HomeMy WebLinkAboutAPA4155pt117~~a~~
tM1f~7<4te't'844in,
by
Staff of the Water Resources Division
of the
Montana Department of Natural Resources and Conservation
TECHNICAL REPORT NO. 11
conducted by
Water Resources Division
Montana Department of Natural Resources and Conservation
32 S. Ewing
Helena, MT 59601
Bob Anderson, Project Manager
Peggy Todd and Dave Lambert, Editors
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 oui coordinated action plans for regional
economic development ..
COMMISSION MEMBERS
State Cochairman
Gov. Thomas L. Judge 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
i i
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 •
Acknowledgments
INTRODUCT!Otl • . • •
ECONOI11C OVERVIEW OF THE YELLOWSTONE RIVER BAS IN
Income • . .
Employment .
Population •
Agri cu 1 tura 1
METHODS • • • • •
LITERATURE REVIEH
• • 0 0 0
Activity
Fish and 1-lildlife; Recreation
Gross Expenditure 1·1ethod .
~1arket Value of Fish l~ethod
Alternative Cost t1ethod ••
Market Value Method ..•.
Interview Method •..•.
Trave 1 Cost Method • . . . • • •
Difficulties in Estimatinq the Impact of Reduced
Streamflows on the Quality of Recreation
Water Quality ••••.•.•.••.•.•
Estimating the Value of ~later for Irrigation
General t~ethods ••••..•...••
Linear Programming Methods •••••.
Evaluating the Demands for Industrial Water
IMPACTS OF ~lATER \HTHDRAHALS
Projections of Future Use
Costs . . . . . . . . . . . . . .
Furbearers and Migratory Birds
Fisheries .•.••.••..•
iv
vi
vii
viii
1
1
1
3
4
5
9
9
9
12
12
15
21
21
21
22
22
22
22
23
24
24
26
26
27
31
35
35
35
35
36
Recreation •••....•••••
Existin~ ~unicinal and Aaricultural
•,Ja ter Qua 1 ity
Benefits ••••..•.••
Evaluation •.•..•••.
l!sers
LEr.AL COIISTPJII:ITS TO !.J.~T[R USE HI TYE Y~LL'lliST'l'IE
RIVER BASH/ .•..••••
Federal Leqal Constraints
r~on tuna Lequ 1 Constraints
Sur111ARY • . . • . • • • • . . .
The Economics of Altered Strear,flo~1
Leoal Constraints on Hater Use
Federal Constraints
t·'ontana Constraints
APPENDIXES
A. Projections of Future lise
B. Linear· f'roqral'lmi nq r~ode 1
LITERATU~E CITED •.•••••••
v
36
38
39
39
42
45
45
48
51
51
53
53
54
55
"' . 57
65
79
1. Yellowstone River Basin •.•.••. . . . . .
2. Relationships of Withdrawals to Costs and Benefits
3. Subbasins Used in the Yellowstone Impact Study
Linear Programming Model ••.•••..•. . .
4. Subbasins Used in Snyder's Linear Programming Model
5. Schematic Diagram of Yellowstone Basin for Snyder's
Linear Programming Model •...••••••.••
. 7
• 15 ··-
• 17
• 29
. . . . . . . . • 28
6. Expected l·larginal Values of an Acre-foot of Water in
Irrigated Agriculture Resulting from Using Snyder's
Linear Programming Model to Impose Minimum Flows on the
Yellowstone River •.••••••••.••.•••.••••••••• 32
vi
1. Employment in the Basic Industries in the Yellowstone
River Basin, 1950, 1960 and 1970 .
2. Coal Extracted in Montana, 1960-75
3. Coal rlining in the YellO~IStone River Basin, 1977
4. Population Trends in the Yellowstone River Basin by
County, 1960, 1970 and 1974 ••.......
5. Average Trapping Income, Fish and r.ame Regions 5 & 7
6. Impact of Lowered Flows on Recreation in the Yellowstone
River Basin .•••••••..••..•.••••. . . . . . . . .
7. Percentage of Increase in Operation Cost Over Present
Costs for Each Projected Level of Develop~ent •• . . . . . . . . .
8.
9.
Impact on Agricultural Profits of Different Levels of
Instream Constraints: 1975 Irrigated Acreaqe
Impact on Agricultural Profits of Different Levels Jf
Instream Constraints: Irrigated Acreage Projected to 2000
10. Values to Irrigators of One Percent Reduction in Instream-
Flow Constraint ••••...•.
11. One Percent of Instream Constraint .••..••
vii
. . . . . . .
. . . . . . .
9
10
11
13
36
37
38
40
41
41
42
a
af
af/y
b/d
cfs
ft
gpm
ha
hm3
hm3/y
km
km2
kwh
LP
mmaf
mmaf/y
mmt/y
mw
t/a
t/d
TDS
acre
acre-feet
acre-feet per year
barrels per day
cubic feet per second
feet
gallons per minute
hectares
cubic hectometers
cubic hectometers per year
kilometers
square kilometers
kilowatt hours
linear programming
million acre-feet
million acre-feet per year
million tons per year
megawatts
tons per acre
tons per day
total dissolved solids
viii
THE RIVER
The Yellowstone River Basin of southeastern Montana, northern Wyoming,
and western North Dakota encompasses approximately 180,000 km2 (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, Stilh~ater, 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 lg72).
THE COfiFLICT
Historically, agriculture has been Montana's most important industry. In
1975, over 40 percent of the primary employment in Montana 1~as 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 from 1968 to 1g73. Since that year,
receipts have declined because of unfavorable market conditions; some
improvement may be in sight, however. In 1970, over 75 percent of the
Yellowstone Basin's land was in agricultural use (State Conservation Needs
Committee 1970). Irrigated agriculture is the basin's largest water use,
consuming annually about 1.5 million acre-feet (af) of water (Montana DNRC
1977).
There is another industry in the Yellowstone Basin which, thouqh it con-
sumes little water now, may reqiJire 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, North and South Dakota, Uyoming, 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 l'lill ion 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,
i dent ifi ed in the i·lorth Centra 1 Power Studv 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.
In 1975, over 22 million tons of coal ~Jere mined in the state, up from
14 million in 1974, ll million in 1973, and 1 million in 1969. By 1g80, even
if no new contracts are entered, Montana's annual coal production will exceed
40 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 industry 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 9ighorn,
Tongue, and PmoJder, 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. Hhat would happen to
water quality after massive depletions? How would a chan9e in water quality
affect existing and future agricultural ,industrial, and municipal users?
\~hat would happen to fish, furbearers, and migratory waterf01·1l 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 ~1ontana 's growing concern for water
in the Yellowstone Basin and elsewhere in the state ~/as 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 \Jater Moratorium Act of 1974, ~1hich delayed action on major
applications for Yellol'lstone 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
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
2
the state would be able to proceed ~tisely with the allocation of that 11ater.
The study which resulted in this series of reports was one of the fruits of
that intention. Several other Yello~tstone water studies ~tere undert3ken
during the moratorium at the state and federal levels. Early in 1977, the
45th l•iontana Legislature extended the ·moratorium to allo~t more time to con-
sider reservations of water for future use in the basin.
THE STUDY
The Yellowstone Impact Study, conducted by the Water Resources Division
of the t-1ontana Department of Natural Resources and Conservation and financed
by the Old '.~est Regional Commission, was designed to evaluate the potential
physical, biological, and water use impacts of ~tater withdra~tals 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 summarizing all aspects of the study and in eleven
specialized technical reports:
Report No. 1
Report No. 2
Report No. 3
Report tlo. 4
Report No. 5
Report llo. 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
Geomorpho 1 ogy of the Yellowstone River Basin, 1·1ontana.
The Effect of Altered Streamflow on the 1·/ater Quality of
the Yellowstone River Basin, Montana.
The Adequacy of r~ontana' s Regula tory Framework for Water
Quality Control
Aquatic Invertebrates of the Yellowstone River Basin,
Hontana.
The Effect of A 1 tered Streamflow on Furbeari ng r~amma 1 s of
the Yellowstone River Oasin, Montana.
The Effect of Altered Streamflow on Migratory Birds of the
Yellowstone River Basin, Montana.
3
Report No. 8
Report ilo. 9
Report No. 10
Report No. ll
The Effect of Altered Streamflow on Fish of the
Yellowstone and Tongue Rivers, Hontana.
The Effect of Altered Streamflow on Existing f·1unicipal
and Agricultural Users of the Yellowstone River Basin,
Montana.
The Effect of A 1 tered Streamflow on Hater-Based Recreation
in the Yellowstone River Basin, Montana.
The Economics of Altered Streamflow in the Yellowstone
River Basin, Montana.
ACKNOWLEDGMENTS
This report was reviewed by and guidance received from Ted J. Doney,
Director of the Montana Department of Natural Resources and Conservation (DNRC),
Orrin Ferris, Administrator of the DNRC's Water Resources Division, and
Carole Massman of the DNRC's Special Staff.
Other DNRC personnel providing assistance were Janet Cawlfield, Lynda
Howell, and Barbara Williams, typists. Graphics were coordinated and per-
formed by Gary Wolf, with the assistance of D.C. Howard, who designed and
executed the cover.
The original work summarized on pages 35· through 3g of this report was
taken from reports No. 3, 6, 7, 8, 9, and 10 of this series, written by:
Duane Klarich and Jim Thomas (Report No. 3), Montana Department of Health and
Environmental Sciences; Peter Martin (Report No. 6), Tom Hinz (Report No. 7),
Allen A. Elser and Robert C. McFarland (Report No. 8), and Max Erickson
(Report No. 10), all of the Montana Department of Fish and Game; and Mike
Brown, Norm Barnard, and Mel McBeath (Report No. 9), all of the Montana
DNRC.
The section of the report entitled "Legal Constraints to Water Use in
the Yellowstone River Basin" was prepared by Al Bielefeld, Field Solicitor
for the U.S. Department of the Interior in Billings, and reviewed and edited
by Ted J. Doney, Director of the DNRC.
Appendix B of this report, "Linear Programming Model," ·was adapted from
a draft written by Phil Threlkeld concerning a model developed by him and
Satish Nayak, both of the Montana DNRC.
4
The purpose of this report is to discuss the economic consequences of the
impacts resulting from lowered streamflows in the Yellowstone River Basin. In-
cluded are an economic description of the study area, a summary of the conclu-
sions made in other reports in this series (see "The Study," pages 3 and 4)
and a literature survey of economic methodologies for evaluting the'impacts of
lowered streamflow. Legal and institutional constraints on water use in the
basin are surveyed.
An economic evaluation of the impacts of lowered streamflows should inves-
tigate both benefits and costs of these withdrawals. The material summarized
from the other reports examines only the costs of altered streamflow. In this
report, an evaluation of the benefits to agriculture of additional depletions
is made by estimating the consequences for agriculture of an instream flow res-
ervation, resulting in an analysis of the net impact of additional withdrawals
from the Yellowstone River.
The study area is shown in figure 1. Billings is the largest city and
economic hub of the basin.
Agriculture, the basin's largest industry, is declining in relative im-
portance. Coal mining is growing rapidly; so is manufacturing. Population
increases and employment trends indicate that the recent surge of economic
growth is continuing.
Growth rates basin-wide are similar to national averages, although Billings
and Colstrip are developing more rapidly. Decreases in rural population and
agricultural employment opportunities continue throughout the region.
Because most economic data is available by county rather than by
river basin, the study area consists of the thirteen counties (figure 1)
which approximate the boundaries of the Yellowstone River Basin.
5
•·
YEllowsTONE RIVER BASIN
Yellowstone River Basin Boundary
Thirteen County Study Area
Park
Sweet Grass
Stillwater
Carbon
Ye 11 ows tone
Big Horn
Treasure
Rosebud
Custer
Powder River
Prairie
Dawson
Richland
0 10 20 40 60 eO 100 Miles
~UHJtt--:j~~==~------~1======~~------.JI:=:=:=:jl
0 10 20 40 60 eO 100 Kilomelers
~~~::J. .... It::::ii .... Jit::::jl
I MUSSELSHELL
WHEATLAND \
N
\
' l
YELLOWSTONE
YELLOWSTONE
RIVER BASIN
GARFIELD
' -----l_
I
I
I
(
McCONE
I L------,
INTAKE
DAWSON
PRAIRIE
\T REA r's,_u..,R'7"E~-....;,:~,-""r~"-J'"'"':
INDIAN
BIG HORN
cusTER
i ------. --e i'. I
POWDER I
ASHLAND BROADUS • I
RESERVATION ~
YELLOWSTONE ' l
NATIONAL PARK ' (
INCOME
Personal income in the basin is growing faster than for the nation as a
whole, primarily because of increased earnings, both direct and indirect,
from coal mining. Incomes from manufacturing and railroads are also above
the state average, while the increases in farm earnings are down relative to
the rest of the state and the nation. From 1970 to 1974, personal irrcome in
Rosebud County increased 68 percent, while personal income in the Yellowstone
Basin increased 47 percent. Per-capita income in the Yellowstone Basin is
higher than the state average •. Uithin the basin, per-capita income tends to
be higher in the downstream counties (Montana DNRC 1976).
EMPLOn1ENT
Agriculture, mining, manufacturing, and railroads are the basic indus-
tries in the basin. Table 1 shows the number of persons .employed in each for
1950, 1960, and 1970.
TABLE 1. Employment in the Basic Industries in the Yellowstone Basin, 1950,
1960, and 1970.
Employment Percentaqe of Totala
1950 1960 1970 1950 1960 1970
Agriculture,
Forestry and
Fisheries 14,214 10,177 7,853 65.0 53.6 51.0
Mining 611 1,024 852 2.8 5.4 5.6
Manufacturing 2,834 4,757 4,414 12.9 25.0 28.7
Rai 1 roads 4,187 3,013 2,253 19.1 15.8 14.6
TOTAL BASIC
EMPLOYMENT 21,846 18,971 15.382 100.0 100.0 100.0
SOURCE: U.S. Department of Commerce 1952, 1961, and 1971.
NOTE: The U.S. Census Bureau classifies agriculture, forestry, and fish-
eries together. In the Yellowstone Basin, employment in forestry and fisheries
is very small, making these figures an adequate measure of agricultural employ-
ment.
aPercentages may not add to 100 because of rounding.
9
Although the number of jobs in agriculture is still larger than the number
in other sectors, a steady decline is apparent. Ne~1 jobs in basic industries
have occurred primarily in mining and manufacturing. However, data on basic
employment should be interpreted cautiously because, statewide and nationally,
the employment level in basic industries has been falling relative to derivative
employment--partially because worker productivity, due to improved technology,
has increased rapidly in many basic industries.
