTION (af/y)
30,000 9,000 0 0 * 9,350
90,000 9,000 0 0 31 '910 16,250
120,000 27,000 58,000 13,000 80,210 22,980
Total
186.7
324.8
462.8
48,350
147,160
321,190
No water consumption is shown for export under the low level of development because, for that development
level, -it is assumed that all export is by rail, rather than by slurry pipeline.
by
Satish Nayak
-67-
MODEL VARIETIES
Although many different types of water models have been proposed and
used for water planning purposes over the past decade, these models have been
classified for the purposes of the Yellowstone Impact Study into two categories:
optimizing (or economic) models and watershed models.
Optimizing models assume that the analyst is interested in finding the
optimal solution providing lowest possible cost or maximum possible profit
under a given set of constraints. These constaints may include water re-
quirements, minimum flows, financial restraints, and other special considera-
tions. These models are primarily meant for economic studies determining
the operating policy for a system of reservoirs, new dam sites from a given
set of potential sites for future demands, the allocation of water among
several competitive users based on return or cost, or combinations of these.
The Yellowstone Impact Study did not consider optimizing models for two
reasons. First, the study did not address itself to such economic problems.
Second, these models consider surface waters only and the study needed a model
that could model the entire hydrologic characteristics of a basin.
Watershed models, on the other hand, attempt to model the hydrologic
characteristics of a basin by defining the relationships among the principal
components of the hydrologic system, for example, precipitation, snow, tempera-
ture, snowmelt, runoff, evapotranspiration, percolation, and ground water. The
following five watershed models were examined for use in the study:
1) The Utah State Model;
2) Streamflow Synthesis and Reservoir Regulation (SSARR);
3) HYD-2;
4) SIMLYD-II; and
5) The State Water Planning Model (SWP).
THE UTAH STATE MODEL
The Utah State Model (Utah State University, 1973) emphasizes water
quality. This model is divided into two parts: the hydrologic system and
the salinity system. The hydrologic system includes programs which model
precipitation (including snow), surface inflow and outflow, ground-water in-
flow and outflow, and evapotranspiration determined through soil moisture.
The salinity system consists mainly of the soil-salt system with its inter-
action with diversion, surface flow and ground-water flow. The Utah State
Model requires the following data:
1) inflow and outflow;
2) precipitation, including snowfall;
3) temperature;
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4) reservoir;
5) soil type with water holding capacity;
6) crop for finding potential evaptranspiration;
7) diversion;
8) salt concentration of ground-water and of reservoir water; and
9) soil chemistry for water quality.
This hybrid model uses an analogue computer to analyze complex rela-
tionships and a digital computer to calculate mass balance and salinity.
Calibration is achieved by adjusting the parameters of the equations itera-
tively unti1 the smallest value is reached for the objective function which
is (Diff) where Diff equals the measured outflow minus the predicted out-
flow.
Because of its hybrid computational procedure and main emphasis on water
quality, the Utah State Model was not selected for the Yellowstone Impact
Study and so it is difficult to say how involved data gathering might have
been. Based on the experience of the SWP model and its similarity with
the Utah State Model, it appears that the data preparation would be a long
process. Calibration seems to be difficult since the model must predict
not only outflow but also salt concentration.
The Utah State Model, which will handle two years of data on a monthly
basis for one river basin, appears to be useful in determining how different
water management practices (for example, irrigation policies, cropping
pattern, leaching) will affect water quality downstream.
STREAMFLOW SYNTHESIS AND RESERVOIR REGULATION (SSARR)
The SSARR, developed by the U.S. Army Corps of Engineers, North Pacific,
Portland, Oregon, is a good model for determining the daily operation of a
system of reservoirs and for forecasting floods and flows. The character-
istics of the SSARR model include a surface-water system, a snow system, a
soil moisture system, a ground-water system, and flood routing. These
characteristics are very broad and a detailed description of them can be
found in Pro ram Descri tion and User Manual for SSARR Streamflow S nthesis
and Reservoir Regulation U.S. Army Corps of Engineers 1972 •
The SSARR requires massive amounts of data taken daily and even. hourly.
The time increments can be as small as 0.1 hour in the case of flood routing.
Many of the data that this model requires would be available only if special
studies were conducted to collect them. In a broad sense, the following
types of data are needed:
1) inflow and outflow;
2) precipitation including _snow;
3) temperature;
4) reservoir storage including area-capacity curves; and
5) tables for parameters such as soil moisture index against percentage
of runoff, precipitation against evaporation reduction factor, per-
centage of season runoff against percentage of snow-covered areai
and many more. The detailed list can be found in the SSARR manua •
-69-
The SSARR is calibrated by a trial-and-error method that appears to be
a long and difficult process since there are many interacting empirical
parameters needing adjustment as more data become available. Although this
model can predict daily flows, the Yellowstone Impact Study requires analyses
over longer periods, and so the SSARR model was not selected.
HYD-2
Program HYD-2, a generalized hydrologic model of a river system that can
analyze up to fifteen stream-flow control points, is essentially an accounting
model needing no calibration (USDI 1974). At each control point, some or all
of which may be reservoirs, a mass balance is carried out and all losses or
gains are accounted for. Although this program models only the surface water
system, gains and losses due to ground-water activities are a part of the
model. This model requires the following data:
1) inflow and outflow;
2) demand at each control point;
3) reservoir storage with area-capacity curves;
4) pan evaporation coefficients at each reservoir site; and
5) losses or gains at each control point due to ground-water activity
in the area.
Since the main data requirements are the inflow and outflow values and
estimated ground-water activity at each control point, the data preparation
is less complicated than for the Utah State, the SSARR, or the SWP. This
model can simulate the monthly yield of a subbasin for fifty years but cannot
be used _for water-quality calculations. HYD-2 was developed by the U.S.
Bureau of Reclamation (USDI 1974).
SIMYLD-II
SIMYLD-II (Texas Water Development Board 1972) is based on the concept
that a physical water resource system can be transformed into a capacitated
network flow problem. Essentially an accounting model, since the mass
balance equation must be satisfied at each control point, SIMYLD-II needs
no calibration and has optimization built into it. This model's data re-
quirements are similar to those of HYD-2 and are as follows:
1) inflow and outflow;
2) reservoir storage with area-capacity curves;
3) demand or diversion at each model point;
4) pan evaporation coefficients at each reJervoir site;
5) priorities for meeting the demands; and
6) operating rules for the reservoirs.
SIMYLD-II is used primarily for two purposes: first, to simulate the
least costly operation of a system subject to a specified sequence of demand
and hydrology; and second, to find the yield of a subbasin or reservoir
within a basin. SIMYLD-II does not have the capability for water-quality
calculations. This model, designed to simulate the operation of more than
-70-
one reservoir in a system, assigns to each reservoir a priority that is
converted to a cost in order to find the optimal solution.
THE STATE WATER PLANNING MODEL
The State Water Planning Model (SWP) (Montana University Joint Montana
Resources Council 1972), a watershed model which can closely simulate the
hydrology of a river basin, includes four major subsystems: a surface water
system dealing with aspects such as precipitation, runoff, inflow, and reser-
voirs; a snow system dealing with snowfall, snowmelt, and sublimation losses;
a ground-water system simulating ground-water activities such as deep percola-
tion, ground-water storage, and ground~water outflow; and a soil-water system
dealing with soil moisture and evapotranspiration losses. This model has been
modified to include water quality calculations in total dissolved solids (TDS).
The SWP requires extensive data preparation including:
(a) inflow and outflow;
(b) precipitation including snowfall;
(c) temperature including frost data;
(d) pan evaporation coefficients at each reservoir site;
(e) soil type with water holding capacity;
(f) crop data for finding consumptive use and potential evapotranspiration;
(g) diversion data; and
(h) regression equations for TDS calculations.
All relationships among the elements of the model are expressed as a
system of linear equations that represent the basin characteristics and are
obtained from knowledge about the area and the relationships described in
hydrologic literature. Calibration criteria are based on a zero trend in
the available ground-water capacity. Calibration is accomplished by running
the program iteratively and changing some of the relationships in the system
of equations.
This model can be used to determine the yield of a basin under a given
operating policy. Although SWP is not meant to provide information for
controlling or correcting the water quality of the outflow, water quality
calculations can be made on the outflow.
MODEL COMPARISON
Although the Utah State Model and the SSARR programs were not used, pre-
liminary evaluation of these programs showed that they would not meet the
requirements of the study. The Utah State Model was eliminated mainly for
its hybrid computational procedure and its narrow emphasis on water quality,
although other factors indicated that it would be unsatisfactory. This study
required a model that could simulate much longer periods than the twenty-four
months that the Utah State Model could simulate. Also, the Utah State Model's
data preparation and model calibration appeared to be a longer and more
difficult process than that in other models that could provide information
more useful to the study. The SSARR was eliminated because of its narrow
-71-
range simulating the day-to-day operation of a system of reservoirs, and
because it requires massive amounts of data that have not been collected.
The HYD-2, SIMYLD-II, and SWP programs were all run for detailed
evaluation and comparison. The results of the evaluation and comparison
may be found in table 43 and the criteria used to evaluate the models are
listed in table 44.
When the comparison was made, it was apparent that SIMLYD-II has all
the capabilities that HYD-2 has plus additional capabilities and therefore
HYD-2 was dropped from consideration. The SWP and the SIMLYD-II programs
were both good models for the study, but the SWP was more complete than SIMYLD-
II. Also, the SWP had water quality abilities that SIMYLD-II lacked. And
using the SWP had another advantage: since the program was developed under
a grant from the Water Resources Division of DNRC to the Water Resources
Research Center at Montana State University, Bozeman, Montana, experts
who worked on that project would be available for any necessary modification
of the SWP program. Therefore, the State Water Plan (SWP) was selected for
the Yellowstone Impact Study and applied to the Yellowstone Basin.
-72-
Type of Model
a Data
Calibration
Simulation
Table 43. Model comparison
State Water Plan
A hydrologic model
using a system of
equations defining
the interaction of
ground-water, sur-
face water, snow-
melt, and other
subsystems.
Only one reservoir
per basin may be
. simulated.
Simulation, :in a
limited sense, can
be carried out for
basins without a
reservoir.
No optimization.
Temperature depend-
ent data are
required.
Soil moisture
data are required.
Lengthy calibration
is required. Com-
puter time for
each calibration run
approximately equals
that for a simulation
run.
HYD-2
An accounting
model mainly
simulating sur-
face waters.
More than one
reservoir per
basin may be
simulated.
Simulation, in a
limited sense,
can be carried
out for basins
without a
reservoir.
No optimization.
No temperature
dependent data
are required.
No soil moisture
data are re-
quired.
No calibration
is needed.
SIMYLD-II
An accounting model
mainly simulating
surface waters.
More than one
reservoir per basin
may be simulated •
Simulation cannot
be carried out
if shortages
occur.
Optimization is
possible.
No temperature
dependent data
are required.
No soil moisture
data·are re-
quired.
No calibration
is needed.
All three models may be used for finding the yield of a basin.
The operating criteria are less rigid and limited for the
SIMYLD-II model than for the SWP or HYD-2 models.
-73-
Table 43 Continued.
Computer time
Learning time
Water quality
State Water Plan
Presently, each
computer run
costs approxi-
mately $30.00
for 360 months.
SWP is not an
"off-the-shelf"
model. A good
understanding of
the subsystems and
their interrela-
tionships is required.
A knowledge of matrix
inversion is desirable.
Water quality is calcu-
lated but not direct-
ly controlled.
HYD-2
Presently, each
computer run
costs approxi-
mately $6.00
for 360 months.
HYD-2 is an "off-
the-shelf" model
of the accounting
variety.
No prov1s1on for
water quality.
SIMYLD-II
Presently, each
computer run
costs approxi-
mately $12.00
to $14.00 for
360 months.
SIMYLD-II is an
"off-the-shelf"
model of the
accounting variety.
The optimization
method requires
an understanding
of network flow
theory.
No provision for
water quality.
aData requirements and preparations are more complex and time consuming for
SWP than for HYD-2 or SIMYLD-II. Monthly data is acceptable to SWP up to 360
months and HYD-2 and SIMYLD-II up to 600 months.
-74-
Table 44. Suggested model evaluation criteria
1. Validity of results.
2. Ease of verification.
3. Ease of learning and use.
4. Cost/benefit.
5. Data requirements.
6. Ease of modifying to simulate different situations (flexibility).
7. SmallP.st time increment which can be used.
B. Accounts for known physical, hydrologic relationships.
9. Assumptions required and their validity.
10. Economics built in (optimizing).
11. Subbasin interaction capability.
12. Calibration effort required.
13. Sophistication of output.
14. Ease of debugging problems.
15. Outputs available in addition to yields and flows.
16. Prediction capability.
17. Existing documentation.
18. Routing capability.
~ 19. Water quality.
l 20. Physical availability to other users.
,I
-75-
HOW THE SWP MODEL WAS USED
The SWP was modified to include water quality calculations and to make
the program ready to use in each subbasin with a minimum of changes. Because
watershed models must be tailored to each subbasin, the program was divided
into two sections, one that included subroutines independent of the subbasin
under study and another containing subroutines dependent on that subbasin. By
limiting the amount of reprogramming of the model necessary for each subbasin,
considerable time and money was saved. The revised program includes many
new subroutines.
The model consists of sixteen linear equations that describe the inter-
relationship of the four major subsystems: including a surfac,e water system,
a snow system, a ground-water system, and a soil water system. Each equation
represents a secondary datum whose value is obtained during the calibration
phase of the modeling. The primary input of the equations consists of inflow,
outflow, precipitation, reservoir storage, and temperature. The system of
linear equations is solved for each month of the study period, keeping a link
from one month to the next, especially in variables dealing with storage.
Despite the program changes and the inclusion of water quality calcula-
tions, the program's variable names, formats, and basic character remained
essentially the same as the program developed by Boyd and Williams (Montana
University 1972).
The water quality subroutine, added to meet the requirement of the Yellow-
stone Impact Study for water quality calculations,can take twelve monthly
regression equations for total dissolved solids (TDS) based on flows. The
subroutine calculates the TDS for the incoming flow as well as the outgoing
flow and has provisions for two level~ of salt pickup by return flows. A
brief description of procedure used w1th the SWP follows.
CALIBRATION
Calibration of all subbasins was based on data (see "Data Preparation,"
below) covering the 360 monthly time increments from 1944 through 1973.
Calibration begins by using a simple program to calculate the initial
coefficients of the model. These initial coefficients are then used in an
annual version of the SWP model that is then run with the data covering the
thirty individual years. The initial coefficients are adjusted and the model
is reiterated two or three times until final values for the annual model's
coefficients are reached.
The annual model (which becomes the monthly model with the reduction in
scale of some factors and the addition of systems simulating such details as
-76-
snow pack and soil moisture) also acts as a basis for assigning certain co-
efficients. The monthly model is calibrated by running data covering the
360 months using the annual ~odel's coefficients and adjusting them until
the model is consistent with the data. The calibration of the monthly
model requires more runs and adjustments of the coefficients of the annual
model since the monthly model uses 360 months of data and considers twice as
many variables. In addition, although the model uses the relationships between
monthly average temperature and variables such as snowmelt, potential evapo-
transpiration, and soil moisture, the responses of these variables are more
dependent upon maximum and m1n1mum temperatures; therefore, determining the
final coefficients for the monthly model requires some subjective judgment.
The monthly model used in this study differs slightly from the original
SWP model. The subsystems for ice formation and irrigation diversion devia-
tion were eliminated to reduce the size of the model's matrix. The sub-
systems for subsurface outflow, subsurface inflow, and snowfall were treated
outside the system of equations, another step to reduce the matrix size.
SIMULATIONS
After the model had been calibrated for a particular subbasin, it was
ready for simulations. Scenarios describing low, intermediate, and high
water use (which are explained in Part 1 of this report) were run for each
subbasin. The model can perform simulations of the following situations
and policies:
1) Keeping a reservoir as full as possible, making releases only when
required to augment flows and releasing excess flows only when the
reservoir is full.
