Application of Operations Research Techniques for Allocation of Water Resources in Utah

107 Pages·2016·10.99 MB·English

by  Calvin G. Clyde

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Reports Utah Water Research Laboratory
January 1971
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Calvin G. Clyde
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Clyde, Calvin G., "Application of Operations Research Techniques for Allocation of Water Resources in
Utah" (1971). Reports. Paper 531.
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ABSTRACT
In this report a methodology is described for determining the optimal allocation of water
supplies in the State of Utah to minimize the cost of meeting an assumed set of water
requirements. A linear programming model was formulated to represent the ten interconnected
hydrologic study areas of the state. The comprehensive model considers virtually all uses, areas,
sources, transfers and costs of water. The model has 204 constraints and 338 variables and was
solved by the simplex method.
Included in the results are the following: ihe opiimai water ailocation or the groundwater,
surface water, and water transfers which minimize the cost; the shadow prices of the resources;
sensitivity analyses to identify the critical cost coefficients in the optimal solution; parametric
analyses to test the effects of changing constraints; and manipulations of the model to test other
factors such as operating rules, legal policies, political and institutional limitations. The tabulated
data were carefully condensed so as to be more easily understood. Flow diagrams and graphs
summarize the important information. The work is fully documented so others can follow what
was done and improve the method or apply the model to other areas.
Keywords: *Water resources planning, *Water management, *Operations research, *Optimal
allocation, *Utah, Hydrology, Surface water, Groundwater, Water storage, Water
transfer, Water requirements, Water supply, Municipal water use, Industrial water use,
Agricultural water use, Wetlands water use, Groundwater recharge, Water reuse,
Mathematical model, Linear programming, Objective function, Constraints, Simplex
method, Cost minimization, State water plan, Legal aspects, Social aspects, Political
factors.
iii
ACKNOWLEDGMENTS
The writers gratefully acknowledge that this research project was supported by the Office of
Water Resources Research, U.S. Department of the' Interior under matching fund grant
B-027-Utah.
The contributions of other individuals and agencies are also gratefully acknowledged as
follows:
Dr. Daniel H. Hoggan for his work on the introduction and general background.
Dr. James H. Milligan for his work in the early stages of the project in developing the
allocation model, for preparing Appendix A, and for preparing the cost data for the model.
Mr. Rick L. Gold for his early work in developing the allocation model.
Mr. Blaine P. Hanson and Mr. Greg Meacham for their contributions as graduate research
assistants.
Dr. J. Stewart Williams for his help in estimating the groundwater recharge potential.
Mrs. Donna H. Falkenborg for editorial assistance.
Miss Brenda Richards for help with the computer data reduction and summarizing.
Dr. Bartell C. Jensen and Dr. A. Bruce Bishop for their review of the manuscript.
To the staff of the Division of Water Resources, Utah Department of Natural Resources for
their cooperation in supplying data and for valuable suggestions during the project.
To staff members of the U.S. Bureau of Reclamation, Region 4, for informal suggestions and
information pertaining to USBR projects and costs.
iv
TABLE OF CONTENTS
Page
INTRODUCTION
Development of the State's Water Resources
National water planning program 1
Utah's water planning program 1
Policy and institutional situation · 2
Systems approach . . · 3
Objectives of the Research .4
Review of the State-of-the Art: The Systems Approach to Water
Resource Planning . . . . . . . . . . · 5
Systems analysis approach in other states .6
Susquehanna River Basin -New York and Pennsylvania .6
River basin -Iowa . . . . . . . . . . . . . .6
Trans-Texas Division, Texas Water System -Texas .6
Entire state -Texas ..... .7
Pecos River Basin -New Mexico .7
Sacramento Basin -California .7
Santa Clara Valley -California .7
San Joaquin Valley -California .7
Statewide -California .7
Previous studies for Utah .8
GENERAL BACKGROUND FOR THE PHYSICAL SYSTEM AND THE
ALLOCATION MODEL . . . . . . . . . . . . . . . . . . .9
Water Resources Requirements, Availability, and Problems in Utah .9
The area .......... . .9
Hydrologic study units . . . . . .9
Population and economic growth 11
Water uses and projected requirements 11
Available resources ....... . 12
Major water and related land resources problems 14
Present Status of Water Resource Development 14
Storage Requirements . . . . . 17
Groundwater Recharge Potential 18
THE ALLOCATION MODEL 27
General Description 27
Mathematical model 27
v
TABLE OF CONTENTS (CONTINUED)
Page
Objective function 27
Constraints 27
Variables 27
Allocation Pattern 28
Demands 28
Availabilities . 28
Transfer of excess water 28
Detailed Description of the Model 28
Model variables . . . . . . 28
Colorado River water transfer 28
Local surface water 32
Groundwater '" . . 32
