and Planning San Central

and Planning San Central
Technical Bulletin 184
March 1968
WATER PRIORITY RIGHTS
And Their Effect on
Farm Planning
In the San Carlos
Irrigation and Drainage District
In Central Arizona
Agricultural Experiment Station
College of Agriculture
The University of Arizona
Tucson, Arizona
Table of Contents
Page
Summary and Conclusions
Introduction
Objectives
Data and Approach
Relevant Water Institutions
Gila River Water Commissioner
Bureau of Indian Affairs
Joint Works
Indian Works
District Works
Division of Waters of the Gila River
Historical Background
Gila River Decree
Water Supplied by the Gila River above Coolidge Dam
Natural -Flow Water Available from Below Coolidge Dam
Apportionment of Natural -Flow Water to District Lands
Apportionment of Pumped and Stored Water
District Water Charges
Frequency of Water-Right Fulfillment
Probability of Receiving Natural-Flow Water
Use of Probabilities in Crop Planning
Gain or Loss Per Natural-Flow Water Period
Probable Total Gains and Losses Related to
Use of Natural-Flow Water
Determining the Acreage to Plant
Effect of Supply of Pumped and Stored Water on
Acreage It Will Pay to Plant
Effect of Cotton Allotments on Acreage Planted
Effect of the Level of Costs and Prices on
Acreage It Will Pay to Plant
Risk Considerations in Planning Use of
Natural -Flow Water
3
6
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7
8
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9
9
9
10
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10
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12
14
15
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18
21
23
28
33
33
41
44
44
46
46
List of Tables
1.
Discharge of Gila River at Coolidge Dam in Acre-feet,
1895 -1962
13
Annual Flows of the San Pedro and Gila Rivers, 1930 -61 - 14
Priority Dates, Accumulative Acreages under each
Priority, and Accumulative Diversion Rates for Said
Acreages in the San Carlos Irrigation and Drainage
16
District
4. Pump Water in the San Carlos Irrigation Project
19
and its Relation to Total Water, 1934 -61
5. Annual Apportionment of Pump and Stored Water
19
per Acre to District Lands, 1936 -62
6. San Carlos Irrigation Project Distribution Losses,
20
1936 Through 1961
7. Basic Water Assessment per Acre in the San Carlos
Irrigation and Drainage District for the Period 1948 -62 - 20
2.
3.
-1-
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Frequency of Priority Fulfillment Within the San Carlos
Irrigation and Drainage District for the 27 -Year
Period, 1936 -62
Natural -Flow Periods, by Months, in which Water is
Utilized for Irrigation of Specified Crops
The Probabilities of Receiving, and of Not Receiving,
Natural -Flow Water During the Irrigation Season of
COTTON for Selected Priorities
The Probabilities of Receiving, and of Not Receiving,
Natural -Flow Water During the Irrigation Season of
BARLEY for Selected Priorities
The Probabilities of Receiving, and of Not Receiving,
Natural -Flow Water During the Irrigation Season of
Grain SORGHUM for Selected Priorities
Yields, Prices, Variable Costs, and Returns over Variable
Costs for Upland Cotton, Barley, and Grain Sorghum
with Three Levels of Water Costs
Acres of Cotton, Barley, or Grain Sorghum Irrigated
per 10-day Natural-Flow Water Period for a 240 -acre
Farm, and Associated Gain or Loss with
Three Water -Cost Levels
Probable Total Gain or Loss From Use of
Natural-Flow Water for Various Numbers of
Periods with an 1869 Water Right
Probable Total Gain or Loss From Use of
Natural -Flow Water for Various Numbers of
Periods with an 1891 Water Right
Probable Total Gain or Loss From Use of
Natural-Flow Water for Various Numbers of
Periods with a 1913 Water Priority
Probable Marginal Gain or Loss per Natural-Flow
Water Period with an 1869 Water Right
Probable Marginal Gain or Loss per Natural -Flow
Water Period with an 1891 Water Right
Probable Marginal Gain or Loss per Natural -Flow
Water Period with a 1913 Water Right
Page
22
23
29
30
31
32
33
35
36
37
38
39
40
List of Figures
Lands Having Water Rights Under the
Gila River Decree. The San Carlos Irrigation and
Drainage District is comprised of that part located
below the Coolidge Dam which is outside the Gila
1. Map Showing
River Indian Reservation
Natural -Flow Water Priorities, San Carlos Irrigation
and Drainage District
3. Probable Marginal Gain and Loss per Natural -Flow
Period for Specified Crops, with Water @ $.50 per
Acre-foot, for Three Different Water Rights - - 4. 1891 Water-Right and Natural-Flow Water cr $.50:
Probable Marginal Gain and Loss per Natural-Flow
Water Period for Specified Crops with Different
Levels of Costs and Prices
48
2.
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24
42
47
WATER PRIORITY RIGHTS
And Their Effect on
Farm Planning
In the San Carlos
Irrigation and Drainage District
In Central Arizona
By
Aaron G. Nelson and P. Thomas Cox'
Summary and Conclusions
A farmer operating within the San Carlos Irrigation and Drainage District must currently plan and make decisions without full
knowledge and control of his most limiting factor water. Increasing the knowledge of the environment and reducing the
uncertainties in which the farmer must make planning decisions
have been dual objectives of this study.
The discussion of the institutional environment surrounding
water division and distribution serves to elucidate some of the
exogenous factors which make planning difficult for the farm
manager within the District. It was found that the complexities
of the institutional structure compounds the decision problem in
that the influence of the farmer over his water supply is negligible.
-
'Both authors are now Agricultural Economists with the Economic Research Service,
U.S.D.A. When the major portion of the manuscript was prepared they were Agricultural
Economist and Research Assistant, respectively, Arizona Agricultural Experiment Station, The
University of Arizona. This study was made as a part of Western Regional Project W -54,
"Appraisal of Opportunities for Adjusting Farming to Prospective Markets."
The authors extend their appreciation to William E. Martin, Maurice M. Kelso, Robert
C. Angus, and Robert S. Firch of the Agricultural Economics Department and to Henry Tucker
in Statistics for their assistance in various aspects of the study, particularly those pertaining to
probabilities. Without the cooperation of San Carlos Project and District officials at Coolidge,
Arizona, the study would not have been possible. C. A. Anderson, District Engineer, and C. C.
Nolan, Hydrographer, U.S. Indian Irrigation Service, were very helpful in providing pertinent
data.
-3-
For example, if farmers within the District are dissatisfied with
the division of water of the upper Gila River, they must take a
claim to the United States District Court. On the other hand, if
farmers and ranchers located in the San Pedro Basin, an historic
source of natural -flow water for the District, were to appropriate
water of the San Pedro, the farmers of the District must appeal
to the Area Director, Bureau of Indian Affairs, to file an injunction to stop such appropriation.
Distance alone is an obstacle. The Gila River Water Commissioner is located at Safford, 153 miles from the District Office at
Coolidge. The United States District Court is at Tucson, 67 miles
away. The Area Director, Bureau of Indian Affairs, is located at
Phoenix, 57 miles distance.
The size of the drainage basin is such that control of the entire
water source is next to impossible. The San Pedro River extends
into Mexico and drains an area of 4,500 square miles. The Gila
River above Coolidge Dam extends into New Mexico and drains
an even larger area.
Being split into fragments, it is difficult or impossible to
administer an integrated water-management program. An institutional lag develops which injects an element of rigidity. As a
result, economic pressures must become great before beneficial
adjustments are made.
The supply of water for irrigation comes from three sources:
(1) natural -flow and stored water from above Coolidge Dam which
comes from the Gila River and its tributaries above the dam,
minus the use of natural flow by the upper valleys and transportation losses occurring in the 66 miles of river channel between
Coolidge Dam and Ashurst-Hayden Diversion Dam; (2) natural
flow from below Coolidge Dam obtained from the erratic flows of
the San Pedro and minor tributaries (because of the flashiness
of the river and the heavy silt-laden water, much of this water is
wasted, or inflicts damage, or adds expense to the operation and
maintenance of the distribution system); and, (3) pumped water
from beneath project lands, which is rapidly being depleted partly
because of pumping from wells immediately adjacent to project
lands and canals which draw from a common ground -water basin.
The stored and pumped water is apportioned early in the year
with the apportionment applying equally to all land within the
district. This enables the farmers to plan their planting to utilize
the water from this source. But these farmers know from experience that additional water will become available throughout the
year from natural flow according to the water priority right
adhering to the land.
A procedure was developed whereby the farm manager can
utilize available information to reduce the uncertainty of crop
planning utilizing natural -flow water.
The past history of the availability of natural -flow water was
determined from stream -flow records. The stream -flow data were
-4-
then converted into frequencies of priority -right fulfillment which
were taken to be the probabilities with which water priority rights
would be filled in future periods. Probability formulae were applied
to combine the probability of each period into the probability of
receiving water in at least r or more periods and of not receiving
water in k or more periods for three selected priorities. These
probabilities were then multiplied by the gain or loss associated
with the planting of selected crops which a farmer might plant
to utilize the additional water available from natural flow. The
gain represents returns over variable costs while loss is defined
as pre- harvest variable costs.
The probable marginal gain, compared with the probable
marginal loss per natural -flow water period, provides the proper
decision criterion used in determining the acreage of the various
crops it will pay to plant. The distinction between probable gain
and loss and potential gain and loss should be recognized. Probable
gain and loss figures represent the average of a number of years
of experienced gains or losses. On the other hand, the potential
gain or loss refers to the maximum gain or loss to be realized in
any given year.
It was noted that probable gain will always be less than
potential gain whenever the probability of receiving water in at
least r or more periods is less than one. Similarly, the probable
loss is always less than the potential loss as long as the probability
of k or more periods not being filled is less than one. Therefore,
farmers with limited risk -bearing ability will do well to give full
recognition to the potential loss which may be realized in determining the acreage of crops to plant to utilize natural-flow water.
Sensitivity analysis of the responsiveness of natural-flow
periods utilized to changes in the cost of water and /or the level
of costs and prices of other inputs and product indicated that
relatively large changes in these variables would be required to
cause the farm manager to change the number of natural -flow
periods expected. Of course, some small changes in the acreages
planted are a result of such variable changes. On the other hand,
large changes result from availability of early versus late water
priorities. For example, 4 natural -flow periods would be utilized
with a 1913 priority in the production of cotton, while 9 would
be utilized with an 1869 priority. Since cotton allotments are based
upon historical planted acreages, the different priorities are already
reflected in allotment differences resulting in little adjustment in
cotton acreage but more in the other crops due to the diverted acreage option.