New basic jobs are occurring in a few specific locations. New mining jobs
within the basin have been primarily located at the coal mines at Sarpy Creek,
Colstrip, and Decker; most of the new manufacturing jobs have been in the
Billings area.
Table 2 illustrates the rapid growth of coal mining in Montana, and table
3 shows the number of jobs at each mine site. From 1972 to 1974, employment
in Rosebud County, site of substantial coal development, increased 26 percent,
and employment in the basin went up by 13 percent. However, some portion of
this rapid growth may be temporary, and employment will probably be reduced up-
on completion of the construction of electrical generating facilities at Colstrip.
Agricultural employment in the basin fell from 65 to 51 percent of total employ-
ment between 1950 and 1970. The impact of this loss in jobs was felt primarily
outside of Yellowstone County. The loss of 990 agricultural jobs in Yellowstone
County was partially compensated by an increase of 854 manufacturing jobs, but
the basin outside of Yellowstone. County lost 5,371 jobs in agriculture and gained
only 456 manufacturing jobs.
TABLE 2.
Year-
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
SOURCE:
Coal Extracted in 11ontana, 1960-75.
Tons Extracted
301,273
358,848
365,850
336,548
344,636
377,248
415,41()
364,509
555,271
1,024,885
3,517,158
7,097,127
8,264,405
10,729,019
13,555,150
22,087,188
f~ontana Energy Advisory Council 1976
10
TABLE 3. Coal Mining in Yellowstone River Basin, 1g76-77
Tonnage Produced
f1i ne County Number of
Name Operator County Seat Employees 1976 1977
Absaroka Morrison-Knutsen Big Horn Hardin lOB 4,083,094 4 '529 ,058
Co., Inc.
Decker Decker Co a 1 Co. Big Horn Hardin 300 10,051,090 10,390,419
Divide Mine Victor Carlson Musselshell Roundup 3 8,728 7,050
Jack. H. Carl son
P.M. P.M. Coal Mining Co. Musselshell Roundup a 8,251 8,677
Coal Creek Bob Schmidt Powder River Broarlus a 1 ,612 16,011
Savage Knife River Coal Richland Sidney 20 312,281) 302,426
Mining Co.
Big Sky Peabody Coal Co. Rosebud Forsyth 70 2 '390 ,809 2,312,334
Rosebud Lon') Construction Rosebud Forsyth 338 9,324,007 9,827,461
.
SOURCE: !1ontana Bureau of Mines and r.eo 1 ogy 1977 and f·lontana Coa 1 Co unci I 1978.
a Unknown.
POPULATION
Table 4 shows that nearly half of the basin's population lives in the
Billings area, and over half lives in the two regional centers of Billings
and 1-lil es City.
From 1960 to 1970, the basin's overall population remained about the
same, but the number of urban dwellers (defined as those livinq in towns of
at least 2,500 persons) increased eight percent, while the number of rural
dwellers fell by ten percent. The population of Billings during this time
increased by 16 percent. Following the national trend, outmigration has been
moderate to high in the rural areas; lack of employment opportunities is
probably a major cause of rural population decline in the basin. Progress in
farm technology has decreased the number of workers needed for agricultural
operations.
However, job opportunities began increasing in the late 1960's, and
from }g70 to 1974 the basin's population began to grow again. From 1968
to 1971, employment opportunities increased six percent, but from 1971 to
1974 they increased 13 percent (U.S. Bureau of Economic Analysis unpublished).
The largest increase in population was in Rosebud County (29.3 percent), due
to the development at Colstrip.
AGRICULTURAL ACTIVITY
Most of the water taken from the Yellowstone for agriculture is used to
irrigate pasture and crops for cattle feed. Farms and ranches within the
basin are generally much larger than the state-wide average. Major grain crops
are wheat, barley, and oats; these are usually grown on nonirrigated land.
Sugar beets and dry beans are grown only on irrigated land, but most irrigated
land is devoted to hay production. About two-thirds of farm income results
from the sale of livestock and livestock products, and the remaining one-third
from the sale of crops.
-------12
TABLE 4. Population trends in the Yellowstone Basin by county 1960, 1970, and 1974.
Percentage
Change July 1, Percentage
1960 1970 1960-1970 1974 Change
County Total Urbana Rura 1 Total Urbana Rura 1 Total Urbana Rural Total 1970-1974
Park 13,168 8,229 4,939 11,197 6,883 4,314 -15.0 -16.4 -12.7 11,900 7.9
Sweet Grass 3,290 -0-3,290 2,980 -0-2,980 -9.4 -0--9.4 3,000 0.7
Stillwater 5,526 -0-5,526 4,632 -0-4,632 -16.2 -0--16.2 5,100 10.1
Carbon 8,317 -0-8,317 7,080 -0-7,080 -14.9 -0--14.9 7,700 8.8
Yellowstone 79,016 65,313 13,703 87,367 76,651 11,716 10.6 15.8 -14.5 95,600 9.4
Big Horn 10,007 2,789 7,218 10,057 2,733 7,324 0.5 -2.0 1.5 10,400 3.4
Treasure 1,345 -0-1,345 1,069 -0-1,069 -20.5 -0--20.5 1,200 2.3
Rosebud 6' 187 -0-6' 187 6,032 -0-6,032 -2.5 -0--2.5 7,800 29.3
Custer 13,227 9,665 3,562 12,174 9,023 3,151 -8.0 -6.7 -11.5 12,100 -0.6
Powder River 2,485 -0-2,485 2,862 -0-2,862 15.2 -0-15.2 2,300 -7.4
Prairie 2,318 -0-2,318 1,752 -0-1,752 -24.4 -0--24.4 1,800 2.7
Dawson 12,314 7,058 5,256 11,269 6,305 4,964 -8.5 -10.7 -5.6 10,900 3.3
Richland 10,504 4,564 5,940 9,837 4,543 5,294 -6.3 -0.5 -10.9 9,900 0.6
TOTAL 167,704 97,618 70,085 168,308 105,138 63,170 0.3 7.7 -9. 8 179 '700 6.7
SOURCE: U. S. Department of Commerce 1961 and 1971; U. S. Bureau of Economic Analysis unpublished.
aurban dwe 11 ers live in a community 1~i th more than 2, 500 inhabitants.
The economic evaluation of water withdrawals is performed by comparing the
value of water for instream uses with the value of water when it is withdrawn
for consumptive use. The optimal allocation of water between instream uses
and withdrawals is that allocation that maximizes the sum of the net benefits
from instream uses and out-of-stream uses. Two important observations allow
definition of the optimal allocation of water between competing uses.
First, the value of additional withdrawals is subject to diminishing
returns, meaning that there is an inverse relationship between the price
farmers are willing to pay for water and the quantity of water available.
Second, withdrawals reduce the total value of uses and activities that depend
on ins tream flows. The "Impacts of Water Withdrawa 1 s" sect ion of this report
on page 35 suggests that small incremental withdrawals I"IOuld not have a signi-
ficant effect on recreational values and wildlife habitats but that large
withdrawals would reduce recreational opportunities and adversely affect the
wildlife. It is likely that additional withdrawals of equal increments would
impose increasing costs on activities dependent on instream flows--in other
words, the losses to recreation and wildlife would increase at an increasing
rate per unit of withdrawals. Figure 2 plots these relationships .
..
0
31:
0 ... .,
~ -3:: -0
Cl)
::1
~
Q
Withdrawals
Figure 2. Relationships of withdrawals to cost and benefits.
15
The line labelled marginal benefits is the demand curve for water with-
drawn from the river for consumptive uses. It has a negative slope because
there are diminishing returns to increments of water i"n these alternative
uses. The demand curve for water in these uses is the margi na 1 benefits
curve because the price consumptive users would be willing to pay for
additional increments of water is equal to the incremental or marginal
benefits they would receive from the water.
The line labelled marginal costs is shown with a positive slope, implying
that additional incremental withdrawals would impose increasing costs on
activities dependent on instream flows. If the increase in c·osts were pro-
portional to withdrawals, the marginal costs curve would be horizontal; if the
increase in costs were less than proportional to withdrawals, the marginal
costs curve would have a negative slope. The optimal allocation of water
between instream and consumptive uses is the quantity Q, where the marginal
costs of withdrawals are equal to the marginal benefits. For any level of
withdrawals less than Q, the benefits of some additional level of withdrawals
exceeds the costs to instream uses of these withdrawals. Conversely, for any
level of withdrawals greater than Q, the costs of these withdrawals exceed
the benefits, and they should not be made.
The costs of increased withdrawals discussed in this chapter are described
in the "Impacts of Water Withdrawals" section of this report on page 35 .
Dollar values have been placed on some of these costs; most, however, have not
been quantified and are treated qualitatively.
The benefits of increased withdrawals are the sum of the demand curves
for the various sectors that take water for consumptive uses. Agricultural use
is the major consumptive use dealt with in the analysis; a linear programming
(LP) model is-used to estimate the value of water for agricultural users.
The LP model was originally developed to estimate the costs imposed on
farmers by the instream-flow reservation requested by the Montana Fish and
Game Commission for the Yellowstone River Basin. (Under the Montana Water
Use Act of 1973, the State of Montana or the United States Government or any
appropriate political subdivision or agency of either may apply for a reservation
of water for existing or future beneficial consumptive use or to maintain a
minimum flow, level, or quality of water. See Montana DNRC 1976. The Montana
Fish and Game Commission made its original Yellowstone Basin reservation request
in 1974; that request was used in the LP model developed by Snyder and discussed
on pages 27 through 33. In October of 1976, the Fish and Game Commission sub-
mitted a revised, slightly higher reservation request, which was used in the
Yellowstone Impact Study's LP modeling). The LP model solves for the cropping
pattern and water allocation that maximize agricultural profits and divides
the Yellowstone Basin into seven subbasins (figure 3). The model was rerun
with Yellowstone Impact Study cost and revenue data, and the benefits of
incremental increases in water supplies available for agricultural withdrawal
were calculated. ·
The objective function values are the net profits per acre (total revenue
minus variable costs) for the cropping strategy for individual crops in each
subbasin. The cropping strategies identify the months through which each
crop can be irrigated and are used to allow for partial irrigation in subbasins
where water is scarce.
16
YEllowsTONE RIVER BASIN
SubbASINS UsEd IN T~E YEllowsTONE
IMpAcT STudy LINEAR PROGRAMMING ModEl
UY Upper Yellowstone
BI Billings Area
BH Bfghorn
·MY Mid-Yellowstone
TO Tongue
PO Powder
LY Lower Yellowstone
0 10 20 40 60 80 100 Miles
'ttiit===i I I I
0 10 20 40 60 80 100 Kilometers
~ I I I I
! MUSSELSHELL
~-WHEATLAND ! \
GOLDEN -----c-_j.-V_A L L ~ _:::__ _·
L -_i.' _,....""'---+_..,
BI
' _j CARBON
' rj
------'1 _ ...... __ - --+< -....1..--
y E L L 0 W S T 0 N E 'j
NATIONAL PARK (
N YELLOWSTONE
RIVER BASIN
\ GARFIELD
' l ''\ __ _
~
BIG HORN
RESERVATION ~·
WYOMING
McCONE
I r
DAWSON
LY
PRAIRIE
PO \
----, ~ ..• I \'-'
I
I
I
~
I
I
1
GLENDIVE)
J
J
I --,
0 > ~
0
o-1 >
\
For example, pas-ture can be irrigated by any of the following schedules:
1) only once in the spring;
2) in the spring and again in July;
3) in the spring and again in July and August; or
4) through the entire irrigation season.
May 1-June 30 are the "spring" of the irrigation season.
The model maximizes the sum of profits for each cropping strategy and
crop in each subbasin, subject to five types of constraints. The inflow con-
straints limit water availability to the estimated inflows into each subbasin.
The instream constraints require that sufficient water be left instream to
satisfy the Montana Fish and Game Commission water reservation request. The
model is run with these constraints set at 100 percent, 90 percent, 75 percent,
50 percent, 25 percent, and 0 percent of the Fish and Game Commission's 1976
reservation request,
The crop constraints limit total acreage to 1975 acreage in estimating
the current value of water. The acreage constraints for 2000 are calculated
by adding the projected increases in acreage for each subbasin as calculated
in Report No. 1 of this series to the acreage constraints used for the 1975
run. Cropping patterns were allowed to vary no more than 10 percent from
historical cropping patterns. Mass conservation constraints defined outflow
to any lower subbasin to be the inflows of the subbasin above minus
agricultural use within the upper subbasin.
The model solves for the maximum profits and the optimal cropping pattern
given the constraints. It also solves for the shadow prices of the constraints--
the amount agricultural profits would increase if the constraint were relaxed
by one unit. The marginal benefits of agricultural withdrawals are calculated
by making repeated runs with different instream-flow constraints. As the
constraints are relaxed, profits increase. The increase in profits is the
value to farmers of relaxing the constraint. Each run of the model generates
a fixed quantity of profits given a specified set of instream flow constraints
and quantity of water available for irrigation, which is the total flow less
the instream constraints. The benefit of an incremental increase in water
availability is the increase in agricultural profits resulting from that
increment of water.
For a more detailed discussion of the LP model, see appendix B.
19
The literature reviewed for this report is discussed below in four
sections. Section I summarizes the literature relevant to reports 6, 7, 8,
and 10 in this series, which deal with furbearers, migratory birds, fish,
and recreation, respectively. Section II evaluates recent literature con-
cerning the economic evaluation of water quality. Section III reviews
alternative techniques for estimating the value of water for irrigation.
Section IV discusses techniques for evaluating the demand for industrial
water uses.
I. FISH AND WILDLIFE; RECREATION
The benefits or advantages of maintaining the existing populations of
fish, furbearers, and birds can be classified as (1) benefits to recreationists
and (2) benefits to fish and wildlife. Economic evaluation of these benefits
requires estimating their importance so that it can be compared with the
costs incurred in preserving them. The economic literature usually has
evaluated these benefits as a part of a benefit-cost analysis of public
investment in water resources. In this context, benefits are measured by
the willingness of beneficiaries to pay for outputs, and costs are measured
by the willingness of persons to pay to keep resources in alternative use.
The central problem is difficulty in the estimation of the beneficiaries'
willingness to pay for recreational opportunities. Typically, recreational
activities are either unpriced or priced at some arbitrary minimal cost that
gives no indication of their real value to users. The lack of market prices
and the necessity of evaluating investments in recreation have produced
numerous techniques for estimating these benefits. Knetsch and Davis (1972)
have described several techniques of benefit-cost analyses of recreation,
among them the following methods: gross expenditure, market value of fish,
alternative cost, market value of recreation, interview, and travel cost.
GROSS EXPENDITURE METHOD
This method uses the costs incurred by the recreationist as a measure of
the benefits from the recreation, an approach defended by asserting that if
the recreation were not worth the expenditures they would not have been made.