2) Keeping a reservoir as full as possible making releases to augment
irrigation flows (when the reservoir inflow is less than the
irrigation flow) plus a minimum required flow such as the Department
of Fish, Wildlife and Parks would request; and
3) A system that has no reservoirs and so has no capacity to augment or
regulate flows except through additional diversion.
DATA PREPARATION
Inflow and outflow data for all subbasins were obtained from computer
files (USDI) and Water Supply Papers provided by the USGS. Precipitation
and temperature data were obtained from the SWP model data bank (Montana Univer-
sity) and the U.S. Climatological Records. Montana Agricultural Statistics
(Montana Department of Agriculture 1946-74) provided crop data for determining
the potential evapotranspiration on a monthly basis for all subbasins. Root
zone capacity was calculated from the soils maps provided by the Soil Conserva-
tion Service. Bureau of Reclamation data on diversion projects in the Yellow-'
stone Basin were used to estimate the diversion requirements for most of the
subbasins on the mainstem. A brief description of the procedure used in
preparing the data follows.
-77-
Priority
The largest use of water in the Yellowstone Basin is for agriculture,
including irrigated farming, dryland farming, and ranching. Municipal and
industrial water uses, though important, are relatively small, at present,
compared to agricultural water use. With recent attention on the coal
development and thermal energy production potential in the southeastern
part of Montana, the water demand for energy has become significant. In
this study, water for energy was treated as an industrial demand. Municipal
and agricultural demands were given priority over energy demand for all
simulation studies.
Exports and Imports
It is assumed that all diversions from the stream are meant for use in
that subbasin; however, there are situations calling for diverted water to
be used in a neighboring subbasin. In such cases, this water is treated as
an export in one subbasin and an import in the receiving subbasin. In most
cases, diversion will be all along the length of the river, but, for the
model, diversions are summed to give the net diversion for the subbasin.
Actual diversion data from projects in the basin were used as the basis
for calculating totaJ diversion in that basin. If the data were not complete,
an average value was used in place of the missing data or period. In basins
where the diversion data were incomplete or nonexisten~ like the Powder River
Basin, the diversion data were created by using consumptive use requirement,
area, precipitation, and the irrigation practice used. The total irrigated
acreage for different subbasins was obtained from irrigated cropland harvested
data found in Montana Aaricultural Statistics (Montana Department of
Agriculture 1946-74).
Streamflow. Inflow and outflow data for each subbasin were obtained from
the gaging stations nearest to the subbasin boundary. In some cases the
gaging stations were either deep inside or outside the drainage boundaries.
In such situations, flows were estimated from the proportions of the drainage
area, a regression equation, or both, or from some relevant information that
can be used in predicting flows. Each basin was treated differently de-
pending on availability of information.
Precipitation. To obtain the average precipitation for the area under
consideration, all weather stations with thirty years of records were con-
sidered. If the station had a few missing observations, they were syn-
thesized by using regression analysis or by averaging. In a few cases, where
the stations were not uniformly spaced or did not cover the entire area, the
Thiessen polygon method was used. In these cases, mean precipitation was
calculated by using the following expression:
A.P.
p =~~ m ~ A.
1
where: P = mean precipitation for the subbasin in inches m
-78-
P. = precipitation of the ith measuring station in inches
l
A. =area corresponding to the ith measuring station in acres
l
If the gaging stations were all uniformly spread over the area, then:
p = m
where: P = average precipitation for the subbasin in inches m
P. = precipitation of the ith measuring station in inches
l
n = total number of measuring stations
Temperature. Temperature data were treated exactly the same way as pre-
cipitation data. All weather stations with adequate records were used in
calculating the mean value. Missing data or values were created using an
appropriate method. The Thiessen polygon method for finding average tempera-
ture was used whenever appropriate: ·
A.T.
T -L l l m -A.
l
where: T = average temperature for the subbasin in Fahrenheit degrees m
T. = temperature at the ith measuring station in Fahrenheit degrees
l
A d . t th . th . t t . . . = area correspon 1ng o e 1 measur1ng s a 1on 1n acres
l
The following equation was used to obtain the average value of the
temperature in cases where the measuring stations were uniformly spaced over
the basin:
T m
where: T = average temperature for the subbasin in Fahrenheit degrees m
.th T. = temperature at the 1 measuring station in Fahrenheit degrees
l
n = total number of measuring stations.
Reservoir Storage. Reservoir storage was considered only if storage could
be used as a regulating device for the flows. In subbasins having more than
one reservoir, the reservoirs were lumped to give the net storage capacity
of the basin. Channel storage was not considered because it could not be
used for regulation of flows.
Root Zone Capacity. A wide range of soil types exists within the root
zone of the drainage area. Each of these soil types exhibits a different
capacity for holding percolating waters. This information was used to deter-
mine the field capacity of the subbasin (i.e. the area weighted average of
soil moisture holding capacity) using the following equation:
FC = lA.C.
J. J.
where: FC = field capacity of the subbasin in million acre-feet
A. = area in million acres per soil type
J.
c. = root zone capacity in feet for A.
J. J.
Potential Evapotranspiration. Potential evapotranspiration values were
determined on a monthly basis for individual ~egetative types. For agricul-
tural crops, the Modified Blaney Criddle method (USDA 1970) was used and for
native vegetation the Thornthwaite method (USDA 1970) was applied. These
quantities were added together to provide the net potential evapotranspiration
for each basin by month. The crop acreage data were obtained from Montana
Agricultural Statistics (Montana Department of Agriculture 1946-74).
THE ANNUAL AND MONTHLY MODELS
ANNUAL MODEL
Definition of the model began with determining the relationships between
the variables. Since the study used the SWP model, the study model used the
same nomenclature and relationships as the original SWP. Definitions of the
annual model's variables (expressed in million acre-feet) follow:
Xl = Surface outflow
X2 = Surface inflow
X3 = Initial storage
X4 = Terminal storage
X5 = Precipitation
X6 = Surface loss or the consumptive use
X7 = Subsurface outflow
XB = Subsurface inflow
X9 = Initial available capacity
XlO = Terminal available capacity
Xll = Percolation
Xl2 = Subsurface discharge
The following equations defined the model's relationships:
1) Surface loss: X6 = -Xl + X2 + X3 -X4 + X5 -Xll + Xl2
2) Subsurface outflow: X7 = Cl + (K3) (Xl)
3) Subsurface inflow: XB = C2 + (K4) (X2)
4) Terminal available capacity: XlO = X7 -XB + X9 -Xll + Xl2
-80-
5) Percolation: Xll = SF (K7)(X2) + KB(X3+X4) + (KlO)(Xl2) + X5
6) Subsurface Discharge: Xl2 = C4 -C3(X9 + XlO)
7) Assumptions: XS = (K2) (X7)
x7 + x8 = Kl cx1 + xz)
(K6) (Xl2) = C4
X9 = XlO
X9 = X5 + X2 (As/Ab)
where: X2 = average inflow into Montana's portion of
the Yellowstone Basin
A = area of the subbasin in acres s
Ab = area of Montana's portion of the Yellowstone
Basin in acres
SF = scale factor
Initial Coefficients (C and K Values)
Choosing the model's initial coefficients (K values) is the most diffi-
cult part of this procedure and requires subjective judgment based on a
thorough knowledge of the hydrology of the basin. Once these K values had
been selected, they were read into a simple program using thirty-year average
values of Xl, X2, X3, X4, and X5 for the basin. The output of this program
consisted of initial coefficients for the annual version of the model (Cl,
C2, C3, C4) and the initial values of X9 and SF. These C values, in turn,
were used to run an annual version of the model using data from each of the
ihirty years. Each time a run was made, the C values were adjusted so that
X9 = XlO which implies that during the thirty-year period, the ground-water
storage is neither built up nor depleted. Once the condition of zero trend
was achieved, the C values had been adjusted until they became the values
of the annual model's coefficients. The coefficients of the monthly model
could then be developed from the coefficients of the annual model through a
similar though more complex process.
Table 45 shows the values of Kl through KlO used for each of the nine
subbasins as well as the final values of Cl, C2, C3, C4, and SF. In addition
to these values, the initial value of X9, the average value of XlO and the
sum of all X6 are listed in the same table.
1 A bar above the variable X's indicates an average value.
-81-
I co rv
I
Coefficient
Kl
K2
K3
K4
K5
K6
K7
K8
K9
KID
Area in
M Acres
C1
C2
C3
C4
SF
x9 Initial x-10
Sum of all
X6
Upper
Yellowstone
.050
.960
.015
.015
.050
2.000
1.000
.zoo
1.000
.500
3.805440
.106151
.131857
. Oll646
.448829
.020880
9.606533
?.634332
93.982705
Clarks Billings
Fork Area
.040 .030
.960 .970
.015 .015
.015 .015
.060 .060
2.000 2.00
1.000 1.00
.200 .250
1.000 2.000
.500 .500
1.001376
. 019017 .079541
.0210U6 .071450
.010041 .068000
.109762 .590000
.176100 .034300
2.677895 2.020000
2. 734140 2.167467
67.403834 78.002623
Table 45. l~odel Coefficients
Hid-Kinsey Lower
Bighorn Yellowstone Tongue Area Powder Yellowstone
.040 .030 .030 .008 .030 .020
.965 .970 .970 .960 .980 .960
.020 .015 .015 .006 .015 .OlD
.020 .015 .015 .006 .015 .010
.060 .060 .020 .060 .020
2.000 2.000 2.000 1. 250 2.000 1.250
1.000 1.000 1.000 .500 1.000 .500
.250 .250 .250 .250 .250 .250
2.000 2.000 2.000 2.000 2.000 2.000
• 500 .500 .500 .500 . 500 .500
2.266788 2.463360 .933812 2.51090 3.980582
.056322 .122501 .005217 • 018502 .005478 .95738
.054806 .ll5654 .005004 .016296 .006587 .087535
.033500 .069932 .003042 .017350 .003684 .004054
.397499 . 954247 .061278 . 2188ll .05367h .228189
.026370 .035561 .003572 .027458 .004255 . 013678
2.788641 3.033000 3.382400 1. 201977 3.624976 5.550416
2.968178 3.4ll503 3.392497 1.279755 3.63?492 5.625278
66.565216 N.A. 82.419387 27.323242 87.031952 139.858505
MONTHLY HODEL
The monthly model was derived from the annual model by adding more
structure. For example, an annual model, having no temperature-dependent
variables, treats evaporation losses from the reservoir or from streams
or from vegetation as a single loss. The monthly model, however, attempts
to separate these losses into different components such as evapotranspiration,
evaporation from reservoirs, and the losses from the stream surface, thus
accounting for seasonal temperature variation. The precipitation, for
example, is assumed to be snowfall or rainfall depending upon the temperature.
The monthly model was composed of the following five subsystems:
1) SSl: Stream-Reservoir
2) SS2: Snow
3) SS3: Runoff
4) SS4: Ground \1ater
5) SS5: Soil Water
These five iubsystems require the following fifteen parameters,
expressed in million acre-feet:
1) SSl Parameters.
2) SS2
Xl = stream out flow
X2 = stream in flow
X3 = initial reservoir storage
X4 = terminal reservoir storage
X6 = stream-reservoir evaporation
Parameters.
Xl4 = sublimation
Xl5 = initial snow storage
Xl6 = terminal snow storage
3) SS3 Parameters.
X5 = precipitation
X20 = runoff evaporation loss
X27 = irrigation import
4) SS4 Parameters.
X7 = ground-water out flow
X8 = ground-water inflow
X9 = initial ground-water capacity
loss
XlO = terminal ground-water capacity
5) SS5 Parameters.
X23 = initial soil-water storage
X24 = terminal soil-water storage
X25 = evapotranspiration loss
-83-
6) SSl-2 (Stream-Reservoir-Snow) Parameters.
XlB = ice formation
X31 = irregular ice formation ( X31 < 0, T ~ 32°)
7) SS2-l (Snow-Stream-Reservoir) Parameter.
X31 = irregular snowmelt (X31>0, T:::S32°)
8) SSl-3 (Stream-Reservoir-Runoff) Parameter.
X28 = irrigation diversion
9) SS3-l (Runoff-Stream-Reservoir) Parameters.
Xl9 = ground-water runoff plus irrigation runoff
X31 =precipitation runoff (T>32°)
10) SSl-4 (Stream-Reservoir-Ground Water) Parameter.
Xll = stream-reservoir percolation
11) SS2-3 (Snow-Runoff) Parameters.
Xl7 = snowmelt
X22 = irregular snowmelt ( X22 < 0, T :::s 32°)
12) SS3-2 (Runoff-Snow) Parameters.
Xl3 = snowfall
X22 = irregular ice formation (X22>0, T ~ 32°)
13) SS3-5 (Runoff-Soil Water) Parameters.
X21 = ground-water infiltration plus irrigation infiltration
X22 = precipitation infiltration ( T > 32°)
14) SS4-3 (Ground Water-Runoff) Parameter.
Xl2 = ground-water discharge
15) SS5-4 (Soil Water-Ground Water) Parameter.
X26 = soil-water percolation
-84-
Three additional parameters were defined:
X29 = irrigation diversion deviation
X30 = irrigation runoff
X32 = 1.0, a system constant
Unity-Coefficient Equations
The five subsystems gave rise to five balance equations:
1) Xl -X2 -X3 + X4 + X6 + Xll + XlB -Xl9 -X27 + X28 -X31 = 0
2) Xl3 -Xl4 + Xl5 -Xl6 -Xl7 + XlB + C(9,22)X22 + C(9,3l)X31 = 0
3) X5 + Xl2-Xl3 + Xl7-Xl9-X20-X21-X22 + X27 + X28 + C(l5,3l)X3~= 0
4) X7 -XB + X9 -XlO -Xll + Xl2 -X26 = 0
5) X21 + C(l6,22)X22 + X23 -X24 -X25 -X26 = 0
C(9,22) = 1.0 when T ::; 32°, otherwise C(9,22) = 0;
C(9,31) = 1.0 when T::; 32°, otherwise C(9,31) = 0· '
C(l5,31) 0 .
= 0; = -1.0 when T>32 , otherwise C(l5,31)
C(l6,22) = 1.0 when T>32°, otherwise C(l6,22) = 0
For parameters other than measured data and those that can be obtained
from the balance equations, empirical relationships were obtained either from
the annual model by scaling them accordingly or by choosing a relationship as
given in the third volume of Devel~p~ent of a ~tate_Water Plan~ing Model
Montana University.l972). The emp1r1cal relat1onsh1ps follow.
Stream-Reservoir Evaporation Loss
1) X6 = C(l,2)X2 + C(l,l9)Xl9 + C(l,28)X28 + C(l,3l)X31 + C(l,32)X32
C(i,j) equals the coefficient for the jth variable in the ith row. For X6,
all coefficients are temperature dependent, and the exact relationship varied
from one subbasin to the next. The general expression for these coefficients
for this equation is:
1 This system of equations uses unity coefficients, C(i,j) coefficients, and
C (i,j) coefficients. Unity coefficients normally belong to a balance equa-
tion and remain the same for all subbasins. C(i,j) coefficients are
temperature-dependent coefficients that vary from one subbasin to another. C
(i,j) coefficients are independent of the temperature and usually are obtained
from the annual.model either by scaling down the coefficients or carrying
them as they are. C(i,j) and C (i,j) coefficients may be found in appendix B.
-85-
C(i,j) = aT+ bT 2
where: T = actual temperature
a and b = constants selected so that the curve of the function
duplicates the curve made when evaporatjon loss is
plotted against temperature
The losses due to evaporation are proportionately larger at higher temperatures
than at lower temperatures. This nonlinearity with temperature is built into
these coefficients. Note that, except for X32, all flows are streamflows,
nnd the losses are called stream losses. The coefficient C(l,32) accounts
for the losses from the reservoirs. The coefficient C(l,32) is calculated
in subroutine SURFAC as follows by multiplying the pan evaporation coefficient
by reservoir surface area.