The probabilities developed in this study enable an assessment
of the probable gain or loss associated with the decision to expect
a given number of natural -flow deliveries. The apportionment of
pumped and stored water is quite independent of that decision.
Thus, it is possible to determine the acreage of crops to plant
with given priorities.
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Only three priorities were analyzed due to limited funds available. But those having priorities around or between these three
could approximate their situations according to the examples
presented. In any case, the aggregate acreage of crops to be
planted on the basis of natural-flow water should not be expanded
beyond the acreage which likely can be irrigated given the relationships discussed herein.
It should be recognized that in many decision problems there
are more variables to be considered than one can handle at a
time, whether using only the human mind or in combination with
a complicated computer with an enormous memory. The researcher
uses simplifying assumptions to reduce the problem to manageable
proportions. Such was the case in this presentation.
Introduction
This study pertains to the San Carlos Irrigation and Drainage
District in Pinal County, a part of the maior irrigated agricultural region of central Arizona. The San Carlos Irrigation and
Drainage District and the irrigated lands within the Gila Indian
Reservation comprise the San Carlos Project, a Bureau of Indian
Affairs development. The location of the San Carlos Project is
shown in Figure 1, page 48.
Crop -production decisions in the San Carlos Irrigation and
Drainage District, hereinafter referred to as the District, are complicated by uncertainty regarding the amount of water which will
be available for irrigation. The uncertainty arises in large part
from variations in the flow of the Gila River from season to season,
and from year to year. However, other factors contribute to the
uncertainty, including variations in the amount of water derived
from other sources, a complicated water-right structure, and
various types of organizations with overlapping authority representing diverse interests and different areas which have an interest
in the water available.
Objectives
The primary objectives of the study are to add to the stock
of knowledge about the farmers' environment and uncertainties
in crop production in the District, and to apply analytical methods
which will facilitate coordinating crop acreage and water availability so as to maximize farm income. Incidental to these main
tasks is the presentation of information on the organizations and
institutions involved to provide background and to facilitate understanding the data and material used in the analysis.
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6
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Data and Approach
Data for the study were obtained from a number of sources.
The Gila River Decree of June 29, 1935,2 provides information on
the legal division of waters of the Gila River and its tributaries,
together with definitions and determination of water priority rights
of individual parcels. The annual reports of the Gila Water Commissioners were the source of stream -flow data from which priority
fulfillment was derived. The San Carlos Irrigation and Drainage
District, Coolidge, Arizona, gave full cooperation in providing data
on water delivery, pump-water availability, and related information, including data on sizes of farms in the District and crop
acreage and yields. Input- output data and calendars of operation
used in making the analysis were based upon a study of costs
and returns for field crops in central Arizona.4
The study was initially completed as a Master's thesis in 1963.
Limitations on time and funds at that time permitted computing
probabilities of water right fulfillment for only three priorities.
Publication of the study was delayed in hopes of being able to
compute the probabilities for the remaining water -right priorities.
However, since this has not been feasible, the study is being
published to make available the information it provides.
With the study being made in the early 1960's, data typical of
that period were used in the analysis. While some costs, notably
wage rates, have increased since that time, no attempt was made
to update them since it was felt that changes have not been sufficiently great to significantly affect the conclusions. Commodity
prices are approximately representative of the current situation.
For example, the upland cotton price used in the analysis was
32.6 cents per pound of lint. This compares with an estimated
1967 free -market price of 21 cents which, with the price support
of 11.53 cents, makes a total of 32.5 cents per pound of lint. Thus,
it is felt that the study is generally applicable under current
conditions.
The approach followed in the study is to first present a portrayal of the institutions involved and their relationship to water
available in the District. A description of the water supply and
the division of waters among the various users is then presented
to provide perspective relative to development and use of waters
of the Gila River. In the latter part of the report a method of
converting past fulfillment of water priorities to probabilities of
receiving water in the future is outlined. The probabilities are
'Globe Equity No. 59, in the District Court of the United States In and For the District
of Arizona, The United States of America vs. Gila Valley Irrigation District, Decree Entered
June 29, 1935.
'Gila Water Commission, "Distribution of Waters of the Gila River," an Annual Report
to the U.S. District Court, Tucson, Arizona.
'Nelson, Aaron G., Costs and Returns for Major Field Crops in Central Arizona, Arizona
Agricultural Experiment Station Tech. But. 174, August, 1965.
-7-
then used in conjunction with costs and returns data for selected
crops to develop payoff matricies which serve as guides in determining the acreage of crops to plant to maximize income. The
effects of variations in the amount of stored and pumped water
available and of acreage-allotment programs are considered in
the concluding sections.
Relevant Water Institutions
Gila River Water Commissioner
The Gila River Water Commissioner, appointed by the U. S.
District Court,5 with headquarters at Safford, Arizona, is responsible for the division of waters of the Gila River. The Water Commissioner is responsible only to the District Judge stationed at
Tucson, Arizona, and disagreements or dissatisfaction by the many
parties involved must be carried to the Court for judication.
The Water Commissioner is required to submit an annual
report to the U. S. District Court of stream flows, storage in the
San Carlos Reservoir, and records of the diversions and apportionments made from Gila River waters. Stream -flow data are
furnished to the Water Commissioner by the United States Geological Survey, Water Resources Branch. Records and graphs of
diversions of water on the San Carlos Project are furnished by
the United States Indian Irrigation Service which is also a good
source for records of rainfall, stream flows, use of water by the
various canal companies and projects, stored water released at
Coolidge Dam, and amount of storage in and evaporation from
the San Carlos Reservoir.
Bureau of Indian Affairs
The United States Indian Irrigation Service, Bureau of Indian
Affairs, is responsible for the maintenance and operation of
Coolidge Dam and the San Carlos Reservoir. It is also responsible
for maintenance and operation of the San Carlos Irrigation Project
(not to be confused with the San Carlos Irrigation and Drainage
District).
The Project and facilities are divided into three operating units
the Joint Works which serve both Indian and non -Indian lands,
the Indian Works serving Indian lands only, and the District
Works serving non-Indian lands of the San Carlos Irrigation and
Drainage District. The latter unit, while included in the San
Carlos Irrigation Project, is independently operated by non -Indian
farmers but is dependent upon the Project for its water supply.
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'Globe Equity No. 59, op. cit., XII, p. 112.
-8-
Joint Works
The Joint Works are under the direction of a Project engineer
with offices in Coolidge who is responsible for the delivery of
water to both the Indian Works and the District Works through
operation and maintenance of Coolidge Dam and San Carlos
Reservoir, Ashurst-Hayden Diversion Dam, Picacho Reservoir
which is used primarily for off -stream regulation, portions of the
Florence -Casa Grande Canal, the North Side Canal, the Pima
Lateral and sublaterals which serve both Indian and District
lands; and all Project wells, pumping plants, and drainage facilities.
The Project engineer is responsible for the distribution, measurement, and record keeping of surface flows and pump water
delivered to District and Indian canals and laterals in accordance
with the division and priorities established in the Gila River
Decree. Any disagreements or dissatisfaction by the parties
involved is referred to the Area Director, Bureau of Indian Affairs.
The Joint Works also includes the power system consisting of
a hydroelectric generating station at Coolidge Dam, a dieselpowered generating station at Coolidge, and 400 miles of transmission and distributional lines and appurtenant facilities. Operation and maintenance costs for the power system are paid from
revenues collected from power sales to private customers in the
area. Power for irrigation pumps operated by the Joint Works is
provided at no cost to District and Indian Works as long as
revenues exceed costs. If a deficit occurs, the difference between
revenues and costs is made up by equal contribution by the
Indian and District Works.
Operation and maintenance costs for the irrigation facilities
of the Joint Works are borne equally by the Indian and District
Works.
Indian Works
The Indian Works include Sacaton Diversion Dam and the
canals, laterals, and distributional facilities serving the Indian
lands. They are administered by the Bureau of Indian Affairs
with offices in Coolidge, Arizona.
District Works
The District Works are operated and maintained by the San
Carlos Irrigation and Drainage District, with offices at Coolidge,
Arizona. The irrigation district is administered by a board of
nine directors elected by landowners of the District and managed by a District engineer employed by the board. The District
Works begin at the turnouts from Joint Works canals and laterals
and include all canals and laterals serving land in the District.
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Division of Waters of the Gila River
Lands having rights to waters of the upper Gila River are
shown on the General Map, Figure 1, Page 48. The District is but
one user among many of waters of the Gila River. The major
users of water, in addition to the San Carlos Project, are the
Safford and Duncan Valleys.
Note the scale of miles and the Arizona Key Map; both serve
to illustrate the wide geographic distribution of lands having
water rights which gives some indication of the complexities of
organization, cooperation, and management problems involved
between and among the upper and lower valleys. Note also the
location of Coolidge Dam which is 66 miles upstream from
Ashurst- Hayden Dam
diversion structure utilized to divert
released water from Coolidge Dam and water from the San Pedro
River.
-a
Historical Background
Lands within the Project have been irrigated by the Pima
Indians and their predecessors since prehistoric times and by
non -Indian settlers since the 1860's. The Gila River Indian Reservation, which includes 50,546 acres of Project lands, was established
by Act of Congress, February 28, 1895. The first judicially recognized diversion of water from the Gila River by non-Indians was
made in 1868.
Diversion by non -Indian settlers continued to increase progressively after 1868 until within a few years the normal flow of
the river had been overappropriated. In periods of low flow, there
was insufficient water to irrigate all lands with water rights. In
1905, federal funds were provided for construction of irrigation
works on the Gila Indian Reservation, and in 1916, appropriations
were made for the construction of Ashurst-Hayden Dam to serve
both Indian and non- Indian lands and Sacaton Diversion Dam to
serve Indian lands only.
Primarily to assure the Gila River Indians of a water supply,
Congress authorized the construction of Coolidge Dam by the
Act of June 7, 1924, better known as the San Carlos Project Act.
Later legislation provided for the development of hydroelectric
power at Coolidge Dam.
Gila River Decree
Controversies of long standing over the rights to use waters
the Gila River were settled by the Gila River Decree of June
29, 1935.6 The following quotation from the Buttes Dam and
of
°Globe Equity No. 59, op. cit.