This method is subject to two criticisms. First, the benefits are overstated
because some of the expenditures would occur 'in the absence of recreational
activity. Expenditures for food, for example, should not be counted because
these costs are necessary in any circumstance. Secondly, it attempts to
measure only the average rather than the marginal value of experience. There
may be an abundance of alternative sites for similar recreational experiences,
so that, although the value of the recreational activity is high, additional
sites for this activity are not needed, and would therefore have a low value
to recreationists. Proper evaluation of an investment in a recreational site or
activity compares the costs of the investment to the additional or specialized
improvements in recreational opportunities.
21
MARKET VALUE OF FISH METHOD
In this method, the recreational value of fishing is evaluated at the
market value of the fish caught. This method ignores the distinction between
fishing as recreation and fishing for food or as an occupation. A catch
increases satisfaction for sport fishermen, but is not the sole criterion of
the value of the activity.
ALTERNATIVE COST METHOD
The cost method is best summarized in the "Principles and Standards"
(U.S. Water Resources Council 1973) used by federal agencies.
The cost of the most likely alternative means of obtaining
the desired output can be used to approximate total value when the
willingness to pay or change in net income methods cannot be used.
The cost of the most likely alternative means will generally
misstate the total value of the output of a plan. This is because
it merely indicates what society must pay by the next most likely
alternative to secure the output, rather than estimating the real
value of the output of a plan to the users. This assumes, of
course, that society would in fact undertake the alternative means.
Because the planner may not be able to determine whether alternative
means would be undertaken in the absence of the project, this
procedure for benefit estimation must be used cautiously.
MARKET VALUE METHOD
The market value method uses a schedule of charges which are estimates of
the market value of the recreational activity. Total recreational value for
the activity is calculated by multiplying the value of an activity (for
example, one fisherman day) by the expected number of activities (annual number
of fisherman days).
The advantages of this method are the ease of calculation of these
benefits and the fact that the values used are estimates of charges that users
might be willing to pay for the activites. Shortcomings are that values do
not consider differences in the quality or uniqueness of certain recreational
activities and that the method uses average values for activity days when
the benefits of additional opportunities are the marginal value of the
incremental opportunities.
INTERVIEW METHOD
Another technique, used by Davis (Knetsch and Davis 1972), is the interview
method which estimates willingness to pay by asking a carefully selected sample
of users a set of questions designed to discover the maximum price they would be
willing to pay for the recreational activities. Thi~ study evaluated outdoor
recreation in the Maine Woods. Davis asked questions on household income,
years of experience in the area, and length of stay in the area, in addition
to questions designed to provide an estimate of willingness to pay. Regression
22
/
equations were estimated with willingness to pay as the dependent variable;
household income, years of experience in the area, and length of stay in the
area were considered as independent variables. A demand curve was then
derived by plotting the number of visits per household that would occur at
each price. Total benefits were calculated by summing the products of all
prices and associated number of visits per household.
Unlike the other methods discussed, the objections to the interview
method are practical rather than theoretical. The users interviewed may bias
the results downward if they feel they may be charged the price they say is
the activity's value to them. It is also possible that they will overstate the
value in order to make a case that an area should be preserved in its present
use.
A recent_study (Horvath 1974), designed to establish an economic
evaluation of wildlife, resulted in a survey linking wildlife-oriented
recreation with the potential or actual values received, calculated in
dollars. Values assigned by a random sampling of 12,068 households in the
southeastern U.S. were divided into three categories: a day of fishing had
a monetary value of $42.g3; a day of hunting, $47.09; and a day of wildlife
enjoyment, $70.41.
Although other studies in this present economic report place lower values
on these types of recreation, the Horvath study found that participants placed
higher monetary values on them than did nonparticipants, a situation which
is not always acknowledged.
TRAVEL COST METHOD
The travel cost method was first suggested to the National Park Service
in 1947 and more fully developed by Clawson and Knetsch (1966) in
Economics of Outdoor Recreation. The travel cost method derives a demand
curve for the recreation experience by using travel cost data as a proxy
or substitute for price. The method requires data on travel costs, use rates
for users in different locations, distance from the user's home to the
recreational site and population of the areas from which the users come. The
site is shown on a map, and concentric circles are drawn around the site;
the average distance and travel cost from each circle or zone are calculated.
Populations and visit rates as a percentage of population are calculated for
each zone. From this data the annual number of visits is calculated as a
function of travel costs to the different zones. Next a demand curve is
estimated by raising costs a constant amount in each circular zone and
calculating the decreased number of visitors that results from each increase
in costs. The incremental additions to travel costs are a proxy for increases
in admission prices. With each simulated increase in the admission prices,
the expected number of visits decreases. The prices used for the demand
curve are the simulated admission prices, and the quantities are the number of
visits that are expected at each price.
Statistical analysis using a regression equation is used to estimate the
demand curve for the recreational opportunities at a site. Total willingness
to pay is found by integrating the area under the estimated demand curve.
23
Burt and Brewer (1971) revised this method to account for the effects
the availability of substitute sites will have on the estimated benefits
of a specific proposed site. The travel cost method is the most sophisticated
and theoretically desirable method. However, data requirements are greater
than for the other methods and considerable econometric skills are required.
Copeland et al. (1976) have summarized the major difficulties with this
method as follows.
Four problems with the travel-cost method have been identified.
(1) The central assumption of the model is that people in the inner
zones will respond to an increase in the admission price by reducing their
visit rates to the visit rates observed by people in outer zones whose
travel costs are the same as the travel cost plus admission price paid by
inner zone users. This will only be true if people in the different zones
have the same incomes, tastes, and preferences. This assumption can be
relaxed only by explicitly including additional variables in the regression
equation. Proxy variables to account for varying tastes and preferences are
difficult to define and evaluate.
(2) When a single trip includes multiple destinations, the joint costs
common to all destinations cannot be attributed solely to the site being
studied. An allocation of joint costs requires additional data, and no
theoretically adequate method exists to make this allocation.
(3) Time spent traveling to the site may be considered a cost or an
enjoyable part of the total recreation experience, and an estimate of time
costs is difficult and imprecise.
(4) The travel cost method is not easily used to evaluate river-based
recreation because there is no unique distance from the users residence to
the river but rather a range of distances to different points along the river.
DIFFICULTIES IN ESTIMATING THE IMPACT
OF REDUCED STREAMFLOWS ON THE QUALITY OF RECREATION
Two problems prevented a quantitative evaluation of the loss in recrea-
tional value that would result from lowered streamflows. Biological and
physical data were not available to adequately describe the physical and
biological impact of lowered flows on the mainstem. Without adequate descrip-
tion of the proposed change, an evaluation of the change was not possible.
In addition, the recreation methodologies discussed previously were designed
to evaluate the total value of a recreational resource rather than the
decremental loss to the total value that would result from physical change.
An adequate method to discuss the decremental change is not available.
II. WATER QUALITY
Baumel and Oates (1975) and numerous other writers (for example,
Thompson 1973 and Freeman et al. 1973) have discussed the theoretical problem
24
of external costs and the use of taxes or pollution charges to correct the
misallocation resulting from external costs. An external cost is a cost
of an individual or firm action that directly and adversely affects the
production opportunities or consumption opportunities of other parties.
Irrigation in the Yellowstone offers a prime example of such external costs.
Return flow from each irrigated field increases the salinity of the river
water and imposes costs on downstream irrigators whose water quality
declines. Upstream irrigators do not bear the full costs of their
decision to expand irrigation because there is no requirement that they
compensate downstream irrigators for the costs imposed on them. Private
costs of upstream irrigators are lower than the social costs which include
the costs to downstream irrigators. Because upstream irrigators don't
bear the full costs of their irrigation decisions, they have an incentive
to expand irrigation beyond the optimum output.
Valantine (1974) identified two methods for measuring the agricultural
costs of increasing salinity. They are (1) the costs of maintaining .
existing yields as salinity increases and (2) the loss of income resulting
from a decline in yields because no corrective action is taken.
Existing yields can be maintained by leaching out the salts with
additional irrigation, installationof a drainage system, conversion to
sprinkler irrigation, or the dilution of river water with higher qu~lity
water from another source.
The loss of income resulting from a decline in revenues because declines
in the salinity levels in the root zone are not prevented is either the loss
due to declines in the yields of existing crops or the loss resulting from
a switch to less profitable salt-resistant crops. Clearly a farmer faced with
increasing salinity suffers increased costs no greater than the least-cost
alternative mentioned above. Valantine cites a 1971 EPA study which concluded
that accepting a decline in yields would result in the minimum penalty cost to
farmers in the study area, the Colorado River Basin, although most farmers
were installing expensive drainage systems and irrigation systems.
In discussing different methods of estimating the dollar losses resulting
from increased salinity Valantine estimated the costs of the different
alternatives. Costs of drainage systems and ditch lining were discussed.
In Valantine's opinion, the best method for estimating the costs of salinity
on irrigators was developed by Sun, who developed a complex mathematical
model which derived the net regional income from the dirferent levels of
salinity.
A study by Pincock (1969) made projections of the salinity damages in
the Wellton-Mohawk Irrigation District in Yuma County, Arizona. Study
procedures were:
1 )
2)
3)
4)
develop total dissolved solids projections (TDS) for 1980 and 2010;
relate salinity levels in the root zone to irrigation water quality
and leaching percentages;
get experimental data relating salinity in the root zone to the
quality of irrigation water and the leaching percentage;
relate salinity in the root zone to crop yields;
25
5) estimate crop water requirements;
6) develop budgeted costs and returns for different cropping patterns
and crop rotations;
7) estimate total agricultural output for the district given cropping
pattern, crop budgets and salinity effects; and
8) estimate net salinity damages.
Pincock concluded that in this district no changes in cropping patterns
were justified and that salinity damages would be insignificant in 1980 and
produce about $460,000 net damages in 2010, which would be about one percent
of the value of the projected total gross output.
III. ESTIMATING THE VALUE OF WATER FOR IRRIGATION
The value of water for irrigation depends on the increase in crop yields.
resulting from the additional water and the price these crops bring on the
market. Economic theory (Ferguson 1969) says that a farmer will increase
the quantity of water used for irrigation up to the point where the cost of the
water is equal to the increase in revenues produced by irrigation. The
quantity of water demanded is inversely related to its price or cost. An
increase in the price or cost of water will reduce the quantity used. Five
methods are available to estimate the value of water in agriculture.
GENERAL METHODS
The first method is simply to observe the prices at which water is bought
and sold·. Hartman and Seastone (1970) observe that within some ditch companies
active water rental markets occur; these prices increase over the irrigation
season and are considered useful measures of the value of water in .these areas.
A second, pursued in a study done at Colorado State University (Hartman
and Anderson 1964), estimated the value of water by applying regression
analysis to farm sales data. The selling prices of farms were regressed on farm
acreage, the average number of acre-feet of water delivered per season, and
the assessed value of improvement. They concluded that the "regression analysis
of this study indicates that water is an important enough consideration in the
total farm price to permit statistically significant estimates to be made of the
values." They found that the values estimated from the regression were signi-
ficantly lower than reported sales prices of water in the study area.
A third method for estimating the value of irrigation water is to use
farm budgets to calculate the increase in profits resulting from a switch from
dryland agriculture to irrigated agriculture. The increase in profits per
acre divided by the water requirements per acre is the value of an acre-foot
of water for the land for which the budget was prepared.
The fourth method, linear programming, is described below.
26
LINEAR PROGRAMMING METHODS
Examples of methods which use linear programming (LP) to estimate the
value of water within a region include a Colorado study (Hartman and
Whittelsey 1961), a study of the Yakima Valley (Butcher et al. 1972), and
an evaluation of the Yellowstone Basin (Snyder 1976). The LP methods calculate
the maximum possible agricultural profits, given constraints of the availability
and productivity of land, cropping patterns, prices and water supplies. By
making successive runs of the model with incremental changes in the constraints
specifying the availability of water, the change in profits is calculated as
a function of the quantity of water supplied. The value of an incremental
addition to the water supply of a region is the increase in profits it
produces. Dividing the changes in profits due to additional water by' the
quantity of the addition gives the per-unit value of the increment.
The Yakima study used a mathematical program with a nonlinear objective
function and estimated the optimal allocation of water between municipal,
agricultural, and hydropower uses. lnstream uses were modeled indirectly
by constraints on instream flows.
A linear program was used by Snyder in the study of the Yellowstone
Basin to estimate the impact that instream-flow requirements and diversion
for the coal industry would have on the marginal value of water for irrigation.
The model maximizes agricultural profit subject to inflow constraints, land
constraints, constraints of the cropping pattern, instream flow constraints,
and withdrawals for the coal industry. The purpose of the model is to
calculate the maximum agricultural profits obtainable with a given set of
constraints and then estimate marginal values of water to irrigation by
tightening the instream flow constraints and solving for the reduction in
agricultural profits that results.
The model divides the Yellowstone.Basin into five areas. Figure-4 shows
the boundaries of the areas. Area 1 includes Park and Sweet Grass counties,
Area 2 includes Carbon, Stillwater and Yellowstone counties, Area 3 is Big
Horn County, Area 4 is comprised of Treasure, Rosebud, Custer and Powder
River counties, and Area 5 includes Prairie, Dawson and Richland counties.
As shown in figure 5, a schematic diagram of the basin as modeled, each area
includes irrigation; in addition, Area 4 also includes a coal mining activity.
The objective function maximizes the sum of the product of per-acre
profits for each crop and cropping strategy in each area and the number of acres
for each crop, cropping strategy, and area. The mathematical formulation of
the objective function is:
Maximize Z = L PijkOijk
where: Z = total profits in the study area
= the return over variable costs in the ith area for the jth
crop which was irrigated through the kth period. ·
= the number of a{~es in the ith area in which the jth crop
was irrigated k period.
27
\lvcmi n<1
Runoff 1\rea 1
~
t
I rr i qat ion
Pro.iect l
,
Runoff Area ?.
Hater from Hyorli n'l
~
t
Irrination
Pro.iec t 2
Runof~ t
A rei\ l
t ~
Irrination
Pro.iect 3
...._ Runoff 1\rr.a ~
\~a ter from \·lyol'li nn
t
Irrination
t Pro,iect 1\
Coal r1inin~ and
Related Enterprises
... P.unoff 1\rea 5
..
I rri qa ti on
Project S
!forth na~ota
Figure 5. Schematic diagram of Yellowstone Basin for Snyder's linear
programming model.
2B
I.
'·
YEllowsTONE RIVER BASIN
SubbASINS UsEd IN SNydER's
LINEAR PROGRAMMING ModEl
AREA 1
Park
S~teet Grass
AREA 2
Carbon
Stillwater
Yellowstone
AREA 3
81 g Horn
SOURCE: Snyder 1976
0 10 20
L.tU-1.1 I
0 10 20
I.H.Ji.j--1
40
I
60
I
40 60
I I
AREA 4
Treasure
Rosebud
Custer
Powder River
AREA 5
Prairie
Dawson
Richland
80
I
100 Miles
I
80 100 Kilometers
I I
N
\
' ?
