Simulation-Optimization Approach to Management of 

Ground-Water Resources in the Albuquerque Area, 

New Mexico, 2006 through 2040 

Prepared in cooperation with the 

CITY OF ALBUQU ERQU E PUBLIC WORKS DEPARTMENT 

Sc ientific Investigations Report 2004-5140 

U.S. Department of the Interior 

U.S. Geological Survey 
Simulation-Optimization Approach to 

Management of Ground-Water Resources 

in the Albuquerque Area, New Mexico, 

2006 through 2040 

By Laura M. Bexfield, Wesley R. Danskin, 

and Douglas P. McAda 

Prepared in cooperation with the 

CITY OF ALBUQUERQUE PUBLIC WORKS DEPARTMENT 

Scientific Investigations Report 2004-5140 

U.S. Department of the Interior 

U.S. Geological Survey 
U.S. Department of the Interior 

G.ale A. Norton, Secretary 

U.S. Geological Survey 

Charles G. Groat, Director 

U.S. Geological Survey, Albuquerque, New Mexico: 2004 

For sale by U.S. Geological Survey, Information Services 

Box 25286. Denver Federal Center 

Denver. CD 80225 

For more information about the USGS and its products: 

Telephone: 1-888-ASK-USGS 

World Wide Web: http://www.usgs.gov/ 

Any use of trade. product. or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government. 

Although this report is in the public domain. permission must be secured from the individual copyright owners to reproduce any copyrighted materials contained within this report. 
CONTENTS 

Page 

Abstract................................................................................................................................................................................. 1 

Introduction ......................................................................................................................................................................... .. 

Water use in the Middle Rio Grande Basin ............................................................................................................... .. 

Purpose and scope ...................................................................................................................................................... . 

Previous investigations ............................................................................................................................................... . 

Acknowledgments ......................... ~ ............................................................................................................................ . 

Background on the study area and the ground-water-flow model.. ..................................................................................... .. 

Description of the study area ...................................................................................................................................... . 

2 

4 

7 

7 

8 

8 

9 

McAda and Barr oil model........................................................................................................................................... 12 

Simulations of future conditions................................................................................................................................. 18 

Simulation-optimization approach........................................................................................................................................ 22 

General design of the simulation-optimization approach .. .... .. . . . ..... .. . .. . . .. .. ... .... .. . . .... .. .... .. . .. .. . ... .. .. . .. ... .. ...... .. .. .. ...... .. 22 

Simulation-optimization approach for the Middle Rio Grande Basin ...................... ............................... ........... ........ 23 

Use of the simulation model to generate response functions............................................................................ 24 

Formulation and solution of mathematical optimization models...................................................................... 27 

Selection of tin1e horizons................................................................................................................................. 28 

Simulation-optimization models for ground-water management in the Albuquerque area.................................................. 31 

Optimization model 1: Minimize net depletion of aquifer storage............................................................................. 34 

Optimal distribution of ground-water withdrawal............................................................................................. 38 

Comparison of GAMS and MODFLOW results............................................................................................... 41 

Comparison of simulation results for optimal and non-optimal distributions of ground-water 

withdrawal........................................................................................................................................... 41 

Optimization model 2: Minimize net infiltration from the Rio Grande...................................................................... 43 

Optimal distribution of ground-water withdrawal............................................................................................. 43 

Comparison of GAMS and MOD FLOW results............................................................................................... 49 

Comparison of simulation results for optimal and non-optimal distributions of ground-water 

withdrawal........................................................................................................................................... 49 

Optimization model 3: Minimize net depletion of aquifer storage, with water-level constraints............................... 54 

Optimal distribution of ground-water withdrawal............................................................................................. 57 

Comparison of GAMS and MOD FLOW results............................................................................................... 57 

Comparison of simulation results for optimal and non-optimal distributions of ground-water 

withdrawal........................................................................................................................................... 59 

Optimization model 4: Minimize net depletion of aquifer storage, with constraints on water levels 

and arsenic concentrations . .. ... .. . . . . . .. ... . . . . . .. .......... ..... . . . . . . . .. . . . . .. . .. .. . . .. .. . .. . . . . . . . .. . . . . . .. .. ... . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 59 

Optimal distribution of ground-water withdrawal............................................................................................. 60 

Comparison of GAMS and MOD FLOW results............................................................................................... 60 

Comparison of simulation results for optimal and non-optimal distributions of ground-water 

withdrawal........................................................................................................................................... 60 

Optimization model 5: Minimize net depletion of aquifer storage after eliminating river "debt".............................. 66 

Optimal distribution of ground-water withdrawal............................................................................................. 67 

Comparison of GAMS and MOD FLOW results............................................................................................... 67 

Comparison of simulation results for optimal and non-optimal distributions of ground-water 

withdrawal........................................................................................................................................... 73 

Applicability of results.......................................................................................................................................................... 73 

Reliability and sensitivity............................................................................................................................................ 73 

Implications for the ground-water system of the Middle Rio Grande Basin and other alluvial basins of the 

Southwestern United States........................................................................................................................... 76 

Limitations and future needs....................................................................................................................................... 77 

Summary ............................................................................................................................................................................... 77 

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 

iii 
FIGURES 

Page 

1.-3. Maps showing: 

I. Selected features of the Middle Rio Grande Basin, central New Mexico . . . .. . . . . . . . .. . . . . . . . . . . . . . .. .. . . . . . . . . . . ............ 3 

2. Water levels representing 1999-2002 conditions in the production zone and estimated water-level 

declines, 1960 to 2002 .............................................................................. · · .... · .. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·.................. 6 

3. Major structural features of the Middle Rio Grande Basin............................................................................ 10 

4. Geologic section along Paseo del Norte in northern Albuquerque.......................................................................... 11 

5. Map showing City of Albuquerque municipal-supply wells................................................................................... 13 

6. Map of model grid showing active model cells in layer 1 of the McAda and Barroll (2002) model...................... 14 

7. Diagram showing configuration of layers in the McAda and Barroll (2002) model............................................... 16 

8. Maps showing distribution of simulated horizontal hydraulic conductivity in the east-west direction for 

selected layers of the McAda and Barroll (2002) model................................................................................... 17 

9. Graph showing annual City of Albuquerque pumping assigned for each simulation of future conditions using 

the McAda and Barroll (2002) model, 1980 to 2040......................................................................................... 20 

10. Map showing simulated water-level change in the production zone (layer 5) between 2000 and 2040 for 

simulation m (small ground-water use)............................................................................................................ 21 

11.-17. Graphs showing: 

I I. Representative response functions for the (A) storage and (B) river plus drains components of the 

water budget after application of stress of 1,000 acre-feet during year 1.......................................................... 25 

12. Representative response functions for water levels after application of stress of 1 ,000 acre-feet 

during year 1 . . . ... . . .. . . . .. . . .. . . ... . . .. . .... . . .. ... . .. . . . .. . ... . .. . ... . . ... .. . ... . ... ... .. .. . ... . ... . ... . . .... . . . .... . . . . . . .... . . . . . ... . ... . . . . . . . ... . . . . . . . . . . .. 26 

I 3. Example calculations of the total response of a hypothetical system to withdrawal from two wells.......... 29 

14. Projected ground-water demand curve for all optimization models ............ .'............................................... 35 

15. Cumulative response over time of aquifer storage to an applied stress, scaled to indicate the response 

per well, for each City of Albuquerque well field............................................................................................ 37 

16. Comparison of (A) storage and (B) river plus drains components of the water budgets from GAMS 

and MODFLOW for optimization model 1 ....................................................................................................... 42 

17. Comparison of selected water-budget components from MOD FLOW for simulations using various 

ground-water withdrawal distributions.............................................................................................................. 45 

18. Map showing simulated water-level change in the production zone (layer 5) between 2000 and 2040 for 

non-optimal ground-water withdrawal............................................................................................................... 46 

19. Map showing simulated water-level change in the production zone (layer 5) between 2000 and 2040 for 

optimal ground-water withdrawal from optimization model 1.......................................................................... 47 

20. Graphs showing cumulative response over time of the river plus drains to an applied stress, scaled to 

indicate the response per well, for each City of Albuquerque well field........................................................... 48 

21. Graphs showing comparison of (A) storage and (B) river plus drains components of the water budgets from 

GAMS and MODFLOW for optimization model 2........................................................................................... 52 

22. Map showing simulated water-level change in the production zone (layer 5) between 2000 and 2040 for 

optimal ground-water withdrawal from optimization model 2 .......................................................................... 53 

23.-26. Maps showing: 

23. Response per well of water levels in the production zone at observation sites in the (A) Gonzales and 

(B) Coronado well fields to withdrawal from each City of Albuquerque well field.......................................... 55 

24. Comparison of water-level changes from GAMS and MOD FLOW for optimization model 3. ................. 58 

25. Comparison of (A) storage and (B) river plus drains components of the water budgets from GAMS 

and MODFLOW for optimization model4 ....................................................................................................... 63 

26. Comparison of water-level changes from GAMS and MOD FLOW for optimization model 4. ................. 64 

27. Map showing simulated water-level change in the production zone (layer 5) between 2000 and 2040 for 

optimal ground-water withdrawal from optimization model 4 .......................................................................... 65 

28. Graphs showing comparison of (A) storage and (B) river plus drains components of the water budgets 

from GAMS and MOD FLOW for optimization model 5 .................................................................................. 71 

29. Graphs showing comparison of water-level changes from GAMS and MOD FLOW for optimization model 5 .... 72 

30. Map showing simulated water-level change in the production zone (layer 5) between 2000 and 2040 for 

optimal ground-water withdrawal from optimization model 5 .......................................................................... 74 

iv 
TABLES 

Page 

1. Water-use estimates for selected counties of the Middle Rio Grande Basin in 1995 .............................................. 5 

2. Simulated annual water budgets for the Middle Rio Grande Basin from the McAda and Barroll (2002) 

model, steady state and year ending October 1999............................................................................................ 19 

3. Summary of major results for future simulations I, II, and III................................................................................ 22 

4. Characteristics of each optimization model............................................................................................................. 33 

5. Annual well-field capacities used for all optimization models................................................................................ 36 

6. Cumulative response of aquifer storage 54 years after unit withdrawal, scaled to indicate the response 

per well, for each City of Albuquerque well field . .. . . . . . . . .. . . . . . . . . ... . . . . ... . . . . . . . . . . . . ...... .. . . . . .. . ........... ......... ... . . . . . . . . . . .. . 38 

7. Optimal distribution of ground-water withdrawal for optimization model 1 ......... .............. ................................... 39 

8. Comparison of water-budget components from the MOD FLOW simulation using the non-optimal 

distribution of ground-water withdrawal for 2000 and simulations using the optimal distribution of 

ground-water withdrawal from each model....................................................................................................... 44 

9. Cumulative response of the river plus drains 54 years after unit withdrawal, scaled to indicate the response 

per well, for each City of Albuquerque well field . . . .. . . . . . .. ... . . . . . . . .. . . . . . . . .. . .. . . . . . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . 44 

10. Optimal distribution of ground-water withdrawal for optimization model 2 .......................................................... 50 

11. Representative arsenic concentrations used for each well field in optimization model 4 ..... .......... .................... .... 59 

12. Optimal distribution of ground-water withdrawal for optimization model 4 ............ ................... .. . ...... .. ....... .. .. ..... 61 

13. Optimal distribution of ground-water withdrawal for optimization model 5 ................................................... ....... 68 

14. Comparison of calculated effects on the river system from GAMS and MODFLOW for optimization model 5... 70 

CONVERSION FACTORS AND VERTICAL DATUM 

Multiply 

inch 

foot 

mile 

By 

2.54 

0.3048 

1.609 

square mile 2.590 

acre-foot 

gallon 

cubic foot per second 

1,233 

3.785 

0.02832 

To obtain 

centimeter 

meter 

kilometer 

square kilometer 

cubic meter 

liter 

cubic meter per second 

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29). 

Horizontal coordinate information is referenced to the North American Darum of 1927 (NAD 27). 

v 

SIMULATION-OPTIMIZATION APPROACH TO MANAGEMENT 

OF GROUND-WATER RESOURCES IN THE ALBUQUERQUE 

AREA, NEW MEXICO, 2006 THROUGH 2040 

By Laura M. Bexfield, Wesley R. Danskin, and Douglas P. McAda 

ABSTRACT 

In response to continually declining water levels 

in the Santa Fe Group aquifer system of the Middle Rio 

Grande Basin, the City of Albuquerque has adopted a 

water-supply strategy that calls for a transition from the 

current (2003) complete reliance on ground-water 

withdrawals to the use of surface-water diversions to 

meet most city water demand. An integrated system of 

water-supply lines will allow ground-water 

withdrawals to supplement surface-water supplies 

during times of high demand or drought. A simulationoptinlization approach was used to investigate how the 

City of Albuquerque could distribute ground-water 

withdrawals among its municipal-supply wells for 

2006 through 2040 to achieve certain management 

objectives for the river-aquifer system of the Middle 

Rio Grande Basin. 

The most recent revision of the U.S. Geological 

Survey ground-water-flow model for the Middle Rio 

Grande Basin was used to simulate the response of the 

aquifer system to unit stresses (ground-water 

withdrawals) applied in each of the 25 well fields 

operated by the City of Albuquerque for municipal 

supply. The resultant "response functions" provided 

important information on the effects of ground-water 

withdrawals in different locations on the quantity of 

water depleted from aquifer storage, the quantity of 

leakage from the Rio Grande and associated groundwater drains, and the magnitude of water-level declines 

over time. The well fields that caused the smallest 

depletion of aquifer storage in the simulation model 

generally also had the largest effect on the river system. 

Most of these fields are located very close to the Rio 

Grande, but others located several miles from the river 

also had a large effect on the river system because the 

wells are completed in high-conductivity sediments 

with a good hydraulic connection to the river system. 

Well fields with the largest effect on aquifer storage and 

the smallest effect on the river system included fields 

located farthest from the Rio Grande and fields 

completed in low-conductivity sediments that allowed 

only a poor connection with the river system, despite 

their location within a couple nliles of the Rio Grande. 

The response functions from the simulation 

model were incorporated into five optimization models 

that were designed in a mathematical programming 

software package and solved with a linear approach. 

The five models were designed to optimize the annual 

withdrawal between 2006 and 2040 from each well 

field to achieve specified objectives. The objectives of 

all five optimization models were to nlininlize the 

effects of ground-water withdrawal on aquifer storage 

and (or) leakage from the river and drains. All five 

models also included constraints related to projected 

annual ground-water demand, annual well field 

capacity, and annual minimum withdrawal per well. 

Selected models also included constraints related to 

maximum allowable water-level decline, maximum 

blended arsenic concentration, and (or) maximum 

induced infiltration from the river system. 

Results from the optinlization models 

demonstrated that altering the relative distribution of 

ground-water withdrawal that was used by the City of 

Albuquerque in 2000 could achieve substantial 

changes to components of the river-aquifer system over 

the period of interest. The models that incorporated 

objectives to minimize use of water from aquifer 

storage indicated that optimization of ground-water 

withdrawals over a 34-year period could result in about 

242,000 acre-feet greater recovery of water in aquifer 

storage than the non-optimal distribution-enough 

water to supply City of Albuquerque customers for 

about 2 years at year-2000 rates of water den1and. 

Simulated water-level rises as a result of this greater 

recovery of aquifer storage were as much as 70 feet in 

parts of Albuquerque between 2000 and 2040. 

Alternatively, a model that incorporated an objective to 

minimize leakage of water from the river system 

indicated that river depletion could be reduced by about 

214,000 acre-feet over a 34-year period. Another 

optimization model was designed to minimize leakage 

from the river system until the quantity of streamflow 

that the City of Albuquerque is legally required to 

contribute to the Rio Grande (to offset the effects of 
ground-water withdrawals until that time) had been 

reduced to zero, and to subsequently minimize use of 

water from aquifer storage. The model indicated that 

this "debt" to the Rio Grande could be eliminated after 

about 9 years by using an optimal withdrawal 

distribution, which is about 9 years earlier than would 

be achieved using the year-2000 distribution of groundwater withdrawal. The objectives of this model also 

could be achieved while keeping water-level declines 

less than about 2.5 feet per year. 

Results of the optimization models were 

evaluated for their ability to approximate the water 

budgets and water-level declines produced by the 

simulation model, as well as for their applicability to a 

range of river-aquifer conditions. Comparison between 

optimization calculations and simulation results 

indicated that all five optimization models provided a 

reasonable approximation of the river-aquifer system 

as represented in the ground-water-flow model, despite 

the nonlinearities inherent in that model. The response 

functions used in the optimization models, and 

therefore the results of the optimization models, also 

were found to be applicable to a reasonable range of 

river conditions and ground-water withdrawal 

scenarios. Although the exact solutions to the 

optimization models would vary with changes in future 

water demand, the locations of municipal-supply wells, 

or other factors, the broader implications of model 

results for the river-aquifer system would remain 

important to the management of regional water 

resources. In particular, information learned about the 

timing and magnitude of effects of ground-water 

withdrawals in different locations on aquifer storage 

and on the river system could be applied to multiple 

management issues in the Middle Rio Grande Basin, 

and perhaps in other alluvial basins of the 

Southwestern United States. 

INTRODUCTION 

In 2003, U.S. Department of the Interior 

Secretary Gale Norton declared the Middle Rio Grande 

Basin (MRGB) of central New Mexico (fig. 1) to be an 

area with a high likelihood of experiencing a watersupply crisis by 2025 (U.S. Department of the Interior, 

2003). The surface waters of the Rio Grande, which is 

the main drainage for the basin, are considered fully 

appropriated (Bartolino and Cole, 2002). The river 

system is hydraulically connected to the sedin1ents of 

the Santa Fe Group aquifer system, from which more 

2 

than 100,000 acre-feet (acre-ft) of ground water is 

pumped each year. Because ground-water pumping can 

affect the river system and New Mexico's obligations 

to Texas under the Rio Grande Compact, the New 

Mexico State Engineer established guidelines in 2000 

for review of applications for ground-water rights 

within the Middle Rio Grande Administrative Area 

(New Mexico Office of the State Engineer, 2003). The 

stated objectives of these guidelines reflect several of 

the major management issues within the MRGB, 

including "to ensure compliance with the Rio Grande 

Compact, to prevent impairment to existing rights, to 

limit the rate of decline of groundwater levels so that 

the life of the aquifer is extended, and to minimize land 

subsidence" (New Mexico Office of the State Engineer, 

2003, p. 1). 

The largest current (2003) user of ground water 

within the MRGB, the City of Albuquerque (COA), has 

adopted a water-supply strategy that calls for a 

transition from complete reliance on ground-water 

withdrawals from about 90 municipal-supply wells to 

the use of surface-water diversions to meet most city 

water demand. City managers decided to begin 

exercising Albuquerque's surface-water rights through 

direct diversions to attempt to delay or avoid the 

potential deleterious effects of continuous and large 

declines in ground-water levels in the major aquifer of 

the MRGB. This substantial shift in the primary source 

of water used for Albuquerque municipal supply will 

have a large effect on the river-aquifer system. 

Although surface-water diversions are anticipated to 

meet most city demand, ground-water withdrawals will 

be needed to supplement surface-water supplies during 

times of high demand or drought. A study conducted 

by the U.S. Geological Survey (USGS), in cooperation 

with the COA Public Works Department, used a 

ground-water-flow model to estimate the effects of 

various distributions of city ground-water withdrawals 

on the water budget and water levels of the aquifer. 

Simulation-optimization techniques were then used to 

determine the ground-water withdrawal distributions 

that could best achieve certain management objectives 

for the river-aquifer system of the MRGB. Many of the 

conclusions from this study also are likely to apply to 

other alluvial basins of the Southwestern United States 

with similar hydrologic regimes and watermanagement issues. 
35 . 

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Middle Rioprande 

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15 ' Base compiled from U.S. Geological Survey digital data, I :100,000, 

1977. 1978; and City of Albuquerque digital data, 1:2,400, 1994 

45 ' 

0 10 20 30 MILES 

0 10 20 30 KILOMETERS 

30 ' 

Jemez J 

Mountains 

,-_ 

-4bo'-' 

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Figure 1. Selected features of the Middle Rio Grande Basin, central New Mexico. 

3 
Water Use in the Middle Rio Grande Basin 

The Santa Fe Group aquifer system of the 

MRGB is currently (2003) the almost exclusive source 

of water for municipal, domestic, commercial, and 

industrial uses in the basin (table 1). Ground water has 

been a primary source of household supply for 

residents of the basin sirice at least the early part of the 

20th century. In 1905, the COA obtained its municipal 

water supply from 10 wells located in the inner valley 

of the Rio Grande (Lee, 1907). By 1940, Albuquerque 

was withdrawing about 4 million gallons (gal) per 

day-more than 4,000 acre-feet per year 

(acre-ft/yr)-to supply approximately 35,000 people 

(Bjorklund and Maxwell, 1961). Rapid regional 

population growth in subsequent years resulted in a 

population in 2000 of nearly 449,000 people in the 

COA and about 690,000 in the MRGB (Bartolino and 

Cole, 2002). During the 1990's, annual ground-water 

pumping by Albuquerque ranged between 

approximately 110,000 and 124,000 acre-ft (files of the 

COA), amounting to about three-quarters of the annual 

basinwide pumping of about 150,000 to 160,000 acreft (McAda and Barroll, 2002; files of the Office of the 

New Mexico State Engineer, Albuquerque). Water-use 

estimates for 1995 for the four counties that have large 

areas within the MRGB, which extends from Cochiti 

Lake on the north to San Acacia on the south, are 

summarized in table 1. 

As a result of large ground-water withdrawals, 

annual outflow from the aquifer system of the MRGB 

is substantially greater than annual inflow to the aquifer 

system (Bartolino and Cole, 2002; McAda and Barron, 

2002). This situation has caused water-level 9eclines 

exceeding 120 feet (ft) in parts of the aquifer (fig. 2) 

(Bexfield and Anderholm, 2002), which has raised 

concerns about the potential for substantial landsurface subsidence in the future (Haneberg, 1995). In 

2002, water-level declines relative to predevelopment 

conditions were largest near COA well fields located 

east of the Rio Grande. However, substantial declines 

associated with pumping by both Albuquerque and 

other users extend beyond Albuquerque limits to other 

communities, including the City of Rio Rancho, the 

Sandia and Isleta Indian Reservations, and Kirtland Air 

Force Base (fig. 2). Because of the hydraulic 

connection between the Rio Grande and the aquifer 

system in the basin, ground-water withdrawals and the 

associated water-level declines have decreased flow in 

the Rio Grande (McAda and Barron, 2002). The Rio 

Grande provides most of the water used for irrigated 

4 

crops in the basin (table 1), estimated at about 63,000 

acres in 1992 (Thorn and others, 1993). Irrigators hold 

most of the senior water rights in the basin (Bartolino 

and Cole, 2002). The reach of the Rio Grande that 

flows through the basin also is home to an endangered 

species, the Rio Grande silvery minnow, and is used by 

Indian Pueblos for ceremonial purposes. 

Recognition that continued use of ground water 

to meet all water demand by the COA is not sustainable 

and may lead to the inception or continuation of a 

number of regional-scale problems, including 

increased drilling and pumping costs, land-surface 

subsidence, deterioration of the quality of available 

ground water, and decreased surface-water availability, 

has led the COA to revise its water-resources strategy. 

By 1997, the COA had started a water conservation 

program and adopted a new formal strategy to begin 

water-recycling projects and to transition toward the 

direct use of surface water to meet most city water 

demand. During the 1960's, the COA was one of 

several entities (including the Middle Rio Grande 

Conservancy District and the municipalities of 

Bernalillo, Los Lunas, and Belen; fig. 1) to contract 

with the U.S. Department of the Interior to purchase 

rights to water associated with the San Juan-Chama 

Transmountain Diversion Project (Bartolino and Cole, 

2002; City of Albuquerque, 2003). Albuquerque owns 

48,200 acre-ft/yr of the water that the project is allowed 

to divert across the Continental Divide from streams in 

the Colorado River Basin to the Rio Grande Basin, 

where the water is stored in reservoirs upstream from 

the city. In addition, the city owns rights to about 

23,000 acre-ft/yr of native Rio Grande water. Currently 

(2003), much of the surface water owned by 

Albuquerque is allowed to flow past the city to offset 

the effects of ground-water withdrawals on the river. As 

designed, the new water-resources strategy calls 

instead for the diversion of 94,000 acre-ft of water per 

year from the Rio Grande just upstream from 

Albuquerque and the return of the 4 7,000 acre-ft/yr that 

is not consumed back to the river at the southern end of 

the city (City of Albuquerque, 2003), beginning in 

2006. Limited ground-water withdrawals would be 

used to supplement water supplies primarily during 

periods of large demand or drought. 

Because the COA is the largest single user of 

ground water in the MRGB, a shift by the COA to a 

municipal water supply based primarily on surfacewater diversions will have substantial effects on the 

river-aquifer system of the basin. Using the McAda and 
Table 1. Water-use estimates for selected counties of the Middle Rio Grande Basin in 1995 

[data fron1 Wilson and Lucero, 1997] 

Surface- Groundwater water Total 

County withdrawal withdrawal withdrawal 

(fig. 1) Category (acre-feet) (acre-feet) (acre-feet) 

Bernalillo Public water supply 0.00 135,467.80 135,467.80 

Domestic 0.00 2,162.33 2,162.33 

Irrigated agriculture and livestock 65,261.43 4,661.87 69,923.30 

Commercial, industrial, mining, and power generation 0.00 5,107.96 5,107.96 

Reservoir evaporation 0.00 0.00 0.00 

County totals: 65,261.43 147,399.96 212,661.39 

Sandoval Public water supply 125.95 15,201.07 15,327.02 

Domestic 0.00 2,529.00 2,529.00 

Irrigated agriculture and livestock 54,629.41 1,166.95 55,796.36 

Commercial, industrial, mining, and power generation 10.00 1,987.60 I ,997.60 

Reservoir evaporation 15,033.00 0.00 15,033.00 

County totals: 69,798.36 20,884.62 90,682.98 

Socorro Public water supply 0.00 2,183.55 2,183.55 

Domestic 0.00 323.23 323.23 

Irrigated agriculture and livestock 122,610.61 38,596.13 161,206.74 

Commercial, industrial, mining, and power generation 0.00 l ,079.76 l ,079.76 

Reservoir evaporation 7,570.00 0.00 7,570.00 

County totals: 130,180.61 42,182.67 172,363.28 

Valencia Public water supply 0.00 4,917.37 4,917.37 

Domestic 0.00 3,302.98 3,302.98 

Irrigated agriculture and livestock 182,737.03 9,361.22 192,098.25 

Commercial, industrial, mining, and power generation 0.00 1,116.73 1,116.73 

Reservoir evaporation 0.00 0.00 0.00 

County totals: 182,737.03 18,698.30 201,435.33 

Totals Public water supply 125.95 157,769.79 157,895.74 

Domestic 0.00 8,317.54 8,317.54 

Irrigated agriculture and livestock 425,238.48 53,786.17 479,024.65 

Commercial, industrial, mining, and power generation 10.00 9,292.05 9,302.05 

Reservoir evaporation 22,603.00 0.00 22,603.00 

Total for all counties: 447,977.43 229,165.55 677,142.98 

5 
35 ' 

15' 

10' 

o5 · 

35' 

oo· 

0 

I 

0 2 

2 

40' 

4 6 MILES 

4 6 KILOMETERS 

35' 106' 30 ' 

:J 

. I 

: 'J',.,C;IIoi""(:J: I I 1 ~ r 1 

I 

I 

I 

I 1 KIRTLAND I I 

I I 

~ r 

I I 

I I 

1:21 ) 

I I 

I 1 

I 

AIR FORCE 

~~s~ BASE 

I / / RESERVATION l__ __._ 

EXPLANATION 

NATIONAL 

FOREST 

CIBOLA 

f-

(J) 

w 

0:: 

0 

u.. 

..J 

<( 

z 

0 

~ z 

Estimated water-level decline. in feet , 1960 to 2002 

No decline 40 to 60 • 100 to 120 

• More than 120 

I 

0 to 20 

20 to 40 

60 to 80 

. 80 to 100 '-----' Decline not estimated 

.o,~' ~ Water-level contour--Interval 20 feet. Dashed where 

t>y inferred . Datum is NGVD 29 

~ Generalized direction of ground-water flow 

Figure 2. Water levels representing 1999-2002 conditions in the production zone and estimated 

water-level declines, 1960 to 2002 (modified from Bexfield and Anderholm, 2002). 

6 
Barroll (2002) ground-water-flow model of the MRGB, 

Bexfield and McAda (2003) simulated the waterbudget and water-level effects of different rates of 

annual ground-water withdrawals by the COA through 

2040. The McAda and Barron (2002) model, which is 

the most recent of several computer models developed 

by the USGS for the basin, incorporates improvements 

in the knowledge of the geohydrology of the basin 

obtained through a 6-year effort started in 1995 by the 

USGS and other agencies (including the New Mexico 

Bureau of Geology and Mineral Resources, the New 

Mexico Office of the State Engineer (NMOSE), the 

COA, and the University of New Mexico) to gain 

additional scientific information needed for waterresources management in the basin (Bartolino, 1997). 

Although the solutions provided by ground-water-flow 

models to posed problems are approximate, models 

that provide a reasonable representation of the complex 

geohydrologic processes of the basin can be very useful 

in water-resources planning by estimating the effects of 

particular stresses on the river-aquifer system (McAda 

and Barrell, 2002). 