-10-
Reservoir report, referred to above, provides pertinent information relative to the Decree.7
This decree resulted from a Bill of Complaint filed in 1925 by the United
States of America in the U. S. District Court for and on behalf of the Indian
lands which were to constitute a part of the San Carlos Project. The complaint
was filed for the purpose of having the project's water rights definitely
determined and defined. Water users and canal companies, both above and
below the proposed San Carlos Reservoir, were named as parties defendant.
The decree recognized the early irrigation activities of the Indians and
the later irrigation practices of both Indian and non- Indian water users. It
awarded lands on the Gila River Indian Reservation an immemorial right to
the use of water for 35,000 acres and rights for 15,546 additional acres with a
priority as of 1924. In addition, it granted rights to 50,000 acres of non- Indian
lands in the San Carlos Project with various dates of priority. All San Carlos
Project water rights are held in trust by the United States of America for the
benefit of both Indian and non -Indian lands.
The decree also established the rights and priorities for land in the
Safford and Duncan- Virden Valleys and other areas.... Decreed rights under
the Gila River Decree by geographical areas are as follows:
Area
Duncan- Virden Valleys
Safford Valley
San Carlos Indian Reservation
Winkelman Valley
San Carlos Irrigation Project
Non- Indian Unit
Indian Unit
Acres
8,061.35
32,512.40
1,000.00
542.14e
50,000
50,546
100, 546.00
Florence-Casa Grande Project
Gila Crossing District (Indian)
1,544.50
2,992.50
147,198.91
...
... ...
also authorized the United States to store
The Gila River Decree
at all times when waters are available
water in San Carlos Reservoir Dam
above Coolidge Dam for such storage with a priority not later than. June 7,
1924. Lands upstream from the reservoir were "apportioned" an amount of
water equal to the amount stored in the reservoir and to be taken from the
natural flow of the river without regard to downstream priorities. (Subject to
limitation of a seasonal year diversion not to exceed 120,000 acre -feet of
water.) This right to divert "apportioned" water by upstream water users is
in addition to the right to divert on regular priorities.
..
The Decree set forth certain principles as follows:
(a) Total allowable diversions from the river during each irrigation
season are 6 acre-feet per acre.
'Bureau of Reclamation, "Report on Buttes Dam and Reservoir, Middle Gila River Project,
Arizona." A Project Development Report, January, 1961, pp. 28 -31.
81n addition, Kennecott Copper Corporation was determined to have the right to use
16,221 acre -feet annually for industrial, domestic, and municipal purposes.
(b) The rate of diversion from the stream
is one cubic foot per second
for each 80 acres. (May be modified at discretion of Commissioner
under specified conditions.)
(c) Diversions may be made only for beneficial purposes.
(d) The irrigation season begins January 1 and ends on December 31
of each year.
The Decree provided for a Commissioner to be appointed by the court to
carry out its provisions . . . The Commissioner is required to know at all
times what water is available and to distribute it properly.
.
The available stored water, as determined by the U. S. District
Court appointed Water Commissioner at the beginning of each
year, is apportioned between the upper and the lower valleys
according to the provisions of the decree. Additional apportionments may be made throughout the year if more stored water
becomes available.
Of the natural -flow water apportioned to the San Carlos Project
by the Water Commissioner, determined from measured stream
flow, the natural flow is divided between the Indian and District
portions of the Project as stipulated in the Gila Decree as follows:
1. Of the first 300 second- feet-60.6% is allocated to the Indian
lands and 39.4% to the Project lands.
2. Of the next 300 second- feet -51.7% goes to the Indian lands
and 48.3% to the Project lands.
3. Over 600 second -feet of natural flow, the division is 56.1%
to the Indian lands and 43.9% to the Project lands.
Water Supplied by the Gila River
Above Coolidge Dam
Coolidge Dam has adequate capacity to collect and store all
of the flow of the Gila River and its tributaries to that point.
Precipitation on the Gila River watershed above the dam is a
matter of great importance since it is the controlling factor in
the amount of water going into storage in the San Carlos Reser-
voir.
The higher elevations contribute some snow melt which adds
to stream flows throughout March and April. The months of
highest rainfall on the upper Gila watershed are the last half of
July and the entire month of August and the months of least
rainfall are May, June, October, and November. The overall mean
annual precipitation for the upper Gila watershed is nine inches
per annum, based on a 39 -year record.9
'The Climate of Arizona, Agricultural Experiment Station Bulletin 279, September, 1956,
p. 69.
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12
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Stream flow for the Gila River, measured as Coolidge Dam,
for the period 1895 -1962 is given in Table 1. Since the water supply
is rarely sufficient to irrigate all the lands having a right to water,
there is not an appreciable carryover of stored water in the San
Carlos Reservoir. Thus, there ensues a wide variation of available stored water from year to year.
The amount of water available to the Project from above
Coolidge Dam is derived primarily from runoff carried in the
Gila River and its tributaries above the dam, minus the use of
the natural -flow water by the upper valleys, minus transportation
losses occurring in the 66 miles of river channel between Coolidge
and Ashurst-Hayden Diversion Dam. The latter loss varies with
the volume of water being released but averages about 20 percent.l°
10Personal conversation with District Engineer, San Carlos Irrigation District, Coolidge,
Arizona.
Table L Discharge of Gila River at Coolidge Dam in Acre -feet,
1895 -1962.*
Year
Acre -feet
Acre -feet
Year
Year
(000)
(000)
(000)
439.0
554.6
465.0
1918
1919
1920
327.5
194.5
1900
1901
1902
1903
1904
Acre -feet
1941
1942
1943
1921
1922
101.7
637.3
404.5
273.7
63.9
1945
1,072.5
162.5
111.8
109.7
134.2
154.0
190.1
77.5
111.1
162.7
1923
1924
1925
1926
1927
375.7
195.4
185.3
266.5
210.7
1946
1947
1948
1949
1950
70.4
50.5
89.7
432.9
35.5
1905
1906
1907
1908
1909
1,491.0
426.7
635.9
338.0
273.4
1928
1929
1930
1951
1952
1953
1931
1932
105.2
219.5
226.8
399.0
425.0
1910
1911
1912
1913
1914
110.0
375.8
384.0
230.3
881.6
1933
1934
1935
1936
1937
1915
1916
1917
1,148.4
1,577.8
293.7
1938
1939
1940
1895
1896
1897
1898
1899
1944
58.5
1954
261.9
46.7
164.6
1955
159.7
182.9
144.9
246.2
193.5
367.1
1956
1957
1958
1959
1960
19.2
149.6
353.6
133.5
195.9
109.4
133.6
271.3
1961
130.5
1962
Mean
228.2
305.2
*Source: San Carlos Irrigation Project, Arizona, "Annual Irrigation Report Calendar
Year 1962," pp. 22 -23.
-
13 -
Natural -Flow Water Available
From Below Coolidge Dam
Additional surface water is obtained from the erratic flows of
the San Pedro River and minor tributaries which enter the Gila
Table 2. Annual Flows of the San Pedro and Gila Rivers, 1930 -61.*
Released
at
Year
Coolidge
Dam
Diverted at
AshurstHayden Dam
Approximate
Waste over
Ashurst- Hayden
Dam'
Gross Gain
Coolidge Dam to
Ashurst-Hayden
1931
1932
1933
1934
1935
1936
1937
1938
1939
220,110
213,880
278,980
340,080
170,900
191,031
236,256
291,347
151,013
122,892
Acre -feet
221,430
232,910
282,060
333,400
188,450
243,335
243,622
302,460
156,400
133,670
103,574
116,824
48,614
11,790
4,838
100,511
15,919
24,140
9,344
22,246
104,894
135,854
51,694
5,110
22,388
152,815
23,285
35,253
14,731
33,024
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
142,250
239,850
373,270
356,661
293,790
192,657
61,960
54,312
64,495
276,758
154,988
294,526
372,230
357,354
287,320
200,284
84,155
68,102
71,409
259,714
48,436
125,270
11,967
34,819
23,957
18,832
7,704
7,411
5,507
24,378
61,174
179,946
10,927
35,512
17,487
26,459
29,899
21,201
12,421
7,334
1950
1951
1952
1953
1954
1955
115,938
46,682
226,265
53,431
120,558
113,018
73,429
78,156
263,504
153,905
11,388
9,818
17,997
2,442
96,726
118,226
2,455
4,030
30,387
30,267
4,210
15,400
16,231
11,512
114,138
137,558
1957
1958
1959
123,116
41,100
228,031
44,361
103,146
93,686
78,796
73,575
242,612
135,501
1960
1961
251,809
40,548
241,272
60,845
26,009
8,182
15,472
28,479
Average
179,024
188,588
35,125
44,689
1930
1956
-2,912
8,611
51,279
48,671
*Source: San Carlos Irrigation Project, Arizona, "Annual Irrigation Report Calendar
Year 1962," p. 24.
'Estimated by engineer in charge of Diversion Darn from occasional measurements.
-
14 -
River below Coolidge Dam. The San Pedro has a reputation of
being among the flashiest rivers in the West. Extreme and
extended variations from the mean have been common, both
within and between year periods.
With present facilities it is possible to divert only a part of
the uncontrolled flood waters from the San Pedro River. The
remainder is wasted. Water of the San Pedro carries immense
quantities of silt, and the present necessary use of silt -laden
water at various times of the year is a serious problem to both
the District and the farmer. Canals, laterals, and ditches require
extra cleaning and care. They are designed oversize to enable
holding of silt until cleaned and still deliver adequate amounts
of water. This increases losses in periods of low flow or when
used to carry pump water. Silt deposited in fields is objectional
as it makes the land more difficult to work and necessitates longer
irrigations in order to secure proper depth of irrigation or water
penetration.
Silt also causes a problem and loss of much water at the
Ashurst-Hayden Diversion Dam. While considerable sediment is
removed by mechanical means at substantial annual cost, an
average of approximately 35,000 acre -feet of water is wasted
annually in sluicing at frequent intervals, in order to continue
diversions into the main canal (Table 2). The water lost in this
process averages about .35 acre-foot annually for each of the
100,546 acres in the San Carlos Project.
The average (mean) natural flow below Coolidge Dam (computed as the difference between the quantity released at Coolidge
Dam and the quantity diverted at Ashurst-Hayden Dam, plus the
approximate waste over the latter dam) was 44,689 acre -feet
annually for the 32 -year period, 1930 -1961. While this source provides considerable water, due to the flashiness of the river and
the heavily silt -laden water, much of this additional water is
wasted, inflicts damage, or adds expense to the operation and
maintenance of the system.
