U.S. Department of the Interior 

U.S. Geological Survey

Numerical-Simulation and ConjunctiveManagement Models of the Hunt–

Annaquatucket–Pettaquamscutt 

Stream-Aquifer System, Rhode Island

By PAUL M. BARLOW and DAVID C. DICKERMAN

U.S. Geological Survey Professional Paper 1636

Prepared in cooperation with the 

TOWN OF NORTH KINGSTOWN,

RHODE ISLAND DEPARTMENT OF ENVIRONMENTAL MANAGEMENT,

RHODE ISLAND WATER RESOURCES BOARD, and the 

RHODE ISLAND ECONOMIC DEVELOPMENT CORPORATION

2001
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

For additional information write to: Copies of this report can be purchased 

Subdistrict Chief U.S. Geological Survey 

Massachusetts-Rhode Island District Branch of Information Services

U.S. Geological Survey Box 25286

Water Resources Division Denver, CO 80225-0286

275 Promenade, Suite 150

Providence, RI 02908

or visit our web site at

http://ma.water.usgs.gov

Library of Congress Cataloging-in-Publication Data

Barlow, Paul M.

Numerical-simulation and conjunctive-management models of the

Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island / by Paul M. 

Barlow and David C. Dickerman.

 p. cm. -- (U.S. Geological survey professional paper ; 1636)

“Prepared in cooperation with the Town of North Kingstown; Rhode Island Department 

of Environmental Management; Rhode Island Water Resources Board; and the Rhode 

Island Economic Development Corporation.”

Includes bibliographical references (p. ).

ISBN 0-607-96440-5

1. Streamflow--Rhode Island--Hunt River--Mathematical models. 2. 

Streamflow--Rhode Island--Annaquatucket River--Mathematical models. 3. 

Streamflow--Rhode Island--Pettaquamscutt River--Mathematical models. I. Dickerman, 

David C. II. Rhode Island. Dept. of Environmental Management. III. Rhode Island. 

Water Resources Board. IV. Rhode Island Port Authority and Economic Development 

Corporation. V. Title. VI. Series.

GB1207 .B37 2001

551.48’09745--dc21 2001023208
Con

CONTENTS

Abstract .............................................................................................................................................................................

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

Purpose and Scope ..................................................................................................................................................

Study Area ...............................................................................................................................................................

Previous and Related Studies ..................................................................................................................................

Acknowledgments ...................................................................................................................................................

Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer System .......................................................................................

Hydrogeologic Units ...............................................................................................................................................

Water-Supply Wells.................................................................................................................................................

Ground-Water Levels and Ground-Water Flow.......................................................................................................

Stream-Aquifer Interactions....................................................................................................................................

Hydrologic Components and Budget ......................................................................................................................

Inflow Components .......................................................................................................................................

Outflow Components.....................................................................................................................................

Hydrologic Budget ........................................................................................................................................

Steady-State Numerical Model .........................................................................................................................................

Development............................................................................................................................................................

Spatial Discretization ....................................................................................................................................

Boundary Conditions and Stresses................................................................................................................

Hydraulic Conductivity .................................................................................................................................

Calibration and Sensitivity Analysis .............................................................................................................

Hydrologic Budget ........................................................................................................................................

Stream-Aquifer Interactions....................................................................................................................................

Contributing Areas and Sources of Water to Supply Wells .....................................................................................

Transient Numerical Model...............................................................................................................................................

Development............................................................................................................................................................

Temporal Discretization and Initial Conditions ............................................................................................

Boundary Conditions and Stresses................................................................................................................

Storage Properties of Aquifer........................................................................................................................

Calibration and Hydrologic Budget ..............................................................................................................

Stream-Aquifer Interactions....................................................................................................................................

Conjunctive-Management Model......................................................................................................................................

Formulation of the Conjunctive-Management Model.............................................................................................

Response-Matrix Technique for Solution of the Conjunctive-Management Model ...............................................

Applications of the Model.......................................................................................................................................

Maintain Current Rates of Streamflow Depletion During July, August, and September..............................

Decrease Current Rates of Streamflow Depletion in the Hunt River During July, August, and 

September, With Current Rates of Streamflow Depletion in the Annaquatucket and 

Pettaquamscutt Rivers .....................................................................................................................

Maintain Current Rates of Streamflow Depletion in the Hunt River During July, August, and 

September, With Increased Rates of Streamflow Depletion Allowed in the Annaquatucket and 

Pettaquamscutt Rivers .....................................................................................................................

Decrease Current Rates of Streamflow Depletion in the Hunt River During July, August, and 

September, With Increased Rates of Streamflow Depletion Allowed in the Annaquatucket and 

Pettaquamscutt Rivers .....................................................................................................................

Summary and Conclusions................................................................................................................................................

References Cited ...............................................................................................................................................................
IV Contents

Appendix A: Water Levels at Observation Wells, 1995–96 ..............................................................................................

Appendix B: Streamflow at Partial-Record Sites, 1995–96 ..............................................................................................

Appendix C: Withdrawals from Public-Supply Wells, 1943–98.......................................................................................

PLATE

(in back pocket)

1. Model-calculated steady-state contributing areas and traveltimes to water-supply wells in the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island

FIGURES

1, 2. Maps showing:

1. Location of the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island .................

2. Drainage boundaries to the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system......................

3, 4. Graphs showing:

3. Water-level altitudes measured in selected wells in the Hunt–Annaquatucket–Pettaquamscutt 

aquifer, 1995–96........................................................................................................................................

4. (A) Water-level altitudes at well NKW-255 and (B) streamflow for the Hunt River at the 

U.S. Geological Survey gaging station for the period January 1987 through December 1996, 

Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system..................................................................

5, 6. Maps showing:

5. Altitude and configuration of the water table in the Hunt-Annaquatucket-Pettaquamscutt aquifer, 

October 7–9, 1996 .....................................................................................................................................

6. Streamflow measurement sites and distribution of gaining and losing stream reaches in the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system, October 8, 1996................................................

7, 8. Diagrams of the

7. Steady-state hydrologic budget components of the Hunt–Annaquatucket–Pettaquamscutt streamaquifer system ...........................................................................................................................................

8. Sources and sinks of water along the boundaries of the Hunt–Annaquatucket–Pettaquamscutt 

stream-aquifer system ...............................................................................................................................

9, 10. Graphs showing:

9. Annual ground-water recharge estimated from streamflow records for (A) Hunt River near East 

Greenwich and (B) Pawcatuck River at Wood River Junction, 1941–96 ..................................................

10. Monthly recharge rates estimated from streamflow records for (A) Hunt River near East Greenwich 

and (B) Pawcatuck River at Wood River Junction, 1941–96.....................................................................

11–13. Maps showing:

11. Spatial extent of active area of simulation model of the Hunt–Annaquatucket–Pettaquamscutt 

stream-aquifer system ...............................................................................................................................

12. Grid and boundary conditions of the simulation model of the Hunt–Annaquatucket–Pettaquamscutt 

stream-aquifer system (A) rows 3–125 and (B) rows 126–205 .................................................................

13. Model-calculated steady-state water table, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer 

system........................................................................................................................................................

14–19. Graphs showing:

14. Model-calculated steady-state streamflows and streamflow depletions for (A) the Hunt River and 

(B) the Annaquatucket River .....................................................................................................................

15. Average monthly measured and model-calculated mid-monthly (A) water-level altitudes at well 

NKW-255 and (B) streamflow at the Hunt River gaging station...............................................................

16. Model-calculated mid-monthly streamflow at the downstream end of the (A) Hunt, (B) Annaquatucket, 

and (C) Pettaquamscutt Rivers ..................................................................................................................

17. Selected simulated response coefficients for the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer 

system........................................................................................................................................................
Con

18. Total ground-water withdrawals during July, August, and September calculated with the 

conjunctive-management model for current rates of streamflow depletion specified for the Hunt 

River and increased rates of streamflow depletion specified for the Annaquatucket and 

Pettaquamscutt Rivers ...............................................................................................................................

19. Total ground-water withdrawals during July, August, and September calculated with the conjunctivemanagement model in which streamflow depletions in the Hunt River are reduced from current 

estimated rates and those for the Annaquatucket and Pettaquamscutt Rivers are allowed to 

increase from current estimated rates, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, 

Rhode Island..............................................................................................................................................

TABLES

1. Characteristics of water-supply wells in the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, 

Rhode Island .......................................................................................................................................................

2. Instantaneous streamflow in the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system........................

3. Gains and losses of streamflow in the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system...............

4. Estimated average annual hydrologic budget for the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer 

system, 1941–96 .................................................................................................................................................

5. Withdrawal rates (1996) specified for water-supply wells in the steady-state model of the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system .....................................................................................

6. Streamflows specified in the steady-state model of the Hunt–Annaquatucket–Pettaquamscutt streamaquifer system .....................................................................................................................................................

7. Model-calculated steady-state water-level altitudes and measured water-level altitudes on October 8, 1996, 

at observation wells in the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system.................................

8. Model-calculated steady-state average annual hydrologic budget for the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system................................................................................................................

9. Model-calculated streamflow leakage and other sources of water to supply wells in the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system .....................................................................................

10. Model-calculated steady-state and transient average annual hydrologic budgets for the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system .....................................................................................

11. Summary statistics of model-calculated, mid-monthly streamflow for the Hunt, Annaquatucket, and 

Pettaquamscutt Rivers.........................................................................................................................................

12. Average 1993–98 monthly withdrawal rates for public water-supply wells in the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system................................................................................................................

13. Model-calculated end-of-month streamflow depletions for the Hunt, Annaquatucket, and 

Pettaquamscutt Rivers for July, August, and September, with 1993-98 average monthly ground-water 

withdrawal rates ..................................................................................................................................................

14. Maximum withdrawal rates specified for public water-supply wells in the conjunctive-management model 

for the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system................................................................

15. Average monthly withdrawal rates (demands) for each water supplier in the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system, 1993–98................................................................................................

16. Monthly withdrawal rates calculated for the current configuration of public water-supply wells for 1993–98 

estimated rates of streamflow depletion in July, August, and September, Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system ...............................................................................................................

17. Monthly withdrawal rates specified for public water-supply wells in a simulation of the transient model of 

the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system......................................................................

18. Monthly withdrawal rates calculated for the modified configuration of public water-supply wells for 

1993–98 estimated rates of streamflow depletion in July, August, and September, Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system................................................................................................................

19. Monthly withdrawal rates calculated for the modified configuration of public water-supply wells and a 

15-percent reduction in the 1993–98 estimated rates of streamflow depletion in the Hunt River in July, 

August, and September, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system ....................................

20. Specified rates of streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers for conditions 

in which streamflow depletions are allowed to increase in the two rivers..........................................................
VI Contents

21. Monthly withdrawal rates calculated for the current configuration of public water-supply wells for 

increased streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers and current rates of 

streamflow depletion in the Hunt River, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system ...........

22. Monthly withdrawal rates calculated for the modified configuration of public water-supply wells for 

increased streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers and current rates of 

streamflow depletion in the Hunt River, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system ...........

23. Summary of the model-calculated total ground-water withdrawals from the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system during July, August, and September......................................................

24. Monthly withdrawal rates calculated for the current configuration of public water-supply wells for 

increased streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers and 35 percent reduction 

in streamflow depletion in the Hunt River, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system .......

CONVERSION FACTORS AND VERTICAL DATUM

CONVERSION FACTORS

Transmissivity and Hydraulic Conductivity: In this report, the units of transmissivity and hydraulic conductivity are

foot squared per day (ft2/d) and foot per day (ft/d), respectively. These are the mathematically reduced forms of

gallon per day per foot [(gal/d)/ft] and gallon per day per foot squared [(gal/d)/ft2], respectively, used by previous

authors such as Rosenshein and others (1968).

VERTICAL DATUM

Sea Level: In this report, sea level refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929)—a

geodetic datum derived from a general adjustment of the first-order level nets of the United States and Canada,

formerly called Sea Level Datum of 1929.

Multiply by To obtain

cubic foot per second (ft3/s) 0.02832 cubic meter per second

cubic foot per second per square mile (ft3/s/mi2) 0.02832 cubic meter per second per square kilometer

foot (ft) 0.3048 meter

foot per day (ft/d) 0.3048 meter per day

foot squared per day (ft2/d) 0.09290 meter squared per day

gallon per minute (gal/min) 0.00006309 cubic meter per second

gallon per minute per foot (gal/min/ft) 0.0002070 cubic meter per second per meter

inch (in.) 25.4 millimeter

inch per year (in/yr) 25.4 millimeter per year

mile (mi) 1.609 kilometer

million gallons per day (Mgal/d) 0.04381 cubic meter per second

square mile (mi2) 2.590 square kilometer

Temperature is given in degrees Fahrenheit ( ̊F), which can be converted to

degrees Celsius ( ̊C) by the following equation

 ̊C=( ̊F-32)/1.8
Ab

Numerical-Simulation and ConjunctiveManagement Models of the Hunt–

Annaquatucket–Pettaquamscutt 

Stream-Aquifer System, Rhode Island

By Paul M. Barlow and David C. Dickerman

Abstract

Numerical-simulation and optimization techniques were used to evaluate alternatives for the conjunctive management of ground- and surface-water 

resources of the Hunt–Annaquatucket–Pettaquamscutt 

stream-aquifer system in central Rhode Island. 

Ground-water withdrawals from the Hunt–

Annaquatucket–Pettaquamscutt aquifer exceeded 

8 million gallons per day during months of peak water 

use during 1993–98, and additional withdrawals have 

been proposed to meet growing demands from within 

and outside of the system boundary. The system is 

defined by the Hunt–Annaquatucket–Pettaquamscutt 

aquifer, which is composed of glacial stratified deposits, and the network of rivers, brooks, and ponds that 

overlie and are in hydraulic connection with the aquifer. Nearly all of the water withdrawn, however, is 

derived from depletions of flow in the rivers, brooks, 

and ponds that overlie the aquifer. Streamflow depletions are of concern to environmental agencies because 

of the adverse effects that reductions in streamflow can 

have on aquatic and riparian ecosystems.

A conjunctive-management model of the streamaquifer system was developed to simultaneously 

address the water-demand and streamflow-depletion 

issues. The objective of the model was to maximize 

total ground-water withdrawal from the aquifer during 

July, August, and September. These three months are 

generally the time of year when water-supply demands 

are largest and streamflows are simultaneously lowest. 

Total withdrawal from the aquifer was limited by a set 

of constraints specified in the model. These constraints 

were (1) maximum rates of streamflow depletion in 

the Hunt, Annaquatucket, and Pettaquamscutt Rivers; 

(2) minimum monthly water demands of each o

water-supply systems that withdraw water from 

aquifer; and (3) minimum and maximum withd

rates at each supply well. 

The conjunctive-management model was 

lated mathematically as a linear program. The m

was solved by a response-matrix technique that 

porates the results of transient, numerical simul

of the stream-aquifer system into the constraint 

the linear program. The basis of the technique w

the assumption that streamflow-depletion rates 

each river were a linear function of ground-wat

withdrawal rates at each well. This assumption 

shown to be valid for the conditions evaluated i

study, primarily because of the very high transm

of the aquifer near many of the wells pumped fo

supply. A transient, numerical model of the syst

was developed to simulate an average annual cy

monthly withdrawal and hydrologic conditions 

sentative of the 56-year period 1941–96. The tr

model was used to generate characteristic stream

depletion responses in each river to simulated w

drawals at each well; these characteristic respon

response coefficients, were then incorporated d

into the streamflow-depletion constraints of the 

program.

Four sets of applications of the conjunctiv

management model were made to determine wh

total ground-water withdrawal from the aquifer 

July, August, and September could be increased 

the current total withdrawal for alternative defin

of the maximum rates of streamflow depletion a

in the Hunt, Annaquatucket, and Pettaquamscut

Rivers. Current conditions were defined as the a

monthly withdrawal rates at each supply well, w
2 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syste

demands of each of the three water-supply systems, 

and estimated streamflow-depletion rates during the 

6-year period 1993–98. Total withdrawal from all wells 

in the system from July through September during 

1993–98 was 506.5 million gallons. Estimated 

streamflow-depletion rates for 1993–98 were calculated by use of the transient model, with the 1993–98 

average monthly withdrawal rates specified at each 

supply well. Streamflow-depletion rates calculated for 

July, August, and September averaged 25 percent of the 

model-calculated pre-withdrawal streamflow rates for 

the Hunt River, 19 percent for the Annaquatucket 

River, and 7 percent for the Pettaquamscutt River.

The first set of applications of the model 

were made with the current estimated rates of streamflow depletion in the Hunt, Annaquatucket, and 

Pettaquamscutt Rivers. Results of these applications 

indicated that total withdrawal from the aquifer during 

July, August, and September could be increased from 

about 8 to 18 percent (from 546.0 to 596.3 million gallons) over the current total withdrawal. The increased 

withdrawal would require modifications to the current 

annual withdrawal schedule of each supply well and, 

for the 18-percent increase, a modified network of 

supply wells that would include two new wells in the 

Annaquatucket River Basin. A second set of model 

applications then was made to determine if current estimated rates of streamflow depletion in the Hunt River 

could be reduced without increasing current estimated 

rates of streamflow depletion in the Annaquatucket or 

Pettaquamscutt Rivers. Decreases in the current rates 

of streamflow depletion in the Hunt River would result 

in increased streamflow in the river during these three 

months. Results showed that current rates of streamflow depletion in the Hunt River during July, August, 

and September could be decreased from 5 to 15 percent, depending on whether the existing or modified 

well network was used.

Subsequent model applications indicated 

that substantial increases in total ground-water withdrawal from the aquifer are possible, but would require 

increased rates of streamflow depletion in the 

Annaquatucket and Pettaquamscutt Rivers. Maximum 

increases in the July through September withdrawal 

from the aquifer of about 39 to 50 percent (from 705.1 

to 760.3 million gallons) over the current total withdrawal were calculated when streamflow-depletion 

rates in the Annaquatucket and Pettaquamscutt Rivers 

were allowed to increase from current estimated rates 

to a maximum of 25 percent of the model-calculated 

pre-withdrawal streamflow for each river during 

August, and September. Alternatively, it was sh

that current estimated rates of streamflow deple

the Hunt River during July, August, and Septem

could be reduced by as much as 35 percent for t

maximum allowed increases in streamflow depl

the Annaquatucket and Pettaquamscutt Rivers; m

mum increased withdrawal from the aquifer, ho

would range from 8 to 18 percent over the curre

withdrawal for the 35-percent reduction in strea

depletion rates in the Hunt River.

Results of the different applications of the 

demonstrate the usefulness of coupling numeric

simulation and optimization techniques for regi

scale evaluation of water-resource management 

natives. The results of the evaluation must be vi

however, within the limitations of the quality of 

available for the Hunt–Annaquatucket–Pettaqua

stream-aquifer system and representation of the 

by a simulation model. An additional limitation 

analysis was the use of an average annual cycle 

monthly withdrawal and hydrologic conditions. 

Ground-water withdrawal strategies may need t

modified to meet streamflow-depletion constrai

during extreme hydrologic events, such as drou

Contributing areas and sources of water t

supply wells also were delineated by use of a st

state model of the stream-aquifer system. The m

was developed to simulate long-term-average gr

water flow and ground-water/ surface-water inte

tions in the system during the 56-year period 19

Sources of water to the wells consisted of precip

and wastewater recharge to the aquifer, streamfl

leakage from natural stream-channel losses, stre

leakage caused by induced infiltration, and later

ground-water inflow from till and bedrock uplan

areas. 

INTRODUCTION

The Hunt–Annaquatucket–Pettaquamscu

(HAP) aquifer in central Rhode Island is the sou

water for the town of North Kingstown and part

towns of Warwick, East Greenwich, and Narrag

Ground-water withdrawals from the HAP aquif

exceeded 8 Mgal/d during months of peak wate

during 1993–98, and additional withdrawals hav

proposed to meet growing demands from within 

outside of the aquifer system boundary. Althoug

aquifer provides substantial amounts of high-qu
Introd

water, these withdrawals cannot be sustained without 

causing depletions of flow in some of the streams that 

overlie the aquifer. Streamflow depletions caused by 

ground-water withdrawals can be an environmental 

problem when such depletions decrease the water 

available to aquatic communities below minimum 

levels required to sustain healthy aquatic and riparian 

ecosystems.

Concerns by the Rhode Island Department of 

Environmental Management (RIDEM) regarding the 

effects of ground-water withdrawals on streamflow 

depletions in the HAP stream-aquifer system prompted 

an investigation to better understand the water 

resources of the system and to evaluate alternatives 

for the conjunctive management of the ground- and 

surface-water resources of the system. The streamaquifer system is defined by the HAP aquifer and the 

network of rivers, brooks, and ponds that overlie and 

are in hydraulic connection with the aquifer (fig. 1). 

The HAP aquifer is the principal water-bearing unit in 

the study area, and is composed of stratified sand-andgravel sediments that were deposited by glacial meltwater. The investigation was done from 1995 to 2000 

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

with the town of North Kingstown, RIDEM, Rhode 

Island Economic Development Corporation (RIEDC), 

and Rhode Island Water Resources Board (RIWRB).

The conflict between ground-water development 

and maintenance of streamflows for aquatic and riparian ecosystems is not unique to the towns of central 

Rhode Island. Many communities across the United 

States are seeking ways to develop sustainable groundwater supplies to meet growing demands, while simultaneously limiting the detrimental effects of such 

development on environmental resources. The methods 

of analysis used for the HAP stream-aquifer system are 

transferable to other areas where such competition 

is present between ground-water development and 

maintenance of streamflows.

Purpose and Scope

This report describes the development, 

application, and evaluation of numerical-simulation 

and conjunctive-management models of the 

Hunt–Annaquatucket–Pettaquamscutt stream-aq

system in central Rhode Island. Steady-state and 

sient numerical models were developed to impro

understanding of the hydrologic budget of the sy

the interaction of ground-water and surface-wate

components of the system, and the contributing 

and sources of water to supply wells in the syste

numerical models were developed and calibrated 

basis of hydrologic data collected during this an

ous investigations. These data include lithologic 

mation for the aquifer; hydraulic properties of th

aquifer and streambed materials; recharge to the 

water levels measured in wells, ponds, and strea

piezometers; streamflow measurements for vario

streams within the system; and ground-water wi

drawal rates from, and wastewater discharge to, 

aquifer. The models are representative of averag

drawal and hydrologic conditions in the system 

56-year period 1941–96. The U.S. Geological Su

modular three-dimensional finite-difference grou

water flow model (McDonald and Harbaugh, 19

Harbaugh and McDonald, 1996), commonly kno

MODFLOW, was used to numerically simulate t

stream-aquifer system. Contributing areas and so

of water to supply wells were determined by trac

ground-water-flow paths with the computer prog

MODPATH (Pollock, 1994), a particle-tracking 

processor package for MODFLOW.

A conjunctive-management model1 of th

stream-aquifer system was developed to simulta

neously address the water-demand and streamfl

depletion issues. The conjunctive-management 

was formulated mathematically as a linear prog

The model was solved by a response-matrix tec

that incorporates the results of transient, numer

simulation of the stream-aquifer system directly 

the constraint set of the linear program. Applica

the conjunctive-management model were made 

determine whether total ground-water withdraw

the aquifer during July, August, and September 

be increased over the current total withdrawal f

native definitions of the maximum rates of strea

depletion allowed in the Hunt, Annaquatucket, 

Pettaquamscutt Rivers.

1The term "conjunctive-management model" commonly is used in the hydrologic literature to refer to the combined use of nu

simulation and optimization to determine and evaluate alternative strategies for simultaneous management of stream-aquifer syste

of the term in this report does not imply that the U.S. Geological Survey recommends specific courses of action for management o

water resources of the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system.
4 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syste

Chipuxet

River

Basin

Sandhill Brook

0 .5 1 

0 .5 1 KILOM

STRATIFIED DEPOSITS

TILL AND BEDROCK

BOUNDARY OF THE

STREAM-AQUIFER SYSTEM

GROUND-WATER DRAINAGE 

 BOUNDARY—Where it differs

from the surface-water drainage basin

boundary

GROUND-WATER AND 

SURFACE-WATER DRAINAGE

BOUNDARY

U.S. GEOLOGICAL SURVEY

GAGING STATION AND IDENTIFIER—

Continuous-record stream-gaging station

WATER-SUPPLY WELL AND

 IDENTIFIER—See table 1

WEST

WARWICK

WEST GREENWICH

EAST GREENWICH

EXETER

NORTH KINGSTOWN

WARWICK

EXPLANATION

NK2

01117500

41 ̊37'30"

71 ̊32'30"

71 ̊27'30"

41 ̊32'30"

NK10 NK9

14A KC1

9A

3A

IW

NK6

SFH3 SFH2

SFH1

NK1

NK2

NK4

NK5

NK8 NK3

NK7

B L O C K I S L A N D S O U N D

0 10 MILES

0 10 KILOMETERS

71°45' 71°30'

41°30'

42°00'

RHODE

ISLAND

MASSACHUSETTS

MASSACHUSETTS

CONNECTICUT

01117500

Study Area

Kingston

Ann aq uatucket

River

Matt atu xet

River

H unt

River

Cocumcos suc Brook

Queens Fort Brook

Carr

Pond

Silver 

Spring

Lake

Secret

 Lake

Belleville

Pond

Potowomut 

Pond

Base map from Rhode Island Geographic Information System

East Greenwich, Slocum, Wickford,

Crompton, 1:24,000, 1988–94

Rhode Island state plane projection

Figure 1. Location of the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island.
Introd

Study Area

The HAP stream-aquifer system covers a 19.0-

square-mile area in the towns of Warwick, East 

Greenwich, North Kingstown, and Exeter, Rhode 

Island (fig. 2). The system lies within parts of the 

Hunt, Annaquatucket, Cocumcossuc, Pettaquamscutt, 

Usquepaug–Queen, and Chipuxet River Basins. The 

Hunt River was called the Potowomut River by 

Rosenshein and others (1968) and the Pettaquamscutt 

River is called the Mattatuxet River in its headwater 

reaches. The surface-water drainage area of the 

system (35.6 mi2) is smaller than the total drainage 

area of the system (39.6 mi2), because ground-water 

and surface-water drainage boundaries are not coincident in the Chipuxet and Usquepaug–Queen River 

Basins (fig. 2). Surface-water runoff in these two 

basins drains to the west of the study area, whereas 

some of the ground water recharged within the basins 

flows eastward. In this report, the study area is defined 

as the entire 39.6-square-mile drainage area shown in 

figures 1 and 2, although most data were collected 

within the 19.0-square-mile area defined by the HAP 

stream-aquifer system. The remainder, 20.6 mi2, is 

upland areas consisting of till, bedrock, and small 

amounts of sand-and-gravel deposits.

The study area consists of a relatively flat valley 

that contains several large but generally shallow ponds 

and lakes. Average depths of Belleville Pond, Carr 

(Pausacaco) Pond, and Silver Spring Lake were 8 ft or 

less during the period 1955–68 (Guthrie and Stolgitis, 

1977). Land-surface altitudes in the valley range from 

about 5 ft above sea level at the downstream end of the 

Hunt and Pettaquamscutt River Basins to a maximum 

of about 250 ft in the headwaters of the Usquepaug–

Queen River Basin. The valley is bounded by uplands 

where land-surface altitudes reach a maximum of 

about 480 ft.

Precipitation was measured during the 56-year 

period 1941–96 at a National Oceanic and Atmospheric Administration climatological station in 

Kingston, Rhode Island (fig. 1), approximately 6.5 mi 

southwest of the center of the study area (National 

Oceanic and Atmospheric Administration, 1998). 

Average annual total precipitation at the station for the 

period was 47.5 in. Monthly precipitation was fairly 

evenly distributed throughout the year, with 3.1 to 

5.0 in. of rain or snow each month. Average annual 

air temperature at the Kingston station only is 

able for the 54-year period 1943–96. During th

time, average annual air temperature was 49.3

monthly average temperatures ranged from 28

in January to 70.4 ̊F in July (average annual to

precipitation for the 54-year period was 47.8 in

Previous and Related 

Studies

Information on the geology and water re

of the study area is available from previous stu

Surficial and bedrock geology have been mapp

Power (1957, 1959), Quinn (1952, 1963), Scha

(1961), Smith (1955, 1956), and Williams (196

Streamflow measurements for the Hunt River h

been made by the USGS at a continuous-recor

streamflow-gaging station (USGS station numb

01117000, fig. 2) since August 1940; these me

ments are available in USGS publications [see 

Socolow and others (1998) for a complete listi

relevant citations]. Continuous-record streamfl

measurements also were made at a site on the 

Annaquatucket River (USGS station number 

01117100, fig. 2) during the period 1961–63 (S

and others, 1998). In addition, three low-flow p

record streamflow sites in the Hunt River Basi

used by Cervione and others (1993) to evaluate 

flow characteristics of selected streams in Rho

Island. Ground-water levels have been measur

monthly at well NKW-255 (fig. 2) since Augus

with the exception of the 2-year period from Ja

1964 through December 1965; these measurem

also are available in USGS publications (see S

and others, 1998). Reconnaissance studies on t

availability of ground water were done by Alle

(1956), Allen and others (1959), Hahn (1959), 

Johnson and Marks (1959), and Lang (1961).