~ ;t ream-Reservoir Percolation
2) Xll = C(2,3)X3 + C(2,4)X4 + C(2,19)Xl9 + C(2,22)X22 + C(2,28)X28 + C(2,3l)X31
These coefficients do not depend on temperatures, and are usually ob-
tained from the annual model. C(2,3) equals C(2,4) which equals l/12th of the
corresponding annual coefficient. C(2,2) has the same value as the correspond-
ing annual coefficient (C value).
Ground-Water Discharge
3) Xl2 = C(3,9)X9 + C(3,10)Xl0 +(C3,32)X32
The values for C(3,9), C(3,1Qj and C(3,32) are obtained by dividing the
corresponding annual coefficients (C values) by 12.
Sublimation
4) Xl4 = C(4,15)Xl5 + C(4,16)Xl6
Sublimation losses were considered to be 2 to 5 percent of the snow
cover. A sublimation loss is actually a function of dew point, wind, and
temperature, but except for temperature no other data are readily available.
Since the losses are not high, an average value was used for all winter months
irrespective of the temperature. The average value changed from one subbasin
to next.
Snowmelt
5) Xl7 = C(5,l))Xl3 + C(l0,15)Xl5
A C(5,13) = -2-
-86-
C(l0,15) = A
where: 2 + Xl5 A = C(T-32)K6 + (~-32) + K7(X5
(bK6)+b 2
' T = actual temperature
b = number of degrees above 32 at which all snow melts.
K6 and K7 are the factors which affect the rate of snowrnel t. The first
component in the above expression accounts for the ternper~ture effect on
snowmelt, whereas the second one considers the impact of rainfall on snowmelt
rate. In the event that A is greater than 1.0, A is set equul to 1, thus
ensuring that snowmelt will not exc~ed the snowpack.
Ground-Hater Runoff plu~ Irrigation Runoff
6) Xl9 = C(6,12)Xl2 + C(6,27)X27 + C(6,28)X28.
Runoff Evaporation Loss
7) X20 = C(7,5)X5 + C(7,12)Xl2 + C(7,17)Xl7 + G(7,28)X28
8) X21 = C(8,12)Xl2 + C(8,27)X27 + C(8,28)X28
Terminal Surface \:later Storaqe
9) X24 = X21 + C(9,22)X22 + X23 -X25 -X26 ~1hen FCil" ·1n
X24 = rc 1,. · v1hen X24<FC 11" , and ·1n ·1n
X24 = FC 1·1hen X24 > FC
where: rc,,. = minimum soil moisture capacity ·1n
Evaoor8tion Loss
10) X25 = X21 + C(l0,22)X22 + X23 -X24 -X26
X25 = PET, l'lhen X24 < FC 11 . '1n
where: PET = potential evapotrans~iration
Percolation
~ X24 ~ FC
11) X26 = C(ll,2l)X21 + C(ll,22)X22 + C(ll,23)X23 + C(ll,32)X32
C(ll,32) = RE (X24-FC) when X24>FC, othen1ise C(ll,32) = 0
-87-
where: RE is a fraction between 0 and 1.
The term (X24 -FC) is the excess water that soil cannot absorb and hence
it must either be runoff or should percolate into ground water or both.
RE(X24 -FC) is the amount of excess water that goes into ground water.
Precipitation Runoff or Balance
12) X31 = Xl -X2 -X3 + X4 + X6 + Xll + Xl8 -Xl9 + X28
These twelve equations coupled with balance equations 2 through 5 (the
first balance equation and the precipitation runoff equation are equivalent)
constituted the monthly model. There were five fewer equations in this model
than the model developed at the Water Resources Research Center under Boyd
and Williams (1972), mainly due to the different treatment of equations for
X7, XS, and Xl3 and the elimination of equations for Xl8 and X30. Since X7,
XS, and Xl3 depend on known quantities Xl, X2, and X5, respectively, there was
no need to consider them as a part of the system of equations for the solution
procedure. Equations for Xl8 and X30 were considered to be unnecessary for
the study. Exclusion of these equations reduces the matrix size from 21 x 21
to. 16 x 16 and thereby reduces cost in computer time by 30 to 40 percent.
Calculations for X7 and XS are carried out in the mainline program, whereas Xl3
(the snowfall system) is obtained from the subroutine COMPUT.
CALIBRATION OF THE MONTHLY MODEL AND CONTROLLABLE VARIABLES
Though the monthly model was derived from the annual model, it still
needed calibration. The calibration procedure was similar to the one used
in the annual model, except that the number of controllable variables was
larger than for the annual model. Some of the important controllable vari-
ables follow.
Rainfall Moving Average
Outflow from a basin, besides being a function' of many variables, was
dependent on the precipitation in that basin. Furthermore, all the outflow
in a given month was not necessarily due to all the precipitation in that
month. It is more than likely that the precipitation in a month influences
the outflow for up to a month or two later. For the calibration of the
Yellowstone River Basin, the precipitation effect was carried over to the next
month. For months when all precipitation was determined to be snowfall, the
precipitation averaging was ignored.
E = a(g) + (1-a)t
where: E = effective rainfall
a = fraction of precipitation in a month resulting in outflow
in that month
-88-
I·,
~
I
g = current month's precipitation
t = previous month's precipitation
Snowfall and Snowmelt
The snow subsystem serves as a mechanism in the model to delay the
runoff due to snowfall from the winter months when the snow falls to the
summer months when it all melts.
( T-b Xl3 = 1 -~)(X5)
where: Xl3 = snowfall
T = temperature in degrees Fahrenheit
b = temperature in degrees Fahrenheit below which all precipi-
tation is snowfall
X5 = precipitation
The value of b was chosen with the topography of the area and the climate
conditions in mind. For example, in the Bighorn Subbasin, the value of b was
20°F.
The snowmelt rate was another important factor in the calibration phase
of the monthly model. Spring runoffs from the basin were mainly due to the
snowmelt, and runoff and snowmelt were matched to reflect the cause and effect
relationship. From the system of equations, one can see that the snowmelt was
a prime component of the soil moisture system, which in'turn was a major
contributor to the ground water recharge. Thus, a snowmelt rate eventually
affected the ground water, potential evapotranspiration, and runoff.
Soil Water Percolation Rate
X26 = SF (X5 + X23)
(d + X5 + X23)
where: X26 = soil water percolation
SF = scaling factor
X5 = precipitation
X23 = initial soil water storage
d = dampening factor
(X5 + X23)
The term (d + X5 + X23) takes into account the effect of precipitation
and the soil moisture condition on the pecolation rate. The dampening factor
d is in most cases equal to 1.0, and by changing the value of SF the ground
water recharge could be changed.
-89-
Initial values for the above controllable variables were selected using
experience and knowledge of the basin. The initial run was then made. The
output from this run became the basis for making changes in some of the
controllable variables, and the model was rerun. This iterative process was
continued until:
1) The initial ground water storage equaled the terminal ground water
storage for the· study period;
2) The average ground water storage equaled the average ground water
storage from the annual model; and
3) The total system loss in the monthly model equaled the total system
loss in the annual model.
The first two conditions were easier to satisfy than the third condition.
For the third condition, a variation up to 5 percent was considered to be
acceptable, whereas the first two conditions were met well within the second
decimal place of accuracy. The monthly model was said to be calibrated if all
of the three conditions were satisfied simultaneously.
The system of equations for the calibration of a subbasin are gathered
below:
1) X6 = C(l,2)X2 + C(l,l9)Xl9 + C(l,28)X28 + C(l,3l)X31 + C(l,32)X32
2) XlO = X7 -XB + X9 -Xll + Xl2 -X26
3) Xll = C(3,2)X2 = C(3,3)X3 + C(3,4)X4 + C(3,19)Xl9 + C(3,28)X28 +
C(3,3l)X31
4) Xl2 = C(4,9)X9 + C(4,10)Xl0 + C(4,32)X32
5) Xl4 = C(5,15)Xl5 + C(5,16)Xl6
6) Xl6 = Xl3 -Xl4 + Xl5 -Xl7 + XlB + C(6,22)X22 + G(6,3l)X31
7) Xl7 = C(7,13)Xl3 + C(7,15)Xl5
8) Xl9 = C(8,12)Xl2 + C(8,27)X27 + C(8,28)X28
9) X20 = C(9,5)X5 + C(9,12)Xl2 + C(9,17)Xl7 + C(9,28)X28
10) X21 = C(l0,12)Xl2 + C(l0,27)X27 + C(l0,28)X28
lJ) X22 = X5 + Xl2-Xl3 + Xl7-Xl9-X20-X21 + X27 + X28 + C(ll,3l)X31
12) X24 = X21 = C(l2,22)X22 + X23-X25-X26, when FC~1in$X24-s;:FC
X24 = FCMin' when X24 < FCMin
X24 = FC, when X24 > FC
-90-
13) X25
X25
= X21 + C(l3,22)X22 + X23 -X24 -X26, when X24 ~ FCM. 1n
= PET, when X24<FCM. 1n
14) X26 = C(l4,2l)X21 + C(l4,22)X22 + C(l4,23)X23 + C(l4,32)X32
C(l4,32) = RE(X24-FC) when X24>FC, otherwise C(l4,32) = 0
15) X29 = X28 (Dummy Equation)
16) X31 = Xl -X2 -X3 + X4 + X6 -Xll + Xl8 -Xl9 + X27 + X28
CALIBRATION PROGRAM AND NEW SUBROUTINES
Although the calibration program used in the Yellowstone Impact Study
was essentially the same as the one prepared by the Montana Water Resources
Research Center (Boyd and Williams 1972), the program was modified to make
the logic less dependent on the basin parameters. In the original version
of the modeJ,basin parameters were fed into the main program and the program
was run. If the model was used for some other basin with different parameters,
the corresponding changes would have had to be incorporated and the whole
program would have had to be run again. Three subroutines--INITIA, EXPORT,
and SURFAC--were added and one subroutine--COMPUT--was modified in order to
make the logic less dependent on the basin parameters. The result was an
essentially data and basin independent calibration program that could be
easily used on all nine subbasins.
Figure 6 shows the hierarchy of the subroutines and their relationship
to each other. These subroutines were called from left to right.
Figure 6. Calibration program subroutines
A brief description of the new subroutines is given below.
INI TIA
The initial values for different subbasins could be read either through
changes in the subroutines or from the data card. In the original program,
the following initial values were specified in the main logic, and the whole
program was compiled and run. If the initial values changed, the original
program had to be recompiled.
The initial values specified were:
1) Initial precipitation for averaging precipitation (SAVE);
-91-
2) Field capacity (FC) and minimum field capacity (FCM. ) ; l.n
3) Coefficients for moving average rainfall ( Q) ;
4) Beginning year and ending year ( 1'1, N); and
5) Number of months ( NP).
Since these values could be read outside the main program, the rest of the
revised program was subbasin independent. With this idea in mind, the sub-
routine INITIA was created. The values that were read into INITIA are:
1)
2)
3)
4)
5)
6)
7)
8)
9)
SAVE--initial precipitation for averaging;
FC, FCM. --field capacity, minimum field capacity; l.n
a--precipitation averaging factor;
;.J,N--beginning and ending year;
Rl,Pl--coefficients for calculating X7 (ground-water outflow);
R2,P2--coefficients for calculating XB (ground-water inflow);
RE--groundwater recharge factor (ground-water recharge due to
saturation of field capacity);
NP--number of months for study period; and
MP--number of months for calibration.
In most cases, the number of months for study period should be the same
as for calibration, however, if calibration is for a shorter period MP
would be different from NP.
Note that the subroutine INITIA has coefficients for calculating X7
(ground-water outflow) and XB (ground-water inflow). The following relation-
ships were used to calculate X7 and X8:
X7 = (Pl)(Xl) + Rl
XB = (P2)(X2) + R2
where: Xl = outflow from the basin
X2 = inflow to the basin
Since Xl and X2 were primary values (i.e., they were read in as an input
to the system) X7 and XB could also be read in as primary values because of the
above relationships.
!n the original program, X7 and XB were a part of the system of equations.
This increased the matrix size. As mentioned above, X7 and XB did not need to
belong to this system of equations, since their values were known as soon as
-92-
I
}
I .
Xl and X2 were known. This feature was exploited in reducinQ the mntrix size.
With the addition of INITIA in the program, X7 and XB are calculated right
after Xl and X2 are read.
EXPORT
This subroutine was added to handle exports from the subbasin. The
export variable 5(27) may, at times, have depended on the month NM. In case
that export was zero, S(27) = 0 for all NM. (NM = month considered.)
SURFAC
In the original calibration program, evaporation loss from the reservoir
was calculated as a certain percentage of the storage. More accurate evapora-
tion losses may be calculated by multiplying the pan evaporation coefficient
by surface area.
When the daily pan evaporation coefficient was available, there was no
need for any correction, such as for wind or humidity. l~ultiplyinq the pan
evaporation coefficient by the surface area.gives a fairly accurate estimate
of evaporation losses. Since the unit of time for the study was one month,
the average pan evaporation coefficient value for the month could be used
without any correction factor.
This subroutine could take 36 storage levels in some uniform steps. The
actual surface are~ was interpdlated linearly between two adjacent levels.
COMPUT
In the original program, snowfall had been treated as a part of the system
of equations. Since snowfall is a function of precipitation and temperature,
both of which are known, snowfall could be calculated outside the system of
equations. The COMPUT subroutine was modified to calculate snowfall. Other
than this change, this subroutine was essentially the same as the original
subroutine.
SIMQUAL--THE SIMULATION PROGRAM
Although SIMQUAL, as the modified simulation program was named, retained
the basic character of the original SWP model, SIMQUAL contained some new
features which included water quality calculations, changes in the output
format, and different criteria for the operation of reservoirs. The SIMQUAL
program had many new subroutines compared to the original SWP program (Montana
University 1972). Figure 7 shows the hiemrchy of SIMQUAL's subroutines.
-93-
Figure 7. Simulation program subroutines
Subroutines DEPLET, COMPUT, SURFAC, EXPORT, INITIA, and QUALTY were sub-
basin dependent; all others were subbasin independent.
Subroutines common to the simulation and calibration programs (those which
occur both in figure 6 and in figure 7) remained essentially the same except
COMPUT. Changes in the COMPUT subroutines were due to rearrangement of the
system of equations. The new subroutines are described briefly.
DEPLET
This subroutine, added to the main program, handled any reallocation of
water as between two states or regions. As an example, for the Yellowstone
Impact Study, inflows from the Tongue River, the Powder River, or the Bighorn
River had to be reduced to allow for Wyoming's share of ~ater from these rivers.
The amount to be allocated was based on the compact between the two states.
As the name implies, this subroutin~ allowed for this depletion. During the
simulation phase, any changed inflow to the subbasin may be read in1 the sub-
routine DEPLET. Arguments of the subroutines are month IT and inflow 5(2).
SURFAC
Subroutine SURFAC calculated the evaporation loss from a reservoir based
on the surface area of the reservoir and the pan evaporation coefficient for
that month. It is assumed that the average value of a pan evaporation co-
efficient for each month will takP. into account factors such as temperature,
humidity, and wind on an average basis.
-94-
INITIA
This subroutine defined the initial values of some of the
By creating this subroutine, the main program became independent of the
subbasin and scenarios.
MODIST
MODIST was a short form of monthly distribution, ranking the data on
a monthly basis and finding ninetieth p~rcentile and median values (i.e. flows
that are exceeded in 90 percent of those months and 50 percent of those months,
for a particular month). It also calculated the mean value on a monthly basis.
For ranking the data, subroutines SORT and COMPAR were called. Subroutine
PLOT was called to plot the ninetieth percentile and fiftieth percentile
values. Arguments of the subroutine were NMO, AA, and YY. AA corresponds
to monthly data, NMO is number of months, YY, if zero implies water quality
year, otherwise water year.
QUAL TV
This subroutine was called by the OUTPUT subroutine to calculate total
dissolved solids (TDS) based on outflow.
Arguments of the subroutine QUALTY were Q, RF, DIV, EN, OF, IT, TDS,
TDSF, TDSQ, TDSL, TDSLl, TDSFl, TDSL2, and TDSF2 where:
Q = outflow or release;
RF = return flow;
DIV = diversion requirement (irrigation plus energy and instream flows);
EN = energy flow;
OF = outflow RF plus instream plvs spill; and
IT = counter on month.