Therefore, little reliance can be placed on the San Pedro and
its tributaries to provide a dependable source of water. To solve
the problem of waste due to silt and the resultant sluicing operation, Buttes Dam has been proposed on the Gila River to store
flash floods and reduce flood and silt damage. The proposed site
is shown on the General Map, Figure 1, Page 48.
Apportionment of Natural -Flow Water
To District Lands
Of the natural-flow water apportioned to the District, further
apportionment to individual land parcels is made based on the
date of the established priority the date of apportionment and
beneficial use of water on the parcel of land and recorded at the
-
-
15 -
county court house. The priority established for each parcel is
given in the Gila River Decree;11 the list is too voluminous to
reproduce here.
This priority procedure was established under Arizona territorial and later State water law which follows the "Doctrine of
Prior Appropriation." The basic parts of this doctrine are:
(1) he who is first in time is first in right; in time of scarcity
the later appropriators must cease their use in reverse order of
priority, and
(2) the use must be a beneficial one; no right is acquired to
water that is not used beneficially."
"Globe Equity No. 59, op. cit.
12C. L. McGuinness, "Water Law with Special Reference to Groundwater," Geological
Survey Circular 117, June, 1951.
Table 3. Priority Dates. Accumulative Acreages under each Priity, and Accumulative Diversion Rates for Said Acreages
in the San Carlos Irrigation and Drainage District.*
Accumulative
Acreage
Second-
957
1,814
2,016
2,176
2,193
16
14
Priorities
Acres
1868
1869
1872
1873
1874
957
857
202
160
1875
1880
1890
1891
1892
309
612
399
974
400
2,502
3,114
3,513
4,487
4,887
1893
1894
1895
1896
1904
326
192
740
310
128
5,213
5,405
6,145
6,455
6,583
1908
1912
1913
1914
1916
430
7,013
7,715
8,925
9,752
10,642
13,000
27,000
50,000
1924
17
A
B
C
702
1,210
827
890
2,358
14,000
23,000
feet
3
3
0.5
4.5
11
6
17
6
6
3
12
Accumulative
Second -feet
16
30
33
36
36.5
41
52
58
75
81
87
90
5
102
107
2
109
8
117
128
148
162
177
216
11
20
14
15
39
234
383
450
833
*Source: Natural -Flow Calculation Sheet, San Carlos Irrigation and Drainage District Office,
Coolidge, Arizona.
- 16 -
The existing priority dates and acreage of each within the
District are given in Table 3. Note the large acreages in the junior
(later) rights as opposed to the small acreages in the senior
(earlier) rights. These priorities, which attach to the land. are
scattered throughout the District according to early development
patterns. Due to the many sales and transfers of properties over
the ensuing years, practically all farm operating units have a
combination of priorities.
The individual priorities are too diverse to man individually,
but a classification of priorities and their distribution are shown
in Figure 2, Page 24. Note the preponderance of early rights nearer
the Gila River and the greater area of later rights in the Casa
Grande area.
At the end of each ten -day period (there are three periods in
each month
-10, 11 -20, and 21 on) the priorities eligible for
natural -flow water, based on recorded flows in the period, are
posted in the District office. Farmers desiring delivery must give
72 hours notice to the District in order that planning and coordination of water deliveries can be achieved.
Natural -flow water originating above Coolidge Dam, posted
and not requested by an eligible priority, is not given to a junior
priority holder but is held in the reservoir and becomes stored
water. Natural -flow water originating below Coolidge Dam, posted
and not requested by an eligible priority, is available to junior
water right holders in the order of their priority. This procedure
is followed because of the lack of storage facilities.
During floods originating below Coolidge Dam, when all priorities through 1924 are satisfied, free water is declared and anyone
may receive water.
-1
Apportionment of Pumped and Stored Water
Upon notice of the Project's share of stored water from the
Court- appointed Water Commissioner, the Project engineer reports
the stored apportionment to the Area Director, Bureau of Indian
Affairs, who, under authority of the Secretary of Interior, then
apportions to the Indians and to the District their stored and
pumped water. As a prerequisite to participation in the benefits
of the San Carlos Project, the non-Indian landowners were required
to execute an agreement entitled "Landowners' Agreement with
the Secretary of the Interior, San Carlos Project; Act of June 7,
1924." This agreement provided in effect that, with the exception
of the amounts required by the landowners for a domestic water
supply, all underground water would be made available to the
Project for development and use as an irrigation -water supply.
It has been the policy of the Bureau of Indian Affairs to reduce
pumping in years of large quantities of stored water in order to
reduce the depletion of the groundwater resource. Conversely, in
years that storage is at minimal amounts, pumps are run at near
-17-
capacity to provide maximum water (Table 4) Pumped water
varied from a high of 142,451 acre-feet in 1950 to a low of 40,423
acre -feet in 1934 and has averaged 96,224 acre -feet annually for
the entire period 1934 -61. Pumped water as a percentage of total
water used has varied from a high of 69 percent in 1953 to a
low of 16 percent in 1941, which was the year of greatest storage
and natural flow during the period. The average pumpage is 40
percent for the entire period. Some farmers, who own land both
in and out of the Project, have supplemented Project water with
water pumped by off- Project, privately owned wells. This water
is not included in Table 4.
By stipulation in the Gila Decree, stored water from the San
Carlos Reservoir and pumped water from Project wells are to be
shared equally by all the lands within the Project. In other words,
every acre has an equal right to available stored and pumped
water. The annual apportionment of pumped and stored water
per acre for the period 1936 -62 is given in Table 5. Note the wide
range from a high of 6.06 acre -feet in 1942 due to the high
rainfall in 1941 and record high storage in the San Carlos Reservoir to a low of .50 acre-foot in 1953.
The unusual geographical distribution of Project lands, when
combined with the location of Project wells and canals and district
laterals, makes it difficult to distribute pumped or stored water
to all lands within the Project. Small areas near the diversion
dam are entirely dependent on surface flows while areas at the
other extremity are often fully dependent upon well water. Many
Project pumps are located where they pump directly into Project
ditches that are of such great size that delivery of pump water
is possible only when surface water is flowing in the canals.
These large canals and laterals, which were constructed oversize to handle the silt problem, contribute to the high distribution
losses of the system which are shown in Table 6. The percentage
losses are shown separately for Indian and District lands and
average 34 and 29 percent, respectively. The losses generally are
relatively high in years of low surface flows. Note the lowest
percentage loss to District lands 17 percent in 1941 corresponds to the greatest surface flow. (See Table 1.)
.
-
-
-
-
District Water Charges
Operation and maintenance costs, which also include the District share of operation and maintenance costs of the Joint Works,
are paid by assessments on all lands of the District holding water
rights. These annual assessments are collected by the Pinal
County Assessor as ex- officio treasurer of the District.
The assessment also includes an amortization payment on the
District's capital debt to the United States, based on the amount
of water in storage in the Coolidge Dam on March 1 of each year.
The District's original contract called for the payment of interest
but it was modified to provide for repayment without interest.
-
18 -
Table 4. Pump Water in the
San Carlos Irrigation
Project and its Relation to Total Water,
Table 5. Annual Apportionment of Pump and
Stored Water per
Acre to District
Lands, 1936 -62.*
1934 -61.*
Year
Pump Watez
Pump Water
as
from
Percentage
of
Projected
Wells
Total Water
Acre -feet
40,423
67,011
108,152
70,694
102,759
102,955
Percent
98,170
55,799
99,543
39
16
21
91,111
113,258
102,522
99,250
122,251
129,852
115,868
20
28
34
54
64
65
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
142,451
99,586
101,549
117,051
97,100
102,565
119,133
55
1960
1961
79,256
73,494
25
55
Average
96,224
40
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
73,356
64,586
94,525
18
22
31
19
40
44
31
68
31
69
45
48
62
48
20
38
Median
Mean
Mode
Year
Acre -feet
1936
1937
1938
1939
3.50
4.10
2.15
1.6167
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
2.106
4.55
6.06
4.92
3.35
2.05
1.00
1.00
1.00
3.30
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1.50
1.00
2.25
.50
1.50
1.50
1.30
1.00
2.00
1.50
1960
1961
1962
2.00
.65
1.55
1936-62
1953-62
1.6167
2.183
1.5
1.5
1.35
1.5
*Source: Annual Reports of Distribution
of Waters of the Gila River by the Gila
Water Commissioner to the U. S. District
Court in and for the District of Arizona.
*Source: San Carlos Irrigation Project,
Arizona, "Annual Irrigation Report Calendar Year 1962," p. 20.
- 19 -
Annual principal payments are determined by the following
schedule:
Water in Storage, March 1
0- 100,000 acre -feet
100,000- 200,000
200,000- 250,000
250,000 -300,000
300,000- 350,000
350,000-400,000
Over 400,000
Principal Payment
$ 12,500
25,000
37,500
50,000
75,000
100,000
125,000
acre -feet
acre -feet
acre -feet
acre-feet
acre-feet
acre -feet
Since the current contract came into effect in 1948, the principal payment in 13 of the 15 years (1948 -62) was $12,500. In the
Table 6. San Carlos Irrigation
Project Distribution
Losses, 1936 through
Year
Table 7. Basic Water Assessment per Acre in the
San Carlos Irrigation
and Drainage District for the Period
1961.*
Percentage Losses
to Lands
District
Indian
1936
1937
1938
1939
17
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
24
27
27
29
36
27
23
25
28
30
30
38
32
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
35
37
39
36
36
1960
1961
49
53
34
29
MEAN
34
29
23
24
24
33
40
41
26
31
36
38
38
36
41
48
46
1948 -62.*
Year
1948
1949
19
20
31
28
17
21
1954
4.90
1955
1956
1957
1958
1959
5.70
5.70
7.10
6.20
6.20
1960
1961
1962
6.00
6.00
7.20
*Source: Office records, San Carlos
Irrigation and Drainage District, Coolidge,
Arizona.
33
27
31
35
31
33
34
1952
1953
3.00
3.60
4.45
4.80
1950
1951
25
Assessment per Acre
$2.20
3.00
-t
<
*Source: San Carlos Irrigation Project,
Arizona, "Annual Irrigation Report, Calendar Year 1962," p. 16.
-20-
other two years it was $25,000. This amounts to $0.25 per acre
and $0.50 per acre of land in the District, respectively. Under this
schedule, the period required for repayment of reimbursable costs
is not a fixed number of years.