A comprehensive study of the hydrologi

characteristics and sustained yield of the HAP 

was done by Rosenshein and others (1968) as 

of a larger study of the entire Potowomut–Wic

area, which includes the HAP basin and adjace

aquifer and upland areas that drain to Narragan

Bay. As part of that study, Rosenshein and othe

(1968) published maps of the transmissivity, 

saturated thickness, and water table of the aqu
6 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syste

Narrag

Unnamed Tributary

Queen River

Chipuxet River

Carr River

Carr

Pond

Silver 

 Spring

 Lake

Secret

 Lake

Carr

Pond

Potowomut 

Pond

WARWICK

NORTH KINGSTOWN WARWICK

 EAST GREENWICH

WEST

WARWICK

COVENTRY

WEST GREENWICH

NORTH KINGSTOWN

SOUTH KINGSTOWN

EXETER

SOUTH KINGSTOWN

WEST GREENWICH

EAST GREENWICH

WARWICK

 EAST 

GREENWICH

NO

KING

Cocumcossuc

Brook Basin

UsquepaugQueen

River

Basin

Hunt River Basin

Cocumcossuc

Brook Basin

Annaquatucket

River Basin

Pettaquamscutt

 River Basin

UsquepaugQueen

River

Basin

Basin

Chipuxet

River

River

Hunt

Ann aq uatucket

River

Mat t at u xet

Rive r

Cocumcussoc Brook

Scrabbletown

Brook

Fry Brook

Fr e nchtown Brook

Pettaquamscutt River

Queens Fort Brook

01117000

01117100

NKW-255

Sandhill Brook

Base map from Rhode Island Geographic Information System,

East Greenwich, Slocum, Wickford, Crompton, 1:24,000,

1988–94 Rhode Island state plane projection

41 ̊

37'

30"

71 ̊32'30" 71 ̊27'30"

41 ̊

32'

30"

0 .5 1 MILE

0 .5 1 KILOMETER

AREA WHERE SURFACE

WATER DRAINS WEST AND

 GROUND WATER DRAINS

 EAST TO THE AQUIFER

BOUNDARY OF THE

STREAM-AQUIFER SYSTEM

DRAINAGE BOUNDARY

 Ground-water drainage

boundary—Where it differs

from the surface-water

drainage basin boundary 

 Ground-water and surface-water

drainage boundary

Surface-water subbasin drainage

 boundary

SURFACE- OR GROUNDWATER MEASURMENT SITE

AND IDENTIFIER

U.S. Geological Survey gaging

station—Continuous-record

stream-gaging station

 U.S. Geological Survey gaging 

station—Discontinued,

continuous-record streamgaging station 

U.S. Geological Survey

 observation well

01117000

NKW-255

01117100

EXPLANATION

Figure 2. Drainage boundaries to the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island.
Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer S

They also prepared an unpublished map of the bedrock surface underlying the study area that is available 

at the USGS office in Providence, Rhode Island. 

Ground-water-level maps for smaller areas of the 

aquifer were made subsequent to that study by Heath 

(1991), GZA GeoEnvironmental (1992), and Fuss and 

O’Neill (1997). As part of this study, Dickerman and 

Barlow (1997) prepared a water-table map for the 

entire aquifer on the basis of water levels measured in 

October 1996. The map was used with streamflow 

measurements made during the same period to identify gaining and losing reaches of the major streams 

in the HAP system.

GZA GeoEnvironmental (1992) developed a 

ground-water-flow model of the Hunt River Basin for 

the purpose of delineating recharge areas and groundwater traveltimes to existing and proposed public 

water-supply wells in the basin. Heath (1991) discussed wellhead-protection areas for public watersupply wells in the Annaquatucket River Basin. 

Conjunctive-management models for streamaquifer systems of the northeastern United States that 

are similar in scope to the model presented in this 

report were developed by Male and Mueller (1992) 

and Mueller and Male (1993) for the Charles River 

Basin, Massachusetts, and by Barlow (1997a) for the 

Quashnet River Basin, Cape Cod, Massachusetts. 

Additional studies that use optimization techniques to 

address simultaneous management of ground-water 

withdrawals and streamflow depletions are described 

by Maddock (1974), Morel-Seytoux and Daly (1975), 

Morel-Seytoux (1975a, b), Illangasekare and MorelSeytoux (1982), and Peralta and others (1988).

Acknowledgments

The authors express appreciation to area residents who provided access to their property for the purpose of measuring water levels and streamflow during 

this investigation. The authors also thank Susan Licardi 

and Michael Martin (North Kingstown Water Department), Peter Angelone (Office of Fish and Wildlife, 

RIDEM), William Harritos (RIEDC), and Timothy 

Brown (Kent County Water Authority) for providing 

information on ground-water withdrawals and to Galen 

McGovern (RIWRB and formerly of the RIDEM), 

Ernest Panciera (RIDEM), and Douglas Heath (U.S. 

Environmental Protection Agency) for assisting in the 

collection of water-level data.

HUNT–ANNAQUATUCKET–

PETTAQUAMSCUTT STREAMAQUIFER SYSTEM

Most of the hydrogeologic data that were 

the development of the numerical models of the 

stream-aquifer system were available from prev

investigations. In addition, water-level and strea

measurements were made during this study to i

the understanding of ground-water flow and str

aquifer interaction. A hydrologic budget also w

mated for the stream-aquifer system for the 194

period.

Hydrogeologic Units

The three major hydrogeologic units in th

area are stratified sand and gravel, till, and crys

and metamorphosed sedimentary bedrock. In ad

sediments composing the streambed and pond b

within the study area form a thin veneer over th

hydrogeologic units. Till and stratified sand and 

are unconsolidated sediments deposited during 

tocene glaciation. Small, isolated, and thinly sa

areas of stratified sand-and-gravel deposits are f

within the upland areas shown as till and bedro

figure 1 (Hahn, 1959; Allen and others, 1959). T

areas of sand and gravel are not reliable sources 

water for large public supplies because they are 

saturated and have low transmissivity. Consequ

they are not considered part of the HAP stream-

system. The properties and areal extent of the h

geologic units have been described by Quinn (1

1963), Smith (1955, 1956), Allen (1956), Power 

1959), Allen and others (1959), Hahn (1959), Jo

and Marks (1959), Shafer (1961), Williams (196

Rosenshein and others (1968).

All large-capacity supply wells in the stu

derive water from the sand-and-gravel deposits 

HAP aquifer). In some locations, the sand-and-

deposits are interbedded with very fine sand and 

(Rosenshein and others, 1968). Hahn (1959), Jo

and Marks (1959), and Rosenshein and others (

also describe small areas within the HAP aquife

stratified sand and gravel is interbedded with til

their analysis of the potential sustained yield of 

aquifer, however, Rosenshein and others (1968) 
8 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syste

differentiate these small areas from other areas of the 

aquifer. Similarly, these areas were not differentiated in 

the present study.

Detailed maps of the transmissivity, bedrock altitude, and saturated thickness of the aquifer were prepared by Rosenshein and others (1968). They used 

aquifer and specific-capacity tests at 31 wells to estimate transmissivity (Rosenshein and others, 1968, 

table 1). In areas where aquifer tests had not been done, 

they calculated transmissivity from descriptions of the 

various materials penetrated by wells that were drilled 

in the aquifer. These calculations were based on the 

relation , where is transmissivity of the 

aquifer, is horizontal hydraulic conductivity of the 

aquifer, and is saturated thickness of penetrated 

material. The values of used in these calculations 

were determined from a multiple-regression analysis 

(Jenkins, 1963) of the results of the 31 aquifer and 

specific-capacity tests (Rosenshein and others, 1968, 

table 1), and ranged from 50 ft/d for fine sand to 

470 ft/d for gravel. The largest value of reported 

by Rosenshein and others (1968, table 1) was 680 ft/d 

near wells NK4 and NK5 (fig. 1).

As part of this study, transmissivity, bedrock altitude, and saturated thickness were modified in two 

areas of the aquifer. These modifications were based on 

hydrogeologic information made available since the 

1960s, and provided to the authors by the town of 

North Kingstown and the Office of Fish and Wildlife, 

RIDEM. Modifications were made in the area of the 

Lafayette State Fish Hatchery (wells SFH1, SFH2, and 

SFH3 on fig. 1) and in the area of North Kingstown 

supply well NK6 (fig. 1). These modifications generally increased the transmissivity and saturated thickness values of the aquifer over those published by 

Rosenshein and others (1968). 

Transmissivity ranges from zero at the boundary 

between the HAP aquifer and upland till and bedrock 

to a maximum reported value of 50,800 ft2/d 

(Rosenshein and others, 1968, table 1). Transmissivity 

in the area of Sandhill and Cocumcossuc Brooks is 

less than 2,700 ft2/d. Transmissivity is greater than or 

equal to 40,000 ft2/d in the Hunt River Basin near 

wells 3A, 9A, 14A, KC1, NK9, and NK10 and in the 

Annaquatucket River Basin near wells NK1, NK2, 

NK4, and NK5. Saturated thickness ranges from 

zero at the boundary between the HAP aquifer and 

upland till and bedrock to about 120 ft in the area that 

parallels the Hunt River west of Potowomut Pond 

(Rosenshein and others, 1968, pl. 3). Saturated thickness generally is less than 20 ft in the area of Sa

and Cocumcossuc Brooks and in the southweste

of the Annaquatucket River Basin in the area be

the Usquepaug–Queen and Chipuxet River Bas

Rosenshein and others (1968, table 1) giv

values of specific yield estimated for the HAP a

that range from 0.05 to 0.18. These values, dete

from short-term aquifer tests, are low and likely 

reflect the true potential of the aquifer to store a

release water in response to fluctuations of the w

table. In contrast to these low estimates, Allen a

others (1963) report values of specific yield ran

from 0.16 to 0.39 for 18 relatively undisturbed s

of stratified sand-and-gravel deposits from the a

Pawcatuck River Basin. The mean and median 

of specific yield for the samples were 0.30 and 

respectively. Furthermore, Moench and others (

determined a specific yield of 0.26 for glacial st

deposits of western Cape Cod, Massachusetts. T

values reported by Allen and others and by Moe

and others are close to average values of specifi

compiled by Johnson (1966) for materials that a

ilar to those of the HAP aquifer.

Allen and others (1963) also determined 

porosity of the 18 sediment samples from the P

tuck River Basin. The measured porosity range

0.25 to 0.50, with mean and median values of 0

These average values are close to the value of 0

determined for glacial stratified deposits of wes

Cape Cod, Massachusetts, by Garabedian and o

(1991).

Rosenshein and others (1968) report that 

veneer of streambed sediments of the Hunt Riv

ages 2 ft thick, but is as much as 10 ft thick loc

These sediments range from organically rich, v

sand and silt to boulders. Field measurements o

vertical hydraulic conductivity of streambed sed

ments at 11 sites on the Hunt River were made 

Rosenshein and others (1968) with a variable-h

permeameter. Vertical hydraulic conductivity of 

streambed sediments ranged from 0.1 ft/d for o

cally rich, fine sand and silt to 15.2 ft/d for med

coarse sand.

Water-Supply Wells

Ground water is withdrawn from the HA

fer from 18 large-capacity water-supply wells (

table 1). These consist of 14 public water-supply 

T K = hm T

Kh

m

Kh

Kh
Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer S

an industrial well, and three fisheries wells. Three 

public-water suppliers withdraw water from the HAP 

aquifer—the town of North Kingstown (NK), Rhode 

Island Economic Development Corporation (RIEDC), 

and Kent County Water Authority (KCWA). The town 

of North Kingstown has 10 supply wells, RIEDC has 3 

wells, and KCWA has a single well (table 1). Ground 

water also is withdrawn at a privately-owned industrial 

well (well IW, Hunt River Basin, fig. 1) and at three 

State-owned wells that provide water to the Lafayette 

State Fish Hatchery (wells SFH1—SFH3, 

Annaquatucket River Basin, fig. 1).

Ground-Water Levels and 

Ground-Water Flow

Monthly measurements of water levels w

made at 14 observation wells distributed throug

the HAP aquifer during the 12-month period fro

November 1995 through November 1996 (with 

exception of December 1995)2. Water-level hyd

graphs for several of these wells are shown in fi

Water-level fluctuations at the wells shown in fi

ranged from about 1.9 ft to 3.8 ft and were larg

wells with the highest mean water-level altitude

levels at NKW-255 for a representative 10-year 

2Ground-water-level measurements made at all observation wells during this investigation are given in appendix A.

1Well was rehabilitated in 1984 and the original 12-inch well screen was replaced with 8-inch well screen.

Table 1. Characteristics of water-supply wells in the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system,

Rhode Island

[Well locations are shown on figure 1. EGW, East Greenwich well; NKW, North Kingstown well; WCW, Warwick well; KCWA, Kent County Wat

ity; NK, Town of North Kingstown; RIEDC, Rhode Island Economic Development Corporation; RIDEM, Rhode Island Department of Environme

agement, Office of Fish and Wildlife. Specific capacity and well yield: based on original aquifer test done when well was installed. USGS, U.S. G

Survey; gal/min, gallons per minute; gal/min/ft, gallons per minute per foot; --, no data]

Watersupply well 

identifier

USGS well

identifier

Water 

supplier

Well depth

(feet)

 Well-screen 

interval

(feet below

land surface)

Top of screen 

altitude

(feet above or

below (-) sea level)

Casing and

screen

diameter

(inches)

Specific

capacity

(gal/min/ft)

We

(ga

Hunt River Basin

KC1 WCW-677 KCWA 118 88–118 -62.0 18 248 

3A EGW-180 RIEDC 98 68–98 -25.7 16 69 

9A WCW-39 RIEDC 61 36–61 -2.5 12 61 

14A WCW-40 RIEDC 80 50–80 -21.0 12 -- 

NK6 NKW-1299 NK 85 65–85 -10.0 18 22 

NK9 WCW-33 NK 114 74–114 -46.0 18 300 

NK10 EGW-3 NK 107 72–107 -44.0 18 140 

IW EGW-147 Industrial 77 57–77 -9.0 8 30 

Annaquatucket River Basin

SFH1 NKW-1323 RIDEM 49 39–49 71.0 16 14 

SFH2 NKW-1345 RIDEM 49 37–49 73.0 18 17 

SFH3 NKW-1346 RIDEM 71 51–71 74.0 18 22 

NK1 NKW-26 NK 50 30–50 24.5 12 68 

NK2 NKW-1156 NK 60 40–60 23.8 12 -- 

NK4 NKW-1297 NK 55 35–55 21.9 12 -- 

NK5 NKW-1298 NK 68 48–68 4.5 12 40 

Pettaquamscutt River Basin

NK3 NKW-1235 NK 67 47–67 -27.0 18 36 

NK7 NKW-1347 NK 65 55–65 -40.0 12 17 

NK8 NKW-1348 NK 55 45–55 -30.0 12 10 
10 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

N D J F M A M J J A S O N D

1995 1996

WATER-LEVEL ALTITUDE, IN FEET ABOVE SEA LEVEL

NKW-1319

0

70

5

10

15

20

25

30

35

40

45

50

55

60

65

WCW-29

WCW-270

NKW-45

NKW-255

NKW-641

NKW-591

(January 1987 through December 1996) also are shown 

in figure 4A for the purpose of comparing hydrologic 

conditions during 1995–96 to those for a longer time 

period. Water levels in the aquifer fluctuate in response 

to changes in the rates of ground-water recharge and 

discharge, which are partly a function of changes in 

climatic conditions. Generally, water levels decline 

from mid-spring to mid-fall because most precipitation 

is returned to the atmosphere by evaporation and transpiration before it reaches the water table. From midfall to mid-spring, lower rates of evaporation and transpiration allow more precipitation to percolate to the 

water table, which results in generally higher water 

levels.

A map of the water table was prepared for 

the HAP aquifer on the basis of water-level measurements made on October 7–9, 1996 (fig. 5). This period 

was selected because the water-level altitude at 

NKW-255 measured on October 8, 1996 (36.31 

above sea level), was close to the average water

altitude at the well measured for the 40-year pe

1955–63, 1966–96 (36.83 ft above sea level). O

this basis, it was assumed that water-level altitu

shown on the map are representative of near-av

conditions. Water levels were measured in 65 o

tion wells, 18 ponds, and 16 streambed piezom

(Dickerman and Barlow, 1997).

Ground water moves through the aquifer 

direction of lower water-level altitudes. The alti

and configuration of the water-table contours (fi

indicate that the general direction of ground-wa

is from the western contact of the HAP aquifer w

and bedrock uplands toward the east, northeast, 

southeast. The aquifer is recharged by precipita

stream leakage, ground-water inflow from adjac

bedrock uplands, and by wastewater discharge. 

natural conditions, ground water discharges to s

ponds, and wetlands; by evapotranspiration to t

atmosphere; and by underflow to adjacent flow 

tems. Water-supply wells, however, intercept gr

water that would have flowed to natural dischar

areas. During the measurement period in Octobe

all but four of the water-supply wells were in op

these four wells were KC1, NK10, 14A, and NK

Although withdrawals lower ground-water leve

and around the wells, the scale of figure 5 is too 

and the distances between observation wells we

large to show individual cones of depression.

Stream-Aquifer Interactions

The hydraulic interaction of the HAP aqu

with rivers, brooks, and ponds was inferred from 

stream changes in streamflow at successive stre

measurement sites, and from paired measureme

ground-water and surface-water levels at stream

piezometer sites. Gaining stream reaches are th

which net ground-water discharge to the stream 

greater than net streamflow leakage to the aquif

therefore, streamflow increases between two me

ment sites. Conversely, losing stream reaches ar

those in which net streamflow leakage to the aq

is greater than net ground-water discharge to th

stream, and streamflow decreases between two 

surement sites. Losing conditions result from n

Figure 3. Water-level altitudes measured in selected wells in 

the Hunt–Annaquatucket–Pettaquamscutt aquifer, Rhode 

Island, 1995–96. (Well locations shown on figure 5.)
Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer Sy

1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

STREAMFLOW,

IN CUBIC FEET PER SECOND (FT3/S)

LONG-TERM AVERAGE STREAMFLOW (46.4 FT3/S) FOR

PERIOD OF RECORD, OCTOBER 1940 - SEPTEMBER 1996

MEASUREMENT ON OCTOBER 8, 1996 (14.7 FT3/S)

32

42

34

36

38

40

WATER-LEVEL ALTITUDE,

IN FEET (FT) ABOVE SEA LEVEL

LONG-TERM AVERAGE WATER-LEVEL ALTITUDE (36.83 FT) FOR

YEARS 1955-63, 1966-96

MEASUREMENT ON OCTOBER 8, 1996 (36.31 FT)

A.

B.

0.5

1,000

0.7

1

2

3

4

5

7

10

20

30

40

50

70

100

200

300

400

500

700

NKW-255

Hunt River

stream-channel losses or from induced infiltration 

of streamflow caused by ground-water withdrawals. 

Paired measurements of ground- and surface-water 

levels at streambed-piezometer sites give the direction 

of flow between the aquifer and stream at each site.

Gaining and losing stream reaches were identified from streamflow measurements made at 19 to 22 

sites in the study area on three dates (table 2). In calculating gains and losses of streamflow, tributary inflows 

between a pair of measurement sites were subtracted 

from the total gain or loss between the two sites 

(table 3). This likely resulted in some error in th

gain/loss calculations because the measurement 

for some of the tributary streams were not imme

upstream of the tributary-mainstem confluence. 

streamflow measurements typically have errors 

affect the accuracy of the gain/loss calculations

result, where the gain or loss of streamflow in a 

small, it may not be possible to accurately deter

whether the reach is gaining or losing.

Figure 4. (A) Water-level altitudes at well NKW-255 and (B) streamflow for the Hunt River at the U.S. 

Geological Survey gaging station for the period January 1987 through December 1996, Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system, Rhode Island. (Locations of well and gaging station shown on fig. 2.)
12 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

40

30

20

20

10

40

30

50

60

20

50

80

60

40

50

60

80

100

120

140

50

30

50

60

50

40

80

100

180

160

140

120

200

220

120

100

80

120

120

100

60

50

40

30

20

20

10

20

20

NK10

NK9

14A

9A

3A

NK6

SFH3

SFH2

SFH1

NK1

NK2

NK4

NK5

NK8 NK3

NK7

IW

KC1

WCW-29

WCW-270

EGW-2

NKW-45

NKW-641

EGW-77

NKW-591

NKW-1319

NKW-1335

NKW-452 NKW-1333

NKW-1330

NKW-1316

NKW-255

STRATIFIED DEPOSITS

TILL AND BEDROCK

WATER-TABLE CONTOUR — Shows altitude of water table in

feet above sea level. Dashed where 

approximately located. Contour 

interval is variable

BOUNDARY OF THE STREAMAQUIFER SYSTEM

GROUND-WATER DRAINAGE 

 BOUNDARY—Where it differs

from the surface-water drainage

basin boundary

GROUND-WATER AND

SURFACE-WATER DRAINAGE

BOUNDARY

WATER-SUPPLY WELL AND

IDENTIFIER

OBSERVATION WELL AND 

U.S. GEOLOGICAL SURVEY 

IDENTIFIER–See figure 3 and

tables A1–A3

100

NK2

NKW-255

EXPLANATION

Base map from Rhode Island Geographic Information System

East Greenwich, Slocum, Wickford,

Crompton, 1:24,000, 1988–94

Rhode Island state plane projection

41 ̊37'30"

71 ̊32'30"

71 ̊27'30"

41 ̊32'30"

0 .5 1 

0 .5 1 KILO

Figure 5. Altitude and configuration of the water table in the Hunt–Annaquatucket–Pettaquamscutt aquifer, Rhode 

Island, October 7–9, 1996. (Modified from Dickerman and Barlow, 1997; not all data points used to create the 

water-table map are shown in this figure.)
Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer Sy

The distribution and rates of streamflow gains 

and losses shown in table 3 vary in response to 

changing climatic conditions and changes in the locations and rates of withdrawals at supply wells. This 

result is particularly evident for the Hunt River, where 

losing reaches migrated between sites G and K on the 

three measurement dates (table 3). Streamflow losses 

between sites G and K on the Hunt River are caused, 

in part, by withdrawals from supply wells near the 

river. Reach R-S on the Annaquatucket River was 

losing on October 8, 1996, but was gaining on April 

24, 1996, when streamflows were higher throughout 

the system (table 2). The large increases in streamflow 

on the Annaquatucket River measured between 

S and T on April 24 and October 8, 1996, are t

result of the large ground-water drainage area 

of Belleville Pond and upgradient of site T.

Streamflow gains and losses on October 

1996, when water levels were measured throug

the HAP aquifer, are shown on figure 6. Gainin

ditions were measured on this date on all reach

the exception of reach G-I on the Hunt River a

reach R-S on the Annaquatucket River (fig. 6 a

table 3). Instantaneous streamflow at the gagin

tion on the Hunt River (site P, fig. 6) on this da

(14.7 ft3/s) was lower than average streamflow 

sured at the gage for the 56-year period from O

1940 through September 1996 (46.4 ft3/s, fig. 

The low streamflow measured on this date is ty

flow in the river during early autumn (fig. 4B). 

other streams in the study area on October 8, 1

also was likely to be lower than average.

The direction of flow between the aquife

and adjoining streams determined from water 

levels measured at the 16 streambed-piezomete

sites on October 8, 1996, was generally consis

with the gaining and losing reaches identified 

from streamflow measurements on that date. 

Table 2. Instantaneous streamflow in the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system, 

Rhode Island

[Site identifiers are shown on figure 6. Streamflow is given in cubic feet 

per second and, in parentheses, million gallons per day. --, no data]

Site

identifier

Instantaneous streamflow

September 20, 

1995

April 24, 

1996

October 8, 

1996

Hunt River Basin

A 0.13 (0.08) 4.10 (2.65) 0.54 (0.35)

B .24 (.16) 5.68 (3.67) .98 (.63)

C 1.52 (.98) 16.6 (10.7) 3.07 (1.98)

D 4.73 (3.06) 23.8 (15.4) 4.81 (3.11)

E 1.24 (.80) 22.1 (14.3) 2.78 (1.80)

F 1.75 (1.13) 23.7 (15.3) 2.95 (1.91)

G 7.57 (4.89) 50.8 (32.8) 10.2 (6.59)

H .04 (.03) 8.88 (5.74) 1.28 (.83)

I 5.65 (3.65) 64.5 (41.7) 7.13 (4.61)

J 5.43 (3.51) 62.7 (40.5) 7.71 (4.98)

K 5.14 (3.32) 61.3 (39.6) 10.6 (6.85)

L -- -- 1.29 (.83) .18 (.12)

M .08 (.05) 3.65 (2.36) .90 (.58)

N .78 (.50) 5.27 (3.41) 1.82 (1.18)

O .71 (.46) 7.08 (4.58) 2.15 (1.39)

P 7.24 (4.68) 83.6 (54.0) 14.7 (9.50)

Cocumcussoc Brook Basin

Q .35 (.23) 4.37 (2.82) 1.14 (.74)

Annaquatucket River Basin

R -- -- 2.68 (1.73) 1.95 (1.26)

S -- -- 3.84 (2.48) 1.36 (.88)

T 7.44 (4.81) 20.7 (13.4) 11.7 (7.56)

Pettaquamscutt River Basin

U 1.36 (.88) 4.75 (3.07) 2.39 (1.55)

V 2.68 (1.73) 12.0 (7.76) 4.0 (2.59)

Table 3. Gains and losses of streamflow in the Hun

Annaquatucket–Pettaquamscutt stream-aquifer sys

Rhode Island

[Stream reaches are shown on figure 6. Streamflow is given in c

per second and, in parentheses, million gallons per day. --, no da

Stream 

reach

Gain or loss (-) in streamflow

September 20, 

1995

April 24, 

1996

Octo

1

Hunt River Basin

A–C 1.15 (0.74) 6.82 (4.41) 1.55 

C–D 3.21 (2.08) 7.20 (4.65) 1.74 

E–F .51 (.33) 1.60 (1.03) .17 

D–G 1.09 (.70) 3.30 (2.13) 2.44 

G–I -1.96 (-1.27) 4.82 (3.12) -4.35 

J–K -.29 (-.19) -1.40 (-.91) 2.89 

L–M -- -- 2.36 (1.53) .72 

M–N .70 (.45) 1.62 (1.05) .92 

N–O -.07 (-.05) 1.81 (1.17) .33 

K–P 1.39 (.90) 15.2 (9.82) 1.95 

Annaquatucket River Basin

R–S -- -- 1.16 (.75) -.59 

S–T -- -- 16.9 (10.90) 10.3 
14 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

Unnamed Tributary

NK2

P

V

D C 1.74

(1.12)

STREAM REACH—Letters

refer to reach identifier.

Number indicates streamflow

gain (positive), or loss

(negative), in cubic foot per

second, and in parentheses,

million gallons per day, for each

individual stream reach

DRAINAGE BOUNDARY

Ground-water drainage

boundary—Where it differs

 from the surface-water drainage

basin boundary

Ground-water and surface-water

drainage boundary

Surface-water subbasin drainage

boundary

SURFACE- OR GROUNDWATER MEASUREMENT

 SITE AND IDENTIFER

 Water-supply well

 Continuous-record stream-gaging

station—See table 2

 Partial-record streamflow site—

See table 2

EXPLANATION

Fry Brook

Frenchtown Brook

Scrabbletown Brook

Cocumcussoc Broo k

Sandhill

Brook

Hunt River

Anna quatucket

River

Mattatu xet

Riv e r

Hu n t

River

Que ens Fo rt Brook

STATE FISH

HATCHERY

Hunt River Basin

UsquepaugQueen

River

Basin

Annaquatucket

River Basin

Pettaquamscutt

River Basin

Cocumcussoc

Brook Basin

STATE FISH

HATCHERY

Basin

Chipuxet

River

NK10 NK9

14A

KC1

9A

3A

NK6

SFH3 SFH2

SFH1

NK1

NK2

NK4

NK5

NK8 NK3

NK7

T

S

D

Q

V

U

R

A

B C

L

M

N

E F

G

H

J

O

P

K

I

10.3

(6.68)

-0.59

(-0.38)

0.72

(0.47)

0.92

(0.59)

0.33

(0.21)

1.95

(1.26)

1.55

(1.00)

1.74

(1.12)

0.17

(0.11)

2.89

(1.87)

2.44

(1.58)

-4.35

(-2.81)

0 .5 

0 .5 1 KIL

Base map from Rhode Island Geographic Information System

East Greenwich, Slocum, Wickford,

Crompton, 1:24,000, 1988–94

Rhode Island state plane projection

41 ̊37'30"

71 ̊32'30"

71 ̊27'30"

41 ̊32'30"

Figure 6. Streamflow measurement sites and distribution of gaining and losing stream reaches in the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island, October 8, 1996.
Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer Sy

At four sites, however, the direction of flow was 

downward even though a streamflow gain was measured in the reach above or below the site. At two of 

these four sites (site F on Frenchtown Brook and site 

S on the Annaquatucket River), the water table was 

more than 4.5 ft below the streambed. The discrepancy between the downward water-level measurements at the piezometer sites and the gaining 

conditions measured in reaches above or below the 

piezometer sites may have resulted because water 

levels measured at the piezometer sites provide a measurement of stream-aquifer interaction at a single 

point along a stream reach, whereas changes in 

streamflow measured between two sites give net gains 

or losses of flow over an entire stream reach. Some of 

the discrepancy between the two types of measurements also may have been caused by measurement 

errors, particularly those for streamflow.