Because the ground-water-flow model of the 

MRGB can provide estimates of the effects of 

individual stresses (particularly specified locations and 

magnitudes of ground-water withdrawals) on water 

levels and on the various components of the water 

budget, the model can be used in combination with 

optimization techniques to help determine pumping 

strategies that will best achieve particular management 

objectives. When the COA shifts to surface water as its 

primary source of municipal water supply, associated 

changes in infrastructure will allow much greater 

flexibility in pumping strategies than has previously 

been possible. Individual city well fields, which are 

limited at the current time (2003) to supplying water to 

only small sections of city customers, will be 

interconnected to allow a single well field to supply any 

of the city's customers. This change (along with 

reduced ground-water withdrawals relative to overall 

well capacity) will permit Albuquerque to select 

pumping strategies that not only meet immediate 

obligations to water customers, but that also benefit the 

multitude of regional water users and the hydrologic 

system as a whole. Examples of management 

objectives that might be beneficial to regional water 

users include minimizing water-level decline in the 

aquifer or minimizing induced leakage from the Rio 

Grande. 

7 

Purpose and Scope 

This report presents results of a simulationoptimization approach to the assessment of strategies 

for ground-water withdrawal by the COA that can be 

used to best achieve particular management objectives 

for 2006 through 2040. The ground-water-flow model 

of McAda and Barrell (2002) for the MRGB was used 

to estimate the effects of specified quantities of groundwater withdrawal from individual COA well fields on 

water levels and water budgets for the aquifer. This 

report discusses the simulated effects and their 

implications for management of water resources in the 

basin. The sin1ulated effects were used in the 

formulation of five constrained optimization models 

designed to achieve specified objectives by adjusting 

the distribution of ground-water withdrawal among 

COA well fields through 2040. The five models 

incorporate objectives of minimizing depletion of 

aquifer storage and (or) minimizing leakage from the 

river system into the aquifer. All five optimization 

models include constraints related to water demand, 

well-field capacity, and minimum withdrawal 

requirements. Three models also include constraints 

related to water-level declines, arsenic concentrations, 

and (or) water-rights issues. This report presents the 

formulation and results of all five optimization 

scenarios. 

Previous Investigations 

Comprehensive publications on the 

geohydrologic framework of the MRGB (also known 

as the Albuquerque Basin) were published in the early 

1990's, perhaps most notably by Hawley and Haase 

(1992) and Thorn and others (1993). Hawley and 

Haase (1992) presented a detailed geologic framework 

for the basin that addressed structure, stratigraphy, and 

lithology. The reader is referred to their publication for 

information about major geologic studies in the basin 

up to that time. Thorn and others (1993) detailed the 

hydrologic knowledge of the MRGB, including the 

work of Bjorklund and Maxwell ( 1961) and subsequent 

investigators. The ground-water-flow model developed 

by Kernodle and others (1995) was based on the 

geohydrologic framework of Haw ley and Haase ( 1992) 

and Thorn and others (1993) and represented a 

significant update to previous ground-water-flow 

models based on earlier knowledge. The Kernodle and 

others ( 1995) model formed the primary basis for 
subsequent modifications by Kernodle (1998), 

Tiedeman and others (1998), and Barroll (2001). 

The McAda and Barroll (2002) ground-waterflow model (hereafter referred to as the McAda and 

Barron model) is the most recent substantial update to 

modeling efforts for the MRGB and is the culmination 

of a focused 6-year effo~t by the USGS and other 

agencies (including the New Mexico Bureau of 

Geology and Mineral Resources, the NMOSE, the 

COA, and the University of New Mexico) to gain 

further insight into the geohydrology of the basin. 

Studies associated with this 6-year effort included 

geologic mapping to improve knowledge of the 

structural and stratigraphic framework of the Santa Fe 

Group sediments, airborne geophysical surveys to 

identify detailed fault patterns and better characterize 

hydrologic properties of geologic units, use of 

environmental tracers to better estimate mountain-front 

recharge and streamflow loss, and investigation of 

ground-water flow using chemical and isotopic data 

(Slate, 1998). Information on the design and results of 

these studies can be found in Bartolino and Cole 

(2002), as well as in collections of extended abstracts 

edited by Bartolino (1997), Slate (1998), Bartolino 

(1999), and Cole (2001). In addition, ongoing study of 

the stratigraphy of the MRGB is described in Connell 

(2001). 

A simulation-optimization approach similar to 

the one used in the study described in this report has 

been used in several previous studies to address various 

aspects of water-resource management. Only a few 

examples of such studies are provided here. A fairly 

large body of literature is available on the use of linear, 

quadratic, and (or) mixed-integer programming 

techniques to determine the optimal placement and 

pumping rates of wells to achieve containment of 

ground-water contaminants at the lowest overall 

extraction rate. Constraints used to guarantee 

containment in these scenarios commonly involve 

bounds on head gradients (Tiedeman and Gorelick, 

1993) or velocity directions (Ratzlaff and others, 

1992). Simulation-optimization also has been applied 

to the identification of ground-water withdrawal 

strategies to control shallow water tables in areas of 

irrigated agriculture. For example, Barlow and others 

(1996) explicitly linked a MOD FLOW (McDonald and 

Harbaugh, 1988) simulation model of ground-water 

flow in the western San Joaquin Valley, California, with 

an optimization program to minimize the areal extent 

of the shallow water table. Conversely, optimization 

8 

techniques have been applied to the problem of 

minimizing water-level decline within specified 

demand constraints. Danskin (1998) used a semiquantitative optimization approach to this problem in 

the Owens Valley of east-central California. Barlow 

and Dickerman (200 1) used a simulation-optimization 

approach to evaluate alternatives for the conjunctive 

management of ground- and surface-water resources in 

eastern Rhode Island, wherein ground-water 

withdrawals were maximized within specified 

limitations on streamflow depletion. As a final example 

of the use of optimization techniques in waterresources management, Nishikawa (1998) used a 

MOD FLOW simulation model of ground-water flow in 

the Santa Barbara, California, area in combination with 

optimization software to minimize the total cost of 

water supply from both ground- and surface-water 

sources while meeting demand and satisfying 

constraints related to water-supply capacity, pumping 

distribution, and heads in the aquifer along the 

seacoast. 

Acknowledgments 

The authors thank Greg Gates with CH2M Hill 

for providing the projections of future water demand 

for the COA that were used in this study. The authors 

also thank John Stomp with the COA Public Works 

Department for supporting this study and for helping to 

identify optimization scenarios that would be of the 

greatest benefit to regional water users. 

BACKGROUND ON THE STUDY AREA 

AND THE GROUND-WATER-FLOW 

MODEL 

A complete understanding of the water-resource 

management issues in the MRGB and the simulationoptimization approach used in this report to address 

them requires knowledge of the study area and the 

ground-water-flow model used to represent it. 

Therefore, this section describes the geohydrologic and 

water-use characteristics of the MRGB, followed by a 

discussion of the design of the McAda and Barron 

model. 
Description of the Study Area 

The geohydrology of the MRGB has been 

described previously by Hawley and Haase (1992), 

Thorn and others (1993), Bartolino and Cole (2002), 

and McAda and Barron (2002). Therefore, only a brief 

summary of the information available in those 

publications is provided here. As defined for this study, 

the MRGB covers about 3,060 square miles (mi2) in 

central New Mexico, delineated by the extent of 

deposits of Cenozoic age between Cochiti Lake on the 

north and San Acacia on the south (fig. 1). The MRGB 

is one of a series of alluvial basins stretchino- alono- an l::> l::> 

area of Cenozoic crustal extension known as the Rio 

Grande Rift and is hydraulically connected to the 

Espanola Basin to the north and the Socorro Basin to 

the south. The basin is bounded along most of the east 

and southeast by the Sandia, Manzano, Los Pinos, and 

Joyita Uplifts (fig. 3), which exceed 10,000 ft in 

altitude in places. The Jemez and Nacimiento Uplifts 

and Jemez Mountains form boundaries of similar 

magnitude along the north and northwest. The 

generally more subdued boundaries along the west and 

southwest include the Lucero and Ladron Uplifts. The 

MRGB is composed of three subbasins, the Santo 

Domingo, Calabacillas, and Belen subbasins (fig. 3), 

which are separated by bedrock structural highs. The 

deep, inner portions of these subbasins, where the 

thickness of alluvial fill exceeds 14,000 ft in places, 

generally are bordered on the sides by relatively 

shallow benches. In addition to major faults that bound 

the MRGB, numerous faults occur within the Santa Fe 

Group sediments of the basin (fig. 3). Faults in the 

region align primarily north to south and offset 

sediments of substantially different lithology in some 

areas. 

The generally unconsolidated to moderately 

consolidated basin-fill sediments of the MRGB include 

primarily the Santa Fe Group deposits of late 

Oligocene to middle Pleistocene age and the post-Santa 

Fe Group alluvium of Pleistocene to Holocene age. 

These sediments tend to be hydraulically connected, 

and together they form the Santa Fe Group aquifer 

system as defined by Thorn and others (1993). Hawley 

and Haase ( 1992) divided the Santa Fe Group deposits 

into broad lower, middle, and upper parts of distinct 

age and depositional environment. The lower Santa Fe 

Group sediments, which range in thickness from less 

than 1,000 to about 3,500 ft, contain a substantial 

fraction of basin-floor playa deposits, which compose 

poor aquifer materials (Hawley and Haase, 1992). The 

9 

middle Santa Fe Group sediments, which range from 

about 250 to 9,000 ft thick, accumulated during a tin1e 

of large sedimentation rates and include substantial 

fluvial deposits in the north in addition to pie&nontslope deposits along basin margins and playa deposits 

in the south (Hawley and Haase, 1992). Sediments of 

the Santa Fe Group are most permeable in the upper 

section, which tends to be less than 1,000 ft thick and 

consists largely of intertonguing piedmont-slope and 

fluvial basin-floor deposits (Hawley and Haase, 1992). 

Quaternary post-Santa Fe Group sediments include the 

valley fill (as much as about 130ft in thickness) that 

accumulated during cutting and partial backfilling 

episodes of the Rio Grande and Rio Puerco (Hawley 

and Haase, 1992). Water-supply wells used by the COA 

are completed primarily in sediments of the upper or 

middle Santa Fe Group (fig. 4). 

In the semiarid MRGB, where potential 

evapotranspiration greatly exceeds precipitation, any 

contribution made to the aquifer system by direct 

recharge of precipitation is negligible. Most recharge 

occurs by infiltration of water through streams, 

subsurface inflow from adjacent basins, or mountainfront/tributary recharge along basin margins (Thorn 

and others, 1993; Kernodle and others, 1995; McAda 

and Barroll, 2002). Recharge also occurs through 

irrigation and septic-field seepage (McAda and Barroll, 

2002). Maps of conditions in the MRGB prior to about 

1960 (Meeks, 1949; Bjorklund and Maxwell, 1961; 

Titus, 1961; Bexfield and Anderholm, 2000) show that 

the primary direction of ground-water flow through the 

basin is north to south, and that components of eastwest flow are largest near basin margins. However, 

ground-water with&·awals by the COA and others have 

since resulted in large-scale alteration of hydraulic 

heads near Albuquerque, so that ground-water 

movement is toward the major pumping centers (both 

east and west of the Rio Grande) from all directions 

(fig. 2). Head declines also have induced greater 

leakage from the river system into the aquifer than 

occurred under predevelopment conditions. Groundwater withdrawals are a major component of modern 

discharge from the aquifer system, as are 

evapotranspiration and loss of water to the drain system 

or to some reaches of the Rio Grande (McAda and 

Barron, 2002). Some ground water also discharges to 

the Socorro Basin to the south.The Rio Grande, which 

is inset in a terraced valley more than 5 miles wide in 

places, extends the entire length of the MRGB from 

north to south and is the main surface-water feature of 
35. 

45 ' 

30' -

35 · 

oo· 

P.i? >" .. 

' \ 

45' -

30 ' 

34' 

-.... 

107. 15 ' 

T 

., Middle Rio . .Grande 

Basin bo dary 

\,U> 

~?-J e. 

L-". 

\ 

~ 

l 

"- .1?,-o ~ .......... ""() 

'. c. 

~ \ <¢ 

/ 

~ 

~ 

... :.·····?········ .... 

i 

\ 

~ 

45 ' 

1 5 ' Base compiled from U.S. Geological Survey digital data, 1:100,000, 

1977, 1978; and City of Albuquerque digital data. 1:2,400, 1994 . 

Faults modified from Mark Hudson and Scott Minor. U.S. Geological 

Survey, written commun., 1999 

0 10 20 30 MILES 

0 10 20 30 KILOMETERS 

106. 15 ' 

EXPLANATION 

Fault 

--- : 

• :OQ! 1 "0 i ~0> : Q>.J>,; 

c 

'iii 

ro 

00 

ro 

'(3 

c 

ro 

u; 

w 

Figure 3. Major structural features of the Middle Rio Grande Basin (subbasin 

locations modified from Grauch and others, 1999). 

10 
~ 

~ 

A 

FEET 

6.000 ., 

5.000 

4,000 

!'sal 

3,000 

Qrp: 

Qp: 

Qpr: 

I QTsa: I 

QTsp: 

Ill 

Walker 2 

r-- ---- East Heights Fault Zone 

Coronado Eubank Blvd . 

strand -;::- strand 

Alameda 

strand Sandia Fault Zone 

"' N West East 

Cii "' 

c N _E .Q 

o-oU 

""'Q) 

"' 

Q) 

.><. 

Q) 

.><. Embudo Embudo 

u; 

Q; 