Total annual assessment charges for the 15 -year period 1948 -62
varied from a low of $2.20 per acre in 1948 to a high of $7.20 per
acre in 1962 (Table 7) The rate varies because of added capital
improvements or flood damage in any given year. Increased
operating and maintenance costs have resulted in an upward
trend in assessment charges.
The basic assessment entitles District farmers to delivery of
two acre -feet of water, if available, per acre. The difference
between the stored and pumped apportionment and the two acrefoot base, if any, can be made up of natural -flow water, if available, at no additional charge.
Rates are established for excess water at $0.50 for the first
acre-foot of water in excess of the two acre -foot base and $1.50
per acre-foot for all water in excess of three acre-feet.
.
Frequency of Water -Right Fulfillment
As indicated by the above discussion, farmers in the District
have fairly reliable information on the amount of pumped and
stored water they will have prior to planting time. However,
similarly reliable information is not available regarding natural flow water. The amount of water which will be available during
the cropping season is not known at the time crops are planted.
In other words, the farmer must determine the acreage to plant
without knowing whether or not he will have water needed to
produce a crop. Under such circumstances, the best alternative
is use of probabilities to estimate the amount of natural -flow water
likely to be obtained. The probabilities employed are based upon
the frequency with which the various water rights have been
filled in the past.
The frequencies with which water rights have been filled were
determined from records of daily stream flows deliverable to the
District as given in the Gila Water Commissioner's Annual Reports.
The accumulated 10 -day flows were compared to the required flow
to fill the priorities given in Table 3. The results are presented in
Table 8, which gives the frequencies with which the various rights
were filled over the 27 -year period, 1936-62.
As shown by these tabulated frequencies, there is a wide
seasonal variation, as well as variation between priorities. Note
that in the high water-requirement months of May, June, and
July the availability of natural flow is least frequent. Except for
the earliest priority -1868 the chance of natural flow during
most of this period is practically negligible. This has a large effect
on water -use planning since stored and pumped water must be
reserved for this period of maximum water requirement.
-
-
21
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Probability of Receiving
Natural-Flow Water
The next step in the analysis is to convert the frequencies
given in Table 8 into probabilities. The decision -maker desires to
know the probability (P) of receiving water in at least a given
number (r) of 10 -day water periods out of the total number (N)
of 10 -day water periods in the irrigation season for a given crop.
To obtain the desired probabilities, it is necessary also to find
the probabilities (q) of not receiving water in a given number (k)
of periods. The 10 -day periods, by months, in which it was assumed
water would be utilized on cotton, barley, and grain sorghum are
given in Table 9. It was assumed to be a matter of indifference
which of these 10 -day periods were supplied with natural flow
water, it being further assumed that stored and pumped water
could be utilized in any of the periods as needed.
Table 9. Natural -Flow Periods. by Months. in which Water is
Utilized for Irrigation of Specified Crops.1
Month
Barley
periods
1- 10:11- 20:21 -end
Upland Cotton
10 -day periods
1- 10:11-20:21 -end
0
0
10 -day
0
X
X
X
X
O
X
X
X
X
January
February
March
X
X
X
X
X
O
O
April
0
0
0
May
June
X
X
0
O
X
Grain Sorghum
10 -day periods
1- 10:11- 20:21 -end
O
O
O
O
O
X
O
X
O
O
X
X
X
X
X
X
X
0
0
O
O
O
O
X
O
X2
X2
0
O
O
O
O
O
O
O
O
O
O
O
O
X
X
X
0
0
0
0
July
August
September
X3
X
X
X
X
X
X
X
October
November
December
0
0
0
0
0
0
0
0
0
O
X
X
X
X
0
X
X
O
O
O
O
O
O
O
O
O
'Based upon Erie, L. J., French, Orrin F., and Harris, Karl, Consumptive Use of Water
by Crops in Arizona, Ariz. Agr. Expr. Station Tech. Bulletin 169, September, 1965; Hobart,
Charles and Harris, Karl, Fitting Cropping Systems to Water Supplies in Centarl Arizona,
Ariz. Agr. Ext. Serv. Circular 127, Rev. Nov. 1950; and Nelson, Aaron G., Costs and Returns
for Major Field Crops in Central Arizona by Size of Farm, Ariz. Agr. Expr. Sta. Tech. Bulletin
174, August, 1965, together with judgment of University of Arizona agronomists.
X indicates periods in which water can be utilized and O represents periods in which
water cannot be utilized.
'Omitted with 1891 and 1913 priorities to reduce computer costs.
'Also omitted with 1913 priority to reduce computer costs.
-
23 -
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Priorities
Priorities
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SCALE OF MILES
5
An indication of how probability theory is utilized to convert
the empirical frequencies into probabilities is given by two basic
theorems.
... p
, pr are the separate probabilities
p2, p3,
of the occurrence of r independent events, the probability P
that all of these events will occur in a single trial is "13
Theorem L "If p,,
(1) P = pl
p2 P3
... Pi ... pr.
For example, out of two possible periods, consider the probability, P, that water is received in period one, p1, and in period
two, p2. The probability, P, that both successes will occur together
is P =p, times p2.
p
, pr are the separate probabilities
P2, P3, . . .
of the occurrence of r mutually exclusive events, the probability P that some one of these events will occur in a single
trial iS "14
Theorem 2. "If pl,
(2)
P=pl+p2+p3+ .. p; .. +pr.
For example, out of two possible periods, consider the probability P that water is received in period one, p,, or in period two,
132- The probability P that success will occur in one of these
periods is P= p1 +p2.
Through combinations of theorems (1) and (2), the probability of receiving water in at least r periods can be calculated.
is given by the following
least
The required probability P
general formula:
r -1
(3) P (at least r) = 1
Pr
r =o
r)
(at
Formula (3) states that the probability of receiving water in at
least r periods is one minus the probability of receiving water in
none of the periods, in exactly one period, in exactly two periods,
in exactly three periods, etc., to exactly r -1 periods. For example,
the probability of receiving water in at least one period, P least 1),
is computed by subtracting the probability of receiving water in
none of the periods, Po, from one. The probability of receiving
water in at least two periods, P (at least 2), is computed by subtracting the sum of the probabilities of receiving water in none
of the periods, Po, and in exactly one period, P,, from one. The
(at
Henry L. Alder and Edward B. Roessler, Introduction to Probability and Statistics, 2nd
Ed., W. H. Freeman Co., p. 56.
'4Ibid., p. 54.
-
26 -
probability of receiving water in at least three periods, P
least
is computed by subtracting the sum of the probabilities of receiving water in none of the periods, Po, in exactly one period,
and in exactly two periods, P2, from one. A similar process is
carried out for P
up to and including where r =N.
least
To arrive at the probability of exactly r requires the following formulae:
(at
3),
P
r)
(at
N
(4)
Pr
=
k=1
Qk
r=0
(5)
N
N-1
i=1
k=1
Zr
Pr =
R#
Qk
7!
i
r=1
N
Pr
(6)
Pi Pj
Z
N-2
Qk
71"
k
i,j
k=1
r=2
N-3
N
(7)
Pr
Pr
P
1,j,m=1
r =3
(8)
Pi P.
Z
=
=
i,j,m
.
k
Qk
7f
i,j,m
mk=1
N
R
E
71-
.
.
r=1
i=1
N-R
Pi
77
k=1
Qk
k
i,j,m...r
r=R
with formulae (4) through (7) utilized to calculate the probabilities
of receiving water in none of the periods, exactly one period,
exactly two periods, and exactly three periods, respectively (in
each case in all possible combinations of r periods). Formula (8)
is the general formula used to determine the probability of receiving water in exactly (all possible combinations of) r periods.
The number of possible combinations of r periods out
of a total N periods can be found by the general formula
N
C
N!
=
. For example, consider the possible combinar! (N r)
tions of 2 periods out of 8 possible periods. The number of com-
r
binations
-
2
!
at a time is:
8!
3! 5!
= 56
combinational equations.
The computational problem can be realized when considering
the vast number of calculations needed eventually to calculate
the probability of at least r successes. As more and more periods
are considered, the number of combinations increases factorially.
- 27 -
When considering a crop such as cotton with a long irrigation
season, the number of calculations can run into the billions. Time
and funds restricted this study to the computation of probabilities
for not more than a maximum of 18 periods for a crop and for
three priorities even though the IBM 7074 computer calculates
at the rate of 180,000 calculations per minute.
Each of the three crops considered upland cotton, barley,
and grain sorghum have different probabilities of receiving
water a given number of periods because of the different growing
seasons involved. The probabilities of receiving natural flow water
in at least r periods, with r going from 1 to N, and also the probabilities of not receiving water in k periods, with k going from
1 to N, are given by crop for the three selected water priorities
in Tables 10, 11, and 12. The probabilities appearing in these
tables are used subsequently in the empirical analysis.
-
-
Use of Probabilities in Crop Planning
Given the probabilities of receiving natural-flow water in a
given number of 10-day periods during the growing season, by
crop, we turn to utilization of these data in planning the cropping
system. For this analysis a farm with 240 acres of cropland was
used. Three crops, upland cotton, barley, and grain sorghum,
were included in the analysis, these being the crops for which
probabilities of receiving natural-flow water were computed. The
amount of water applied per acre for each crop was estimated
to be 4.5, 2.5, and 3.0 acre -feet, respectively.
The following assumptions were used relative to natural-flow
water delivery: (1) The delivery of natural -flow water per acre
averages 0.086 acre -foot per delivery period. This figure, obtained
from the District, is an average amount. It varies a little, depending upon the water loss from the point of diversion. (2) When
natural -flow water is declared and posted at the end of a 10 -day
period, the farmer will accept delivery in the next 10 days, provided he has a crop upon which the water may be utilized. (3)
Water received during the 10 -day delivery periods throughout
the year is serially independent. This assumption was not tested
due to limitations of time and expense associated with the serial correlation problem involved.