Hydrologic Components and 

Budget

A hydrologic budget was estimated for the HAP 

stream-aquifer system for the 56-year period 1941–96. 

The budget identifies and quantifies the hydrologic 

inflow and outflow components of the stream-aquifer 

system and provides data that are used in the development and calibration of the numerical models of the 

system. The hydrologic components of the system are 

illustrated in figure 7. The system shown in figure 7 is 

assumed to be in a steady-state condition (that is, there 

are no changes in water storage in the system); as a 

consequence, storage changes are not identified.

Precipitation (PR) is the ultimate source of water 

to the study area. Some of this precipitation is returned 

to the atmosphere by evaporation and transpiration at 

or near land surface (ETS). Precipitation that is not 

returned to the atmosphere either flows directly to the 

surface-water drainage system as direct runoff (DR) or 

is recharged to the ground-water system (RPR). Direct 

runoff and ground-water recharge that occur in the till 

and bedrock uplands enter the stream-aquifer system as 

streamflow (SFI) or lateral ground-water inflow (GWI).

Within the stream-aquifer system, some water is 

recharged to the aquifer by streamflow leakage that 

results from natural stream-channel losses (SLN) or 

induced infiltration caused by ground-water withdrawal 

(SLI). Ground water is discharged from the HA

aquifer to the rivers, brooks, and ponds that ma

up the surface-water network (GWD); this disch

is referred to as the base flow of streams. Groun

water also discharges by evapotranspiration wh

the water table is near land surface (ETGW), suc

along streams and in wetlands; by ground-wate

withdrawal (QW); and by underflow out of the b

at the downgradient boundary of the stream-aqu

system (GWU). Of the water that is withdrawn f

the aquifer (QW), some is exported out of the ba

(QE), some is used consumptively within the ba

(QC), some is discharged to the headwaters of t

Annaquatucket River at the Lafayette State Fish 

Hatchery (QAR), and some is returned to the aqu

by wastewater discharge (RWW). Streamflow lea

the system at the downgradient boundaries of e

of the river basins (SFO).

The following two sections describe meth

used to quantity each of the inflow and outflow 

nents of the hydrologic budget for the 1941–96 

Only those components that are sources and sin

along the boundaries of the stream-aquifer syste

included in the hydrologic budget (fig. 8). Inflo

ponents (sources) along the boundaries of the sy

are RPR, RWW, GWI, SFI, QAR, and DR; outflow 

nents (sinks) are SFO, ETGW, GWU, and QW. Pre

tion (PR), near-surface evapotranspiration (ETS

internal flows (SLN, SLI, and GWD), and two of 

components of ground-water withdrawal (QE an

are not needed, or included, in the budget.

RPR, DR, and ETGW were estimated with 

analysis techniques that are based on streamflow 

records at continuous-record gaging stations. Th

techniques require that various assumptions be 

made with respect to the streamflow record and 

logic conditions in the basin; these assumptions 

discussed in detail by Rutledge (1993 and 2000

One of these assumptions is that there are no gr

water withdrawals within the basin from which 

streamflow record is derived. Because there hav

been withdrawals from the Hunt River Basin th

out the 1941–96 period, the streamflow record o

nearby basin where much less ground water has 

been withdrawn also was used to estimate RPR, 

and ETGW, for comparison to the values of these 

three variables determined for the Hunt River B
16 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

PR

PR

ETS

ETS

RPR

RPR

RWW

SFI

SFI

SFI

SFI

SFI

GWI

GWI

GWI

SLN

SLN

SLN

SLI

GWD

GWD

ETGW

QW

QW

QW

QE

QC

QAR GWU

SFO

SFO

SFO

SFO

DR

DR

PR

ETS

DR

RPR

RWW

SFI

GWI

SLN

SLI

GWD

ETGW

QW

QE

QC

QAR

GWU

SFO

STRATIFIED DEPOSITS

TILL AND BEDROCK

BOUNDARY OF THE STREAMAQUIFER SYSTEM 

STUDY AREA BOUNDARY

GENERAL DIRECTION OF WATER

MOVEMENT

HYDROLOGIC BUDGET 

COMPONENT

Precipitation

Near-surface evapotranspiration

Direct runoff to surface water

Ground-water recharge

from precipitation

Ground-water recharge from

wastewater discharge

Streamflow from till and

bedrock upland

Lateral ground-water inflow

from till and bedrock upland

Streamflow leakage to aquifer

by natural channel losses

Streamflow leakage to aquifer

by induced infiltration

Ground-water discharge to surface water

Ground-water evapotranspiration

Ground-water withdrawal

Ground-water export

Consumptive use

Ground-water withdrawal that is 

discharged to the Annaquatucket River

Ground-water underflow

Streamflow out of basin

0 .5 

0 .5 1 KI

Base map from Rhode Island Geographic 

Information System, East Greenwich, Slocum, 

Wickford, Crompton, 1:24,000, 1988–94

Rhode Island state plane projection

SFO

EXPLANATION

41 ̊37'30"

71 ̊32'30"

71 ̊27'30"

41 ̊32'30"

Figure 7. Steady-state hydrologic budget components of the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer sy

Rhode Island.
Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer Sy

The record of the Pawcatuck River at Wood River Junction, 

Rhode Island (USGS gaging station 01117500, fig. 1), was 

selected because (1) the gaging station is relatively close to the 

HAP study area (about 18.3 mi southwest of the Hunt River 

gaging station); (2) the record includes the entire 1941-96 period; 

and (3) the percentage of stratified deposits within the drainage 

area of the gaging station (47 percent) is similar to that within the 

drainage area of the Hunt River gaging station (52 percent). This 

similarity is important because geology affects the flow and 

storage of water within a basin.

On an areal basis, average annual streamflow at the Hunt 

and Pawcatuck River gaging stations during the 1941–96 period 

was very similar, with 27.6 in. for the Hunt River and 26.4 in. for 

the Pawcatuck River. Average annual near-surface evapotranspiration (ETS) can be estimated for each basin by subtracting average 

annual streamflow from the average annual precipitation to each 

basin, which was estimated to have been 47.5 in/yr for the 1941–

96 period. Therefore, average annual ETS is estimated to have 

been 19.9 in/yr for the Hunt River Basin and 21.1 in/yr for the 

Pawcatuck River Basin for the 56-year period.

Inflow Components

Ground-water recharge from p

itation (RPR) is the major source of w

the HAP stream-aquifer system. Ann

monthly precipitation recharge rates 

estimated by analysis of streamflow 

for the Hunt and Pawcatuck Rivers w

computer program RORA (Rutledge

RORA is based on a method that est

recharge from vertical displacements 

streamflow record. The program requ

that a recession index be specified fo

basin for which recharge is estimated

recession index is the time required f

streamflow during periods of base-fl

recession to decline through one loga

(log) cycle on a semi-logarithmic plo

streamflow (on the log axis) and time 

linear axis). The recession index was 

mined for each basin with the compu

gram RECESS (Rutledge, 1993). Re

periods during December through M

were used in the analysis because ET

can be assumed to be negligible duri

these winter months. The recession i

determined for the Hunt River Basin 

was 20.2 days per log cycle and for t

Pawcatuck River Basin was 29.8 day

log cycle.

Average annual ground-water 

recharge rates calculated from stream

records for the Hunt and Pawcatuck 

gaging stations for the 1941–96 perio

25.4 in. and 25.5 in., respectively. Th

effective recharge rates over the entir

including areas of stratified sand and 

till, bedrock, wetlands, and ponds. T

average annual recharge rates are sim

those calculated for other basins of R

Island (Dickerman and others, 1990, 

Dickerman and Bell, 1993; Bent, 19

Barlow, 1997a). The total average an

volumetric recharge rate to the HAP 

aquifer system for the 1941–96 perio

estimated at 35.5 ft3/s, and was calcu

by multiplying the recharge rate of 

25.4 in/yr estimated for the Hunt Riv

Basin by the 19.0 mi2 area of the HA

system.

RPR RWW QAR DR

GWU

SFO

QW

GWI

SFI

ETGW

EXPLANATION

SOURCES

RWW

QAR

DR

GWI

SFI

GWU

SFO

QW

ETGW

RPR Ground-water recharge

from precipitation

Ground-water recharge from

wastewater discharge

Ground-water withdrawal that is 

discharged to the Annaquatucket

River

Direct runoff to surface water

Lateral ground-water inflow

from till and bedrock upland

Streamflow from till and

bedrock upland

SINKS

Ground-water underflow

Streamflow out of basin

Ground-water evapotranspiration

Ground-water withdrawal

Figure 8. Sources and sinks of water along the boundaries of the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island.
18 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

The variability of annual ground-water recharge 

within the two river basins for the 1941–96 period is 

shown by the graphs in figure 9. The maximum estimated annual recharge rate for the Hunt River Basin 

(45.1 in.) occurred in 1983 and the minimum estimated 

annual recharge rate (11.5 in.) in 1966 (fig. 9A). The 

graphs clearly indicate a period of very low recharge 

during the mid 1960s that is coincident with a period of 

severe drought throughout the northeastern United 

States. Average monthly recharge rates calculated for 

the 1941–96 period for the Hunt River Basin range 

from 0.6 in. for September to 4.3 in. for March 

(fig. 10A); a similar range was calculated for the 

Pawcatuck River Basin (0.9 in. for August to 4.0 in. for 

March; fig. 10B). For both basins, the variability of 

monthly recharge rates is smallest during July through 

October when recharge rates are lowest, as indicated by 

the standard deviation of calculated monthly recharge 

rates during the 56-year period (fig. 10).

The second component of ground-water recharge 

is wastewater discharge to the aquifer (RWW), such as 

produced by septic systems. Very few sewered areas 

are present within the HAP stream-aquifer system; 

most water delivered for domestic and other uses is 

returned to the aquifer by on-site discharge facilities. 

The amount of wastewater discharge to the aquifer 

during the 1941–96 period was estimated from information on the locations and rates of water-supply 

deliveries for the town of North Kingstown available 

for 1996. For this analysis, it was assumed that the rate 

of wastewater discharge is constant throughout the 

year. It also was assumed that wastewater recharged 

to the aquifer does not cause vertical displacements 

in the streamflow record of the Hunt River, and, as a 

consequence, that wastewater recharge is not included 

in the estimate of RPR.

Unsewered areas that receive town water were 

identified by overlaying a map of the town’s waterdistribution system onto a map of the HAP streamaquifer system. The town’s water-distribution system 

consists of several zones in which water-delivery rates 

are reported quarterly. From the water-delivery data, 

a total wastewater recharge rate of 1.2 ft3/s was estimated. This estimate may be high because no reduction 

was made to account for consumptive losses, which 

are usually estimated to be about 10 percent of water 

deliveries.

Part of the ground water that is recharged 

till and bedrock upland areas reaches the HAP 

aquifer system by lateral ground-water inflow a

boundary between the upland areas and HAP aq

(GWI). An estimate of GWI was determined by 

plying the effective average-annual recharge rat

mated for the Hunt River Basin (25.4 in/yr) by 

amount of upland area that is not drained by str

(6.8 mi2). The total average annual rate of later

ground-water inflow for the period 1941–96 wa

estimated at 12.7 ft3/s.

Streamflow from till and bedrock upland 

(SFI) was estimated from streamflow measurem

made at four partial-record gaging sites establis

the four largest streams draining the upland are

(fig. 6): Scrabbletown Brook (site A), unnamed 

tary to the Hunt River (site B), Frenchtown Bro

E), and Fry Brook (site H). Measurements were 

once each month during the 16-month period fr

August 1995 through November 1996 (with the 

tion of December 1995). These four streams ha

total drainage area within the till and bedrock u

of 12.1 mi2, which is 91.7 percent of the total u

area that is drained by streams that flow to the H

stream-aquifer system (13.2 mi2) (0.6 mi2 of up

area drains away from the stream-aquifer system 

Cocumcossuc Brook). Streamflow measuremen

made as close as possible to the boundary betw

till and bedrock upland areas and the HAP syste

total drainage area to the four partial-record site

12.4 mi2, which includes 0.3 mi2 of the HAP sy

All streamflow measurements made at these sit

given in appendix B.

Streamflow measurements made at each o

partial-record sites on each of the measurement 

were graphically correlated (by use of logarithm

plots) to the average daily streamflow on the sa

dates at the continuous-record streamflow-gagin

station on the Pawcatuck River at Wood River Ju

From these correlation graphs, an average annu

streamflow was determined for each of the four 

for the 1941–96 period that corresponds to the a

annual streamflow for the same period for the P

tuck River at Wood River Junction (194 ft3/s). T

resulting combined average annual streamflow 

these four streams is 23.9 ft3/s, of which more t

percent is for Frenchtown Brook (13.5 ft3/s). Th

streamflow originating within the till and bedro

upland drainage areas of these four streams is s
Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer Sy

less than 23.9 ft3/s because of the small area (0.3 mi2) 

within the HAP system that is drained by the streams. 

If it is assumed that the rate of runoff per square mile of 

drainage area for the entire 13.2 mi2 till and bedrock 

upland area drained by streams that flow to the HAP 

system is the same as the 12.4 mi2 drained by the four 

measured streams [1.93 (ft3/s)/mi2], then the total average annual streamflow from the entire 13.2-square-mile 

upland area is estimated to have been 25.5 ft3/s during 

the 1941–96 period. The correlation graphs also were 

used to estimate average monthly streamflows for 

each of the four streams for the 1941–96 period

estimated combined average monthly streamflo

all four streams range from a minimum of 4.5 f

September to a maximum of 48.5 ft3/s in March

Figure 10. Monthly recharge rates estimated from 

streamflow records for (A) Hunt River near East Gre

and (B) Pawcatuck River at Wood River Junction, Rh

Island, 1941–96.

Jan. Feb. Mar. Apr. May June July Aug.Sept. Oct. N

RECHARGE, IN INCHES RECHARGE, IN INCHES

0

6

1

2

3

4

5

0

6

1

2

3

4

5

A.

B.

EXPLANATION

Average monthly recharge 

 plus one standard deviation

Average monthly recharge

Average monthly recharge 

 minus one standard deviation

HUNT RIVER

PAWCATUCK RIVER

Figure 9. Annual ground-water recharge estimated from 

streamflow records for (A) Hunt River near East Greenwich 

and (B) Pawcatuck River at Wood River Junction, Rhode 

Island, 1941–96.

10

50

15

20

25

30

35

40

45

1940 1950 1960 1970 1980 1990 1997

10

50

15

20

25

30

35

40

45

ANNUAL RECHARGE, IN INCHES

A.

B.

Average annual

recharge, 1941–96

Average annual

recharge, 1941–96

HUNT RIVER

PAWCATUCK RIVER
20 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

An additional source of streamflow to the 

HAP system is ground water that is withdrawn at the 

Lafayette State Fish Hatchery (wells SFH1, SFH2, 

and SFH3 on fig. 1) and then discharged to the 

Annaquatucket River after use in the hatchery (QAR, 

fig. 7). Average annual discharge from the hatchery is 

estimated to have been 2.0 ft3/s during 1941–96, on 

the basis of measurements made in 1995–96 and 

discussions with hatchery personnel (Peter Angelone, 

Rhode Island Department of Environmental 

Management, oral commun., 1996).

Direct runoff (DR) to a stream can be calculated 

by subtracting ground-water base flow from total flow 

in the stream. Ground-water base flow in the Hunt and 

Pawcatuck Rivers was estimated with the hydrographseparation computer program PART (Rutledge, 1993). 

The theoretical basis of the program is described by 

Rutledge (1993). The average annual base flow calculated for the 1941–96 period was 22.3 in. for the Hunt 

River and 23.8 in. for the Pawcatuck River. Because 

average annual streamflow for each river during the 

same period was 27.6 in. and 26.4 in., respectively, 

average annual direct runoff for the period (streamflow 

minus base flow) is estimated to have been 5.3 in. for 

the Hunt River Basin and 2.6 in. for the Pawcatuck 

River Basin. Differences between the two values likely 

are caused by physical differences between the two 

basins, including the amount of stratified sand and 

gravel and wetlands in each basin and the topographic 

slope of each basin, and by errors introduced into the 

estimate of base flow for each basin as a result of 

ground-water withdrawals. Based on the estimate of 

direct runoff for the Hunt River Basin (5.3 in/yr), the 

total average annual rate of direct runoff from within 

the HAP stream-aquifer system and from the undrained 

upland areas (a total area of 25.8 mi2) for the 1941–96 

period was estimated at 10.1 ft3/s.

Outflow Components

Streamflow (SFO) is the major outflow component from the HAP stream-aquifer system. Rates of 

outflow were estimated for five streams: the Hunt 

River, Cocumcossuc Brook, Annaquatucket River, 

Pettaquamscutt River, and Queens Fort Brook. Continuous streamflow measurements for the 1941–96 period 

of analysis only are available for the Hunt River, during 

which time the average annual streamflow at the point 

at which the river leaves the basin (site P, fig. 6) was 

46.4 ft3/s. Queens Fort Brook is a naturally losing 

stream that is dry over most of its length during most of 

the year (Kliever, 1995). Average annual stream

for the brook is assumed to be zero. Average an

streamflows for Cocumcossuc Brook, Annaqua

River, and Pettaquamscutt River were estimated 

same manner as was done for the four streams th

into the stream-aquifer system from upland area

Partial-record streamflow-gaging sites were esta

on Cocumcossuc Brook, Annaquatucket River, 

Pettaquamscutt River, where these rivers leave 

basin (sites Q, T, and V). Streamflow was meas

each site once each month during the 16-month 

from August 1995 through November 1996 (wi

exception of December 1995). From these mea

ments, logarithmic correlation graphs were dev

between flow in each of the streams on each of 

measurement dates and the average daily stream

on the same dates at the continuous-record strea

gaging station on the Pawcatuck River at Wood 

Junction. The average annual streamflow determ

from the correlation graphs for the 1941–96 per

was 4.0 ft3/s for Cocumcossuc Brook, 17.0 ft3/s 

Annaquatucket River, and 9.5 ft3/s for Pettaqua

River. Therefore, total average annual streamflo

of the basin in the five streams was estimated at 

76.9 ft3/s.

The average annual rate of evapotranspira

from the water table (ETGW), which is sometim

referred to as riparian evapotranspiration (Rutle

1993), is equal to the difference between the av

annual ground-water recharge rate (RPR) to an a

and average annual base-flow rate out of the aq

(which, as described previously, is equal to the 

water discharge rate, GWD). ETGW was estimate

the Hunt and Pawcatuck River Basins from the 

of precipitation recharge and ground-water base 

for each basin determined with programs RORA 

PART for the 1941–96 period (described previo

The resulting estimates of ETGW are 3.1 in/yr fo

Hunt River Basin and 1.7 in/yr for the Pawcatuc

River Basin. These estimates are average rates o

entire areal extent of each basin; in areas where 

transpiration actually occurs, the rate of evapotr

ration is likely to be much higher than these bas

averages. These estimated rates of ETGW are sim

to those determined by means of the same estim

methods for other river basins of southern Rhod

Island (Dickerman and others, 1997; Barlow, 19

and for the Buzzards Bay Basin in southeastern 

Massachusetts (Bent, 1995). Based on the estim

3.1 in/yr determined for the Hunt River Basin, t
Hunt–Annaquatucket–Pettaquamscutt Stream-Aquifer Sy

average annual rate of evapotranspiration from the 

water table within the 19.0 mi2 stream-aquifer system 

was estimated at 4.3 ft3/s for the 1941–96 period.

Small amounts of ground water flow out of the 

stream-aquifer system as ground-water underflow 

(GWU) where Cocumcussoc Brook and the Hunt, 

Annaquatucket, and Pettaquamscutt Rivers leave the 

stream-aquifer system. The only location of substantial 

underflow is across a 0.5-mile width of aquifer near 

the outflow point of the Annaquatucket River (site T, 

fig. 6). The rate of underflow in this area was determined from Darcy’s law. Transmissivity of the aquifer 

was estimated from plate 2 of Rosenshein and others 

(1968), and the hydraulic gradient of the water table 

was estimated from the water-table map of the area 

given in Dickerman and Barlow (1997). The average 

annual underflow rate estimated for this area is 

1.0 ft3/s.

Ground water has been withdrawn at public 

water-supply wells in the HAP aquifer throughout the 

56-year period of analysis. During that time, the 

number of wells in use, the locations of withdrawal, 

and the rates of withdrawal have changed. Because 

there are 14 public water-supply wells in the aquifer 

and 56 years of analysis, a total of 784 record-years of 

withdrawal data are needed for the analysis. Included 

in this total are years in which withdrawal at a particular well was zero because the well was not yet installed 

or was not operated. These years of zero withdrawal 

are necessary because streamflow data for the same 

period reflect both withdrawal and non-withdrawal 

conditions. Unfortunately, withdrawal records for 

public water-supply wells in the basin are incomplete. 

Of the 784 record-years needed, only 551 record-years, 

or 70 percent of the total, were found to have been 

archived and available. Most or all of the withdrawal 

records were available for 1941–61, 1970–75, and 

1990–96, but many records were unavailable for 1962–

69 and 1976–89. Monthly withdrawals for each public 

water-supply well in the system for the 1941–96 period 

are given in appendix C.

Because the withdrawal record for the system is 

incomplete, it was not possible to determine the actual 

average annual withdrawal rates for each well. Instead, 

an estimate of the average annual withdrawal rate in 

each basin during the 56-year period was made from 

the available record, under the assumption that the 

average of the known record would approximately 

equal the average of the true record. This assumption 

is supported by the fact that withdrawal records were 

available for different time periods throughout t

total 56-year period of analysis (1941–61, 1970

and 1990–96) and were not concentrated at eith

the beginning or end of the analysis period. The 

ing average annual withdrawal rates at public w

supply wells for the 1941–96 period was estima

4.4 ft3/s for the Hunt River Basin, 1.0 ft3/s for t

Annaquatucket River Basin, and <0.1 ft3/s for t

Pettaquamscutt River Basin; total average annu

withdrawal from these wells, therefore, was est

at 5.4 ft3/s.

Ground water also has been withdrawn at 

industrial facility in the Hunt River Basin and a

Lafayette State Fish Hatchery in the Annaquatu

River Basin. Although withdrawal rates at these 

facilities are not available for the entire 1941–9

period, estimated average rates of withdrawal fo

were provided by personnel at each facility. The

were 0.4 ft3/s at the industrial facility and 2.0 ft

the fish hatchery. Assuming that the average wi

drawal rates at these wells for the 1941–96 perio

the same as the 1996 average withdrawal rates, 

additional withdrawals increase the total estima

average annual withdrawal rates from the Hunt 

Annaquatucket River Basins to 4.8 ft3/s and 3.0 

respectively. Total average annual withdrawal fr

wells in the stream-aquifer system (QW) during 

1941–96 period, therefore, was estimated at 7.8 

Hydrologic Budget

An average annual hydrologic budget for 

HAP stream-aquifer system for the 1941–96 per

be determined on the basis of the inflow and ou

components estimated in the preceding two sec

The steady-state average annual budget for the 

is

 . 

The estimated average annual hydrologic budge

the system is summarized in table 4.

As shown in the table, there is an error in 

estimated budget of -3.0 ft3/s. This error, which 

about 3.4 percent of the average of the total infl

outflow components (88.5 ft3/s), is the result of 

factors. These include (1) use of the streamflow 

of the Hunt River to estimate some of the budge

RPR RWW GWI SFI QAR + + ++ + DR

SFO = ETGW GWU QW + ++ ± error
22 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

components (RPR, DR, and ETGW), even though 

ground-water withdrawals have affected the record; 

(2) the assumption that the average annual wastewater 

recharge rate for the 56-year period is equal to that 

estimated for 1996; (3) use of a uniform recharge rate 

in the upland areas equal to the estimated rate of precipitation recharge to the HAP stream-aquifer system; 

(4) inaccuracies in the correlation graphs developed 

between streamflow in the HAP stream-aquifer system 

with streamflow in the Pawcatuck River Basin; (5) an 

incomplete record of ground-water withdrawal rates 

from the system; and (6) the assumption that the 

system is at steady state.

Although not included in the hydrologic budget, 

an estimate of the rate of ground-water export from the 

HAP stream-aquifer system (QE) can be made from the 

budget components. This rate is equal to the difference 

between the rate of ground-water withdrawal from the 

aquifer (QW ; 7.8 ft3/s) and the rate at which this water 

is returned to the stream-aquifer system. The total rate 

at which water is returned to the system is equal to 

the sum of the rate of discharge to the headwate

the Annaquatucket River at the Lafayette State 

Hatchery (QAR; 2.0 ft3/s) and the rate of wastew

discharge (RWW; 1.2 ft3/s). Therefore, the estima

rate of ground-water export from the system dur

56-year period is 4.6 ft3/s, or about 59 percent o

estimated total ground-water-withdrawal rate.

STEADY-STATE NUMERICAL 

MODEL

Ground-water flow in the HAP aquifer wa

lated with the U.S. Geological Survey modular 

dimensional finite-difference ground-water flow 

(McDonald and Harbaugh, 1988; Harbaugh and 

McDonald, 1996), commonly known as MODF

The spatial extent of the active area of the mode

is, the area of the model in which ground-water 

were simulated—is shown in figure 11. As show

the figure, ground-water flow was only simulate

within the stratified deposits. The active area of 

model is much smaller than the full lateral exten

model domain, which is 57.9 mi2. The model g

aligned approximately parallel to the northeast-

ing valleys of the Hunt River and Sandhill Broo

southeast-trending valley of the Pettaquamscutt 

The steady-state model simulated average flow 

tions that are presumed to represent the 56-year 

1941–96.

Development

Spatial Discretization

The model domain was discretized into a 

205 rows by 197 columns of square cells that ar

form size of 200 ft on each side (fig. 12). In the 

dimension, the model domain consists of a max

of four layers and extends from the water table 

intersection of the HAP aquifer with underlying 

rock. The layers were discretized with reference 

water-table map of October 1996 (Dickerman a

Barlow, 1997) and the bedrock-elevation map p

by Rosenshein and others (1968) and modified 

this study. A water-table elevation was calculate

each cell of the top layer of the model by overla

geographically referenced digital coverage of th

Table 4. Estimated average annual hydrologic budget for the 

Hunt–Annaquatucket–Pettaquamscutt stream-aquifer 

system, Rhode Island, 1941–96 

[Budget components shown schematically on figure 7]

Hydrologic budget component

Rate of flow

Cubic feet

per second

Million

gallons

per day

Estimated inflow

Recharge

Precipitation (RPR).......................... 35.5 23.0

Wastewater return flow (RWW)........ 1.2 .8

Lateral ground-water inflow (GWI) .... 12.7 8.2

Streamflow from uplands (SFI) .......... 25.5 16.5

Ground water discharged to 

Annaquatucket River (QAR)............ 2.0 1.3

Direct runoff (DR) .............................. 10.1 6.5

Total inflow..................................... 87.0 56.3

Estimated outflow

Streamflow (SFO) ............................... 76.9 49.7

Evapotranspiration (ETGW)................. 4.3 2.8

Ground-water underflow (GWU) ........ 1.0 .7

Ground-water withdrawal (QW).......... 7.8 5.0

Total outflow................................... 90.0 58.2

Budget error (inflow-outflow)................. -3.0 -1.9
Steady-State Numerical M

NK10 NK9

14A KC1

9A

3A

NK6

SFH3 SFH2

SFH1

NK1

NK2

NK4

NK5

NK3 NK8

NK7

IW

NK10 NK9

14A KC1

9A

3A

NK6

SFH3 SFH2

SFH1

NK1

NK2

NK4

NK5

NK3 NK8

NK7

IW

STRATIFIED DEPOSITS

TILL AND BEDROCK

ACTIVE AREA OF

SIMULATION MODEL

BOUNDARY OF THE

STREAM-AQUIFER SYSTEM

GROUND-WATER DRAINAGE

BOUNDARY—Where it differs

from the surface-water drainage

basin boundary

GROUND-WATER AND 

SURFACE-WATER DRAINAGE

BOUNDARY

WATER-SUPPLY WELL AND

IDENTIFIER

NK2

Base map from Rhode Island Geographic Information System

East Greenwich, Slocum, Wickford,

Crompton, 1:24,000, 1988–94

Rhode Island state plane projection

0 .5 1 M

0 .5 1 KILOMET

41 ̊37'30"

71 ̊32'30"

71 ̊27'30"

41 ̊32'30"

EXPLANATION

Figure 11. Spatial extent of active area of simulation model of the Hunt–Annaquatucket–Pettaquamscutt streamaquifer system, Rhode Island.
24 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

9A

KC1 14A

NK9 NK10

3A 

NK6 

NK2

IW

R O W 

C O L U M N

10

20

30

40

50

60

70

80

90

100

110

120

125

J

H

F

A

B

6

0

1

0 2

0

3

0

4

0

5

0

7

0

8

0

9

0

1

0

0

6

0

1

0

2

0

6

0 7

0

8

0 9

0 1

0

0

1

1

0

5

0 4

0

3

0

10

3

20

30

40

50

60

70

80

90

100

110

120

125

125

3

Potowomut

Pond

MODEL GRID

BOUNDARY OF ACTIVE AREA OF MO

No ground-water flow across this bounda

SIMULATED STREAM 

SPECIFIED FLOW FROM TILL AND BE

TO AQUIFER—Flow specified in either

layers 1 or 2

SPECIFIED FLOW OUT OF AQUIFER—

water underflow near Annaquatucket Riv

INACTIVE CELL

SPECIFIED STREAMFLOW SITE AND

 IDENTIFIER—See table 6

WATER-SUPPLY WELL AND IDENTIFIE

HYPOTHETICAL WATER-SUPPLY WEL

AND IDENTIFIER

A

EXPLANATION

0 .5 1 MILE

0 .5 1 KILOMETER

A.