c 

~~~ "' ~ strand strand 

---- a'r5a 

Tsar 

o ·-o o e Q) ap u~~ 

-"' -

QTsa 

QTsa 

Tsal Tsal 

0 1 MILE -' 

0 1 KILOMETER 

Vertical coordinate information referenced to NGVD 29 

Vertical exaggeration x 2 

EXPLANATION 

:.;: "':.;: 

QTsp 

QTsp 

Los Padillas Formation (historical to uppermost Pleistocene)--Unconsolidated to poorly consolidated , fine- to coarse-grained 

sand and rounded gravel with interbeds of fine-grained sand, silt, and clay derived from the Rio Grande 

Piedmont and stream alluvium , undivided (historical to middle Pleistocene) 

Fluvial deposits , piedmont alluvium , and stream alluvium , undivided (historical to middle Pleistocene ) 

Axial-fluvial deposits of the ancestral Rio Grande , undivided (lower Pleistocene to Pl iocene); part of the upper Santa Fe 

Group of Hawley and Haase (1992) 

QTsa2 : Upper sandy mudstone marker bed (Pliocene) 

QTsa 1: Lower sandy mudstone marker bed (Pl iocene) 

Piedmont deposits (lower Pleistocene to Miocene); part of the upper Santa Fe Group of Hawley and Haase (1992) 

Arroyo Oj ito Formation , Atrisco Member (Piiocene)--Moderately to well consolidated , locally cemented succession of finegrained silty sandstone and mudstone; part of the middle Santa Fe Group of Hawley and Haase (1992) 

Lower fluvial deposits (Pliocene to upper Miocene); part of the middle Santa Fe Group of Hawley and Haase (1992) 

Lower Tertiary and Cretaceous sedimentary rocks , undivided (Paleogene-Cretaceous) 

Fault showing relative movement 

Municipal-supply well 

TKu 

QTsp 

Figure 4. Geologic section along Paseo del Norte in northern Albuquerque (modified from Connell , 1997). 

See figure 5 for section location . Formations and member names usage of New Mexico Bureau 

of Geology and Mineral Resources. 

A' 

FEET 

6,000 

5,000 

4,000 

3.000 
the basin (fig. 1 ). The mean annual discharge of the Rio 

Grande at Albuquerque was about 1,400 cubic feet per 

second for 1974 through 2000 (Ortiz and others, 2001), 

which equals an annual volume of riverfiow of about 

1.01 million acre-ft. Human influences on the flow of 

the modern-day Rio Grande include reservoirs, 

irrigation diversions and return flows, inflow from 

wastewater-treatment plants, and inflow from the San 

Juan-Chama Project. Within the MRGB, 

anthropogenic structures confine the Rio Grande to a 

single channel and divert water from the river into a 

network of irrigation canals that extend throughout the 

inner valley. Ground-water drains intercept seepage 

from the irrigation canals, applied irrigation water, and 

the Rio Grande and ultimately discharge this water 

back into the river. The system of drains prevents the 

water table from rising close enough to land surface to 

harm crops. Tributaries that contribute flow to the Rio 

Grande within the MRGB include the Santa Fe River, 

Jemez River, Rio Puerco, and Rio Salado; of these, 

only the Jemez River is perennial through most of its 

length within the basin. Within the MRGB, the Rio 

Grande and the Jemez River lose water to the aquifer 

throughout most reaches (McAda and Barrell, 2002). 

As indicated in table 1, combined surface-water 

withdrawals for the major counties of the MRGB are 

larger than combined ground-water withdrawals. The 

main consumptive use of surface water is for irrigated 

agriculture, primarily along the Rio Grande and the 

Jemez River. Surface water also is consumed by 

reservoir evaporation, recharge to ground water, and 

evapotranspiration by riparian vegetation (Bartolino 

and Cole, 2002). Nonconsumptive uses of surface 

water in the basin include recreation and ceremonial 

use by Pueblos. Within the basin, the Rio Grande also 

provides habitat for the endangered Rio Grande silvery 

minnow. As indicated in the "Introduction," the COA 

plans to begin withdrawing most of its municipal 

supply directly from the Rio Grande in 2006. 

Albuquerque currently (2003) withdraws the largest 

amount of ground water from the basin, pumping about 

114,000 acre-ft in 2000. The more than 90 municipalsupply wells owned by Albuquerque are scattered 

throughout the city (fig. 5). As discussed by Bartolino 

and Cole (2002), other municipalities that currently 

withdraw ground water for public supply include 

Bernalillo, Rio Rancho, Bosque Farms, Los Lunas, and 

Belen. Kirtland Air Force Base, the University of New 

Mexico, and private utilities such as Sandia Peak 

Utility Company and New Mexico Utilities 

12 

Incorporated also operate public-supply wells. Other 

users of ground water within the basin include 

numerous domestic-well owners and several 

commercial operations, such as Intel Corporation in 

Rio Rancho. 

McAda and Barroll Model 

The McAda and Barrell model of ground-water 

flow in the Santa Fe Group aquifer system of the 

MRGB is a three-dimensional, finite-difference model 

developed using MODFLOW-2000 (Harbaugh and 

others, 2000). The model is intended to enhance 

understanding of the geohydrology of the MRGB and 

to provide a tool to aid in management of water 

resources in the basin. Only certain aspects of the 

model are discussed here, and the reader is referred to 

McAda and Barrell (2002) for additional information. 

The McAda and Barrell model covers about 

2,350 mi2, which is smaller than the total area of the 

MRGB. Although the model extends to the basin 

boundaries on the north and south (fig. 6), it extends 

only to selected faults on the east and west that are 

thought to fom1 distinct hydrologic boundaries 

(McAda and Barrell, 2002). The area represented by 

the model is divided into a horizontal uniform grid 

containing 156 rows and 80 columns, each spaced 

3,281 ft (1 kilometer) apart. The grid is oriented northsouth to align with the principal directions of 

anisotropy caused by structural features and patterns in 

sedimentation. 

The simulated thickness of the Santa Fe Group 

aquifer system in the McAda and Barrell model varies 

from about 100 ft near some basin margins to about 

14,000 ft in the basin interior, extending from the water 

table (typically 4,700 to 5,600 ft above NGVD 29) to 

pre-Santa Fe Group basement rocks as much as 9,000 

ft below NGVD 29. The aquifer system is divided into 

nine model layers (fig. 7). The upper five layers are of 

variable thickness across the modeled area, depending 

on the altitude of the steady-state simulated water table 

relative to the bottom altitude of layer 5. Layer 1 is 

relatively thin (30ft thick directly below the Rio 

Grande) to simulate ground-water/surface-water 

interaction in the inner valley. Layers 2 through 5 are 

50, 100, 220, and 400ft thick, respectively, directly 

below the Rio Grande under simulated steady-state 

conditions (fig. 7). Layers 6 and 7 have constant 

thicknesses of 600 and 1,000 ft, respectively, 

throughout the modeled area. The top one-third of the 
35 . 

15' 

10 ' 

as· 

35 . 

oo · 

106. 45 ' 

\ 

/ 

! 

\ 

' o- \ t<> -. 

40 ' 

,.... .- ·· - ··s .... c/ er3 /' ··- I 

35 ' 

,. ...... . ,..; - -·· 

i 

106. 30 ' 

CIBOLA 

NATIONAL 

FOREST 

CIAOLA 

NATIONAl 

,... .. / Arroyo 

KIRTLAND 

AIR FORCE 

BASE 

..J 

< z 

0 

~ z 

< ..J 

0 

m 

u 

INDIAN RESERVATION 

Base comprled from U.S Geologrcal Survey drgrlal data. 1:100.000, 

1977, 1978; and Crty of Albuquerque drgrtal data , 1:2,400. 1994 

0 2 4 6 MILES 

0 2 4 6 KILOMETERS 

EXPLANATION 

MUNICIPAL-SUPPLY WELLS: 

t-1 Line of section ~ Line delineating wells 

A A' (fig. 4) included in the same field 

Lomas Well field name 

• 1 Well and well number 

Figure 5. City of Albuquerque municipal-supply wells. 

13 
30 

15 ' 

35 ° 

00' 

45 

30' 

;:: 

n 

" z 

5 

n 

0 

c 

z 

~ 

n 

~ 

£: 

n 

0 

c: 

z 

~ 

Base derived from U.S. Census Bureau digital 

Tiger data and from U.S. Geological Survey 

digital data. Scale 1:100,000 

t;lti · 

0 

f5 10 15 20 25 MILES r ...~..._ T T 

0 5 10 15 20 25 KILOMETERS 

(/) 

Ql 

" 0. 

a;· 

~ 

0 

c 

.. 't» " 

s· 

"' 

~ 0 Ql 

c " :J N ... QI 

. "' Ql 

~ TORRANCE 0 

c COUNTY 

;:>. 

Ql 

s· 

"' 

EXPLANATION 

• River cell 

• River and riverside-drain cell 

Tributary-recharge cell 

• Mountain-front-recharge cell 

Subsurface-recharge cell 

• Tributary- and subsurface-recharge cell 

~ z 

~ ., 

"' n 

0 

c 

z 

~ 

Figure 6. Model grid showing active cel ls in layer 1 of the McAda and Barrell (2002) model 

(modified from McAda and Barrell, 2002, fig . 7). 

14 
Santa Fe Group thickness below the bottom of layer 7 

is assigned to layer 8, and the bottom two-thirds are 

assigned to layer 9 (fig. 7). Cells in layers 1-7 are active 

where the center of the cell is higher in altitude than the 

base of the Santa Fe Group, whereas cells in model 

layers 8 and 9 are active only where their combined 

thickness is at least 1 ,200 ft. To allow the simulated 

water table to transfer to the next lower cell as 

simulated water levels decline below the bottom of a 

cell, layers 1-4 are represented as convertible between 

confined and water-table conditions (Harbaugh and 

others, 2000). Model layers 5-9 are represented as 

always confined. 

Horizontal hydraulic conductivity, vertical 

hydraulic conductivity, specific storage, and specific 

yield are the hydrologic properties used to represent the 

Santa Fe Group aquifer system in the McAda and 

Barroll model. The horizontal hydraulic conductivity 

in the east-west direction (along model rows; Kx) of the 

model ranges from 0.05 to 45 feet per day (ft/d). 

Distributions of simulated horizontal hydraulic 

conductivity in the east-west direction are shown in 

figure 8 for layers 4 and 5, from which most groundwater withdrawal by the COA is simulated to occur. 

The hydraulic conductivity in the north-south direction 

(along model columns; Ky) of the model ranges from 

0.05 to 60ft/d. The horizontal anisotropy ratio (Ky /Kx) 

varies over the model domain from 1: 1 to 5: 1. 

Hydraulic conductivity between model cells is reduced 

in some areas where selected faults are simulated as 

horizontal flow barriers (fig. 8). A vertical anisotropy 

ratio (Kx IKJ of 150: 1 is applied over the model 

domain. This results in simulated vertical hydraulicconductivity values ranging from 3 x 10-4 to 3 x 10-1 

ft/d. Specific storage is simulated to be 2 X 1 o-6 fr I and 

specific yield is simulated to be 0.2 (dimensionless). 

The McAda and Barroll model simulates 

ground-water flow in the MRGB from 1900 to March 

2000. A steady-state simulation was performed prior to 

each transient simulation of the historical period, 1900 

to 2000, which is represented by 51 stress periods of 

varying length. Five-year stress periods are used from 

1900 to 1974, 1-year stress periods are used from 1975 

through 1989, and seasonal stress periods are used 

beginning in 1990. The irrigation-season (or summerseason) stress periods extend from March 16 through 

October 31 and represent the period of time that most 

irrigation canals are typically operational. The winterseason stress periods extend from November 1 to 

March 15. 

15 

The two types of mathematical boundary 

conditions used in the McAda and Barroll model are 

specified flow and head-dependent flow. At a specifiedflow boundary, water is recharged to or discharged 

from the sin1ulated aquifer system independent of 

sin1ulated head in the aquifer. A no-flow boundary, 

which is a specific case of a specified-flow boundary, is 

imposed at the bottom of layer 9 of the model. 

Mountain-front, tributary, and subsurface recharge; 

canal, crop-irligation, and septic-field seepage; and 

ground-water withdrawal are simulated as specifiedflow boundaries. Mountain-front, tlibutary, and 

subsmiace recharge from adjacent ground-water basins 

are specified to be constant throughout the simulation 

period, whereas canal, crop-irrigation, and septic-field 

seepage and ground-water withdrawal vary through the 

simulation period on the basis of historical data. 

Ground-water withdrawal from production wells 

with large screened intervals, such as those operated by 

the COA, must be divided among the various model 

layers that the screened intervals span. The screened 

intervals of COA wells (available in Bexfield and 

others, 1999) extend across as much as 1 ,000 ft of 

aquifer and four model layers (layers 3 through 6). A 

previous well-bore flow logging study in selected COA 

wells indicated that higher conductivity aquifer layers 

often do not provide the greatest proportion of flow to 

a well because of encrustation of the well screen or 

other factors (Thorn, 2000). Therefore, simulated 

ground-water withdrawal for these wells is assigned to 

model layers without consideration of aquifer 

conductivity. In most cases, withdrawal is assigned in 

proportion to a known percentage of the well screen 

installed within each layer. Exceptions occur when the 

withdrawal assigned to a particular layer would be very 

small or when assumptions must be made about 

unknown construction details of a well. The specified 

flows associated with ground-water withdrawal in the 

model are simulated to pass to the next lower cell if the 

cell for which withdrawal is assigned goes dry (see 

McAda and Barroll (2002) for modifications made to 

the Well Package of the MODFLOW-2000 code). This 

modification to the MOD FLOW code allows the 

recorded historical withdrawal quantities to occur even 

as water levels decline, rather than terminating the 

portion of withdrawal assigned to a cell that goes dry. 

In the McAda and Barroll model, the Rio 

Grande, Cochiti Lake, Jemez River, Jemez Canyon 

Reservoir, riverside drains, interior drains, and riparian 

evapotranspiration are simulated as head-dependent 
WEST 

Land surface 

Layer 2 50-80 feet thick 

Layer3 

Layer4 

Layer selected to represent 

the production zone of Layer 5 the aquifer 

800 feet below Rio Grande 

Layer 6 

Layer7 

Screened 

interval 

Deep City of 

Albuquerque 

municipalsupply well 

Typical City of 

Albuquerque 

municipalsupply well 

100-160 feet thick 

210-350 feet thick 

390-640 feet thick 

600 feet thick 

1 ,000 feet thick 

2,400 feet below Rio Grande 

LayerS 

Layer9 

Not to scale 

400-3,900 feet thick 

800-7,800 feet thick 

Pre-Santa Fe Group 

basement rock 

Figure 7. Configuration of layers in the McAda and Barroll (2002) model 

(modified from McAda and Barroll, 2002, fig. 8). 

16 

EAST 
Model layer 4 

0 5 10 15 20 25 MILES 

f---r ,_ 

0 5 1 0 15 20 25 KILOMETERS 

Model layer 5 

EXPLANATION 

Horizontal hydraulic conductivity in the east-west direction , 

in feet per day--Shows hydraulic 

conductivity along model rows . 

Hydraulic conductivity in the 

north-south direction (along 

model columns) is calculated by 

multiplying the values indicated 

below times the appropriate 

horizontal-anisotropy ratio 

between 1 and 5, as described 

by McAda and Barroll (2002) 

• 0.05 • 5.3 

• 0.5 8.0 

• 1.0 

• 1.5 

• 2.0 

D 15 

• 30 

D 45 

-- Horizontal flow barrier 

Figure 8. Distribution of simulated horizontal hydraulic conductivity in the east-west direction for selected 

layers of the McAda and Barroll (2002) model (modified from McAda and Barrol l, 2002, fig . 12). 

17 
flow boundaries (McAda and Barrell, 2002). At a headdependent flow boundary, water is recharged or 

discharged as a function of simulated hydraulic head in 

the aquuer system and specified information for the 

boundary, such as a specified Jiver stage or a specified 

evapotranspiration surface. Sp~ified boundary 

information varies through the simulation period on the 

basis of historical data. The model can estimate the 

effectsof changes in aqooer-system stresses on the 

fluxes at head-dependent flow boundaries. 

Changes in seepage between the Rio Grande and 

the aquifer as a result of changes in water-table altitude 

are of particular interest for management of water 

resources in the MRGB. Factors used by the model to 

simulate the connection between the Rio Grande and 

the aquifer include the hydraulic conductivity, 

thickness, and area of the riverbed. Hydraulic 

conductivity (in feet per day) dividedby riverbed 

thickness (in feet) was adjusted during model 

calibration from 0.5 per day to 0.1 per day to match 

flow loss estimated by Veenhuis (2002) for the Rio 

Grande and riverside drains combined. Riverbed area 

in each cell was estimated by combining geographicalinformation-system coverages of perennially and 

seasonally flooded areas of the Rio Grande with 

historically measured seasonal low and high flows at 

Albuquerque. Except for the seasonal stress periods 

( 1990-2000), the specified stage of the river was 

assumed to be the stage determined from USGS 

topographical maps. For 1990-2000, the seasonality of 

the Rio Grande was simulated by adjusting both 

riverbed area and river stage on the basis of average 

flow and the ratio of the perennially flooded area to the 

perennially and seasonally flooded area within each 

model cell. These calculations are described in detail in 

McAda and Barrell (2002). The riverside drains 

located on either side of the Rio Grande throuahout b 

most of the MRGB are closely associated with the river 

and are simulated as separate entities within the same 

model cells as the Rio Grande. Because of their varying 

functions, as described by McAda and Ban·oll (2002), 

the riverside drains are simulated to allow for either the 

loss or gain of water. 

The McAda and Barrell model was calibrated to 

measured hydraulic heads and water-budget 

components. In particular, the model-simulated 

predevelopment water table matched well with 

measured predevelopment water levels throughout 

most of the basin, including the general vicinity of 

Albuquerque. The model also was successful at 

reproducing the direction and magnitude of water-level 

changes in individual wells over time. The model 

18 

slightly overpredicted drawdown at the water table and 

in the production zone of the aquifer in the 

Albuquerque area through winter 2000, but residuals 

for water levels at both depths were within reasonable 

ranges. In general, the model also simulated known 

vertical hydraulic gradients well. In addition, the two 

quantitative flow targets available along the Rio Grande 

showed good agreement between simulated and 

measured values. Qualitative evaluation of waterbudget components al,so indicated good consistency 

between simulation of the Rio Grande and Jemez River 

smface-water systems and the observed behavior of 

these systems, such as from seepage runs. Simulated 

annual water budgets for the basin in steady state and 

for the year ending October 1999 are shown in table 2. 

The table clearly shows the effects of introduction of 

the irrigation system and of substantial ground-water 

withdrawal on inflow and outflow components of the 

water budget, relative to predevelopment times. For 

example, the budgets indicate that the riverside and 

interior drains capture much of the seepage from the 

Rio Grande, canals, and crop irrigation. The drains 

ultimately return this· water to the river. 

Simulations of Future Conditions 

The McAda and Barrell model was used to 

evaluate the future consequences of potential groundwater withdrawal strategies by the COA on 

components of the hydrologic system, including water 

levels, aquifer storage, and river leakage (Bexfield and 

McAda~ 2003). Minor modifications were made to 

allow layer 5 of the model to be convertible and to add 

two additional COA wells that began pumping for 

municipal supply shortly before 2000. Nearly all the 

most recent input parameters from the McAda and 

Barrell model, which extended through 2000, were 

duplicated without modification to lengthen the model 

through 2040. These parameters included the ones for 

mountain-front recharge, tributary recharge, underflow, 

recharge from irrigation and septic-tank seepage, drain 

conditions, and evapotranspiration conditions. Also, 

with the exception of COA data, the most recent data 

available in the McAda and Barrell model for groundwater withdrawal were duplicated for each year 

through 2040. Conditions in the Rio Grande were 

varied seasonally to match projections of future 

surface-water availability provided by Greg Gates 

(CH2M Hill, consultant to the City of Albuquerque, 

written commun., 2001), as described in more detail in 

Bexfield and McAda (2003). 
Table 2. Simulated annual water budgets for the Middle Rio Grande Basin from the McAda and 

Barron (2002) model, steady state and year ending October 1999 

[All values are in acre-feet per year] 

Steady state Year ending October 1999 

Inflow 

Mechanism (to aquifer) 

Mountain-front recharge 12,000 

Tributary recharge 9,000 

Subsurface recharge 31,000 

Canal seepage 0 

Crop-irrigation seepage 0 

Rio Grande and Cochiti Lake 63,000 

Riverside drains 0 

Interior drains 0 

Jemez River and Jemez Canyon Reservoir 15,000 

Ground-water withdrawal 0 

Septic-field seepage 0 

Riparian evapotranspiration 0 

Subtotal 130,000 

Inflow from or outflow to aquifer storage 0 

Total 130,000 

Error (inflow minus outflow) 

Three future sin1ulations using different COA 

pumping rates were designed to represent scenarios of 

medium (I), large (II), and small (III) ground-water 

use. For simulation I, ground-water withdrawal from 

all city municipal-supply wells was maintained at 

known year-2000 rates for each year through 2040 

(fig. 9), representing medium ground-water use. For 

simulation II (representing large ground-water use), 

city pumping was adjusted to simulate the use of 

ground-water withdrawal to meet all projected water 

demand, which is expected to rise substantially through 

2040. For simulation Ill (representing small groundwater use), city pumping was adjusted to match 

projections of future ground-water use that assume 

surface water is available to meet much of the total 

water demand, resulting in decreased pumping. 

"Spikes" in the otherwise fairly smooth increase in 

projected ground-water withdrawals for simulation III 

(fig. 9) represent years of drought and correspondingly 

low surface-water availability. Greg Gates (written 

commun., 2001) provided all projections of future 

water demand and surface-water availability. Annual 

adjustments to COA pumping in the model were made 

by applying a multiplying factor to known year-2000 

pumping rates (Bexfield and McAda, 2003). 

Comparisons among the results for simulations 

I, II, and III indicate that the various scenarios of 

Outflow Inflow Outflow 

(from aquifer) (to aquifer) (from aquifer) 

0 12,000 0 

0 9,000 0 

0 31,000 0 

0 90,000 0 

0 35,000 0 

0 316,000 0 

0 0 208,000 

0 0 133,000 

0 17,000 0 

0 0 150,000 

0 4,000 0 

129,000 0 84,000 

129,000 514,000 575,000 

0 60,000 0 

129,000 574,000 575,000 

1,000 -1,000 

19 

ground-water withdrawal had substantially different 

effects on water-level declines in the Albuquerque area 

and on the contribution of each water-budget 

component to the total budget for the ground-water 

system. Whereas water levels in all three simulations 

declined between 2000 and 2040 in some areas around 

Albuquerque, water levels in simulation III (small 

ground-water use) also rose over large areas (fig. 1 0). 

In simulation III (small ground-water use), the water 

table generally dec I ined less than about 10 1 ft from 

steady state through 2040, as compared with 162 ft in 

simulation I (medium ground-water use) and 199 ft in 

simulation II (large ground-water use) (table 3). In 

addition to smaller water-level declines, the reduced 

pumping of simulation III resulted in substantially 

smaller inflow to the ground-water system from aquifer 

storage and river leakage than either simulation I or II. 

The cumulative retention of water in the river between 

2000 and 2040 as a result of reduced pumping was 

about 732,000 acre-ft more than that for the medium 

ground-water use simulation and 872,000 acre-ft more 

than that for the large ground-water use simulation 

(table 3). The cumulative retention of ground water in 

storage in simulation III (small ground-water use) was 

1,536,000 acre-ft more than that for the medium 
180,000 

160,000 

Simulation I 

- - ~ ~ Simulation II 

140,000 Simulation Ill 

tli If 120,000 

uJ 

0::: 

~ 

~ 

<5 

z 

a: 

~ 

:::::> 

a.. 

~ 1-

0 

1-

100,000 

80,000 

60,000 

40,000 

20,000 

0 

1980 1990 2000 2010 2020 2030 2040 

Figure 9. Annual City of Albuquerque pumping assigned for each simulation of future 

conditions using the McAda and Barroll (2002) model, 1980 to 2040 

(from Bexfield and McAda, 2003, fig. 5). 

20 
35 " 

45 ' 

30' 

15' 

35" 

00' 

45 ' 

30' 

34 " 

107"15 ' 107"00' 

J 

l 

/emezlnd•an , 

Re-1j,ervat•o l 

.... -1 

~~ 

I ...I' 

'~ 1 oo-

'-o 

) 

?Ia 

Indian 

Reservat•on 

Middle Rio 1Grande 

Basin bouRdary 

' \. -

laguna~ lnd1an • 1 • __ 

Rcse\rvat1on ,~ ~; _ _ _ ; 

; Cdnonoto 

_____ .. _' - ~... lnd•an 

~0 

1 

~Gto ~ 

Islet• 

Indian 

RP\eorvatlon 

.. '.~0 

"','"2. 

\'\ 

\ 

) 

I 

.l 

< 

\ 

> 

.I 

\ 

1 5 ' Base compiled from U.S. Geological Survey digital data, 1 :I 00,000, 

1977, 1978; and City of Albuquerque digital data, I :2,400, 1994 

45' 

0 10 20 30 MILES 

0 10 20 30 KILOMETERS 

30 ' 

I 

106" 15 ' 

EXPLANATION 

Water-level change, 

in feet 

Ri se 

• More than 25 

• 25to 15 

15 to 5 

Decline 

5 to 20 

20 to 40 

Model 

boundary 

l 

I 

-l 

Figure 10. Simulated water-level change in the production zone (layer 5) between 2000 and 2040 

for simulation Ill (small ground-water use) (from Bexfield and McAda, 2003, fig . 19). 

21 
ground-water use simulation and 2,257,000 acre-ft 

more than that for the large ground-water use 

simulation (table 3). The reduced pumping of 

simulation ill resulted in a slight increase in loss of 

ground water to evapotranspiration and drain flow 

compared with the other simulations. 

Overall, the results of these future simulations 

indicated that reduced ground-water withdrawal by the 

COA through 2040 would have beneficial effects on the 

regional ground-water system, including substantially 

reduced water-level declines (and, in some areas, 

occurrence of water-level rise), increased aquifer 

storage, and reduced infiltration of surface water from 

the Rio Grande. The large magnitude of changes 

observed in water levels and water-budget components 

also suggested that a simulation-optimization approach 

to the distribution of future COA ground-water 

withdrawal could reasonably achieve an improved 

withdrawal distribution that would enhance beneficial 

effects on these features of the river-aquifer system. 

SIMULATION-OPTIMIZATION APPROACH 

For the simulation-optimization approach to 

water-resource management, multiple methods and 

software applications are available to couple and solve 

the simulation and optimization components of the 

modeling system. The methods used in this study are 

described after an introduction to the general 

techniques of the simulation-optimization approach. 

General Design of the SimulationOptimization Approach 

The simulation-optimization approach to waterresource management allows for the direct 

incorporation of the dynamics of a physical system, as 

represented by a sin1ulation model (such as a groundwater-flow model), into an optimization program that 

can maximize or minimize a management objective 

(Barlow and others, 1996). The mathematical 

formulation of the optimization model uses simulation 

model output to search effectively for the "best" 

solution to a particular problem. This approach is more 

efficient than trial-and-error use of a simulation model. 

The main equation in the statement of an 

optimization problem is the objective function, which 

will be maximized or minimized to achieve the desired 

solution. The objective function is composed of the 

decision variables, whose values define the solution of 

the problem. An example of a typical objective 

function for a ground-water management problem is: 

11 

f = L. q1 

j=l 

(1) 

where q is the decision variable that represents one of 

then stresses (such as ground-water withdrawal) 

imposed on the ground-water system at various 

locations, j (Ahlfeld and Mulligan, 2000). The values 

that can be taken by decision variables are restricted by 

constraints that are imposed on the problem. Exa1nples 

of types of constraints that are comn1only imposed on 

ground-water problems are individual stress bounds 

(such as allowable withdrawal rates from individual 

wells), bounds on total stress, head-bound constraints 

(such as allowable drawdown), head-difference 

constraints, and boundary-flux constraints. An example 

of a common constraint is: 

(2) 

Table 3. Summary of major results for future simulations I, II, and III 

[from Bexfield and Me Ada, 2003] 

From 2000 to 2040, cumulative volume (in acre-feet) of: 

95th percentile of 

water-table decline Outflow to 

from steady state Net inflow from Net inflow evapotrans- Outflow to 

Simulation (in feet) river leakage from storage piration drain flow 

I (medium pumping) 162 5,498,000 2,146,000 3,351,000 5,132,000 

II (large pumping) 199 5,638,000 2,867,000 3,346,000 5,117,000 

lil (small pumping) 101 4,766,000 610,000 3,389,000 5,239,000 

22 
where h~ is the upper bound on hydraulic head at I 

location i (Ahlfeld and Mulligan, 2000). The objective 

function and the constraints must be designed to 

accurately reflect the physical processes involved in the 

management problem and to provide a meaningful 

solution. For a well-posed problem, multiple solutions 

typically satisfy all the constraints, but the "best" 

solution also minimizes or maximizes the objective 

function. 

To solve a constrained optimization problem in 

ground-water management, the response of the groundwater system to a change in stress must be known. 

Typically, the stress is ground-water withdrawal and 

the response of interest is the change in hydraulic head 

or water-budget components (recharge and discharge). 

The characteristic change in the system, commonly 

determined from the simulation model for an assigned 

unit change in ground-water withdrawal at a specified 

location, generally is referred to as a "response 

function." Most widely applied methods of solution 

assume that the response of the ground-water system is 

a linear function of the rate of ground-water 

withdrawal. This assumption simplifies solution 

because the effects on the system of withdrawal at 

various locations become additive. For exa1nple, the 

total decline in hydraulic head at a particular location 

becomes the sum of the head decline caused at that 

location by each individual pumped well. Also, 

doubling the withdrawal from each well doubles the 

total head decline. Whenever the assumption of 

linearity in response is used, its appropriateness for the 

system under study must be evaluated. 

Simulation-Optimization Approach for the 

Middle Rio Grande Basin 

As described in the "Introduction," the focus of 

the study described in this report is to determine the 

optimal distribution of projected ground-water 

withdrawals from COA municipal-supply wells that 

would help to achieve specific management objectives 

for the regional river-aquifer system of the MRGB. To 

construct a detailed simulation-optimization approach 

that was appropriate to the problem, certain parameters 

of the study had to first be defined. Specifically, 

decisions were required with respect to management 

horizons, projections of future water demand and 

availability, operational details for water delivery, and 

modeling techniques. Managers with the COA were 

included in discussions of study parameters to ensure 

23 

that decisions with respect to management issues and 

operational details had practical application to the 

city's water-supply system. 

Broad aspects of the study were defined as 

follows: 

1. All optimization scenarios would start in 

2006, the first year that surface water is 

assumed to be available to meet most 

municipal demand and that all municipal 

wells are projected to be connected into the 

same citywide system. 

2. All optimization scenarios would end in 

2040 to conespond with the planning 

horizon established by the NMOSE in 

issuing guidelines for ground-water permit 

applications and permissible water-level 

declines in the Middle Rio Grande 

Administrative Area (New Mexico Office 

of the State Engineer, 2003). 

3. Projections of future total water demand 

and ground-water demand used in the 

optimization scenarios would be those 

previously developed by Greg Gates 

(written commun., 2001). 

4. Ground-water withdrawals by the COA 

would be optimized for management by 

well field, rather than by individual well, 

and would be designed to assume that the 

number and geographical distribution of 

wells available in 2000 were available 

throughout the period of optimization. 

5. Ground-water withdrawals would be 

optimized for management on an annual 

basis (rather than, for exan1ple, a monthly 

basis). 

6. Management objectives would be related to 

components of the water budget, which 

would result in these budget components 

being involved in most response functions. 

7. The McAda and Barroll model would be 

used without substantial modification (such 

as modifications to the number or length of 

stress periods or the sources and quantities 

of recharge) to generate all response 

functions. 

With these guidelines, detailed design of methods for 

generating the response functions and for creating and 

solving the mathematical optimization models was 

possible. 