Yields, prices, and variable costs per acre which were used
in the analysis are given in Table 13. Only variable costs of production were considered since the analysis pertains to the short run situation; i.e., fixed costs such as property taxes and depreciation are not affected by variations in the amount of water
available from one year to the next. Since the analysis pertains
to use of natural -flow water, variable costs and returns over
variable costs are shown with three levels of water costs charged
farmers for natural flow water: $0.00 for natural-flow water
-
28 -
1
co
I,
1R
.00191
.00035
.00026
.37800
.17684
.05917
.01320
.98060
.93061
.81328
.61558
18
16
17
15
14
12
13
11
10
9
8
7
6
5
4
3
2
1
0
Ka
.99809
.99965
.99974
.82316
.94083
.98680
.622001
.01940
.06939
.18672
.38442
.00001
.00007
.00062
.00404
0.0
0.0
0.0
0.0
Q4
165
15
14
12
13
10
11
9
8
7
6
5
4
3
2
1
0
R
16
.00012
14
15
13
9
8
7
6
5
4
3
2
1
0
K
.01509
.00271
.00039
.00014
.54867
.33264
.15952
.05783
.99005
.96170
.88882
.74923
.99976
.99813
1.0
.99998
P
1891
.99988
.98491
.99729
.99961
.99986
.45133
.66736
.84048
.94217
.00995
.03830
.11118
.25077
0.0
.00002
.00024
.00187
Q
8
.05026
.01351
8
9
.00269
.00041
.00008
.00005
.00004
.00004
12
13
155
14
11
10
15
12
13
14
11
10
9
5
6
7
6
7
5
.74943
.53138
.30796
.14145
4
3
2
.99992
.99995
.99996
.99996
.94974
.98649
.99731
.99959
.25057
.46862
.69204
.85855
.00031
.0 042 8
.02662
.09900
0
.99969
.99572
.97338
.90100
1
Q
K
P
4
1
2
3
0
R
1913
2P is
1K is
4Q is
is the number of periods
(or more) under consideration.
the probability of at least r (or more) periods fulfilled.
the number of periods not fulfilled.
the probability of K (or more) periods not fulfilled.
`The added expense of consideration of additional periods was judged to be greater than the benefits derived so these were not considered. (Computer time required rises rapidly as combinations rise exponentially.)
17
18
16
15
14
12
13
11
10
9
8
7
6
5
4
3
2
.99999
.99993
.99938
.99596
1.0
1.0
1.0
1.0
0
1
PZ
R1
1869
Table 10. The Probabilities of Receiving, and of Not Receiving, Natural -Flow Water During the Irrigation
Season of COTTON for Selected Priorities,
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Table 13. Yields. Prices. Variable Costs. and Returns over Variable Costs for Upland Cotton, Barley, and Grain Sorghum with Three Levels of Water Costs,
Item
Upland
Cotton
Barley
Grain
Sorghum
Production
Unit
Yield
Price per unity
Gross income
Lbs.
1150
0.326
$
Cwt.
Cwt.
42
35
$
2.34
$
2.05
374.90
81.90
86.10
Preharvest variable costs2
With water @ $0.00
With water @
.50
With water @ 1.50
76.23
78.48
82.98
30.28
31.53
34.03
34.61
36.11
39.11
Total variable costs2
With water @ $0.00
With water @
.50
With water @ 1.50
151.87
154.12
158.62
36.72
37.97
40.47
41.39
42.89
45.89
Returns over variable costs2
With water @ $0.00
With water @
.50
With water @ 1.50
223.03
220.78
216.28
45.18
43.93
41.43
44.71
43.21
40.21
'Prices used were 5 -year average as reported in Arizona Agriculture, 1959 -63.
'Based on: Nelson, Aaron, G., op. cit. It was assumed the value of cottonseed was
equivalent to ginning costs. When the allocation of stored and pumped water is less than two
acre-feet, no charge is made for natural -flow water to bring the total delivery to two acre-feet.
A charge of $.50 is made for the third acre -foot, and $1.50 for the fourth and fifth acre -feet
delivered.
delivered as part of the two acre -foot entitlement under the
annual per-acre assessment levied by the District; $0.50 for the
third acre-foot of water delivered; and $1.50 for the fourth and
fifth acre -foot delivered.
In the analysis the terms gain and loss are used in place of
the conventional terms, returns and costs, primarily for convenience. However, the meaning of loss differs somewhat from the
conventional usage of cost as indicated by the following definitions:
1. Gain represents returns over variable costs involved in
producing a crop.
2. Loss is defined as equivalent to preharvest variable costs;
i.e., the loss which is realized if a crop is not harvested. It is
recognized that preharvest variable costs may somewhat overstate the loss realized if a crop is abandoned early in the season.
However, since the time of abandonment will vary, preharvest
costs were used since they represent the maximum probable loss.
Hence, the procedure followed constitutes a conservative approach
in crop planning.
-32-
Table 14. Acres of Cotton. Barley or Grain Sorghum Irrigated
per 10 -day Natural -Flow Water Period for a 240 -acre
Farm. and Associated Gain or Loss with Three Water Cost Levels.
Acres
Crop
Irrigated
AF per
AF
$0.00
per
Delivery Applied Delivery
Period,. per Acre Period Gain: Loss:
$1.50
$0.50
Gain:
(7)
Loss: Gain:
(8)
(9)
Loss:
(10)
(2)
(3)
(4)
(5)
20.64
4.5
4.587
$1023
$349
$1014
$358
$991
$381
20.64
2.5
8.256
372
248
363
264
338
281
Grain
sorghum 20.64
3.0
6.880
310
241
296
248
275
268
(1)
(6)
Cost of Water
Upland
cotton
Barley
'Natural -flow delivery per period (which averages .086 acre -feet multiplied by the water right acres (assumed to be 240 acres) .
'Acres irrigated per delivery, given in the second column, multiplied by the gain or loss,
rounded to whole dollars, given in Table 13.
Gain or Loss Per Natural -Flow Water Period
The gain or loss obtained by using natural -flow water received
from one natural -flow period to produce upland cotton, barley,
and grain sorghum is given in Table 14. For a 240 -acre farm, the
maximum delivery is 20.64 acre -feet (240 times 0.086). If this
amount of water is used to produce upland cotton, 4.587 acres
can be irrigated. The gain or loss for this acreage, with three
levels of natural -flow water cost, is shown in columns 5 to 10 of
Table 14. Similarly, 8.256 acres of barley or 6.88 acres of grain
sorghum can be irrigated with the 20.64 acre -feet of water, with
gains or losses as shown in the table. Hence, the gain and loss
figures given in Table 14 represent the gain or loss per natural flow water delivery period. While this is a relatively simple point,
it is basic in subsequent analysis.
Probable Total Gains and Losses
Related to Use of Natural -Flow Water
Probable total gain or loss for the three crops from use of
natural-flow water for various numbers of natural-flow periods,
- 33 -
with three water priorities, is given in Tables 15, 16, and 17. The
gains and losses were computed as follows:
Probable gain = Gain per natural-flow period (Table 14) X
probability of receiving natural-flow water in
at least r periods (Tables 10, 11, 12) X number of periods.
Probable loss
= Loss
per natural-flow period (Table 14) X
probability of not receiving water in k or
more periods (Tables 10, 11, 12) X number
of periods.
For example, the probable gain given in Table 15 for upland
cotton of $1,023 with one natural-flow period was derived as
follows:
$1,023
x 1.0 x
1
= $1,023
The probable gain of $8,568 with nine natural-flow periods was
computed as follows:
$1,023 X .93061
x
9
= $8,568
Similarly, the probable loss of $218 with nine natural-flow periods
was computed as follows:
$349 X .06939 X
9=$218
-
As indicated by the material presented, data in Tables 15, 16,
and 17 reflect the probable gains or losses with the level of
yields, prices, and costs used from planting an acreage of the
various crops sufficient to utilize natural-flow water from the
specified number of natural-flow periods. For example, since 4.587
acres of cotton can be produced with the 20.64 acre-feet of water
received in one natural-flow period (Table 14), 13.76 acres can be
produced with water from three natural-flow periods. With a 1913
water priority and water @ $0.00 per acre-foot, the probable total
gain is $2,765 and the probable total loss is $104.
Calculations of probable total gain or loss have been extended
in Tables 15, 16, and 17 in each case to the point where the total
probable loss exceeds the total probable gain. It may appear, on
first thought, that it would pay to expand acreage of a crop to
the point where probable total gain and probable total loss are
equal. However, this is not the case. The incremental gain and
loss related to use of natural-flow water must be considered in
determining the most profitable acreage to plant.
-
-
34
-
Table 15. Probable Total Gain or Loss From Use of Natural -Flow
Water for Various Numbers of Periods with an 1869
Water Right.
Water Cost per Acre-foot
Number
of
Normal -Flow
Periods
$0.00
3
4
4092
5
6
5115
6134
7
8
9
7132
8025
8568
54
218
10
11
12
13
8320
6927
4640
2352
652
1476
2605
3735
1
$ 372
2
744
1116
2
$
Gain
Upland Cotton
$1014
$
2028
$1023
2046
3069
1
$1.50
$0.50
Loss
Gain
0
0
0
0
0
1
10
3042
4056
5070
6080
Loss
Gain
0
0
0
$ 991
0
0
3964
4955
5942
0
11
224
6909
7774
8300
668
1514
2672
3831
8060
6701
4495
2278
0
o
0
$ 338
676
1014
0
1
7069
7955
8493
10
56
8247
6866
4600
2331
Loss
$
1982
2973
0
0
0
0
1
59
238
711
1611
2844
4077
Barley
$
0
0
0
0
$ 363
1488
1860
2228
0
0
1452
1815
2174
0
0
1352
1690
0
0
3
2024
3
2578
2857
2939
17
273
2516
2788
2868
18
84
291
2343
2596
2670
90
309
2651
1942
1047
712
1433
2278
2587
1895
1022
758
1526
2425
2409
11
12
1
$ 310
619
922
0
0
$ 275
2
3
4
1184
44
5
192
6
1303
1154
7
754
3
4
5
6
7
8
9
10
$
3
79
$
$
726
1089
Grain Sorghum
$ 296
$
0
0
6
549
1101
591
881
1130
1244
1101
720
- 35 -
6
45
197
565
1133
0
19
807
1642
2581
1765
951
549
818
1050
1156
1023
669
$
0
0
7
49
213
611
1224
Table
16-
Probable Total Gain or Loss From Use of Natural -Flow
Water for Various Numbers of Periods with an 1891
Water Right.