H1

Figure 12. Grid and boundary conditions of the simulation model of the Hunt–Annaquatucket–Pettaquamscutt stream

aquifer system, Rhode Island, (A) rows 3–125 and (B) rows 126–205.
Steady-State Numerical M

6

0

7

0

8

0

9

0

1

0

0

1

1

0

1

2

0

1

3

0

1

4

0

1

5

0

1

6

0

1

7

0

1

8

0

1

9

0

1

9

7 5

0

126

130

140

150

160

180

170

190

200

170

180

150

160

180

170

190

200

205

140

150

130

126

6

0 7

0 8

0 9

0

1

0

0

1

1

0

1

2

0 1

3

0

1

4

0

1

5

0 1

6

0

1

7

0 1

8

0

1

9

0

1

9

7

5

0

SFH3

SFH2

SFH1

NK1

NK2

NK4

NK5

H2

H1

NK3

NK8

NK7

W

R

B.

Carr

Pond

Belleville

Pond

Secret

Lake

R O W 

C O L U M N

0 .5 1 MILE

0 .5 1 KILOMETER

water-table map onto a geographically referenced coverage of the model grid. The elevation at which the 

HAP aquifer intersects bedrock was calculated for each 

vertical stack of cells by overlaying a geographically 

referenced digital coverage of the bedrock-elevation 

map onto the model-grid coverage. The top layer of 

each stack of cells extends to a maximum depth of 10 ft 

below the water table. This uppermost layer is r

tively thin in order to simulate shallow ground-

flow near surface-water bodies as accurately as 

ble. The maximum thickness of the second and 

layers is 30 ft thick; layer 2 extends from 10 ft t

maximum of 40 ft below the water table and lay

extends from 40 ft to a maximum of 70 ft below 

Figure 12. Grid and boundary conditions of the simulation model of the Hunt–Annaquatucket–Pettaquamscutt strea

aquifer system, Rhode Island, (A) rows 3–125 and (B) rows 126–205—Continued.
26 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

water table. Layers 2 and 3 are less than 30 ft thick 

where the HAP aquifer is truncated by underlying bedrock. The fourth layer extends from the bottom of the 

third layer to the HAP aquifer/bedrock contact. 

Because the thickness of the aquifer varies laterally, the 

number of active layers within each vertical stack of 

cells varied laterally as well. The active area of each 

model layer decreased in size from the top to the 

bottom layer.

Areas of the HAP aquifer where saturated thickness was less than 5 ft were made inactive to ensure 

numerical stability of the model. This criterion resulted 

in many cells near the boundary between the HAP 

aquifer and adjoining till and bedrock uplands being 

made inactive, and a modeled area that was smaller 

than the measured extent of the HAP aquifer (compare 

boundary of HAP stream-aquifer system to active area 

of model in fig. 11).

Boundary Conditions and 

Stresses

The active area of the model was surrounded laterally by no-flow boundaries (fig. 12). The boundaries 

were based on the water-table map of the HAP aquifer 

developed by Dickerman and Barlow (1997) and 

hydrogeologic information provided in Rosenshein 

and others (1968). No-flow boundaries were specified 

along ground-water-flow lines that separate the modeled area from adjacent aquifer areas that were not 

simulated. These flow lines were located along the 

northern end of the model above the Hunt River and 

Potowomut Pond, along the eastern boundary of the 

model, and in the Pettaquamscutt River Basin. A noflow boundary condition also was specified along the 

ground-water drainage divide between the HAP aquifer 

and adjoining Chipuxet River Basin ground-water-flow 

system (fig. 12B).

Ground-water inflow from upland areas not 

drained by streams (GWI) was accounted for by injecting water into simulated wells located in the first or 

second layer of the model just inside the boundary 

between the HAP aquifer and adjoining till and bedrock (or just inside the boundary between the simulated 

area of the HAP aquifer and adjoining areas where saturated thickness was less than 5 ft). Total inflow along 

these boundaries was calculated by multiplying the 

estimated effective recharge rate of 25.4 in/yr for the 

Hunt River Basin by the total area of undrained till and 

bedrock uplands and unsimulated aquifer areas 

cent to the boundaries. Ground-water underflow 

near the Annaquatucket River where it leaves th

system was accounted for by withdrawing 1.0 f

water from simulated wells in the top layer of th

model in that area (fig. 12B).

The position of the water table was not sp

but was calculated during the simulation. If the 

tion of the calculated water table fell below the 

elevation of one or more of the model layers wi

vertical stack of cells, then those cells above the 

table became inactive. Model cells that containe

were below the water table remained active in t

simulation.

Recharge to the water table was represen

specified flow rate applied to the uppermost act

in each vertical stack of cells. Recharge from pr

tion (RPR) was specified at a rate of 25.4 in/yr to 

areas of the HAP aquifer except those overlain 

ponds and lakes. Recharge to ponds and lakes w

specified at a rate of 19.5 in/yr, which equalled 

ference between the 1941–96 average annual pr

tion rate of 47.5 in. and the estimated average a

rate of free-water-surface evaporation of 28 in. 

shallow lakes in the area (Farnsworth and others

map 3). Recharge from wastewater (RWW) was s

fied in those areas of the model that receive pub

water supplies but are unsewered. Recharge rate

wastewater specified in the model ranged from 

4.6 in/yr, and the total amount of wastewater ap

the model was 1.2 ft3/s.

Evapotranspiration from the water table (

was simulated with the evapotranspiration pack

MODFLOW. Measurements of the maximum r

maximum depth of evapotranspiration from the 

table are not available for the HAP aquifer. Con

quently, it was necessary to assume values for t

variables. A maximum evapotranspiration rate f

water table of 21.0 in/yr was assumed; this valu

equal to the estimated average growing-season 

through October) rate of free-water-surface evap

from shallow lakes in the study area (Farnswort

others, 1982, map 2). This rate also is similar to 

average annual near-surface evapotranspiration 

(ETS) determined for the Hunt and Pawcatuck R

Basins for 1941–96 (19.9 and 21.1 in/yr, respec
Steady-State Numerical M

The maximum depth of evapotranspiration from the 

water table was assumed to equal 4 ft below land 

surface. 

As described in the section on hydrologic outflow components, withdrawal records for supply wells 

in the HAP aquifer are incomplete for the 1941–96 

period. Because of this incomplete record, average 

annual withdrawal rates for each well could not be 

determined accurately for the period. Instead, the average annual withdrawal rate at each well during 1996 

was specified in the model (table 5). These withdrawal 

rates were used because withdrawal records for each 

well are complete for 1996 and because the total 

withdrawal rates from each basin during 1996 a

close to the total withdrawal rates from each ba

estimated for 1941–96 (see values given in disc

on hydrologic outflow components). Difference

between the total 1996 average annual withdraw

and estimated average annual withdrawal rates 

1941–96 are about 0.5 ft3/s for each of the Hun

Annaquatucket River Basins and about 0.2 ft3/s 

Pettaquamscutt River Basin. These differences 

small, particularly when compared to the measu

estimated) 1941–96 average flows of the three m

rivers at their locations of outflow from the stre

aquifer system—46.4 ft3/s for the Hunt River, 17

for the Annaquatucket River, and 9.5 ft3/s for th

Pettaquamscutt River.

Streams were simulated in the model wit

stream-routing package developed for MODFL

by Prudic (1989). This package simulates hydra

interaction between an aquifer and adjoining str

and tracks the amount of water within each sim

stream. All streams were simulated in the top la

of the model, and each stream was divided into 

that corresponded to individual model cells (fig

Most of the simulated streams flow through pon

and lakes that are in hydraulic connection with 

HAP aquifer. Flow between the HAP aquifer an

these ponds and lakes also was simulated with t

stream-routing package.

Flow between each stream reach and corr

sponding model cell is calculated by the stream-

package from the equation

 , 

where

is flow rate between each stream reach a

model cell (L3/T),

is streambed conductance (L2/T),

is average water level specified for the s

reach (L), and

is ground-water level calculated for the 

cell (L).

Ground water discharges to the simulated stream 

; streamflow recharges the aquifer when 

(provided there is streamflow in the reach). If, h

the calculated ground-water level ( ) falls belo

specified elevation of the bottom of the streamb

Qs Cs Hs = ( ) – h

Qs

Cs

Hs

h

h Hs > 

h

Table 5. Withdrawal rates (1996) specified for water-supply 

wells in the steady-state model of the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system, Rhode Island 

[Well locations are shown on figure 1]

Watersupply 

well

identifier

Model cell Withdrawal rate

Layer Row Column

Cubic 

feet per

second

Million 

gallons

per day

Hunt River Basin

KC1 4 35 21 0.50 0.32

3A 4 58 22 .35 .23

9A 2 30 21 .25 .16

14A 3 30 23 .61 .39

NK6 3 109 53 .38 .25

NK9 4 36 21 1.82 1.18

NK10 4 38 21 0 0

IW 3 79 26 .39 .25

Total for basin................................. 4.30 2.78

Annaquatucket River Basin

SFH1 3 162 78 .98 .63

SFH2 3 161 77 .98 .63

SFH3 3 160 76 0 0

NK1 2 149 114 .28 .18

NK2 2 150 115 .21 .14

NK4 2 154 117 .27 .18

NK5 3 161 118 .76 .49

Total for basin................................. 3.48 2.25

Pettaquamscutt River Basin

NK3 3 151 187 .28 .18

NK7 3 153 188 .03 .02

NK8 3 153 187 .01 .01

Total for basin................................. 0.32 0.21

Total for all basins .......................... 8.10 5.24
28 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

the reach ( ), then the calculated flow rate 

between the stream reach and corresponding 

model cell is a constant value equal to

. (3)

After is calculated for a reach, it is added to or 

subtracted from the streamflow of the upstream 

reach, and the resulting streamflow is routed to 

the adjacent downstream reach.

Streamflow must be specified in the first 

reach of each stream. Streamflow values greater 

than zero were specified for those streams that 

enter the HAP stream-aquifer system from upland 

areas (sites A, B, F, H, and J in fig. 12A and 

site W in fig. 12B) and at the headwater of the 

Annaquatucket River (site R, fig. 12B) where 

ground water is discharged to the stream at the 

Lafayette State Fish Hatchery. Streamflows specified in the model are given in table 6. The total 

streamflow specified at streams that enter the 

system from upland areas (26.5 ft3/s; table 6) was 

slightly larger than that estimated for the 1941–96 

period (25.5 ft3/s; table 4) to account for areas of 

the HAP aquifer with a saturated thickness less 

than 5 ft that were made inactive.

The average head and streambed elevation 

specified for each stream reach were determined 

from field measurements or estimated from topographic maps of the area. The thickness of the 

streambed of each reach was assumed to equal 

1 ft, except in ponds and lakes where it was 

assumed to equal 2 ft. Therefore, the elevation of 

the bottom of the streambed of each reach was 

either 1 ft or 2 ft below the measured or estimated 

streambed (or pond bottom) elevation.

The streambed conductance specified for 

each reach was determined from the equation 

(Prudic, 1989, p. 7)

 , (4)

where

is the streambed conductance of the reach 

(ft2/d),

is the hydraulic conductivity of the 

streambed in the reach (ft/d),

Hsbot

Qs Cs Hs Hsbot = ( ) –

Qs

Cs

KsWsLs

bs

= -------------------

Cs

Ks

is the width of the stream reach (ft),

is the length of the stream reach (ft), and

is the thickness of the streambed in the reach 

The width of each stream reach was determined from 

measurements or estimated on the basis of the width 

streams at nearby streamflow-measurement sites. The 

of each stream reach was taken to be 200 ft, which is 

length of the side of each model cell. Hydraulic cond

of streambed sediments was measured at 11 sites in th

River by Rosenshein and others (1968). These estima

values (0.1 to 15.2 ft/d) were applied to the different 

based on field observations of the streambed sedimen

the proximity of the reaches to streams where the stre

sediments were known. The resulting streambed con

tances estimated for the model ranged from a minimu

500 ft2/d along the upper reaches of the Annaquatuck

to a maximum of about 30,000 ft2/d along Sandhill B

and the lower reaches of the Annaquatucket River. St

bed conductances specified for ponds and lakes range

1,000–20,000 ft2/d. Sixty-six percent of the reaches (

ing those lying within simulated ponds and lakes) ha

estimated conductance of 20,000–30,400 ft2/d.

Ws

Ls

bs

Table 6. Streamflows specified in the steady-state model o

Hunt–Annaquatucket–Pettaquamscutt stream-aquifer syst

Rhode Island 

[Site identifiers are shown on figure 12]

Site

identifierStream name

Model cell Stream

Layer Row Column

Cubicfeet per

second

Hunt River Basin

A Scrabbletown Brook 1 119 35 2.25 

B Unnamed tributary 

#1 to Hunt River

1 103 37 2.95 

F Frenchtown Brook 1 74 13 13.50 

H Fry Brook 1 59 8 6.40 

J Unnamed tributary 

#2 to Hunt River

1 28 6 .80 

Annaquatucket River Basin

R Annaquatucket River 1 160 78 1.95 

Pettaquamscutt River Basin

W Unnamed tributary 

to Pettaquamscutt 

River

1 180 177 .62 
Steady-State Numerical M

Hydraulic Conductivity

The horizontal hydraulic conductivity of the 

HAP aquifer ( ) was determined for each vertical 

stack of cells by dividing the transmissivity by the total 

saturated thickness of the stack of cells. Transmissivity 

values were determined by overlaying a geographically 

referenced digital coverage of the transmissivity map 

of the HAP aquifer, which was prepared by Rosenshein 

and others (1968) and modified during this study, onto 

the model-grid coverage. Saturated thickness values 

were calculated by subtracting the bedrock elevation 

estimated for the bottom layer of each stack of cells 

from the water-table elevation of the top layer of the 

stack of cells. Uniform values of horizontal hydraulic 

conductivity were used in each layer of each stack, 

with the exception that a horizontal hydraulic conductivity of 50,000 ft/d was assigned to grid cells in the top 

layer of the model that were coincident with large 

ponds and lakes (fig. 12). The large value of hydraulic 

conductivity was used to simulate the lack of resistance 

to flow through the ponds and lakes.

A uniform anisotropic ratio of vertical to 

horizontal hydraulic conductivity of 1:5 was used 

throughout the model grid. This ratio is similar to 

that determined for stratified deposits of sand and 

gravel in Rhode Island and Cape Cod, Massachusetts 

(Dickerman and others, 1990; Masterson and Barlow, 

1997; Barlow, 1997b).

Calibration and Sensitivity Analysis

The model was calibrated to water-level altitudes 

measured on October 8, 1996, at 23 observation wells 

distributed throughout the stream-aquifer system 

(fig. 13); average annual streamflow measured on 

the Hunt River at the USGS gaging station; and estimated average annual streamflows for Cocumcossuc 

Brook, Annaquatucket River, Queens Fort Brook, and 

Pettaquamscutt Brook. Water-level altitudes measured 

at the 23 observation wells were assumed to be representative of average annual conditions, based on the 

measured water-level altitude at observation well 

NKW-255 on October 8, 1996, which was near its 40-

year average level (fig. 4A). The values of various 

model variables were adjusted during the calibration 

process. First, the rate of precipitation recharge was 

increased by 10 percent from the initial estimate of 

25.4 in/yr, to 28.0 in/yr. This increase was done 

because simulated streamflows were lower than the 

measured (or estimated) average annual stream

at the five measurement sites. Rates of ground-w

inflow at the boundaries between the HAP aqui

adjoining till and bedrock upland areas also we

increased by 10 percent for consistency with th

increased recharge rate. An average annual prec

tion recharge rate of 28.0 in/yr is consistent wit

ous estimates determined for aquifers of central 

southern Rhode Island (Dickerman and others, 

1997; Dickerman and Bell, 1993; Barlow, 1997

Estimates of the horizontal hydraulic con

ity of the aquifer were modified to produce imp

matches between measured and calculated wate

Most of the modifications were increases to the 

estimates of , particularly in areas close to t

boundary between the HAP aquifer and till and 

rock uplands. The average of each layer of 

ibrated model (excluding areas of ponds and lak

layer 1) ranges from 169 ft/d to 191 ft/d, which 

to the 200 ft/d estimated for sand-and-gravel de

of the HAP aquifer by Rosenshein and others (

The minimum of each layer is 25 ft/d and t

imum of each layer ranges from 531 ft/d to 

ft/d. The value specified for the anisotropic ratio 

tical to horizontal hydraulic conductivity was n

changed during model calibration. 

Finally, adjustments were made to some 

initial estimates of streambed conductance spec

for the stream reaches. The adjustments include

decreasing the largest estimate of streambed co

tance from 30,400 ft2/d to 20,000 ft2/d, and inc

the initial estimates specified for the upper reac

the Annaquatucket and Pettaquamscutt River B

Streambed conductances of the calibrated mode

range from 1,000 ft2/d to 20,000 ft2/d; 67 perce

the reaches have a conductance of 20,000 ft2/d. 

changes made to streambed conductances were 

to be reasonable, given the large number of vari

( , , , ) that must be estimated to cal

the streambed conductance of each reach.

Calculated water-level altitudes at each o

observation wells for the calibrated model are s

with the measured values in table 7. The mean o

absolute value of the difference between calcula

measured water-level altitudes (referred to as th

water-level residual) is 2.97 ft, which is less tha

cent of the total relief of the water table (170.98 

measured at the observation wells on October 8

Kh

Kh

Kh

Kh

Kh

Ks Ws Ls bs
30 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

0 .5 

0 .5 1 KILO

STRATIFIED DEPOSITS

TILL AND BEDROCK

BOUNDARY OF THE

STREAM-AQUIFER

SYSTEM

BOUNDARY OF ACTIVE 

AREA OF MODEL

GROUND-WATER

DRAINAGE BOUNDARY—

Where it differs from the surfacewater drainage basin boundary

GROUND-WATER AND 

SURFACE-WATER DRAINAGE

BOUNDARY

MODEL-CALCULATED STEADYSTATE WATER-TABLE CONTOUR—

Shows altitude of water table in feet above

sea level. Contour interval is variable

WATER-SUPPLY WELL AND IDENTIFIER

OBSERVATION WELL AND U.S. GEOLOGICAL

 SURVEY IDENTIFIER—Site where model-calculated

and measured water-table altitudes were compared

during model calibration. See table 7

NK2

EXPLANATION

100

41 ̊3

71 ̊32'30"

71 ̊27'30"

41 ̊32'30"

WCW-29

WCW-270

NKW-45

NKW-41 

EGW-41

NKW-641

NKW-1321

NKW-1320

NKW-512

NKW-602

EGW-77

NKW-627

NKW-591

NKW-1319

NKW-1335

NKW-1333

NKW-452

NKW-1316

NKW-1330

NKW-543

NKW-543

NKW-86

NKW-255

NKW-1338

NK10

NK9 14A

KC1

9A

3A

IW

NK6

SFH3 SFH2

SFH1

NK1

NK2 NK4

NK5

NK3

NK8

NK7

120

140

120

160

180

100

100

100

120

60

80

80

60

60

50

50

40

30

10

30

20

50

40

20

10

30

20

60 80

100

50

50

Base map from Rhode Island Geographic Information System

East Greenwich, Slocum, Wickford,

Crompton, 1:24,000, 1988–94

Rhode Island state plane projection

60

80

40

Figure 13. Model-calculated steady-state water table, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system

Rhode Island.
Steady-State Numerical M

A map of the simulated water table for steady-state 

conditions is shown in figure 13. Overall, there is good 

agreement between the configuration of the simulated 

water table and the measured water table shown in 

figure 5. Calculated streamflows at the five measurement sites are 42.3 ft3/s for the Hunt River, 2.9 ft3/s for 

Cocumcossuc Brook, 0.6 ft3/s for Queens Fort Brook, 

13.8 ft3/s for Annaquatucket River, and 9.7 ft3/s for 

Pettaquamscutt River. Total calculated streamflow out 

of the simulated stream-aquifer system, therefore, is 

69.3 ft3/s.

A sensitivity analysis was done to determ

relative response of calculated water levels and 

flow to uniform changes in the simulated values 

recharge, horizontal and vertical hydraulic cond

ity, and streambed conductance. Each variable w

individually increased and decreased by 10 perc

its calibrated value in a series of eight simulatio

Results of the sensitivity analysis indicate that m

calculated water levels were most sensitive to v

tions in the values specified for recharge and ho

hydraulic conductivity, and least sensitive to ch

in the values specified for vertical hydraulic con

tivity and streambed conductance. Model-calcu

streamflow for the three largest rivers (the Hunt

Annaquatucket, and Pettaquamscutt) were most 

tive to increases and decreases in the values spe

for recharge.

Hydrologic Budget

The steady-state, average annual hydrolo

budget of the stream-aquifer system calculated w

calibrated model is shown in table 8. Recharge 

precipitation is the largest component of inflow 

system and streamflow is the largest componen

flow from the system. The calculated total flow 

through the system, about 83 ft3/s, is similar to t

rate estimated for the system for the 1941–96 p

(about 88.5 ft3/s, table 4). There are, however, a 

differences between the model-calculated hydro

budget and the estimated hydrologic budget. Fi

direct runoff is not simulated within the modele

Consequently, total inflow and outflow rates sho

and are, somewhat less for the model budget th

the estimated budget. This result may be one re

why total streamflow calculated by the model a

five outflow measurement sites (69.3 ft3/s) is le

the total streamflow measured (or estimated) at 

sites during 1941–96 (76.9 ft3/s; table 4). Secon

because the precipitation recharge rate specified 

model (28.0 in/yr) is larger than that for the esti

budget (25.4 in/yr), the rates of precipitation rec

and lateral ground-water inflow are larger for the 

budget (53.8 ft3/s; table 8) than for the estimate

budget (48.2 ft3/s; table 4). Finally, because the 

extent of the active area of the model is smaller 

the areal extent of the stream-aquifer system (fi

Table 7. Model-calculated steady-state water-level altitudes 

and measured water-level altitudes on October 8, 1996, 

at observation wells in the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system, Rhode Island 

[Well locations are shown in figure 13. USGS well identifier: EGW, East 

Greenwich well; NKW, North Kingstown well; WCW, Warwick well. 

USGS, U.S. Geological Survey]

USGS well

identifier

Model

location

(layer, row,

column)

Water-level altitude

Calculated

(feet above 

sea level)

Measured

(feet above

sea level)

Difference

(feet)

WCW-29 1, 8, 33 6.86 1.41 5.45

WCW-270 1, 23, 31 16.02 19.58 -3.56

NKW-41 1, 29, 49 15.12 14.05 1.07

NKW-45 1, 43, 43 28.47 29.47 -1.00

EGW-41 1, 54, 19 30.76 31.23 -.47

NKW-627 1, 66, 28 39.45 38.66 .79

NKW-641 1, 69, 43 41.91 41.38 .53

NKW-1321 1, 93, 53 49.53 45.28 4.25

EGW-77 1, 96, 39 42.98 43.16 -.18

NKW-591 1, 102, 72 53.30 52.12 1.18

NKW-602 1, 111, 53 53.82 47.32 6.50

NKW-1320 1, 117, 60 59.38 52.04 7.34

NKW-512 1, 130, 71 66.41 63.10 3.31

NKW-1319 1, 139, 83 69.04 67.64 1.40

NKW-452 1, 135, 133 43.39 44.01 -.62

NKW-1335 2, 146, 102 52.38 57.91 -5.53

NKW-1333 3, 150, 112 49.73 50.08 -.35

NKW-1316 1, 160, 148 37.84 37.13 .71

NKW-1330 2, 170, 128 65.87 68.36 -2.49

NKW-255 1, 170, 159 40.74 36.31 4.43

NKW-543 2, 177, 111 89.53 93.71 -4.18

NKW-86 2, 180, 69 169.19 172.39 -3.20

NKW-1338 2, 188, 107 113.80 104.36 9.44
32 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

the relative amounts of precipitation recharge and 

lateral ground-water inflow to the total inflow of each 

budget differ.

Stream-Aquifer Interactions

The calibrated model provides information on 

stream-aquifer interactions that supplements data collected in the field. This information includes the locations and rates of ground-water discharge to streams, 

streamflow leakage to the aquifer, and streamflow 

depletions caused by ground-water withdrawals. The 

model also can be used to estimate streamflow conditions before withdrawals began.

 Total ground-water discharge to the simulated 

surface-water network for the average hydrologic 

conditions simulated by the model is 52.0 ft3/s, 

whereas total streamflow leakage to the HAP a

calculated by the model is 11.2 ft3/s. Streamflo

age consists of both natural stream-channel los

(SLN) and induced infiltration (SLI). To determi

locations and rates of natural stream-channel los

induced infiltration, it was necessary to compar

streamflow-leakage rates calculated for each sim

stream cell with the calibrated model to those c

lated for conditions of no withdrawals at the sim

wells. Two such conditions were simulated: in 

simulation, withdrawals were eliminated at all 

wells; in a second simulation, withdrawals wer

nated at all wells except those at the Lafayette S

Fish Hatchery. The second simulation was nece

isolate the effects of ground-water withdrawals 

fish hatchery.

Streamflow-leakage rates calculated for t

two simulations indicate that the average annua

induced infiltration caused by ground-water wi

als is 1.2 ft3/s of the total 11.2 ft3/s of streamflo

age to the HAP aquifer. Total average annual in

infiltration for the Hunt River Basin is 0.7 ft3/s

Annaquatucket River Basin is 0.3 ft3/s; and for 

Pettaquamscutt River Basin is 0.2 ft3/s. The rem

streamflow leakage to the HAP aquifer, 10.0 ft3

the average annual rate of natural stream-chann

losses. These losses take place primarily along 

reaches that are close to the boundary of the HA

fer with upland areas of till and bedrock, and at 

reaches on the downgradient ends of the larger 

Some of the locations of the largest natural stre

channel losses are Frenchtown Brook above its 

ence with the Hunt River (3.8 ft3/s); the downg

end of Belleville Pond (1.0 ft3/s); the upper rea

Scrabbletown Brook (0.9 ft3/s); the upper reach 

Annaquatucket River (0.8 ft3/s); and the downg

end of Potowomut Pond (0.7 ft3/s). Streamflow 

calculated along the upper reach of the Annaqu

River consists of water that is withdrawn from th

aquifer and discharged to the headwaters of the 

when that water is no longer discharged, the riv

dry along this reach, and leakage to the underly

aquifer ceases. The calculated losses of water a

Frenchtown Brook and the Annaquatucket Rive

Table 8. Model-calculated steady-state average annual 

hydrologic budget for the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system, Rhode Island 

[Budget components shown schematically in figure 7]

Hydrologic budget component

Rate of flow

Cubic

feet per 

second

Million

gallons

per day

Inflow

Recharge

Precipitation (RPR) ........................ 34.3 22.2

Wastewater return flow (RWW)...... 1.2 .8

Lateral ground-water inflow (GWI)... 19.5 12.6

Streamflow from uplands (SFI) ......... 26.5 17.1

Ground water discharged to 

Annaquatucket River (QAR) .......... 2.0 1.3

Total inflow.................................... 83.5 54.0

Outflow

Streamflow (SFO) .............................. 69.3 44.8

Evapotranspiration (ETGW)............... 4.6 3.0

Ground-water underflow (GWU)....... 1.0 .6

Ground-water withdrawal (QW) ........ 8.1 5.2

Total outflow.................................. 83.0 53.6

Budget error (inflow-outflow)................ 0.5 0.4
Steady-State Numerical M

supported by water-level altitudes measured beneath 

the two streams on October 8, 1996, which indicated 

that the water table was at least 4.5 ft beneath the 

streambeds at that time.