Stored local surface water 32
Evaporation loss . . . 33
Return flow 33
Groundwater recharge 33
Outflow ..... . 33
Miscellaneous variables 33
The objective function . 34
Components of cost 34
Water transfers . 34
Development and distribution 34
Pumping 34
Treatment ....... . 34
Storage . . . . . . . . . 34
Recharging surface water to groundwater 34
Variable cost coefficients 34
Inter-basin transfer 34
Diversion to agriculture 37
Diversion to municipal and industrial 37
Diversion of groundwater to wetlands 37
Groundwater recharge . . . . . . . 37
Reclaiming municipal and industrial waste water 37
Storage of local surface water 37
Constraints 37
Water availability 37
vi
TABLE OF CONTENTS (CONTINUED)
Page
Water requirements ...... . 37
Reservoir storage and evaporation loss 37
Return flows ...... . 37
Free groundwater for wetlands 37
Limits .. 37
Variable bounds 46
Inter-basin transfer 46
Additional surface water storage 46
Surface and groundwater outflow 46
RESULTS FROM THE MODEL . . . 51
Results from the Optimal Solution 51
Optimum value of the objective function 51
Optimal allocation 51
Resource shadow prices 53
Post-Optimal Analysis . 53
Sensitivity analysis 53
Parametric analysis 53
Other Results 56
Effect of changing irrigation efficiency 56
Effect of changing groundwater policy 56
Effect of limitation on inter-basin transfer 56
Effect of changing growth projections 56
Effect of giving up some present diversions 56
Effect of changing the probability on storage ..... . 57
Effect of changing p~licy of maintaining Great Salt Lake level 57
Effect of assuming no development has taken place . 57
Effect of continually relieving constraints and bounds 57
EVALUATION OF THE METHOD 59
LITERATURE CITED . . . . . 61
APPENDIX A: GENERAL THEORY OF THE ALLOCATION MODEL 63
APPENDIX B: COMPUTER PRINT-OUT OF THE SOLUTION OF THE BASIC
ALLOCATION MODEL ................. . 67
APPENDIX C: FLOW DIAGRAMS FOR ALLOCATION MODELS 83
vii
LIST OF FIGURES
Figure Page
Hydrologic study units of Utah . 10
2 Reservoir storage requirement for the Great Salt Lake Desert
hydrologic study unit . . . . . . . . . . . . . . .. .......... 19
3 Reservoir storage requirement for the Bear River hydrologic
study unit .................... .......... 19
4 Reservoir storage requirement for the Weber River hydrologic
study unit ............................... 20
5 Reservoir storage requirement for the Jordan River hydrologic
study unit ............................... 20
6 Reservoir storage requirement for the Sevier River hydrologic
study unit ..................... ......... 21
7 Reservoir storage requirement for the Cedar-Beaver hydrologic
study unit ..................... ......... 21
8 Reservoir storage requirement for the Uintah Basin hydrologic
study unit ..................... ......... 22
9 Reservoir storage requirement for the West Colorado hydrologic
study unit ............................... 22
10 Reservoir storage requirement for the South and East Colorado
hydrologic study unit . . . . . . . . . . . . . . . . .. ........ 23
11 Reservoir storage requirement for the Lower Colorado hydrologic
study unit ..................... 23
12 Reservoir storage requirement at a probability of 75 percent 24
13 Reservoir storage requirement at a probability of95 percent 24
14 Generalized matrix of the least-cost linear programming allocation
model ..... . . . . . . . . 29
15 Flow diagram of the allocation model 30
16 Present allocation of water in Utah (1965) 31
17 Constraints for availability of local surface water 38
18 Constraints for availability of groundwater . . . 38
19 Constraints for water diversion requirements for municipal and
industrial use ..................... 39
20 Constraints for water diversion requirements for agricultural use 40
21 Constraints for water depletion requirements for wetland use 41
viii
LIST OF FIGURES (CONTINUED)
Figure Page
22 Constraints for reservoir draft requirements 41
23 Constraints for water storage requirements 42
24 Constraints for net evaporation loss from reservoirs (other than
Bear and Utah Lakes) . . . . . . . . . . . . . . .. ......... 43
25 Constraints for waste water return flow from municipal and
industrial use ............... 43
26 Constraints for return flow from agricultural use 44
27 Constraints for free groundwater for wetlands 44
28 Constraints for groundwater artificial recharge limits 45
29 Constraints for inter-basin transfer limits 45
30 Constraints for inflow and outflow limits 45
31 Complete matrix of the allocation model 47
32 Flow diagram for the basic model (1965) 52
33 Allocations for the basic model as function of time 54
34 Excess water for the basic model as function of time 55
35 Allocations as affected by time and inflow to the Great Salt Lake 58
C-1 Basic model . . . . . . . . . 85
C-2 No groundwater recharge model 89
C-3 No further groundwater development model 92
C-4 Only Bonneville Unit of CUP transfer from Upper Colorado River
Basin to Great Basin model 95
C-5 Changed growth projection model 98
C-6 Not fixed present diversions model . 104
C-7 Storage probability of 0.95 model . 108
C-8 Inflow to Great Salt Lake 2:: 800,000 ac-ft/yr model . 112
C-9 Inflow to Great Salt Lake 2:: 1,088,000 ac-ft/yr model . 116
C-10 No previous development model . 120
C-l1 Continual constraint relief model . 124
ix