Water Cost per Acre -foot
Number
of
Normal -Flow
Periods
1
2
3
$0.00
$1023
2046
3063
Loss
$
Gain
Upland Cotton
$1014
2028
0
3036
2
0
4051
4919
5456
14
67
223
4016
4876
7
5365
8
4490
3063
4
5
6
9
10
1632
$1.50
$0.50
Gain
Loss
$
0
0
2
14
Gain
$ 991
Loss
$
1982
2967
0
0
2
15
73
5408
69
239
3925
4765
5285
254
611
1260
2096
2933
5318
4451
3036
1618
628
1293
2150
3009
5197
4350
2967
1581
669
1376
2288
3202
0
0
1
$ 338
675
1
$ 372
2
743
1105
1
Barley
$ 363
725
7
1079
8
1004
10
1432
1657
1685
37
135
365
1398
1617
1644
40
144
388
1301
1505
1531
185
497
1460
1042
763
1290
1425
1017
812
1373
1327
947
1039
1757
3
4
5
6
7
8
$
$
$
0
1
51
Grain Sorghum
3
$ 309
607
845
4
917
5
751
6
438
1
2
$
1
$ 295
1
$ 274
10
66
580
807
10
68
539
750
251
621
1105
876
717
418
258
639
1137
814
666
389
-36-
$
$
1
11
74
279
691
1229
Table
17.
Probable Total Gain or Loss From Use of Natural -Flow
Water for Various Numbers of Periods with a 1913
Water Priority.
Water Cost per Acre -foot
Number
of
Normal -Flow
Periods
$0.00
Gain
1
$1019
2
3
1992
2765
4
6
7
3067
2718
1890
1012
1
$ 362
2
3
4
5
$0.50
Gain
Loss
Upland Cotton
$1010
$
1
$
$1.50
Loss
Gain
2
$ 987
19
1929
2679
20
113
382
893
1582
2290
104
1974
2741
106
350
818
1449
2097
3040
2694
1874
1004
359
839
1487
2152
2971
2633
1831
18
Loss
$
981
2
Barley
$ 353
7
$ 329
662
801
7
55
646
58
210
781
224
601
727
62
238
720
488
512
915
702
545
5
476
974
654
443
580
1036
1
$ 298
10
$ 264
2
455
471
92
345
319
761
$
$
$
8
Grain Sorghum
$ 284
3
513
531
9
83
310
507
86
319
4
360
684
343
704
$
490
-
37 -
$
$
11
Table 18. Probable Marginal Gain or Loss per Natural -Flow Water
Period with an 1869 Water Right 1
Water Cost per Acre -foot
Period
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
10
11
$0.00
Gain
$1023
1023
1023
$
1023
1023
1019
Gain
1014
1014
1010
0
0
991
991
0
0
1
987
1
989
886
9
46
164
538
168
967
865
526
10
44
48
179
(240)
(1350)
(2215)
473
900
1233
434
824
1129
0
0
0
372
372
368
0
350
279
82
14
62
(246)
(1381)
(2266)
Barley
$ 363
363
363
3
721
1158
$
0
0
0
0
0
3
$ 338
338
338
66
207
319
253
74
(281)
(692)
467
768
(261)
(644)
15
$
O
0
0
$
338
338
334
342
272
80
194
439
444
846
363
363
359
0
(288)
(709)
Loss
$ 991
991
991
1014
1014
9
$
Gain
0
0
0
1
(248)
(1393)
(2287)
$1.50
Loss
Upland Cotton
$1014
$
0
0
0
0
0
998
893
543
$ 372
372
372
$0.50
Loss
0
0
0
0
0
3
16
71
219
498
817
Grain Sorghum
1
$ 310
2
309
303
0
$ 296
295
6
290
5
262
119
249
114
6
(149)
38
148
357
3
4
$
O
(143)
'Figures in parenthesis are negative numbers.
-38-
$
0
0
6
$ 275
274
269
39
152
368
232
106
(133)
$
0
0
7
42
164
398
Table 19. Probable Marginal Gain or Loss per Natural-Flow Water
Period with an 1891 Water Right.l
Water Cost per Acre -foot
Period
1
2
3
4
5
6
7
8
9
$0.00
Gain
$1023
1023
1017
$0.50
Loss
$
988
868
537
(91)
(875)
(1427)
Gain
Upland Cotton
$1014
0
0
2
1014
1008
12
53
980
860
156
388
649
836
$1.50
Loss
0
0
Gain
Loss
$ 991
0
0
2
991
985
532
12
55
170
958
840
520
58
181
(90)
(867)
(1415)
389
665
857
(88)
(847)
(1383)
415
707
912
2
13
$ 372
371
362
0
6
Barley
$ 363
362
354
6
327
225
28
30
98
230
319
219
27
104
244
297
204
26
134
312
7
(225)
398
(219)
424
(204)
542
1
2
3
4
5
1
$
0
$ 338
0
1
337
329
1
7
32
9
41
Grain Sorghum
1
2
3
4
5
$ 309
298
238
72
(166)
$
9
$ 295
285
56
227
58
185
69
370
(159)
190
381
1
'Figures in parenthesis are negative numbers.
- 39 -
$
1
9
$ 274
265
211
64
$
1
10
63
205
Table 20. Probable Marginal Gain or Loss per Natural-Flow Water
Period with a 1913 Water Right.'
Water Cost per Acre-foot
Period
$0.50
$0.00
Gain
Gain
Loss
$1.50
Loss
Gain
Loss
Upland Cotton
1
2
3
$1021
974
776
4
302
5
(350)
(829)
6
$
1
17
85
$1010
964
246
468
631
$
2
$ 987
17
18
292
269
511
689
767
87
942
750
299
253
480
648
(338)
(802)
(346)
(820)
$
2
93
Barley
i
2
3
4
$ 362
300
139
$
7
48
155
(81)
$ 353
293
135
$
(79)
302
7
51
$ 329
$
8
166
272
126
176
321
(73)
342
54
Grain Sorghum
i
2
3
$ 298
215
18
$
9
74
227
$
284
206
17
'Figures in parenthesis are negative numbers.
-40-
$
10
$ 264
76
233
191
16
$
11
81
253
Determining the Acreage to Plant
The probable marginal gain, compared with the probable
marginal loss per natural-flow water period, provides the proper
decision criterion to use in determining the acreage of the various
crops it will pay to plant. The figures, derived from Tables 15, 16,
and 17 are shown in Tables 18, 19, and 20. In each case the marginal figure is the additional gain or loss associated with expanding the acreage of a crop to make use of one additional naturalflow period of water. For example, with an 1869 water right and
with water priced at $.50 per acre-foot, increasing the acreage
of cotton to use seven periods rather than six periods of naturalflow water, increased the probable total gain to $7,069 from $6,080
(Table 15). Hence, the probable marginal gain for the 7th naturalflow period of water was. $989 (Table 18). Similarly, the probable
total loss increases from $1 with six natural-flow periods to $10
with seven natural-flow periods (Table 15). Hence, the marginal
loss for the 7th natural-flow period is $9 (Table 18).
As is evident from Tables 18, 19, and 20, probable marginal
gains gradually decline and eventually become negative (figures
in parenthesis are negative). Similarly, probable marginal losses
gradually increase. The point where the probable marginal gain
and probable marginal loss is equal indicates the acreage where
the probability of maximizing income is greatest. Hence, with an
1891 water right (Table 19) and water priced at $.50 per acre-foot,
maximum income from barley probably would be realized by
planting an acreage which would utilize between five and six
natural-flow periods of water. Some farmers may not want to
expand the acreage to this point, preferring to reduce the risk
of loss. This point will be explored subsequently.
Probable marginal gains and losses shown in Tables 18, 19,
and 20 are portrayed in chart form in Figure 3. Probable gain or
loss per normal flow-water period is shown on the vertical axis
and the number of natural-flow periods on the horizontal axis.
As indicated in the above discussion, probable marginal gain
gradually declines as the probability of receiving natural-flow
water declines below 1, and the probable marginal loss gradually
increases as the probability of not receiving natural-flow water
increases from 0. It is interesting to study Figure 3 in comparison
with the probabilities given in Tables 10, 11, and 12.
In producing crops in the San Carlos District, pumped and
stored water is used in conjunction with natural-flow water since
natural-flow water often is not available when needed. Hence,
the total acreage of crops to plant depends upon the amount of
pumped and stored water available, plus the probable amount of
natural-flow water which will be available during the cropping
season. However, in planning the acreage of crops to plant, water
from the two sources usually should be considered separately.
Since the amount of pumped and stored water which will be available is known with a fairly high degree of certainty before sum-
41
-
GAIN OR
LOSS
.
_.`.'
$100
$400--
$300$200r-
0
$100
:,
''
$1000
Grain Sorghum
GAIN
$300 4!'71111 "`"
$200
_
/
,,r
A1891
1869
LOSS
GAIN
N
:i973
/
.
.;
N
>
Barley
d
869
7897
® `,
LOSS
° N.
Upland Cotton
®
$800
e
s
`a
Ó
S
,
$600
,
,
;
$400;
?
'
é
é
$200
,/1891
^ Wafer
1913
Water
\ Right
%Right
1
2
3
4
5
1869
6'a ter
6
7
Right
8
9
10
Natural -Flow Period
Figure 3. Probable Marginal Gain and Loss per Natural -Flow
Period for Specified Crops, with Water @ $.50 per Acrefoot, for Three Different Water Rights.
-42-
mer crops are planted, the acreage of crops which can be grown
with this quantity of water can be determined quite accurately.
Then the acreage for which natural -flow water probably will be
available can be added.15
As indicated by the above discussion, the acreages of upland
cotton, barley, and grain sorghum it will pay to plant to utilize
natural -flow water which probably will be available, are obtained
from Tables 18, 19, and 20. With natural -flow water @ $.50 per
acre -foot, the acreages with the three water rights are derived
as indicated by the following tabulation:
Water
Priority
1869
Crop
Number of Acres Irrigated
Natural -Flow per NaturalPeriods
Flow Period
Upland cotton
9
Barley
8
Grain sorghum
4
4.587
8.256
6.880
Acres it Will
Pay to Plant
41
66
28
21
1891
Upland cotton
6
Barley
5
Grain sorghum
3
4.587
8.256
6.880
28
41
21
14
1913
Upland cotton
4
Barley
2
Grain sorghum
2
4.587
8.256
6.880
18
16
14
8
The number of natural -flow periods in the tabulation is the
highest number where probable marginal gain exceeds probable
marginal loss. It is evident that marginal gain exceeds marginal
Ioss for a fraction of the next higher period. The fraction, with
50-cent natural -flow water, is indicated by the intersection of the
gain and loss curves in Figure 3. A farmer wishing to expand the
acreage planted to the limit may use fractional periods, derived
from such curves, in the above tabulation.