Use of the Simulation Model to Generate 

Response Functions 

Response functions for use in the optimization 

models of this study were generated with the McAda 

and Barroll model. Because management objectives for 

the optimization models were related to components of 

the water budget, response functions were needed to 

indicate how these components respond to a change in 

stress in the aquifer system. In addition, response 

functions were generated for hydraulic heads in the 

aquifer because constraints on water-level decline were 

included in some of the optimization models. 

Generation of response functions for use in the 

optimization models required 26 simulations using the 

McAda and Barroll model-one simulation for each of 

the 25 COA well fields (to generate a separate 

characteristic response for a unit increase in groundwater withdrawal in each field) and one "base" 

simulation with constant ground-water withdrawal 

over time in each of the well fields. The base simulation 

provided the background conditions upon which a unit 

increase in withdrawal (unit stress) was added for each 

well field. Results of the base simulation were 

subtracted from results of each of the other 25 

simulations to calculate the characteristic response for 

each well field. 

The base simulation was designed to be fairly 

representative of typical hydrologic conditions 

projected to exist during the time period of interest for 

the optimization scenarios. By matching the typical 

hydrologic conditions as closely as possible, enors 

related to non-linearities in the ground-water-flow 

model were minimized. The siinulation began with the 

hydraulic-head distribution from the McAda and 

Barroll model at the end of the winter 1999-2000 stress 

period. Most input parameters from the summer 1999 

and winter 1999-2000 stress periods of the McAda and 

Banoll model were then duplicated without 

modification to lengthen the model to accommodate 

the period of interest. The exceptions were conditions 

in the Rio Grande and ground-water withdrawals by the 

COA. Average river conditions (stage and riverbed 

area) were calculated for the summer and winter stress 

periods from seasonal data in the McAda and Barroll 

model for 1990 to 2000; these average river conditions 

were used in all years of the base simulation. A 

constant annual rate of about 25,000 acre-ft for groundwater withdrawal by the COA was used in all years of 

the base simulation, with 76.2 percent of the 

withdrawal occurring during the summer stress period 

24 

and 23.8 percent during the winter stress period (an 

average division of withdrawal determined from 

historical monthly data). This total annual withdrawal 

rate of 25,000 acre-ft is nearly equal to the average of 

the annual projected rates of withdrawal for the first 10 

years after surface-water deliveries begin in 2006. The 

withdrawal for the base simulation was distributed 

among all COA wells in the same proportion that 

withdrawal was actually distributed during 2000. 

In each of the other 25 simulations, the 

withdrawal rate for each well in a single well field was 

increased by 1,000 acre-ft for one year. Again, 76.2 

percent of the increase was applied to the summer 

stress period (for 2006) and 23.8 percent was applied to 

the winter stress period (for 2006-07). All water-budget 

components were saved for each time step of the 

simulation, and hydraulic heads were saved for every 

cell of the model at the end of each winter stress period. 

Results from the base simulation were subtracted from 

the results of each of these 25 simulations to generate 

the response functions for each well field. For the 

water-budget components, the differences in water 

volume for each time step were summed to determine 

annual responses. Representative response functions 

for the Griegos and Leyendecker well fields, scaled by 

the number of wells in each field, are shown for waterbudget components and water levels in figures 11 and 

12, respectively. Because the Rio Grande and the 

riverside drains have a close hydraulic connection, the 

responses of these two components of the water budget 

were combined into a single response function (fig. 

11 ). Also, any change in the river component of the 

water budget resulting from a change in recharge from 

the Jemez River was assumed to be negligible because 

of the large distance of all COA well fields from the 

Jemez River. Of the response functions generated for 

water levels, only those for the 25 simulation-model 

cells that were most affected by withdrawals in each of 

the 25 individual COA well fields were ultimately used 

in the optimization modeling, as discussed in more 

detail in the section describing optimization model 3. 

As illustrated by the representative response 

functions of figures 11 and 12, the timing and 

magnitude of the greatest response of a particular 

aspect of the ground-water system can vary 

substantially depending on the location of the applied 

stress. Factors that can affect responses include 

horizontal distance from the site or feature of interest 

(such as the Rio Grande), aquifer properties between 

the location of applied stress and the site or feature of 
0:: 

L:5 

>-

0:: 

w 

o._ 

[jj 

w 

lJ.. 

uJ 

0:: 

u 

<( 

~ 

w 

(/) 

z 

0 

o._ 

(/) 

w 

0:: 

w 

~ 0:: 

0 

tn 

~ >-

0:: 

1,000 

750 

500 

250 

0 

-250 

150 

~ 125 1-

w 

w 

lJ.. 

uJ 5 100 <( 

~ 

w 

(/) 

z 

0 

o._ 

(/) 

w 

0:: 

(/) 

z 

<! 

0:: 

0 

(/) 

::J 

..J 

o._ 

0:: 

~ 0:: 

75 

50 

25 

0 

0 

0 

Water leaving 

storage 

Water entering 

storage 

2 4 6 

2 4 6 

(A) Storage 

Griegos well field 

Leyendecker well field 

8 1 0 12 14 16 18 20 22 24 26 28 30 32 34 

YEARS AFTER INITIATION OF STRESS 

8 

(B) River plus drains 

Griegos well field 

Leyendecker well field 

10 12 14 16 18 20 22 24 26 28 30 32 34 

YEARS AFTER INITIATION OF STRESS 

Figure 11. Representative response functions for the (A) storage and (B) river plus drains components 

of the water budget after application of stress of 1 ,000 acre-feet during year 1. 

25 
3.0 

2.5 

1-

w 

w 

LJ... 2.0 ~ 

u.i 

(f) 

z 

0 

(L 

(f) 

w 1.5 0::: 

_J 

w 

> 

w 

_J 

cY 

w 1.0 1-

<( 

~ 

0.5 

0.0 - 0 2 4 6 

Response at the observation site in the Griegos well field 

to withdrawal from the Griegos well field 

Response at the observation site in the Leyendecker well field 

to withdrawal from the Griegos well field 

Response at the observation site in the Griegos well field 

to withdrawal from the Leyendecker well field 

Response at the observation site in the Leyendecker well field 

to withdrawal from the Leyendecker well field 

---

8 10 12 14 16 18 20 22 24 26 28 30 32 34 

YEARS AFTER INITIATION OF STRESS 

Figure 12. Representative response functions for water levels after application of stress 

of 1 ,000 acre-feet during year 1. 

26 
interest, and the depth interval of the applied stress. For 

example, the river plus riverside drain response to a 

unit withdrawal from the Griegos well field reaches a 

peak at a much earlier time than the response to a unit 

withdrawal from the Leyendecker well field (fig. liB); 

also, the peak response from withdrawal at the Griegos 

field is larger. These differences in the response of the 

river and riverside drains likely result primarily from 

the shorter distance of the river and riverside drains 

from the Griegos field compared to the Leyendecker 

field (fig. 5). However, the water-level response 

functions for the two well fields (fig. 12) indicate that 

withdrawal from the Griegos field creates a 

substantially larger initial decline in water levels in the 

immediate vicinity of the Griegos field than withdrawal 

from the Leyendecker field causes in the inm1ediate 

vicinity of the Leyendecker field, despite the proximity 

of the Griegos field to the Rio Grande. This initial 

difference in water-level response, therefore, is likely 

related primarily to the simulated hydraulic 

conductivity in the vicinity of each well field. The 

faster dissipation of the water-level response in the area 

of the Griegos well field relative to the Leyendecker 

well field once again demonstrates the likely influence 

of proxinuty to the river (a major source of recharge). 

Variety in characteristic responses among the 

well fields is desirable for an optimization problem 

because it allows identification of a management 

option that provides substantial advantages over other 

options. Differences among responses for the various 

well fields, as well as selection of observation sites and 

features of interest, are discussed in more detail in the 

"Simulation-optimization models for ground-water 

management in the Albuquerque area" section, which 

describes the individual optimization scenarios. Also, 

sensitivity of the response functions to aspects of the 

base simulation and of the increased applied stress are 

addressed in the "Applicability of results" section. 

Formulation and Solution of Mathematical 

Optimization Models 

Formulation and solution of all optimization 

models for this study were pelformed using the 

General Algebraic Modeling System (GAMS), a 

mathematical programming software package (GAMS 

Development Corporation, 1998), coupled with the 

MINOS solver (Stanford Business Software, Inc., 

2003). The relatively large number of decision 

variables (25 stress sites with different withdrawal rates 

for each of 34 years) and constraints involved in the 

27 

opti1nization models, along with other complexities 

that included stress periods of unequal length in the 

simulation model, limited the number of software 

applications that would be appropriate for this study. 

GAMS provided the necessary ability to design, 

program, and solve large models with multiple 

constraints. MINOS was selected as the solver because 

it was designed for large-scale optimization problems, 

both linear and nonlinear (Stanford Business Software, 

Inc., 2003). 

The assumption that the response of the groundwater system is a linear function of the rate of groundwater withdrawal (as discussed in the "General design 

of the simulation-optimization approach" section) was 

used in formulating all optimization models in GAMS. 

The McAda and Barroll simulation rnodel does include 

some nonlinear features, but their overall effects on the 

response of the ground-water system to stresses were 

evaluated and were found to be relatively small. 

Nonlinearities are introduced by the unconfined or 

semiconfined behavior of the ground-water system 

throughout the depth of COA pumping. However, these 

nonlinearities should be negligible because water-level 

decline or rise that results from changes in groundwater withdrawal rates is very small compared with the 

total thickness of the aquifer. Nonlinearities also are 

introduced by the representation of evapotranspiration 

and flow in interior drains as piecewise-linear functions 

of calculated water-level altitudes. As discussed in the 

"Simulations of future conditions" section, future 

simulations pelformed with the McAda and Barroll 

model for widely differing rates of ground-water 

withdrawal by the COA produced relatively little effect 

on evapotranspiration and drain flow as compared with 

other water-budget components; combined effects on 

evapotranspiration and drain flow were less than about 

6 percent of the total difference in ground-water 

withdrawal volumes between simulations (Bexfield 

and McAda, 2003). Therefore, nonlinear effects from 

the model representatiOJ! of these two aspects of the 

ground-water system were expected to be small. One 

other potential source of nonlinear effects was 

predicted to be the model-simulated rise of water levels 

back to altitudes assigned to model cells that had 

previously gone dry. There-wetting option in the layerproperty flow package of MODFLOW-2000 

(Harbaugh and others, 2000) was not used because 

experimental model simulations that included it 

indicated problems with solution instability. Therefore, 

water levels were merely allowed to rise above the top 
of the uppermost layer that had stayed wet throughout 

the simulation up to that time. The degree to which 

nonlinearities in the simulation model caused results of 

model simulations and their associated optimization 

models to diverge is addressed in the "Simulationoptimization models for ground-water management in 

the Albuquerque area" section. 

For this study, the general design of the 

optimization models in GAMS involved an objective 

function that minimized the sum of particular effects of 

ground"" water withdrawals on the ground-water system 

for all years. For each optimization model, constraints 

included the total annual demand to be met by groundwater withdrawal, the total annual capacity of each 

well field, and the minimum annual withdrawal 

required from each well field to maintain equipment in 

working order. Additional constraints related to waterlevel altitudes, water-quality issues, and water-rights 

issues were applied to selected models, as described 

below in the "Simulation~optimization models for 

ground-water management in the Albuquerque area" 

section. 

Effects on the ground-water system were 

calculated using the individual response functions 

simulated by the McAda and Barron model for a 

single-year increase in withdrawal of 1,000 acre-ft per 

well in each of the 25 COA well fields. The response 

functions were scaled by coefficients that GAMS 

adjusted for withdrawal at each well field during each 

year when solving the optimization. The total response 

of a particular water-budget component or hydraulic 

head in a given year is defined as the total effect of all 

withdrawals during that year and previous years on the 

budget component or head. For the first year of the 

model, this total response equals the sum of the 

products of the first year's response from withdrawal at 

each well field with the coefficient assigned by GAMS 

for the withdrawal at that field, giving: 

25 

Total response 1 = L (c1, 1)(r1, 1) (3) 

J=l 

where c

1, 1 is the GAMS-adjusted coefficient for 

withdrawal at well fieldj in year 1 and r

1

,1 is the 

response of the ground-water system in the first year 

after withdrawal at well fieldj. For the second year of 

the model, the total response equals the sum of the 

28 

response from withdrawal in year 2 and the residual 

response from withdrawal in year 1, which gives: 

25 

Total response2 = L [(c. 2)(r · 1) + (c · 1 )(r · 2)] (4) ), ], ), ), 

j = l 

where c

1

,

2 is the GAMS-adjusted coefficient for 

withdrawal at well field j in year 2 and r

1,

2 is the 

response of the ground-water system in the second year 

after withdrawal at well field j. This same general 

approach works for every year of the model because all 

boundary conditions are assumed to be constant, 

meaning that the effect of a unit withdrawal in year 2 

on the water budget and hydraulic heads in year 3 is 

assumed to be exactly the same as the effect of a unit 

withdrawal in year 1 on the water budget and hydraulic 

heads in year 2. Therefore, to calculate the total 

response of the ground-water system in a particular 

year, the GAMS-adjusted coefficient for that year is 

multiplied by the response for the first year after 

withdrawal, whereas the GAMS-adjusted coefficient 

for the previous year is multiplied by the response for 

the second year after withdrawal, the GAMS-adjusted 

coefficient for the year before that is multiplied by the 

response for the third year after withdrawal, and so on. 

Then, the overall response of the ground-water system 

to withdrawal in all years is the sum of the total 

response for each individual year. An example of the 

calculation of the total response of an imaginary 

system to withdrawal from two wells during a 5-year 

period is shown in figure 13. 

For each optimization model of this study, 

GAMS, in combination with MINOS, deternlines the 

optimal coefficient for withdrawal at each well field 

during each year for an equation of the same general 

form as equation 3. The final coefficients are chosen to 

satisfy the objective function witllin the constraints of 

the individual optimization model. 

Selection of Time Horizons 

As discussed earlier in the "Simulationoptimization approach for the Middle Rio Grande 

Basin" section, the optimization models for this study 

were intended to provide the optimal distribution of 

ground-water withdrawals from COA wells between 

2006 and 2040 (a total of34 years) to acllieve particular 

management objectives for the river-aquifer system of 

the basin. The end of the time period was selected to 
1-

z~ =>...J 

ow 

~-~~-

w~w (/)ow Za::u. 

ou.w 

a.....JO:: 

(/)<{(.) 

~~<{ 

0::~~ wo 

!:!::r: 

::>I-

~~ 

1- ~ -N 

z...J 

=>...J 

ow 

25 

20 

15 

10 

5 

0 

25 

20 

EXPLANATION 

Aquifer response to 

unit withdrawal in 

model year: 

e- 1 

·--- 2 ---3 

•··· 4 0 5 

~-~~-

w~w (/)ow Za::u. 

ou.w 

a.....JO:: 

0:: fB~o <{ 

0::~~ wo 

15 

10 

For models, assume 

minimization of total aquifer 

response with a constraint 

requiring total withdrawal 

equal to 1 unit per year 

!:!::r: 5 ::>I-

~~ 0 

2 3 

MODEL YEAR 

4 

Solution for a 

2-year model: 

Final adjusted coefficients, c j,t 

Model year, t 

Solution for a 

5-year model: 

1 2 

i1~ 21 1.0 1.0 

Calculations for the 2-year model: 

Total response 2 years= [Total response1] + [Total response21 

2 

Total response 2 years= L {[(cj, 1)(}, 1>1 + [(cj,2)(rj, 1> + (cj, 1)(rj,2)]} 

j=1 

~ 2 

5 

1.0 

0.0 

Final adjusted coefficients, c j,t 

Model year, t 

2 3 4 

1.0 1.0 0.0 

0.0 0.0 1.0 

= {[(0.0)(20)] + [(0.0)(20) + (0.0)(7)]} + {[(1.0)(12)] + [(1.0)(12) + (1.0)(11)]} = 0 + 35 = 35 

Calculations for the 5-year model: 

Total response 5 years= [Total response1] + [Total response2] + [Total response3] + [Total response4] + [Total responses] 

2 

Total response 5 years= L {[(cj, 1 )(j, 1 )] + [(c j,2 )(rj, 1) + (cj, 1 )(rj,2)] + [(c j,3 )(rj, 1) + (cj,2 )(rj,2) + (cj, 1 )(j,3)] + [(cj.4Hj, 1) + 

j=1 

(c j,3 )(rj,2) + (cj,2 )(rj,3) + (cj, 1 )(j,4)] + [(c j,5 )(rj, 1) + (cj,4 )(rj,2) + (cj,3Hj,3) + (cj,2 )(rj,4)]} 

= {[(1.0)(20)] + [(1.0)(20) + (1.0}(7)] + [(1.0)(20) + (1.0)(7) + (1.0)(3)] + [(0.0)(20) + (1.0)(7) + (1.0)(3) + 

(1.0)(0)] + [(0.0)(20) + (0.0)(7) + (1.0)(3) + (1.0)(0)]} + {[(0.0)(12)] + [(0.0)(12) + (0.0)(11 )] + 

[(0.0)(12) + (0.0)(11) + (0.0)(8)] + [(1.0)(12) + (0.0)(11) + (0.0)(8) + (0.0)(1)] + [(1.0)(12) + (1.0)(11) + 

(0.0)(8) + (0.0)(1)]} = 90 + 35 = 125 

5 

0.0 

1.0 

Figure 13. Example calculations of the total response of a hypothetical system to withdrawal from two wells. 

29 
correspond with the planning horizon established by 

the NMOSE in issuing guidelines for ground-water 

permit applications and permissible water-level 

declines in the Middle Rio Grande Administrative Area 

(New Mexico Office of the State Engineer, 2003). 

However, the selection of 2040 as the end of the 

management time horizon is not intended to imply that 

effects on the ground-water system beyond that year 

are of no consequence. On the contrary, the 

management objectives of this study, which relate to 

mitigation of the deleterious effects of ground-water 

withdrawal on river infiltration and (or) ground-water 

levels, would generally be perceived by regional water 

managers as long-term objectives with no specific 

ending date. Therefore, the ideal models for this study 

would take into account the full response of the 

ground-water system to an individual stress, even when 

the time necessary for that response to dissipate 

completely extended beyond the chosen management 

horizon through 2040. Only then could a ground-water 

withdrawal distribution be determined that would have 

the optimal effect on a system response being targeted 

for long-term management. 

Once response functions had been generated 

with the McAda and Banoll model, they were 

evaluated to determine how much of the complete 

response of the ground-water system to the applied 

stress was captured during 34 years. Although the 

effects of increased withdrawal of 1,000 acre-ft for a 

single year (mid-March 2006 to mid-March 2007) had 

almost entirely dissipated for several well fields 34 

years later, the effects of the increased withdrawal in 

many other well fields were still quite substantial. For 

example, in year 34, the response of the \iver plus 

drains component of the water budget to withdrawal 

from the Griegos well field was only about 2.6 percent 

of the maximum response; however, the response to 

withdrawal from the Leyendecker well field was still 

about 18.8 percent of the maximum response (fig. 11). 

The length of time required for river-aquifer system 

responses to dissipate completely is a reflection of the 

distances between the locations of applied stress and of 

system response (for example, the Rio Grande), in 

addition to the physical properties of the system 

between those two points. In the MRGB, the response 

functions indicate that the river-aquifer system 

commonly continues to adjust to moderate stresses 

even decades after these stresses are applied. 

Because the long-term effects of ground-water 

withdrawals are relevant to this study, the response 

30 

functions generated from the simulation model for use 

in the optimization models were extended to capture as 

much information as reasonably possible about the 

overall response of the ground-water system. 

Therefore, the model simulations and associated 

response functions were extended for 54 years beyond 

the application of the unit stress. Simulations were 

terminated at this time because of the likely limitations 

of the predictive ability of the simulation model so far 

beyond the last year when data observations were 

available for input and because of issues with solution 

stability after such a long period of sustained 

withdrawals, particularly at basin margins close to sites 

of withdrawal. For all but five well fields, at least 75 

percent of the effects on aquifer storage from the single 

year of increased withdrawal had dissipated after 54 

years. Therefore, the selected length of the response 

functions, which is a result of the time horizon for 

response of the river-aquifer system in the MRGB to an 

applied stress, should be sufficient to capture all but a 

relatively small part of system response. 

Efforts to design study methods that would 

account for the long-term response of the river-aquifer 

system to stresses resulted in extension of the time 

horizons of the optimization models as well as of the 

response functions. To include all 54 years of 

information provided by the response functions in the 

calculations performed by the optimization models, the 

models also had to be extended in length to at least 54 

years. However, the nature of the optimization 

formulations necessitated an even further extension of 

the time horizon of the models to take full advantage of 

information provided by the response functions and 

arrive at the optimal long-term solution for each model. 

As described in the preceding section, in any 

particular year x, only the response of the ground-water 

system in the first year after withdrawal is relevant to 

the calculation of the effects of withdrawal during year 

x. In year (x+ 1), only the response of the ground-water 

system in the second year after withdrawal is relevant 

to the calculation of the continuing effects of 

withdrawal during year x. If the model ended in year 

(x+l), the optimal withdrawal distribution determined 

for year x would be determined on the basis of only the 

first 2 years of all response functions, rather than on the 

basis of the entire long-term response of the system 

(that is, all years of the response functions). This 

concept is illustrated in the example calculations for the 

2-year model in figure 13. The approach of ending the 

model at the final year of interest is appropriate when 
effects on the ground-water system beyond the final 

year of the optimization model are irrelevant to the 

objectives of the model. However, when the long-term 

effects of withdrawal beyond the years being modeled 

are relevant to the objectives of an investigation, the 

optimal withdrawal distribution during each year of the 

model should be selected on the basis of the long-term 

response of the system, to the full extent of available 

know ledge (rather than on the basis of only a part of the 

known response). Inclusion of the full extent of 

available knowledge in the withdrawal distribution 

selected for each year of the model requires extending 

the model beyond the final year of interest. The model 

must be extended to a total length equaling the length 

of the period of interest plus the length of the response 

functions, minus 1 (because any individual year of 

interest overlaps with the first year of the response 

function). This approach is illustrated by the 5-year 

model in figure 13. Extension of the model from 2 to 5 

years resulted in a change in the optimal withdrawal 

distribution for years 1 and 2, which are assumed to be 

the years of interest and which are the only years of the 

model that have the full effect of withdrawal on the 

system taken into account. 

For this study, which has long-term objectives, 

consideration of the full extent of knowledge about the 

effects of withdrawal was important for each year of 

the 2006-40 management period. Therefore, the 

optimization model time horizon was extended to be 34 

years (the length of the period of interest) plus 54 years 

(the length of the response functions), minus 1, which 

equals a total length of 87 years. 

To summarize, the long-term management 

objectives of this study necessitated adjustment to the 

time horizons used in the optimization modeling. 

Long-term management objectives analogous to the 

ones of this study are common in simulationoptimization modeling for water-resource 

management, and the issues addressed here should be 

considered when approaches are designed to solve 

similar management problems elsewhere. For this 

study, even though the current planning horizon for the 

basin requires that results be provided for only 34 

years, the goal to provide the optimization models with 

information about the complete response of the system 

to individual stresses for this study required an 

extension of the time horizon for the response functions 

to 54 years. Then, the goal to provide the optimization 

model with the same complete information on system 

response during year 54 as it had during year 1 required 

31 

that the length of the optimization model be extended 

to 87 years. Within the optimization model, the 

response after 54 years of all components of the 

ground-water system to the single year of increased 

withdrawal was manually set to zero. This effectively 

told the optin1ization model that all system responses 

after 54 years were negligible, which appeared 

reasonable based on the simulated response functions. 

Therefore, the well field that had the most 

advantageous effect on the river-aquifer system 

through year 54 was assumed in the model to still have 

the most advantageous effect on the system for any 

years beyond 54. Although the optimization models 

designed for this study have a total length of 87 years, 

results for only the first 34 years are appropriate to the 

scenarios being investigated, and so only those results 

are reported here. 

SIMULATION-OPTIMIZATION MODELS 

FOR GROUND-WATER MANAGEMENT IN 

THE ALBUQUERQUE AREA 

As discussed in the "Introduction," the COA 

plans to begin using surface water from the Rio Grande 

as its main municipal supply in 2006. At that time, all 

city well fields are expected to be interconnected, and 

Albuquerque will have the ability to distribute 

supplemental ground-water withdrawals an1ong the 

well fields in a manner that will achieve particular 

management objectives. In a broad sense, the 

management objectives addressed in this study are to 

satisfy the water demand of city customers while 

minimizing adverse effects on the river-aquifer system. 

One adverse effect is substantial decline of water levels 

in the aquifer (depletion of aquifer storage), which can 

potentially result in increased drilling and pumping 

costs for Albuquerque and neighboring municipalities, 

deterioration of the quality of available ground water, 

and land-surface subsidence. Induced infiltration of 

water from the Rio Grande can also be considered an 

adverse effect because, although it helps to maintain 

water levels in the aquifer, it reduces the availability of 

surface water for downstream users and habitat 

preservation. 

Other than aquifer storage, the component of the 

overall hydrologic system of the MRGB that responds 

substantially to ground-water withdrawals is the river 

system-in particular, the Rio Grande and associated 

riverside and interior ground-water drains. With 

sustained ground-water withdrawals, aquifer storage is 
reduced and ground-water levels decline across an area 

that becomes more extensive through time. Water-level 

declines continue to propagate until the associated 

changes in hydraulic gradient result in sufficient 

reductions in the rates of natural discharge and (or) 

increases in the rates of induced recharge to balance the 

rate of ground-water withdrawal-a condition that may 

never be achieved. The rates of most sources of 

recharge to the Santa Fe Group aquifer system (such as 

mountain-front, tributary, and subsurface recharge and 

canal, crop-irrigation, and septic-field seepage) are 

relatively fixed in magnitude over time scales of 

decades or longer and are simulated in the McAda and 

Barrell model as specified inflows that cannot change 

as ground-water levels decline. The primary hydrologic 

features in the MRGB that can provide additional 

recharge to the aquifer system when ground-water 

levels decline are the Rio Grande and the riverside 

drains. (Some additional recharge could also be 

induced from the Jemez River, Jemez Canyon 

Reservoir, and Cochiti Reservoir (fig. 1), but these 

features are more distant from Albuquerque and less 

extensive.) Similarly, the discharge features that can be 

affected by ground-water-level declines are located in 

the inner valley of the Rio Grande. These features are 

the Rio Grande, the interior and riverside ground-water 

drains, and the areas of riparian evapotranspiration. 

Therefore, other than changes in aquifer storage, most 

of the effects of ground-water withdrawal in the basin 

can be observed in changes in the rates of recharge 

from the Rio Grande and riverside drains or changes in 

the rates of discharge through ground-water drains and 

evapotranspiration. 

All ground-water withdrawal by th~ COA has an 

indirect effect on the features of the river system of the 

MRGB as described above. The magnitude and timing 

of that effect depend on the locations and rates of 

ground-water withdrawal and the aquifer properties 

between the locations of withdrawal and the features of 

the river system. When the city begins drawing water 

from the Rio Grande for direct delivery to customers, 

each acre-foot of decreased ground-water withdrawal 

will be substituted with an acre-foot of surface-water 

withdrawal. Therefore, city water use will have a more 

immediate, direct effect on the river system and on the 

availability of surface water for downstream use or for 

aquifer recharge. In contrast, the associated decrease in 

the use of ground water will allow water levels in the 

aquifer to rise over time, which will decrease the 

quantity of induced infiltration of water from the river 

32 

system. Because COA water-supply wells are located 

at various distances from the river system in aquifer 

materials with varying properties, the distribution of 

ground-water withdrawal among these wells can 

influence how quickly water levels in the aquifer 

recover and how greatly the river system of the MRGB 

is affected by ground-water withdrawals. In general, 

when ground water is withdrawn from wells that have 

a good connection to the river system, induced 

infiltration occurs relatively quickly and is relatively 

large, which allows for the use of less water from 

aquifer storage and results in less water-level decline. 

However, this pumping strategy also results in less 

water being available in the river at any particular time 

for downstream uses. When ground water is instead 

withdrawn from wells that have a poor connection to 

the river, effects on the river system generally are 

delayed and drawn out in time, resulting in a smaller 

effect at any given point. However, more water is drawn 

from aquifer storage, causing greater water-level 

declines. Response functions generated by the McAda 

and Ban·oll model for COA well fields help to illustrate 

these concepts and are discussed below. 

The five optimization models of this study are 

designed to explore distributions of ground-water 

withdrawal that can address the two primary 

management objectives for the water resources of the 

MRGB discussed above, given certain management 

constraints. In particular, withdrawal strategies are 

investigated that could (1) minimize water-level 

decline/maximize water-level recovery in the aquifer, 

(2) minimize the quantity of infiltration induced from 

the river system, or (3) be a combination of (1) and (2). 