These arguments, required for TDS calculations, were transferred back to the
OUTPUT routine for further calculations and output.
TDS calculations are shown schematically in figure 8.
-95-
I Q, TDSI II (Outflow from the model)
I
jQUD, LUDj fqrR, LIRl IOEN, LEN!
I QUD QRET ll_~c_D~_:> ______ --QEN I
QUD + QRET, LUD + LIR QCONS + QEN, LEN
(salts contained in out flow) (salts lost from the system)
where: Q = net outflow = QUD + QIR + QEN
QUD = undiverted water in million acre-feet
QIR = diverted irrigation water in million acre-feet = QRET + QCONS
QRET = return flow in million acre-feet
QCONS = consumptive use of diverted irrigation water in million
acre-feet
QEN = energy plus consumptive industrial water
LUD, LIR, LEN = total dissolved solids in tons in QUD, QIR, and
QEN, respectively.
Figure B. Schematic representation of TDS calculations.
Figure 8 shows that the total salt lost from the system was due to
industrial or energy water. Salts in the irrigation diversion were assumed
to come back to the mainstem through return flow. Thus the outflow was
QUD + QRET with total load of LUD + LIR.
TDS was calculated using a monthly regression equation:
TDS = f(Q,c)
where: Q = flow in million acre-feet;
c = a constant; and
f = a function giving the relationship between TDS and (Q,c)
-96-
LUD = TDSI(QUD
LIR = TDSI ( QIR)
LEN = TDS I( QEN)
Outflow TDSI = LUD + LIR
QUD + QRET
In addition to finding the outgoing quality, the following quantities were
also calculated in this subroutine:
1) Total load diverted in tons for irrigation, TDST:
2) TDS in parts per million, TDS(ll);
3) Outgoing load in tons, TDSL(II);
4) Outgoing TDS, TDSF(ll);
5) Total load in the stream TDSQ(II);
6) Total outgoing load with half ton/acre salt pick up, TDSLl(Il);
7) Total outgoing load with one ton/acre salt pick up, TDSL2(II); and
8) TDSFI(II), TDSF2(II) outgoing water quality with half-ton and one-ton
salt pick up per acre, respectively.
Water quality calculations were based on yearly intervals extending from
April through March, whereas other calculations were based on the water year
which extends from October through September. Consequently, the first six
months and the last six months of the thirty-year study period were ignored
in water quality calculations.
The total load in tons that was diverted for irrigation is from April
through October. This diverted load returned to the stream during the same
year--April through March--with the distribution shown in table 46.
Table 46. Percentage by month of TDS returning to ~treamflow.
Apr. May June July Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar.
11% 14% 18% 18% 4%
-97-
The subroutine QUALTY was called after every simulated twelve months. This
was mainly due to different amounts of salt load in the stream from one year
to the next.
PRINT
This subroutine was primarily meant for printing headings on the monthly
values of outflow, inflow, and water quality in TDS. Arguments of the sub-
routine were AA, NMO, and YY. AA corresponded to monthly data, NMO to the
number of months, and YY, if zero, implied water quality year (April through
March), otherwise water year.
MEAN
This subroutine mainly calculated the simple average or time weighted
average and volume weighted average of TDS. These averages were calculated by
the month and also by the year. Arguments of the subroutine were NMO, AA, BB,
and YY. AA contained TDS data and BB, the flow data. NMO and YY have the same
meaning as defined above.
SORT and COMPAR
These subroutines were called by the MODIST subroutine for ranking the
data in ascending order.
PLOT
Subroutine PLOT plotted the fiftieth and ninetieth percentile values
(i.e. those values exceed 50 and 90 percent of the time) of outflow, inflow,
and water quality. Arguments of the subroutine were NMO, AA, BB, SF, and
YY. AA corresponded to fiftieth percentile data and BB represented ninetieth
percentile data. SF was the scale factor and equaled 80 percent of the
largest value of fiftieth percentile data; YY, if zero, implied water quality
year, (April through March), otherwise water year.
-98-
TYPES OF SIMULATION
When all subbasins had been calibrated, they were ready for simulation
runs. An ideal model--for simulation is the one that allows a wide range
of operating criteria to be used in each simulation. Unfortunately, most
models can carry out simulations only over a given set of rules and a limited
number of operating criteria. The swp model is no exception.
In this study, the SWP was used to study three types of simulations.
Type 1
In type 1 simulations, the operating rules were to release water from
the reservoir to meet the minimum flow requirement, to keep storage as high
as possible, but to give releases to maintain minimum flows a higher priority
than storage. Under such conditions, the annual yield was the maximum
amount of water that could be withdrawn from the reservoir for each year of
the study period while maintaining a minimum storage level.
Type 2
In type 2 simulations there was no storage in the basin and consequently
what could not be used was lost from the system. The maximum amount of water
that could be used was dictated by the minimum flows in the study period.
Type 3
Type 3 simulations differed from type 1 in the operating policy. The
operating policies were to release wat~r from the reservoir to give the irri-
gation demand highest priority and always satisfy that demand (d), and to
store water in the dam if the inflow to the dam exceeded the demand plus the
reservations for minimum flows. If the inflow was less than the demand d,
thenthe flow was augmented by the release from the dam to meet the demand d.
If the inflow was less than 6 + d, where n is the minimum required flow, but
more than d, then nothing could be stored and inflow was passed through the
dam. If inflow exceeded n + d, the excess inflow over n + d could be stored,
if storage space were available.
The simulation program as written by Boyd and Williams (1972) was useful
for type 1 simulations. The main logic of the program had to be modified to
include type 3 simulations. Besides changing the logic, the simulation program
was modified to include water quality calculations based on total dissolved
solids ( TDS) •
-99-
;I
:I
SCENARIOS
Each subbasin had up to three scenarios for simulating high, inter-
mediate, and low water use. In each scenario the demands for irrigation,
energy, and municipal use were lumped together. The model in this form did
not discriminate among the demands explicitly based on their use; however,
it discriminated among them indirectly whenever necessary. For example,
if the total demand for irrigation, energy, and municipal water could not
be satisfied for the period of study, then the program assumed that the irri-
gation and municipal demands had a higher priority than the energy demand.
Satisfying the ir~igation and municipal demands implied that although all of
the irrigation and municipal demands could be satisfied, there would not be
enough water to meet all of the energy demand. The same model could be run
satisfying part of the energy demand. Finding the demand that could be
satisfied was essentially the same as finding the yield of the subbasin. Since
the quality of water leaving the subbasin was a function of irrigation diver-
sion return flows, it was important to identify the satisfied demands.
For subbasins that had no reservoir, the portion of the logic for storing
water was eliminated and other portions of the program were changed.
In type 3 simulations, the data were arranged in a different way. For
example, suppose that the total demand for irrigation plus energy, municipal,
and instream requirements is d and the minimum flow demand is 6. As per the
operating rule, water can be stored if the inflow exceeds b + d. The dam can
release water to meet d, but can release no water to augment the flows for the
minimum flow requirement. The demand d is read in as RA(I) in the program and
d + 6 is read in as FG(I). The decision to store or to release water is de-
termined by the inflow. If the inflow exceeds FG(I), water can be stored.
The amount to be stored will depend on the storage level. In case the inflow
is between RA(I) and FG(I) there would be no need to augment the flows since
demand RA(I) would be satisfied. Water would not be stored because the inflow
is less than FG(I). For inflows less than RA(I), flows would be augmented
to meet demand RA(I). The main consequence of the above mentioned operating
rule was the reduction in the yield of the subbasin, because the reservoirs
were not allowed to store as much as they could.
In simulation, the system of equations used was exactly the same as used
in calibration with the exception of the role played by the following equation:
X31 = Xl -X2 -X3 + X4 + X6 + Xll + XlB -Xl9 + X27 + X28
The above equation was used for solving for X31 in the calibration phase, but in
the simulation this was used for solving for Xl or X4.
Xl = X2 + X3 -X4 -X6 -Xll -XlB + Xl9 -X27 -X28 + ·x31
or
X4 = Xl + X2 + X3 -X6 -Xll -Xl8 + Xl9 -X27 -X28 + X31
An implicit assumption in this logic is that the demand d has higher
priority than the minimum flow demand, but this can be changed if necessary.
I
-100-
Thus, by interchanging the role of XI nr X4 with X31, the same equati~n
could be used in simulation.
When the above equation was used for solving for XI, the set of equations
was said to be in mode 1. When solving for X4, it was said to be in mode 4.
The equations for the simulation follow:
1) XI = X2 + X3 -X4 -X6 -Xll -XlB + Xl9 -X27 -X28 + X31
2) X6 = C(2,2)X2 + C(2,19)Xl9 + C(2,28)X28 + C(2,3l)X31 + C(2,32)X32
3) XlO = X7 -XB + X9 -Xll + Xl2 -X26
4) Xll = C(4,2)X2 + C(4,3)X3 + C(4,4)X4 + C(4,19)Xl9 + C(4,28)X28 +
C(4,3l)X31
5) Xl2 = C(5,9)X9 + C(5,10)Xl0 + C(5,32)X32
6) Xl4 = C(6,15)Xl5 + C(6,16)Xl6
7) Xl6 = Xl3-Xl4 + Xl5-Xl7 + XlB + C(7,22)X22 + C(7,3l)X31
8) Xl7 = C(B,l3)Xl3 + C(B,l5)Xl5
9) Xl9 = C(9,12)Xl2 + C(9,27)X27 + C(9,28)X28
10) X20 = C(l0,5)X5 + C(l0,12)Xl2 + C(l0,17)Xl7 + C(l0,28)X28
11) ~ X21 = C(ll;l2)Xl2 + C(ll,27)X27 + C(ll,28)X2B
12) X22 = X5 + Xl2 -Xl3 + Xl7 -Xl9 -X20 -X21 -X27 + X28 + C(l2,3l)X31
13) X24 = X21 + C(l3,22)X22 + X23- X25-X26 when FCMin~X24 ~ FC
X24 = FCM. when X24 < FCM. 1n 1n
14)
X24 = FC when X24 > FC
X25 = X21 + C(l4,22)X22 + X23 -X24 -X26 when X24 < FCM. otherwise 1n
X25 = PET
15) X26 = C(l5,2l)X21 + C(l5,22)X22 + C(l5,23)X23 + C(l5,32)X32
where: C(l5,32) = RE(X24 -FC) when X24 = FG, otherwise
C(l5,32) = 0
16) X29 = X28 (Dummy equation).
-101-
..
Reordering of equations and coefficients was necessary becamse of the
inverse subroutine used in the program. The logic was changed from mode
1 to mode 4 and vice versa, depending upon the storage condition. If the
storage was full, the system was solved for outflow Xl, and hence mode 1,
otherwise, in mode 4.
AREA SIMULATIONS
THE UPPER YELLOWSTONE, CLARKS FORK
YELLOWSTONE, AND KINSEY AREA SUBBASINS
These three subbasins were not simulated. Rather the projected water
requirements for these subbasins for each of the three levels of development
were merely subtracted from their historical outflow, so that the simulations
for downstream subbasins would reflect all upstream water use in addition to
their own.
THE BILLINGS AREA SUBBASIN
Inflow to the Billings Area Subbasin for a particular level of develop-
ment was the sum of the outflows from the Upper Yellowstone and Clarks Fork
Yellowstone subbasins for the same level of development. By using a similar
procedure for each subbasin, the cumulative effect of development could be
simulated for the lower subbasins in the Yellowstone basin.
The water requirements for the low, intermediate, and high levels of
development in the Billings Area Subbasin are shown in table 47. These re-
quirements reflect only the water that would be needed to meet irrigation
and municipal demands. None of the levels of development called for water to
meet energy demands or minimum-flow requirements. For all three levels of
development, flows would be neither augmented nor stored because the sub-
basin has no dam to regulate flows.
The results of the simulations of the three levels of development are
shown in tables 48 and 49. The simulation indicated that the Billings Area
Subbasin would have enough water to meet the demands of a high level of
development, although the demands would reduce the flows in June, July,
August, and September below their historical levels. The demands of the low
and intermediate levels of development would not significantly reduce historical
flows. Generally, none of the simulations indicated appreciable degradation
of water quality although it is likely that the few low-flow months under
the high level of development would result in a drastic-degradation in
water quality.
THE BIGHORN SUBBASIN
Because of the presence of the Yellowtail Dam, the Bighorn Subbasin would
meet its demands under high and intermediate levels of development. The low
level of development was not considered for this subbasin because the water
-102-
requirements would be insignificant compared to the historical flow of the
river. Table 50 shows the flow requirements for the intermediate and high
levels of development. These flow requirements include energy, irrigation,
and municipal demands but no minimum-flow requirements. In both levels of
development, it was assumed that the Yellowtail Dam would be available to
augment or store streamflows throughout the simulation period. A depletion
allowance consistent with the Yellowstone River Compact was made in the Big-
horn Subbasin's inflows. · ·
Table 47. Billings area subbasin water requirements (in acre-feet).
Projected Level of Development
Month Low ' Intermediate High
Oct 485 685 905
Nov 290 295 325
Dec 290 295 325
Jan 290 295 325
Feb 290 295 325
Mar 290 295 325
Apr 485 685 905
May 2,815 5,240. 7,895
June 3,590 6,895 10,235,
July 6,500 12 '715 18,955
Aug -5,140 10,000 14,880
Sept 2,425 4,565 6,730
TOTAL 22,890. 42,260 62,130
"'"::-,,
The results of the simulations of the high and intermediate levels of
development are shown in table 51. The demands of the high level of develop-
ment would easily be satisfied without affecting natural· flows significantly,
although the ninetieth-percentile flows (those flows exceeded 90 percent of
. the time in a given month) would be low for July and August. This, however,
was due to the operational policy used for the dam in the simulation. In
any event, a release from the dam exceeded the requirement orily if it was a
spill from the dam. Like the high level of development simulation, the
intermediate level of development simulation indicated little effect on the
natural outflow.
In either case, the water quality of the outflow would remain almost
unchanged from the natural outflow's water quality because the total demand
for both simulations would be small compared to the natural outflow. Total
dissolved solids would vary from 477 to 634 mg/1 for the intermediate level
and from 477 to 650 mg/1 for the high, a small range due to the Yellowtail
Dam which reduces fluctuations in water quality.
-103-
Table 48. Outflow of the Billings area subbasin (in acre-feet).
Level of Development
Low Intermediate High
Fiftieth Ninetieth Fiftieth Ninetieth Fiftieth Ninetieth
Month percentile percentile percentile percentile percentile percentile
Oct 245,036 163,456 244,956 163,380 244,866 163,295
Nov 219,666 188,062 219,982 188,379 220,263 188,660
Dec 178,411 133,290 178,661 133,545 178,882 133,769
Jan 153,036 100,470 153,219 100,663 153,367 100,820
Feb 159,451 120,568 159,567 ]20,690 159,657 120,787
MHr 210,452 143,850 210,636 144,040 210,786 144,195
Apr 241,904 167,308 241,574 166,985 241,219 166,637
May 697,674 360,719 691,032 334,079 684,165 327,214
June 1 '545 ,894 1,065,127 1,537,069 1,056,308 1,528,209 1,047,449
July 804,278 379,376 787~143 362,245 769,993 345,099
Aug 230,954 119,876 217,809 106,737 204,654 93,589
Sept 184,038 108,507 178,382 102,850 172,690 97,157
NOTE: A fiftieth-percentile flow is the flow that is exceeded 50 percent of
the time in a particular month, and the ninetieth-percentile flow is that flow
that is exceeded 90 percent of the time in a particular month.