Total streamflow depletion caused by withdrawals at all wells except those at the hatchery is 5.9 ft3/s, 

which is all but 0.3 ft3/s of the total simulated withdrawals at the wells (6.2 ft3/s). The remaining 

0.3 ft3/s consists of a reduction in ground-water 

evapotranspiration and small roundoff and model 

mass-balance errors. Total streamflow depletion calculated for the Hunt River Basin is 4.1 ft3/s; for the 

Cocumcossuc River Basin is less than 0.1 ft3/s; for 

the Annaquatucket River Basin is 1.4 ft3/s; and for 

the Pettaquamscutt River Basin is 0.3 ft3/s. The 

streamflow-depletion rates indicate that before withdrawals began at the public water-supply wells and 

the industrial well (IW), average streamflow at the five 

outflow measurement sites (excluding direct runoff 

within the HAP stream-aquifer system) are estimated 

to have been about 46.4 ft3/s for the Hunt River, 

3.0 ft3/s for Cocumcossuc Brook, 0.6 ft3/s for Queens 

Fort Brook, 15.2 ft3/s for Annaquatucket River, and 

10.0 ft3/s for Pettaquamscutt River.

Model-calculated streamflows and streamflow 

depletions for the Hunt and Annaquatucket Rivers as a 

function of distance along each stream are shown in 

figures 14A and 14B, respectively. River mile 0.0 on 

each figure is the uppermost reach (model cell) of each 

of the simulated streams (fig. 12). Calculated streamflows are shown for the calibrated model and for the 

simulation in which withdrawals were specified only at 

the fish-hatchery wells. Differences in the calculated 

streamflows between the two simulations are shown by 

the streamflow-depletion curves.

Natural stream-channel losses are calculated 

for the uppermost reach of the Hunt River, where 

Scrabbletown Brook enters the HAP stream-aquifer 

system from till and bedrock upland areas (fig. 14A). 

The river loses flow until about mile 0.6, at which point 

ground-water discharge causes the river to become 

gaining. The river remains mostly gaining until the area 

of large ground-water withdrawals just below the confluence with Fry Brook (about river mile 4.0). In this 

area, the streamflow-depletion rate increases sh

and streamflow losses result from induced infilt

Below the area of withdrawals, the river again m

gains flow except along the downgradient end o

Potowomut Pond.

Natural stream-channel losses are calcula

the first 2.0 mi of the Annaquatucket River, exte

from the headwaters of the river at the fish hatc

to the upgradient end of Belleville Pond (fig. 14

Ground-water discharge to Belleville Pond is su

tial; as a result, there are large gains in streamfl

through the pond. These calculated gains are co

with those measured during this investigation (t

Natural streamflow losses are calculated on the 

gradient end of Belleville Pond. Streamflow dep

begin at about river mile 2.1, and are largest ne

supply wells (river mile 3.0–3.1).

Contributing Areas and Sources of 

Water to Supply Wells

Contributing areas and sources of water w

delineated for the public water-supply wells and 

hatchery wells by use of the calibrated steady-s

model. The contributing area of a well is the su

area of the water table where water entering the 

ground-water system eventually flows to the we

(Franke and others, 1998). The land area that di

overlies the contributing area is often protected 

uses that could cause contamination of the unde

water table. Potential sources of water to wells 

HAP stream-aquifer system are precipitation an

wastewater recharge, streamflow leakage from n

channel losses, streamflow leakage caused by in

infiltration, and lateral ground-water inflow from 

and bedrock upland areas.

Contributing areas and sources of water w

delineated with the computer program MODPA

(Pollock, 1994), which calculates three-dimens

flow paths from the results of the MODFLOW 

state simulation. MODPATH uses a semi-analy

particle-tracking scheme to track the movement 

hypothetical particles of water through the simu
34 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

STREAMFLOW, IN CUBIC FEET PER SECOND

RIVER MILE IN MODEL

STREAMFLOW, IN CUBIC FEET PER SECOND

Streamflow depletion

Streamflow depletion

Aquifer/upland boundary onScrabbletown Brook

NK6

Unnamed tributaryto Hunt River

Industrial well

Unnamed tributaryto Hunt River

Frenchtown Brook, 3A

Fry Brook

Headwaters at LafayetteState Fish Hatchery

Belleville Pond

Secret Lake

tributary

State Highway

NK1NK2NK4NK5

PotowomutPond

SandhillBrook

Hunt River gage at ForgeRoad, East Greenwich

NK10

NK9

KC1

14A

9A

50

10

15

20

25

30

35

40

45

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

20

10

15

0.5 1.0 1.5 2.0 2.5 3.0 3.5

A. Hunt River

B. Annaquatucket River

1

0

5

0

5

0

WITHDRAWALS AT 

 FISH HATCHERY ON

WITHDRAWALS AT AL

 WELLS (CALIBRATED 

EXPLANATION

Figure 14. Model-calculated steady-state streamflows and streamflow depletions for (A) the Hunt River and (B) the 

Annaquatucket River, Rhode Island. (Streamflows calculated for model cells along the center line of Potowomut and B

Ponds were used.)
Steady-State Numerical M

ground-water-flow system, and to calculate the time of 

travel of these particles from points of recharge to 

points of discharge (Pollock, 1994). MODPATH 

requires specification of the porosity of the aquifer for 

each cell of the model grid. A uniform porosity of 0.35 

was specified for the stratified deposits simulated by 

the model. This value is based on measurements of 

porosity made on sediment samples from the adjoining 

Pawcatuck River Basin (Allen and others, 1963) and 

for similar sediments on western Cape Cod, Massachusetts (Garabedian and others, 1991). A porosity of 1.0 

was specified for the simulated ponds and lakes. This 

value did not affect the analysis, however, because all 

contributing areas delineated for the supply wells are 

upgradient to simulated ponds and lakes.

The contributing area to each well was delineated by overlaying a 2 × 2 array of particles onto the 

simulated water table. Particles then were tracked from 

the water table to their points of discharge from the 

simulated HAP aquifer. The origin of those particles 

that were captured by each simulated well defined 

the contributing area to that well. Contributing areas 

shown in this report were delineated with the option in 

MODPATH to stop particles at cells containing weak 

internal sinks. In the HAP model, internal sinks are 

gaining streams, withdrawal wells, and areas of evapotranspiration. Cells with weak internal sinks are those 

in which the amount of water removed by the internal 

sink is less than the total amount of water that flows 

into the cell. Weak sinks cause some ambiguities in the 

delineation of contributing areas because it cannot be 

determined whether a particle that enters a cell with a 

weak internal sink should be removed by the sink or 

should continue through the flow system. Internal sinks 

are not a problem when all of the water that flows into 

the cell is removed by the sink (a strong internal sink). 

Though there are weak internal sinks in the HAP 

model, these sinks did not affect the delineation of contributing areas to the majority of wells, as determined 

by comparing contributing areas delineated for the 

wells with the option to stop particles at cells containing weak sinks with those delineated for the wells with 

the option to allow particles to pass through weak 

sinks. Contributing areas to NK7 and NK8, however, 

were strongly affected by the weak-sink problem 

because of the very low withdrawal rates simulated 

for the wells (table 5). As a consequence of the weaksink problem, contributing areas are not presented 

for these two wells.

The amount of streamflow leakage contri

to each well’s withdrawal was determined by tr

particles from losing stream reaches to their poi

discharge from the flow system. Twenty seven p

were distributed uniformly in a three-dimension

(3 × 3 × 3) within each losing stream cell. To es

the amount of streamflow leakage reaching each 

supply wells, a volumetric flow rate was assign

each particle. This volumetric flow rate was dete

by dividing the streamflow-leakage rate to the a

in the cell in which the particle originated by th

number of particles placed in each cell (27). The 

bution of streamflow leakage to each supply we

then calculated by summing the individual flow 

all particles captured by each well. The approac

determining the type of streamflow leakage with

losing stream cell—that is, either natural stream

channel losses or induced infiltration—was des

in the preceding section of this report. The total 

amounts of natural stream-channel losses and in

infiltration contributing to each well’s withdraw

(shown as a percentage of total withdrawal rate

well as the total amount of water from other sou

withdrawn from each well, are shown in table 9

other sources of water are precipitation and was

recharge within the active area of the model and 

ground-water inflow from till and bedrock uplan

outside of the active area of the model. 

Contributing areas delineated for supply w

the HAP stream-aquifer system are shown on p

The areal extent of the contributing area of each 

a function of the withdrawal rate of the well, th

recharge rate (or areal distribution of recharge r

the HAP aquifer within the contributing area, a

amount of water captured by the well from sour

other than recharge. The largest contributing are

shown on plate 1 are those for wells NK9 and N

Although the withdrawal rate simulated for wel

(1.18 Mgal/d) is much greater than that simulat

well NK5 (0.49 Mgal/d), the areal extent of the 

uting area to each well is nearly equal (0.39 mi2 

well NK9 and 0.34 mi2 for well NK5). The sim

in the size of the contributing areas delineated f

these two wells is explained in part in that well 

captures some of its withdrawal from induced i

tion from the Hunt River; other factors that con

to the relative size of these two contributing are

differences in the recharge rates to the HAP aqu
36 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

within each well’s contributing area and the amount of 

water captured by each well from lateral ground-water 

inflow along the boundary of the model. The smallest 

contributing area delineated for any of the wells is that 

for well 3A (pl. 1). This well captures 95 percent of 

its withdrawal from natural stream-channel losses 

along Frenchtown Brook. Streamflow losses along 

Frenchtown Brook are supported by water-level 

measurements made during this study that indicated 

a downward hydraulic gradient from the brook to 

the underlying HAP aquifer.

Some of the contributing areas do not ove

wells (pl. 1), including those for KC1, 3A, NK6

SFH2, and NK5. Although several hydrogeolog

well-design factors affect the location of these c

uting areas, an important factor is the position o

screened interval of these wells. In each case, th

screened interval is in either the second, third, o

layer of the model, which allows recharge in the 

diate vicinity of the wells to flow above the scre

interval.

Streamflow leakage was calculated to be a 

of water to seven wells, all but five of which are 

Hunt River Basin (table 9). As shown in the tab

induced infiltration is calculated to be a source o

to wells 14A, KC1, and NK9 in the Hunt River 

Induced infiltration is not a source of water to a

the wells in the Annaquatucket River Basin. Th

appears to be a contradiction to the conclusion 

the calculated rate of induced infiltration in the 

Annaquatucket River Basin was 0.3 ft3/s for the 

drawal rates simulated by the calibrated model 

previous section “Stream-Aquifer Interactions”

of the induced infiltration in the Annaquatucket 

Basin comes from Secret Lake, downgradient o

NK1, NK2, NK4, and NK5. The explanation fo

apparent contradiction is that the induced infiltr

not captured by the wells, but discharges from t

system at other locations; although the hydrauli

stresses caused by withdrawals at these wells ar

enough to induce infiltration from the lake to th

HAP aquifer, the stresses are too small to cause 

induced water to be captured by the wells. New

and Wilson (1988) refer to this induced water a

"induced throughflow."

In addition to calculating particle flow pa

through the simulated aquifer, MODPATH also 

lates the total traveltime of each particle from it

at the water table to its withdrawal at a supply w

(pl. 1). Calculated traveltimes for particles capt

the wells for the conditions simulated by the ca

model range from a minimum of 0.1 years to a 

mum of 51.2 years. The average traveltime to m

the wells is less than 5 years, with the exception 

wells KC1 (average traveltime 5.2 years), NK9 

1Three particles, with a combined flow rate of less than 0.01 cubic 

feet per second, are captured by NK1.

Table 9. Model-calculated streamflow leakage and other 

sources of water to supply wells in the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system, Rhode Island

[Well locations are shown on figure 1. Other sources: refers to groundwater recharge from precipitation and wastewater discharge to the Hunt–

Annaquatucket–Pettaquamscutt aquifer, and ground-water recharge to 

till and bedrock upland areas that enters the Hunt–Annaquatucket–

Pettaquamscutt aquifer by lateral ground-water inflow]

Watersupply 

well

identifier

Source of water, as percentage of

well’s total withdrawal rate

Streamflow

leakage to aquifer 

by natural

channel losses

Streamflow

leakage to aquifer 

by induced

infiltration

Other 

sources

Hunt River Basin

9A 75.9 0 24.1

14A 39.1 36.7 24.2

KC1 56.6 16.2 27.2

NK9 0 16.2 83.8

3A 94.7 0 5.3

NK6 0 0 100.0

Annaquatucket River Basin

NK1 0 10 100.0

NK2 0 0 100.0

NK4 0 0 100.0

NK5 0 0 100.0

SFH1 30.2 0 69.8

SFH2 0 0 100.0

Pettaquamscutt River Basin

NK3 0 7.4 92.6
Transient Numerical M

years), NK4 (6.1 years), and NK5 (11.9 years). Considerable variation was found in the range of particle 

traveltimes to each of the wells, as shown on plate 1. 

Particle traveltimes to the wells are a function of many 

factors, including withdrawal rates of the wells, 

recharge rates to the aquifer, lateral ground-water 

inflow rates, and the hydraulic conductivity and 

porosity of the aquifer.

In conclusion, it should be noted that the contributing areas and sources of water delineated for wells in 

the HAP stream-aquifer system are unique to the particular set of hydrologic and well-design conditions 

simulated by the calibrated, steady-state flow model 

of the system. The areal extent and shape of the contributing areas would likely be different if changes 

were made to any of the model hydraulic variables or 

stresses, such as the distribution of hydraulic conductivity of the aquifer, withdrawal rates of the wells, or 

recharge rates to the aquifer.

TRANSIENT NUMERICAL 

MODEL

A transient model was developed to simulate 

average annual hydrologic conditions in the HAP 

stream-aquifer system. Average annual hydrologic conditions are defined as the average conditions during 

each of the 12 months during the 56-year period 1941–

96. The primary purpose of simulating transient conditions was to quantify monthly streamflow depletions in 

the Hunt, Annaquatucket, and Pettaquamscutt Rivers 

caused by time-varying withdrawals at the supply 

wells. The model-calculated streamflow depletions 

are the basis by which the numerical model of the 

HAP system is incorporated into the conjunctivemanagement model developed for the system. The 

transient model was designed to simulate dynamic 

equilibrium, which is defined here as the condition in 

which there is no net change in storage in the simulated 

system over the average annual hydrologic cycle. Calculated water-level altitudes and streamflows vary over 

the annual cycle, but at the end of the cycle, the system 

returns to the condition that existed at the beginning of 

the cycle. This approach was taken to ensure th

drawal strategies determined by the conjunctive

management model could be sustained indefinit

without causing long-term reductions in aquifer 

storage.

Development

 The transient model has the same areal a

tical extent as the steady-state model. Several o

data sets developed for the steady-state model a

were used for the development of the transient m

including those for hydraulic conductivity and t

and bottom elevations of each cell.

Temporal Discretization and 

Initial Conditions

The annual hydrologic cycle was divided 

monthly time periods. The length of each perio

the number of days in the month. In MODFLOW

12 periods are referred to as stress periods, beca

specified hydrologic stresses change from one p

the next. Within each period, however, stress rat

constant. Thirty time steps were used for each s

period, regardless of the particular month. Time 

increased in length during each stress period to 

numerical stability of the model. The first time 

each stress period was less than 0.2 day, and the 

time step in each stress period was about 3.0 da

Water-level altitudes specified for each m

cell at the beginning of the transient simulation 

those determined by the calibrated, steady-state 

Stress conditions specified for the initial condit

were those for the month of January (stress con

are described in detail in the next section). Beca

initial conditions affect the transient response o

simulated system, it was necessary to repeat the 

cycle of transient stresses until there was no cha

storage over a 1-year cycle (that is, until dynam

librium was attained). It was found empirically 

five annual cycles (a total of 60 stress periods) w

adequate to produce dynamic equilibrium. The 

change in storage during the fifth year of simula
38 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

was 0.1 percent, which was very close to the desired 

value of zero. At dynamic equilibrium, simulation 

results on the first day of the year were equal to those 

on the first day of the previous year.

Boundary Conditions and 

Stresses

The types of boundary conditions and stresses 

specified in the transient model were equivalent to 

those used for the steady-state model (fig. 12). In the 

transient model, however, stress rates vary over the 

annual cycle. The monthly stresses specified in the 

transient model are described below.

Average monthly precipitation recharge rates 

estimated for the Hunt River Basin for the 1941–96 

period (fig. 10A) were increased by 10 percent for consistency with the increase that was made to the average 

annual recharge rate during calibration of the steadystate model. The resulting monthly precipitation 

recharge rates specified to all areas of the model except 

ponds and lakes ranged from 0.6 in. for September to 

4.7 in. for March, with a total annual recharge of 

28.0 in. In addition to precipitation recharge, some 

areas of the HAP aquifer also receive recharge from 

wastewater disposal. Constant rates of wastewater 

disposal equal to those specified in the steady-state 

model were simulated; the total recharge rate from 

wastewater disposal over the entire model area was 

1.2 ft3/s. Monthly recharge rates to ponds and lakes 

were calculated by subtracting average monthly freewater-surface evaporation rates from average monthly 

precipitation rates measured from 1941–96 at the 

Kingston climatological station. Total free-watersurface evaporation during the May through October 

growing season is estimated to be 21.0 in. (Farnsworth 

and others, 1982, map 2). Based on the total annual 

free-water-surface evaporation of 28.0 in. (Farnsworth 

and others, 1982, map 3), this gives a total of 7.0 in. 

of free-water-surface evaporation for the months of 

November through April. Average monthly free-watersurface evaporation rates are therefore about 3.5 in. 

during May through October and 1.2 in. during 

November through April. Net monthly recharge rates 

specified to ponds ranged from zero in June and 

3.9 in. for November, with a total annual rechar

to ponds and lakes that is slightly higher (by 0.7 

than the value of 19.5 in. specified in the steady

model.

Monthly rates of lateral ground-water infl

from upland areas not drained by streams were 

mined by proportioning the amount of annual in

each boundary cell among the 12 months on the 

of the percentage of annual precipitation rechar

each particular month. For example, a recharge 

4.7 in. (March) is 16.8 percent of the total avera

annual recharge of 28.0 in. Consequently, 16.8 

of the total average annual lateral ground-water 

to the HAP aquifer from upland areas was spec

for March. The daily rate of inflow at each cell 

each month then was determined by dividing th

monthly inflow to the cell by the number of day

the month.

 Monthly evapotranspiration rates from th

table were determined by assuming that the tota

age annual amount of water-table evapotranspir

(21.0 in.) occurs at an equal rate throughout the 

growing-season months of May through Octobe

sequently, maximum water-table evapotranspira

rates averaging 3.5 inches per month were speci

May through October; rates of zero inches per m

were specified for the remaining months of the 

As in the steady-state model, the maximum dep

evapotranspiration from the water table was ass

to equal 4 ft below land surface.

Monthly withdrawal rates at each public 

supply well were set equal to the 1996 average m

withdrawal rates for each well. This rate was se

consistency with the 1996 average annual withd

rates specified in the steady-state model. Consta

withdrawal rates were specified for the industri

and each of the three supply wells at the Lafaye

State Fish Hatchery (table 5). Total monthly wi

drawal rates simulated for all wells ranged from 

6.71 ft3/s to 10.1 ft3/s, and averaged 8.12 ft3/s.
Transient Numerical M

Monthly streamflow rates were specified for the 

first reach of each stream that enters the HAP system 

from till and bedrock uplands (sites A, B, F, H, and J in 

fig. 12A and site W in fig. 12B) and at the headwater of 

the Annaquatucket River (site R, fig. 12B). Methods 

used to estimate 1941–96 average monthly rates of 

inflow for streams that enter the system from upland 

areas were described in the “Hydrologic Components 

and Budget” section. Additionally, a constant rate of 

streamflow of 1.95 ft3/s was specified at the headwater 

of the Annaquatucket River where ground water is 

discharged to the stream at the Lafayette State Fish 

Hatchery (table 6). Total monthly streamflows specified 

to the transient model ranged from a minimum of 

6.6 ft3/s in September to a maximum of 56.7 ft3/s in 

March. Average annual specified streamflow at these 

sites was 28.1 ft3/s, which is close to that of the steadystate model, 28.5 ft3/s. Physical characteristics of the 

simulated streams (streambed conductance, streambed 

elevation, and so forth) were equivalent to those specified in the steady-state model.

Storage Properties of Aquifer

A uniform value of specific yield of 0.28 was 

specified for the stratified deposits simulated in the 

model. This value is the same as the median specific 

yield determined for 18 samples of stratified deposits 

from the adjacent Pawcatuck River Basin (Allen and 

others, 1963); it also is close to the value of 0.26 determined by Moench and others (2000) for stratified glacial deposits of western Cape Cod, Massachusetts. A 

specific yield equal to 1.0 was specified for the simulated ponds and lakes. A uniform value of the storage 

coefficient of the aquifer of 3.0 × 10-4, which corresponds to a 30-foot saturated thickness of aquifer with 

a specific storage of 1.0 × 10-5 ft-1, was specified for 

each cell in layers 2-4 of the model. The value of specific storage is based on the estimate of 1.3 × 10-5 ft-1

made by Moench and others (2000) for the specific 

storage of stratified glacial deposits of Cape Cod, 

Massachusetts.

Calibration and Hydrologic 

Budget

The model was calibrated to average mon

water-level altitudes measured at NKW-255 dur

the periods 1955–63 and 1966–96, and to meas

or estimated average monthly streamflow of the 

Annaquatucket, and Pettaquamscutt Rivers. As w

steady-state model, direct runoff is not simulated 

transient model; therefore, calculated streamflo

not reflect the highest flow rates that typically o

during storms. Observation well NKW-255 is th

well in the study area with a period of record th

long enough to be used for model calibration. A

the water-level record at the well does not exten

the full 56-year period used for model developm

the record was assumed to provide a good indic

the average range of water-level altitude fluctua

the well.

Calculated water-level altitudes at well 

NKW-255 are shown in figure 15A with the ave

monthly water-level altitudes measured at the w

the combined 40-year period 1955–63, 1966–9

calculated hydrograph is shifted upward from th

sured one by about 4 ft because of model error; 

shown in table 7, the steady-state water-level al

calculated for the well is 40.74 ft but the measu

water-level altitude on October 8, 1996, was 36

The annual fluctuation of the calculated hydrog

similar to the measured hydrograph, reaching a 

mum water-level altitude during April and a mi

altitude during September and October, althoug

calculated range in water-level altitudes over the 

cycle (3.5 ft) is greater than the observed range 

During the calibration process, four values of sp

yield were tested (0.15, 0.25, 0.28, and 0.30). A

value of specific yield was increased, the range 

culated water-level altitudes for the well decreas

example, for a specific yield of 0.30, the calcula

annual range was 3.2 ft. In the absence of more 

the specific yield of the HAP aquifer, however, 

of 0.28 was retained.
40 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

STREAMFLOW, IN CUBIC FEET PER SECOND

WATER-LEVEL ALTITUDE, 

IN FEET ABOVE SEA LEVEL

MEASURED

CALCULATED

10

90

20

30

40

50

60

70

80

34

44

36

38

40

42

A.

B.

EXPLANATION

NKW-255

Hunt River

Average monthly measured streamflows and 

calculated mid-monthly streamflows for the Hunt 

River for the 56-year period (1941–96) are shown in 

figure 15B. In both cases, the maximum streamflow is 

in March and the minimum streamflow is in September. 

Because the model does not simulate direct runoff, the 

calculated streamflow hydrograph should be lower 

than the measured hydrograph, which is the cas

all months except May through July. Average an

streamflow calculated for the river by the transi

model is 42.0 ft3/s, which is close to the value o

42.3 ft3/s calculated by the steady-state model. 

lated maximum and minimum streamflows for 

Annaquatucket River are 16.9 ft3/s in April and 

Figure 15. Average monthly measured and model-calculated mid-monthly (A) water-level 

altitudes at well NKW-255 and (B) streamflow at the Hunt River gaging station, Rhode Island.
Transient Numerical M

11.4 ft3/s in October, which are close to the estimated maximum and minimum average monthly streamflows for the 

river of 20 ft3/s in March and April and 11.5 ft3/s in August 

through October. Calculated maximum and minimum 

streamflows for the Pettaquamscutt River are 15.1 ft3/s in 

April and 5.4 ft3/s in October, which also are close to the 

estimated maximum and minimum average monthly 

streamflows for the river of 15.0 ft3/s in March and April 

and 4.5 ft3/s in August through October.

Although improvements between measured and calculated water-level altitudes and streamflows might have 

been made by modifying the specified rates of recharge, 

streamflow from upland areas, or lateral ground-water 

inflow from upland areas, this was judged to be inappropriate given the limited availability of data for these variables.

The average annual hydrologic budget for the HAP 

stream-aquifer system calculated with the calibrated transient model is shown with that for the steady-state budget in 

table 10. Overall, good agreement was found between the 

several hydrologic components of the two models. The 

average rate of inflow to and outflow from 

storage is 13.2 ft3/s over the annual cycle (

10).

Stream-Aquifer Interactions

Model-calculated mid-monthly strea

flows at the downstream end of the Hunt, 

Annaquatucket, and Pettaquamscutt Rivers 

1941–96 period are shown in figure 16. Cal

streamflows shown in the figure are for the 

brated model and for a simulation in which 

drawals were specified only at the fish-hatc

wells. Calculated streamflow hydrographs 

Annaquatucket and Pettaquamscutt Rivers 

less variability over the annual cycle than d

hydrograph for the Hunt River (fig. 16), wh

consistent with measured (or estimated) str

flow variability for these streams. A statisti

summary of the calculated mid-monthly st

flows for each of the three rivers, as well a

percentage of the area of each river basin t

underlain by glacial stratified deposits, are g

table 11. The statistics shown in table 11 ar

the simulation in which withdrawals were 

fied only at the fish-hatchery wells; results 

to those in the table were obtained with sim

of the calibrated model.

The coefficient of variation of month

streamflows (table 11) is a measure of the r

variability of monthly streamflows among 

three rivers. The coefficient of variation cal

for the Hunt River exceeds those for the 

Annaquatucket and Pettaquamscutt Rivers 

11). Data provided in the table also indicat

the coefficient of variation of calculated str

flows decreases as the percentage of stratifi

deposits that underlies each basin increases

decreases are consistent with the results of 

ous studies of streamflow in the northeaste

United States (see, for example, Thomas, 1

which have shown that the variability of st

flow decreases as the percentage of stratifie

deposits in a basin increases. The large are

Belleville Pond in the Annaquatucket River 

which was simulated with a storage coeffic

1.0, also may contribute to the relatively lo

ability of streamflow observed for that basi

Table 10. Model-calculated steady-state and transient average 

annual hydrologic budgets for the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system, Rhode Island

[Budget components are in cubic feet per second and, in parentheses, million 

gallons per day; budget components shown schematically in figure 7]

Hydrologic budget component Steady-state 

model

Transient 

model

Inflow

Recharge

Precipitation (RPR) ......................... 34.3 (22.2) 34.3 (22.2)

Wastewater return flow (RWW)....... 1.2 (.8) 1.2 (.8)

Lateral ground-water inflow (GWI).... 19.5 (12.6) 19.3 (12.5)

Streamflow from uplands (SFI) .......... 26.5 (17.1) 26.1 (16.9)

Ground water discharged to 

Annaquatucket River (QAR) ........... 2.0 (1.3) 2.0 (1.3)

Storage................................................ 0 (0) 13.2 (8.5)

Total inflow......................................... 83.5 (54.0) 96.1 (62.2)

Outflow

Streamflow (SFO) ............................... 69.3 (44.8) 69.3 (44.8)

Evapotranspiration (ETGW)................ 4.6 (3.0) 4.5 (2.9)

Ground-water underflow (GWU)........ 1.0 (0.6) 1.0 (0.6)

Ground-water withdrawal (QW) ......... 8.1 (5.2) 8.1 (5.2)

Storage................................................ 0 (0) 13.2 (8.5)

Total outflow....................................... 83.0 (53.6) 96.1 (62.0)

Budget error (inflow-outflow) ................ 0.5 (0.4) 0 (0.2)
42 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

STREAMFLOW, IN CUBIC FEET PER SECOND

EXPLANATION

WITHDRAWALS AT FISH 

HATCHERY ONLY

WITHDRAWALS AT ALL WELLS

(CALIBRATED MODEL)

A. Hunt River

B. Annaquatucket River

C. Pettaquamscutt River

0

30

10

20

0

30

10

20

0

90

10

20

30

40

50

60

70

80

Jan. Feb. Mar Apr. May June July Aug. Sept. Oct. Nov. Dec.

Figure 16. Model-calculated mid-monthly streamflow at the 

downstream end of the (A) Hunt, (B) Annaquatucket, and 

(C) Pettaquamscutt Rivers, Rhode Island.