Also, the magnitude of the effects that various 

withdrawal strategies can have on the water budget and 

water levels of the aquifer system is examined. As 

described below and shown in table 4, optimization 

models 1, 3, and 4 have objectives related to 

minimizing net depletion of aquifer storage and, by 

extension, overall water-level decline. Optimization 

model 2 has an objective related to minimizing effects 

on the river system. Optimization model 5 combines 

the two primary objectives. The simulation model 

included in the simulation-optimization techniques 

used here is not capable of simulating detailed river 

management throughout the basin or exact river 

conditions for a particular day and location, but it is 

capable of simulating the overall effects of groundwater management on the river system under typical 

conditions. Therefore, although the techniques used in 
this study do not provide guidance on day-to-day 

management of the water resources of the basin, they 

do provide insight into the timing and magnitude of the 

response of the various components of the hydrologic 

system to imposed stresses, which is essential to 

overall management to achieve primary objectives. 

All five optimization models described in the 

following sections were determined to be feasible, and 

the model output for each was evaluated for the optimal 

distribution of ground-water withdrawal each year, the 

overall effect on water-budget components and water 

levels (when relevant), and the apparent validity of the 

results when compared with the response functions. 

The optimal distribution of ground-water withdrawal 

for each model was then input to a simulation using the 

McAda and Barroll model, and the effects on the 

ground-water system predicted by the optimization 

model and the simulation model were compared. This 

comparison indicated the general magnitude of 

nonlineality in the representation of the aquifer system 

in the McAda and Barroll model, and, therefore, the 

appropliateness of using a linear approximation of the 

system. Results of the simulations using optitnal 

withdrawal distributions also were compared with 

results using the withdrawal distribution of 2000 (that 

is, the proportion of total withdrawal drawn from each 

well field in 2000) for each year through 2040. This 

comparison was used to examine the degree to which 

management objectives could be better met by us.ing 

the solutions to the optimization models. 

Table 4. Characteristics of each optimization model 

Model number 

and name 

Minimize net 

depletion of aquifer storage 

2 

Minimize net 

infiltration from 

the Rio Grande 

3 

Minimize net 

depletion of aquifer storage, with 

water-level constraints 

4 

Minimize net 

depletion of aquifer storage, with 

constraints on 

water levels and 

arsenic concentrations 

5 

Minimize net 

depletion of aquifer storage after 

eliminating river 

"debt" 

Objective 

Minimize use of water from aquifer storage 

for all years (2006 to 2040) 

Minimize leakage from the river system for 

all years (2006 to 2040) 

Minimize use of water from aquifer storage 

for all years (2006 to 2040) 

Minimize use of water from aquifer storage 

for all years (2006 to 2040) 

Constraints 

Meet projected annual ground-water demand 

Do not exceed maximum annual capacity for any well field 

Withdraw at least 40 acre-feet from each well annually 

Same as model 1 

Same as model 1, plus: 

Do not produce more than the maximum annual water-level 

decline of2.5 feet at any observation site 

Same as models I and 3, plus: 

Do not allow the arsenic concenh·ation ofblended ground water 

to exceed the maximum concentration of I 0 micrograms per 

liter during any year 

Minimize leakage from the river system Same as models I and 3, plus: 

until river "debt" owed by the City of Albu- Once river "debt" is first eliminated, do not allow the accumuquerque is eliminated, then minimize use lation of any additional river "debt" 

of water from aquifer storage for all 

remaining years 

33 
Optimization Model 1: Minimize Net 

Depletion of Aquifer Storage 

For the first optimization model, the 

management objective was to determine the 

distribution of withdrawal from COA well fields that 

would minilnize overall depletion of aquifer storage 

through 2040 (table~). In effect, minimizing overall 

depletion of aquifer storage would mini1nize waterlevel decline (or maximize water -level rise) across the 

entire region as a whole, without regard to spatial 

considerations. This approach allowed the problem of 

water-level decline to be addressed without requiring 

individual response functions for the change in water 

level in each model cell. The decision variables for the 

model were, therefore, the annual declines in the 

overall volume of aquifer storage caused by increased 

withdrawal in each city well field for each year, giving 

an objective function to be minimized of: 

87 25 

f = L L (cj,r)(sj,) (5) 

t = lj =I 

where cj,t is the GAMS-assigned coefficient of groundwater withdrawal for each of the 25 well fields (j) 

during each of the 87 years of the model (t), and sj,t is 

the change in aquifer storage (storage response) for 

each well field during each year as a result of the unit 

increase in withdrawal (1,000 acre-ft for 1 year). The 

values of the storage-response variable, sj,r, were 

determined as described in the "Use of the simulation 

model to generate response functions, section. The 

coefficient of withdrawal, cj,t, was restricted to values 

of zero or greater, signifying in GAMS thfit ground 

water was being withdrawn from the aquifer; negative 

values, which would have signified the injection of 

water, were not permitted. 

All three constraints in model 1 were directly 

related to the required ground-water withdrawals 

(table 4). The first constraint was that the predicted 

ground-water demand for each year be met. This 

constraint was achieved by placing a lower bound on 

the total withdrawal for each year that equaled the 

ground-water demand for the corresponding year. The 

ground-water demand as projected for 54 years 

(through 2060) by Greg Gates (written comrnun., 

2001) was used. However, his annual projections by 

calendar year were adjusted to apply to years running 

from mid-March to mid-March to match the design of 

stress periods in the McAda and Barroll model. 

34 

Because no projections were available beyond 54 

years, the slope of the demand curve for the last several 

years of available projections was used to extend the 

demand curve out to the end of the model; no attempt 

was made to duplicate periods of drought that were 

built into the first 54 years of projections (fig. 14). An 

upper bound on ground-water withdrawal was not 

required in the optimization model because, in this 

case, the objective function dictates that withdrawal not 

be any greater than necessary. The second constraint 

was that the maxin1um annual capacity for a well field 

(detennined from files of the COA, including historical 

withdrawal data and measured capacities) not be 

exceeded in any year. This constraint was achieved by 

placing an upper bound on the annual withdrawal from 

each well field that equaled the annual well field 

capacity (table 5). The well field capacity was assumed 

to be constant for each well field throughout the time 

period of the model. The third constraint was that a 

certain minimum quantity of water be withdrawn from 

each well field during each year to maintain equipment 

in working order. The lower bound on withdrawal from 

each well field was assigned to ensure that the 

minimum withdrawal from each well was 40 acre-ft/yr. 

This initial optilnization model was intended to 

demonstrate which well fields cause the least depletion 

of aquifer storage for a unit increase in ground-water 

withdrawal over the period of simulation (as simulated 

by the McAda and Barroll model) and how much 

depletion would result when an optimal distribution of 

withdrawal was used, as opposed to a distribution 

similar to the one used in 2000. By keeping the 

constraints on this optimization model relatively 

simple, a fail·ly general blueprint for minimizing waterlevel declines could be achieved. Also, the results of a 

relatively simple model could be compared with the 

response functions generated from the simulation 

model to determine whether the results were 

reasonable and whether the formulation of the model 

was correct. To keep the first model sufficiently simple, 

only three relatively nlinor constraints were applied. 

The first optil11ization model required only one 

set of response functions. These response functions 

were for the effect of withdrawal from an individual 

well field on the_ storage component of the water budget 

for the aquifer system. The cumulative response over 

time of aquifer storage obtained from the McAda and 

Barroll model (as described in the "Use of the 

simulation model to generate response functions, 
200,000 

180,000 

Iw 160,000 w 

u.. 

w 

0::: 140,000 

0 

<( 

~ 120,000 0 

z 

<( 

~ 100,000 w 

0 

0::: 

w 80,000 I-

<( 

s 

0 60,000 z 

:::> 

0 

0::: 

G 40,000 

20,000 

0 

2000 2020 2040 2060 2080 2100 2120 

Figure 14. Projected ground-water demand curve for all optimization models. 

35 
Table 5. Annual well-field capacities used for all optimization models 

[All values are in thousands of acre-feet] 

Well field 

(fig. 5) Capacity 

. Atrisco 11.27 

Burton 23.11 

Charles 28.89 

College 6.32 

Coronado 8.15 

Duranes 24.54 

Gonzales 11.24 

Griegos 10.56 

Leavitt 8.96 

Leyendecker 16.32 

Lomas 11.64 

Love 20.33 

Miles 4.15 

section) for each COA well field is shown in figure 15; 

the functions have been scaled by the number of wells 

in each field to indicate the response per well. The 

functions in figure 15 display the same storage 

response information as presented for two example 

well fields in figure 11A, except that the functions in 

figure 15 are cumulative. (The cumulative storage 

responses shown in figure 15 decrease over time 

because using water from storage to satisfy the groundwater withdrawal during the first year makes a positive 

contribution to the cumulative response, whereas the 

subsequent replenishment of aquifer storage through 

leakage of river water to the aquifer system is a 

negative term in the summation.) This graphical 

method of presenting the storage response emphasizes 

the overall, long-term effect of withdrawal from any 

individual well field on aquifer storage. Table 6lists the 

cumulative effect per well on aquifer storage through 

the last year of the response function (year 54) for each 

well field, ranked from the smallest to the largest effect. 

Because response functions for the river plus drains 

component of the water budget were needed for 

optimization model 2 and had already been generated 

for that purpose, they were used to calculate the effects 

of the solution to optimization model 1 on the river 

system. However, the response functions for the river 

plus drains are not discussed in detail until the section 

on optimization model 2 below. 

36 

Well field 

(fig. 5) Capacity 

Ponderosa 23.58 

Ridgecrest 23.56 

San Jose 7.06 

Santa Barbara 5.52 

Thomas 24.45 

Vol Andia 30.24 

Volcano Cliffs 11.60 

Walker 14.44 

Webster 9.93 

West Mesa 9.24 

Yale 13.35 

Zamora 7.93 

As discussed· briefly above in the "Use of the 

simulation model to generate response functions" 

section, the response of aquifer storage to withdrawal 

from different COA well fields can vary substantially, 

depending on the location of the applied stress both 

within the hydraulic-conductivity field of the 

simulation model and in relation to major hydrologic 

features. The information in figure 15 and table 6 

clearly indicates the differences an1ong the responses 

of aquifer storage to withdrawal from the various well 

fields and provides insight into operation of the 

hydrologic system as represented by the McAda and 

Barroll model. 

Each cumulative storage response in figure 15 

shows a similar overall pattern, wherein the volume of 

water in aquifer storage is immediately depleted by a 

quantity approaching the 1 ,000-acre-ft increase in 

withdrawal in year 1, and then gradually is replenished 

subsequent to the year in which the 1,000-acre-ft 

increase was applied. However, the magnitude of initial 

storage depletion and the speed of storage recovery 

differ substantially. As might be expected, these 

differences appear to be closely related to the general 

distance of the well field from the Rio Grande (the 

major surface drainage of the area) and the ease of 

comn1unication between the location of the well field 

and the river, as specified in the McAda and Barroll 

model through hydraulic conductivity and horizontalflow barriers. For example, withdrawals from the San 
u..i 1,000 

(/) 

z Coronado 0 

(l_ 800 (/) --- Burton --- Duranes 

w 

O:::t- Charles Gonzales 

w w (.?W 

<l::U. 

600 College Griegos 

on:: 

o:::w - 1-0 

CfJ<l:: 

wz 

400 -- -------- 2':-

I-

:5 200 :::::> 

:2 

:::::> 

0 0 

6 12 18 24 30 36 42 48 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

w- 1,000 

(/) 

z 

0 

(l_ 800 Leyendecker - Ponderosa (/) 

w Lomas Ridgecrest O::: t- ww (.?W Love San Jose 600 - - - <l:: LL 

o::: w 

0 0::: 

1-0 ' (/)<l:: 400 Wz ' ....... >-

f= -....... 

5 - :::::> 200 -- --- --- :2 ----- - :::::> 

0 

0 

6 12 18 24 30 36 42 48 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

1,000 

u..i 

(/) 

z --- Thomas Webster 0 800 (l_ 

(/) Vol Andia 

w 

O:::t- ---- Volcano Cliffs --- Yale 

w w (_?W 600 ----- Zamora 

~~ --- 0 0::: --- 1-0 

CfJ<l:: 400 

wz 

> - f= - 5 200 --- :::::> --- --- :2 

:::::> 

------ 0 

0 

6 12 18 24 30 36 42 48 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

Figure 15. Cumulative response over time of aquifer storage to an applied stress, scaled 

to indicate the response per well , for each City of Albuquerque wel l field . 

37 

54 

54 

54 
Table 6. Cumulati e response of aquifer storage 54 years after unit withdrawal, scaled to indicate 

the response per well, for each City of Albuquerque well field 

[ II va lue are in acre-feet] 

Well fi eld Cumulative 

(fig. 5) response 

109 

Griego I 16 

Atri co I 19 

Durancs 127 

Coronado I '9 

Webster 141 

ol Andi a 15 I 

Yale !59 

anta Barbara !60 

Miles 165 

Leyendecker 166 

Gonza lc 167 

Walker 170 

Jo e, Griegos, Atri sco, and Durane well field , which 

arc all located within about a mile of the Rio Grande 

(fig. 5), result in a mailer initial depletion of aqui fer 

storage per well than the other well fi elds. Withdrawal 

from the ewell fields al o generally re ult in fa ter 

torage recovery than ob erved for other field . 

Recovery in the Gonzale field, which i located within 

about a mile of the Rio Grande (fig. 5), might be slower 

than in the other field li ted abo e becau e the 

Gonzale well are located out ide the area of the mo t 

permeable recent ri ver alluvium. A table 6 indicate , 

the well fi eld with the lea ·t long-term depletion of 

torage per well after San Jo e, Griegos, A trisco, and 

Durane are the Coronado, Web ·ter, and Vol Andi a 

field . Even though the e fie lds are located farther from 

the Rio Grande than other uch as Yale and Zamora, 

the well are completed in highly conducti ve ance tral 

Rio Grande depo it that provide a better hydraulic 

connecti on to the ri ver (fig. ). The fi ve well field that 

cau. e the greate t long-term depletion of aquifer 

. torage per well are all located west of the Rio Grande 

in I w- ondu ti vity ed iment that reduce their 

connection to the ri ver, even in compari on with well 

field · located much farther from the ri ver, such a the 

Loma and Love field . 

Becau e of the manner in which optimi zation 

model I was de igned (see the " Formulation and 

olution of mathemati ca l optimi zation model " 

ection). once the minimum required withdrawal ha 

38 

Well fi eld umulative 

(fig. 5) response 

Pond ro a I 0 

Thoma I 4 

harles 184 

Burton I 9 

Love 215 

Ridgecrest 22 1 

Lorna 24 

Lcavin 2 5 

We t Me a 301 

Zamora 364 

ollege 374 

Volcano Cli fTs 482 

been a igned to each CO well field for an individual 

year, the model should uccessively add withdrawal 

from the well field with the , malle t long-term 

depletion of aquifer torage per well, unti l either the 

max imum capacity of the well fi eld i reached or the 

ground-water demand for that year i ati ned. Table 6 

indicate that the model hould, th refore. add 

withdrawal fi r t from the an Jo ewell field, followed 

by Griego , Atri co. Durane , and so on. Thus, the 

r ult f thi relatively ·imple optimi zation m del an 

be readily verified. 

Optimal Distribution of Ground-Water Withdrawal 

The optimal di tribution of ground-water 

withdrawal a calculated by GAMS for optimization 

model I is pre ented in table 7. s anticipated, once the 

minimum withdrawal requirement of 40 acre-ft/yr wa 

ful fi lled for each COA well (to a much a 280 

acre-ft/yr for each well field, depending on the number 

of well per field), the model added withdrawal 

succes ively from the San Jose, Griego , A tri . c , 

Durane , Coronado, Webster, and Vol Andi a well field 

until either the max imum capac ity of the well fi eld wa 

reached or the ground-water demand for that year was 

ati fled. T hrough 2040, gr und-water demand 

remains small enough that ground-water withdrawal 

greater than the required minimum per well is needed 

from onl y these even well fields. 
w 

<D 

Well fi eld 

(fig. 5) 

At risco 

Buno n 

Charles 

Co ll ege 

Coronado 

Durancs 

Gonzales 

Griegos 

Leavitt 

Leyendecker 

Lomas 

Love 

Mi les 

Ponderosa 

Ridgecrest 

San Jose 

Santa Ba rbara 

Thomas 

Vo l Andia 

Vo lcano Cliffs 

Wa lker 

Webster 

West Mesa 

Ya le 

!..Iamora 

Table 7. Optimal distribution of ground-water withdrawal for optimization modell 

(All values are in thousands of acre-feet] 

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 

3.03 I 1.26 0. 16 1.57 0. 16 6. I 0 I 1.26 5.30 1.73 3.53 5.52 7.02 8. 79 I 0.55 I 1.26 I 1.26 I 1.26 I 1.26 I 1.26 11.26 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 8.14 8. 14 

0.28 7.80 0.28 0.28 0.28 0.28 6.85 0.28 0.28 0.28 0.28 0.28 0.28 0.28 1.33 3.08 4.83 I 0.69 24.52 24.52 

0.12 0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0.12 0. 12 0. 12 0. 12 0. 12 0. 12 0.12 0. 12 0. 12 0.12 0. 12 0. 12 0.12 

I 0.56 I 0.56 4.68 I 0.56 6. 12 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 I 0.56 

0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0.12 0. 12 0. 12 0.12 0. 12 0. 12 0.12 0.12 0. 12 0.12 0. 12 0. 12 

0. 16 0.16 0. 16 0. 16 0. 16 0. 16 0. 16 0. 16 0. 16 0. 16 0. 16 0.16 0.16 0. 16 0.16 0.16 0. 16 0.16 0.16 0. 16 

0. 12 0.12 0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0. 12 0.12 0. 12 0.12 0. 12 0. 12 0. 12 0. 12 0.12 

0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 

0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 

0. 16 0.16 0. 16 0. 16 0. 16 0. 16 0. 16 0.16 0. 16 0. 16 0. 16 0. 16 0.16 0.1 6 0.16 0.16 0.16 0.16 0. 16 0.16 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 

7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 

0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 

0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 

0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 

0.12 0.12 . 0. 12 0.12 0.12 0.12 0. 12 0. 12 0. 12 0.12 0. 12 0. 12 0.12 0. 12 0.12 0.12 0.12 0.12 0.12 0.12 

0. 16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0. 16 0.16 0.16 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 7.22 8.97 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0. 12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0 08 0.08 0 08 0 08 
~ 

0 

Table 7. Optimal distribution of ground-water withdrawal for optimization modell--Concluded 

Well field 

(fig. 5) 

Atrisco 

Bunon 

Charles 

College 

Coronado 

Duranes 

Gonza les 

Griegos 

Leavin 

Leyendecker 

Lomas 

Love 

Miles 

Ponderosa 

Ridgecrest 

San Jose 

Santa Barbara 

Thomas 

Vo l Andia 

Volcano Cliffs 

Wa lker 

Webster 

West Mesa 

Ya le 

Zamora 

2026 

11.26 

0.20 

0.20 

0.08 

8.14 

24.52 

0.12 

10.56 

0. 12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0. 12 

0. 16 

6.62 

0.1 2 

0.12 

0.08 

2027 

11.26 

0.20 

0.20 

0.08 

0.08 

13.59 

0. 12 

10.56 

0. 12 

0. 16 

0. 12 

0.28 

0.04 

0. 16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0. 12 

0.12 

0.08 

2028 

11 .26 

0.20 

0.20 

0.08 

0.08 

15.34 

0.1 2 

10.56 

0. 12 

0. 16 

0. 12 

0.28 

0.04 

0. 16 

0.20 

7.05 

0.04 

0.28 

0.24 

0. 12 

0. 16 

0.08 

0.12 

0.12 

0.08 

2029 

11. 26 

0.20 

0.20 

0.08 

0.08 

17.09 

0. 12 

10.56 

0. 12 

0. 16 

0. 12 

0.28 

0.04 

0. 16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2030 

11.26 

0.20 

0.20 

0.08 

0.08 

18.84 

0.1 2 

10.56 

0.12 

0. 16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2031 

11.26 

0.20 

0.20 

0.08 

0.08 

20.57 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2032 

11 .26 

0.20 

0.20 

0.08 

0.08 

22.30 

0. 12 

10.56 

0. 12 

0. 16 

0. 12 

0.28 

0.04 

0. 16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0. 12 

0. 12 

0.08 

2033 

11.26 

0.20 

0 20 

0.08 

0.98 

24.52 

0. 12 

10.56 

0. 12 

0.16 

0. 12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0. 12 

0.12 

0.08 

2034 

11 .26 

0.20 

0.20 

0.08 

8. 14 

24.52 

0.12 

10.56 

0.12 

0.16 

0. 12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0. 16 

6.58 

0. 12 

0. 12 

0.08 

2035 

11.26 

0.20 

0.20 

0.08 

8.14 

24.52 

0.12 

10.56 

0.12 

0.16 

0. 12 

0.28 

0.04 

0. 16 

0.20 

7.05 

0.04 

0.28 

12.60 

0. 12 

0. 16 

9.93 

0.12 

0.12 

0.08 

2036 

11.26 

0.20 

0.20 

0.08 

5.8 1 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0. 12 

0.12 

0.08 

2037 

11.26 

0.20 

0.20 

0.08 

8. 14 

24.52 

0.12 

10.56 

0.12 

0. 16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

5.28 

0. 12 

0.12 

0 08 

2038 

11.26 

0.20 

0.20 

0.08 

8. 14 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

1.23 

0. 12 

0.12 

0.08 

2039 

11 .26 

0.20 

0.20 

0.08 

8.14 

24.52 

0. 12 

10.56 

0. 12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

1. 89 

0.12 

0.16 

9.93 

0. 12 

0.12 

0.08 
Comparison of GAMS and MODFLOW Results 

The optimal distribution of ground-water 

withdrawal determined by GAMS for COA well fie ld 

for 2006 through 2040 (table 7) wa provided as input 

to the McAda and BarToli imul ation model. The water 

budget of thi imul ation with optimal ground-water 

withdrawa l was compared with the water-budget 

alculation of the optimi zation model. To make th 

compari on between budget a accurate as po ible, 

the model simulation wa performed u ing the same 

input parameters that were u ed when response 

function for the optimi zation mode l were generated 

(see the "U e of the imul ation mode l to generate 

re ponse function " ection); only the qu antity and 

di tribution of ground-water withdrawal by the COA 

differed. The GAMS ca lculations of the effect of 2006 

to 2040 withdrawa l on the net torage and river plu 

drain components of the water budget for the aquife r 

ystem, which were computed u ing there pon e 

function generated from the imulation model, were 

ummed with the imulated effect of pre-2006 

ground-water withdrawa l on these components of the 

water budget after 2006, which had been determined 

using two imul ation of the McAda and BarToli 

model. The first model imul ation through 2040 

included known COA withdrawals through the end of 

2000 and projected city withdrawa l through 2006, 

fo llowed by no c ity withdrawal . The econd mode l 

imulation through 2040 inc luded no ci ty withdrawal 

during any year. The water-budget re ults of the econd 

imul ation were ubtracted from tho e of the first 

imulation to determine the lingering effects of COA 

withdrawa ls prior to 2006 on component of the water 

budget beyond 2006. The urn of the effects of 2006 to 

2040 withdrawal calcu lated by GAMS with the 

simul ated effect of pre-2006 withdrawa l provide the 

overall effect of COA ground-water withdrawa l on 

each budget component. Thi value was compared with 

the MODFLOW budget output from the simulation 

with the optimal withdrawa l minu the budget output 

from a imulation with no COA withdrawa l at any time, 

aga in giving the overall effect of only COA withdrawa l 

on each budget component. 

The overall re ult from GAMS and 

MODFLOW fo r both the torage and river plus drain 

compon nt of thewaterbudget arevery imil arduring 

the fir t 1 0 year of the modeled period (fig. 16), 

differing by les than 10 percent each yea r. During or 

oon after 20 15, the re ult of the two model beg in to 

41 

differ more apprec iably for both budget c mponent ; 

the GAMS m del overpred i t the use of water from 

aquifer torage and und r-pred ict the ontributi on of 

river plu drain leakage to the aquif r y. tern a 

compared to the MOD FLOW model. If the G M and 

MODFLOW result for 2006 to 2040 withdrawa l onl y 

are compared, by subtra ting the MODFLOWimulated effects of pre-2006 ground-water withdrawal 

( ee the da hed lin in fig. 16), th di~ ren e 

between the two model b ome more apparent. The e 

differ nee are largest f r the storage component. of 

the water budget, particular! during time when 

ground-water withdrawal are flu t.u ating over a broad 

range, re ·ulting in correspondingly large fluctuation. in 

imulated hydraulic heads. However, the differen e 

are generally le than 6,000 acre-ft and no more than 

7,2 15 acre-ft fo r any particular year, and both mode ls 

capture the ame major feature of the trend. in budg t 

components over time (fig. 16). Given that the 

differences represent onl y a mall percentage (le . . than 

2 percent) of the tota l volume of wat r mo ing through 

the aquifer ystem in an indivi dual year ( imulat.ed 

aq uifer inflow/outflow for the yea r ending in 0 t ber 

1999 wa about 575 ,000 acre-ft; McAda and Barr II , 

2002), these re ult indicate that the GAM model i 

prov iding a rea onab le approx imation to the M da 

and BarToli si mul ati on model de pite the pre nee f 

nonlinearitie in the imul ati on model. 

Comparison of Simulation Results for Optimal and 

Non-Optimal Distributions of Ground-Water 

Withdrawal 

The water budget and water level f the 

simul ation with optimal ground-water withdrawal a lso 

were compared with the re ults of a imul ati on with the 

ame qu antity of total withdrawa l, but with the 

continued u e of the non-optimal year-2000 

withdrawal distribution , to eva luate the magnitude of 

change that could be achieved. The imul ation using 

the non-optimal withdrawal di tribution was very 

imil ar to simulati on Ilf performed by Bex fi eld and 

McAda (2003) using the McAda and Ban·oll mode l, a 

de cri bed in the "Simulation. of future condition " 

ection , except that a constant ri ver condition wa used 

to all ow direct comparison with the simul ation u ing 

the optimal withdrawa l di tribution. Compa1ison of the 

net volume f change in budget component from 2006 

to 2040 for both imul ation indicates that the optimal 

di tributi on of ground-water withdrawa l re ult in 
w 

=>a:: 0<( 

a::w 

~>­ oa:: 

:::JW 

roo.. 

_lf- <(w 

u..W 

ou, 

~~ -u ()<( 

u.. z 0-

1-- - _J(/) 

:::>_J (/)<( 

w!;: a::<( 

<(~ CI)I 

<(1--

w~ 

(!)a:: <( w a::l-- 0<( 

I-!;: (/) , 

z o -z 

W:::J 

<.!JO 

za:: 

~(.!) 

() 

60,000 

40,000 

20,000 

0 

-20,000 

-40,000 

-60,000 

2005 

120,000 

40,000 

20,000 

0 

2005 

(A) Storage 

MODFLOW 

GAMS 

- - - Simulated effects of pre-2006 

ground-water withdrawal 

(from MODFLOW) 

Water leaving 

storage 

Water entering 

storage 

2010 2015 2020 2025 

(B) River plus drains 

MOD FLOW 

GAMS 

- - - Simulated effects of pre-2006 

ground-water withdrawal 

fro~ MODFLOW) 

....... ....... ....... ....... ....... ....... ....... 

----

---

2030 2035 

--------- 2010 2015 2020 2025 2030 2035 

2040 

2040 

Figure 16. Comparison of (A) storage and (B) river plus drains components of the water 

budgets from GAMS and MODFLOW for optimization model 1. 

42 
about 242,000 acre-ft greater recovery of water in 

aquifer storage than the non-optimal distribution (table 

8 and fig. 17). Nearly all this storage recovery is 

derived from increased leakage from the Rio Grande 

and the system of ground-water drains. The increased 

storage recovery in the optimal case compared with the 

non-optimal case results in a greater magnitude of 

water-level rise in the production zone of the aquifer 

across much of the eastern part of Albuquerque and in 

isolated areas west of the Rio Grande (figs. 18 and 19). 

However, water-level decline in the optimal case is 

increased along the Rio Grande, particularly near the 

San Jose, Griegos, Atrisco, and Duranes well fields, 

because this is the area where ground-water withdrawal 

is concentrated for the optimal case. This comparison 

demonstrates that optimization of the distribution of 

ground-water withdrawal can result in a significant 

reallocation of water among the various components of 

the water budget for the aquifer system. The 

comparison also indicates that nearly all this 

reallocation occurs between the storage and river plus 

drains components of the budget. 

Optimization Model 2: Minimize Net 

Infiltration from the Rio Grande 

Design of the second optimization model was 

nearly ·identical to that of the first optimization model, 

except that the decision variables were changed to 

achieve the management objective of minimizing net 

infiltration from the Rio Grande (table 4). Because the 

ground-water drains in the Rio Grande Valley are 

closely interrelated with the river itself, the decision 

variables for the model were the annual volume of 

leakage from the river plus the drains, as caused by 

increased withdrawal in each city well field for each 

year. The objective function was of the same form as 

presented in equation 5: 

87 25 

! = I I c c j. ( )( z j, , ) c 6) 

I= !j =I 

where c}.T is again the GAMS-assigned coefficient of 

ground-water withdrawal for each of the 25 well fields 

(j) during each of the 87 years of the model (t), and lJ,t 

is the change in river plus drains leakage for each well 

field during each year as a result of the unit increase in 

withdrawal (1,000 acre-ft for 1 year). Also, the 

constraints applied in optimization model 2 were the 

43 

same as those detailed above for optimization model 1. 

Similar to model1, this second optimization model was 

intended to provide a general blueprint for how groundwater withdrawals could be distributed among the 

COA well fields to minimize effects on the surfacewater system, as well as to demonstrate the magnitude 

of the decrease in river infiltration that could be 

achieved by optimizing the distribution of withdrawals. 

The second optimization model required a set of 

response functions for the effect of withdrawal from an 

individual well field on the river plus drains component 

of the water budget for the aquifer system. Figure 20 

shows the cumulative response over time of the river 

plus drains obtained from the McAda and Barrell 

model (as described in the "Use of the simulation 

model to generate response functions" section) for each 

COA well field; the functions have been scaled by the 

number of wells in each field to indicate the response 

per well. The functions in figure 20 display the same 

information on river plus drains response as presented 

for two example well fields in figure 11 B, except that 

the functions in figure 20 are cumulative. These graphs 

show that, even after ground-water withdrawal ceases 

at the end of year 1, water continues to enter the aquifer 

system from the river and drains to replenish the water 

drawn out of storage during year 1. For each well field, 

table 9 lists the cumulative effect per well on the river 

plus drains in the final year of the response function, 

ranked from the smallest to the largest effect. 

Optimal Distribution of Ground-Water Withdrawal 

As with the response functions for aquifer 

storage discussed for optimization model 1, the 

response functions for the river plus drains vary quite 

substantially, depending on the location of the applied 

stress. Two broad patterns of response are evident in the 

cumulative functions shown in figure 20. For well 

fields located within about 1 or 2 miles of the Rio 

Grande, such as the At:risco and Duranes fields, the 

river plus drains response is largest in the first year after 

the applied stress, and begins to level off relatively 

quickly. For well fields located a longer distance from 

the Rio Grande, the response of the river plus drains 

typically is delayed and drawn out over a longer period 

of time (fig. 20). Well fields far from the Rio Grande 

also generally demonstrate a substantially smaller 

cumulative response than fields near the river. 
Table 8. Comparison of water-budget components from the MOD FLOW simulation using 

the non-optimal distribution of ground-water withdrawal for 2000 and simulations using 

the optimal distribution of ground-water withdrawal from each model 

[Values represent volumes resulting from operation of City of Albuquerque municipal-supply 

wells only; na, not applicable] 

Cumulative volume from 2006 to Difference relative to the non2040 (in acre-feet) of: optimal case (in acre-feet) of: 1 