Table 49. Average outflow (in acre-feet) and TDS (in mg/1) of the Billings
area subbasin
Level of Development ·
Low Intermediate High
Natural
Month Flow TDS Flow TDS Flow TDS Flow
Oct 248,041 268 247,966 269 247,881 270 262,944
Nov 227,485 278 227 '776 279 228,059 279 227,424
Dec 173,022 305 173,270 306 173,488 306 173,048
Jan 15:3,559 312 153,747 312 153,900 313 153,655
Feb 167,798 289 167,916 289 168,009 290 167,954
Mar 222,461 267 222,650 268 222,803 268 222,558
Apr 249,442 253 249,117 253 248,768 254 253,506
May 688,842 156 682,185 156 675,321 157 746,377
June 1,565,048 117 1,556,220 117 1,547,358 118 . 1,636,944
July 830,338 131 813,202 132 796,052 134 932,201
Aug 252,659 228 239,513 231 226,358 235 344,169
Sept 199,550 283 193,892 286 188,199 289 263,177
TOTAL 4,978,245 4,927,454 4,876,196 5,383,957
-104-
I
t ;
I·
,'
'
i ,,
Table 50. Bighorn subba~in water requirements (in acre-feet)
Level of Development
Honth Intermediate High
Oct 750 2, 775
Nov 490 2,385
Dec 490 2,385
Jan 490 2,385
Feb 490 2,385
Mar 490 2,385
Apr 750 2,775
May 3,880 7,470
June 4,920 9,035
July 8,830 14,900
Aug 7,010 12,170
Sept 3,360 6,685
TOTAL 31,950 67,735
Table 51. Outflow (in acre-feet) and TDS (in mg/1) of the Bighorn Subbasin
Level of Development
Intermediate High
Fiftieth Ninetieth Fiftieth Ninetieth
Month Percentile Percentile Average TDS Percentile Percentile Average TDS
Oct 194,045 140,169 197,372 625 188,241 134,252 191,535 627
Nov 184,077 142,153 184,734 ' 631 180,204 138,223 180,780 632
Dec 164,977 109,022 160,842 612 160,974 104,977 156,861 613
Jan 143,349 100,767 153,433 552 139,343 96,807 149,412 554
Feb 144,398 107,600 169,476 477 140,336 103,678 165,413 477
Mar 211,631 157,238 232,825 503 207,573 153,146 228,792 504
Apr 204,188 119,215 201,080 624 198,322 113,168 195,063 626
May 259,527 135,198 282,443 592 236,007 109,680 256,963 595
June 566,793 137,846 546,688 594 534,673 105,791 514,631 596
July 261,441 30,130 312,457 579 204,851 2,340 260,706 584
Aug 81,338 36,351 lll ,056 625 35,368 2,340 67,477 650
Sept 155,622 91,851 157,206 634 131,494 57,261 128,967 640
TOTAL 2,709,612 2,496,600
NOTE: See note to table 48.
-105-
THE MID-YELLOWSTONE SUBBASIN
The water requirements for the low, intermediate, and high levels of
development in the Mid-Yellowstone Subbasin are given in table 52. These re-
quirements include demands for energy, irrigation, and municipal use but no
minimum flow requirement. The Mid-Yellowstone Subbasin was assumed to have no
ability to augment or store flows.
Table 52. Mid-Yellowstone subbasin water requirements (in acre-feet)
Level of Development
Month Low Intermediate High
Oct 3,320 6,950 12,700
Nov 3,070 6,445 11 '940
Dec 3,070 6,445 11,940
Jan 3,070 6,445 11,940
Feb 3,070 6,445 11,940
Mar 3,070 6,445 11,940
Apr 3,320 6,950 12,700
May 6,350 13,005 21,780
June 7,360 15,025 24,815
July 11,165 22,595 36,160
Aug 9,380 19,055 30,860
Sept 5,845 11,995 20,265
TOTAL 62,090 127,800 218,980
The fiftieth-and ninetieth-percentile outflow values for all simulated
levels of development in the Mid-Yellowstone Subbasin are given in table 53.
The ninetieth-percentile flows would be high for all months but August. Dur-
ing the simulated month of August 1961, there was some shortage for both the
intermediate and high levels of development; this was the only shortage
indicated.
The average values of TDS, displayed along with average flows in table
54, indicate that water quality would become slightly poorer during the simu-
lated low flows of 1961, When the large proportion of irrigation return flow in the
outflow substantially decreased water quality.
THE TONGUE SUBBASIN
Table 55 gives the water requirements for the Tongue River under the low,
intermediate, and high levels of development. The "Projected Demand" columns
show demands for irrigation, municipal use, and energy. At the high level of
development, not all of the irrigation, municipal, and energy requirements
could be satisfied. Since the irrigation and municipal demands have higher
priority, only 4,435 acre-feet of the projected energy demand of 9,835
-106-
acre-feet per month could be met. For the high level of development, the
"Projected Demand" column also shows minimum-flow requirement judged by the
Montana Fish and Game Department to be a "bare-bones" requirement: 900 acre-
feet per month for June through February, 2700 acre-feet per month for March,
April, and May. For the remaining two levels of development, the minimum-flow
requirement is shown only in the second column. For the intermediate develop-
ment level that minimum-flow requirement is 60 percent of the instream flow
assumed by the Water Work Group of the Northern Great Plains Resources Program
(NGPRP ]974); for the low level of development, all of the NGPRP-assumed
instream flow was included. A reservoir with a capacity of 320,000 acre-feet
was assumed for the high and intermediate levels of development, and a reservoir
with a capacity of 112,000 acre-feet was assumed for the low level of develdp-
ment.
Table 53. Outflow of the Mid-Yellowstone subbasin (in acre-feet)
Level of Development
Low Intermediate High
Fiftieth Ninetieth Fiftieth Ninetieth Fiftieth Ninetieth
Month Percentile Percentile Percentile Percentile Percentile Percentile
Oct 462,205 323,536 459,151 320,492 448,648 310,188
Nov 409,310 333,575 406,677 330,930 398,081 322,045
Dec 337,255 217,102 334,446 214,307 325,382 205,456
Jan 296,842 194,918 293,910 191,983 284,947 182,934
Feb 302,286 225,893 299,204 222,809 290,037 213 '586
Mar 388,389 294,533 485,442 291,594 476,136 282,481
Apr 465,915 326,058 462,291 322,432 451,155 311 '278
May 988,032 439,194 975,673 426,837 935,515 386,800
June 2,129,436 1,175,717 2,114,182 1,160,467 2,064,900 1,111,223
July 1,080,117 408,825 1,053,213 381,985 968,080 325,307
Aug 305,904 142,989 284,700 121,804 215,827 64,785
Sept 342,057 210~790 331,134 199,867 291,202 137,652
NOTE: See note to table 48.
The fiftieth-and ninetieth-percentile flows for the three simulations
are given in table 56. The 320,000 acre-foot reservoir used in the intermediate-
and high-level simulations could satisfy a total annual demand of about 130,000
acre-feet. The fiftieth-and ninetieth-percentile values would be almost equal
for those two levels of development, implying that the outflow consisted only
of the irrigation return flows plus instream requirements.
-107-
Table 54. Average outflow (in acre-feet) and TDS (in mg/1) of the Mid-Yellowstone
subbasin
Level of Development
Low Intermediate High
Natural
Month Flow TDS Flow TDS Flow TDS Flow
Oct 460,062 460 457,015 460 446,660 465 478,565
Nov 417,964 486 415,323 486 406,554 490 423,122
Dec 323,390 558 320,589 558 311,654 562 341,435
Jan 300,485 476 297,545 576 288,413 581 318~323
Feb 344,890 529 341,800 529 332,483 532 368,217
Mar 493,392 441 490,452 441 481,304 443 493,009
Apr 456,588 462 452,962 462 441,822 467 466,004
May 941,441 311 929,090 313 889,073 320 1,013 '584
June 2,103,569 198 2,088~318 201 2,039,064 203 2,164,446
July 1,166,987 269 1,140,055 271 1,059,693 280 1,326,683
Aug 359,878 504 338,680 508 272,129 530 501,157
Sept 362,990 524 352,061 529 310,895 556 442,866
TOTAL ·7,731,636 7,623,890 7,279,744 8,337,411
Table 55. Tongue subbasin water requirements (in acre-feet)
Level of Development
Low Intermediate High
Projected Projected Demand Projected Projected Demand Projected
Month Demand Plus Minimum Flow Demand Plus Minimum Flow Demand
-Oct 1,175 7,175 4,370 7,970 6,000
Nov 955 6,955 3,930 7,530 5,400
Dec 955 9,055 3,930 8,790 5,400
Jan 955 9,055 3,930 8,790 5,400
Feb 955 9,055 3,930 8,790 5,400
Mar 955 12,995 3,930 11,130 5,400
Apr 1,175 14,975 4,370 12,650 6,000
~1ay 3,810 29,310 9,335 24,935 13,960
June 4,685 30,185 11,390 26,690 16,595
July 7,985 30,185 17,975 31,300 26,470
Aug 6,445 12,445 14,900 18:500 21,860
Sept 3,370 9,370 8,760 12,360 12,645
TOTAL 33,420 180,760 90,750 179,435 130,530
-108-
Table 56. Outflow of the Tongue River subbasin (in acre-feet) .
Level of Development
Low Intermediate High
Fiftieth Ninetieth Fiftieth Ninetieth Fiftieth Ninetieth
Month Percentile Percentile Percentile Percentile Percentile Percentile
Oct 6,585 1,562 4, 770 1,170 2,655 2,655
Nov 6,365 4,943 4,335 2,338 1,997 1,997
Dec 8,390 5,667 5,665 2,862 1,778 1 '778
Jan 8,320 1:319 5,300 4,624 l,ss8 1,558
Feb 8,245 5,834 5,150 2,745 1,339 1,339
Mar 23,812 12,260 7,640 7:640 3,358 3,358
Apr 23,129 11,375 8,860 5,133 3,578 3,578
May 44,807 15,337 17,205 9,237 5,113 5,113
June 103,865 4,479 57,310 2,045 40,320 3,472
July 13,994 1,315 2,630 2,630 4,849 4,845
Aug 1,315 1,315 2,630 2,630 4,849 4,849
Sept 6,730 730 4,182 1,460 3,094 3,094
NOTE: See note to table 48.
Table 57. Average outflow (in acre-feet) and TDS (in mg/1) of the Tongue subbasin
Level of Development
Low Intermediate High
Natural Incoming
Month Flow TDS Flow TDS Flow TDS Flow TDS
Oct 9,078 516 4,567 752 2,744 779 16,995 607
Nov 9,832 670 4,816 766 2,261 793 18,369 696
Dec 9,964 739 5,514 798 2,080 835 12,893 756
Jan 10,496 675 5,609 753 2,168 768 11 '092 719
Feb 16,584 412 8,740 464 3,992 494 16,414 491
Mar 40,952 416 26,354 432 20,830 422 39,248 431
Apr 27:936 542 18,732 560 14,194 555 32,325. 550
May 51,155 440 36,080 470 26,765 464 48,955 443
June 101,622 262 76,818 283 65,115 285 95,469 265
July 18,857 381 11,263 517 8,453 562 30,657 348
Aug 2,589 857 2,869 1,137 4,849 768 9,397 423
Sept 6,391 597 3,700 785 3,094 752 12,167 507
TOTAL 305,456 205,062 156,545 343,981
-109-
Table 57 gives the values of average outflows and levels of TDS for each
level of development in the Tongue Subbasin. Under the low level of develop-
ment; water quality calculations showed only slight degradation. Under the
intermediate level of development, TDS calculations indicate a slight de-
terioration in water quality. Because most of the outflow during August would
consist of irrigation return flows, that month would have the worst water
quality. At the high level of development, TDS levels indicate poor water
quality in most months, a result of what would be reduced outflow having a
large proportion of irrigation return flows. lnstream flows would be crucial
in maintaining water quality. By increasing the instream requirement, water
quality degradation could be reduced, especially in low-flow months.
Under the low level of development, the irrigation, municipal, and energy
demand as well as all of the NGPRP-requested minimum flow could be completely
satisfied, even assuming the smaller reservoir. The fiftieth-and ninetieth-
percentile values (table 56) indicate that August would be the only critical
month at this level of development.
For the intermediate level of development, the total water demand was
about 91,000 acre-feet. As explained above, the 320,000-acre-foot reservoir
would yield 130,000 acre-feet annually, leaving 40,000 acre-feet per year
available for other uses. Up to 60 percent of the minimum flow suggested by
the NGPRP could be satisfied with this water. This minimum flow would not
be augmented by releases of stored water from the dam. If the natural inflow
to the reservoir is less than or equal to the minimum-flow requirement, then
no water could be stored. If the natural inflow is more than the minimum-flow
requirement, then the excess could be stored or used to meet the "projected
demand" of table 55. In either case, stored water could be released to meet
·projected consumptive demand. The fiftieth-and ninetieth-percentile flow
values show that, except in July and August, there would be water in the
stream in addition to the return flows.
THE POWDER SUBBASIN
Table 58 gives the water requirements used in simulations of the Powder
Subbasin. The high level of development called for 230,000 acre-feet for
irrigation water alone; the assumed active storage in the subbasin was only
275,000 acre-feet. After five trial simulations, it became apparent that not
all of the water demand of the intermediate and high levels of development
could be satisfied. Instead, those two projected levels of development were
replaced by the "55 percent" level, which consisted of 55 percent of the high-
level irrigation demand, the full high-level municipal demand and no water for
energy or for minimum-flow requirements. Nor were minimum-flow requirements
considered for the low level of development.
-110-
Table 58. Powder subbasin water requirements (in acre-feet)
Level of Development
Month Low 55 Percent
Oct 820 1,335
Nov 70 95
Dec 70 95
Jan 70 95
Feb 70 95
Mar 70 95
Apr 820 1,335
May 9,850 16,225
June 12,855 21,185
July 24,140 39,800
Aug 18,870 31,115
Sept 8,345 13,745
TOTAL 76,050 125,215
The simulation recognized Wyoming's 42-percent share of the Powder River's
water by including only 58 percent of the historical inflows' values in the
simulation, with the exception that in no month were the historical inflows'
values reduced by more than 7,140 acre-feet (42 percent of 17,000 acre-feet)
regard~ess of the size of the historical monthly flow.
The annual yield of the subbasin was calculated assuming a reservoir
having a yield of 125,000 acre-feet. This yield was based on the assumption
that the reservoir's inflow included flows from the Little Powder River, an
impossibility at the.Moorhead site, which is the most probable location for
the reservoir. The 125,000-acre-foot yield might be achieved if two dams
were built, one on the Little Powder and one on the Powder.
The_results of the simulations are given in table 59.
If a dam were built, the water quality of the river below the dam would be
changed. Seasonal variations in water quality would be averaged, resulting
in a net improvement in water quality. The amount of improvement is unknown.
Even at the low level of development the irrigat~on demand would be 76,000
acre-feet, a third of which would come back to the river as return flo"w. TDS
levels would range from 1,000 to 3,400 mg/1. Mixing in the reservoir could
achieve substantial improvement in water quality. At this level of development,
the fiftieth-and ninetieth-percentile values were the same for most months,
meaning that the outflow would consist mostly of the return flows from irrigation.
The average flows for each month, however, would be much higher than the fifti-
eth-percentile flow, showing the variability in the flow of the river.
-111-
Table 59. Outflow (in acre-feet) and TDS (in mg/1) of the Powder subbasin
Level of Development
Low 55 Percent
Fiftieth Ninetieth Fiftieth Ninetieth
Month Percentile Percentile Average TDS Percentile Percentile Average TDS
Oct 2,000 2,000 5,856 2,079 3,000 3,000 3,363 3,799
Nov 1,250 1,250 6,542 1,630 1,800 1,800 2,706 3 '22'6
Dec 1,000 1,000 4,673 1,937 1,500 1,500 2,356 3,216
Jan 750 750 4,257 1,976 1,130 1,130 2,085 3,000
Feb 2,982 500 13,043 1,036 750 750 6,136 1,402
Mar 34,922 750 61,954 739 1,130 1,130 46,946 750
Apr 30,600 3,315 43,997 1,061 19,797 1,500 30,941 1,149
May 51,484 16,066 55,376 1,096 31,586 4,040 38,324 1,310
June 84,438 3,500 102,888 1,028 63,416 5,260 89,507 1,116
July 4,500 4,500 20,483 1,552 6,760 6,760 14,383 3,372
Aug 4,500 4,500 4,970 3,548 6,760 6,760 6,760 8,089
Sept 2,500 2,500 3,667 3,145 3,760 3,760 3,760 4,084
TOTAL 327,706 247,267
NOTE: See note to table 48.