Table 11. Summary statistics of model-calculated, mid-monthly streamflow for the Hunt, Annaquatucket, and Pettaqua

Rivers, Rhode Island

[Simulation conditions: withdrawals only at wells at the Lafayette State Fish Hatchery. ft3/s, cubic foot per second]

River

basin

Percentage of basin underlain

by stratified deposits

Streamflow at downstream end of river

Range

(ft3/s)

Mean

(ft3/s)

Standard

deviation

(ft3/s)

Coeffic

varia

(dimensi

Hunt.............................................. 52 16.8–82.9 46.2 24.3 0.5

Annaquatucket.............................. 75 12.7–18.2 15.4 1.7 .1

Pettaquamscutt ............................. 64 5.9–15.3 10.1 3.2 .3
Conjunctive-Management M

As a result of these factors, streamflow in the Hunt 

River approaches that of the Annaquatucket River 

during periods of low flow, even though the drainage 

area for the Hunt River is more than twice that of the 

Annaquatucket River. This model-calculated trend is 

supported by streamflow measurements made during 

this study (table 2). For example, streamflow measured 

at the gage on the Hunt River (site P, fig. 6) on September 20, 1995, was 7.24 ft3/s, while that measured at the 

downstream end of the Annaquatucket River (site T, 

fig. 6) on the same date was 7.44 ft3/s. In contrast, 

during high-flow conditions (April 24, 1996), flows on 

the two streams were substantially different—83.6 ft3/s 

for the Hunt River and 20.7 ft3/s for the Annaquatucket 

River.

The difference between each pair of hydrographs 

shown in figure 16 is the total streamflow depletion in 

each river basin caused by ground-water withdrawals. 

Monthly streamflow depletions are largest for the Hunt 

River, ranging from 3.7 ft3/s to 5.2 ft3/s, and averaging 

4.2 ft3/s for the annual cycle. This average depletion 

is close to that calculated by the steady-state model 

of 4.1 ft3/s. Monthly streamflow depletions in the 

Annaquatucket River Basin range from 1.2 ft3/s to 

2.2 ft3/s, and average 1.5 ft3/s for the annual cycle 

(compared to 1.4 ft3/s calculated for the steady-state 

model); monthly streamflow depletions in the 

Pettaquamscutt River Basin range from 0.1 ft3/s to 

0.6 ft3/s, and average 0.4 ft3/s for the annual cycle 

(compared to 0.3 ft3/s calculated for the steady-state 

model). Some of the difference between the average 

annual depletions calculated with the transient model 

and those calculated with the steady-state model are 

because of round-off of the calculated values.

For the average annual withdrawal and hydrologic conditions simulated with the steady-state model, 

each stream reach either gains water from, or loses 

water to, the HAP aquifer. For transient simulations, 

however, a stream reach can be gaining during one part 

of the year and losing during another part of the year. 

For example, along a 0.6-mile reach of the Hunt River 

near wells NK9, KC1, 14A, and 9A, the average annual 

rate of loss of streamflow calculated with the transient 

model is 0.69 ft3/s. During the months of March 

through May, however, when streamflow is high and 

withdrawal rates low, the reach becomes gaining, 

with the largest rate of streamflow gain (0.34 ft3/s) 

during April.

CONJUNCTIVE-MANAGEMENT 

MODEL

A conjunctive-management model was d

oped for the HAP stream-aquifer system to dete

whether sustained ground-water withdrawals du

July, August, and September could be increased 

current average rates, while streamflow-depletio

rates caused by ground-water withdrawals are s

neously maintained at desired levels during the 

3-month period. These 3 months were selected b

they generally coincide with the time of year w

water-supply demands are largest and streamflo

simultaneously lowest. Current conditions are d

as the average monthly withdrawal rates and es

streamflow-depletion rates during 1993–98. Th

ence period was selected because withdrawal re

for public water-supply wells in the aquifer are 

plete for 1993–98 (table 12), and because the av

monthly withdrawal rates for this 6-year period 

reflect current average withdrawal conditions an

water-supply demands than does the 1996 with

record that was used for calibration of the trans

model.

Current rates of streamflow depletion cau

by withdrawals at the public water-supply wells 

were estimated for the Hunt, Annaquatucket, an

Pettaquamscutt Rivers by simulation of the tran

model. In a first simulation, the 1993–98 averag

monthly withdrawal rates were specified for eac

(table 12). The annual pattern of 1993–98 mont

withdrawals was simulated for 5 years to attain 

dynamic equilibrium, under the assumption tha

1993–98 withdrawals would be continued indefi

with the other stresses simulated by the transien

model. A second simulation then was made in w

there were no withdrawals at the public water-s

wells. Streamflow depletions were calculated b

tracting streamflows calculated in the first simu

from those calculated in the second simulation. 

calculated streamflow-depletion rates at the end 

August, and September at the downstream end 

Hunt, Annaquatucket, and Pettaquamscutt Rive

summarized in table 13. The calculated streamfl

depletion rates are largest for the Hunt River, ra

from 4.30 to 4.75 ft3/s; those for the Annaquatu

River range from 2.01 to 3.00 ft3/s and those fo

Pettaquamscutt River range from 0.30 to 0.64 f

(table 13). The calculated rates also are largest 
44 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

Hunt River when expressed as a percentage of the 

pre-withdrawal streamflow calculated for each river 

(that is, streamflows calculated for each river with no 

withdrawals at the public water-supply wells)—22–28 

percent for the Hunt River, 16–21 percent for the 

Annaquatucket River, and 5–9 percent for the 

Pettaquamscutt River.

Formulation of the ConjunctiveManagement Model

The conjunctive-management model developed 

for the system was formulated and solved by use of 

optimization techniques. Formulation of the model 

refers to the process of defining the conjunctiv

management problem mathematically by a set 

decision variables, an objective function, and a 

of constraints. The decision variables of the m

were monthly withdrawal rates at each of the 

public water-supply wells; values for each dec

variable were calculated by the optimization s

technique. Mathematically, the decision variab

were expressed as , which is the withdra

rate at well in month . The subscript rang

from for January through for 

December. The model had a maximum of 192 

sion variables, one for each of 16 existing and 

thetic public water-supply wells (table 14) for 

of 12 months.

Qwi t ,

it t

t = 1 t = 12

Table 12. Average 1993–98 monthly withdrawal rates for public water-supply wells in the Hunt–Annaquatucket–Pettaqu

stream-aquifer system, Rhode Island

[Withdrawal rates are million gallons per day. Well locations are shown on figure 1. Shading used to emphasize withdrawal rates for July, August, 

September]

Watersupply well 

identifier

January February March April May June July August September October November D

Hunt River Basin

KC1 0.27 0.08 0.08 0.16 0.32 0.80 0.94 0.80 0.53 0.28 0.32 

3A .29 .26 .23 .24 .23 .29 .35 .21 .18 .18 .20 

9A .07 .17 .11 .12 .10 .11 .19 .29 .33 .21 .13 

14A .22 .32 .22 .20 .25 .29 .39 .44 .33 .32 .37 

NK6 .31 .32 .30 .40 .43 .43 .55 .39 .29 .23 .19 

NK9 .58 .64 .65 .47 .55 1.11 1.39 1.47 1.27 1.00 .88 

NK10 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

Total for 

basin ........ 1.74 1.79 1.59 1.59 1.88 3.03 3.81 3.60 2.93 2.22 2.09 

Annaquatucket River Basin

NK1 .28 .27 .28 .34 .43 .59 .58 .42 .26 .22 .15 

NK2 .20 .14 .13 .20 .32 .34 .38 .24 .18 .17 .16 

NK4 .29 .28 .25 .30 .37 .50 .57 .46 .36 .33 .25 

NK5 .30 .27 .32 .30 .44 .63 .75 .56 .40 .34 .34 

Total for 

basin ........ 1.07 0.96 0.98 1.14 1.56 2.06 2.28 1.68 1.20 1.06 0.90 

Pettaquamscutt River Basin

NK3 .09 .10 .09 .06 .07 .14 .22 .20 .17 .17 .14 

NK7 .01 .00 .04 .05 .05 .04 .09 .06 .03 .02 .01 

NK8 .00 .00 .02 .03 .04 .06 .09 .08 .04 .01 .00 

Total for 

basin ........ 0.10 0.10 0.15 0.14 0.16 0.24 0.40 0.34 0.24 0.20 0.15 

Total for all 

basins ...... 2.91 2.85 2.72 2.87 3.60 5.33 6.49 5.62 4.37 3.48 3.14 
Conjunctive-Management M

The objective function of the model was to maximize total ground-water withdrawals from the HAP 

aquifer during July, August, and September and is 

given as

 , (5)

where is the total number of wells and is the 

number of days in month . Values of the objective 

function were in units of million gallons withdrawn 

during the 3-month period.

The value of the objective function was 

limited by a set of constraints on maximum rates of 

streamflow depletion in the Hunt, Annaquatucket, 

and Pettaquamscutt Rivers; minimum monthly water 

demands by each of the three water suppliers (KCWA, 

RIEDC, and NK); and minimum and maximum 

withdrawal rates at each of the wells.

Maximum rates of streamflow depletion were 

required to be less than or equal to specified maximum 

rates at streamflow constraint sites located at the most 

downstream model cell of each of the three rivers (sites 

P, T, and V shown on fig. 6):

 , (6)

where is streamflow depletion at streamflow 

constraint site in month and is the 

maximum rate of streamflow depletion allowed at site 

 in month . The downstream locations of each of the 

three rivers were used for the constraint sites be

they are the locations where streamflow depleti

largest in each of the basins. Maximum rates of 

streamflow depletion specified at the three cons

sites are described in the applications of the mo

Thirty-six streamflow-depletion constraints wer

specified in the model—one for each of the thre

in each of the 12 months.

maximize NDt

Qwi t ,

t = 7

9

∑

i = 1

NW

∑

NW NDt

t

Qsd j t , Qsd j t , ( )max ≤

Qsd j t ,

j t Qsd j t , ( )max

j t

Table 13. Model-calculated end-of-month streamflow 

depletions for the Hunt, Annaquatucket, and Pettaquamscutt 

Rivers, Rhode Island, for July, August, and September, with 

1993–98 average monthly ground-water withdrawal rates

[River sites shown on figure 6. Streamflow depletion is given in cubic feet per 

second and, in parentheses, million gallons per day]

River

(site

identifier)

Model-calculated, end-of-month

streamflow depletion

July August September

Hunt (P) ..................... 4.70 (3.04) 4.75 (3.07) 4.30 (3.78)

Annaquatucket (T)..... 3.00 (1.94) 2.59 (1.67) 2.01 (1.30)

Pettaquamscutt (V) .... .64 (.41) .46 (.30) .30 (.19)

aAssumed increased capacity of 1.00 Mgal/d at wells 3A a

bMaximum withdrawal rate during 1993–98. cAssumed maximum withdrawal rate equal to that of well 

dAssumed maximum withdrawal rate.

Table 14. Maximum withdrawal rates specified for p

water-supply wells in the conjunctive-management m

the Hunt–Annaquatucket–Pettaquamscutt stream-aq

system, Rhode Island

[Unless otherwise noted, maximum withdrawal rates are equal to 

based on original aquifer test at site. Withdrawal rates are million 

per day. Well locations are shown on figure 1. KCWA, Kent Cou

Water Authority; NK, Town of North Kingstown; RIEDC, Rhode 

Economic Development Corporation; No., number]

Well 

No.

Water

supplier

Current well

configuration

Modified 

configura

Watersupply 

well 

identifier

Maximum 

withdrawal 

rate

Watersupply 

well 

identifier

M

wi

Hunt River Basin

1 KCWA KC1 2.59 KC1 

2 RIEDC 3A 1.80 3A 

3 RIEDC 9A 2.10 9A 

4 RIEDC 14A 1.44 14A 

5 NK NK6 1.37 NK6 

6 NK NK9 b2.21 NK9 

7 NK NK10 2.16 NK10 

Annaquatucket River Basin

8 NK NK1 1.44 NK1 

9 NK NK2 c1.44 NK2 

10 NK NK4 c1.44 NK4 

11 NK NK5 1.75 NK5 

12 NK H1 

13 NK H2 

Pettaquamscutt River Basin

14 NK NK3 1.44 NK3 

15 NK NK7 b.81 NK7 

16 NK NK8 .40 NK8 
46 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

Total monthly withdrawals from all wells in each 

of the three water-supply systems were required to be 

greater than or equal to the average monthly demands 

of each supplier during the 1993–98 period (table 15). 

This constraint was written for each supplier as

 , (7)

where is the demand for supplier in 

month , and and are the lowermost and 

uppermost well numbers in supply system (well 

numbers shown in table 14). Thirty-six water-demand 

constraints were specified—one for each of the three 

suppliers in each of the 12 months.

Constraints on minimum and maximum withdrawal rates at each well were written as

 , (8)

where and are the minimum 

and maximum withdrawal rates at well in month . 

The minimum withdrawal rate at all wells equalled 

zero and did not need to be explicitly specified in the 

model. The maximum withdrawal rate for each well 

(table 14) was assumed to be the larger of the well’s 

yield based on the aquifer test done when the well was 

first installed (table 1) or the maximum withdrawal rate 

during 1993–98. For wells NK2 and NK4, how

maximum withdrawal rate equal to that for near

NK1 (1.44 Mgal/d) was assumed. This was don

because yield data for these two wells were not 

available, and because maximum withdrawal ra

each well during 1993–98 were low compared t

maximum rates possible for nearby wells. Max

withdrawal rates for the two hypothetical wells 

discussed in the applications section. A maximu

192 constraints for maximum withdrawal rates 

specified.

In addition to constraints on withdrawal r

each individual well, constraints on combined w

drawal rates also were specified for two pairs of 

First, a maximum combined withdrawal rate of 

Mgal/d was specified for wells NK1 and NK2 f

month as

 , 

where the subscripts 8 and 9 are the well numb

given in table 14. This constraint was necessary 

because the yields of these wells have been obse

decrease when the combined withdrawal rate ex

1.60 Mgal/d.

Second, a minimum combined withdrawa

of 0.47 Mgal/d was specified for wells NK9 and 

for each month as

 . 

A minimum combined withdrawal rate from the

wells is necessary for system operation; the val

0.47 Mgal/d was the minimum combined avera

monthly withdrawal rate from the wells during 

98 (table 12). In addition, wells NK9 and NK10 

pump simultaneously. To explicitly address this 

constraint would have required use of integer va

which would have complicated the solution pro

Instead, a maximum combined withdrawal rate 

the two wells equal to the maximum withdrawa

NK9 (2.21 Mgal/d, see table 14) was specified 

 . 

This approach is valid because the two wells ar

close to one another and have very similar effec

streamflow depletion in the Hunt River, as deter

Qwi t ,

i WL =

WU

∑ DWS t , ≥

DWS t , WS

t WL WU

WS

Qwi t , ( )min Qwi t , Qwi t , ( )max ≤ ≤

Qwi t , ( )min Qwi t , ( )max

i t

Qw8, t + 1.60 Qw9, t ≤ Mgal d⁄

0.47 Mgal d⁄ Qw6, t + Qw7, t ≤

Qw6, t + 2.21 Qw7, t ≤ Mgal d⁄

Table 15. Average monthly withdrawal rates (demands) for 

each water supplier in the Hunt–Annaquatucket–

Pettaquamscutt stream-aquifer system, Rhode Island, 

1993–98

[Withdrawal rates are million gallons per day]

Month

Kent 

County 

Water 

Authority

Rhode Island 

Economic 

Development 

Corporation

Town of North 

Kingstown

January........... 0.27 0.58 2.05

February......... .08 .74 2.03

March............. .08 .55 2.07

April............... .16 .56 2.16

May ................ .32 .58 2.71

June ................ .80 .69 3.85

July................. .94 .93 4.62

August............ .80 .94 3.88

September ...... .53 .84 3.00

October .......... .28 .71 2.46

November....... .32 .70 2.13

December....... .54 .64 1.95
Conjunctive-Management M

by simulations with the transient model. Therefore, 

withdrawal rates at the wells can be interchanged 

without affecting the streamflow-depletion constraints.

In summary, the conjunctive-management 

model was formulated mathematically to maximize 

withdrawals from wells in the HAP aquifer during July, 

August, and September (equation 5), subject to constraints on streamflow depletions caused by groundwater withdrawals (equation 6), water demands 

(equation 7), and withdrawal rates at the wells 

(equations 8-11).

Response-Matrix Technique for 

Solution of the ConjunctiveManagement Model

The optimization method used to solve the 

conjunctive-management model is based on a widely 

applied technique for solving many types of groundwater management problems called the responsematrix technique. The basis of the technique is the 

assumption that the rate of streamflow depletion at 

each streamflow constraint site is a linear function of 

the rates of ground-water withdrawal at each public 

water-supply well. By assuming linearity, it is possible 

to determine total streamflow depletion at a constraint 

site by summation of the individual streamflow depletions caused by each well. Detailed descriptions of the 

response-matrix technique are given by Gorelick and 

others (1993) and Ahlfeld and Mulligan (2000). Specific applications of the technique to problems in 

stream-aquifer management are given by Maddock 

(1974), Morel-Seytoux and Daly (1975), MorelSeytoux (1975a,b), Illangasekare and Morel-Seytoux 

(1982), Peralta and others (1988), Male and Mueller 

(1992), Mueller and Male (1993), and Barlow (1997a). 

The technique is valid as long as (1) the saturated 

thickness and transmissivity of the HAP aquifer do not 

vary substantially with changes in withdrawal rates and 

(2) other nonlinear effects simulated by the transient 

model, such as head-dependent boundary conditions, 

do not substantially affect the linear relation between 

ground-water withdrawals and streamflow depletions. 

The validity of these assumptions are addressed at the 

end of this section.

Implementation of the response-matrix 

technique requires calculation of characteristic 

streamflow-depletion responses at each of the three 

streamflow constraint sites to simulated unit 

withdrawals at each of the 16 existing and hypothetical 

wells. To calculate the characteristic responses, 

simulations of the transient model were made. I

simulation, the withdrawal rate specified for on

the wells was increased from its 1993–98 rate b

0.5 Mgal/d for 1 month (the month of January w

used); at the end of the month, the withdrawal r

the well was returned to its 1993-98 rate. The si

month increase of 0.5 Mgal/d is referred to as th

unit withdrawal at well . The amount of 

flow depletion resulting from the unit withdraw

determined by subtracting streamflow rates calc

by the model with the unit withdrawal active fro

those calculated by the model with the unit with

inactive. Streamflow-depletion responses to the 

withdrawals are defined as . Streamflow

depletion response coefficients ( ) are then 

as

 . 

The response coefficients are dimensionless and 

from 0.0 to 1.0. For the assumption of linearity 

valid, the values of the response coefficients for 

well/streamflow-constraint-site pair must remai

constant for all simulated withdrawal and hydro

conditions.

Response coefficients determined by the 

sient model for five of the well/streamflow-con

site pairs (fig. 17) indicate that there is substant

variability in the quantity and timing of streamfl

depletion responses to the simulated unit withd

For example, the effect of the unit withdrawal a

well 3A on streamflow in the Hunt River is rapi

a large depletion of streamflow in the first mont

very little depletion in the months following the 

withdrawal. This variability of streamflow respo

unit withdrawals is advantageous, because it pr

flexibility in determining withdrawal schedules 

wells that increase the yield of the aquifer while 

ing the streamflow-depletion constraints. Factor

affect streamflow responses are the relative posi

the wells and streamflow constraint sites (includ

vertical positions of the screened interval of eac

the geometry and hydraulic properties of the aq

and the streambed conductance and other physi

characteristics of the streams. Although not sho

figure 17, response coefficients for wells NK7 an

are nearly identical to those shown for well NK

response coefficients for wells 9A, 14A, and NK

Qwi

* i

Qsd j t , *

rjit , ,

rjit , ,

Qsd j t ,

*

Qwi

* = -----------------
48 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

END OF MONTH

0

1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

RESPONSE COEFFICIENT (CHANGE IN STREAMFLOW FOR

UNIT WITHDRAWAL RATE AT WELL), DIMENSIONLESS

Response of Hunt River at site P to unit 

withdrawal at well 3A

Response of Hunt River at site P to unit 

withdrawal at well NK9

Response of Hunt River at site P to unit 

withdrawal at well NK6

Response of Annaquatucket River at site T to unit 

withdrawal at well NK4

Response of Pettaquamscutt River at site V to 

unit withdrawal at well NK3

1 2 3 4 5 6 7 8 9 10 11 12

similar to those shown for well NK9; and those for 

wells NK1, NK2, and NK5 are similar to those shown 

for well NK4.

Because of the assumed linearity of the system, 

total streamflow depletion at each constraint 

site and for each month can be calculated with the 

response coefficients by summation of the individual 

streamflow depletions caused by each well in each 

month. This summation is written as

 , (13)

where

.

The two-part definition of is required as a 

consequence of the annual cycle of withdrawals. For 

example, streamflow depletions in January ( ) 

can be affected by withdrawals in December ( ). 

Although the summation includes 12 terms for 

well/streamflow-constraint-site pair, many of th

terms equal zero, because many of the response 

coefficients equal zero (fig. 17). 

The response coefficients are the link bet

the numerical and conjunctive-management mo

of the HAP stream-aquifer system. The respons

coefficients are incorporated into the conjunctiv

management model by replacing the definition 

of in the streamflow-depletion constrain

(equation 6) by the right-hand side of equation 

The constraints are then written as

 . 

Equation 14 replaces equation 6 in the conjunct

management model.

Difficulties arose in the use of the respon

matrix technique because the numerical model 

HAP stream-aquifer system is weakly nonlinear

Qsd j t ,

j t

Qsd j t , rjik , , Qwi k, '

k = 1

12

∑

i = 1

NW

= ∑

k' = t k – + 1, for t k – + 0 1 >

k' 12 = + ( ) t k – + 1 , for t k – + 0 1 ≤ 



k'

t = 1

t = 12

Qsd j t ,

rjik , , Qwi k, '

k = 1

12

∑

i = 1

NW

∑ Qsd j t , ( )max ≤

Figure 17. Selected simulated response coefficients for the Hunt–Annaquatucket–Pettaquamscutt 

stream-aquifer system, Rhode Island. (Unit withdrawal rate of 0.5 million gallons per day. Well 

locations shown on fig. 1; streamflow sites P, T, and V shown on fig. 6.)
Conjunctive-Management M

nonlinearities are the result of two factors. First, the 

HAP aquifer is unconfined, which means that the 

saturated thickness and transmissivity change as withdrawal rates at the wells change. Second, evapotrans–

piration and streamflow leakage were simulated as 

piecewise-linear functions of calculated water-level 

altitudes. Because of these nonlinearities, the response 

coefficients for each well/streamflow-constraint-site 

pair can change as withdrawal rates change, and such 

changes can affect the solution of the conjunctivemanagement model. These types of nonlinearities have 

been addressed in ground-water management problems 

by sequential (or iterative) linearization of the nonlinear problem (Danskin and Gorelick, 1985; Danskin and 

Freckleton, 1989; Gorelick and others, 1993, p. 206–

208; Barlow, 1997a; and Ahlfeld and Mulligan, 2000, 

p. 160–163). The sequential-linearization approach was 

not used here, however, because it is computationally 

intensive and because simulations with the transient 

model indicated that the response coefficients change 

very little as the simulated withdrawal conditions 

change. These simulations consisted of different unit 

withdrawal rates, different background withdrawal 

conditions (specifically, either the 1993–98 average 

monthly withdrawal condition or a condition of no 

withdrawal at any of the supply wells), and different 

months in which the unit withdrawal was active. The 

primary reason that the response coefficients change 

very little for the different withdrawal conditions is that 

the HAP aquifer is highly transmissive near many of 

the wells. As a consequence, drawdowns caused by 

different simulated withdrawal conditions do not 

cause substantial changes in the saturated thickness or 

transmissivity of the aquifer in these areas.

In addition to the nonlinear effects, another complicating factor to the use of the response-matrix technique is that the length of the stress periods in the 

transient model are not constant, but range from 28 to 

31 days. This is in contradiction to one of the assumptions of the response-matrix technique that requires 

stress periods to be of equal length. Because the length 

of the stress periods used in the model do not vary substantially, however, violation of this assumption is 

unlikely to markedly affect solution of the model.

By assuming linearity of the streamflow 

responses to ground-water withdrawals, the modified 

conjunctive-management model defined by equations 

5, 7–11, and 14 constitutes a linear program. The 

LINDO linear-programming computer software 

(LINDO Systems, 1996) was used to solve each 

specific application of the conjunctive-managem

model described in the next section. The progra

mathematically searches for the monthly withdr

rates at each well that maximize the yield of the 

subject to the set of constraints. The validity of 

response-matrix, linear-programming technique 

was used in this work was evaluated for several 

cations of the model. The evaluations consisted 

simulating the withdrawal rates calculated by L

with the transient model, and then ensuring that 

the resulting streamflow depletions calculated f

July, August, and September were less than or c

to the streamflow-depletion rates specified in th

conjunctive-management model.

Applications of the Model

Four sets of applications of the conjunctiv

management model were made for alternative d

tions of the maximum rate of streamflow deplet

allowed at streamflow constraint sites on the Hu

Annaquatucket, and Pettaquamscutt Rivers (tha

alternative definitions of in equati

The purpose of varying the specified maximum 

streamflow depletion was to quantify the amoun

withdrawal that is possible during July, August, 

September for different streamflow-depletion cr

Four sets of alternatives were evaluated:

Set 1: Maintain current rates of streamflow dep

in all three rivers during July, August, a

September.

Set 2: Decrease current rates of streamflow dep

in the Hunt River during July, August, a

September, with current rates of stream

depletion in the Annaquatucket and 

Pettaquamscutt Rivers.

Set 3: Maintain current rates of streamflow dep

in the Hunt River during July, August, a

September, with increased rates of strea

depletion allowed in the Annaquatucket 

Pettaquamscutt Rivers.

Set 4: Decrease current rates of streamflow dep

in the Hunt River during July, August, a

September, with increased rates of strea

depletion allowed in the Annaquatucket 

Pettaquamscutt Rivers.

Current rates of streamflow depletion are those 

mined with the transient model for the 1993–98 

withdrawal rates (table 13). Note that by decrea

Qsd j t , ( )max
50 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

current rates of streamflow depletion in the Hunt River, 

streamflow in the river would be increased over the 

current estimated rates. 

Streamflow depletion in the Hunt River was not 

allowed to increase in any of the alternatives. This was 

done because streamflow depletions calculated for the 

Hunt River for current withdrawal rates (table 13) are 

larger than those for either the Annaquatucket or 

Pettaquamscutt Rivers, both in absolute quantity and 

as a percentage of the pre-withdrawal streamflow 

calculated for each river.

For each alternative, two configurations of the 

public water-supply wells were tested. The first configuration (referred to as the current well configuration) 

consisted of the current system of 14 wells with their 

associated maximum withdrawal rates (table 14). The 

second configuration (referred to as the modified well 

configuration) was a modified system of 16 wells that 

consisted of the current 14 wells; an assumed increased 

capacity of 1.00 Mgal/d at wells 3A and NK6; and two 

additional hypothetical wells, H1 and H2 (table 14), in 

the Annaquatucket River Basin, each with an assumed 

maximum withdrawal rate of 1.00 Mgal/d. The locations of the two hypothetical wells are shown on 

figure 12B. Well sites 3A, NK6, H1, and H2 were identified in discussion with RIEDC and the town of North 

Kingstown as locations where increased yields from 

the aquifer may be possible. Further testing of these 

sites would be required to determine whether the 

model-calculated withdrawals that are in exceedance of 

current withdrawal rates could actually be attained at 

the sites. All withdrawals from well 3A were allocated 

to RIEDC and all withdrawals from wells NK6, H1, 

and H2 were allocated to the town of North Kingstown.

The value of the objective function calculated 

for each alternative was compared to the current, 1993–

98 average total withdrawal during July, August, 

and September, which is 506.5 Mgal (based on data 

in table 15). Results of each set of alternatives are 

described in the following four subsections; total 

ground-water withdrawals calculated for all 

alternatives are summarized in the last subsection.

Maintain Current Rates of Streamflow 

Depletion During July, August, and 

September

The first set of alternatives was made to determine whether current withdrawal rates from the 

aquifer can be increased during July, August, and 

September without increasing current estimated rates 

of streamflow depletion in the Hunt, Annaquatu

Pettaquamscutt Rivers during these months. Ma

allowed streamflow depletions for each river fro

July through September are those shown in tabl

Streamflow depletions during each of the remai

months of the year were constrained to be less t

equal to the calculated maximum monthly strea

depletion rate in each river, which was 4.75 ft3/

the Hunt River, 3.00 ft3/s for the Annaquatucke

and 0.64 ft3/s for the Pettaquamscutt River (tab

These constraints were designed to prevent larg

increases in streamflow depletion from October 

through June.