YELLOWSTONE
RIVER BASIN
GARFIELD
4
YELLOWSTONE
2
,
I
!.._
INDIAN
BIG HORN
RESERVATION ~·
I
I
I
(
McCONE
I ,__--,
I
DAWSON
~ -------li····
I
I POWDER I
ASHLAND
I
4
Per-acre profits are the difference between revenue from the crop and the
variable costs required to produce the crop. Variable costs include labor
costs, power costs, seeds, and capital costs. The constraints on water
availability are the actual inflows and flows between areas for each of the
10 years studied. The constraints on land availability restrict acreage of
each crop to historical cropping patterns plus or minus 10 percent. The minimum-
flow constraints require that specified quantity must be transferred from the
area with the constraint to the area downstream.
lnstream flow constraints were imposed in areas 2, 4, and 5. These
constraints represent the water reservation requests made by the Montana Fish
and Game Commission (page 16). The model was run with instream constraints
set at 100, 75, 50, 25, and 0 percent of the Fish and Game Commission 1974
reservation request.
Snyder concluded that the instream requests would reduce the quantity of
water available to future irrigators and increase the marginal value of water
for irrigation. Present irrigation would not be affected because the reservation
claim on water would be junior to existing rights.
To estimate the marginal values, a frequency distribution with alternative
levels of water reservation over a 44-year period for the Yellowstone River
was calculated. The expected or average value of water for the ten-year
period being studied was calculated by multiplying the probability of the
occurrence of each class of flows by the value per acre-foot associated with
each level of instream flow constraints and coal diversions.
The sum of these values is the estimate of the marginal value of water
at a given level of instream flow constraints. By repeating this procedure
at different levels of instream constraints, a function relating marginal
values of water to instream flow constraints is estimated. Figure 6 shows
this when calculated on the assumption that diversions for the coal industry
are 3000 acre-feet/month. The marginal value of an acre-foot of water is the
increase in agricultural profits that would occur if one more acre-foot was
available. Figure 6 shows that an increase in instream constraints increases
the marginal value of water. This occurs because, when less water is available
for irrigation, marginal increases in the water supply will be used to irrigate
high-quality land growing relatively high-value crops. When more water is
available, marginal values decline because the additional water goes on poor
soil and lower valued crops. Marginal values are not shown for constraints
set at 75 percent and 100 percent of the Fish and Game Commission reservation.
In some years model inflows to certain subbasins were less than the instream
flow constraints; hence, there was no feasible solution.
IV. EVALUATING THE DEMAND FOR INDUSTRIAL WATER
Stroup and Townsend (1974) estimated the values of water for electric
generation in the northern Great Plains area. Water values were calculated
by estimating the difference in annual cost between wet and dry cooling
towers on coal-fired electric generating plants. Cooling towers are required
to reduce the temperatures and lower the outlet pressure on the turbines. A
31
"' ... c
0
0
c:
Cl>
::::t
c >
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0
0% 25%
Percentage of Fish and Game Commission
Requested Minimum Flows
50%
Fiqure 6. Expected marginal values of an acre-foot of water in irrigated
agriculture resulting from using Snyder's linear programming model to impose
minimum flows on the Yellowstone River.
wet cooling tower works by spraying water in the tower and allowing evaporation
to provide cooling. A dry cooling tower circulates water through a closed system
of piping similar to a giant car radiator, and the cooled water is recirculated
through the plant.
A dry-cooled plant requires a larger capital investment and higher OM&R
costs than a wet-cooled plant. Dry cooling is economically preferable to wet
cooling only when water is so costly that the additional investment required by
a dry-cooled plant is more than offset by the savings that result from decreased
water consumption.
Stroup and Townsend used two different methods to estimate the maximum
price per acre-foot that a generating plant with a wet cooling tower could
32
I
pay and still find wet cooling cheaper than the dry cooling option. This
break-even price is the value of water for these firms because at any price less
than the break-even price wet cooling is cheaper than dry cooling, while for
any price above the break-even point water costs are so high that dry cooling
is the cheaper cooling method. One method estimated the average difference in
annual cost between wet and dry cooling and divided that figure by the annual
water use of the wet-cooled plant. By this method the break-even point for
dry towers is $197.09/af. The second method estimates the opportunity cost
of the power foregone due to the loss in efficiency of a dry-cooled plant that
results when the plant is less efficient in warm weather. At 8 mills/kwh
the break-even cost of water is $106/af.
The researchers conclude that the value of water used to cool thermal
electric generating plants is between $100/af and $200/af. This value will
vary with climatic conditions at the site and may change as more experience
is gained with dry-cooled plants.
33
PROJECTIONS OF FUTURE USE
In order to adequately and uniformly assess the potential effects of
water withdrawals on the many aspects of the present study, it was necessary
to make projections of specific levels of future withdrawals. The methodology
by which this 11as done is explained in Report No. 1 in this series, in which
the three projected levels of development, low, intermediate, and high, are
also explained in more detail. Summarized in Appendix A, these three future
levels of development were formulated for energy, irrigation, and municipal
water use. Annual water depletions associated with the future levels of
development were included in the projections. These projected depletions,
and the types of development projected, provide a basis for determining the
level of impact that would occur if these levels of development were carried
through.
COSTS
The purpose of this section is to briefly summarize the impacts of low-
ered flows that were predicted by reports NO. 3, 6, 7, 8, 9, and 10 in this
series. These impacts, largely negative, are the principal opportunity costs
of agricultural withdrawals.
These costs wi 11 be compared on pages 39 to 43 with the benefits to
farmers of increased withdrawals. This estimation of future impacts was based
on the three projected levels of development discussed above. For the most
part, the physical impacts of this projected development on the basin's en-
vironment were small. That, among other reasons, made difficult the quantif-
ication of the impacts, and the following discussion is mostly qualitative.
FURBEARERS AND MIGRATORY BIRDS
Alterations in channel morphology present the major threat to habitats
and populations of furbearers (Report No. 6 in this series) and native water-
fowl (Report No. 7). Of the principal furbearers, beaver, mink, and muskrat,
beaver are most vulnerable to changes in water level. High water can flood
dams and wash a~1ay food caches; 1 ow 1 eve 1 s expose the anima 1 s to predation
and, in combination with cold temperatures, can result in caches being frozen
down. A braided channel provides a favorable habitat for beaver, and changes
in channel morphology that would reduce the number and size of the islands
would adversely affect beaver.
The stabilization of bars and islands and the increased density of veg-
etation due to reduced flood flows and reduced furbearer population would
damage nesting sites and increase predation. Reduced fish populations would
probably reduce the populations of birds that prey on fish. Additional irri-
gation would increase feeding areas and attract more migrant fieldfeeding
35
ducks and geese, but hunter pressure would also incre~se.
Koch (Report No. 2 of this series) concluded that historical depletions
in the basin have been on the order of estimated future depletions and that
the physical appearance of the mainstem of the Yellowstone has not been alter-
ed appreciably. It is likely,· then, that future depletions, if confined to
diversion and pumping rather than onstream storage, would ht~ve a similarly
small impact. Thus, the projected withdrawals would not apprectably affect
the habitat for furbearers and birds.
Table 5 summarizes information on trapping income in the basin. Trap-
ping does not make a noticeable contribution to income in the regton. In
1972, personal income in the Yellowstone Basin was $112,9B9,000. The average
income mentioned in table 5 is gross income, and the contribution of trapping
to personal income in the area consists of gross income minus trapping costs.
Trapping costs have not been estimated.
TABLE 5. Average trapping income, Fish and r,ame Regions 5 and 7, 1960-1974.
Animal Average Price
Beaver $10.33
Mink 10.52
Muskrat _g1
TOTAL
FISHERIES
Annual
Average Catch
2410
872
3559
Average Annual Income
$24,895.00
9,173.00
3,221.00
$37,289.00
Number of
Trappers
124
107
120
Report No. 8 in this series studied the Tongue River to determine the
impacts that differing levels of reduced flows would have on the Tongue River
fishery. In the low level of development the report concluded that rearing
flows in the fall would be inadequate 3 years out of 4. Rearing flows would
be inadequate 9 years out of 10 in the intermediate and high levels of devel-
opment. The low-level projection would have a minimal impact in winter. while
the intermediate impact is described as "high" and the impact of the high-
level projection is described as "severe." The impacts of the low, intermed-
iate, and high levels of development on the fishery during the spring are
summarized as minimal for the low~evel projection, high for the intermediate
level, and severe for the high level.
No studies were done on the other fisheries in the Yellowstone Basin.
RECREATION
An evaluation of the costs of reduced recreational values (Report No. 10
36
of this series) would require additional information on various conditions,
such as how reduced fish populations would affect fishing success and how
reduced fishing success 1~ould affect the value that fishermen place on fishing.
Table 6 summarizes impacts lowered flows would have on the five recrea-
tional sections studied.
TABLE 6. Impact on lowered flows on recreation in the Yellowstone River Basin.
River Sections a
Activity 1 2 3 4 5
Boating -2 -2 -2 -3 -2
Rockhounding -1 -1 -1 -1 -3
Fishing -3
Waterskiing -1
Swimming -2 -3
Access +3 +3 +3 +3 +3
TOTALS -2 -3 0 -2 -5
NOTE: Each number in the table is the product of an impact modification
number and the weight (or importance), based on current use, attached to each
activity in each area. A negative number means that lowered flows decrease
recreational values, while a positive number means that lowered flows improve
recreational opportunities. All study sections are along the mainstem of the
Yellowstone River. Activities not shown in table 6, such as walking for pleas-
ure and picknicking, are not expected to be affected by reduced flows and are
not listed here.
aThe five river sections are:
1. Big Timber to the mouth of the Clarks Fork River
2. Mouth of Clarks Fork River to the mouth of the Bighorn River
3. Mouth of the Bighorn River to the mouth of the Tongue River
4. Mouth of the Tongue River to the mouth of the Powder River
5. Mouth of the Powder River to North Dakota border
Access is an essential complement of the recreational pursuits. The
costs of these losses are the lowest of either the costs of eliminating the
recreational losses or the decline in the value of recreational activity that
occurs because mitigation of the adverse impacts is too costly. For example,
the costs of poorer fishing due to reduced fish populations is the lower cost
of either successfully restocking the fishery or the decline in the value of
recreational fishing because catches are down.
37
EXISTING MUNICIPAL AND AGRICULTURAL USERS
In order to determine any adverse effects that a decrease in the access-
ibility of water, as a result of reduced flows, would have on the existing
municipal and agricultural water users in the Yellowstone River Basin, the
Yellowstone Impact Study included an investigation of the diversion systems
of three municipalities and a number of agricultural users.
Billings, Miles City, and Glendive, the municipalities studied, draw
their water supplies directly from the Yellowstone River. Using the projec-
tions of future development explained in appendix A. the future service pop-
ulations and Yellowstone River water surface elevations for each of the three
water supply systems were compared with the amount of electrical power now
being used by the plants, the amount of water now pumped from the river, the
cost of chemically treating the water, and recent streamflow records. This
analysis showed that the cost of providing municipal water for Billings, Miles
City, and Glendive will increase in the future, as shown in table 7. The in-
crease, though, will occur primarily because of increased water consumption
due to population growth and because of probable increases in the price of
electricity; the reduced water surface elevations, as projected for the three
levels of development, would have an insignificant impact on municipal water
system costs.
TABLE 7. Percentage of increase in operation cost over present costs for each
projected level of development.
City
Billings
Miles City
Glendive
Low
53
85
32
Intermediate
53
93
33
High
60
146
33
Four pumping and twelve gravity irrigation diversions were examined to
determine the effect of lowered streamflow on each diversion. The efficiency
of the irrigation pumping plants studied is greatly reduced during extremely
low river flows. In other words, when flows in the river decrease, pumping
costs increase. For the projected levels of development, pumping costs would
increase from 0.2 percent for one site at the low level of development to 11.1
percent for another at the high level of development.
Three of the gravity irrigation diversions selected for study possess
diversion dams across the river. These diversions have no problems getting
water into the distribution system when flows in the river are low because
their headgates are below the crest of the diversion dams. Therefore, if nec-
essary, these projects could physically divert all of the water from the river
when flows in the river are less than the capacity of the canal--although
existing water rights downstream would probably make it illegal to do so. Nine
gravity irrigation diversions were studied which do not include diversion dams.
These have only minor headgate structures built at the head end of the canals.
Most have problems getting sufficient water during low streamflows in the
Yellowstone River even at the present level of development. These problems
38
would increase in intensity and frequency at the projected levels of develop-
ment. Among the solutions to these water accessibility problems are: pro-
vision of adequate instream flow in the river; installation of permanent, im-
pervious diversion dams in the main river channels opposite the side channels
that the diversions are now on; and channelization of the river so that most
of the flow is directed toward the diversion.
WATER QUALITY
The conclusions of the water quality portion of the Yellowstone Impact
Study (Report No. 3 of this series) are:
1) The Upper Yellowstone Subbasin and the Bighorn Subbasin would
experience relatively minor degradation of water quality under all
three levels of development. Eighty percent of the additional agri-
cultural development and all of the future energy development is pro-
jected to occur in eastern Montana, so only that portion of the basin
east of Billings was analyzed for changes in water quality.
2) The Tongue Subbasin and the Powder Subbasin would experience signif-
icant deterioration of water quality under all levels of development.
Waters in the lower portions of each basin would be of questionable
value for most beneficial uses.
3) The Mid-Yellowstone Subbasin and the Lower Yellowstone Subbasin would
sustain moderate increases in salinity under the low and intermediate
levels of development.
4) The Lower Yellowstone Subbasin would experience no significant effects
at lower levels of development, and major reduction in water quality
at the high level of development.
The negative effects would be more severe under the high level of devel-
opment--especially in dry years and during August through October of average
years. Degradation would not be severe enough to preclude use of the water
for common beneficial uses, but more refined and expensive management and
treatment practices may be required.
The costs imposed on agriculture by lowered water quality are the lower
of either the decreased value of the crops grown because yields are lower or
the increased costs required to avoid the loss of crop values. Likewise, the
costs of a decline in water quality for municipal users are the lower of either
the costs of the damage done by the degraded water or the costs of maintaining
water quality standards. Possible damages include reductions in the useful
lives of utility distribution pipes, water using devices, and heating systems,
the cost of increased use of bottled water, and damages to parks, gardens,
and home plantings.