Net inflow to Net inflow to 

aquifer from aquifer from 

river plus drains Net change in river plus drains Net change in 

Model leakage storage2 leakage storage 

Non-optimal withdrawal 1,559,000 116,000 na na 

Optimization model I 1,800,000 358,000 241,000 242,000 

Optimization model 2 1,345,000 -118,000 -214,000 -234,000 

Optimization model 3 1,800,000 358,000 241,000 242,000 

Optimization model 4 1,790,000 347,000 231,000 231,000 

Optimization model 5 1,747,000 303,000 188,000 187,000 

1 A positive value signifies that the value is larger for the optimal case than for the non-optimal case; a negative value 

signifies that the value is smaller for the optimal case than for the non-optimal case 

2

Inftow to the aquifer system from storage (storage depletion) is negative; outflow from the aquifer system to storage is 

positive (storage recovery) 

Table 9. Cumulative response of the river plus drains 54 years after unit withdrawal, scaled to 

indicate the response per well, for each City of Albuquerque well field 

[All values are in acre-feet] 

Well field Cumulative Well field Cumulative 

(fig. 5) response (fig. 5) response 

Volcano Cliffs 492 Miles 782 

Zamora 599 Leyendecker 782 

College 600 Santa Barbara 784 

West Mesa 662 Yale 791 

Leavitt 672 Gonzales 794 

Lomas 706 Webster 798 

Ridgecrest 733 Vol Andia 800 

Love 742 Coronado 806 

Burton 765 Duranes 823 

Ponderosa 769 Griegos 828 

Charles 771 Atrisco 840 

Thomas 772 San Jose 842 

Walker 779 

44 
0 

-.:t 

0 

N 

0 

f---

<.0 

0 

0 

N 

2 

0fa:::w 

400,000 

300,000 

200,000 

LL W 100,000 

wU, 

~w 

<{0::: 

0:::0 

0<!: 0 tn~ 

z 

~ -100,000 f 

z 

<{ 

:r: 

0 tiJ -200,000 

z 

-300,000 

2 ,000 ,000 

1,750,000 

1,500,000 

1,250,000 

1,000,000 

750 ,000 

500 ,000 

250,000 

0 

~ 

~ 

~ 

l 

I 

~ /"" 

' I 

~ 

Non- Optimization 

optimal model 1 

Optimization 

model 2 

Optimization Optimization Optimization 

model 3 model 4 model 5 

Non- Optimization Optimization Optimization Optimization Optimization 

o ptimal model 1 model 2 model 3 mode l 4 model 5 

Figure 17. Comparison of selected water-budget components from MODFLOW for simulations 

using various ground-water withdrawal distributions. Values represent volumes 

resulting from operation of City of Albuquerque municipal-supply wells only. 

45 
35. 

45' 

30' 

107"15' 

I 

} 

I 

107"00' 

; 

·t 

l•a 

ndr.'ln 

Re rvat on 

Middle Rio 1Grande 

Basin bou"dary 

' ... .. 

45 ' 30 ' 106. 15' 

~ T 

<q 

15 ' r35. 

00 ' 

45' 

30' 

34. 

15 ' 

\'-iO " / I 

taguna 

tndl.!~" 

Re ervat10n 

\. 

' ' '{. 

~ 

f--

f--

~0 

"" "'{o/, oo-o 

'• 

slcta 

lndr.ln 

Rescrvatron 

I 

\ 

-... ~o . ~ ..... ~ 

\'0 

) 

I 

l 

c 

\ 

., 

' 

\ 

~ 1 JanAcaci 

Base compiled from U.S. Geological Survey digital data, 1:100,000, 

1977, 1978; and City of Albuquerque digital data. 1:2.400, 1994 

0 

f-- ---,- 0 10 

10 

L_T 

20 

20 

-.-'--

30 KILOMETERS 

30 MILES 

-, 

EXPLANATION 

Water-level change, 

in feet 

Ri se 

30 to s 

Decline 

5 to 25 

25 to 50 

_]_ __j 

Figure 18. Simulated water-level change in the production zone (layer 5) between 

2000 and 2040 for non-optimal ground-water withdrawal. 

46 
35 ' 

45' 

30 ' '--

15 ' 

107' 15' 

L 

107' 00 ' 

l&a 

lrdla< 

Rest.·rvdtiO 

Middle Rio Grande 

Basin bou1A.dary 

' " 

L .----:---:· aguna • , .. 

lnd1an 

RP.,ervauon 

p.iO 

/' 

I 

\. l ' 

35 " 1-- ' "\.'{. oo · '"" Jose ../ '- \..., 

I 

I 

r - -

45 ' r34' j_ 

l51tta 

ldr<ln 

Rt!>('rvation 

1 5 · Base compiled from U.S. Geological Survey digital data, 1:100,000. 

1977. 1976; and City of Albuquerque digital data, 1:2.400, 1994 

0 

~ 

0 

10 

T10 20 

20 30 MILES 

30 KILOMETERS 

30' 106' 15' 

T 

-l 

EXPLANATION 

Water-level cha nge, 

in feet 

Rise 

• More than 60 

• 60 to 30 

30to S 

Decl ine 

S to 25 

2S to SO 

• so to 7S 

Figure 19. Simulated water-level change in the production zone (layer 5) between 2000 

and 2040 for optimal ground-water withdrawal from optimization model 1. 

47 
1,000 (/) 

z 

<i':row 

a::w 800 ----- rnU;- ::JW 

....JO:: 

Cl.u 

0::<1: 600 --- ---- ~~ ------ O::u.i 

wrn 400 Atrisco Coronado >Z -o --- Burton --- Duranes 

~fu ::JW 200 Charles Gonzales ~a:: 

::J --- -- - u 

0 

6 12 18 24 30 36 42 48 54 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

1,000 (/) 

z 

~tli -------- ow 800 

rnl7 --- -- ::JW -- ....JO:: -- Cl.U 

a:: <X: 600 ,. -- wz / 

>-

a:w 

wrn 400 

>z Leavitt Miles 

-o 

~fu Leyendecker - Ponderosa 

::Jw 200 ~a:: Lomas Ridgecrest 

::J 

u 

0 

6 12 18 24 30 36 42 48 54 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

1,000 

(/) Santa Barbara z 

~tli 800 --- Thomas 

ow 

rnl7 ::JW Vol Andia - _., --- Cl.U 

....JO:: 

600 --- Volcano Cliffs -- a:: <X: 

wz 

>-

a:w --- wrn 400 --- -- Walker >z -o - --- Webster ~fu ::Jw West Mesa ~a:: 200 

::J --- Yale u 

0 

6 12 18 24 30 36 42 48 54 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000ACRE-FEET 

Figure 20. Cumulative response over time of the river plus drains to an applied stress, scaled 

to indicate the response per well , for each City of Albuquerque well field. 

48 
However, similar to geographic patterns seen in the 

response functions for aquifer storage, some well fields 

located farthest from the Rio Grande (such as the 

Lomas and Love fields) show a greater long-term effect 

on the river and drains than fields located closer to but 

west of the Rio Grande (such as the Volcano Cliffs and 

West Mesa fields) because the low-conductivity 

sediments west of the river (fig. 8) result in a poor 

connection between the ground-water and surfacewater systems (table 9). In the McAda and Barron 

model, the connection between the two systems in this 

area also is reduced by simulation of selected major 

faults as hydrologic barriers to ground-water flow. The 

order of well fields with the smallest to largest longterm effect on the river plus drains (table 9) is nearly 

opposite the order of well fields with the smallest to 

largest long-term effect on aquifer storage (table 6), as 

would be expected given that these are the two primary 

sources of water to the aquifer system that can vary in 

magnitude. Analysis of a few cases indicated that 

deviations from a directly opposite order of wells 

probably are primarily the result of slight differences in 

the response of evapotranspiration to the applied 

stresses at different locations (evapotranspiration is 

represented in a nonlinear manner in the simulation 

model). 

Similar to optimization model 1, the relatively 

simple. design of optimization model 2 allows the 

resulting optimal distribution of ground-water 

withdrawal to be easily verified using the information 

presented in table 9. As anticipated, once the minimum 

withdrawal requirement of 40 acre-ft/yr was fulfilled 

for each COA well, the model added withdrawal 

successively from the Volcano Cliffs, Zamora, College, 

West Mesa, Leavitt, Lomas, Ridgecrest, and Love well 

fields until either the maximum capacity of the well 

field was reached or the ground-water demand for that 

year was satisfied (table 10). Through 2040, groundwater demand remains small enough that ground-water 

withdrawal greater than the required minimum per well 

is needed from only these eight well fields. 

Comparison of GAMS and MODFLOW Results 

In the same manner described for optimization 

model 1, the optimal distribution of ground-water 

withdrawal determined by GAMS for optimization 

model 2 was provided as input to a simulation using the 

McAda and Barroll model, and the water budgets from 

GAMS and MODFLOW were compared. As figure 21 

indicates, the match between the water budgets from 

49 

GAMS and MODFLOW is slightly better for 

optimization model 2 than for optimization model 1, 

particularly if the MODFLOW-simulated effects of 

pre-2006 ground-water withdrawal are subtracted from 

the overall results of both models. Again, the best 

overall match occurs at early times. The differences 

between results for the GAMS and MODFLOW 

models are generally less than 5,000 acre-ft and no 

more than 5,851 acre-ft for any particular year. Both 

models capture the same major features of the trends in 

budget components over time, although the GAMS 

model does not reproduce some of the smaller scale 

fluctuations demonstrated by the MOD FLOW results 

in the river plus drains contribution (fig. 21 ). These 

results support the conclusion that GAMS is providing 

a reasonable approximation to the McAda and Barroll 

simulation model. 

Comparison of Simulation Results for Optimal and 

Non-Optimal Distributions of Ground-Water 

Withdrawal 

As with optimization model 1, the water budget 

and water levels of the simulation with the optimal 

ground-water withdrawal distribution from 

optimization model 2 were compared with the results 

of the simulation with continued use of tl1e non-optimal 

year-2000 withdrawal distribution. Comparison of the 

net volume of change in budget components from 2006 

to 2040 for both simulations indicates that the optimal 

distribution of ground-water withdrawal results in 

about 214,000 acre-ft less river plus drains leakage and 

about 234,000 acre-ft greater aquifer storage depletion 

than the non-optimal distribution (table 8 and fig. 17). 

Greater evapotranspiration in the optimal case accounts 

for most of the 20,000-acre-ft difference between the 

increase in use of storage and the decrease in river plus 

drains leakage compared to the non-optimal case. 

Although the optimal distribution of ground-water 

withdrawal for optimization model 2 minimizes 

leakage from the river and drains, it also results in large 

water-level declines in the production zone of the 

aquifer west of the Rio Grande, where most groundwater withdrawal is concentrated (fig. 22). Water-level 

declines in the production zone in the area of the 

Volcano Cliffs well field exceed 200 ft between 2000 

and 2040. Because the results of the optimization 

model include little withdrawal east of the Rio Grande, 

water levels in this area show substantial rise between 

2000 and 2040 (fig. 22). 
Ol 

0 

Well field 

(fig. 5) 

Atrisco 

Burton 

Charles 

College 

Coronado 

Duranes 

Gonzales 

Griegos 

Leavitt 

Leyendecker 

Lomas 

Love 

Miles 

Ponderosa 

Ridgecrest 

San .lose 

Santa Barbara 

Thomas 

Vol Andia 

Volcano Cliffs 

Walker 

Webster 

West Mesa 

Yale 

Zamora 

Table 10. Optimal distribution of ground-water withdrawal for optimization model 2 

[All values are in thousands of acre-feet] 

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 

0.16 0.16 

0.20 0.20 

0.20 0.20 

1.00 6.32 

0.08 0.08 

0.28 0.28 

0.12 0.12 

0.12 0.12 

0.12 1.44 

0.16 0.16 

0.16 

0.20 

0.20 

0.08 

0.08 

0.28 

0.12 

0.12 

0.12 

0.16 

0.16 

0.20 

0.20 

0.08 

0.08 

0.28 

0.12 

0.12 

0.12 

0.16 

0.16 

0.20 

0.20 

0.08 

0.08 

0.28 

0.12 

0.12 

0.12 

0.16 

0.12 0.12 0.12 0.12 0.12 

0.28 0.28 0.28 0.28 0.28 

0.04 0.04 0.04 0.04 0.04 

0.16 0.16 0.16 0.16 0.16 

0.20 0.20 0.20 0.20 0.20 

0.16 

0.20 

0.20 

4.07 

0.08 

0.28 

0.12 

0.12 

0.12 

0.16 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

0.49 

0.16 

0.16 

0.20 

0.20 

3.27 

0.08 

0.28 

0.12 

0.12 

0.12 

0.16 

0.16 

0.20 

0.20 

0.08 

0.08 

0.28 

0.12 

0.12 

0.12 

0.16 

0.16 

0.20 

0.20 

1.50 

0.08 

0.28 

0.12 

0.12 

0.12 

0.16 

0.16 0.16 0.16 0.16 0.16 0.16 0.16 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 

3.49 4.99 6.32 6.32 6.32 6.32 6.32 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 

0.28 0.28 0.28 0.28 0.28 0.28 0.28 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.16 0.16 0.16 0.16 0.16 0.16 0.16 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 

0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 

0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 

0.16 0.16 

0.20 ·o.2o 

0.20 0.20 

6.32 6.32 

0.08 0.08 

0.28 0.28 

0.12 0.12 

0.12 0.12 

4.33 8.96 

0.16 0.16 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

0. I 2 11.63 I 1.63 

0.28 0.28 0.28 

0.04 0.04 0.04 

0.16 0.16 0.16 

0.20 13.09 14.84 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.04 

0.28 

0.12 

0.04 

0.28 

0.12 

0.04 

0.28 

0.12 

0.04 

0.28 

0.12 

0.04 

0.28 

0.12 

0.04 

0.28 

0.12 0.12 0.12 0.12 

0.04 

0.28 

0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 

0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 

0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 

I 1.59 I 1.59 I 1.59 I 1.59 11.59 11.59 11.59 11.59 11.59 I 1.59 11.59 11.59 I 1.59 I 1.59 I 1.59 I 1.59 11.59 I 1.59 11.59 11.59 

0.16 0.16 

0.08 0.08 

0.12 9.23 

0.12 0.12 

7.93 7.93 

0.16 

0.08 

0.12 

0.12 

0.10 

0.16 0.16 0.16 Q16 Q16 Ql6 Ql6 Ql6 Ql6 Q16 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 

0.12 0.12 0.12 9.23 0.12 0.12 0.12 0.12 0.12 0.56 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

7.39 1.54 7.93 7.93 7.93 7.55 7.93 7.93 7.93 7.93 

0.16 0.16 

0.08 0.08 

2.32 4.08 

0.12 0.12 

7.93 7.93 

0.16 

0.08 

5.83 

0.12 

7.93 

0.16 

0.08 

7.58 

0.12 

7.93 

0.16 

0.08 

9.23 

0.12 

7.93 

0.16 

0.08 

9.23 

0.12 

7.93 

0.16 

0.08 

9.23 

0.12 

7.93 
0'1 

~ 

Table 10. Optimal distribution of ground-water withdrawal for optimization model 2--Concluded 

Well field 

(fig. 5) 

Atrisco 

Burton 

Charles 

College 

Coronado 

Duranes 

Gonzales 

Griegos 

Leavitt 

Leyendecker 

Lomas 

Love 

Miles 

Ponderosa 

Ridgecrest 

San Jose 

Santa Barbara 

Thomas 

Vol Andia 

Volcano Cliffs 

Walker 

Webster 

West Mesa 

Yale 

Zamora 

2026 2027 

0.16 0.16 

0.20 0.20 

0.20 0.20 

6.32 6.32 

0.08 0.08 

0.28 0.28 

0.12 0.12 

0.12 0.12 

8.96 7.23 

0.16 0.16 

11.63 

0.28 

0.04 

0.16 

12.49 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

0.12 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2028 2029 

0.16 0.16 

0.20 0.20 

0.20 0.20 

6.32 6.32 

0.08 0.08 

0.28 0.28 

0.12 0.12 

0.12 0.12 

8.96 8.96 

0.16 0.16 

0.14 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

1.89 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.24 

I 1.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2030 2031 

0.16 0.16 

0.20 0.20 

0.20 0.20 

6.32 6.32 

0.08 0.08 

0.28 0.28 

0.12 0.12 

0.12 0.12 

8.96 8.96 

0.16 0.16 

3.64 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.24 

I 1.59 

0.16 

0.08 

9.23 

0.12 

7.93 

5.37 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.24 

I 1.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2032 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

7.10 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2033 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

10.22 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2034 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

11.63 

0.28 

0.04 

0.16 

12.45 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2035 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

11.63 

4.90 

0.04 

0.16 

23.54 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2036 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

11.63 

0.28 

0.04 

0.16 

3.62 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2037 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

11.63 

0.28 

0.04 

0.16 

11.15 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2038 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

11.63 

0.28 

0.04 

0.16 

7.10 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 

2039 

0.16 

0.20 

0.20 

6.32 

0.08 

0.28 

0.12 

0.12 

8.96 

0.16 

11.63 

0.28 

0.04 

0.16 

I 7.45 

0.12 

0.04 

0.28 

0.24 

11.59 

0.16 

0.08 

9.23 

0.12 

7.93 
(A) Storage 

w 60,000 

=>a::: 

a<~: O:::w MODFLOW 

>- a a::: GAMS :::>W 40,000 c:oCl.. _JI-

<l:w --- Simulated effects of pre-2006 u..W ground-water withdrawal 

ow, (from MODFLOW) >- w t--0::: 20,000 -u 

u<~: 

u..z 0- I- - _JU) :::>_J 

U)<( 0 wS: 

a::: <I: 

U)I 

<(~ - -- <(I- -- 00::: 

w~ -20,000 ..... -- ..... ~w / 

ot- / I-<( 

U)~ / 

zo -40,000 / -z / W:::> 

<.:>o Za::: 

~<.:> 

u -60,000 

2005 2010 2015 2020 2025 2030 2035 2040 

(B) River plus drains 

~ - 120,000 

-U) U;t 

MOD FLOW ~s: t-- <1: _J a::: 100,000 

=> o GAMS 

U)I Wt- --- Simulated effects of pre-2006 ground- ~~0::: U) O::: l'5 80,000 

water withdrawal (from MODFLOW) 

<(W>-

C/)~0::: 

<(, ~s: ~ 

0:::01-- OzW 60,000 U):::>w 

:::>OU. _lO:::W 

Cl..<.:JO::: 

a:::wu w:::><l: 40,000 ~az 

a::: a::: - ::2:w 

o=> a:::O ...... u..=> 

s:~ 

20,000 --- 9u.. 

u..o --------- ~ 0 

2005 2010 2015 2020 2025 2030 2035 2040 

Figure 21. Comparison of (A) storage and (B) river plus drains components of the water 

budgets from GAMS and MODFLOW for optimization model 2. 

52 
35 ' 

45 ' 

30 ' 

15' 

35 ' 

oo · 

45 ' 

30 ' 

34' 

107' 15' 

''( ) 

... 

l 

) 

J 

107'00' 

z,. 

lnd1an 

Reservation 

\. 

Middle Rio Grande 

Basin bou11'l.dary 

' ... - - - , ... 

I 

Lag~na -------: ,:, , ~ 

lnd1an , , 1 __ 

Reservation ~ ~ , ' 

~ < Indian 

\ 

_ -~_\ .. Can~;Ki.to- - i 

- - - - ---· - -: _ReSiorvatiOn 

\. 

~0 \ 

' 

l' \\ 

,, 

oO'o 

~ 

Isleta 

Indian 

Reservation 

15' Base compiled from U.S. Geological Survey digital data. I :100,000. 

1977, 1978; and City of Albuquerque digital data, 1:2,400, 1994 

45 ' 

0 10 20 30 MILES 

0 10 20 30 KILOMETERS 

30 ' 106' 15' 

,' 

-, 

------ EXPLANATION 

Water-level change, 

in feet 

Ri se 

• More than 60 

• 60 to 30 

• 30 to 5 

Decline 

5 to 25 

25 to 50 

• so to 75 

• More than 75 

Figure 22. Simulated water-level change in the production zone (layer 5) between 2000 

and 2040 for optimal ground-water withdrawal from optimization model 2. 

53 
Optimization Model 3: Minimize Net 

Depletion of Aquifer Storage, with WaterLevel Constraints 

Design of the thlrd optimization model was 

again similar to that of the first optimization model 

(table 4). The same decision variables and objective 

function were used. Also, the three constraints on 

quantities of ground-water withdrawal remained. The 

only difference in the third optimization model was the 

addition of a fourth constraint, which limited waterlevel decline in the production zone of the aquifer to no 

more than 2.5 ftlyr on average from 2000 through 2040 

in any simulation-model cell. This limit on water-level 

decline was selected because it is the same rate of 

decline used by the NMOSE to define a Critical 

Management Area, in which owners of declared water 

rights will not be granted permits to increase groundwater diversions beyond the quantity previously placed 

to beneficial use (New Mexico Office of the State 

Engineer, 2003). This third optimization model was 

intended to show how the optimal withdrawal 

distribution (as determined in optimization model 1) 

must be altered to meet limitations on water-level 

declines at individual locations and how this altered 

distribution would affect depletion of aquifer storage 

through 2040. 

The addition of a water-level constraint to the 

optimization model required the incorporation of 

response functions for the effects of ground-water 

withdrawal not only on aquifer storage but also on 

water levels in the production zone of the aquifer 

(corresponding to layer 5 of the McAda and Barrell 

model). Response functions were incorporated only for 

those 25 simulation-model cells that were most 

affected by withdrawals in each of the 25 individual 

COA well fields; all other model cells would 

necessarily exhibit smaller water-level changes 

resulting from COA withdrawals. Because the waterlevel constraint was designed to limit the total waterlevel decline relative to early 2000 that had been caused 

by COA ground-water withdrawals, information on 

existing water-level declines in 2000 from city 

withdrawals and on the lingering effects of pre-2006 

city withdrawals on post-2006 water levels had to be 

retrieved from the McAda and Barroll model and 

incorporated into the optimization model. This 

information was retrieved from the McAda and Barrell 

model using two separate simulations through 2040. 

The first model simulation included known COA 

54 

withdrawals through the end of 2000 and projected city 

withdrawals through 2006, followed by no city 

withdrawals. The second model simulation included no 

city withdrawals during any year. Water levels for 2000 

in the first simulation were subtracted from those of the 

second simulation to determine the existing water-level 

declines in 2000 that were caused by COA pumping. 

Water levels for 2006 through 2040 in the first 

simulation were subtracted from those of the second 

simulation to determine the lingering effects of pre2006 city withdrawals on post-2006 water levels. 

In the optimization model, the total water-level 

change in a given year relative to 2000 was calculated 

by sumn1ing the water-level declines caused by city 

withdrawals in that year with the water-level declines 

caused by city withdrawals in previous years, and then 

subtracting the water-level declines that already existed 

in 2000 (as a result of city withdrawals) relative to 

steady-state (predevelopment) conditions. The waterlevel constraint assigned in the first year (2006) of the 

optimization model was 17.5 ft (seven times 2.5 ft) of 

decline, which reflects the total allowable water-level 

decline resulting from ground-water withdrawal each 

year from 2000 through 2006 (7 years of withdrawal). 

The water-level constraint for each successive year was 

2.5 ft greater than the constraint in the previous year, 

resulting in a constraint of 100 ft of decline in the final 

(34th) year of the model. 

Figure 23 shows response functions for water 

levels attwo selected sites around Albuquerque to 

withdrawal from each city well field; the functions 

have been scaled by the number of wells in each field 

to indicate the response per well. The optimization 

model actually included 625 individual water-level 

response functions, one for the water-level response at 

a location in each individual well field to withdrawal at 

each individual well field. As discussed previously, the 

water-level constraint of optimization model 3 limits 

the annual water-level decline in the production zone of 

the aquifer to no more than 2.5 ftfyr from 2000 through 

2040 to conform to NMOSE guidelines for resource 

management in the MRGB (New Mexico Office of the 

State Engineer, 2003). Because water levels are used 

only as constraints and not as decision variables, the 

overall order of the cumulative effect of individual well 

fields on particular water-level response locations is not 

important to the solution of the optimization problem. 
(A) Response at the observation site in the Gonzales well field 

10 

tD 

w 

LL Atrisco ~ Coronado 

w --- Burton --- Duranes (/) 

z Charles Gonzales 0 0.1 Q_ 

(/) College --- Griegos w 

0::: 

> 

w 

w 

_J 

_J 

0.01 ---------------- c( 

w 0.001 

~ 

~ 

0.000 1 

6 12 18 24 30 36 42 48 54 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

10 

tD 

w 

LL 

~ Leavitt Miles 

w 

(/) --- Leyendecker --- Ponderosa z 

0 0.1 Lomas Ridgecrest Q_ 

(/) 

w Love --- San Jose 

0::: 

_J 0.01 w 

> w 

_J ----- c( 0.001 --........... w 

~ 

~ 

0.0001 

6 12 18 24 30 36 42 48 54 

YEARS AFTER IN ITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

10 

fw 

w Santa Barbara Walker LL 

~ --- Thomas --- Webster 

w Vol Andia West Mesa (/) 

z 0.1 Yale 0 

Q_ --- Volcano Cliffs --- (/) Zamora w 

0::: 

_J 

> 

w 0.0 1 --- w 

_J ..., c( 

w 0.001 f-

<I: 

~ 

0.0001 

6 12 18 24 30 36 42 48 54 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

Figure 23. Response per well of water levels in the production zone at observation sites in 

the (A) Gonzales and (B) Coronado well fields to withdrawal from each City 

of Albuquerque well field. 

55 
(B) Response at the observation site in the Coronado well field 

10 

tD 

lU 

lL At risco Coronado 

~ 

u..i --- Burton --- Duranes (/) 

z Charles Gonzales 

0 0.1 (}_ College (/) --- Griegos 

lU 

0::: 

_J 0.01 lU 

[;j 

_J 

0:. 0.001 lU 

~ 

~ 

0.0001 

6 12 18 24 30 36 42 48 54 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

10 

tD 

lU Miles lL 

~ --- Leyendecker - Ponderosa 

u..i 

(/) Lomas Ridgecrest 

z 

0 0.1 --- Love --- San Jose (}_ 

(/) 

lU 

0::: 

_J 0.01 lU 

[;j 

_J 

0:. 0.001 lU 

~ 

~ 

0.0001 

6 12 18 24 30 36 42 48 54 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

10 

tD 

lU Santa Barbara Walker lL 

~ --- Thomas --- Webster 

u..i Vol Andia West Mesa (/) 

z 

0 0.1 --- Volcano Cliffs --- Yale (}_ 

(/) Zamora lU 

0::: 

_J 0.01 lU 

[;j 

_J 

0:. 

lU 0.001 

~ 

~ 

0.0001 

6 12 18 24 30 36 42 48 54 

YEARS AFTER INITIATION OF APPLIED STRESS OF 1,000 ACRE-FEET 

Figure 23. Response per well of water levels in the production zone at observation sites in 

the (A) Gonzales and (B) Coronado well fields to withdrawal from each City 

of Albuquerque well field--Concluded . 

56 
As the graphs in figure 23 indicate, the response 

of the water level at an individual observation site 

varies substantially with the location of the applied 

stress. The response depends primarily on the distance 

of the observation site from the applied stress, although 

the hydrologic features and aquifer properties between 

the observation site and the site of stress also affect the 

response. For observation sites located closest to the 

site of stress, the maximum water-level response 

occurs in the first year after the stress is applied and 

subsequently attenuates. For observation sites located 

farthest from the site of stress, the maximum waterlevel response occurs later in time and is of lesser 

magnitude. Water-level responses also are later and of 

lesser magnitude when the materials between the 

observation site and the site of the applied stress are 

less conductive. A stress applied at a well field with a 

good connection to the Rio Grande (such as Griegos 

well field) generally has a smaller effect on water levels 

than a stress applied at a well field with a poorer 

connection to the Rio Grande (such as College well 

field) because induced infiltration from the river system 

decreases the quantity of aquifer-storage depletion. 

As shown in figure 23, the simulated response of 

the water level at an individual observation site was not 

always completely smooth throughout the entire length 

of the response. The reason for deviations from a 

smoot11 response is not known, but these deviations 

likely are related to nonlinearities in the simulation 

model. Attempts to attain smoother responses through 

the use of more restrictive head-closure criteria or the 

re-wetting package ofMODFLOW were unsuccessful. 

However, the deviations from a smooth response 

generally were orders of magnitude less than the peak 

response and, therefore, should have an insignificant 

effect on model results. 

Optimal Distribution of Ground-Water Withdrawal 

The optimal distribution of ground-water 

withdrawal for optimization model3 is nearly identical 

to the optimal distribution for optimization model 1 

(table 7). Except in 2007, when optimization model 3 

pumps the San Jose field at capacity, the Atrisco field at 

8,110 acre-ft, the Duranes field at 12,430 acre-ft, and 

the Griegos field at 9,080 acre-ft, the optimal 

distributions are the same for both models. These very 

similar results are possible because the constraint 

allowing no more than 2.5 ft of water-level decline per 

year is binding on the solution in only the second year 

of the model and for only two observation sites (the 

57 

sites located in the Griegos and Atrisco well fields). For 

the solutions to both models, ground water is 

withdrawn from the San Jose, Griegos, and Atrisco 

well fields in each of the first 2 years of the model and 

additionally from the Duranes well field (located 

between the Griegos and Atrisco fields) in the second 

year of the model. To prevent water-level declines in 

the Griegos and Atrisco fields from exceeding 20 ft 

relative to year-2000 levels in 2007, optinuzation 

model 3 distributes more of the withdrawal to the 

Duranes field and less to the Griegos and Atrisco fields. 

Comparison of GAMS and MODFLOW Results 

The optimal distribution of ground-water 

withdrawal determined by GAMS for optimization 

model 3 was provided as input to a simulation using the 

McAda and Barron model, and both water budgets and 

water levels from GAMS and MODFLOW were 

compared. Because the solutions to optimization 

models 1 and 3 were nearly identical, the water budgets 

for GAMS and MOD FLOW for optimization model 3 

showed only insignificant differences from the water 

budgets for optimization model 1. Therefore, the reader 

is referred to the preceding discussion of water-budget 

results from optinuzation model 1, and no further 

discussion is provided here. With respect to water-level 

changes calculated by both the GAMS and 

MODFLOW models relative to ycar-2000 conditions, 

the average difference in calculated changes was less 

than 8 ft for all but three observation sites. For several 

observation sites, figure 24 shows that water-level 

changes calculated by the two models ru·e very similar 

for all years. For several other observation sites, waterlevel changes calculated by the two models are very 

similar during the first 10 years but begin to deviate 

thereafter, possibly because of relatively large swings 

in the annual quantity of ground-water withdrawal 

simulated around this time period. Matches are poorest 

for the observation sites in the Lomas, Love, and 

Ridgecrest well fields. All these fields are located near 

the eastern extent of the simulation model, where 

historical water-level declines have been largest; 

because of drying model cells and subsequent waterlevel recovery, nonlinear behavior is particularly 

significant in this part of the simulation model. No 

water-level declines observed from the MODFLOW 

model exceeded the constraints applied in the GAMS 

model. Overall, the GAMS model appears to have 

provided a reasonable approxi1nation to water-level 

changes simulated by the McAda and Barroll model. 
w 

0!-

zw 

~w 

ILL 

oz 

_J -

wo >O 

wo 

_JN 

'W 0::(.) 

wz !-_ 

~(f) 

!: 

120 

100 

80 

60 

40 

20 

0 

-- Coronado 

Burton 

College 

2005 2010 2015 2020 2025 2030 2035 2040 

40 

w 

0!- 20 

zw 

~w 

ILL 0 

oz 

_J -

~ g -20 wo 

_JN 

a:~ -40 

~~ 

~(f) -60 

-80 

-- Duranes 

Gonzales 

-- Miles 

2005 2010 2015 2020 2025 2030 2035 2040 

w 

0!-

zw 

~w 

ILL 

<.>z 

_J -

wo 

>o 

w o _JN 

a:~ 

~~ ~(f) 

!: 

120 

100 

80 

60 

40 

20 

0 

- Leavitt 

- Volcano Cliffs 

-- West Mesa 

2005 2010 2015 2020 2025 2030 2035 2040 

120 

w 

0 1- 100 

zw 

~w 

I LL 80 

oz 

_J -

W o [fj g 60 _J N 

a:~ 40 

~~ 

~(f) 20 

0 

2005 2010 2015 2020 2025 2030 2035 2040 

w 

01-

~tl:J ILL 

<.>z 

_J-

~~ •w 

c:::u 

wz )-_ 

~(/) 

!: 

w 

40 

20 

0 

-20 

-40 

-60 

-80 

2005 2010 2015 2020 2025 2030 2035 2040 

120 

0 1- 100 

zw 

~w 

ILL 80 <.>z 

_J -

~g 60 w o _JN 

a:~ 40 

~~ ~(f) 20 !: 

w 

0!-

zw 

~w 

ILL 

oz 

_J -

Wo >O 

wo 

_JN 

a:~ 

~~ 

~(f) 

w 

0 

2005 2010 2015 2020 2025 2030 2035 2040 

120 

100 

80 

60 

40 

20 

0 

2005 2010 2015 2020 2025 2030 2035 2040 

120 

0 1- 100 

zw 

~w 

ILL 80 

oz 

_J -

~g 60 wo 

_J N 

a:~ 40 

~~ 

~(f) 20 

0 

2005 2010 2015 2020 2025 2030 2035 2040 

EXPLANATION 

MODFLOW results 

GAMS results 

Figure 24. Comparison of water-level changes from GAMS and MODFLOW for optimization model 3. 

58 
Comparison of Simulation Results for Optimal and 

Non-Optimal Distributions of Ground-Water 

Withdrawal 

The results of the simulation model using the 

optimal distribution of ground-water withdrawal from 

optimization model 3 differed only slightly from the 

results using the optimal distribution from optimization 

model 1. Therefore, the reader is referred to the 

previous discussion that compares results for the 

optimal and non-optimal distributions with respect to 

optimization model 1 ~ no further discussion is provided 

here. 

Optimization Model 4: Minimize Net 

Depletion of Aquifer Storage, with 

Constraints on Water Levels and Arsenic 

Concentrations 

The design of the fourth optimization model was 

nearly identical to that of the third optimization model 

(table 4). The same decision variables and objective 

function were used. Also, the three constraints on 

quantities of ground-water withdrawal and the 

constraint on water-level declines remained. The only 

difference in the fourth optimization model was the 

addition of a constraint on the total blended arsenic 

concentration of the ground water withdrawn for 

municipal supply, which was not allowed to exceed the 

U.S. Environmental Protection Agency (USEPA) 

drinking-water standard of 10 micrograms per liter that 

will go into effect in 2006 (U.S. Environmental 

Protection Agency, 2003). As table 11 :indicates, most 

well fields west of the Rio Grande and in the far 

northeast part of Albuquerque have average arsenic 

concentrations greater than 10 micrograms per liter. 

Only nine well fields, located mostly in the central and 

southeastern parts of Albuquerque, have average 

concentrations less than 10 microgran1s per liter. 

For each year of the model, the blended arsenic 

concentration was calculated by multiplying the 

fraction of the total withdrawal drawn from each well 

field by the average of the median arsenic 

concentrations from all wells in that well field. The 

upper bound of the blended arsenic concentration was 