Total ground-water withdrawal for July, A

and September determined for the current well c

ration was 546.0 Mgal, which is an overall incr

of 7.8 percent from the current total withdrawal 

506.5 Mgal. The increase consists of a 12.6 per

increase over current withdrawals for July and a 

percent increase over current withdrawals for S

ber. These are modest increases that indicate litt

bility in the current configuration of wells to pr

for substantial increased withdrawals while cur

rates of streamflow depletion are maintained in 

three rivers.

The increased yield would require implem

tation of the monthly withdrawal rates calculate

LINDO for each well, which are given in table 1

that there are very small discrepancies (≤0.04 M

between the total monthly withdrawal rates calc

for all basins for October through June (bottom 

table 16) and the 1993–98 total monthly withdr

rates for all basins for these months (bottom row 

table 12). These discrepancies result from round

errors in the withdrawal rates of individual well

from errors introduced by the response-matrix s

procedure.

The patterns of withdrawals calculated fo

three water-supply systems indicate the followi

1. Monthly withdrawal rates calculated for 

well KC1 (table 16) are equal to the cur

withdrawal rates for the well (table 12). 

Because water-supply demands for KCW

the HAP aquifer can be met only by wit

als from their single well in the Hunt Ri

Basin (KC1), the well must withdraw at 

that is at least equal to each month’s dem

There is, however, little opportunity for 
Conjunctive-Management M

increased withdrawals from the HAP aquifer 

for the KCWA system because the system 

consists of a single well.

2. Calculated withdrawals from wells in the RIEDC 

system (table 16) are concentrated at well 3A 

during the months of October through June, but 

are distributed among wells 3A, 9A, and 14A 

during July through September. This withdrawal pattern differs from the current pattern 

of withdrawals (table 12), in which each well 

is active during every month. An increase of 

0.50 Mgal/d (15.5 Mgal) over the current July 

withdrawal rate is calculated for the RIEDC 

system for this alternative. 

3. A comparison of the calculated withdrawals 

for North Kingstown wells (table 16) with current withdrawal patterns (table 12) indicates 

(a) higher total withdrawals from the Hu

River Basin during November through A

(b) use of well NK6 only during July, A

and September, and at its maximum spe

rate of 1.37 Mgal/d; (c) use of wells in t

Annaquatucket River Basin only during 

May through October; and (d) higher to

withdrawals from the Pettaquamscutt R

Basin during January through June and O

and November. An increase of 0.32 Mg

(9.9 Mgal) in July and of 0.47 Mgal/d 

(14.1 Mgal) in September is calculated 

town of North Kingstown water-supply 

The large increase in yield for the system

pared to the other two water-supply syst

results from the large number of wells i

system and the distribution of the wells 

Table 16. Monthly withdrawal rates calculated for the current configuration of public water-supply wells for 1993–98 es

rates of streamflow depletion in July, August, and September, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer sy

Rhode Island

[Withdrawal rates are million gallons per day. Well locations are shown on figure 1. Shading used to emphasize results for July, August, and Septem

Watersupply

well identifier

January February March April May June July August September October November D

Hunt River Basin

KC1 0.27 0.08 0.08 0.16 0.32 0.80 0.94 0.80 0.53 0.28 0.32 

3A .58 .74 .55 .56 .58 .69 .51 .51 .00 .71 .70 

9A .00 .00 .00 .00 .00 .00 .00 .43 .84 .00 .00 

14A .00 .00 .00 .00 .00 .00 .92 .00 .00 .00 .00 

NK6 .00 .00 .00 .00 .00 .00 1.37 1.37 1.37 .00 .00 

NK9 1.62 1.61 1.65 1.75 .00 .00 .47 .00 .47 .58 1.72 

NK10 .00 .00 .00 .00 .55 1.69 .00 .54 .00 .00 .00 

Total for 

basin ....... 2.47 2.43 2.28 2.47 1.45 3.18 4.21 3.65 3.21 1.57 2.74 

Annaquatucket River Basin

NK1 .00 .00 .00 .00 .00 .00 .00 .00 .00 1.44 .00 

NK2 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK4 .00 .00 .00 .00 .00 .00 .93 .00 1.44 .00 .00 

NK5 .00 .00 .00 .00 1.75 1.75 1.75 1.66 .00 .00 .00 

Total for 

basin ....... 0.00 0.00 0.00 0.00 1.75 1.75 2.68 1.66 1.44 1.44 0.00 

Pettaquamscutt River Basin

NK3 .00 .00 .00 .00 .00 .00 .00 .31 .19 .43 .41 

NK7 .43 .41 .41 .41 .41 .41 .42 .00 .00 .00 .00 

NK8 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

Total for 

basin ....... 0.43 0.41 0.41 0.41 0.41 0.41 0.42 0.31 0.19 0.43 0.41 

Total for all 

basins ..... 2.90 2.84 2.69 2.88 3.61 5.34 7.31 5.62 4.84 3.44 3.15 
52 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

the three river basins; these factors provide 

flexibility in the withdrawal schedules 

calculated for each well.

The monthly withdrawal rates calculated by the 

conjunctive-management model (table 16) were simulated in the transient model for a 5-year period. With 

this withdrawal pattern, seven of the nine streamflowdepletion constraints specified for July, August, and 

September were met in the fifth year of simulation (that 

is, at dynamic equilibrium). Of the two streamflowdepletion constraints that were not met, the maximum 

difference between specified and calculated streamflow-depletion rates was 0.07 ft3/s for the Hunt River in 

the month of July. This value is a small difference from 

the specified depletion of 4.70 ft3/s, and substantiates 

the response-matrix solution technique.

Because of the similarity of some of the re

coefficients, it is possible to interchange calcula

withdrawal rates among those wells with simila

response coefficients, while still maintaining th

of the objective function and meeting the mode

straints. For example, table 16 indicates that we

is active only during July; well NK10 in May, Ju

August; well NK1 in October; and well NK3 fr

August through November. A simulation of the 

sient model was made to illustrate that there is 

flexibility in the withdrawal patterns calculated 

linear program, and that, in some cases, these w

drawal patterns can be simplified. In the simula

withdrawal rates from those wells with little act

during the year were shifted to wells within the 

water-supply system that have similar response 

cients and are active during more months of the 

Specifically, as shown in table 17, the July with

Table 17. Monthly withdrawal rates specified for public water-supply wells in a simulation of the transient model of the 

Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island

[Withdrawal rates are million gallons per day. Well locations are shown on figure 1. Shading used to emphasize results for July, August, and Septe

Watersupply

well identifier

January February March April May June July August September October November D

Hunt River Basin

KC1 0.27 0.08 0.08 0.16 0.32 0.80 0.94 0.80 0.53 0.28 0.32 

3A .58 .74 .55 .56 .58 .69 .51 .51 .00 .71 .70 

9A .00 .00 .00 .00 .00 .00 .92 .43 .84 .00 .00 

14A .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK6 .00 .00 .00 .00 .00 .00 1.37 1.37 1.37 .00 .00 

NK9 1.62 1.61 1.65 1.75 .55 1.69 .47 .54 .47 .58 1.72 

NK10 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

Total for 

basin........ 2.47 2.43 2.28 2.47 1.45 3.18 4.21 3.65 3.21 1.57 2.74 

Annaquatucket River Basin

NK1 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK2 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK4 .00 .00 .00 .00 .00 .00 .93 .00 1.44 1.44 .00 

NK5 .00 .00 .00 .00 1.75 1.75 1.75 1.66 .00 .00 .00 

Total for 

basin........ 0.00 0.00 0.00 0.00 1.75 1.75 2.68 1.66 1.44 1.44 0.00 

Pettaquamscutt River Basin

NK3 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK7 .43 .41 .41 .41 .41 .41 .42 .31 .19 .43 .41 

NK8 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

Total for 

basin........ 0.43 0.41 0.41 0.41 0.41 0.41 0.42 0.31 0.19 0.43 0.41 

Total for all 

basins ...... 2.90 2.84 2.69 2.88 3.61 5.34 7.31 5.62 4.84 3.44 3.15 
Conjunctive-Management M

at well 14A was shifted to well 9A; withdrawals from 

NK10 were shifted to NK9; the October withdrawal at 

NK1 was shifted to NK4; and withdrawals from NK3 

were shifted to NK7. With this modified withdrawal 

pattern, calculated streamflow depletions for the Hunt, 

Annaquatucket, and Pettaquamscutt Rivers in July, 

August, and September were less than or equal to the 

specified rates for all but one of the streamflow constraint sites during one of the months. The one exception was the streamflow depletion calculated for July 

for the Pettaquamscutt River, which exceeded the specified constraint value by only 0.02 ft3/s. The transient 

model could be used to test whether other withdrawal 

patterns (with equivalent overall withdrawal rates) also 

could meet the model constraints.

Total ground-water withdrawal for July, A

and September determined for the modified we

figuration was 596.3 Mgal, which is an overall i

of 17.7 percent from the current average total w

drawal of 506.5 Mgal. The increase consists of 

percent increase over current average withdraw

July and a 30.0 percent increase over Septembe

drawals. The larger increase in total withdrawal

pared to the current well configuration, results f

larger number of wells and increased total with

capacity from all wells that is provided by the m

well configuration.

Monthly withdrawal rates calculated for t

modified well configuration are shown in table 

contrast to withdrawal patterns calculated for th

Table 18. Monthly withdrawal rates calculated for the modified configuration of public water-supply wells for 1993-98 e

rates of streamflow depletion in July, August, and September, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer sy

Rhode Island

[Withdrawal rates are million gallons per day. Well locations are shown on figure 1. Shading used to emphasize results for July, August, and Septem

Watersupply

well identifier

January February March April May June July August September October November D

Hunt River Basin

KC1 0.27 0.08 0.08 0.16 0.32 0.80 0.94 0.80 0.53 0.28 0.32 

3A .58 .74 .55 .56 .58 .69 .93 .95 .00 .71 .31 

9A .00 .00 .00 .00 .00 .00 .00 .00 .84 .00 .40 

14A .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK6 .00 .00 .00 .00 .00 .00 2.37 .89 1.89 .00 .00 

NK9 1.62 1.62 1.66 1.75 .00 .00 .00 .00 .47 .00 1.74 

NK10 .00 .00 .00 .00 .47 1.00 .47 .47 .00 1.25 .00 

Total for 

basin ....... 2.47 2.44 2.29 2.47 1.37 2.49 4.71 3.11 3.73 2.24 2.77 

Annaquatucket River Basin

NK1 .00 .00 .00 .00 .08 .69 .00 .00 .00 .80 .00 

NK2 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK4 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK5 .00 .00 .00 .00 1.75 1.75 1.75 1.21 .00 .00 .00 

H1 .00 .00 .00 .00 .00 .00 .24 .00 .76 .00 .00 

H2 .00 .00 .00 .00 .00 .00 1.00 1.00 1.00 .00 .00 

Total for 

basin ....... 0.00 0.00 0.00 0.00 1.83 2.44 2.99 2.21 1.76 0.80 0.00 

Pettaquamscutt River Basin

NK3 .00 .00 .00 .00 .00 .00 .00 .31 .19 .00 .00 

NK7 .43 .41 .41 .41 .41 .41 .41 .00 .00 .00 .00 

NK8 .00 .00 .00 .00 .00 .00 .00 .00 .00 .41 .40 

Total for 

basin ....... 0.43 0.41 0.41 0.41 0.41 0.41 0.41 0.31 0.19 0.41 0.40 

Total for all 

basins ..... 2.90 2.85 2.70 2.88 3.61 5.34 8.11 5.63 5.68 3.45 3.17 
54 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

current well configuration (table 16), no increases in 

withdrawals are calculated for the RIEDC system. This 

appears to be caused by the increased withdrawal rate 

allowed at well NK6 in the modified well configuration. Relatively large withdrawals can be sustained at 

this well during July through September because 

streamflow depletion in the Hunt River reacts slowly 

to withdrawals from the well (fig. 17). Also, for this 

alternative, hypothetical well H2 withdraws at its maximum specified rate of 1.00 Mgal/d from July through 

September, and hypothetical well H1 withdraws during 

July and September.

Streamflow depletions calculated for the three 

rivers for July, August, and September with the withdrawal rates calculated for this alternative (table 18) 

were less than or equal to the specified constraint 

values for seven of the nine streamflow-depletion constraints in July, August, and September. Of the two constraints that were not met, the maximum difference 

between specified and calculated streamflow-depletion 

rates was 0.17 ft3/s for the Hunt River in the month of 

July. This is a small difference from the specified 

depletion of 4.70 ft3/s.

Decrease Current Rates of Streamflow 

Depletion in the Hunt River During July, 

August, and September, With Current 

Rates of Streamflow Depletion in the

Annaquatucket and Pettaquamscutt Rivers

The second set of alternatives was made to 

determine whether estimated current rates of streamflow depletion in the Hunt River can be decreased 

during July, August, and September, (1) while current 

water-supply demands are met and (2) without 

increasing streamflow depletions in the Annaquatucket 

or Pettaquamscutt Rivers. Decreasing current rates of 

streamflow depletion in the Hunt River would result 

in increased streamflow in the river. As in the first 

set of alternatives, maximum allowed streamflowdepletion rates during July, August, and September 

for the Annaquatucket and Pettaquamscutt Rivers are 

constrained to be less than or equal to those calculated 

for 1993–98 average withdrawal rates; streamflow 

depletions in all rivers during each of the remaining 

9 months of the year were constrained to be less than 

or equal to the estimated current maximum mon

rate of streamflow depletion in each river (table 

To determine the maximum decreases in stream

depletion in the Hunt River that could be attaine

during July, August, and September, the estima

rent rates of streamflow depletion for each mon

lowered by uniform increments of 5 percent in 

of LINDO simulations; the maximum decrease

determined when the next 5-percent increment r

in an infeasible solution (that is, one or more of 

model constraints could not be met).

For the current configuration of supply w

calculated maximum increases in streamflow tha

be attained for the Hunt River for July, August, 

September are only 5 percent of existing stream

depletion rates calculated for these months, or f

0.22 ft3/s in September to 0.24 ft3/s in August. T

small increase in streamflow that is possible wi

current configuration of wells is not surprising, 

the small increase in total withdrawal that was c

lated in the first set of alternatives for the curren

supply-well configuration. Total ground-water w

drawal for July, August, and September for this 

tive is 526.1 Mgal, which is an overall increase 

3.7 percent from the current average total withd

(506.5 Mgal). This small increase relative to tha

lated for the current well configuration in the fir

alternatives is a result of the lower rates of strea

depletion allowed for the Hunt River in this alte

For the modified configuration of supply 

the calculated maximum increases in streamflow 

could be attained for the Hunt River for July, A

and September are 15 percent of existing stream

depletion rates calculated for these months, or f

0.65 ft3/s in September to 0.71 ft3/s in August. T

ground-water withdrawal for July, August, and S

ber for this alternative is 525.2 Mgal, which is a

all increase of only 3.7 percent from the current 

average total withdrawal (506.5 Mgal). The mo

nificant difference between withdrawal rates cal

for this alternative (table 19) and those calculat

the modified well configuration in the first set o

natives (table 18) is that calculated withdrawals 

well NK6 during July and September are substa

lower for this alternative.
Conjunctive-Management M

Maintain Current Rates of Streamflow 

Depletion in the Hunt River During July, 

August, and September, With Increased 

Rates of Streamflow Depletion Allowed in the 

Annaquatucket and Pettaquamscutt Rivers

As noted previously, estimated rates of streamflow depletion are larger for the Hunt River than for 

either the Annaquatucket or Pettaquamscutt Rivers. 

The estimated average streamflow depletion in the 

Hunt River for the months of July through September 

is 25 percent of the estimated pre-withdrawal 

streamflows in the river, whereas those for the 

Annaquatucket and Pettaquamscutt Rivers are 1

cent and 7 percent, respectively. In the third and 

sets of alternatives, specified rates of streamflow 

tion for the Annaquatucket and Pettaquamscutt 

were allowed to increase to a maximum of 25 p

of the estimated pre-withdrawal streamflow in e

river during July through September (table 20), 

determined with the transient numerical model. 

maximum increases in the allowed rates of strea

depletion are 0.56 to 1.20 ft3/s for the Annaqua

Table 19. Monthly withdrawal rates calculated for the modified configuration of public water-supply wells and a 15-per

reduction in the 1993–98 estimated rates of streamflow depletion in the Hunt River in July, August, and September, H

Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island

[Withdrawal rates are million gallons per day. Well locations are shown on figure 1. Shading used to emphasize results for July, August, and Septem

Watersupply

well identifier

January February March April May June July August September October November D

Hunt River Basin

KC1 0.27 0.08 0.08 0.16 0.32 0.80 0.94 0.80 0.53 0.28 0.32 

3A .58 0.74 .55 .56 .58 .69 .99 .75 .00 .71 .33 

9A .00 .00 .00 .00 .00 .00 .00 .20 .84 .00 .38 

14A .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK6 .00 .00 .00 .00 .00 .00 .83 .89 1.13 .00 .00 

NK9 1.62 1.62 1.66 1.75 .00 .00 .00 .00 .47 .00 .00 

NK10 .00 .00 .00 .00 .47 .80 .47 .47 .00 .61 1.74 

Total for 

basin ....... 2.47 2.44 2.29 2.47 1.37 2.29 3.23 3.11 2.97 1.60 2.77 

Annaquatucket River Basin

NK1 .00 .00 .00 .00 .08 .89 .00 .00 .00 1.44 .00 

NK2 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK4 .00 .00 .00 .00 .00 .00 .16 .00 .00 .00 .00 

NK5 .00 .00 .00 .00 1.75 1.75 1.75 1.21 .00 .00 .00 

H1 .00 .00 .00 .00 .00 .00 .00 .00 .76 .00 .00 

H2 .00 .00 .00 .00 .00 .00 1.00 1.00 1.00 .00 .00 

Total for 

basin ....... 0.00 0.00 0.00 0.00 1.83 2.64 2.91 2.21 1.76 1.44 0.00 

Pettaquamscutt River Basin

NK3 .00 .00 .00 .00 .00 .00 .00 .31 .19 .00 .00 

NK7 .43 .41 .41 .41 .41 .41 .41 .00 .00 .41 .40 

NK8 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

Total for 

basin ....... 0.43 0.41 0.41 0.41 0.41 0.41 0.41 0.31 0.19 0.41 0.40 

Total for all 

basins ..... 2.90 2.85 2.70 2.88 3.61 5.34 6.55 5.63 4.92 3.45 3.17 
56 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

River and 1.16 to 1.22 ft3/s for the Pettaquamscutt 

River (table 20). Increasing current rates of streamflow 

depletion in the Annaquatucket and Pettaquamscutt 

Rivers would result in decreased streamflow in these 

rivers.

Four sets of LINDO simulations were made for 

each well configuration, in which the allowed increases 

in streamflow depletion for the Annaquatucket and 

Pettaquamscutt Rivers were incrementally set at 25-, 

50-, 75-, and 100-percent of the maximum allowed 

rates (table 20). In each simulation, streamflow depletions during the remaining 9 months of the year were 

constrained to be less than or equal to the maximum 

monthly rate, which in each case equals the July rate. 

Specified rates of streamflow depletion in the Hunt 

River were maintained at current estimated rates, as 

was done for the first set of alternatives.

Substantial increases in ground-water 

withdrawals are calculated for the several simulations, 

because streamflow is allowed to decrease in the 

Annaquatucket and Pettaquamscutt Rivers (fig. 18). 

For the current configuration of supply wells, total 

withdrawals during July through September range from 

a minimum of 546.0 Mgal for current rates of streamflow depletion specified for the Annaquatucket and 

Pettaquamscutt Rivers to a maximum of 705.1 Mgal 

for the maximum allowed decreases in streamflow in 

the two rivers (fig. 18). This is a maximum increase 

of 39.2 percent over the current total withdrawal of 

506.5 Mgal. For the modified well configuratio

withdrawals range from 596.3 Mgal to 760.3 M

(fig. 18), which is a maximum increase of 50.1 

over the current total withdrawal.

Table 20. Specified rates of streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers, Rhode Island, for 

conditions in which streamflow depletions are allowed to increase in the two rivers

[All values are in cubic foot per second]

Month

Modelcalculated

pre-withdrawal

streamflow

Modelcalculated

current

rates of

streamflow

depletion

(from table 13)

Specified rate of streamflow depletion in the

Annaquatucket and Pettaquamscutt Rivers

25 percent of

maximum allowed 

increase in

streamflow

depletion

50 percent of

maximum allowed 

increase in

streamflow

depletion

75 percent of

maximum allowed 

increase in

streamflow

depletion

100 perc

maximum 

increa

stream

deple

Annaquatucket River

July ...................... 14.24 3.00 3.14 3.28 3.42 3.5

August.................. 13.56 2.59 2.79 2.99 3.19 3.3

September ............ 12.84 2.01 2.31 2.61 2.91 3.2

Pettaquamscutt River

July ...................... 7.44 .64 .94 1.25 1.55 1.8

August.................. 6.52 .46 .75 1.05 1.34 1.6

September ............ 5.84 .30 .59 .88 1.17 1.4

0 25 50 75

PERCENTAGE OF MAXIMUM ALLOWED INCR

STREAMFLOW DEPLETION IN THE ANNAQUA

AND PETTAQUAMSCUTT RIVERS

TOTAL GROUND-WATER WITHDRAWAL,

IN MILLION GALLONS

CALCULATED FOR CURRENT

WELL CONFIGURATION

CALCULATED FOR MODIFIED

WELL CONFIGURATION

Current (1993-98) average total withdrawal

500

800

550

600

650

700

750

Figure 18. Total ground-water withdrawals during July

and September calculated with the conjunctive-manag

model for current rates of streamflow depletion specifie

Hunt River and increased rates of streamflow depletio

specified for the Annaquatucket and Pettaquamscutt R

Rhode Island.
Conjunctive-Management M

Monthly withdrawal rates calculated for the current and modified well configurations for the maximum 

allowed decrease in streamflows in the Annaquatucket 

and Pettaquamscutt Rivers are shown in tables 21 and 

22. Monthly withdrawals calculated for the current 

well configuration (table 21) indicate the following.

1. As with the previous alternatives, monthly withdrawal rates calculated for well KC1 remain at 

the 1993–98 rates.

2. Calculated withdrawals from wells in the 

RIEDC system are concentrated at well 3A 

from October through June, but are distributed 

among wells 3A, 9A, and 14A from July 

through September. Well 14A withdraws at its 

maximum rate (1.44 Mgal/d) during July. A net 

increase over the current total withdraw

for the RIEDC system during July of 30

(0.98 Mgal/d) is calculated for this alter

3. For the North Kingstown water-supply sys

(a) well NK6 withdraws only during Jul

August, and September, and at its maxim

specified rate of 1.37 Mgal/d; (b) withdr

only occur in the Annaquatucket River B

during May through September; (c) wel

NK4 withdraws at its maximum rate of 

1.44 Mgal/d during July and September 

well NK5 at its maximum rate of 1.75 M

from June through August; (d) withdraw

from the Pettaquamscutt River Basin ar

larger than current rates (table 12) for al

months except December; and (e) well N

Table 21. Monthly withdrawal rates calculated for the current configuration of public water-supply wells for increased 

streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers and current rates of streamflow depletion in the 

River, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island

[Withdrawal rates are million gallons per day. Well locations are shown on figure 1. Shading used to emphasize results for July, August, and Septem

Watersupply

well identifier

January February March April May June July August September October November D

Hunt River Basin

KC1 0.27 0.08 0.08 0.16 0.32 0.80 0.94 0.80 0.53 0.28 0.32 

3A .58 .74 .55 .56 .58 .69 .13 .52 .00 .71 .70 

9A .00 .00 .00 .00 .00 .00 .34 .42 .84 .00 .00 

14A .00 .00 .00 .00 .00 .00 1.44 .00 .00 .00 .00 

NK6 .00 .00 .00 .00 .00 .00 1.37 1.37 1.37 .00 .00 

NK9 .00 .82 .86 .96 .00 .00 .47 .00 .47 1.46 .00 

NK10 .84 .00 .00 .00 .47 .90 .00 .47 .00 .00 1.32 

Total for 

basin ....... 1.69 1.64 1.49 1.68 1.37 2.39 4.69 3.58 3.21 2.45 2.34 

Annaquatucket River Basin

NK1 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK2 .00 .00 .00 .00 .00 .00 .26 .00 1.01 .00 .00 

NK4 .00 .00 .00 .00 .00 .00 1.44 .61 1.44 .00 .00 

NK5 .00 .00 .00 .00 1.03 1.75 1.75 1.75 .00 .00 .00 

Total for 

basin ....... 0.00 0.00 0.00 0.00 1.03 1.75 3.45 2.36 2.45 0.00 0.00 

Pettaquamscutt River Basin

NK3 .00 .00 .00 .00 .00 .00 1.24 .00 .97 1.00 .00 

NK7 .81 .81 .81 .81 .81 .81 .00 .81 .00 .00 .41 

NK8 .40 .40 .40 .40 .40 .40 .00 .20 .00 .00 .40 

Total for 

basin ....... 1.21 1.21 1.21 1.21 1.21 1.21 1.24 1.01 0.97 1.00 0.81 

Total for all 

basins ..... 2.90 2.85 2.70 2.89 3.61 5.35 9.38 6.95 6.63 3.45 3.15 
58 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

withdraws at its maximum rate from January 

through June and during August, and well NK8 

withdraws at its maximum rate from January 

through June and during November. The net 

increases in total withdrawals from the North 

Kingstown system over current withdrawals are 

59.2 Mgal (1.91 Mgal/d) in July, 41.2 Mgal 

(1.33 Mgal/d) in August, and 67.8 Mgal 

(2.26 Mgal/d) in September. 

Monthly withdrawals calculated for the m

well configuration for the maximum allowed de

in streamflow in the Annaquatucket and Pettaqu

Rivers (table 22) are similar to those calculated 

the modified well configuration for the current r

of streamflow depletion in the two rivers (table 

Because of the allowed decreases in the flow in 

two rivers, however, total withdrawals from we

the Annaquatucket and Pettaquamscutt River B

Table 22. Monthly withdrawal rates calculated for the modified configuration of public water-supply wells for increased 

streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers and current rates of streamflow depletion in the 

River, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island

[Withdrawal rates are million gallons per day. Well locations are shown on figure 1. Shading used to emphasize results for July, August, and Septem

Watersupply

well identifier

January February March April May June July August September October November D

Hunt River Basin

KC1 0.27 0.08 0.08 0.16 0.32 0.80 0.94 0.80 0.53 0.28 0.32 

3A .58 .74 .55 .56 .58 .69 1.03 1.20 .00 .00 .73 

9A .00 .00 .00 .00 .00 .00 .00 .00 .84 .71 .00 

14A .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK6 .00 .00 .00 .00 .00 .00 2.37 .27 2.37 .00 .00 

NK9 .84 .82 .86 .96 .00 .00 .00 .00 .47 .00 1.59 

NK10 .00 .00 .00 .00 .47 .90 .47 .47 .00 1.28 .00 

Total for 

basin ....... 1.69 1.64 1.49 1.68 1.37 2.39 4.81 2.74 4.21 2.27 2.64 

Annaquatucket River Basin

NK1 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK2 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 

NK4 .00 .00 .00 .00 .00 .00 .32 .00 .98 .00 .00 

NK5 .00 .00 .00 .00 1.03 1.75 1.75 1.75 .00 .00 .00 

H1 .00 .00 .00 .00 .00 .00 1.00 .00 1.00 .00 .00 

H2 .00 .00 .00 .00 .00 .00 1.00 1.00 1.00 .00 .00 

Total for 

basin ....... 0.00 0.00 0.00 0.00 1.03 1.75 4.07 2.75 2.98 0.00 0.00 

Pettaquamscutt River Basin

NK3 .00 .00 .00 .00 .00 .00 1.24 .00 .98 .00 .00 

NK7 .81 .81 .81 .81 .81 .81 .00 .81 .00 .81 .54 

NK8 .40 .40 .40 .40 .40 .40 .00 .20 .00 .37 .00 

Total for 

basin ....... 1.21 1.21 1.21 1.21 1.21 1.21 1.24 1.01 0.98 1.18 0.54 

Total for all 

basins ..... 2.90 2.85 2.70 2.89 3.61 5.35 10.12 6.50 8.17 3.45 3.18 
Conjunctive-Management M

are higher from July through September than for the 

alternative in which current rates of depletion were 

specified. Streamflow depletions calculated by the transient model for the three rivers for July, August, and 

September with the withdrawal rates calculated for 

this alternative (table 22) were less than or equal to 

the specified constraint values for eight of the nine 

streamflow-depletion constraints in July, August, and 

September; the constraint specified for the Hunt River 

in July was exceeded by 0.17 ft3/s.