In the 55 percent simulation, the outflows would consist mostly of irriga-
tion return flows. The fiftieth-percentile flows would be high in the months
of April, May, and June due to spring runoff and snowmelt in the upper portion
of the basin. All ninetieth-percentile flows would be irrigation return flows.
The irrigation projected for the 55 percent level would drastically degrade
the water quality at the mouth of the river. The average TDS of inflows would
be 1,200 mg/1, while that of the outflows would range from 1,100 to 4,000 mg/1
in most months. Again, however, mixing in a reservoir could reduce TDS loads
significantly.
THE LOWER YELLOWSTONE SUBBASIN
The water requirements projected for the
levels of development are given in table 60.
demands for irrigation, energy, and municipal
specified.
high, intermediate, and low
These requirements include
use. No minimum flow was
Inflow to the Lower Yellowstone Subbasin would be the sum of the outflows
of the Powder and Kinsey Area Subbasins. Because no reservoir was assumed for
the Lower Yellowstone Subbasin, the flows could not be stored or augmented.
-112-
Table 60. Lower Yellowstone subbasin water requirements (in acre-feet)
Level of Development
Month Low Intermediate High
Oct 410 785 2,255
Nov 30 30 1,125
Dec 30 30 1,125
Jan 30 30 1,125
Feb 30 30 1,125
Mar 30 30 1,125
Apr 410 785 2,255
May 4,930 9,825 15,815
June 6,430 12,840 20,335
July 12,080 24,135 37,290
Aug 9,450 18,860 29,380
Sept 4,180 8,320 13,555
TOTAL 38,040 75,700 126,510
The results of the simulations are shown in table 61 and 62. The
fiftieth-and ninetieth-percentile flows under all levels of development indicate
that the demands could be satisfied but that a shortage would occur when demand
exceeded inflow. A shortage would have occurred in August 1961 for all levels
of development. The intermediate level of development would have less impact
on flows than would the high level of development and the low level of develop-
ment would have no significant impact.
TDS concentrations would increase, but even under the high level of
development, average water quality would remain relatively good due to the high
flows during periods of large irrigation return flows. During months of low
flows, water quality-degradation would be greater.
The simulations for the Lower Yellowstone Subbasin are important in that
they represent the effect of all projected development in the Yellowstone Basin.
The annual average outflow of the Lower Yellowstone Subbasin for the low, inter-
mediate, and high levels of development would be 7,731,626 acre-feet,
7,623,890 acre-feet, and 7,279,803 acre-feet, respectively. The average annual
outflow, 1944-73, was 8~317,411 acre-feet. On the average, there would be
enough water to satisfy the projected demand, but in some months of some years
there would not be enough even for low-level development, as indicated by the ·
simulated shortage in August 1961.
-113-
Table 61. Outflow of the lower Yellowstone subbasin (in acre-feet)
Level of Development
Low Intermediate High
Fiftieth Ninetieth Fiftieth Ninetieth Fiftieth Ninetieth
Month Percentile Percentile Percentile Percentile Percentile Percentile
Oct 453,165 305,608 450 '778 305,093 437,762 294,921
Nov 441,005 340,600 422,969 337,869 410,592 325,594
Dec 350,824 234,670 339,545 231,366 325,177 217,052
Jan 316,982 201,851 301 ,5B9 198,777 295,093 183,233
Feb 338~537 249,182 329,219 243,590 313,099 228,098
Mar 612,714 304,539 512,839 296,179 574,039 279,314
Apr 538,938 388,858 513,823 363,422 496,380 346,372
May 1,037,764 480,471 1,001 '548 440,103 953,657 387,916
June 2,217,203 1,123,425 2,155,473 1,101,047 2,091,092 1,051,323
July 1,085,902 393,907 1,049,411 358,134 961,489 296,861
Aug 353,761 138 '179 323,394 109,601 251,367 48,601
Sept 326,062 174,059 309 '139 160~003 266,401 98,503
NOTE: See note to table 48.
Table 62. Average outflow (in acre-feet) and TDS (in mg/1) of the lower Yellow-
stone subbasin
Level of Deve~opment
Low Intermediate High
Natural
Month Flow TDS Flow TDS Flow TDS Flow
Oct 466,078 552 459,071 561 445,522 570 504,187
Nov 439,383 577 429,514 585 417,049 594 452 '667
Dec 339,180 636 331,424 640 317,270 646 354,445
Jan 321,902 648 314,522 653 299,309 664 342,515
Feb 377,602 565 363,556 572 346,679 579 396,331
Mar 652,078 496 613,719 504 . 607,521 508 707,417
Apr 588,151 538 564,206 544 547,420 548 617,821
May 988,728 368 943,250 377 893,574 386 1,050,604
June 2,304,475 291 2,240,210 291 2,186,485 291 2,379,886
July 1,231,810 304 1,179,48B 307 1,091,427 313 1,420,334
Aug 384,481 451 353,74B 458 284,934 482 483,946
Sept 345,388 557 327,167 566 282,328 583 426,303
TOTAL 8,439,256 8,119,875 7,719,518 9 '136 ,456
-114-
-115-
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A-1
A-2
PROJECTED WATER REQUIREMENTS IN THE YELLOWSTONE
RIVER BASIN IN THE YEAR 2000
TABLES
Monthly and annual water requirements in the upper Yellowstone
subbasin, year 2000, under three levels of development
Monthly and annual water requirements in the Clarks Fork
Yellowstone subbasin • • • • • • • • • • • • •
A-3 Monthly and annual water requirements in the Billings area
subbasin • • • • • • • • • • • • • • • • • • • •
A-4 Monthly and annual water requirements in the Bighorn subbasin
to year 2000 under three levels of development • • • • •
A-5 Monthly and annual water requirements ~n the Mid-Yellowstone sub~
basin to year 2000 under three levels of development . . . .
A-6 Monthly and annual water requirements in the Tongue
subbasin to year 2000 under three levels of development . . .
A-7 Monthly and annual water requirements in the Kinsey area subbasin
to year 2000 under three levels of development . . . . .
A-8 Monthly and annual water requirements in the Powder subbasin
to year 2000 under three levels of development . . . . . .
A-9 Monthly and annual water requirements in the lower Yellowstone
subbasin to ·year 2000 under three levels of development . .
-117-
PAGE
118
119
120
121
. 122
. 123
124
125
126
TABLE A-1. Monthly and annual water requirements in Upper Yellowstone subbasin,
year 2000 under three levels of development (af).
ENERGY IRRIGATION MUNICIPAL TOTAL
Divert Deplete Divert Deplete Divert Deplete Divert Deplete
LOW-LEVEL DEVELOPMENTb
Jan
Feb
Mar
Apr 380 250 380 250
May 4,950 3,300 4,950 3,300
Jun 6,470 4,315 6,470 4,315
Jul 12,180 8,125 12,180 8,125
Aug 9,520 6,350 9,520 6,350
Sep 4,190 2,790 4,190 2,790
Oct 380 250 380 250
Nov
Dec
ANNUAL 38,070 25,380 38,070 25,380
INTERMEDIATE-LEVEL DEVELOPt1ENTc
Jan
Feb
Mar
Apr 760 510 760 510
May 9,900 6,600 9,900 6,600
Jun 12,950 8,630 12,950 8,630
Jul 24,370 16,250 24,370 16,250
Aug 19,040 12,695 19,040 12,695
Sep 8,380 5,585 8,380 5,585
Oct 760 510 760 510
Nov
Dec
ANNUAL 76,160 50,780 76,160 50,780
HIGH-LEVEL DEVELOPMENTd
Jan
Feb
Mar
Apr 1,140 760 1,140 760
May 14,850 9,900 14,850 9,900
Jun 19,420 12,950 19,420 12,950
Jul 36,560 24,370 36,560 24,370
Aug 28,565 19,040 28,565 19,040
Sep 12,565 8,380 12,565 8,380
Oct 1,140 760 1,140 760
Nov
Dec
ANNUAL 114,240 76,160 114,240 76,160
aThe irrigation diversion rate is 3 acre-feet/acre; the depletion rate is
2 acre-feet/acre.
bAssumptions: (no energy development); (12,690 acres of new irrigation)e;
(negligible increase in population.)
cAssumptions: (no energy development); (25,390 acres of new irrigation)e;
(negligible increase in population).
dAssumptions: (no energy development); (38,080 acres of new irrigation)e;
(negligible increase in population).
eirrigation is assumed to be developed with loans at 10 percent amortized
over 10 years.
-118-
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TABLE A-2. Monthly and annual water requirements in Clarks Fork Yellowstone
subbasin, year 2000 under three levels of development (af).
ENERGY IRRIGATIONa MUNICIPAL TOTAL
Divert Deplete Divert Deplete Divert Deplete Divert
HIGH-LEVEL DEVELOPMENTb
Jan
Feb
Mar
Apr 65 40 65
May 840 560 840
Jun 1,100 735 1,100
Jul 2,080 1,385 2,080
Aug 1,620 1,085 1,620
Sep 710 475 710
Oct 65 40 65
Nov
Dec
ANNUAL 6,480 4,320 6,480
Deplete
40
560
735
1,385
1,085
475
40
4,320
NOTE: The assumptions for both the low and intermediate levels of development
were that there would be a negligible increase in energy development, population,
and number of acres irrigated. Therefore, the amount of water depletion would
also be negligible and is not shown.
aThe diversion rate for irrigation is 3 acre-feet/acre; the depletion rate is
2 acre-feet/acre.
bAssumptions: negligible increase in energy development, population; irrigate
2,150 new acresc.
cAssumptions: , irrigation to be developed with loans at 10 percent amortized
over 10 years.
-119-
TABLE A-3. Monthly and annual water requirements in Billings Area subbasin,
year 2000 under three levels of development (af)
ENERGY IRRIGATION 8 MUNICIPAL TOTAL
Divert Deplete Divert Deplete Divert Deplete Divert Deplete
LOW-LEVEL DEVELOPMENTd
Jan 580 290 580 290
Feb 580 290 580 290
Mar 580 290 580 290
Apr 195 130 580 290 775 420
May 2,525 1,680 580 290 3,105 1,970
Jun 3,300 2,200 580 290 3,880 2,490
Jul 6,210 4,140 580 290 6,790 4,430
Aug 4,850 3,235 580 290 5,430 3,525
Sep 2,135 1,425 580 290 2,715 l '715
Oct 195 130 580 290 775 420
Nov 580 290 580 290
Dec 580 290 580 290
ANNUAL 19,410 12,940 6,960 3,480 26,370 16,420
INTERMEDIATE-LEVEL DEVELOPMENTe
Jan 590 295 590 295
Feb 590 295 590 295
Mar 590 295 590 295
Apr 390 260 590 295 980 555
May 5,045 3,365 590 295 5,635 3,660
Jun 6,600 4,400 590 295 7,190 4,695
Jul 12,420 8,280 590 295 13,010 8,575
Aug 9,705 6,470 590 295 10,295 6,765
Sep 4,270 2,845 590 295 4,860 3,140
Oct 390 260 590 295 980 555
Nov· 590 295 590 295
Dec 590 295 590 295
ANNUAL 38,820 25,880 7,080 3,540 45,900 29,420
HIGH-LEVEL DEVELOPMENTf
Jan 650 325 650 325
Feb 650 325 650 325
Mar 650 325 650 325
Apr 580 390 650 325 1,230 715
May 7,570 5,045 650 325 8,220 5,370
June 9,910 6,600 650 325 10,560 6,925
Jul 18,630 12,420 650 325 19,280 12,745
Aug 14,555 9,705 650 325 15,205 lO ,030
Sep 6,405 4,270 650 325 7,055 4,595
Oct 580 390 650 325 1,230 715 Nov 650 325 650 325
Dec 650 325 650 325
ANNUAL 58,230 38,820 7,800 3,900 66,030 42,720
a Agricultural irrigation diversion rate is 3 af/acre; depletion rate is 2 af/acre.
bMunicipal water use at 200 gal/d/pers. for diversion; 100 gal/d/pers. depletion.
cirrigation development carried on with 10 percent loans amortized over
10-year period.
dAssumptions: (no energy development); (6,470 new irrigated acres)c;
(31,270 increase in population).
eAssumptions: (no energy
increase in population).
development), (12,940 new irrigated acres)~ (31 ,804
. f
Assumptions: (no energy development), (19,410 acres new irrigation of
feasible land)c, (34,565 increase in population).
-120-
TABLE A-4. Monthly and annual water requirements in Bighorn subbasin, year
2000 under three levels of development (af).
ENERGY IRRIGATIONa MUNICIPALb TOTAL
Divert Deplete Divert Deplete Divert Deplete Divert Deplete
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
70
70
70
70
70
70
70
70
70
70
70
70
ANNUAL 840
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
490
490
490
490
490
490
490
490
490
490
490
490
5,880
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
28,140
70
70
70
70
70
70
70
70
70
70
70
70
840
490
490
490
490
490
490
490
490
490
490
490
490
5,880
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
2,345
28,140
LOW-LEVEL DEVELOPMENTd
130
1,700
2,220
4,180
3,260
1,435
130
13,055
90
1,130
1,480
2,785
2,175
960
90
8, 710
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
INTERMEDIATE-LEVEL DEVELOPMENTe
260
3,390
4,430
8,340
6, 520
2,870
260
175
2,260
2,955
5,560
4,345
1,910
175
26,070 17,380
HIGH-LEVEL DEVELOPMENTf
390
5,085
6,650
12,520
9,785
4,300
390
39,120
260
3,390
4,430
8,345
6,525
2,870
260
26,080
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
80
80
80
80
80
80
80
80
80
80
80
80
960
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
·Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
40
40
40
40
40
40
40
40
40
40
40
40
480
70
70
70
200
1,770
2,290
4,250
3,330
1,505
200
70
70
13,895
490
490
490
750
3,880
4,920
8,830
7,010
3,360
750
490
490
31,950
2,425
2,425
2,425
2,815
7,510
9,075
14,945
12,210
6,725
2,815
2,425
2,425
68,220
aAgricultural irrigation diversion rate is 3 af/y/acre; depletion rate is
2 af/acre.
70
70
70
160
1,200
1,550
2,855
2,245
1,030
160
70
70
9,550
490
490
490
665
2,750
3,445
6,050
4,835
2,400
665
490
490
23,260
2,385
2,385
2,385
2,645
5,775
6,815
10,730
8,910
5,255
2,645
2,385
2,385
54,700
bMunicipal water use at 200 gal/d/pers. for diversion; 100 gal/d/pers. depletion.
cirrigation development carried on with 10 percent loans amortized over
10-year period.
dAssumptions: (17.1 mmt strip mine increase); (4,435 new irrigated acres)c;
(2,334 increase in population).
eAssumptions: (5.9 mmt slurry, 29.3 mmt strip mines increase); (8,690 new
irrigated acres)c; (3,145 increase in population).
fAssumptions: (1-1,000 mw 14.8 mmt slurty, 36.9 mmt strip mines increase);
(13.040 acres new irrigation of feasible land)
-121-
TABLE A-5. Monthly and annual water requirements in Mid-Yellowstone subbasin,
year 2000 under three levels of development (af).