set at 10 micrograms per liter. The median arsenic 

concentrations for all but two wells crune from 1988-97 

data generally collected biannually by the COA from 

all its municipal-supply wells (Bexfield and others, 

1999). Median arsenic concentrations for Gonzales 3 

and Zamora 2, which were drilled in 1997, were 

provided by William Lindberg (City of Albuquerque, 

written commun., 2003) and were determined from 

samples collected from the time of drilling through 

April 2003. This model design assumes that no surface 

water is being blended with the ground-water supply 

and that each well in a field will always contribute an 

equal proportion of water compared to the total volume 

withdrawn from that field and blended for delivery to 

customers. The design also assumes little vru·iation 

ru·ound the median for the arsenic concentration of 

ground water withdrawn from each well. Although 

these conditions undoubtedly will not always be met, 

this opti1nization model should provide a reasonable 

Table 11. Representative arsenic concentrations used for each weU field in optimization model 4 

[All values are in micrograms per liter] 

Well field Arsenic Well field Arsenic 

(fig. 5) concentration (fig. 5) concentration 

Atrisco 12.0 Ponderosa 19.3 

Burton 10.2 Ridgecrest 3.0 

Charles 2.4 San Jose 19.7 

College 41.0 Santa Barbara 11.0 

Coronado 22.0 Thomas 5.7 

Duranes 9.1 Vol Andia 7.2 

Gonzales 15.0 Volcano Cliffs 13.3 

Griegos 8.3 Walker 25.0 

Leavitt 35.7 Webster 31.0 

Leyendecker 4.8 West Mesa 34.3 

Lomas 2.7 Yale 10.3 

Love 2.3 Zamora 15.5 

Miles 16.0 

59 
approximation of how substantially the optimal 

withdrawal distribution to minimize the depletion of 

aquifer storage must be altered to meet the USEPA 

arsenic standard and how substantially this altered 

distribution will affect depletion of aquifer storage 

through 2040. Because historical data indicate that the 

surface-water supply should generally have a smaller 

arsenic concentration than the ground-water supply, 

this model, which assumes no blending between the 

two water sources, should provide a "worst-case 

scenario" answer that indicates the greatest alteration 

that will have to be made to the optimal withdrawal 

dist:Iibution to satisfy the arsenic standard. 

Optimal Distribution of Ground-Water Withdrawal 

The constraint on arsenic concentration results in 

a substantially different optimal distribution of groundwater withdrawal for optimization model 4 (table 12) 

as compared to optimization models 1 (table 7) and 3. 

Of the seven well fields used in the optimal 

distributions of models 1 and 3 to minimize depletion 

of storage, four (San Jose, Atrisco, Coronado, and 

Webster) have average arsenic concentrations that 

exceed 10 micrograms per liter. Although ground water 

can still be withdrawn from these four fields for 

optimization model 4, the quantity of withdrawal from 

well fields with arsenic concentrations less than 10 

micrograms per liter must be sufficient to reduce the 

concentration of the overall blend of water to 10 

micrograms per liter. Because the model uses as much 

withdrawal as possible from the well fields with the 

least effect on storage (despite their average arsenic 

concentrations) to achieve the model objective, the 

arsenic constraint is binding in all years of the model. 

During the 34 years of the model, most ground-water 

withdrawal is preferentially from the Griegos, Atrisco, 

and Duranes well fields. Withdrawal from these well 

fields is supplemented by withdrawal from the San 

Jose, Vol Andia, and Coronado well fields during years 

of greater demand. Similar to that of optimization 

model 3, the water-level constraint of optimization 

model 4 is binding only in 2007. However, for model 4, 

the constraint is binding on three observation sites (in 

the Griegos, Atrisco, and Duranes well fields) rather 

than two. Therefore, the water-level constraint again 

has a small effect on the optimal distribution of groundwater withdrawal in the second year of the model. 

60 

Comparison of GAMS and MODFLOW Results 

Water budgets and water levels from GAMS and 

from a MODFLOW simulation using the optimal 

distribution of withdrawal for optimization model4 

showed similar correlation as for optimization models 

1 and 3 (figs. 25 and 26). Once again, the results from 

GAMS and MOD FLOW for both the storage and river 

plus drains components of the water budget were very 

similar during about the first 10 years of the modeled 

period but began to differ more appreciably after about 

2015; the GAMS model continually overpredicts the 

use of water from aquifer storage and underpredicts the 

contribution of river plus drains leakage to the aquifer 

system by as much as about 7,000 acre-ft compared to 

the MOD FLOW model. Also, the average difference in 

water-level changes calculated by GAMS and 

MODFLOW was about 8 ft or less for all observation 

sites except the ones in the Lomas, Love, and 

Ridgecrest well fields. 

Comparison of Simulation Results for Optimal and 

Non-Optimal Distributions of Ground-Water 

Withdrawal 

Comparison of the water budget from the 

simulation using the optimal ground-water withdrawal 

distribution from optimization model 4 and the water 

budget of the simulation using the non-optimal year2000 withdrawal distribution indicates that the optimal 

distribution of ground-water withdrawal results in 

about 231,000 acre-ft greater recovery of water in 

storage between 2006 and 2040 (table 8 and fig. 17). 

This quantity is about 10,000 acre-ft less storage 

recovery than resulted from the optimal distribution of 

ground-water withdrawal from optimization model 1, 

which included minimal constraints. Therefore, only 

about 4 percent of the cumulative "savings" in aquifer 

storage from optimization model 1 is lost when 

constraints on water-level decline and arsenic 

concentration are added. The storage recovery from the 

optimal distribution of ground-water withdrawal in 

optimization model4 results in a pattern of water-level 

change (fig. 27) that is very similar to the one resulting 

from the optimal distribution from model 1 (fig. 19). 

For optimization model4, there is slightly more waterlevel decline along the Rio Grande and slightly more 

water-level rise in the northern part of Albuquerque. 
~ 

Well field 

(fig. 5) 

Atrisco 

Burton 

Charles 

College 

Coronado 

Duranes 

Gonzales 

Griegos 

Leavitt 

Leyendecker 

Lomas 

Love 

Miles 

Ponderosa 

Ridgecrest 

San Jose 

Santa Barbara 

Thomas 

Vol Andia 

Volcano Cliffs 

Walker 

Webster 

West Mesa 

Yale 

Zamora 

Table 12. Optimal distribution of ground-water withdrawal for optimization model 4 

[All values are in thousands of acre-feet] 

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 

6.16 

0.20 

0.20 

0.08 

0.08 

8.51 

0.20 

0.20 

0.08 

0.08 

0.37 5.71 

0.20 0.20 

2.18 7.11 10.75 6.86 5.76 6.32 6.93 7.40 7.95 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 

8.49 9.04 

0.20 0.20 

9.58 I 0. I 3 11.26 11.26 11.26 

0.20 0.20 0.20 0.20 0.20 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 

0.20 0.20 

0.08 0.08 

0.08 0.08 

0.20 0.20 

0.08 0.08 

0.08 0.08 

0.20 

0.08 

0.08 

4.08 13.10 0.28 3.07 0.28 6.20 14.28 5.65 3.19 4.43 5.80 6.83 8.05 9.26 I 0.48 I 1.68 12.89 I 7.43 24.52 24.52 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

10.56 8.82 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.16 

0.12 0.12 0.12 

0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.28 0.28 0.28 0.28 0.28 0.28 0.28 

0.04 0.04 0.04 0.04 

0.16 0.16 0.16 0.16 

0.20 0.20 0.20 0.20 

0.12 1.53 0.96 0.12 

0.04 0.04 0.04 0.04 

0.28 0.28 0.28 0.28 

0.04 0.04 

0.16 0.16 

0.20 0.20 

0.59 0.12 

0.04 0.04 

0.28 0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.12 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.12 

0.28 

0.12 

0.28 

0.12 0.12 0.12 0.12 

0.28 

0.12 

0.28 0.28 0.28 0.28 

0.04 0.04 0.04 0.04 0.04 0.04 0.04 

0.16 0.16 0.16 0.16 0.16 0.16 0.16 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.04 0.04 0.04 0.04 0.04 0.04 0.04 

0.28 0.28 0.28 0.28 0.28 0.28 0.28 

0.12 

0.16 

0.12 

0.16 

0.12 0.12 

0.28 0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.04 

0.16 

0.20 

0.12 

0.04 

0.28 

0.12 0.12 

0.16 0.16 

0.12 0.12 

0.28 0.28 

0.04 0.04 

0.16 0.16 

0.20 0.20 

0.31 5.73 

0.04 0.04 

0.28 0.28 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

6.13 

0.04 

0.28 

0.24 4.95 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 16.76 18.12 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 
O'l 

1\) 

Table 12. Optimal distribution of ground-water withdrawal for optimization model 4--Concluded 

Well field 

(fig. 5) 

Atrisco 

Burton 

Charles 

College 

Coronado 

Duranes 

Gonzales 

Griegos 

Leavit1 

Leyendecker 

Lomas 

Love 

Miles 

Ponderosa 

Ridgecrest 

San Jose 

Santa Barbara 

Thomas 

Vol Andia 

Volcano Cliffs 

Walker 

Webster 

West Mesa 

Yale 

Zamora 

2026 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

. 10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

5.60 

0.04 

0.28 

16.29 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2027 

11.26 

0.20 

0.20 

0.08 

0.08 

20.09 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

0.55 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2028 

11.26 

0.20 

0.20 

0.08 

0.08 

21.69 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

0.70 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2029 

11.26 

0.20 

0.20 

0.08 

0.08 

23.29 

0.12 

10.56 -

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

0.85 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2030 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

1.06 

0.04 

0.28 

0.55 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2031 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

1.44 

0.04 

0.28 

1.90 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2032 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

1.83 

0.04 

0.28 

3.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2033 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

2.53 

0.04 

0.28 

5.66 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2034 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

5.59 

0.04 

0.28 

16.26 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2035 

11.26 

0.20 

0.20 

0.08 

1.82 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

28.77 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2036 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

3.61 

0.04 

0.28 

9.41 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2037 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

5.30 

0.04 

0.28 

15.25 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2038 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

4.39 

0.04 

0.28 

12.11 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2039 

11.26 

0.20 

0.20 

0.08 

0.08 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

6.71 

0.04 

0.28 

20.14 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 
>- f- - -(f) O....J 

LL<( 

03:: 

,_ <( ....JO:: 

::::>o C/JI 

w,_ 

a: -

<(3::~ (f)O:: 

<(W >- C/J~o:: 

~3::g: <(, 

O::Ofozw 

C/J => w ::::> O U, ....JO::W 

CL00:: 

o::w O w::::><( 

2': az o::o::-

::2 w o => o:: O LL::::> 

3:: (() 0~ _Jl.L 

LL0 

~ 

60,000 

40,000 

20,000 

0 

-20,000 

-40,000 

-60,000 

2005 

120,000 

100,000 

80,000 

60,000 

40,000 

20,000 

0 

2005 

(A) Storage 

MODFLOW 

GAMS 

Simulated effects of pre-2006 

ground-water withdrawal 

(from MODFLOW) 

Water leaving 

storage 

Water entering 

storage 

2010 2015 2020 2025 

(B) River plus drains 

MOD FLOW 

GAMS 

--- Simulated effects of pre-2006 groundwater withdrawal (from MOD FLOW) 

...... ...... ...... ...... ...... 

' ...... ...... ...... -. -. --

2010 2015 2020 2025 

---

2030 2035 2040 

------

2030 2035 2040 

Figure 25. Comparison of (A) storage and (B) river plus drains components of the water 

budgets from GAMS and MODFLOW for optimization model 4. 

63 
120 80 

w w 0f- 100 0f- 60 zw 

4:W ~lij IlL 80 ILL 40 uz U z ...J-.. ...Jwo w· > O 60 ~~ 20 wo 

...J N 

'W 40 ' W 0 o::u o:: u wz w z f- _ f-_ 

~U) 20 4: U) -20 ~ 

0 -40 

2005 2010 2015 2020 2025 2030 2035 2040 2005 2010 2015 2020 2025 2030 2035 2040 

40 120 

w w 0f- 20 0f- 100 z w z w 4: W 4:W 

IlL 0 IlL 80 u z u z ...J ...J w o -20 w o >O >O 60 w o w o ...J N ...JN 

'W -40 ' W o:: u O:: u 40 w z w z f-_ f-_ 

~U) -60 4: U) 20 ~ 

-80 0 

2005 2010 2015 2020 2025 2030 2035 2040 2005 2010 2015 2020 2025 2030 2035 2040 

120 120 

w w C)f- 100 0 f- 100 z w z w 4:W 4:W Ill.. 80 I ll.. 80 u z u z ...J ...J w o 60 w a >O >O 60 wo w o ...JN ...J N ' W 40 'W o::u O:: u 40 wz wz f-_ f-_ 

4:U) 20 4:U) 20 ~ ~ 

0 0 

2005 2010 2015 2020 2025 2030 , 2035 2040 2005 2010 2015 2020 2025 2030 2035 2040 

120 120 

w w 0f- 100 0f- 100 zw z w 4: W 4:W IlL 80 IlL 80 u z uz ...J ...J wo 60 wo > O > O 60 w o wo ...J N ...JN 

'W 40 ' W o:: u 40 o:: u wz w z f-_ f-_ 

U) 20 ~U) 20 

0 0 

2005 2010 2015 2020 2025 2030 2035 2040 2005 2010 2015 2020 2025 2030 2035 2040 

EXPLANATION 

MODFLOW results 

--- GAMS results 

Figure 26. Comparison of water-level changes from GAMS and MOD FLOW for optimization model 4. 

64 
35 " 

45 ' 

30 ' 

107" 15' 107"00' 

-r------- IT''J;::e,::::n;::ez:-;l;::nd"'i•:-:n:-r• --

1 J Rt>servation 1 

\ ....,_T-:J:) .. { 

&~ 0 _ roy0 &~ <1 / ~c ,c Rjo .. 1 ( 0 -

' '< ) 

} 

I 

' IV' 

'- ~ 

·<:&- '-0 

) 

Zia 

lndidn 

Reservat•on 

Middle Ri o Grande 

Basin bou1Rdary 

\. "- - - ' 

1 5. ------------: Laguna ,;, , .. 1 

35 " 

oo · 

45 ' 

30 ' 

34 " 

lndtan , 1 • __ 

Re~ervatton ~ ';:' , ' \"" I- - .. -I ~ Canonc•to ' .. ; lndtan 

t'\\ 

\ 

' '£, 

'" J Jose 

'- - l•leta 

Indian 

Rcscrvatton 

1 5 · Ba•e compiled from U.S. Geological Survey digital data, 1:100,000, 

1977, 1978; and City of Albuquerque digital data, 1:2.400, 1994 

0 

1-

0 10 

10 

20 

20 30 MILES 

30 KILOMETERS 

30 ' 106"15' -----

EXPLANATION 

Water-level change, 

in feet 

Rise 

• More than 60 

• 60 to 30 

30to5 

Decline 

S to 2S 

2S to SO 

• SO to 7S 

Figure 27. Simulated water-level change in the production zone (layer 5) between 2000 

and 2040 for optimal ground-water withdrawal from optimization model 4. 

65 
Optimization Model 5: Minimize Net 

Depletion of Aquifer Storage after 

Eliminating River "Debt" 

The fifth and last optimization model combines 

the decision variables and objective functions of 

models 1 and 2 with tbe water-level constraints of 

model3 (table 4). The NMOSE requires the COA to 

allow a specific quantity of Rio Grande and San JuanChama diversion water, for which it owns water rights, 

to flow past Albuquerque each year to offset the effects 

on the Rio Grande from the city's ground-water 

withdrawals for that year and previous years. After 

switching to the use of surface water as its primary 

municipal supply in 2006, the COA will still be 

required to compensate for the lingering effects of 

previous large ground-water withdrawals on the Rio 

Grande, in addition to compensating for the effects of 

ground-water withdrawals at the new, lower 

magnitude. The COA has stored water in upstream 

reservoirs for the purpose of paying off this 

accumulated river "debt" for previous and new groundwater withdrawals while also diverting large quantities 

of surface water for its new water-supply strategy. 

Before optimizing ground-water withdrawals to 

minimize depletion of aquifer storage, the COA plans 

to withdraw ground water in a manner that will 

minimize infiltration from the Rio Grande and pay off 

its river "debt" as quickly as possible. This fifth 

scenario was designed to optimize ground-water 

withdrawal to minimize infiltration from the Rio 

Grande until the city's river "debt" is paid off, then to 

subsequently minimize depletion of aquifer storage 

while accumulating no new river "debt" and limiting 

water-level declines in all simulation-model cells to no 

more than 2.S ft/yr through 2040. 

The objectives of this optimization scenario were 

achieved by designing two individual optitnization 

models (SA and SB) and inserting the results from SA 

into SB. The objective of model SA was to mini1nize 

infiltration from the Rio Grande until the city's river 

"debt" was eliminated. The decision variables and 

objective functions were the same as in optimization 

model 2. Also, the three constraints on ground-water 

withdrawal from optimization model 2 were 

maintained. A fourth constraint was added to limit 

water-level declines. Also, information on the water 

rights owned by the COA, projected surface-water 

diversions, and the lingering river "debt" accumulated 

from ground-water withdrawal by the city prior to 2006 

was programmed into model SA. Albuquerque's water 

66 

rights were assumed to be constant at 48,200 acre-ft 

from the San Juan-Chama Project and 23,000 acre-ft of 

native Rio Grande water throughout the modeled 

period. Also, return flow to the Rio Grande was 

assumed to remain at a constant fraction equaling half 

of total water demand for each individual year. The 

lingering river "debt" from previous ground-water 

withdrawals was deternlined using the McAda and 

Barrell model. The first model simulation through 

2040 included known COA withdrawals through the 

end of 2000 and projected city withdrawals through 

2006, followed by no city withdrawals. The second 

model simulation through 2040 included no city 

withdrawals during any year. The water-budget results 

of the second simulation were subtracted from those of 

the first simulation to determine the lingering effects of 

COA withdrawals prior to 2006 on infiltration from the 

Rio Grande beyond 2006. Then, the city's river "debt" 

or "surplus" for each year of optimization model SA 

was calculated by summing the projected surface-water 

diversion for that year, the projected effects on the river 

from the optimal ground-water withdrawal distribution 

for that year and any past years after 2006 (as 

determined by GAMS), and the lingering effects from 

pre-2006 ground-water withdrawal (as determined 

with the McAda and Barrell model). This sum was 

subtracted from the sum of the city's annual water 

rights (assumed constant) and one-half of the total 

projected water demand for that year (the quantity 

estimated to be delivered to the river through the city's 

wastewater treatment plant). The length of model SA 

was determined by trial and error and was the number 

of years needed to make this "debt"/"surplus" 

calculation equal zero or a positive number. It was not 

necessary for this model to extend to twice the length 

of the response functions (as was done for all the other 

optimization models) because it had a short-term 

management objective. 

The second optimization model, SB, had the 

san1e general design as optimization model 3 in terms 

of the decision variables, the objective function (to 

minimize depletion of aquifer storage), the three 

constraints on ground-water withdrawal, the constraint 

on water-level decline, and the model duration. Also, 

the same information relevant to the river "debt"/ 

"surplus" calculation of modelS A was added to model 

SB. For each of the first several years of model SB, 

equal to the length of model SA, the upper bound on 

river "debt" was set equal to the minimum possible 

value determined from model SA. This constraint 

forced model SB to use the same optimal distribution of 
ground-water withdrawal as determined from SA to 

minimize effects on the Rio Grande until the river 

"debt" was eliminated. For all years afterward, model 

5B was allowed to determine the optimal distribution 

of ground-water withdrawal to minimize depletion of 

aquifer storage, but with the additional constraint that 

no new river "debt" be subsequently accumulated (that 

is, the lower bound on the value of the river "debt"/ 

"surplus" calculation was set to zero). Thus, the overall 

design of optimization model 5 achieved the intention 

of minimizing the effects of ground-water withdrawal 

on the Rio Grande until the city's river "debt" was 

eliminated, then minimizing the depletion of aquifer 

storage while not accumulating new river "debt" or 

excessive water-level declines. 

Optimal Distribution of Ground-Water Withdrawal 

Optinuzation model SA used the response 

functions for the river plus drains (fig. 20) to determine 

the optimal withdrawal of ground water that would 

minin1ize leakage into the aquifer until river "debt" was 

eliminated. Trial and error with the length of the model 

showed that "debt" could be eliminated in 9 years. The 

optimal distribution of withdrawal calculated by model 

SA does not match the distribution calculated for the 

first 9 years of model 2, which had the san1e overall 

objective. The distributions differ for two main 

reasqns. First, because the objective of minimizing 

river plus drains leakage applied in model SA for only 

these 9 years (as opposed to being a long-term 

objective), the model could determine the optimal 

distribution of withdrawal using only the first 9 years of 

the river plus drains response functions rather than the 

entire 54 years used by optimization model 2. 

Secondly, model 2 did not include the water-level 

constraint that was present in model SA. The waterlevel constraint was binding for all 9 years at the 

observation site in the Lomas field and for year 2 at the 

sites in the Volcano Cliffs and Ridgecrest fields. The 

resulting optimal distribution of withdrawal (table 13) 

uses the Lomas, Love, Ridgecrest, and Volcano Cliffs 

well fields at varying rates greater than the required 

minimum. 

For model 5B, which was designed to use the 

solution from model SA for the first 9 years, the 

optimal distribution of ground-water withdrawal was 

the same as that calculated in optimization models 1 

and 3 for every year starting in 2017. In 2015 and 2016, 

the constraint precluding accumulation of river "debt" 

was binding and resulted in a different optimal 

distribution than the one calculated for models 1 and 3. 

67 

In 2015, the optimal distribution called for withdrawal 

from the San Jose, Coronado, and Webster well fields, 

whereas in 2016, the San Jose, Griegos, At:Iisco, and 

Coronado well fields were included in the optimal 

distribution. As with models 1 and 3, the well fields 

included in the optimal distributions of withdrawal for 

2017 through 2039 were the San Jose, Griegos, 

Atrisco, Duranes, Coronado, Webster, and Vol Andia 

fields. 

Comparison of GAMS and MODFLOW Results 

Sinlilar to results for the previous models, 

comparison of the water budgets from GAMS and 

MOD FLOW for the optimal distribution of withdrawal 

from optimization model 5 indicates that the models 

agree quite well for about the first 10 years (fig. 28). 

Afte1ward, the GAMS model continually overpredicts 

the use of water from aquifer storage and underpredicts 

the contribution of river plus drains leakage to the 

aquifer system by as much as about 6,100 acre-ft 

compared with the MOD FLOW model. Because the 

GAMS model continually predicts less river plus 

drains leakage than the MODFLOW model, GAMS 

calculations indicate that there would be no liver 

"debt" during years when MODFLOW indicates that 

as much as about 3,600 acre-ft of river "debt" would 

exist (table 14). This comparison shows that the GAMS 

solution could require slight modifications to ensure 

that requirements related to the future effects of COA 

ground-water withdrawals on the river system are met. 

Water-level changes calculated by GAMS and 

MOD FLOW for optimization model 5 agreed within 

an average of 10 ft for all observation sites except the 

site in the Lomas well field (fig. 29). During each of the 

first 9 years of the model, the optimal distribution of 

ground-water withdrawal includes withdrawal from the 

Lomas well field. Because agreement between GAMS 

and MOD FLOW for the effect of withdrawal from the 

Lomas well field on water-level declines in the area is 

not as good as for other well fields, the MODFLOW 

simulation indicates that water-level declines at the 

observation site in the Lomas well field would exceed 

the water-level constraints of the GAMS model by as 

much as 4.9 ft duiing years 3 through 9 of the model. 

All other water-level declines from the MODFLOW 

simulation remain within the constraints applied in 

GAMS. 
Well field 

(fig. 5) 

Atrisco 

Burton 

Charles 

College 

Coronado 

Duranes 

Gonzales 

Griegos 

Leavitt 

Leyendecker 

Lomas 

Love 

Miles 

Ponderosa 

Ridgecrest 

San Jose 

Santa Barbara 

Thomas 

Vol Andia 

Volcano Cliffs 

Walker 

Webster 

West Mesa 

Yale 

Zamora 

Table 13. Optimal distribution of ground-water withdrawal for optimization model 5 

[All values are in thousands of acre-feet] 

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 

0.16 0.16 0.16 0.16 

0.20 0.20 0.20 0.20 

0.20 0.20 0.20 0.20 

0.08 0.08 0.08 0.08 

0.08 0.08 0.08 0.08 

0.16 

0.20 

0.20 

0.08 

0.08 

0.16 0.16 

0.20 0.20 

0.20 0.20 

0.08 0.08 

0.08 0.08 

0.16 0.16 0.16 2.80 7.02 8.79 10.55 11.26 11.26 I 1.26 11.26 11.26 11.26 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 . 0.20 0.20 

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 

0.08 0.08 7.14 2.80 0.08 0.08 0.08 0.08 0.08 0.08 0.08 8.14 8.14 

0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 1.33 3.08 4.83 10.69 24.52 24.52 

.0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 10.56 

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 

0.16 

0.12 0.12 0.12 

0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 

4.91 4.27 6.63 6.76 8.07 7.85 7.15 

0.28 9.84 0.28 0.28 0.28 0.28 4.95 

0.04 0.04 0.04 0.04 0.04 0.04 0.04 

0.16 0.16 0.16 0.16 0.16 0.16 0.16 

8.80 

0.28 

0.04 

0.16 

9.90 0.12 0.12 

0.28 0.28 0.28 

0.04 0.04 0.04 

0.16 0.16 0.16 

0.12 0.12 

0.28 0.28 

0.04 0.04 

0.16 0.16 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.12 

0.16 

0.12 

0.16 

0.12 0.12 

0.28 0.28 

0.04 0.04 

0.16 0.16 

0.12 

0.16 

0.12 

0.16 

0.12 0.12 

0.28 0.28 

0.04 0.04 

0.16 0.16 

0.12 

0.16 

0.12 

0.16 

0.12 0.12 

0.28 0.28 

0.04 0.04 

0.16 0.16 

15.66 16.74 5.18 12.34 5.18 15.77 23.54 14.03 9.36 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 

0.12 0.12 0.12 0.12 0.12 0.12 

0.04 0.04 0.04 0.04 0.04 0.04 

0.28 0.28 0.28 0.28 0.28 0.28 

0.24 0.24 0.24 0.24 0.24 0.24 

0.12 5.85 0.12 0.12 0.12 0.12 

0.16 0.16 0.16 0.16 0.16 0.16 

0.08 0.08 0.08 0.08 0.08 0.08 

0.12 0.12 0.12 0.12 0.12 0.12 

0.12 0.12 0.12 0.12 0.12 0.12 

0.08 0.08 0.08 0.08 0.08 0.08 

0.12 0.12 0.12 3.95 

0.04 0.04 0.04 0.04 

0.28 0.28 0.28 0.28 

0.24 0.24 0.24 0.24 

0.12 0.12 0.12 0.12 

0.16 0.16 0.16 0.16 

0.08 0.08 0.08 9.93 

0.12 0.12 0.12 0.12 

0.12 0.12 0.12 0.12 

0.08 0.08 0.08 0.08 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

7.05 7.05 

0.04 0.04 

0.28 0.28 

0.24 0.24 

0.12 0.12 

0.16 0.16 

0.08 0.08 

0.12 0.12 

0.12 0.12 

0.08 0.08 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

7.05 7.05 

0.04 0.04 

0.28 0.28 

0.24 0.24 

0.12 0.12 

0.16 0.16 

0.08 0.08 

0.12 0.12 

0.12 0.12 

0.08 0.08 

7.05 7.05 

0.04 0.04 

0.28 0.28 

0.24 0.24 

0.12 0.12 

0.16 0.16 

0.08 0.08 

0.12 0.12 

0.12 0.12 

0.08 0.08 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

7.22 

0.12 

0.12 

0.08 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

8.97 

0.12 

0.12 

0.08 
0'1 

c..o 

Table 13. Optimal distribution of ground-water withdrawal for optimization model 5--Concluded 

Well field 

(fig. 5) 

Atrisco 

Burton 

Charles 

College 

Coronado 

Duranes 

Gonzales 

Griegos 

Leavitt 

Leyendecker 

Lomas 

Love 

Miles 

Ponderosa 

Ridgecrest 

San Jose 

Santa Barbara 

Thomas 

Vol Andia 

Volcano Cliffs 

Walker 

Webster 

West Mesa 

Yale 

Zamora 

2026 

11.26 

0.20 

0.20 

0.08 

8.14 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

6.62 

0.12 

0.12 

0.08 

2027 

11.26 

0.20 

0.20 

0.08 

0.08 

13.59 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2028 

11.26 

0.20 

0.20 

0.08 

0.08 

15.34 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2029 

11.26 

0.20 

0.20 

0.08 

0.08 

17.09 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2030 

I 1.26 

0.20 

0.20 

0.08 

0.08 

18.84 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2031 

I 1.26 

0.20 

0.20 

0.08 

0.08 

20.57 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2032 

11.26 

0.20 

0.20 

0.08 

0.08 

22.30 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2033 

11.26 

0.20 

0.20 

0.08 

0.98 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2034 

11.26 

0.20 

0.20 

0.08 

8.14 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

6.58 

0.12 

0.12 

0.08 

2035 

I 1.26 

0.20 

0.20 

0.08 

8.14 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

12.60 

0.12 

0.16 

9.93 

0.12 

0.12 

0.08 

2036 

11.26 

0.20 

0.20 

0.08 

5.81 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

0.08 

0.12 

0.12 

0.08 

2037 

11.26 

0.20 

0.20 

0.08 

8.14 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

5.28 

0.12 

0.12 

0.08 

2038 

11.26 

0.20 

0.20 

0.08 

8.14 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

0.24 

0.12 

0.16 

1.23 

0.12 

0.12 

0.08 

2039 

11.26 

0.20 

0.20 

0.08 

8.14 

24.52 

0.12 

10.56 

0.12 

0.16 

0.12 

0.28 

0.04 

0.16 

0.20 

7.05 

0.04 

0.28 

1.89 

0.12 

0.16 

9.93 

0.12 

0.12 

0.08 
Table 14. Comparison of calculated effects on the river system from GAMS and MOD FLOW for 

optimization model 5 

[All values are in acre-feet] 

Annualized net Annualized net 

river plus drains River debt/ river plus drains River debt/ Percent difference between 

leakage from surplus from leakage from surplus from GAMS and MODFLOW 

Year MOD FLOW MODFLOW1 GAMS GAMS1 river plus drains leakage2 

2006 56,526 -10,130 56,592 -10,196 0.1 

2007 54,603 6,652 54,774 6,480 0.3 

2008 52,773 -16,898 52,969 -17,093 0.4 

2009 50,886 -8,333 51,101 -8,547 0.4 

2010 49,071 -11,432 49,317 -11,678 0.5 

2011 47,302 -158 47,488 -344 0.4 

2012 45,602 12,389 45,711 12,280 0.2 

2013 43,998 588 43,913 674 -0.2 

2014 42,436 -2,299 41,975 -1,837 -1.1 

2015 42,271 -1,213 41,058 0 -2.9 

2016 44,565 -2,402 42,163 0 -5.4 

2017 46,157 -3,377 42,497 284 -7.9 

2018 46,780 -3,118 42,319 1,343 -9.5 

2019 47,092 -2,549 42,189 2,354 -10.4 

2020 47,239 -I ,816 42,131 3,292 -10.8 

2021 47,352 -1,053 42,156 4,143 -II .0 

2022 47,455 -280 42,234 4,941 -11.0 

2023 48,247 3,905 43,168 8,984 -10.5 

2024 51,701 28,614 46,599 33,715 -9.9 

2025 54,265 26,925 48,900 32,291 -9.9 

2026 56,070 21,896 50,378 27,588 -10.2 

2027 55,111 -3,566 49,044 2,510 -11.0 

2028 54,241 -1,810 48,616 3,815 -10.4 

2029 53,705 -398 48,699 4,608 -9.3 

2030 53,418 764 48,991 5,190 -8.3 

2031 53,286 1,762 49,348 5,699 -7.4 

2032 53,301 2,613 49,795 6,118 -6.6 

2033 53,602 4,562 50,451 7,712 -5.9 

2034 55,082 15,873 51,267 19,688 -6.9 

2035 57,234 28,563 52,542 33,256 -8.2 

2036 58,152 2,251 53,345 7,058 -8.3 

2037 58,644 8,421 53,905 13,159 -8.1 

2038 58,891 3,244 54,347 7,788 -7.7 

2039 59,570 12,054 54,957 16,668 -7.7 

1 A positive number represents river "surplus"; a negative number represents river "debt" 

2

((GAMS-MODFLOW)/MODFLOW) X 100 

70 
(A) Storage 

w 60,000 

::Ja:: 

0<( 

a::w MODFLOW ~>-

oa:: 

::JW [])Cl. 40,000 GAMS 

--'I- <Cw --- Simulated effects of pre-2006 ground- u_W 

ou, water withdrawal (from MODFLOW) 

>-w 

f--0:: 20,000 -o 0<( 

LLz 0-

I- - _J(fJ 

::J--' (f)<( 0 w~ a::<C 

lfJI 

<(~ --- <(I-

(Ja:: 

w~ -20,000 

-- "" ~w .,... .,... of- / I-<( 

(f)~ / 

zo -40,000 / -z / W::J .,... 0o .,... Za:: / 

~0 / 

0 -60,000 

2005 2010 2015 2020 2025 2030 2035 2040 

(B) River plus drains 

>- 120,000 t:u) 

O....J u_<C 

0~ MODFLOW 

I-<( 

...Jet:: 100,000 

::JO GAMS ifJI Wfa::- Simulated effects of pre-2006 ground- <(~~ (fJO:: 80,000 water withdrawal (from MOD FLOW) 

<CW>-

lfJ~a:: 

<(, ~~~ 

0::01--

ozw 60,000 

lfJ::Jw 

::JOU, ....J((W 

Cl.(JO:: 

a::wO 

w::J<C 40,000 ~az ....... a:: a::- ....... ~w ....... o::J ...... a::O 20,000 ...... u_::J -. -. 

o<i 

LLO 

~[]) 

_Jl.L 

----------- ~ 0 

2005 2010 2015 2020 2025 2030 2035 2040 

Figure 28. Comparison of (A) storage and (B) river plus drains components of the water 

budgets from GAMS and MODFLOW for optimization model 5. 

71 
w 

<:ltzw 

<{W 

IU. 

uz 

...J-. 

Wo 

>o 

wo 

...JN 

a:~ 

~~ <{(j) 

~ 

w 

<:ltzw 

<{W 

IU. 

Uz 

...J -

~~ ' W 

cru 

~~ <{(j) 

~ 

w 

<:lt-

~t±J IU. 

Uz 

...J- w • 

~~ •w 

cru 

wz 1- - <{(j) 

~ 

w 

<:ltzw 

<{ W IU. 

u z ...J • w o >O 

w o ...J N 

' W a: () 

wz I-_ 

<{(j) 

~ 

120 

100 

80 

60 

40 

20 

0 

2005 2010 2015 2020 2025 2030 2035 2040 

50 

30 

10 

-10 

-30 

-50 

-70 

2005 2010 2015 2020 2025 2030 2035 2040 

100 

80 

60 

40 

20 

0 

-20 

2005 2010 2015 2020 2025 2030 ~035 2040 

120 

100 

80 

60 

40 

20 

0 

2005 2010 2015 2020 2025 2030 2035 2040 

w 

<:ltzw 

<{W 

IU. 

Uz 

...J-

~~ 'W 

cru 

wz 1-- <{(j) 

~ 

w 

<:lt-

~t±J IU. 

uz 

...J-

~~ •w 

cru 

wz 1-- <{(j) 

~ 

w 

<:lt-

~t±J IU. 

Uz 

...Jw . 

~~ •w 

cru 

wz 1-- <{(j) 

~ 

w 

<:ltzw 

<{W 

IU. 

uz 

...J • wo >O 

wo 

...JN 

a:~ 

~~ <{(j) 

~ 

80 

60 

40 

20 

0 

-20 

-40 

2005 201 0 2015 2020 2025 2030 2035 2040 

90 

70 

50 

30 

10 

-10 

-30 

-50 

-- Charles 

Lomas 

- Love 

2005 2010 2015 2020 2025 2030 2035 2040 

100 

80 

60 

40 

20 

0 

-20 

2005 2010 2015 2020 2025 2030 2035 2040 