BENEFITS
The linear programming model estimates the reduction in agricultural
profits resulting from instream flow constraints which reduce the quantity
of water available to irrigators. The value of withdrawals to irrigators
39
is calculated as the amount fanners would be willing to pay to secure a
reduction in the instream-f]ow constraints. Their col1ectiile willingness to
pay in order to achieve an incremental reduction in the instrea,m-flow con-
straint is equal to the reduction in profits that they suffer due to that
increment of the instream-flow constraint. If, for example, an increase of
10 percent in the instream constraint cost irrigators $500,000 in lost profits
because less water was available, then irrigators would be willing to pay up
to $500,000 to avoid the increase; $500,000, therefore, is the value of this
water to the irrigators.
The LP model was run with two sets of inflow constraints, two sets of
acreage constraints, and six sets of instream constraints. The inflow con-
staints correspond to flows that are equaled or exceeded 50 percent of the
years and flows that are equaled or exceeded 90 percent of the years. Acre-
age constraints used were those corresponding to 1975 irrigated acreage and
the estimated irrigated acreage in 2000.
The model was run with instream flow constraints corresponding to 100
percent, 90 percent, 75 percent, 50 percent, 25 percent, and 0 percent of
the 1976 Montana Fish and Game Commissi·on reservation request (see page· 16
for each of the following combinations of .flows and acreage constraints:
1) 50th-percentile flows
1975 acreage
2) 50th-percentile flows
2000 acreage
3) 90th-percenti 1 e flows
1975 acreage
4) 90th-percentile flows
2000 acreage
No estimation of water values with 90th-percentile flows was possible
because the instream constraints exceeded the available inflows in one or
more subbasins in some periods, and an LP solution was infeasible.
Table 8 shows impact on agricultural profits of different levels of in-
stream-flow constraints with 50th-percentile flows and current irrigated acre-
age.
TABLE 8. Impact on agricultural profits of different levels of instream
constraints: 1975 irrigated acreage.
Percentage of lnstream
Flow Constraint
0
25
50
75
90
100
Agri cultura 1
Profits ·
$117,691,299
117,691,299
11Z,691 ,299
117,691,299
117,691,299
117,735,909
40
Short Term Profit Lost Due
To Increased Instream Con-
straints
0
0
0
0
0
$44,610
The decrease in profits of $44,160 that occurs when the instream constraint
is increased from 90 percent to 100 percent is due to a slight shortage in the
Bighorn Subbasin. This decrease is only .04 percent of total estimated profits
in the Yellowstone Basin, confirming that in a year with 50th-percentile flows
the instream constraints require that less water be maintained instream than
is left after current irrigation needs are met.
Less obvious is the conclusion that the marginal value of water for irri-
gation is currently about zero. Unappropriated. water is available for the
cost of filing for a permit to appropriate water; for farmers along the river
there are no economical uses for the water, even though it is freely available.
The benefits of withdrawals above current level are presently zero.
Table 9 shows the impact on agricultural profits of different levels of
instream-flow requirements with 50th-percentile flows and the number of acres
that are expected to be under irrigation in 2000.
TABLE 9. Impact on agricultural profits of different levels of instream
constraints: irrigated acreage projected to 2000.
Percentage of Instream
Flow Constraint
0
25
50
75 go
100
Agricultural
Profits
$145 '744 ,493
145,717,946
145,635,874
145,524,041
145,373,792
144,210,838
An Increase in this In-
stream Constraint Reduces
Short Term Profits by
0
26,547
82,072
111 ,833
150,249
1,162,954
Table 10 is derived from Table 9 and shows the amount irrigators would
be willing to pay to secure a one-percent reduction in the instream-flow con-
straint for each of the separate intervals estimated.
TABLE 10. Values to irrigators of one-percent reduction in instreaM-flow constraint.
Percentage ofFish and Game
Commission Constraint
100~90
90-75
75-50
50-25
25-0
Short-term Value to Irrigators of 1 Percent
Reduction in the Instream Constraint
$116,295
10,017
4,473
3,282
1,062
Table 11 shows the volumes of water in acre-feet that make up one percent
of the instream constraint for each basin and time period.
41
TABLE 11. One percent of instream constraint.
Time Period UY
Winterb fi,545
Sprinqc 12,912
July 5,339
August 2,598
September 1,785
a see fi 9ure 3.
boecember 1-May 1
Cf1ay 1-June 30
BI
12,868
16,619
5,777
2,951
2,201
Subbasins a
BH HY TO
12,231 27,999 1,194
5,354 30,458 725
?. • 141 8,566 249
1, 722 4,305 94
1, 547 4,165 100
PO LY
8,445 31,415
967 32,690
122 9,375
24 4,305
23 4,165
Comparison of table 10 with table 11 sho~1s that the marginal value to
irrigators of these increments of flow is low relative to the volume of water
involved with a one-percent change in the instream requirements. This is be-
cause the instream constraints reduce the number of irrigated acres only in
August and September and reduce only the water available for irrigating pas-
ture. The instream constraints used did not seriously restrict irrigated ag-
riculture in the Yellowstone Basin.
The profits are the difference between the total revenue obtained from
the sale of the crops and the variable costs of growing the crops. The est-
imated decline in profits is the decline that would occur if water constraints
were suddenly imposed in the spring and the capital investments in irrigation
equipment lay idle during the irrigation season. These annual losses would
be less in the long run because, if a permanent scarcity of water existed,
farmers would be able to reduce their losses by selring equipment that is use-
ful only for irrigated crops and adjusting to an operation with less irrigation.
In other words, the costs imposed by instream constraints overstate the annual
costs that would occur if farmers could anticipate the water availability over
a period of years and adjust the nature of their operations.
The distinction between the total value of the water for irrigation and
the marginal value must be clearly understood. The total value of water is
estimated to be the total agricultural profits as listed in table 12 while
the marginal value is the increase in profits that would result from a small
increase in the supply of water.
EVALUATION
The purpose of an evaluation is to compare the advantages and disadvan-
tages of a proposed action and to determine whether the advantages outweigh
the disadvantages. The advantages of increased water withdrawals are the
value of additional water for irrigation, municipal, and industrial expansion
and improved recreational access. The disadvantages include increased pump-
ing costs for irrigation and towns and reduced recreational values for fish-
ing , boating, swimming, and waterskiing. Lower levels of water quality raise
costs for irrigated agriculture and municipal water users.
42
An evaluation of these diverse consequences clearly requires a common
denominator for comparison of the advantages and disadvantages of increased
withdrawals. An economic evaluation weights these consequences by society's
willingness to pay to receive the benefits or avoid the losses. It would
have to be determined whether the people who benefit from increased with-
drawals would be willing to pay more to maintain the withdrawals than the
people bearing the costs of withdrawals would be willing to pay to prevent
the increased withdrawals. Incremental withdrawals are socially desirable
only as long as the people who benefit from these withdrawals value their
gains to be worth more than the value that the persons who suffer losses
place on those losses. Two further observations make clear the enormity
of this task of evaluation.
First, the evaluation compares two different states of society. What
would life be like in the study area if current flow levels·are maintained?
What would life be like if flows are reduced? How would reduction in flow
levels affect the value people place on their water-dependent activities?
Second; the evaluation measures comparatively the benefits and costs of
withdrawals to the people who will occupy the Yellowstone Basin in the future.
The scenarios used to determine the size of the projected withdrawals assume
increased irrigation and a highly developed industrial sector in. 2000. Will
an industrial society with a larger population value the recreational oppor-
tunities available with instream flows more than current consumptive users
value the use of that water?
Immediately one is impressed with the enormity of the task and the lack
of information necessary to complete the task. The Yellowstone Impact Study
has provided some useful information regarding the consequences of increased
withdrawals, but not enough is known to be able to evaluate the economic de-
sirability of increased withdrawals.
43
L~ ~ to-watett uu
in tk ~~ i<UJe!t '844Ue
This section summarizes the legal constraints to water use in the
Yellowstone River Basin. Legal constraints can include a wide range of
laws and legal doctrines; for purposes of this section, however, only those
constraints which may have a direct affect on water use are listed. There-
fore, the list is not intended to be exhaustive. Refer also to Report No. 4
in this series, The Adequacy of Montana's Regulatory Framework for Water
Quality Control.
The term "legal constraints" should not be misconstrued to mean laws
or legal doctrines which hinder water use. Superficially, those listed may
indeed hinder the use of water. However, laws and legal doctrines are
developed in a free society to provide order. Laws regulating or affecting
water use are examples. A specific example is the Montana Water Use Act,
which regulates the appropriation of water. Through such regulation, the
process of acquiring rights to the use of water is more orderly, and in the
end that regulation may actually promote the use of water.
The legal constraints listed below include constraints resulting from
court decisions as ~:ell as stututory ilnd constitutionill constraints.
FEDERAL LEGAL CONSTRAINTS
1. Reclamation Act of 1902, as amended and supplemented (32 Stat. 388;
43 U.S.C. 431, 524 and 423e). Irrigable lands to which irrigation water from
a federal reclamation project can be delivered is generally limited to
160 acres in the ownership of a single person or entity or 320 acres in the
ownership of husband and wife.
2. Winters Doctrine. Lands within an Indian reservation or other
federal lands withdrawn from the public domain (such as most federal forest
lands) hold a reserved right to use the waters which are within, crossing,
abutting or beneath the reservation. This reserved right, even though
unexercised, enjoys a continuing priority as of the date the reservation
was established. The quantity of the reserved right is that amount of water
needed to serve the purposes for which the reservation was established.
Arizona v. California, 373 U.S. 546, at 601 (1963).
Reserved water rights (commonly called "Winters Doctrine rights",
stemming from the U.S. Supreme Court case of Winters v. United States,
207 U.S. 564 (1908) which originated the concept) are largely unquantified
in any definite source. Further, there is continuing debate and litigation
attempting to define the scope of these rights. Since the quantity or
legal scope of reserved rights is uncertain, many states, including Montana,
are unable to accurately determine the amount of water remaining for
allocation under state law, particularly near federally reserved lands or
Indian reservations. No problem is a bigger source of consternation to
state water rights and water planning officials.
45
Litigation to adjudicate federal and Indian reserved water rights on
the Tongue and Bighorn river drainages in Montana has been brought in federal
court in Billings under three separate lawsuits. The litigation, instigated
by the United States Government and by the Crow and Cheyenne tribes, is
at this point only in the preliminary stages. It will be years before the
cases are ultimately decided, but the actions are valid evidence of the
problems unquantified and unknown reserved water rights can create. If
the federal government and the tribes succeed in their claims, many existing
water users under state law may be precluded from future use of water. In
addition, the Department of Natural Resources and Conservation has reports
of several potential water users in the Tongue and Bighorn drainages who
have taken a "wait and see" attitude, rather than apply for future water
development.
Until they are eventually quantified and defined, either by litigation,
agreement, or Congressional action, reserved water rights will undoubtedly
be a major constraint on water use in the Yellowstone River basin.
3. The Federal Power Act of 1g2o, as amended (41 Stat. 1063; 16 U.S.C.
79la et ~.),requires nonfederal entities who propose to construct a power
or navigation facility to secure a license issued by the Federal Energy
Re9ulatory Commission before any construction which will affect either
(a) waters over which Congress has jurisdiction or (b) public lands or
reservations of the United States.
4. The Fish and Wildlife Coordination Act, as amended (72 Stat. 563;
16 U.S.C. 661 et ~.),requires that any public or private agency proposing
to impound or divert water or to modify any stream must consult the U.S.
Fish and Wildlife Service and take appropriate action to prevent loss or
damage to fish and wildlife resources.
5. The Yellowstone River Compact (65 Stat. 663), entered into by the
states of Montana, Wyoming, and North Dakota, provides for the division of
waters of the four major tributaries of the Yellowstone River between
Wyoming and Montana and forbids the diversion of water from the Yellowstone
River Basin without the unanimous consent of Wyoming, Montana, and North
Dakota.
Under Article V of the Compact, the waters of the four tributaries are
divided as follows, based on streamflows at their mouths:
1) Clarks Fork Yellowstone River
to Wyoming 60%
to Montana 40%
2) Bighorn River
to Wyoming 80%
to Montana 20%
46
Under this law, permits from the Corps of Engineers are also required before
any dredge or fill activities may begin in water covered by the Act. (These
are known as Section 404 permits. Nearly all waters of the Yellowstone River.
and its tributaries are covered.)
9. The Clean Air Act, as amended (81 Stat. 485; 42 U.S.C. 1857 et ~.)
provides for the establishment and enforcement of air quality standards by the
Environmental Protection Agency in cooperation with the affected states.
10. The National Environmental Policy Act of 1g7o (NEPA) (83 Stat. 852;
42 U.S.C. 4321 et ~.) requires that where federal funds or property are
involved, the development of natural resources must be preceded by an analysis
and weighing of the environmental impacts of such development.
11. The Wilderness Act of September 3, 1g64 (78 Stat. 890; 16 U.S.C. 1131,
et ~.),prohibits permanent roads and improvements (except as authorized
by the President) within any wilderness area designated by the Act or by
subsequent legislation.
12. The Historic Sites, Buildings and Antiquities Act of 1g35, as
supplemented and amended (74 Stat. 220; 16 U.S.C. 469 et ~.). The presence
of historical or archaeological data within the site of any federal or
federally licensed or assisted activity may require that the activity be pre-
ceded by a survey by the Secretary of the Interior to determine if such data
shall be recovered and preserved.
13. The Endangered Species Act of 1973 (87 Stat. 884; 16 U.S.C. 1531
et ~-)requires that federal agencies take such action necessary to ensure
that actions authorized, funded, or carr,ied out by them do not jeopardize
the continued existence of endangered species or result in the destruction or
modification of the habitat of such species.
14. The Surface Mining Control and Reclamation Act of 1g77 (gl Stat. 445;
18 U.S.C. § 1114; 30 U.S. C. §§ 1201 et ill·) imposes limitations on the
surface mining of coal and other minerals, not only with respect to surface
reclamation and surface owner's consent, but also with respect to designating
areas which cannot be surface mined.
MONTANA LEGAL CONSTRAINTS
1. The Montana Water Use Act of 1973 (Sec. 89-865 et seq., R.C.M. 1947)
provides that after July l, 1973, a right to the use of Montana waters may
be initiated only through application for a permit from the Montana Department
of Natural Resources and Conservation. The Act stipulates that the use of
water for slurry of coal outside Montana's borders is not a beneficial use
(Sec. 89-867(2), R.C.M. 1947). Although it has never been tested in court,
this law is probably superceded in the Yellowstone River Basin by the
Yellowstone River Compact, which specifically authorizes the diversion of
water in one signatory state for use in another.