The aggregate acreage of crops to be planted on the basis of
natural -flow water should not be expanded beyond the acreage
which likely can be irrigated. The probabilities used in the above
tabulations are for individual crops, not for a cropping system.
Therefore, the probabilities do not allow for duplication in water
15This procedure is appropriate in most years. However, in years when the supply of
stored and pumped water is very low, the acreage planted to use natural flow water would
have to be limited since stored and pumped water is needed for use on a "fill in" basis when
natural flow water is not available.
-
43 -
use when two or more crops use natural-flow water during the
same period. In the above tabulation, the number of natural-flow
periods of water which it is profitable to use, compared with the
average number of periods filled during the irrigation seasons for
the three crops, are as follows:
Natural-Flow Water Right
1889
1891
1913
Number of natural-flow periods
used (from the above tabulation)
21
14
8
Average number of natural-flow
periods filled (derived from
tables 8 and 9)
21
15
9
Hence, on the average, it appears a sufficient number of naturalflow periods probably are filled to provide the water which can
be profitably used with the three crops included in the cropping
system and with yields, prices, inputs, and costs employed in the
analysis. However, if another crop, such as alfalfa hay, were
included in the cropping system the aggregate amount of naturalflow water it would pay to use might well exceed the aggregate
amount which likely would be received. Probabilities of receiving
natural-flow water based upon a cropping system are needed in
analysis of this point, but limitations on time and funds did not
permit such an extension of the study.
Effect of Supply of Pumped and Stored Water
On Acreage it will Pay to Plant
The amount of pumped and stored water available usually
will not have much effect on the acreage of crops it will pay to
plant to utilize natural-flow water. As indicated above, the two
sources of water usually are considered independently in determining the acreage to plant. It should be recognized, however,
that water from the two sources generally must be used conjunctively in producing crops since the flow of natural-flow water
does not correspond with water requirements of crops. Hence, as
indicated above in Footnote 16, if the supply of pumped and stored
water is very low it may limit the acreage planted to utilize
natural-flow water. It should also be recognized that when there
is an abundance of pumped and stored water, the acreage available may be inadequate to utilize all the natural-flow water which
it normally would pay to use.
Effect of Cotton Allotments on Acreage Planted
The effect of cotton allotments on the acreage planted to
utilize natural-flow water depends on a number of factors such
as the water right, the amount of stored and pumped water avail-
44
-
able, and the degree of restriction caused by the allotment Consider, for example, a 240-acre farm with an 1891 water right and
a cotton allotment of 90 acres. As indicated earlier in the report,
the average amount of pumped and stored water available is 1.5
acre-feet, or 360 acre-feet for a 240-acre farm. Thus, with a cotton
program such as was in effect in 1965, our 240-acre farmer might
have planted crops as indicated by the following tabulation:
Total
Upland
Cotton
Barley
Grain
Sorghum
Water per acre, AF
4.5
2.5
3.0
Acres based upon pumped and
stored water
Pumped and stored water required, AR__
62
279
32
81
0
0
94
360
6
28
5
41
3
21
14
Acres based upon natural-flow water
Total acres planted
90
73
21
184
Crops
-
Number of natural-flow periods which
it would pay to use with water
90
With the current cotton program, assuming the farmer reduced
his cotton acreage by 35 percent, water would be available to
utilize most of the idle cropland (240 184 = 56 acres) for producing barley and grain sorghum. The acreage figures might be
about as follows:
-
Upland
Cotton
Acres based upon pumped and
stored water
Barley
Grain
Sorghum
Total
30.5
49
33
112.5
28.0
41
21
90.0
Acres based upon natural-
flow water
Idle acres
-
-
Total
90
90
Diverted acres
31.5
54
31.5
6.0
240.
-
With earlier water rights, or if the amount of pumped and
stored water available were above average, some natural-flow
water which might be profitably used probably would go unused.
-45 -
Effect of the Level of Costs and Prices
On Acreage It Will Pay to Plant
As a general rule, the acreage it will pay to plant to utilize
natural-flow water is not affected very much by changes in the
level of costs and prices.
It will be noted in Tables
18, 19, and 20
that changing the cost of natural -flow water from $0.00 to $0.50
to $1.50 per acre -foot does not change the number of periods of
natural-flow water it will pay to use. There is a change, of course,
but it is too small to be reflected in the tables.
The effect of changing the level of costs and prices on the
acreage it will pay to plant to utilize natural -flow water is portrayed graphically in Figure 4. The "Budget level" gain and loss
curves in Figure 4 are the same as the gain and loss curves with
an 1891 water right in Figure 3. Similar gain and loss curves are
included in Figure 4 to show the effect of increasing and decreasing variable costs, other than the cost of natural-flow water, by
15 percent; and also the effect of changing the level of commodity
prices. While these changes have an effect on the acreage it will
pay to plant, none of them have a sufficiently large effect to change
the number of periods of natural-flow water which it will pay to
use. Even dropping the price of cotton lint to 25 cents per pound
does not materially affect the acreage which could be profitably
planted.
Risk Considerations in Planning
Use of Natural -Flow Water
The discussion presented above has been in terms of the
probable gain and loss associated with use of natural -flow water.
The distinction between probable gain and loss and potential gain
and loss should be recognized. Probable gain and loss figures represent the average of a number of years. Gains will be realized
in some years and losses in others. The average of the gains,
including the zeros, is the probable gain. Similarly, the average
of the losses, including the zeros, is the probable loss. If the probable loss were deducted from the probable gain, the result would
be the probable net gain over a period of years. On the other hand,
the potential gain or loss refers to the gain or loss to be realized
in any given year.
The distinction between probable gain or loss and potential
gain or loss can be illustrated by reference to data given above.
As indicated in Table 14, the gain associated with use of one
natural -flow period of water to produce cotton is $1,023 and the
loss is $349. With a 1913 water priority and with natural -flow
water at 50 cents per acre-foot, the probable total gain from
three natural -flow periods of water is $2,741 and the probable
total loss is $106 (Table 17). The comparable potential total gain
is $3,069 (3 X $1,023) and the potential loss is $1,047 (3 X $349).
-46-
GAIN OR
LOSS
$400
PRICES INCRE/AS
COSTS REDO O
BUDGET LEVÉ(
$1300
$200
C0 5
i
S
IÑCREA®E
Grain Sorghum
0.,aO
PRICÉS REDUCED 1Só
$100
GAIN COSTS INCREASED 15/0
"BUDGET LEVEL
%
0
/COSTS REDUCED 150
15 a.
..........%
`i
LOSS
$400
$300
$200-
COSTS
REDUCED
LEVEL
BUDGET
1
1NC
15%:°
COSTS INCREASED
PRICES REDUCED
.
Barley
"4(4
750
0,0
$100LOSS
COSTS INCREASED 15%
BUDGET LEVEL
COSTS REDUCED 15%
0
$1200
COSTS
REDUCED
BUDGET
\
15%
LEVEL
$1000
COSTS
INCREASED
15%
\
i
$800
$600
Upland Cotton
COTTON
LINT
25(t
LB
%GAIN
4
INC
$400
COSTS
15%
`.
Na.
/BUDGET LEVEL
ÿ /COSTS
REDUCED
15%
$200
d,i/LOSS
2
3
4
5
6
7
Natural -Flow Period
Figure 4.
Water Right and Natural -Flow Water @ $.513:
Probable Marginal Gain and Loss per Natural -Flow
Water Period for Specified Crops with Different Levels
of Costs and Prices.
1891
-
47 -
The probable gain is always less than the potential gain whenever the probability of receiving water in at least r or more
periods is less than 1. Similarly, the probable loss is always less
than the potential loss as long as the probability of k or more
periods not being filled is less than 1. Moreover, as the probability
of receiving water in at least r or more periods declines from 1,
the difference between the probable gain and potential gain
increases. Similarly, as the probability of k or more periods not
being filled increases from 0, the spread between probable and
potential loss widens.
Hence, if a farmer wishes to minimize his risks of loss in use
of natural -flow water, he should limit the acreage planted to that
which can be irrigated with the number of natural-flow periods
which have a high probability of being filled. For example, with
an 1891 water right and natural-flow water @ $.50 per acre-foot,
the probable loss is nil when the acreage of cotton planted is
limited to that which can be irrigated with two natural-flow
periods of water (Table 16). However, if the acreage is expanded
to use nine natural -flow periods of water, the probable loss is
increased to $2,150 and the potential loss to $3,222 (9 X $358).
Farmers with limited risk- bearing ability will do well to give full
recognition to the potential loss which may be realized in determining the acreage of crops to plant to utilize natural -flow water.
Figure
1.
Map Showing Lands Having Water Rights Under the
Gila River Decree. The San Carlos Irrigation and Drainage District is comprised of that part located below the
Coolidge Dam which is outside the Gila River Indian
Reservation.
-48-
Salt
Phoenix
-WO er
.._
Ì--
/i
i
..
,
N_M
MARICOPA
Mesa
COUNTY
PINAL
COUNTY
GR
Miami
Globe
,
.
Z
01
u
GILA
COUNTY
p,N
3
Superior
`
Dam
._
i.
(Buttes
>-
~
Z
Z_'ó
O
u
Florence
Dam
Site
n
G
Kelvin
\.
)
i
Calva
G 4
1-
6
4
Kearny
t..\
Dam
i
óti,
Ashurst- Hayden
.`
Coolidge
.2.
RESERVATION
SAN CARLOS INDIAN
i
2`/
`
1
..,
r
c
°jd
v.."'
¡
Y.. Ha Yyden
70
NN
"...z
'
e
.....
im
m
rCJf
. ._
i
,
Morenci
Clifton
O
Safford
Valley
áZ
O,á
. /'
Dam
Site
Safford
Thatche
V
z
O
`l!
O
u
San Manuel
O
COUNTY
PINAL
COUNTY
PIMA
Duncan
Duncan
á
I
e,
á
j
KEY
MAP
Tucson
10
0
COUNTY
COUNTY
COCHISE
GRAHAM
Lands having water rights
under Gila River Decree
=
:
Camelback %...
Winkelman
u
G
20
SCALE OF MILES
United States Department of the Interior
Bureau of Reclamation
Middle Gila River Project Arizona
Buttes Dam and Reservoir
-
April
1,
1957
Revised Oct. 14, 1960
Valley
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