120 

100 

80 

60 

40 

20 

0 

2005 2010 2015 2020 2025 2030 2035 2040 

EXPLANATION 

MODFLOW results 

GAMS results 

Figure 29. Comparison of water-level changes from GAMS and MODFLOW for optimization model 5. 

72 
Comparison of Simulation Results for Optimal and 

Non-Optimal Distributions of Ground-Water 

Withdrawal 

Comparison of the water budget from the 

simulation using the optimal ground-water withdrawal 

distribution from optimization model 5 with the water 

budget of the simulation using the non-optimal year2000 withdrawal distribution indicates that the optimal 

distribution of ground-water withdrawal results in 

about 187,000 acre-ft greater recovery of water in 

storage between 2006 and 2040 (table 8 and fig. 17). 

This quantity is about 55,000 acre-ft less storage 

recovery than resulted from the optimal distribution of 

ground-water withdrawal from optimization model 3, 

which did not include any objectives or constraints 

related to river "debt." Thus, even though the first 9 

years of optimization model 5 are focused on 

minimization of river leakage rather than storage 

depletion, a substantial quantity of water is still "saved" 

in aquifer storage throughout the model period 

compared with the non-optimized case. The additional 

water in aquifer storage results in a very similar pattern 

of water-level change between 2000 and 2040 for 

optimization model 5 (fig. 30) as for optimization 

model 1 (fig. 19). 

APPLICABILITY OF RESULTS 

In addition to providing solutions to specific 

management issues, the simulation-optimization 

approach used in this study provides insight into 

characteristics of the ground-water-flow system in the 

MRGB that apply to other problems within the basin 

and that likely apply to other alluvial basins in the 

Southwestern United States. This section discusses the 

reliability and sensitivity of the results for the particular 

optimization models included in this study, as well as 

the broader implications of the study for the MRGB 

and other river-aquifer systems. Future studies that 

could aid in management of the river-aquifer system 

also are addressed. 

Reliability and Sensitivity 

The reliability of the five optimization models of 

this study in providing the optimal solutions to achieve 

their objectives depends on several factors related to 

the design of both the simulation and optimization 

73 

models. First of all, the river-aquifer system of the 

MRGB must be conceptualized and mathematically 

represented in the McAda and Barroll model in a 

manner that closely approximates the behavior of the 

real system. As discussed in the "Previous 

investigations" section, the simulation model 

incorporates the findings of multiple recent 

investigations intended to improve knowledge of the 

geohydrology of the basin. The "McAda and Barroll 

model" section describes the results of model 

calibration/validation, which indicated that the 

simulation results match reasonably well with the 

predevelopment water levels, quantitative flow targets, 

and patterns in water-level decline (although waterlevel decline in the Albuquerque area is slightly 

overpredicted). Therefore, the simulation model 

appears to provide a reliable representation of the 

effects of ground-water withdrawal on the aquifer 

system. Also, response functions obtained from the 

McAda and Barroll model show patterns that 

correspond with geohydrologic knowledge of the 

basin. For exan1ple, withdrawal from well fields 

located closest to the Rio Grande and completed in 

conductive sediments with good connection to the Rio 

Grande has a greater effect on the river system than 

withdrawal from fields located farthest from the Rio 

Grande and completed in sediments with relatively 

poor conductivity. 

To provide the optimal solution to a stated 

problem, the optimization models designed for this 

study must use response functions that are 

characteristic of the response of the aquifer system (as 

represented by the simulation model) for a reasonable 

range of time and hydrologic conditions. The 

sensitivity of response functions generated from the 

McAda and Barron model to a range of conditions and 

stresses within the river-aquifer system was tested 

using multiple model simulations. Specifically, river 

conditions, unit stresses, and background withdrawal 

rates used in generation of the response functions were 

varied within reasonable ranges to examine the effects 

on ground-water system responses. 

Mean monthly streamflow data for the Rio 

Grande between 1942 and 2000 were used to construct 

model input files for typical high and low seasonal river 

conditions. For the response of the system to 

withdrawal from each particular well field, two 

simulations were run with either a high or low river 

condition for all years of the simulation. For each of 

four well fields (Duranes, Leavitt, Ridgecrest, and 
35" 

45 ' 

30 ' 1--

15 ' 1--

107' 15 ' 107"00' 

l d 10...,...--

lt n 

z. 

lndran ) 

I R Wflldt :Jr"' 

ldgund 

lndran 

Middle Rio 1Grande 

Basin bou~dary 

' ...... 

· .. , , 

Rt•SNIJ,,trOP 

RiO 

r / 

I 

\. 

35" 

oo· 

l_ -

I 

45 ' ~ 

30 ' r--

.f.to 

1 

34" 

I 

\-

' "\.{, 

\ '::> Jose ..r 'C.-'"" 

,,,.,. 

Indian 

Re~erva tr on 

15 • Ba•e compiled from U.S. Geological Survey digital data, 1:100,000. 

1977, 1978; and City of Albuquerque digital data, 1:2,400, 1994 

0 10 20 30 MILES 

0 10 20 30 KILOMETERS 

30' 106"15' 

r 

l 

' 

EXPLANATION 

Water-level change, 

in feet 

Rise 

• More than 60 

• 60 to 30 

30 to 5 

Decline 

5 to 25 

25 to 50 ----j 

• 50 to 75 

l_ 

Figure 30. Simulated water-level change in the production zone (layer 5) between 2000 

and 2040 for optimal ground-water withdrawal from optimization model 5. 

74 
Thomas) chosen to be representative of a variety of 

locations and aquifer characteristics, the response 

functions generated under these consistently high and 

low river conditions were compared with the response 

functions used in the optimization models, which had 

the same background withdrawal rate and unit stress 

but used an average river condition calculated from 

data for 1990 to 2000 (which was very similar to the 

average river condition calculated from the 1942 to 

2000 data). For each well field, the mean difference in 

the annual response of the water-budget components 

for the high and low river conditions from the average 

condition was less than 3 percent with the exception of 

the Duranes well field, which showed a mean 

difference of about 13.5 percent between the average 

and low river conditions for the storage response. For 

the response of water levels in the production zone of 

the aquifer at 12 selected observation sites, the mean 

difference was about 2 percent or less for all fields 

except Duranes, where the difference was almost 12 

percent for water-level responses between the average 

and low river conditions. The greatest difference in 

response functions for the well field located closest to 

the river system and the area of riparian 

evapotranspiration was anticipated. Overall, the 

differences observed were small enough to indicate 

that the response functions used in the optimization 

mode.ls were appropriate for a reasonable range of river 

conditions. 

The response functions also were evaluated for 

sensitivity to the background rate of COA withdrawal 

used in generating them. In addition to the 25,000-acreft/yr background rate (approximating the average 

projected withdrawal between 2006 and 2015) of the 

simulations from which the final response functions 

used in the optimization models were obtained, 

background rates of about 45,000 acre-ft/yr and about 

114,000 acre-ft/yr were tested. The 45,000-acre-ft/yr 

rate approximated the average projected withdrawal 

rate for 2006 through 2040, whereas the 114,000-acreft/yr rate approximated the rate of withdrawal in 2000. 

Comparing results for the 45,000- and 25,000-acre-ft 

rates, the average differences in the annual budget 

responses for the four well fields tested (Duranes, 

Leavitt, Ridgecrest, and Thomas) ranged from 2.9 to 

14.6 percent; the average differences in the water-level 

responses ranged from less than 1 to 17.5 percent. 

Therefore, both the budget and water-level responses 

were quite similar for the 45,000- and 25,000-acre-ft 

background rates. Comparing results for the 114,000-

75 

and 25,000-acre-ft rates, the average differences for the 

four well fields ranged from 5.9 percent (for the storage 

response to withdrawal from the Leavitt field) to 39.3 

percent (for the storage response to withdrawal from 

the Ridgecrest field) in annual budget responses, with 

most average differences less than 25 percent. The 

average differences in the water-level responses ranged 

from 18.7 to 49.9 percent. These results indicate that 

nonlinearities in the simulation model can have a 

substantial effect on budget and water-level responses 

when the background withdrawal rate varies within a 

wide range. Similar to the simulations performed using 

different river conditions, model simulations also were 

performed to investigate the effects of using different 

unit stresses. When the unit stress was increased from 

1,000 to 3,000 acre-ft per well for a year, both the 

average annual budget and water-level responses to 

withdrawal in the Duranes, Leavitt, Ridgecrest, and 

Thomas well fields deviated by only as much as 3.5 

percent from the response multiplier of 3.0 that would 

represent the increased response for a perfectly linear 

model of the system. Both positive and negative unit 

stresses (the negative stress equating to a decrease in 

pumping) of 333 acre-ft per well for a year were 

simulated for the Coronado, Yale, and Zamora well 

fields. These fields were selected because they were 

among the few fields with sufficient withdrawal from 

each well at the selected background pumping rates to 

allow the full decrease in withdrawal to be applied 

without resulting in the injection of water. The average 

annual budget responses for the positive unit stress of 

333 acre-ft per well deviated by only as much as about 

2.4 percent from the multiplier of 0.33 that would 

represent the decreased response for a perfectly linear 

model when the stress was reduced from 1,000 acre-ft 

to 333 acre-ft per well; for average annual water-level 

responses in the production zone, the deviation was as 

much as about 9.2 percent. Comparison of results 

between the positive and negative unit stresses of 333 

acre-ft/yr showed that the budget responses were equal 

but opposite in sign to within about 3.6 percent and that 

water-level responses were equal but opposite in sign to 

within about 9.3 percent. Therefore, the response 

functions used in the optimization models appear to be 

appropriate for a reasonable range of unit stresses, · 

either positive or negative. 

Overall, the response functions used in this study 

are more sensitive to the background withdrawal rate 

than to river conditions or to the unit stress applied to 

each well field. Although the differences in response 
functions generated for the various background 

withdrawal rates do not invalidate the results of the 

optimization models, the sensitivity test indicates that 

the appropriateness of the background withdrawal rate 

selected for a particular optimization problem should 

be evaluated. For this study, the match between GAMS 

and MODFLOW results using response functions 

generated with the background withdrawal rate of 

45,000 acre-ft was compared with the match using 

response functions generated with the background 

withdrawal rate of 25,000 acre-ft. This evaluation 

indicated that the lower withdrawal rate was more 

appropriate given the objectives and constraints of the 

optimization models being studied. If some aspects of 

the optimization problems were to change 

substantially, use of the same background withdrawal 

rate might or might not be appropriate. 

When a linear approach to the design and 

solution of optimization models is used (as in this 

study), the model results are reliable only if they can 

provide a reasonable approximation of the behavior of 

the ground-water system despite its nonlinearities. As 

discussed in the "Formulation and solution of 

mathematical optimization models" section, nonlinear 

aspects of the ground-water system as represented in 

the McAda and Barroll model are the semiconfined 

character of the aquifer, the process of 

evapotranspiration, and interaction of the interior drain 

system with the shallow aquifer. Simulations 

performed with the McAda and Barroll model prior to 

the beginning of the optimization study indicated that 

these nonlinearities generally played only a minor role 

in simulation results. As a part of this study, effects of 

the optimal distributions of withdrawal from the five 

optimization models on water levels and components 

of the water budget were calculated using both GAMS 

and MOD FLOW. Comparison of the effects as 

calculated by the two types of models indicated that the 

linear optimization models were providing a 

reasonable approximation of the system as represented 

by the simulation model. Although budget results from 

the two models generally began to diverge after about 

the first 10 years, the degree of divergence was small 

compared with the overall quantity of water simulated 

as moving through the ground-water system. 

Of course, reliability of the results of an 

optimization model also depends on having a problem 

that is well posed and that is correctly represented 

mathematically. For this study, the first optimization 

models studied were designed to be simple enough to 

76 

allow direct comparison between the model results and 

the response functions used in model construction. 

Evaluation of these results indicated that the models 

provided the solutions that were anticipated from the 

relations among the response functions. Even as more 

complex objectives and constraints were added to the 

optimization scenarios, comparison of the response 

functions, the optimal distributions of ground-water 

withdrawal, calculations of effects on the ground-water 

system in GAMS, and results of MODFLOW models 

using both optimal and non-optimal withdrawal 

distributions demonstrated that the optimization 

models were providing appropriate solutions. 

Although results of the optimization models 

presented in this study are appropriate for the problems 

that have been posed, the applicability of the exact 

solutions of these models is necessarily limited by the 

accuracy of predictions of future conditions. 

Predictions of total water demand and of the 

availability of surface water for municipal supply (and, 

consequently, of the demand for ground water) are by 

their nature quite uncertain. Also, the likelihood is 

great that by 2040 municipal-supply wells currently in 

production will become unusable and new municipalsupply wells or well fields will come into production. 

Other aspects of the natural system and the watersupply system also may change in ways that have 

substantial effects on the applicability of the exact 

solutions to the optimization models. Nevertheless, the 

results of this study provide insight into the operation 

of the river-aquifer system of the MRGB that is 

applicaple regardless of the exact conditions under 

which future water deliveries must be made, as 

discussed in the following section. 

Implications for the Ground-Water System 

of the Middle Rio Grande Basin and Other 

Alluvial Basins of the Southwestern 

United States 

The response functions and model solutions 

generated for this study provide important information 

about the response of the ground-water system of the 

MRGB to applied stresses. In particular, the results 

indicate the general timing and magnitude of waterbudget and water-level responses. Much of this 

information is applicable to a variety of posed 

problems for management of the river-aquifer system 

of the basin and even has transfer value to other alluvial 

basins in the Southwestern United States. For example, 
response functions indicate that the time horizon 

required for the effects on the water budget and water 

levels of a 1,000-acre-ft stress (applied to the aquifer 

system over the period of 1 year) to dissipate 

completely can reasonably exceed 50 years. Therefore, 

the effects of even moderate annual ground-water 

withdrawals on river infiltration, aquifer storage, and 

water levels in river-aquifer systems of the same 

general size and hydrogeology as the MRGB can be 

substantial for ground-water management on the time 

scale of decades. Because of the length and magnitude 

of the effects of stresses, consideration of the full 

response of the river-aquifer system over time when 

management issues are addressed with sirnulationoptiinization techniques is important. 

The response functions generated for this study 

also illustrate the importance of various physical 

factors in determining the effects of a stress in an 

individual location on the components of the riveraquifer system. In particular, the response functions 

demonstrated that distance between the location of an 

applied stress and the river system is often not as 

important as the aquifer properties between the two 

features in determining the magnitude and timing of 

induced infiltration. Water levels are si1nilarly affected 

by the degree of hydraulic connection between the 

location of the applied stress and the river. Knowledge 

of th~ COA well fields where withdrawal has the 

largest effect on aquifer storage or on the river system 

is applicable to a variety of management issues, under 

a broad set of conditions with respect to water demand 

and surface-water availability. The same physical 

factors shown to be important to the response functions 

generated for COA well fields also would be important 

in other areas of the MRGB, as well as in alluvialaquifer systems elsewhere. 

The optimization models included in this study 

also indicate the general magnitude of changes in 

aquifer-system response that can be expected from 

altering distributions of major ground-water 

withdrawal in the MRGB over a planning horizon of a 

few decades. The models that incorporated objectives 

related to minimizing use of water from aquifer storage 

demonstrated that optimization of ground-water 

withdrawals over a 34-year period can result in a 

"savings" in aquifer storage of enough water to supply 

COA customers for about 2 years at year-2000 rates of 

water demand. Models indicate that this "savings" in 

aquifer storage can result in water-level rises of as 

much as 70 ft in parts of Albuquerque between 2000 

77 

and 2040. Models further indicate that the NMOSE 

guidelines for average annual water-level declines 

through 2040 (New Mexico Office of the State 

Engineer, 2003) are not likely to be exceeded by COA 

ground-water withdrawals for most locations and years 

under current (2003) management objectives and 

projections of water demand. Results from modelS 

show that alterations to the distribution of groundwater withdrawals by the COA could result in 

elimination of river "debt" about 9 years earlier than 

would be achieved using the year-2000 distribution of 

withdrawals. These results indicate that a simulationoptimization approach to ground-water management in 

the MRGB (and, therefore, likely in other 

Southwestern alluvial basins) can achieve substantial 

changes to components of the river-aquifer system. 

Limitations and Future Needs 

This study is able to indicate the general 

magnitude and timing of effects of changes in water 

management by a significant ground-water user in the 

MRGB on components of the river-aquifer system. 

However, the models and techniques used are not 

adequate to silnulate detailed aspects of the surfacewater system of the basin. For example, the models 

cannot include sufficient information to determine 

whether the full surface-water diversions planned by 

the COA would result in drying of the Rio Grande 

within the basin during any particular year. Therefore, 

the interests of all water users in the MRGB could not 

be addressed by this study. More detailed smface-water 

projections and models would be required to deal 

appropriately with surface-water issues. In the future, 

the models used here-as well as any detailed models 

of the surface-water system in the MRGB-would 

benefit from continued and perhaps enhanced 

monitoring of ground-water levels and of streamflow in 

the Rio Grande and associated irrigation canals and 

drains. Improved knowledge of ground-water/surfacewater interactions within the MRGB also would be 

beneficial to future modeling efforts. 

SUMMARY 

Concerns about considerable water-level 

declines in the Santa Fe Group aquifer system have led 

the COA, which is the largest single user of ground 

water in the MRGB of central New Mexico, to adopt a 
new strategy that calls for the direct use of surface 

water from the Rio Grande to meet most municipal 

water demand. This strategy will still require the use of 

ground-water withdrawals for municipal supply during 

times of high demand or drought. When the new 

strategy is implemented, all municipal-supply wells are 

anticipated to be tied into a single supply system for the 

entire city, as opposed to the current (2003) system, in 

which individual supply wells can supply only limited 

areas of the city. This configuration will allow 

management of the ground-water supply system as a 

whole to achieve particular objectives with respect to 

the river-aquifer system. 

The USGS, in cooperation with the COA Public 

Works Department, used a simulation-optimization 

approach to determine the optimal distribution of 

ground-water withdrawal by the COA between 2006 

and 2040 to achieve particular management objectives. 

The simulation model used in the approach was the 

McAda and Barroll ground-water-flow model, which 

incorporates knowledge of the geohydrology of the 

basin gained through a recent multiyear, multiagency 

investigation effort. The McAda and Barroll model was 

used to generate response functions that indicated the 

response of the ground-water system to a unit quantity 

of withdrawal from individual COA well fields. These 

response functions were incorporated into a linear 

approach for the design and solution of the 

optimization models. The mathematical programming 

software package GAMS was used in combination 

with the MINOS solver to achieve the solution to each 

linear optimization model. 

All five optimization models included in the 

study described in this report had objectives related to 

minimization of the effects of ground-water 

withdrawal on aquifer storage and (or) leakage from 

the river and drains. The five models were designed to 

optimize the annual withdrawal from each well field, 

rather than each individual well, using projections of 

future total demand and ground-water demand. 

Because the objectives of the models were intended to 

take into account long-term effects on the river-aquifer 

system, both the response functions used in the 

optimization models and the duration of the 

mathematical models themselves were extended 

beyond 2040. This design allowed the full effect on the 

system for 54 years to be considered for every year of 

modeled ground-water withdrawal through 2040. 

The first optimization model was designed to 

minimize total use of water from aquifer storage 

between 2006 and 2040, within constraints on annual 

ground-water demand, annual well-field capacity, and 

annual minimum withdrawal per well. Response 

functions showing the effect of ground-water 

withdrawal from an individual well field on aquifer 

storage for the following 54 years indicated that the 

well fields that would deplete aquifer storage the least 

over that time period were the San Jose, Griegos, 

Atrisco, Duranes, Coronado, Webster, and Vol Andia 

well fields. These fields include four (San Jose, 

Griegos, Atrisco, and Duranes) that are located close to 

the Rio Grande and three others that are located farther 

from the Rio Grande but that have wells completed in 

high-conductivity sediments, allowing a good 

hydraulic connection to the river system. Only these 

seven well fields were included in the optimal solution 

to optimization model 1 at withdrawal rates exceeding 

the assigned minimum. The design of optimization 

model 1 allowed easy comparison between the 

response functions and the model solution, which 

indicated that the model provided the solution that was 

expected. Effects of the optimal distribution of 

withdrawal on the water budget of the aquifer system as 

calculated in GAMS were compared with the effects 

indicated by a MODFLOW simulation using the 

optimal distribution. The comparison indicated that the 

GAMS model reasonably approximated the aquifer 

system as represented in the McAda and Barroll model 

(within only about 2 percent of the overall quantity of 

water simulated to move through the system), despite 

nonlinearities known to exist in the sin1ulation model. 

· Comparison of results from the MOD FLOW 

simulation using the optimal distribution of groundwater withdrawal with a simulation using a nonoptimal distribution approximating the distribution 

used in 2000 indicated that the optimal distribution 

results in about 242,000 acre-ft greater recovery of 

water in aquifer storage. Nearly all this storage 

recovery is derived from increased leakage from the 

river system. The increased storage recovery of the 

optimal case compared with the non-optimal case 

results in a greater magnitude of water-level rise in the 

production zone of the aquifer beneath much of 

Albuquerque. 

78 

The second optimization model was designed to 

minimize total leakage of water from the river system 

between 2006 and 2040, within the same constraints 

used in optimization model 1. Response functions 

showing the effect of ground-water withdrawal from an 

individual well field on leakage from the river plus 
drains for the following 54 years indicated that the well 

fields that would induce the least leakage over that time 

period were the Volcano Cliffs, Zamora, College, West 

Mesa, Leavitt, Lomas, Ridgecrest, and Love well 

fields. Five of these fields (Volcano Cliffs, Zamora, 

College, West Mesa, and Leavitt) are located west of 

the Rio Grande, in low-conductivity sediments that 

provide a poor connection to the river system; the 

McAda and Barron n1odel also simulates selected 

major faults in the area as hydrologic barriers to 

ground-water flow. The other three fields are located at 

large distances from the Rio Grande. Only these eight 

well fields were included in the optimal solution to 

optimization model 2 at withdrawal rates exceeding the 

assigned minimum. Analysis of model results 

indicated that the model provided the expected solution 

based on the response functions and that the GAMS 

model provided a reasonable approximation of the 

aquifer system as represented in MODFLOW. A 

MODFLOW simulation using the optimal distribution 

of ground-water withdrawal indicated that the optimal 

distribution results in about 214,000 acre-ft less river 

plus drains leakage and about 234,000 acre-ft greater 

storage depletion than the non-optimal distribution. 

The optimal distribution of model 2 also results in large 

water-level declines in the production zone of the 

aquifer west of the Rio Grande, where most of the 

ground-water withdrawal is concentrated. 

The third optimization model was designed with 

the same objective and constraints as optimization 

model 1, with an added constraint on the allowable 

water-level decline for each year of the model relative 

to the decline present in 2000. This model required the 

use of response functions quantifying the effect of 

ground-water withdrawal from each well field on the 

water-level decline at each of 25 observation sites (one 

site located within each well field). The solution for 

optimization model 3 was nearly identical to the 

solution for optimization model 1 because the 

constraint allowing no more than 2.5 ft of water-level 

decline per year was binding on the solution in only the 

second year of the model and for only two observation 

sites (the sites located in the Griegos and Atrisco well 

fields). The optimal withdrawal differed only in 2007, 

resulting in nearly the same enhanced recovery of 

aquifer storage relative to the non-optimal case as was 

observed for optimization model 1. Comparison of 

water-level declines calculated by GAMS and declines 

simulated by MODFLOW using the optimal 

79 

withdrawal distribution showed that the average 

difference was less than 8ft for most observation sites. 

The fourth optimization model was designed 

with the same objective and constraints as optimization 

model 3, with the added constraint that the arsenic 

concentration of the blended ground water could not 

exceed the USEPA drinking-water standard of 10 

micrograms per liter. For this model, the arsenic 

concentration of water drawn from each well field was 

assumed to be equal to the average of the median 

concentrations from all wells in the field, as determined 

from available chemical data (typically, samples 

collected at least biannually over a period of 10 years). 

The constraint on arsenic concentration was binding in 

every year of the model, producing a solution that still 

used many of the san1e well fields as the solutions to 

optimization models 1 and 3 (the Griegos, Atrisco, 

Duranes, San Jose, Vol Andia, and Coronado fields), 

but with different ratios of withdrawal among the 

fields. Optimization model 4 again provides a 

reasonable approxin1ation between the GAMS and 

MOD FLOW results for both the water budget and 

water-level declines. The addition of the constraints on 

water-level declines and arsenic concentration in 

optimization model 4 results in a solution with only 

about 10,000 acre-ft less storage recovery than the 

solution for optimization model 1. 

Optimization model 5 incorporated multiple 

objectives and constraints. The overall objective of the 

model was to minimize leakage from the river system 

until the "debt" owed by the COA to the Rio Grande as 

a result of ground-water withdrawals until that time had 

been eliminated, and to subsequently minimize use of 

water from aquifer storage. Constraints were the san1e 

as those used in optimization model 3 (related to 

ground-water demand, well-field capacity, minimum 

well-field withdrawal, and water-level decline), with 

the addition of a constraint that precluded 

accumulation of river "debt" after it was first 

eliminated. Calculations by the optimization model, 

which incorporated information on COA water rights 

and projected surface-water use and return flows, 

indicated that river "debt" could be eliminated after 9 

years by withdrawing ground water from the Lomas, 

Love, Ridgecrest, and Volcano Cliffs well fields at rates 

greater than the required minimum. The constraint 

requiring the accumulation of no subsequent river 

"debt" was binding in years 2015 and 2016. Thereafter, 

the solution to optimization model 5 was identical to 

the solution of optimization models 1 and 3. Overall, 
the solution to optimization model 5 resulted in about 

187,000 acre-ft greater recovery of water in storage 

between 2006 and 2040 than the non-optimal 

withdrawal distribution. Tbis quantity is about 55,000 

acre-ft less storage recovery than resulted from the 

optimal distribution of ground-water withdrawal from 

optimization models 1 and 3. 

The five optimization models presented in this 

study provide a reasonable approximation of the riveraquifer system as represented in the McAda and 

Barron ground-water-flow model, despite the 

nonlinearities inherent in that model. The McAda and 

Barron model was designed to aid in management of 

the water resources of the MRGB, and has been 

previously shown to closely reproduce the observed 

effects of stresses on the aquifer system. Analysis of 

the response functions generated by the McAda and 

Barroll model and used in the optimization models 

indicates that they should be applicable to a reasonable 

range of river conditions and ground-water withdrawal 

scenarios for the basin. Although the exact solutions to 

the optimization models presented in this report would 

vary with changes in future water demand, the 

locations of municipal-supply wells, or other factors, 

the broader implications of the model results would 

remain important to the management of regional water 

resources. In particular, information learned about the 

timing and magnitude of the effects of ground-water 

withdrawals in different locations on aquifer storage 

and on the river system could be applied to multiple 

management issues in the MRGB, and perhaps in other 

ruluvial basins of the Southwestern United States. Also, 

the models and techniques described in this report 

indicate that optimizing the distribution of groundwater withdrawal within the MRGB can achieve 

substantial changes in the quantity of aquifer-storage 

"savings," ground-water-level rise, and surface-water 

infiltration that occurs over the period of a few decades. 

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*U.S. GOVERNMENT PRINTING OFFICE: 2004- 773·102 / 54042 Region No.8 

82 

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