48
1
2. Moratorium on Yellowstone River A ro riations. Effective March 12,
1974, a t ree-year moratorium was estab 1shed on Yellowstone River Basin
appropriations exceeding 20 cfs or for reservoir impoundments exceeding
14,000 acre-feet (Sees. 89-8-103 through 89-8-105, R.C.M. 1947). The 1977
Montana Legislature extended the moratorium through December 31, 1977. In
December 1977, the Montana Supreme Court extended the Moratorium.
3. Reservations of Water. The Montana Water Use Act of 1973, in Sec.
89-890, R.C.M. 1947, provides for the reservation of water by agencies of the
state of Montana and of the.federal government. These reservations can
include instream uses and must be approved by the ~1ontana B.oard of Natural
Resources and Conservation. Over 30 applications were received on the
. Yellowstone River Basin alone; these applications are currently scheduled to
be acted upon by the Board before the expiration of the Yellowstone Moratorium.
Depending upon the decision of the Board, water reservations under the
provision could be a constraint to future water use in the Yellowstone River
Basin in Montana. For example, the Montana Department of Fish and Game has
applied for an instream flow of approximately 8.2 mmaf at Sidney. If that
application were granted by the Board, other future uses of water would be
1 imited.
4. The Montana Environmental Policy Act of 1971 (Sec. 69-6501 et ~··
R.C.M. 1g47) provides, similarly to NEPA, that state agency actions which
may significantly affect the quality of the human environment shall be
preceded by an analysis and weighing of the environmental impact of such
actions.
5. The Montana Major Facility Siting Act (Sec. 70-801 et ~-, R.C.M.
1947) requires that a certificate of environmental compatability and public
need be issued by the Board of Natural Resources and Conservation as a
condition to the construction of facilities for the generation or transporta-
tion of electricity, gas, or liquid hydro-carbon products; for the transport
of water, when such transport is associated with a major facility; for the
enriching of uranium; for the conversion of coal; for the use of geothermal
resources; or for in situ gasification of coal.
6. The Montana Floodway Management Act of 1971 (Sec. 89-3501 et ~-·
R.C.M. 1947) provides for the designation of flood plains and floodways by
.the Board of Natural Resources and Conservation and the subsequent regulation
from obstructions of such areas by local governing bodies. Several areas in
the Yellowstone Basin have been so designated.
7. The Montana Water Pollution Act (Sec. 69-4801 et ~·· R.C.M. 1947)
forbids the pollution of state waters and requires a permit from the Montana
Department of Health and Environmental Sciences for any activity which is
likely to cause such pollution.
8. The Montana Air Pollution Act (Sec. 69-3906 et ~·· R.C.M. 1947)
authorizes the MOntana Board of Health and Environmental Sciences to establish
and enforce air quality standards and to require permits for any facility,
that may contribute to air pollution.
49
el.ectric generating plants and concluded that the value of this water fell.
within a range of $100 to $200 per acre-foot.
The Yellowstone Impact Study's evaluation of the impacts of the withdrawals
resulting from the three projected levels of development summarized in appendix
A was performed qualitatively. These impacts are considered to be the costs of
additional withdra1·1als and can be compared to the benefits of additional with-
drawals for agriculture, summarized below.
The projected derletions would have no significant impacts on furbearer~
and birds because channel morphology would be unlikely to change. The im-
pacts of lowered flows on the Tongue River fisheries are described as "min-
imal" for the low level of development, "high" for the intermediate, and
"severe" for the high. Lowered flows would adversely affect boating, rock-
hounding, fishing, waterskiing, and swimming, while improving access for all
recreational activities. Lowered flows would not have a significant impact
on the pumping costs for the municipal water supply systems of Billings,
Miles City, and Glendive. Lowered streamflows would pose a water-access-
ability problem only for those gravity diversions which cannot control water
levels in the river at the headgates. Irrigation pumping costs could in-
crease up to 11 percent during low-flow months if the depletions projected
in the high level of development occurred.
For all three levels of development, water quality degradation would
be minor in the Upper Yellowstone and Bighorn subbasins. Significant de-
terioration would occur in the Tongue and Powder subbasins with all levels
of development. The Mid-Yellowstone and the Lower Yellowstone subbasins
would suffer moderate or greater increases in salinity if the projected de-
pletions occurred.
The benefits of additional withdrawals for agriculture were estimated
with a linear programming model which maximized agricultural profits sub-
ject to constraints on water availability and irrigated land. The objective
function maximized profit per acre for different crops and cropping strat-
egies in each of seven subbasins. Objective function values are the differ-
ence between total revenue and variable costs, meaning that the model est-
imates only the short-term costs of decreased water availability. The
acreage constraints restricted crop acreages to total 1975 acres or project-
ed acreages for the year 2000 in each subbasin, and cropping patterns were
allowed to vary no more than 10 percent from historical cropping patterns.
The water availability constraints allowed only the difference between mod-
eled inflows and the instream constraint to be developed for irrigation.
The value of water for irrigation was estimated by the decrease in agricul-
tural profits resulting from a decrease in water availability.
The results obtained from the LP model were that the maximum instream-
flow constraint considered would decrease agricultural profits 1n the basin
in the year 2000 from $145,744,493 (the amount of agricultural profits if
no instream constraint is imposed) to $144,210,838--a net decrease of $1,162,954.
Irrigators in the basin would be willing to pay $116,295 to secure a one-
percent reduction in this instream constraint if the instream constraint
imposed were between 90 and 100 percent of the maximum considered. For per-
centages of the instream constraint between 0 and 90 percent, the reduction
in agricultural profits would be less, and irrigators would be willing to
pay much smaller amounts to secure the one-percent reduction.
52
Because the instream constraints would reduce the number of irrigated
acres only in August and September and would reduce only the water avai-lable
for irrigating pasture, the marginal value to irrigators of the increments
of flow used as instream constraints is low. The instream constraints used
did not seriously restrict irrigated agriculture in the Yellowstone Basin.
LEGAL CONSTRAINTS ON WATER USE
Constitutional mandates, legal decisions, and laws--both federal and
state--constrain the municipal, industrial, and agricultural use of water
in the Yellowstone River Basin by requiring water uses to conform to agreed-
upon goals and priorities established in the public interest through due
process of law. The summary of federal and state laws and doctrines in
this report is not exhaustive; Report No. 4 in this series, The Adequacy of
Montana's Regulatory Framework for·water Quality Control, explores the Mont-
ana legal framework for water use in greater detail.
FEDERAL CONSTRAINTS
Perhaps the biggest constraint on water use in the Yellowstone River
Basin is an unknown--namely, the scope of reserved water rights stemming
from the U.S. Supreme Court's decision, Winters v. United States (1908).
The Winters Doctrine, as extracted from the ruling and modified by subse-
quent decisions, states that federal or Indian land reserves withdrawn from
the public domain (such as most federal forest land) hold a reserved right
to the use of water within, crossing, abutting, ·or beneath the reservation.
Whether or not exercised, the reserved right has continuous priority for
an amount of water needed to serve the purposes for 1·•hich the land reser-
vation was established. Because the size of these reserved water rights
is uncertain (they are potentially great), many states (including Montana)
cannot gauge the amount of water remaining for allocation under state law,
particularly near federally reserved land or Indian reservations.
Litigation in federal court to adjudicate federal and Indian reserved
water rights under the Winters Doctrine in the Tongue and Bighorn river
basins will be years in deciding the ultimate scope of the reserved rights.
Success of this litigation, brought by ~he U.S. Government and by the Crow
and Cheyenne Tribes, would affect many existing Montana water uses regardless
of the extent of water rights under the law.
Other federal constraints on the use of water in Montana include the
general environmental-preservation policy of the United States expressed
in the National Environmental Policy Act and other acts regulating a variety
of activities directly or indirectly affecting the use and diversion of water.
These include constructing facilities for po~1er generation, dams and divers ions,
and navigation facilities, or applying for permits for activities that affect
water and air quality, the integrity of wilderness, the preservation of arch-
eological and historical sites, and endangered species. Of particular in-
terest is the new federal power to regulate strip mining and subsequent land
reclamation under the 1977 Surface Mining Control and Reclamation Act.
A federally supervised agreement among the states of Montana, Wyoming,
53
55
PROJECTIONS OF FUTURE USE
FIGURES
A-1. The tline Planning Subbasins of the Yellowstone Basin.
A-1.
A-2.
A-3.
A-4.
A-5.
A-6.
TABLES
Increased Water Requirements for Coal Development
in the Yellowstone Basin in 2000 ..
The Increase in Water Depletion for Energy
by the Year 2000 by Subbasin ....... .
Feasibly Irrigable Acreage by County and Subbasin
by 2000, High Level of Development ..... .
The Increase in Water Depletion for Irrigated Agriculture
by 2000 by Subbasin . . .
The Increase in Water Depletion for Municipal Use by 2000
The Increase in Water Depletion for Consumptive Use
by 2000 by Subbasin . .
57
. .
59
59
60
61
62
62
63
In order to adequately and uniformly assess the potential effects of water
withdrawals on the many aspects of the present study, projections of specific
levels of future withdrawals were necessary. The methodology by which these
projections were done is explained in Report No. 1 in this series, in which
also the three projected levels of development, low, intermediate, and high, are
explained in more detail. Summarized belo11, these three future levels of
development were formulated for energy, irrigation, and municipal water use
for each of the nine subbasins identified in figure A-1.
ENERGY WATER USE
In 1975, over 22 million tons of coal (19 million metric tons) were mined
in the state, up from 14 million (13 million metric) in 1974, 11 million (10
million metric) in 1973, and 1 million ( .9 million metric) in 1969. By 1980,
even if no new contracts are entered, Montana's annual coal production will
exceed 40 million tons (36 million metric tons). Coal reserves, estimated at
over 50 billion economically strippable tons (45 billion metric tons) (Montana
Energy Advisory Council 1976), pose no serious constraint to the levels of
development projected, which range from 186.7 (170.3 metric) to 462.8 (419.9
metric) million tons stripped in the basin annually by the year 2000.
Table A-1 shows the amount of coal mined, total conversion production,
and associated consumption for six coal development activities expected to take
place in the basin by the year 2000. Table A-2 shows water consumption by sub-
basin for those six activities. Only the Bighorn, Mid-Yellowstone, Tongue, Powder,
and Lower Yellowstone subbasins would experience coal mining or associated
development in these projections.
IRRIGATION WATER USE
Lands in the basin which are now ei.ther fully or partially irrigated total
about 263,000 ha (650,000 acres) and consume annually about 1,850 hm3 (.1,5 mmaf)
of water. Irrigated agriculture in the Yellowstone Basin has been increasing
since 1971 (Montana DNRC 1975). Much of this expansion can be attributed to
the introduction of sprinkler irrigation systems.
After evaluating Yellowstone Basin land suitability for irrigation, con-
sidering soils, economic viability, and water availability (only the Yellowstone
River and its four main tributaries, Clarks Fork, Bighorn, Tongue, and Powder,
were considered as water sources), this study concluded that 95,900 ha (237,000
acres) in the basin are financially feasible for irrigation. These acres are
identified by county and subbasin in table A-3; table A-4 presents projections
of water depletion.
Three levels of development were projected·. The lowest includes one-third,
the intermediate, two-thirds, and the highest, all of the feasibly irrigable
acreage.
58
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
! .. ussE~s .. ~n
! .... r .. l~&"D ! GO~O[" \
--j~3'"'t', -;r·.;:-::_---~--~ ._ ~ ~ ;_j
-1g
' "' \ =
·~.,~ ... ,)
\ " & Ill • • [ ~ D
j
WYOMl:>IC
Figure A-1. The nine planning subbasins of the Yellowstone basin.
TABLE A-1.
Level of
Developrr.ent
low
Intennediate
High
lOW
lnten::ediate
High
tow
Intennediate
High
COflVERSIONS:
Increased water requirements for coal development in the Yellowstone
Basin in 2000.
Electric
Generation
8.0
24.0
32.0
2000 mw
6000 mw
8000 mw
30,000
90.000
120.000
I
Coal Development Activity
Gasifi-I
cation Sync rude I .
COAL t41N£D (mt/y)
7. 6 0.0
7.6 o.o
22.8 36.0
COI-lVERS [Q,'l PRODUCT ION
250 rncfd 0 b/d
250 rrrncfd 0 b/d
Ferti-1
l i zer
0.0
0.0
3.5
0 t/d
0 t/d
750 flTilCfd _200 .ooo b/d 2300 t/d
WATER cO:ISUMPTirW (af/y)
9.000 0 0
9,000 0 0
27 .ooo 58,000 13,000
1 r:r.lt/y (short) " .907 rrmt/y (metric)
I af/y = .Q0123 hm3/y
Export I
171.1
293.2
368.5
a
31,910
80.210
Strip .
:-Hninq
9.350
16,250
22,980
TO till
185.7
324.8
46~ .a
48,350
147.160
321.190
arlo water consumption is shown for e,port under the low level of develop~:~ent because, for that
development level, ft is assumed that all export is by rail, rather than by slurry pipeline.
59
TABLE A-2. The increase in water depletion for energy by the year 2000
by subbasin.
INCREASE Ill DEPLETION (af/y)
uec. Gasifi-Syn-Ferti-Strip
Subbasin Generation cation crude lizer Export Mining Total
LOW LEVEL OF DEVELOPMENT
Bighorn 0 0 0 0 0 860 860
~lid-Yellowstone 22,500 9,000 0 0 0 3,680 35 '180
Tongue 7,500 0 0 0 0 3,g5o 11 ,450
Powder 0 0 0 0 0 860 860
Lower Yellowstone 0 0 0 0 0 0 0
Total 30,000 9,000 9,350 48,350
INTERt~EDIATE LEVEL OF DEVELOPMENT
Bighorn 0 0 0 0 4,420 1 ,470 5,890
Mid-Yellowstone 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 OF 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' 170 118,030
Powder 15,000 0 0 0 5,550 2,050 22.600
Lower Yellowstone 0 0 0 13,000 0 0 13 .ooo
Total 120,000 27,000 58,000 13,000 80,210 22,980 321,191)
CONVERSIONS: 1 af/y • .00123 hm 3ty
NOTE: The four subbasins not sho•m (Upper Yellowstone, Billings Area, Clarks Fork
Yellowstone, Kinsey Area) are not expected to experience water depletion associated
with coal development.
60
TABLE A-3. Feasibly irrigable acreage by county and subbasin by 2000, high level
of development.