ENERGY IRRIGATIONa MUNICIPALb TOTAL
Divert Deplete Divert Deplete Divert Deplete Divert Deplete
Jan 2,930
Feb 2,930
Mar 2,930
Apr 2,930
May 2,930
Jun 2,930
Jul 2,930
Aug 2,930
Sep 2,930
Oct 2,930
Nov 2,930
Dec 2,930
ANNUAL 35,160
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
75,480
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
139,440
2,930
2,930
2,930
2,930
2,930
2,930
2,930
2,930
2,930
2,930
2,930
2,930
35,160
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
6,290
75,480
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
11,620
139,440
LOW-LEVEL DEVELOPMENTd
250
3,280
4,290
8,075
6,310
2, 775
250
25,230
170
2,190
2,860
5,380
-4,200
1,850
170
'16,820
280
280
280
280
280
280
280
280
280
280
280
280
3,360
INTERMEDIAT~-LEVEL DEVELOPMENTe
505
6,560
8,580
16,150
12,610
5,550
505
335
4,375
5, 720
10,765
8,410
3,700
335
310
310
310
310
310
310
310
310
310
310
310
310
50,460 33,640 3,720
HIGH-LEVEL DEVELOPMENTf
760
9,840
12,870
24,215
18,920
8,325
760
75,690
505
6,560
8,580
16,150
12,610
5,550
505
50,460
645
645
645
645
645
645
645
645
645
645
645
645
7,740
140
140
140
140
140
140
140
140
140
140
140
140
1,680
155
155
155
155
155
155
155
155
155
155
155
155
1,860
320
320
320
320
320
320
320
320
320
320
320
320
3,840
3,210
3,210
3,210
3,460
6,490
7,500
11,285
9,520
5,985
3,460
3,210
3,210
63,750
6,600
6,600
6,600
7,105
13,160
15,180
22,750
19,210
12,150
7,105
6,600
6,600
129,660
12,265
12,265
12,265
13,025
22,105
25,135
36,480
31,185
20,590
13,025
12,265
12,265
222,870
aAgricultural irrigation diversion rate is 3 af/acre; depletion rate is
2 af/acre.
3,070
3,070
3,070
3,240
5,260
5,930
8,450
7,270
4,920
3,240
3,070
3,070
53,660
6,445
6,445
6,445
6,780
10,820
12,165
17,210
14,855
10,145
6,780
6,445
6,445
110.980
11,940
11,940
11,940
12,445
18,500
20,520
28,090
24,550
17,490
12,445
11,940
11,940
193,740
bMunicipal water use at 200 gal/d/pers. for diversion; 100 qal/d/pers. depletion.
clrrigation development carried on with 10 percent loans amortized over
10 year period.
dAssumptions: (15-1,000 mw, 1-250 mmcfdgas, 59.9 mmt strip mines new de-
velopment); (8,410 new irrigated acres)c; (15,887 increase in population).
eAssumptions: (3-1,000 mw, 1-250 mmcfd gas, 20.5 mmt slurry, 102.6 mmt strip
mines); (16,820 new irrigated acresf; (17,771 increase in population).
fAssumptions: (3-1,000 mw, 2-250 mmcfd gas, 1-100,000 b/d syn-crude, 51.6 mmt
slurry, 128.9 mmt strip); (25,230 acres new irrig of feasible land)c; (36,250
increase population).
-122-
TABLE A-6. ~1onthly and annual water requirements in Tongue subbasin, year 2000
under three levels of development (af).
ENERGY I RR IGA TI DNa MUNICIPALb TOTAL
Divert Deplete Divert Deplete Divert Deplete Divert Deplete
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
Jan
Feb
Mar
Apr
t~ay
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
955
955
955
955
955
955
955
955
955
955
955
955
ll ,460
3,900
3,900
3,900
3,900
3.900
3,900
3,900
3,900
3,900
3,900
3,900
3,900
46,800
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
ll8 ,020
955
955
955
955
955
955
955
955
955
955
955
955
11,460
3,900
3,900
3,900
3,900
3,900
3,900
3,900
3,900
3,900
3,900
3,900
3,900
46,800
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
9,835
118,020
L0\~-LEVEL DEVELOPMENTd
220
2,855
3, 730
7,030
5,490
2,415
220
21,960
145
1,900
2,490
4,685
3,660
1,615
145
14,640
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
INTERMEDIATE-LEVEL DEVELOPMENTe
440
5,705
7,460
14,045
10,970
4,830
440
290
3,800
4,975
9,360
7,315
3,230
290
43,890 29,260
60
60
60
60
60
60
60
60
60
60
60
60
720
HIGH-LEVEL DEVELOPMENTf
660
8,560
11,195
21,070
16,460
7,245
660
65,650
440
5,710
7,465
14,050
10,975
4,830
440
43,910
130
130
130
130
130
130
130
130
130
130
130
130
1,560
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
NeiJ.
Neg.
Neg.
Neg.
30
30
30
30
30
30
30
30
30
30
30
30
360
G5
65
65
65
65
65
65
65
65
65
65
65
780
955
955
955
1,175
3,810
4,685
7,985
6,445
3,370
1,175
955
955
33,420
3,960
3,960
3,960
4,400
9,665
ll ,420
18,005
14,930
8, 790
4,400
3,960
3,960
91,410
9,965
9,965
9.965
10,625
18,525
21,160
31,035
26,425
17,210
10,625
9,965
9,965
185,430
aAgricultural irrigation diversion rate is 3 af/acre/; depletion rate is
2 af/acre.
955
955
955
1,100
2,855
3,445
5,640
4,615
2,570
1,100
955
955
26,100
3,960
3,930
3,930
4,220
7,730
8,905
13,290
ll,245
7,160
4,220
3,930
3,930
76,420
9,900
9,900
9,900
10,340
15,610
17,365
23,950
20,875
14,730
10,340
9,900
9,900
162,710
b~1unicipal water use at 200 gal/d/pers. for diversion; 100 gal/d/pers. depletion.
cirrigation development carried on with 10 percent loans amortized over 10-year
period.
dAssumptions: (1-500 mw; 77 mmt strip mines new development); (7.320 new
irrigated acreslc; (1.895 increase in population) ; no allowance for Wyoming
water depletion, maximum reservoir stora~e 112,000 af minimum; reservoir level
67, DOD a f. If natural flow exceeds all demands (including fish and gHme needs),
excess water is stored if space is available-releases made only to supplement
consumptive demands.
eAssumptions: (2-.l,OOO mw; 26.4 mmt slurry 132 mmt strip); (14,630 new irri-
gated acres)c: (2,949 increase in population) maximum reservoir storage 320,000 af,
minimum desirable is 50,000 af; instream flow is 60?o of NGPRP recommended flow
and stored water is not used to meet this requirement, study period 1944-1973;
l~yoming depletion is 40?o of flow at the state line, up to a maximum of 3,000 af;
first priority is irriqation and municipal with enerqy production receiving
balance •. 1'/atP.r not stored if natural outflow is less than or equal to instream
needs. If more,_ stored or used consumptively, stored water may be released for
consumptive purposes.
fAssumptions (3-1,000 mw, l-250 mmcfld gas, 1,100,000 b/d syncrude, 66.3 mmt
slurry, 165.8 mmt strip mine); (21,950 new irrigated acres)c, (6,829 increase in
population). l·laximum storage is 320,000 af; no minimum; instream flow calculated
for two cases: a) 45 cfs during 1·1arch, April, and May and 15 cfs at all other times,
and b) instream flow zero (qugmented if no inflow available) study period 1944-73;
l~yominiJ depletion 40?o of the flow at stateline up to maximum of 7,500 af; instream
fish and game and irrigation demands receive priority, water for energy use after
that; balance of energy water requirement comes by aqueduct from the mainstem of
the Yellowstone River.
-123-
TABLE A-7. Monthly and annual water requirements in Kinsey Area subbasin, year
2000 under three levels of development (af)
ENERGY IRRIGATIONa MUNICIPAL TOTAL
Divert Deplete Divert Deplete Divert Deplete Divert
LOW-LEVEL DEVELOPMENTc
Annual 4,740 3,160 4,741
INTERMEDIATE-LEVEL DEVELOPMENTd
Jan
Feb
Mar
Apr -95 60 95
May 1,230 . 820 1,230
Jun 1,610 1,075 1,610
Jul 3,035 2,025 3,035
Aug 2,375 1,585 2,375
Sep 1,040 695 1,040
Oct 95 60 95
Nov
Dec
ANNUAL 9,480 6,320 9,480
HIGH-LEVEL DEVELOPMENTe
Jan
Feb
Mar
Apr 140 95 140
May 1,850 1,230 1,850
Jun 2,420 1,610 2,420
Jul 4,555 3,035 4,555
Aug 3,550 2,375 3,550
Sep 1,565 1,040 1,565
Oct 140 95 140
Nov
Dec
ANNUAL 14,220 9,480 14,220
aAgricultural irrigation diversion rate is 3 af/acre; depletion rate is
.2 af/acre.
Deplete
3,160
60
820
1,075
2,025
1,585
695
60
6,320
95
1,230
1,610
3,035
2,375
1,040
95
9,480
birrigation development carried on with 10 percent loans amortized over 10 year
period.
cAssumptions: (no energy development); (1,580 new irrigated b acres) ; (neg.
increase in population).
dAssumptions: (no energy development); (3 ,160
crease in population).
irrigated b (neg. in-new acres) ;
~Assumptions: (no energy development); (4,740 acres new irrigation of feasible
land) ; (neg. increase in population).
-124-
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
TABLE A-8. Monthly and annual water requirements in Powder subbasin, year 2000
under three levels of development (af)
ENERGY
Divert
70
70
70
70
70
70
70
70
70
70
70
70
Deplete
70
70
70
70
70
70
70
70
70
70
70
70
IRRIGATIONa
Divert Deplete
LOW-LEVEL DEVELOPMENTd
750
9,780
12,785
24,070
18,800
8,275
750
500
6,520
8,525
16,045
12,535
5,515
500
MUNICIPALb TOTAL
Divert Deplete Divert Deplete
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
Neg.
70
70
70
820
9,850
12,855
24,140
18,870
8,345
820
70
70
70
70
70
570
6,590
8,595
16,115
12,605
5,585
570
70
70
ANNUAL 840 840 75,210 50,140 Neg. Neg. 76,050 50,980
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
ANNUAL 18,840
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1,800
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
ANNUAL 22,560
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
1,570
INTERMEDIATE-LEVEL DEVELOPMENTe
1,500
19,555
25,570
48,140
37,610
16,545
1,500
1,000
13,04,0
17,050
32,090
25,070
11,030
1,000
100
100
100
100
100
100
100
100
100
100
100
100
18,840 150,420 100,280 1,200
HIGH-LEVEL DEVELOPMENTf
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
1,880
2,255
29,330
38,350
72,190
56,405
24,815
2,255
22,560 225,600
1,500
19,550
25,570
48,130
37,605
16,545
1,500
150,400
190
190
190
190
190
190
190
190
190
190
190
190
2,280
50 1,670
50 1,670
50 1,670
50 3,170
50 21,225
50 27,240
50 49,810
50 39,280
50 18,215
50 3,170
50 1.670
50 1,670
1,620
1,620
1,620
2,620
14,660
18,670
33,710
26,690
12,650
2,620
1,620
1,620
600 170,460 119,720
95 2,070
95 2,070
95 2,070
95 4,325
95 31,400
95 40,420
95 74,260
95 58,475
95 26,885
95 4,325
95 2,070
95 2,070
1,975
1,975
1,975
3,475
21,525
27,545
50' 105
39,580
18,520
3,475
1,975
1,975
1,140 250,440 174,100
aAgricultural irrigation diversion rate is 3 af/acre; depletion rate is 2 af/acre.
bMunicipal water use at 200 gal/d/pers. for diversion, 100 gal/d/pers. depletion.
clrrigation development carried on with 10 percent loads amortized over
10-year period.
dAssumptions: (17.1 mmt strip mines); (25,070 new irrigated acres)c; (3,339
increase in population.
eAssumptions: (1-100 mw, 5.9 mmt slurry); (29.3 mmt strip mines); (50,140 new
irrigated acres)c; (5,297 increase in population).
fAssumptions: (1-1,000 mw, 14.8 mmt slurry); (36.9 mmt strip mines); 75-200
acres new irrigation of feasible land)c; (9,893 increase in population).
-125-
TABLE A-9. Monthly and annual water requirements in Lower Yellowstone subbasin,
year 2000 under three levels of development (af)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
ANNUAL
ENERGY IRRIGA TIONa MUNICIPALb TOTAL
Divert
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
13,020
Deplete Divert Deplete Divert
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
1,085
13,020
LOW-LEVEL DEVELOPMENTd
380
4,900
6,400
12,050
9,420
4,150
380
37,680
250
3,270
4,270
8,040
6,280
2,760
250
25,120
60
60
60
60
60
60
60
60
60
60
60
60
720
INTERMEDIATE-LEVEL DEVELOPMENTe
755
9,795
12,810
24,105
18,830
8,290
755
500
6,525
8,535
16,070
12,550
5,520
500
60
60
60
60
60
60
60
60
60
60
60
60
75,340 50,200 720
HIGH-LEVEL DEVELOPMENTf
1,130
14,690
19,210
36,165
28,255
12,430
1,130
113,010
755
9,795
12,810
24,100
18,830
8,290
755
75,335
80
80
80
80
80
80
80
80
80
80
80
80
960
Deplete Divert Deplete
30
30
30
30
30
30
30
30
30
30
30
30
360
30
30
30
30
30
30
30
30
30
30
30
30
360
40
40
40
40
40
40
40
40
40
40
40
40
480
60
60
60
440
4,960
6,460
12,110
9,480
4,210
440
60
60
38,400
60
60
60
815
9,855
12,870
24,165
18,890
8,350
815
60
60
30
30
30
280
3,300
4,300
8,070
6,310
2,790
280
30
30
25,480
30
30
30
530
6,555
8,565
16,100
12,580
5,550
530
30
30
76,060 50,560
1,165
1,165
1,165
2,295
15,855
20,375
37,330
29,420
13,595
2,295
1,165
1,165
126,990
1,125
1,125
1,125
1,880
10,920
13,935
25,225
19,955
9,415
1,880
1,125
1,125
88,835
aAgricultural irrigation diversion rate is 3 af/acre, depletion rate is
2 af/acre.
bMunicipal water use at 200 gal/d/pers. for diversion, 100 gal/d/pers. depletion.
cirrigation development carried on with 10 percent loans amortized over 10-year
period.
dAssumptions: (no energy development); (12,560 new irrigated acres)c; (3,381
increase population).
eAssumptions: (no energy development); (25,100 new irrigated acres)c; (3,381
increase in population).
fAssumptions: (1-2,300 t/d fertilizer plant); (37,670 acres new irrigation of
feasible land)c; (4,125 increase in population).
-126-
Table B-1
Table B-2
Table B-3
Table B-4
Table B-5
Table B-6
CO-EFFICIENTS AND CONSTANTS FOR SUBBASIN MODEL RUNS
TABLES
Temperature-indenpendent coefficients . . . . . .
Temperature-dependent coefficients:
less than 32°F • • • • • • •
Temperature-dependent coefficients:
0 greater than 32 F • • • • •
Temperature-dependent coefficients:
temperature . . . . . . . . . . . .
temperature . . . . . .
constants
Initial values: independent of scenario
Initial values: dependent on the scenario
-127-
PAGE
112
113
114
115
116
116
I .......
N co
I
Coefficients
C(3,2)
C(3,3)
C(3,6)
C(3,ll)
C(3,19)
C(3, 28)
C(4,12)
C(4,32)
Upper
Yellowstone
.020893
.000347
.000367
-1.0
.010450
0.0
-• 7
.037402
Clarks
Fork
.017610
.000294
.000294
-1.0
.008805
0.0
-.427
.009147
TABLE B-1. Temperature-independent coefficients
Subbasins
Billings Mid-Kinsey Lower
Area Bighorn Yellowstone Tongue Area Powder Yellowstone
.034310 .26370 .004255 .003570 .035561 .004262 .013678
.000731 .000110 .000090 .000110 .000741 .000089 .000285
.000731 .000110 .000090 .000110 .000741 .000089 .000285
-24.0 -1.0 -.80 -.60 -24.0 -.40 -.80
.017155 .013185 .002128 .001785 .017781 .002131 .000839
-.034310 -.026370 -.002128 -.001785 -.035561 -.004262 -.013678
-6.0 -1.3 -1.0 -1.0 -6.0 -2.0 -1.0
.049167 .033125 .004473 .003660 .079521 .004473 .019016
I ......