County
Park
Sweet Gras
Stillwater
CarbOn
Yellow-
stone
Big Horn
Tre<~sure
Rosebud
Powder
River
Custer
Prairie
Dawson
Rtcl'lland
Wibaux
BASI'l
TOTALS
Upper ClarkS Billlngs Big Hid Tongue Kinsey Powder lower
ellowstone Fork Area Hom Yellowstone River An"'a River Yellowstone
21 ,664
10 ,2n4
6.209
38.076
2.160
2.160
19.412
13,037
9.591
11,408
4,230
19,412 13,037 25.229
2 .ISS
9.727
10.035
21 • 94 7
(6.853
3 .092 26 .•\33
1,644 1 ,914 8.231
18.355
10,421
633
4.736 75.205 37,670
COUVERSIOOS: 1 acre • .<105 ho!l
:lOT£: The number of irrigable acres for the low and intennedi.ne develoo::-.@nt levels are one-third
and biO-thlrds, resoectively. of the nur.:bers given here. This table should not be considered an e.o:haustlve
listing of all feasibly irriqa~le acrea~e ln the Yellowstone Basin; it includes only the acreaqe identified
County
Totals
21,664
10,20·~
fi.20?
2,160
19,412
15.222
9,591
21 ,135
46,853
. 43 ,795
11 .789
18,355
10,421
633
237,472
as feasibly irriCJable accordinq to the geoqraphic and econonic constraints e.ocplained elsewhere in this report.
MUNICIPAL WATER USE
The basin's projected population increase and associated municipal water
use depletion for each level of development are shown in table A-5. Even the
13 hm3;y (10,620 af/y) depletion increase by 2000 shown for the highest develop-
ment level is not significant compared to the projected depletion increases for
irrigation or coal development. Nor is any problem anticipated in the availability
of water to satisfy this increase in municipal use.
\~ATER AVAILABILITY FOR CONSUIIPTIVE USE
The average annua~ yield of the Yellowstone River Basin at Sidney, t1ontana,
at the 1970 level of development, is lO,B50 hm3 (8.8 million af). As shown
in table A-6, the additional annual depletions required for the high projected
level of development total about 999 hm3 (812,000 acre-feet). Comparison of
these two numbers might lead to the conclusion that there is ample water for
such development, and more. That conclusion would be erroneous, however,
because of the extreme variation of Yellowston-e Basin streamflows from year
to year, from month to month, and from pla-ce to place. At certain places and
at certain times the water supply will be adequate in the fores-eeable future.
But in some of the tributaries and during low-flow times of many years, water
availability problems, even under the low level of development, will be very real
and sometimes very serious.
61
TABLE A-4. The increase in water depletion for irrigated agriculture by 2000
by subbasin.
Subbasin
Upper Yellowstone
Clarks Fork.
Bi 11 i ngs Area
Bighorn
Mid-Yellowstone
Tongue
Kinsey Area
Powder
Lower Yellowstone
TOTAL
Acreage
Increase
HIGH LEVEL OF DEVELOPMENT
38,080
2,160
19,410
13,040
25,230
21 '950
4,740
75,200
37,670
237,480
Increase in
Depletion (af/y)
76,160
4,320
38,820
26,080
50,460
43,900
9,480
150,400
75,340
474,960
INTERMEDIATE LEVEL OF DEVELOP~1ENT
BASIN TOTAL 1 158,320 316,640
LOW LEVEL OF DEVELOPMENT
BASIN TOTAL 79' 160 158,320
CONVERSIONS: 1 acre = .405 ha
1 af/y = .00123 hm3fy
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.'
TABLE A-5. The increase in water depletion for municipal use by 2000.
Population Increase in
Level of Development Increase Depletion (af/y)
Low 56 ,858 5,880
Intennediate 62,940 6,g6o
High 94,150 10,620
CONVERSIONS: 1 af/y = .00123 hm3/y
62
TABLE A-6. The increase in water depletion for consumptive use by 2000
by subbasin.
Increase in Depletion (af/y)
Subbasin Irrigation Energy Municipal Total
LOW LEVEL OF DEVELOPMENT
Upper Yellowstone 25,380 0 0 25,380
Clarks Fork 1 ,440 0 0 1 ,440
Billings Area 12.940 0 3,480 16,420
Bighorn 8,700 860 negligible 9,560
~lid-Yellowstone 16,820 35.180 1,680 53,680
Tongue 14,640 11 • 450 negligible 26,090
Kinsey Area 3.160 0 0 3,160
Powder 50,140 860 360 51 ,360
Lower Yellowstone 25,120 0 360 25,480
TOTAL 158,340 48,350 5,880 212,570
INTERMEDIATE LEVEL OF DEVELOPIIENT
Upper Yellowstone 50,780 0 0 50,780
Clarks Fork 2,880 0 0 2,880
Billings Area 25,880 0 3,540 29,420
Bighorn 17,380 5,890 300 23,570
Mid-Yellowstone 33,640 75,490 1 ,360 110,990
Tongue 29.260 46,900 300 76,460
Kinsey Area 6,320 0 0 6,320
Powder 100,280 18,380 600. 119,760
Lower Yellowstone 50,200 0 360 50,560
TOTAL 316,620 147,160 6,960 470,740
HIGH LEVEL OF DEVELOPMEUT
Upper Yellowstone 76. 160 0 0 76.160
Clarks Fork 4,320 0 0 4 ,320
Billings Area 38,820 0 3,900 42,720
Bighorn 26,080 28.150 480 54,710
Mid-Yellowstone 50,460 139,410 3,040 193,710
Tongue 43.900 118,030 780 162,710
Kinsey Area g,480 0 0 9,480
Powder 150,400 22,600 1.140 174,140
Lower Yellowstone 75,340 13,000 480 88,82C
TOTAL 474,960 321,1QO 10,620 806.770
CONVERSIONS: 1 af/y = .00123 hm3/y
63
LINEAR PROGRAMMING MODEL
Introduction. . . . . . . .
Objective Function. . . . .
Inflow Constraints .....
Cropping and Acreage Constraints.
lnstream Flow Constraints ..
Summary of Model Formulation ...
Output. . . . . . . .... · . .
FIGURES
B-1 Agricultural Optimization Model. ...
TABLES
B-1 Irrigation Strategies Used in the LP Model .... .
B-2 LP Model: Crop/Irrigation Strategies ....... .
B-3 LP Model: Crop Yields, Variable Costs, and Returns.
B-4 LP Model: Irrigation Costs. . . . . . .. .
B-5 LP Model: Objective Function Values ...... .
B-6 Time Periods Used in the LP r~odel ........ .
B-7 LP Model: Historical Outflows ......... .
B-8 LP Model: Net Inflows From Miscellaneous Sources.
B-9 LP Model: Crop Water Requirements .....
B-10 LP Model: Cropping and Acreage Constraints.
B-ll LP Model: Jnstream Flow Constraints ...... .
65
66
68
72
74
76
76
76
67
69
69
70
71
71
72
73
73
74
75
77
INTRODUCTION
The linear programming model used for this report was developed by the
Montana Department of Natural Resources and Conservation (1977) to estimate the
losses that instream flow reservations would impose on irrigated agriculture
in the Yellowstone Basin. It is a more elaborate version of a model developed
by Snyder (1976) for the same purpose. The model maximizes agricultural
profits in the basin subject to constraints on the availability of water and
land and existing cropping patterns. Agricultural profits are the sum of the
per-acre profits for each crop in each subbasin multiplied by the number of
acres of each crop. Water constraints are inflows minus instream constraints;
the land constraints restrict irrigation to existing or projected future
acreage and cropping patterns. The model includes seven subbasins within the
Yellowstone Basin (shown in figure·3 on page 17):
UY
BI
BH
MY
Upper Yellowstone
Billings
Big Horn
Mid Yellowstone
TO
PO
LV
Tongue River
Powder River
Lower Yellowstone
The boundaries of these seven subbasins correspond to the boundaries of the
nine subbasins used in the Yellowstone Impact Study development projections
(figure A-1 of appendix A on page 59), with the exceptions that the Clarks
Fork Yellowstone subbasin is included here in the Upper Yellowstone subbasin
and the Kinsey in the Lower Yellowstone.
Because data on cropping patterns is available from the Montana
Department of Agriculture (lg76) by county rather than by drainage subbasin,
it was necessary to aggregate county data in order to arrive at subbasin
cropping figures. The following groupings were used:
Upper Yellowstone Subbasin: Sweet Grass, Park, Stillwater, and Carbon
counties.
Billings Subbasin: Yellowstone County.
Bighorn Subbasin: Big llorn County.
Mid-Yellowstone Subbasin: Treasure County plus 73 percent of Rosebud
County and 26 percent of Custer County.
Powder Subbasin: 82 percent of Powder River County and 58 percent of
Custer County.
Tongue Subbasin: 18 percent of Powder River County, 27 percent of
Rosebud County, and 16 percent of Custer County.
Lower Yellowstone Subbasin: Prairie, Dawson, and Richland counties.
Figure B-1 is a schematic diagram of the basin as modeled. The model
includes, for each subbasin, an inflow, diversion for crops, minimum flow
constraint, and outflows (which. equal the inflows for the subbasin below.)
66
<>
--+9 ~ Upper
BASIN
Yellow~tone s ba
n
9 DEPLETION
<> INFLOW
~ & FLOW CONSTRAitlT
Billings
Subbasin
n
w
~
T Mid .Q Big ---w ------~.,._~!Yellowstone I-'(J 0-----.~IHorn Subbasin ,,,,,,,, t
R -A
!rongue I __ _,.,~
0 .,.!:!ubbas in
& ___ , __ _,_~ 6
0 .,_ Eubbas in
Po~1der ~
Fiqure B-1. Agricultural optimization model.
67
OBJECTIVE FUNCTION
The model maximizes agricultural profits in the Yellowstone Basin by
maximizing the objective function:
Maximize Z = ~ PijkQijk
where: Z = total profits in the study area
= the profits per acre in the ith subbasin for the jth
crop as grown with the kth irrigation strategy.
Qijk = the number of acres in the ith subbasin used for growing
the jth crop when grown with the kth irrigation strategy.
Per-acre profits are crop revenues minus variable costs. Variable costs
include the costs of seeds, labor, and harvesting and are defined as the costs
that would be avoided if the crop were not planted in the spring. Specifically
excluded are capital costs such as acquisition costs for a sprinkler system.
The crops grown in each subbasin conform to current cropping patterns.
The five crops included in the model are listed with their abbreviations.
AL
SB
cs
BA
PA
Alfalfa
Sugar Beets
Corn Silage
Barley
Pasture
The cropping pattern used is the one reported in Montana Department of
Agriculture 1976, with the exception that the acreage of irrigated pasture
was derived by subtracting the Montana Department of Agriculture 1976 acreage
from DNRC's estimates of total irrigated acreage, under the assumption that
any irrigated land not used for producing crops is used as pasture. The crops
included in the model in several cases are composite crops, and cost and
revenue figures reflect the average value of several related crops. The crop
in the model called corn silage includes all silage crops, including ensiled
hay and beet tops. The crop called barley includes all irrigated grains--
barley, winter wheat, durum wheat, spring wheat, and oats. Alfalfa is con-
sidered to include all hay. The crop labeled sugar beets includes both
sugar beets and dry beans.
Each crop can be irrigated with different strategies.
strategy is defined by the number of consecutive periods a
The irrigation strategies are defined in table B-1.
An irrigation
crop is irrigated.
The irrigation strategies available for each crop differ and were
defined to include only strategies which were economically feasible and/or
biologically pertinent. For example, sugar beets require full-season irrigation
for adequate sugar production; grain crops, on the other hand, are·harvested
in July, thus not requiring late-season irrigation. The growth curve for corn
silage indicated that a single irrigation would produce minimal results. Table
B-2 shows the irrigation strategies used with each crop.
68
TABLE B-1. Irrigation strategies used in the LP model.
Irrigation Strategy
0
1
2
3
4
TABLE B-2. LP Model: Crop /I rri gat ion
Irrigation
Strategy AL
0 X
1 X
2 X
3 X
4 X
Time of Irrigation
crop is grown without irrigation
crop is irrigated only in the spring
crop is irrigated in the spring and July
crop is irrigated in the spring, July,
and August
crop is irrigated in all periods
Strategies
Cron
SB cs BA PA
X X X
X X
X X X
X X
X X X
Objective function values were calculated by preparing partial farm
budgets for all the irrigation strategies identified for each crop in each
subbasin. Data for the full-irrigation strategies were taken from Report
No. 1 in this series, except that a pasture alternative was included. The
"pasture alternative was treated the same as the alfalfa hay alternative
except that yields were reduced to 14.5 tons/acre and the selling price was
lowered to $36 per ton to account for the lower protein content of grasses.
Only the variable costs and returns listed in Report No. 1 were included in
the model.
Separate farm budgets were prepared for the dryland alternatives
from data provided by the U.S. Bureau of Reclamation which was compatible
with the budgets for the irrigated alternatives. Dryland yields were
obtained from estimates published in soil survey reports (USDA 1967, 1971,
1972, 1976).
Variable farm costs and returns for the partial-irrigation strategies
were assumed to vary directly with expected yields. Thus, yields for the
partial-irrigation strategies were set at intermediate levels based on
growth curves developed by the Montana Agricultural Experiment Station as
quoted in Snyder ( 1976). Tab 1 e B-3 1 is ts the yields, cos"ts and returns for
each crop and irrigation strategy.
Irrigation cost data, which include only the variable costs of pumping
water to the farm and operating a center-pivot sprinkler system, were taken
from Report No. 1 in this series for the average lift and distance reported
for each subbasin. Partial-irrigation costs were assumed to vary directly
69
with crop water requirements as calculated from the Irrigation Guide for
Montana (USDA 1973). Table B-4 lists the irrigation costs used in this study,
and table B-5 combines all the cost and return data and lists the resultant
net profits used in the objective function.
TABLE B-3. LP Model: Crop Yields, Variable Costs, and Returns
Crop
Alfalfa
Sugar Beets
Corn Silage
Barley
Pasture
Irrigation
Strategy
0
1
2
3
4
4
0
2
3
4
0
1
2
0
1
2
3
4
Yield
(tons)
1.5
3.1
4.0
4.3
5.0
21110.5a
9
13.0
19.5
21.0
33/7b
60/l3b
74fl6b
1.3
3.0
3.6
4. 1
4.5
Cost
($)
13
26
34
35
42
127
41
53
89
96
20
36
44
12
28
34
33
42
Return
($)
60
125
161
173
201
830
152
288
329
354
74
134
165
43
99
118
135
148
Net Farm Return
($)
47
99
127
137
159
711
111
170
240
258
54
98
121
31
71
84
97
105
aFirst number equals tons of beets; second number equals tons of ensiled
tops.
bFirst number equals bushels of grain; second number equals tons of straw.
70
TABLE B-4. LP Model: Irrigation Costs ($)
Subbasin
Irrigation
Crop Strategies UY BI BH rw TO PO LV
Alfalfa 0 0 0 0 0 0 0 0
1 6 7 6 7 6 6 7
2 12 14 13 14 12 12 14
3 17 21 18 19 17 17 20
4 19 23 21 22 20 20 23
Sugar Beets 4 17 21 19 20 18 18 20
Corn Silage 0 0 0 0 0 0 0 0
2 6 8 7 8 7 7 8
3 12 14 13 13 12 12 14
4 14 16 14 15 14 14 16
Barley 0 0 0 0 0 0 0 0
1 5 7 6 7 6 6 7
2 10 12 11 11 10 10 12
Pasture 0 0 0 0 0 0 0 0
1 5 6 5 6 5 5 6
2 10 12 11 11 10 10 12
3 14 17 15 16 14 14 16
4 17 20 18 19 17 17 20
TABLE B-5. LP Model: Objective Function Values ($/acre) .
Subbasin
Crop
Strategy UY BI BA MY TO PO LV
ALO 47 47 47 47 47 47 47
All 93 92 93 92 93 93 92
AL2 115 113 114 113 115 115 113
AL3 120 116 119 118 120 120 117
AL4 140 135 138 137 139 139 136
SB4 694 690 692 691 693 693 691
cso 111 111 111 111 111 111 111
CS2 164 162 163 162 163 163 162
CS3 228 226 227 227 228 228 226
CS4 244 242 244 240 244 244 242
BAO 54 54 54 54 54 54 54
BAl 93 91 92 91 92 92 91
BA2 111 109 110 110 111 111 109
PAO 31 31 31 31 31 31 31
PAl 66 65 66 65 66 66 65
PA2 74 72 73 73 74 74 72
PA3 83 80 82 81 83 83 81
PA4 89 86 88 87 89 89 86
71
INFLOW CONSTRAINTS
Each subbasin was modeled by a series of mass conservation equations
whereby water flowing out of the subbasin equaled inflow minus water con-
sumptively used within the subbasin. Water requirements were limited to
consumptive use only, since data were not available to model the timing and
location of return flows. Each subbasin was modeled by the equation:
I-A-0=0 (1)
where: I = inflows from all sources
A = agricultural water use
0 = outflow to next lower subbasin
The model was first calibrated using 1975 water data generated by the
water model described in Report No. 1 of this series and 1975 agricultural
statistics (Montana Department of Agriculture 1976) disaggregated by subbasin.
This initial calibration was designed to correct the model for miscellaneous
inflows from small tributaries and for nonmodeled consumptive uses such as
municipal and industrial use. The miscellaneous inflows were then used to
modify the inflow factor shown in equation 1, above.
Inflows to four of the subbasins (Upper Yellowstone, Bighorn, Tongue
River and Powder River) are exogenous to the model. These inflows from
Wyoming were modified by the miscellaneous flows and used as a right-hand-
side (RHS) constraint in the model. Inflows to the remaining three subbasins
were based on the outflows of the next upstream basin(s) as modified by
miscellaneous flows.
The model was run with two levels of inflows. Fiftieth-percentile inflows
are the inflows that are equaled or exceeded 50 percent of the years. Ninetieth-
percentile inflows are the inflows that are equaled or exceeded 90 percent of
the years.
Flows were measured in acre-feet per time period. Five time periods are
used in the model, as shown in table B-6. The time periods were primarily
based on irrigation requirements, but, since streamflow data were available
only on a monthly basis, some adjustments were made.
TABLE B-6. Time periods used in the LP Model
Time Period
Winter
Spring
July
August
September
Interva 1
Oct. 1-April 30
May 1-June 30
July 1-July 31
August 1-August 31
September 1-September 30
72
Abbreviation
w
M
J
A s
Miscellaneous flows ~1ere assumed to vary proportionately with the mainstem
flows. Therefore, miscellaneous inflows for the 90th-percentile runs were
calculated by multiplying the ratio of 90th-percentile flows to 50th-percentile
flows by the estimated 50th-percentile runoff. In other words, it is assumed
that if, for example, 90th-percentile flows in the mainstem are 40·percent of
50th-percentile flows, then runoff occurring in a 90th-percentile year will be
40 percent of runoff occurring in a 50th-percentile year. Table B-7 shows
historical outflows and table B-8 shows the estimated miscellaneous inflows.
TABLE B-7. LP Model: Historical Outflows (acre-feet)
Time Period I Subbasin
UY Bl BH MY TO PO LY
50th-Percentile Flows
Winter 1,353,162 1,427,092 1,223,121 2,799,926 119,410 129,974 3,141,526 Spring 2,385,198 2,373,054 745,296 3,313,794 125,250 164,107 3,460,945 July 899,400 906,166 312,406 1,240,724 25 ,204 27 ,601 1 ,244,322 August 244,700 247,691 172,343 428,158 11,541 4,164 431.778
90th-Percentile Flows
Winter 1,022,900 1,036,390 806,944 1 ,946,339 50,963 52,055 2,067,846 Spring 1,553,700 1,535,328 268,713 1,803,924 26,043 37,011 1 ,786,826 July 475,300 481,261 58,461 547,511 3,135 2,889 532,541 August 218,800 211,401 78.132 275,029 1 • 107 861 237,778 September 173,800 172,160 98,694 252,952 ], 190 535 218.388
TABLE B-8. LP Model: Net Inflows from Miscellaneous Sources (acre-feet)
Time Period I Subbasin
UY BI BH MY TO PO LY
50th-Percentile Flows
Winter 1 • 353.162 73,930 1,223,121 129,713 119,410 129,297 92,216
Spring 2,485,568 25,679 771 ,935 226,083 174 ,040 198,218 -103,823a
July 1,014,330 52,786 344,027 57,827 39,178 64,267 904°
August 411,621 33,393 166,181 18,455 19,362 33,402 5,545
September 283,715 20,021 182,419 21 ,827 15,184 17,559 5,999
90th-Percentile Flows
Winter 1,022,900 53,690 806,944 104.071 50,963 52,055 60,699
Spring 1,619,080 16,614 278,318 123,072 36,188 44,704 -201 ,097•
July 536,036 28,034 64,378 25,518 4,873 6,727 -2 ,112•
August 278,573 21 ,890 90,767 11 ,081 2,767 3,119 2,954
September 201 ,511 13,916 104,464 12,895 1 ,566 2,256 3,034
°For the Lower Yellowstone Subbasin, negative values are shown in the spring and
July because the calibration showed a net depletion, rather than inflow, for those time
periods.
73
CROPPING AND ACREAGE CONSTRAINTS
Table B-9 sho~1s the per-acre water requirements for each crop, time period,
and subbasin used in the model. These figures, multiplied by the number of
acres of each crop in a particular subbasin (table B-10), yield the agricultural
water use figure {A) in equation 1 on page 72.
TABLE B-9. LP Model: Crop Water Requirements (acre-feet/acre)
Subbasin
Crop Section UY BI BH MY TO PO LV
AL M .45 .49 .49 . 57 .53 .53 . 57
J .50 . 52 .52 . 57 .55 .55 . 57
A .41 .43 .43 .47 .45 .45 .47 s . 17 . 18 . 18 .24 .21 .21 .24
SB M .20 . 21 .21 .25 .24 .24 .25
J .49 .52 .52 .55 . 54 .54 .55
A .49 . 52 .52 . 56 .54 . 54 .56 s . 21 .23 .23 .30 .27 .27 .30
cs M .09 . 12 . 12 . 15 . 14 . 14 . 15
J .40 .43 .43 .48 .46 .46 .48
A . 41 .43 .43 .47 .45 .45 .47 s . 12 . 14 . 14 . 17 . 16 . 16 . 17
BA M .43 .46 .46 .55 . 51 . 51 .55
J . 51 . 52 . 52 . 53 . 53 . 53 .53
PA M .39 .41 . 41 .48 .44 .44 .44
J . 41 .42 .42 .46 .44 .44 .46
A .34 .36 .36 .40 .33 .38 .40 s .20 .21 . 21 .26 .24 . 24 .26
Table B-10 shows the acreage constraints used in the model during calibra-
tion runs. The actual acreages in each crop in 1975 as reported by the Montana
Department of Agriculture (1976) were used as constraints when the model was
calibrated, with the exception of irrigated pasture, as explained on page 68.
In subsequent runs the same cropping pattern was used, but the constraints
allowed the acreage in any crop to increase or decrease up to 10 percent of
the historical pattern. These maximum and minimum constraints for the runs
corresponding to estimated acreage in 1975 and 2000 are shown in table B-10.
The acreages given in table B-10 for the year 2000 are based on the inter-
mediate level of development discussed in appendix A.
74
TABLE 8·10. LP Model: Cropping and Acreage Constraints
Calibration Run and 1975 Acreage 2000 Acreage
Percentage of
Subbasin Acres in the Nuntler of Ma,.;imum Minimum Total Maximum Miniri\Im
and Crop Subbasin Acres Acres a Acres a Acres Acres a Acres a
UYSB 4 8,750 9,614 11 ,679
UYBA 7 17,400 15,600 16 ,722
UYAL 69 163,500 179,850 201,461
UYCS 2 5,100 5.610 5,839
UYPA 18 43,860 39,474 43,000
TOTAL 100 238.610 265,430
BlSB 11 10,620 11,682 13,654
BlBA 14 14,400 12,960 14,218
BlAL 15 14,600 16,060 18,619
BICS 10 10,000 11 ,000 12,412
BIPA 50 50,280 45,252 50.778
TOTAL 100 99,900 112,840
BHSB 3 2,130 2,343 2,419
BHBA 14 9,300 8,370 9.235
BHAL 50 32,600 34,860 40,310
BHCS 13 8,600 9,460 10,773 10,480
BHPA 19 11 ,970 12,533
TOTAL 100 64,600 73,290
MYSB 9 6,089 6,676 8,873
MYBA 18 12,410 11 ,169 14,520
HYAL 26 18,047 19,852 25,634
MYCS 17 11 ,789 12.968 16,761
MYPA 31 21,334 19,201 25,006
TOTAL 100 69,649 89,629
TOSS 3 838 922 1,390
TOBA IS 4,004 3,604 5,686
TOAL 31 8,523 9,375 14,361 roes 13 3,439 3,783 6,022
TOPA 39 10,681 9,613 17,782
TOTAL 100 27,485 42,115
POSB 2 1,473 1.620 2,484
POBA 6 3,586 3,227 6.097
POAL 26 16.230 17.853 32.291
POCS 7 4,572 5.029 8,694
POPA 59 36,905 33.215
TOTAL 100 62.766 112,906 59.953
LYSB 24 22,430 24,673 31,178
LYBA 23 21,700 19,530 24,447
LYAL 20 19.000 20.900 25.932
LYCS 12 10,800 11,880 15,589
LYPA 21 19,070 17,163 22.321
TOTAL 100 93,000 118,100
aonly binding constraints are reported in the columns headed "Maximum Acres" and "Minimum Acres."
75
INSTREAM-FLOW CONSTRAINTS
As a final constraint on the model, several instream flow requirements
were formulated to simulate potential water use by other sectors of the
economy, such as municipalities, industry, or fish and wildlife. Six levels
of instream flow requirements were used, which varied from 0 to 100 percent
of the Montana Fish and Game Commission's 1976 reservation request (see
page 16). Because of differences in the data bases and subbasin boundaries
used by the Montana DNRC and the Fish and Game Commission, modifications
of the Fish and Game Commission's figures were required in some subbasins
to permit feasible modeling. Table B-11 shows the instream constraints used
in the model.
SUMMARY OF MODEL FORMULATION
The objective of the model was to maximize net profits from agricultural
production in the basin subject to constraints on: (1) available land
resources, (2) anticipated cropping patterns, (3) available water, and
(4) alternative uses of the water. The model was first calibrated to
current conditions (1975). The calibration was designed to balance the
water use/availability equation and to account for all water not specifically
defined in the model. The model was then run using all possible combinations
of:
1) Two natural flow patterns (50th-and 90th-percentile flows)
2) Two levels of agricultural development (1975 and 2000)
3) Six levels of instream-flow constraints (0 to 100 percent of the
Montana Fish and Game Commission's 1976 reservation request)
OUTPUT
Output of the LP model contains three types of information: the value
of the objective function, the number of acres of each crop and cropping
strategy, and the shadow price of each constraint. The shadow price of a
constraint is the amount the value of the objective function would increase
if the constraint were relaxed by one unit. The results of the LP model are
described on pages 39 to 42 of this report.
76
TABLE B-11. LP Model: Instream Flow Constraints (acre-feet)
Percentage of Fish and Game Commission Reservation Request
Time
Period 100 90 75 50 25
UPPER YELLOWSTONE
Winter 854,477 754,029 640,857 427,238 213,619
Spring 1,291,239 1 • 162.115 968,429 645,619 322,809
July 533,951 480,566 400,463 266,976 133,488
August 259,834 233,851 194,876 129.917 64,959
September 178,512 160,660 133,884 89.256 44,628
BILLINGS
Winter 1 ,286,875 1,158,188 965,156 643,438 321,719
Spring 1,661,949 1,495,754 1,246,462 830,975 415,487
July 577.784 520,005 433,338 2<:8,892 144,446
August 295,140 265,626 221 ,355 147,570 73,785
September 220,165 198,149 165,124 110,083 55,041
BIG HORN
Winter 1,223,121 1,223,121 1,055,785 703,857 351 ,928
Spring · 535,410 481 ,869 401 ,557 267,705 133,852
July 214,164 192,747 160,623 107,082 53.541
August 172,200 154,890 129.150 86,100 43,050
September 154,700 139,230 116,025 77 ,350 35,675
MID-YELLOWSTONE
Winter 2,799,926 2,799,926 2,345,509 1,563,673 781 ,836
Spring 3,045,889 2.741 ,299 2,284,416 1,522,944 761 ,472
July 856,656 770,990 642,492 428,328 214,164
August 430,500 387,450 322,875 215,250 107,625
September 416,500 374,850 312,375 208,250 104,125
TONGUE
Winter 119,410 108,351 90,292 60.195 30,097
Spring 72,580 65,322 54,435 36,290 18.145
July 24,990 22,491 18,742 12,495 6,247
August 9,467 8,520 7.100 4,734 2,367
September 10,054 9,049 7,540 5,027 2,513
POWDER
Winter 844,500 76,005 63,338 42.225 21 ,112
Spring 96.770 87,098 72,577 48,485 24,192
July 12,290 11 ,001 9,218 6,145 3,072
August 2,460 2,214 1 ,845 1 ,230 615
September 2,330 2.142 1. 785 1 ,190 595
LOWER YELLOWSTONE
Winter 3,141,526 2,245,954 2,371,628 1 ,581 ,086 790,543
Spring 3,269,052 2. 931 ,046 2,445,039 1 ,630,076 815,015
July 937,500 843,750 703,125 463.750 234,375
August 430,500 387,450 322,875 215,250 107,625
September 416,600 374,850 312,375 208,250 104,125
77
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