N
1.0
I
Upper Clarks
Coefficients Yellowstone Fork
C(l,2) .25EL .25EL
C(l ,19) .50EL .5EL
C(l ,28) -.2SEL -• 5EL
C(l,31) 0.0 0.0
C(l ,32) 0.0 0.0
C(3,31) 0.0 0.0
C(4,9) -.00067 .00055
C(4,10) -.00067 .00055
C(S,l5) .024 .024
C(5,16) .024 .024
C(6,22) 0.0 0.0
C(6,31) -1.0 -1.0
C(7,13) 0.0 0.0
C(7,15) 0.0 0.0
C(8,12) .4-.5EL .4-.5EL
C(8,28) 0.0 0.0
C(9,5) S.OEL S.OEL
C(9,12) .5EL .SEL
C(9,17) S.OEL S.OEL
C(9,28) .BEL .BEL
C(l0,12) 0.0 o.o
C(l0,2B) 0.0 0.0
C(ll,31) 0.0 0.0
C(l2,22) 0.0 0.0
C(l4,21) 0.0 0.0
C(l4,22) 0.0 0.0
C(l4 ,23) o.o 0.0
p = .004 X EXP (.06 X (32 -T))
r = .004 X EXP (.205043 X (32 -T))
EL = evaporation loss
TABLE B-2. Temperature-dependent coefficients
0 Temperature less than 32 F
Billings Mid-Kinsey Lower
Area Bighorn Yellowstone Tongue Area Powder Yellowstone
.50EL .25EL .25EL .25EL .5EL ' .25EL .25EL
.5EL .50EL .5EL .SEL .5EL .50EL .5EL
-.5EL -.25EL -.25EL -• 25EL -• 5EL -.25EL -.25EL
0.0 o.o 0.0 o.o 0.0 o.o 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
-.005666 -.0022 -.0002 -.0002 -.005829 -.0002 .0002
-.005666 -.0022 -.0002 -.0002 -.005829 -.0002 .0002
12 .012 .012 .012 p .012 .012
12 .012 .012 .012 p .012 .012 o.o 0.0 0.0 o.o 0.0 0.0 0.0
-1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 o.o 0.0 0.0 0.0 0.0 0.0 o.o
0.0 o.o 0.0 0.0 0.0 0.0 0.0
.5-.5EL .5-.5EL .4-.SEL .5-.5EL .5-.5EL .4-.5EL .4-.5EL
0.0 0.0 o.o 0.0 0.0 0.0 0.0
5.0EL 5.0EL 5.0EL 5.0EL 5.0EL 5.0EL 5.0EL
.5EL .5EL .5EL .SEL .SEL .5EL • 5EL
.SEL 5.0EL 5.0EL .5EL .5EL 5.0EL S.OEL
l.OEL l.OEL .BEL .BEL l.OEL .BEL .BEL o.o 0.0 0.0 o.o 0.0 0.0 0.0
0.0 0.0 0.0 o.o 0.0 0.0 0.0
0.0 0.0 o.o 0.0 0.0 0.0 0.0
0.0 0.0 o.o 0.0 0.0 0.0 0.0 o.o 0.0 o.o 0.0 0.0 0.0 0.0
0.0 0.0 o.o 0.0 0.0 o.o o.o
0.0 0.0 0.0 0.0 0.0 o.o o.o
I ....... w
0
I
TABLE B-3. Temperature-dependent coefficients
Temperature greater than 32°F
Upper Clarks Billings Mid-
Coefficients Yellowstone Fork Area Bighorn Yellowstone Tongue
C(l,2) EL l.OEL .SEL .7SEL l.OEL l.OEL
C(l,l9) EL l.OEL .SEL .SEL l.OEL l.OEL
C(l, 2B) -.2SEL -.2SEL -.SEL -• 2SEL -.2SEL -.2SEL
C(l,31) .SEL .SEL .SEL .SEL .SEL .SEL
C(l ,32) EVP EVP .SEL EVP 0.0 EVP
C(3,31) .0104SO .0104SO .Ol71SS .0191BS .013792 .0017BS
C(4,19) -.00097 -.00097 -.OOS666 -.002792 -.001666 -.0002S4
C(4,10) -.00097 -.00097 -.OOS666 -.002792 -.001666 -.0002S4'
C(S,lS) 0.0 0.0 0.0 o.o 0.0 0.0
C(S,l6) 0.0 0.0 0.0 o.o 0.0 0.0
C(B,22) 0.0 0.0 0.0 o.o 0.0 0.0
C(6,31) 0.0 o.o 0.0. 0.0 0.0 0.0
C(7,13) .5A .5A .5A .5A .5A .5A
C(7,15) A A A A A A
C(B,l2) .4-.5EL .4-.5EL .5-.SEL .5-.SEL .4-.SEL .S-.SEL
C(B,2B) .3-.BEL .3-.BEL .3-EL ~3-.. BEL .3-.BEL .3-.BEL
C(9~5) S.OEL S.OEL S.OEL 5.0EL 5.0EL 5.0EL
C(9,12) .SEL .SEL .SEL .SEL .SEL .SEL
C(9,17) S.OEL S.OEL .SEL S.OEL S.OEL 5.0EL
C(9;2B) .BEL .BEL EL EL .SEL .BEL
C(l0,12) .s .s .s ~5 .s .5
C(l9,2B) .7 .7 .7 .7 .7 .7
C(ll,3l) -1.0 -1.0 -1.0 -1.0 -1.0 -1.0
C(l2,22) 1.0 1.0 1.0 1.0 1.0 1.0
C(l6,21) • Sd .5d .Sd .Sd .5d .Sd
C(l6,22) . Sd .Sd .5d • 5d .Sd • Sd
C(l6,23) d d d d d d
EVP is calculated in Sub routine SURFACE and transferred to mainline.
EL = evaporation loss
A = snowmelt rate
d = dampening factor
~~·--~----
Kinsey Lower
Area Powder Yellowstone
.SEL l.OEL . l.OEL
.SEL l.OEL l.OEL
.SEL -.2SEL -.2SEL
.SEL .SEL .SEL
.SEL EVP EVP
.00177Bl .00212B .006B39
-.OOSB29 -.000307 -.00033B
-.OOSB29 -.000307 -.00033B
0.0 0.0 0.0
0.0 0.0 0.0
0.0 o.o 0.0
0.0 0.0 0.0
.SA .SA .SA
A A A
.S-.SEL .4-.SEL .4-.SEL
.3-EL .3-.BEL .3-.BEL
5.0EL 5.0EL S.OEL
.SEL .SEL .SEL
.5EL S.OEL 5.0EL
EL .BEL .BEL
.5 .s .5
.7 .7 .7
-1.0 -1.0 -1.0
1.0 1.0 1.0
.Sd • Sd • Sd
.Sd • Sd • 59
d d d
I ...... w ......
I
Constants
SF
b
K6
K7
c
d
F
G
M
N
p
*D =
A =
T =
X13 =
X5 = X23 -.
.-. ---------::.--------
TABLE B-4. Temperature-dependent coefficients
Constants*
D SF (X5 + X23) = (d + X5 + X23)
A C(T-32)K6 + (Tz32)2
+ K7 (XS + Xl5 ) = (bK6) + b 2
EL = CT + dT 2
Xl3 = (l -~ ) XS when 32 < T < M 32
Xl3 = 0 when T > M
M - T Xl3 = --;;rp-XS when G ~ T ~ 32; except in Powder Subbasin, where Xl3 = 1 - 5 QRT (J-G ) XS 24
Xl3 = XS when T < G
Subbasins
Upper Clarks Billings Mid-Kinsey Lower
Yellowstone Fork Area Bighorn Yellowstone Tongue Area Powder Yellowstone
.01865 .036 .034029 .1470 .02120 . .03145 .0036 .012578 .0758
31.0 31.0 13.0 13.0 10.0 13.0 10.0 10.0 10.0
20.0 20. 50. 50.0 50.0 40.0 30.0 40.0 30.
.05 5 .05 5 .12 -5 .07 5 .12 -5 .05 -5 .05 5 .07 5 .05 5
14Xl0=7 14Xl0=7 ll.8Xl0 _7 12Xl0=7 ll.8Xl0 _7 13.4Xl0_7 14Xl0=7 16Xl0=7 14Xl0=7 45Xl0 45Xl0 12.5Xl0 43Xl0 12.5Xl0 47.2Xl0 45Xl0 50Xl0 45Xl0
16.0 16.0 32.0 20.0 32.0 16.0 16.0 14.0 16.0
16.0 16.0 32.0 20.0 32.0 16.0 12.0 14.0 12.0
40.0 40.0 81.0 40.0 81.0 40.0 40.0 40.0
10.5 10.5 49.0 10.5 49.0 10.5 10.5 10.5
3.0 3.0 2.0 3.0 2.0 3.0 3.0 3.0
soil water percolation
rate of snowmelt
temperature in Fahrenheit
snowfall
precipitation
initial soil water storage
I .....
v.J
N
I
Subbasins RE Q
Billings Area .40 .85
Bighorn .40 .80
Mid-Yellowstone .40 .85
Tongue .40 .80
Powder .40 .80
Lower Yellowstone .40 .80
Subbasins
Billings Area
Bighorn
Mid-Yellowstone
Tongue
Powder
Lower Yellowstone
Table B-5~ Initial values
(independent of the scenario)
SAVE FC FCMin Ql
.24370 .825 .0825 .015
.317350 .94 .094 .02
.396737 1.125 .1125 .015
.015368 .852 .03834 .015
.305471 .830 .083 .015
.358272 1.66 .166 .010
Table B-6. Initial values
(dependent' on the scenario)
Scenario 53
High 0.0
Inter. 0.0
Low 0.0
High 1.1
Inter. 1.1
High 0.0
Inter. o.o
Low 0.0
High .32
Inter. .32
Low .112
Inter. .Z75
Low • Z75
High 0.0
Inter. 0.0
Low 0.0
---------~ ~-~ ~--~-----
Q2 Pl P2 t-1 N
.015 .006623 .005956 1944 1973
.02 .056322 .054806 1944 1973
.015 .010ll8 .009549 1944 1973
.015 .000435 .000417 1944 1973
.015 .000457 .000549 1944 1973
.OlD .095730 .087535 1944 1973
STD2 EN
0.0 0.0
0.0 0.0
0.0 0.0
1.1 .002345
1.1 .000490
0.0 • Oll620
0.0 .006290
0.0 .002930
.32 .004385
.32 .003900
.ll2 .000955
• 275 o.o
• 275 .000070
o.o .001085
0.0 o.o
0.0 0.0
TABLES PAGE
TABLE C-1 Yellowstone River at Billings: regression equations. 118
TABLE C-2 Tongue River near Miles City: regression equations. 119
TABLE C-3 Powder River at Locate: regression equations. 120
TABLE C-4 Big Horn River: regression equation. 121
TABLE C-5 Yellowstone near Miles City: regression equation. 121
TABLE C-6 Yellowstone River near Sidney: regression equations. 122
-133-
TABLE C-1. Yellowstone River at Billings: regression equations
Month Best Fit Equation 2 Significance r
Jan log TDS = 3.16424 -.12912 log Q .073 NS
Feb log TDS = 3. 54116 -.20614 log Q .106 NS
Mar TDS = 1527.71 -235.17461 log Q .766 **
Apr log TDS = 4.24384 -.34054 log Q .645 **
May TDS = 924.22705 -131.16983 log Q .606 **
June log TDS = 2.57791 -.08230 log Q .063 NS
July TDS = 935.46143 -135.05623 log Q .827 **
Aug log TDS = 4.27605 -.35261 log Q .850 **
Sept TDS = 1622.26001 -251.31508 log Q .868 **
Oct log TDS = 5.05812 -.48689 log Q .834 **
Nov TDS = 2255.61938 -368.94141 log Q • .806 **
Dec TDS = 2119.83569 -346.26465 log Q .510 **
ALL MONTHS log TDS = 4.82194 -.44798 log Q .934 **
NOTE: TDS = Average Monthly Total Dissolved Solids, mg/1
Q = Monthly Discharge, acre feet
** = Significant at 1~~ level
* = Significant at 5% level
NS = Not Significant at 5% level
-134-
TABLE C-2. Tongue River near Miles City: ~egression equations
Month Best Fit Equations 2 Significance r
Jan log TDS = 2.968046 -.00001178 Q .373 **
Feb log TDS = 2.8869196 -.0000093196 Q .718 **
Mar TDS = 1445.71 -217.25081 log Q .539 **
Apr TDS = 1524.68 -217.70712 log Q .867 **
May TDS = 1348.75 -191.64864 log Q .546 **
June TDS = 1221.21 -189.03383 log Q .750 **
July TDS = 1513.50 -260.70199 log Q .815 **
Aug TDS = 1686.28 -301.87476 log Q .819 **
Sept log TDS = 3.51775 -.20078 log Q .869 **
Oct TDS = 1647.14 -265.4541 log Q .787 **
Nov TDS = 3.69492 -.21753 .627 **
Dec TDS = 2375.20 -408.74805 .420 **
ALL MONTHS TDS = 1672.10 -267.88599 log Q .583 **
NOTE: TDS = Average Monthly Total Dissolved Solids, mg/1
Q = Monthly Discharge, acre feet
** = Significant at 1~~ level
* = Significant at 5~~ level
NS = Not Significant at 5% level
-135-
TABLE C-3. Powder River at Locate: r.egression equ~tions
Month Best Fit Equations 2 Significance r
Jan TDS = 2009.9 -.04002 Q .154 NS
Feb TDS = 3965.75-663.84961 log Q .745 **
Mar log TDS = 3.14148 -.0000027288 Q .857 **
Apr TDS = 1603.99 -.00769 Q .764 **
May TDS = 2952.23 -408.35352 log Q .179 NS
' June log TDS = 3.50657 -.10353 log Q .256 NS
July TDS = 4378.26 -707.0542 log Q .580 *
Aug TDS = 2171.01 -136.30793 log Q .067 NS
Sept log TDS = 3.35371 -.06055 log Q .170 NS
Oct TDS = 3479.57 -521.59961 log Q .517 NS
Nov log TDS = 3.37988 -.00002 Q .855 **
Dec log TDS = 3.40523 -.00002 Q .749 **
NOTE: TDS = Average Monthly Total Dissolved Solids, mg/1
Q = Monthly Discharge, acre feet
** = Significant at 1~~ level
* = Significant at 5~~ level
NS = Not Significant at 5% level
-136-
TABLE C-4. Big Horn River: regression equation
Monthly Values for TDSSX are
Jan = 551 Feb = 589 March = 609
Apr = 602 May = 610 June = 590
July = 527 Aug = 447 Sept = 475
Oct = 604 Nov = 567 Dec = 571
NOTE: TDS = 57.1 + .93596 TDSSX
where TDS = Average Monthly Total Dissolved Solids, mg/1
TDSSX = TDS near St. Xavier
TABLE C-5. Yellowstone near Miles City: regression e~uation
Log TDS = 5.7522 -.545 log Q
where TDS = Average Monthly Total Dissolved Solids in mg/1
Q = Monthly Discharge in acre feet
-137-
TABLE C-6. Yellowstone River near Sidney: regression equations
Month Best Fit Equation 2 Significance r
Jan log TDS = 4.45663 -.2983 log Q .655 **
Feb TDS = 2469.44 -339.72412 • 580 **
Mar TDS = 2785.62 -392.1665 .571 * -
Apr ' log TOS = 2.83667 -.0000001614 Q .634 **
May TDS = 561.71 -.00017959 Q
June TDS = 198.98 + .00003539 Q
July TDS = 917.41 -101.69664 log Q .250
Aug TDS = 2303.31 -327.66333 log Q .602 **
Sept log TDS = 2.85842 -.0000002973 Q .543 *
Oct TDS = 3745.50 -561.71338 log Q .722 **
Nov TDS = 3852.08 -579.99414 log Q .629 **
Dec TDS = 754.84 -.000344 Q .446 NS
NOTE: TDS = Average Monthly Total Dissolved Solids, mg/1
Q = Monthly Discharge, acre feet
** = Significant at 101 10 level
* = Significant at 50' 10 level
NS = Not Significant at 5~o level
-138-
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-141-