Decrease Current Rates of Streamflow 

Depletion in the Hunt River During

July, August, and September, With 

Increased Rates of Streamflow Depletion 

Allowed in the Annaquatucket and 

Pettaquamscutt Rivers

The fourth set of alternatives was made to determine the amount of decrease in streamflow depletion in 

the Hunt River that could be attained from July through 

September for increased rates of streamflow depletion 

specified for the Annaquatucket and Pettaquamscutt 

Rivers. As was done in the second set of alternatives, 

the maximum decreases in streamflow depletion in the 

Hunt River that could be attained were determin

series of LINDO simulations in which the estim

current rates of streamflow depletion for each m

were lowered by uniform increments of 5 perce

the maximum decreases were determined when 

next 5-percent increment resulted in an infeasib

tion. For each simulation, streamflow depletion 

Hunt River during the remaining 9 months of th

year was constrained to be less than or equal to 

mated current maximum monthly rate (4.75 ft3/

Streamflow-depletion rates in the Annaquatuck

Pettaquamscutt Rivers were allowed to increase 

percent and then 100 percent of the maximum a

increases (table 20); that is, flow in the two rive

allowed to decrease.

Total ground-water withdrawals calculate

the several simulations are summarized in table 

shown in figure 19. Also shown in the table and 

figure are ground-water withdrawals calculated 

the previous applications of the model. The trad

between increased total ground-water withdraw

the aquifer during July, August, and September 

decreased streamflow depletion in the Hunt Riv

summarized in figure 19. The shaded area of fig

Table 23. Summary of the model-calculated total ground-water withdrawals from the Hunt–Annaquatucket–Pettaquam

stream-aquifer system, Rhode Island, during July, August, and September

[Values are in million gallons. --, not simulated]

Percentage 

reduction in 

streamflow 

depletion in 

the Hunt River

Percentage of maximum allowed increases in streamflow depletions in the

Annaquatucket and Pettaquamscutt Rivers

No increases 25 percent 50 percent 75 percent 100 perc

Well configuration Well configuration Well configuration Well configuration Well config

Current Modified Current Modified Current Modified Current Modified Current M

0 546.0 596.3 586.8 638.6 626.8 680.1 666.5 721.1 705.1 

5 526.1 573.5 -- -- 607.3 -- -- -- -- 

10 infeasible 549.3 -- -- 585.6 634.3 -- -- 665.3 

15 -- 525.2 -- -- 562.7 -- -- -- -- 

20 -- infeasible -- -- 537.9 586.5 -- -- 621.2 

25 -- -- -- -- 513.4 -- -- -- -- 

30 -- -- -- -- infeasible 538.2 -- -- 573.5 

35 -- -- -- -- -- 512.4 -- -- 547.3 

40 -- -- -- -- -- infeasible -- -- infeasible in
60 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

0 5 10 15 20 25 30 35 40

PERCENTAGE REDUCTION IN STREAMFLOW DEPLETION IN THE HUNT RIVER

TOTAL GROUND-WATER WITHDRAWAL, IN MILLION GALLONS

EXPLANATION

450

800

500

550

600

650

700

750

APPROXIMATE AREA IN WH

MODEL SOLUTIONS ARE

INFEASIBLE

SPECIFIED ALLOWED INCR

 IN STREAMFLOW DEPLET

 IN THE ANNAQUATUCKET 

 PETTAQUAMSCUTT RIVER

CALCULATED FOR CURREN

WELL CONFIGURATION

CALCULATED FOR MODIFIE

WELL CONFIGURATION

CURRENT (1993–98) AVERA

TOTAL WITHDRAWAL

 None

 50 percent of maximum

 100 percent of maximum

is the approximate region in which solutions to the 

conjunctive-management model are infeasible; that is, 

one or more model constraints can not be met by any 

combination of well withdrawals.

The calculated maximum decrease in streamflow 

depletion that could be attained for the Hunt River from 

July through September is about 35 percent of existing 

streamflow-depletion rates calculated for the months, 

or from 1.51 ft3/s in September to 1.66 ft3/s in August. 

These reductions in streamflow depletion in the Hunt 

River would require a maximum increase of 1.20 ft3/s 

in the streamflow-depletion rate in the Annaquatucket 

River and of 1.22 ft3/s in the streamflow-depletion rate 

in the Pettaquamscutt River. Decreases in streamflow 

depletion in the Hunt River greater than 35 percent 

would require that one or more of the following actions 

be taken: (1) decreases in current water-supply 

demands; (2) larger increases in allowed streamflow 

depletions in the Annaquatucket and Pettaquamscutt 

Rivers than were allowed in this evaluation; or 

ferent configurations of wells (and of maximum 

drawal rates at the wells) than were used in this 

evaluation.

Monthly withdrawal rates calculated for e

well for the current well configuration and for c

tions of maximum allowed increases in streamfl

depletion in the Annaquatucket and Pettaquams

Rivers and a 35-percent depletion in streamflow 

tions in the Hunt River are shown in table 24. T

withdrawal from all wells during the 3-month p

547.3 Mgal, which is an overall increase of 8.1 

from the current average total withdrawal of 

506.5 Mgal. Total withdrawal from all wells for 

same conditions but for the modified well config

is 595.8 Mgal (table 23, fig. 19), which is an ov

increase of 17.6 percent from the current averag

withdrawal.

Figure 19. Total ground-water withdrawals during July, August, and September calculated with the conjunctivemanagement model in which streamflow depletions in the Hunt River are reduced from current estimated rates an

those for the Annaquatucket and Pettaquamscutt Rivers are allowed to increase from current estimated rates, Hun

Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island.
Summary and Conclus

SUMMARY AND CONCLUSIONS

Ground-water withdrawals from the Hunt–

Annaquatucket–Pettaquamscutt (HAP) stream-aquifer 

system in central Rhode Island exceeded 8 Mgal/d 

during months of peak water use during 1993–98, and 

additional withdrawals have been proposed to meet 

growing demands from within and outside of the 

system boundary. Nearly all of the water withdrawn, 

however, is derived from depletions of flow in the rivers, brooks, and ponds that overlie the HAP aquifer. 

Concerns by the Rhode Island Department of Environmental Management regarding the effects of groundwater withdrawals on streamflow depletions in the 

HAP stream-aquifer system prompted an invest

to better understand the water resources of the s

and to evaluate alternatives for the conjunctive 

management of the ground- and surface-water 

resources of the system. The investigation was 

from 1995 to 2000 by the U.S. Geological Surv

in cooperation with the town of North Kingstow

RIDEM, Rhode Island Economic Development 

Corporation, and Rhode Island Water Resource

The stream-aquifer system covers a 19.0-

mile area and is defined by the HAP sand-and-g

aquifer and the network of rivers, brooks, and p

that overlie and are in hydraulic connection wit

aquifer. Average annual flows in the three large

Table 24. Monthly withdrawal rates calculated for the current configuration of public water-supply wells for increased 

streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers and 35 percent reduction in streamflow depletio

Hunt River, Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system, Rhode Island

[Withdrawal rates are million gallons per day. Well locations are shown on figure 1. Shading used to emphasize results for July, August, and Septem

Watersupply

well identifier

January February March April May June July August September October November D

Hunt River Basin

KC1 0.27 0.08 0.08 0.16 0.32 0.80 0.94 0.80 0.53 0.28 0.32 

3A .58 .74 .55 .56 .58 .69 .43 .25 .00 .71 .70 

9A .00 .00 .00 .00 .00 .00 .00 .69 .84 .00 .00 

14A .00 .00 .00 .00 .00 .00 .50 .00 .00 .00 .00 

NK6 .00 .00 .00 .00 .00 .00 .00 .00 .15 .00 .00 

NK9 .84 .82 .86 .47 .00 .00 .47 .00 .47 1.25 .00 

NK10 .00 .00 .00 .00 .47 .47 .00 .47 .00 .00 2.14 

Total for 

basin ....... 1.69 1.64 1.49 1.19 1.37 1.96 2.34 2.21 1.99 2.24 3.16 

Annaquatucket River Basin

NK1 .00 .00 .00 .49 .00 .43 .00 .00 .00 .00 .00 

NK2 .00 .00 .00 .00 .00 .00 .07 .00 1.01 .00 .00 

NK4 .00 .00 .00 .00 .00 .00 1.44 .60 1.44 .00 .00 

NK5 .00 .00 .00 .00 1.03 1.75 1.75 1.75 .00 .00 .00 

Total for 

basin ....... 0.00 0.00 0.00 0.49 1.03 2.18 3.26 2.35 2.45 0.00 0.00 

Pettaquamscutt River Basin

NK3 .00 .00 .00 .00 .00 .00 .16 .25 .96 .81 .00 

NK7 .81 .81 .81 .81 .81 .81 .81 .81 .00 .00 .00 

NK8 .40 .40 .40 .40 .40 .40 .24 .00 .00 .40 .00 

Total for 

basin ....... 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.06 0.96 1.21 0.00 

Total for all 

basins ..... 2.90 2.85 2.70 2.89 3.61 5.35 6.81 5.62 5.40 3.45 3.16 
62 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

streams in the system during 1941–96 were measured 

or estimated to have been 46.4 ft3/s for the Hunt River, 

17.0 ft3/s for the Annaquatucket River, and 9.5 ft3/s 

for the Pettaquamscutt River. Ground water is withdrawn from the HAP aquifer at 18 large-capacity 

water-supply wells, which consist of 14 public watersupply wells, an industrial well, and 3 fisheries wells. 

Three water-supply systems withdraw water at the 14 

public water-supply wells; these are the town of North 

Kingstown, Rhode Island Economic Development 

Corporation, and Kent County Water Authority. Total 

average annual withdrawal from all 18 wells was 

estimated to have been 7.8 ft3/s during 1941–96, of 

which an estimated 4.6 ft3/s, or 59 percent of the total 

withdrawal, was exported from the HAP system.

Steady-state and transient numerical models 

were developed to simulate ground-water flow and 

ground-water/surface-water interactions in the HAP 

stream-aquifer system. The models are representative 

of average withdrawal and hydrologic conditions in the 

HAP system during the 1941–96 period. The steadystate model simulates long-term-average hydrologic 

stresses, whereas the transient model simulates an average annual cycle of monthly hydrologic stresses. The 

long-term-average total flow rate through the system 

calculated with the steady-state model was about 

83.0 ft3/s, which was close to the flow rate of about 

88.5 ft3/s estimated independently from hydrologic 

and water-use data for the system. The models do 

not simulate direct runoff within the HAP streamaquifer system, which partly explains the lower flow 

rate calculated by the steady-state model. Estimated 

rates of streamflow depletion caused by ground-water 

withdrawals at the 14 public water-supply wells and 

industrial well were calculated by the models. 

Streamflow depletion consists of captured groundwater discharge and induced infiltration of streamflow. 

Monthly streamflow-depletion rates calculated by 

the transient model for the Hunt River ranged from 

3.7 ft3/s to 5.2 ft3/s, and averaged 4.2 ft3/s over the 

annual cycle; those for the Annaquatucket River ranged 

from 1.2 ft3/s to 2.2 ft3/s, and averaged 1.5 ft3/s; 

and those for the Pettaquamscutt River ranged from 

0.1 ft3/s to 0.6 ft3/s, and averaged 0.4 ft3/s. Streamflowdepletion rates calculated by the steady-state model for 

the long-term-average conditions were nearly e

the average annual rates calculated with the tran

model.

Contributing areas and sources of water t

supply wells in the HAP stream-aquifer system 

delineated by use of the steady-state model. Sou

water to the wells consisted of precipitation and 

water recharge to the HAP aquifer, streamflow l

from natural stream-channel losses, streamflow 

caused by induced infiltration, and lateral groun

inflow from till and bedrock upland areas. Strea

leakage was calculated to be a source of water t

wells, all but five of which are in the Hunt River 

Calculated traveltimes of simulated water partic

from the water table to the supply wells average

than 5 years for most wells, but ranged from 0.

to 51.2 years for the conditions simulated.

A conjunctive-management model of the 

stream-aquifer system was developed to simulta

neously address the water-demand and streamfl

depletion issues. The objective of the model wa

maximize total ground-water withdrawal from th

aquifer during July, August, and September. Th

three months are generally the time of year whe

water-supply demands are largest and streamflo

simultaneously lowest. Total withdrawal from th

aquifer was limited by a set of constraints speci

the model. These constraints were (1) maximum 

of streamflow depletion in the Hunt, Annaquatu

and Pettaquamscutt Rivers; (2) minimum month

water demands of each of the three water-suppl

systems that withdraw water from the aquifer; a

(3) minimum and maximum withdrawal rates a

supply well.

The conjunctive-management model was 

formulated mathematically as a linear program. 

model was solved by a response-matrix techniq

that incorporates the results of transient, numer

simulation of the HAP stream-aquifer system in

the constraint set of the linear program. The bas

the technique was the assumption that streamflo

depletion rates in each river were a linear functi

of ground-water-withdrawal rates at each well. 

assumption was shown to be valid for the condi

evaluated in this study, primarily because of the 

very high transmissivity of the aquifer near man

the wells. The transient model was used to gene
Summary and Conclus

characteristic streamflow-depletion responses in 

each river to simulated unit withdrawals at each 

well; these characteristic responses, or response coefficients, were then incorporated directly into the 

streamflow-depletion constraints of the linear program.

Four sets of applications of the conjunctivemanagement model were made to determine whether 

total ground-water withdrawal from the HAP aquifer 

during July, August, and September could be increased 

over the current total withdrawal for alternative 

definitions of the maximum rates of streamflow depletion allowed in the Hunt, Annaquatucket, and 

Pettaquamscutt Rivers. Current conditions were 

defined as the average monthly withdrawal rates at 

each supply well, water demands of each of the three 

water-supply systems, and estimated streamflowdepletion rates during the 6-year period 1993–98. Total 

withdrawal from all wells in the system from July 

through September during 1993–98 was 506.5 million 

gallons. Estimated streamflow-depletion rates for 

1993-98 were calculated by use of the transient model, 

with the 1993–98 average monthly withdrawal rates 

specified at each supply well. Streamflow-depletion 

rates calculated for July, August, and September 

averaged 25 percent of the model-calculated prewithdrawal streamflow rates for the Hunt River, 19 

percent for the Annaquatucket River, and 7 percent 

for the Pettaquamscutt River.

The first set of applications of the model 

were made with the current estimated rates of streamflow depletion in the Hunt, Annaquatucket, and 

Pettaquamscutt Rivers. Results of these applications 

indicated that total withdrawal from the HAP aquifer 

during July, August, and September could be increased 

from about 8 to 18 percent over the current total withdrawal. The increased yield would require modifications to the current annual withdrawal schedule of each 

supply well and, for the 18-percent increase, a modified 

network of supply wells that would include two new 

well sites in the Annaquatucket River Basin. A second 

set of model applications then was made to determine 

if current estimated rates of streamflow depletion in 

the Hunt River could be reduced without increasing 

current estimated rates of streamflow depletion in the 

Annaquatucket or Pettaquamscutt Rivers. Decreases in 

the current rates of streamflow depletion in the Hunt 

River would result in increased streamflow in the river 

during these three months. Results showed that 

rates of streamflow depletion in the Hunt River 

July, August, and September could be decreased 

to 15 percent, depending on whether the existin

modified well network was used.

Subsequent model applications indicated 

that substantial increases in total ground-water 

drawal from the HAP aquifer are possible, but w

require increased rates of streamflow depletion 

the Annaquatucket and Pettaquamscutt Rivers. 

mum increases in the July through September y

of the HAP aquifer of from 39 to 50 percent ov

the current total withdrawal were calculated wh

streamflow-depletion rates in the Annaquatucke

Pettaquamscutt Rivers were allowed to increase 

their current estimated rates to a maximum of 2

cent of the model-calculated pre-withdrawal str

flow for each river during July, August, and Sep

Alternatively, it was shown that current estimat

rates of streamflow depletion in the Hunt River 

July, August, and September could be reduced b

as much as 35 percent for the maximum allowe

increases in streamflow depletion in the Annaqu

and Pettaquamscutt Rivers; maximum increased 

withdrawal from the HAP aquifer, however, wo

range from only 8 to 18 percent over the curren

total withdrawal for the 35-percent reduction in 

streamflow-depletion rates in the Hunt River.

Results of the different applications of the 

demonstrate the usefulness of coupling numeric

simulation and optimization for regional-scale e

tion of water-resource management alternatives

results of the evaluation must be viewed, howev

within the limitations of the quality of data avai

for the Hunt–Annaquatucket–Pettaquamscutt st

aquifer system and representation of the system 

simulation model. An additional limitation of th

ysis was the use of an average annual cycle of m

withdrawal and hydrologic conditions. Ground-

withdrawal strategies may need to be modified 

streamflow-depletion constraints during extrem

hydrologic events, such as droughts.
64 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

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APPENDIX A:

Water Levels at Observation Wells, 1995–96

Appen

Table A1. Monthly water levels and altitudes at network observation wells in the Hunt–Annaquatucket–Pettaquamscut

aquifer system, Rhode Island, 1995–96

[USGS well identifiers and locations are shown on figure 5. All values are in feet. MP, measuring point; USGS, U.S. Geological Survey; WL, wate

USGS well 

identifier

Altitude of 

MP

November 21, 1995 January 17, 1996 February 14, 1996 March 13, 

WL below

 MP

WL 

altitude

WL below 

MP

WL 

altitude

WL below 

MP

WL 

altitude

WL below 

MPa

WCW-29 36.27 35.05 1.22 34.90 1.37 33.99 2.28 33.65 

WCW-270 44.07 22.35 21.72 24.29 19.78 23.24 20.83 23.18 

EGW-2 30.15 5.75 24.40 9.10 21.05 5.70 24.45 7.78 

EGW-77 49.23 6.02 43.21 5.79 43.44 5.35 43.88 5.52 

NKW-45 47.62 18.91 28.71 18.70 28.92 17.33 30.29 17.10 

NKW-255 45.64 8.95 36.69 9.66 35.98 8.13 37.51 7.76 

NKW-452 59.07 15.07 44.00 14.75 44.32 13.09 45.98 12.59 

NKW-591 61.44 8.96 52.48 8.70 52.74 7.40 54.04 7.32 

NKW-641 53.47 11.96 41.51 12.27 41.20 10.37 43.10 9.82 

NKW-1316 47.81 10.00 37.81 10.15 37.66 9.24 38.57 8.90 

NKW-1319 99.32 34.59 64.73 34.60 64.72 32.15 67.17 32.27 

NKW-1330 86.52 18.96 67.56 19.05 67.47 18.27 68.25 17.94 

NKW-1333 67.41 17.29 50.12 16.65 50.76 16.32 51.09 16.31 

NKW-1335 76.73 19.94 56.79 18.05 58.68 14.80 61.93 13.86 

 April 24, 1996 May 15, 1996 June 19, 1996 July 24, 1

WL below 

MP

WL

 altitude

WL below 

MP

WL 

altitude

WL below 

MP

WL 

altitude

WL below 

MPa

WCW-29 36.27 33.16 3.11 33.33 2.94 34.05 2.22 34.25 

WCW-270 44.07 22.71 21.36 23.17 20.90 24.20 19.87 24.36 

EGW-2 30.15 5.47 24.68 7.88 22.27 10.36 19.79 9.35 

EGW-77 49.23 5.06 44.17 6.08 43.15 6.07 43.16 5.81 

NKW-45 47.62 16.52 31.10 16.82 30.80 17.45 30.17 17.79 

NKW-255 45.64 7.26 38.38 7.56 38.08 8.66 36.98 8.83 

NKW-452 59.07 12.58 46.49 12.95 46.12 14.10 44.97 14.69 

NKW-591 61.44 7.15 54.29 8.00 53.44 9.68 51.76 9.30 

NKW-641 53.47 9.15 44.32 9.60 43.87 10.82 42.65 11.10 

NKW-1316 47.81 8.81 39.00 9.18 38.63 10.08 37.73 10.25 

NKW-1319 99.32 31.17 68.15 31.76 67.56 33.72 65.60 32.07 

NKW-1330 86.52 17.46 69.06 17.43 69.09 17.75 68.77 17.87 

NKW-1333 67.41 16.36 51.05 16.39 51.02 18.10 49.31 17.24 

NKW-1335 76.73 12.41 64.32 12.70 64.03 14.51 62.22 15.70 

August 21, 1996 September 25, 1996 October 8, 1996 November 20

WL below 

MP

WL 

altitude

WL below 

MP

WL 

altitude

WL below 

MP

WL 

atitude

WL below 

MPa

WCW-29 36.27 34.70 1.57 34.57 1.70 34.86 1.41 34.50 

WCW-270 44.07 24.75 19.32 24.38 19.69 24.49 19.58 24.03 

EGW-2 30.15 9.46 20.69 9.41 20.74 9.90 20.25 12.20 

EGW-77 49.23 6.42 42.81 6.74 42.49 6.07 43.16 5.96 

NKW-45 47.62 18.14 29.48 18.04 29.58 18.15 29.47 17.81 

NKW-255 45.64 9.41 36.23 8.64 37.00 9.33 36.31 9.02 

NKW-452 59.07 15.15 43.92 14.90 44.17 15.06 44.01 14.52 

NKW-591 61.44 10.20 51.24 9.05 52.39 9.32 52.12 8.68 

NKW-641 53.47 11.97 41.50 11.76 41.71 12.09 41.38 11.55 

NKW-1316 47.81 10.80 37.01 10.10 37.71 10.68 37.13 10.25 

NKW-1319 99.32 32.57 66.75 30.88 68.44 31.68 67.64 30.81 

NKW-1330 86.52 18.15 68.37 18.02 68.50 18.16 68.36 17.89 

NKW-1333 67.41 17.32 50.09 16.75 50.66 17.33 50.08 16.66 

NKW-1335 76.73 16.96 59.77 17.35 59.38 18.82 57.91 17.79 
erical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer System, RI

Day

Daily mean water level, in feet below land surface datum

1995 1996 1997

December January February March April May June July August September October November December January February March

1 -- 11.66 9.84 9.45 9.18 8.41 9.49 10.57 10.79 11.53 11.24 10.45 11.63 9.45 9.24 9.68

2 -- 11.68 9.83 9.45 9.15 8.43 9.54 10.59 10.67 11.55 11.27 10.46 11.47 9.45 9.30 9.68

3 -- 11.69 9.82 9.45 9.14 8.51 9.57 10.60 10.75 11.59 11.29 10.48 11.23 9.48 9.33 9.74

4 -- 11.72 9.82 9.49 9.17 8.57 9.60 10.54 10.82 11.62 11.32 10.52 11.22 9.54 9.37 9.78

5 -- 11.75 9.82 9.50 9.21 8.61 9.63 10.60 10.87 11.65 11.36 10.55 11.22 9.55 9.23 9.81

6 -- 11.77 9.83 9.48 9.26 8.66 9.67 10.67 10.92 11.68 11.39 10.59 11.21 9.58 9.06 9.80

7 -- 11.79 9.83 9.40 9.29 8.71 9.71 10.71 10.95 11.65 11.42 10.61 11.19 9.63 9.13 9.86

8 -- 11.79 9.81 9.32 9.32 8.73 9.74 10.75 10.99 10.90 11.40 10.63 10.59 9.66 9.17 9.90

9 -- 11.78 9.79 9.32 9.33 8.76 9.78 10.79 11.03 10.92 10.44 -- 10.21 9.69 9.18 9.94

10 -- 11.73 9.78 9.33 9.27 8.78 9.82 10.83 11.04 11.08 10.42 -- 10.20 9.69 9.21 9.96

11 -- 11.71 9.74 9.31 9.17 8.79 9.85 10.88 11.04 11.19 10.60 -- 10.22 9.74 9.24 9.98

12 -- 11.75 9.70 9.26 9.09 8.81 9.88 10.93 11.09 11.26 10.71 -- 10.23 9.79 9.27 10.01

13 -- 11.69 9.72 9.20 9.05 8.85 9.92 10.34 11.09 11.32 10.78 -- 10.22 9.83 9.33 10.05

14 11.37 11.53 9.72 9.21 9.02 8.90 9.96 8.97 10.94 11.36 10.82 -- 10.20 9.87 9.32 10.07

15 11.38 11.55 9.75 9.20 9.03 8.93 10.00 9.26 11.01 11.41 10.86 -- 10.19 9.92 9.10 9.91

16 11.40 11.60 9.78 9.19 8.75 8.96 10.04 9.58 11.08 11.46 10.89 -- 10.16 9.82 9.19 9.83

17 11.41 -- 9.78 9.18 8.24 8.97 10.09 9.80 11.14 11.46 10.92 -- 10.10 9.64 9.24 9.89

18 11.42 11.43 9.82 9.17 8.31 8.98 10.12 9.96 11.18 11.04 10.95 -- 9.88 9.74 9.28 --

19 11.43 11.32 9.89 9.16 -- 8.98 10.17 10.08 11.22 10.90 10.97 -- 9.79 9.81 9.29 --

20 11.43 10.46 9.93 9.01 8.38 9.00 10.20 10.16 11.26 10.96 10.41 -- 9.46 9.87 9.36 --

21 11.44 10.34 9.72 8.89 8.41 9.03 10.20 10.24 11.31 11.02 10.09 11.58 9.45 9.93 9.38 --

22 11.46 10.41 9.37 8.91 8.44 9.07 10.21 10.32 11.36 11.06 10.26 11.61 9.44 9.97 9.39 --

23 11.49 10.44 9.48 8.95 8.44 9.12 10.24 10.39 11.39 11.08 10.36 11.64 9.44 9.92 9.46 --

24 11.50 10.43 9.46 8.99 8.46 9.16 10.29 10.45 11.40 11.10 10.39 11.68 9.43 9.96 9.49 --

25 11.52 10.37 9.32 9.01 8.50 9.21 10.32 10.51 11.39 11.11 10.40 11.71 9.39 9.56 9.53 --

26 11.53 10.31 9.37 9.03 8.52 9.25 10.37 10.56 11.41 11.14 10.41 11.58 9.39 9.20 9.56 --

27 11.55 10.24 9.40 9.07 8.55 9.29 10.41 10.61 11.45 11.16 10.42 11.37 9.37 9.41 9.58 --

28 11.58 9.97 9.40 9.09 8.62 9.33 10.46 10.66 11.43 11.17 10.41 11.48 9.37 9.27 9.63 --

29 11.61 9.86 9.43 9.09 8.65 9.36 10.50 10.71 11.38 11.18 10.42 11.55 9.37 9.10 -- --

30 11.63 9.83 -- 9.12 8.49 9.40 10.54 10.76 11.44 11.21 10.42 11.60 9.39 9.18 -- --

31 11.65 9.82 -- 9.15 -- 9.44 -- 10.81 11.49 -- 10.43 -- 9.42 9.21 -- --

Mean -- 11.08 9.69 9.21 8.84 8.94 10.01 10.41 11.14 11.26 10.76 -- 10.13 9.63 9.32 --

Maximum -- 11.79 9.93 9.50 9.33 9.44 10.54 10.93 11.49 11.68 11.42 -- 11.63 9.97 9.63 --

Minimum -- 9.82 9.32 8.89 8.24 8.41 9.49 8.97 10.67 10.90 10.09 -- 9.37 9.10 9.06 --
Appen

Table A3. Daily mean water levels at recorder observation well NKW 1319 in the Hunt–Annaquatucket–Pettaquamscut

aquifer system, Rhode Island

[Well location shown on figure 5. Well depth below land surface datum: 41.70 feet. --, no data available]

Day

Daily mean water level, in feet below land surface datum, 1996

January February March April May June July August September O

1 -- 31.78 32.01 32.34 31.19 32.57 33.48 32.23 32.43 

2 -- 31.75 32.02 32.38 31.07 32.64 33.52 32.18 32.47 

3 -- 31.76 32.07 32.39 31.00 32.70 33.54 32.07 32.49 

4 -- 31.76 32.14 32.39 30.99 32.77 33.55 31.99 32.51 

5 -- 31.77 32.17 32.43 30.99 32.82 33.50 31.97 32.55 

6 -- 31.82 32.21 32.48 31.04 32.85 33.47 31.98 32.59 

7 -- 31.85 32.19 32.52 31.10 32.89 33.46 32.03 32.63 

8 -- 31.85 32.09 32.58 31.13 32.93 33.46 32.08 32.46 

9 -- 31.86 32.08 32.60 31.19 32.99 33.49 32.14 32.04 

10 -- 31.89 32.08 32.57 31.24 33.04 33.54 32.21 31.74 

11 -- 31.85 32.06 32.56 31.29 33.09 33.58 32.28 31.61 

12 -- 31.89 32.04 32.49 31.34 33.14 33.62 32.33 31.57 

13 -- 31.93 -- 32.40 31.42 33.18 33.61 32.38 31.56 

14 -- 31.95 -- 32.31 31.49 33.23 33.39 32.38 31.54 

15 -- 32.04 32.10 32.27 31.56 33.29 32.75 32.38 31.54 

16 -- 32.08 32.09 32.20 31.62 33.35 32.63 32.38 31.57 

17 -- 32.13 32.12 31.98 31.68 33.41 32.63 32.38 31.60 

18 -- 32.21 32.10 31.61 31.67 33.46 32.63 32.38 31.44 

19 -- 32.31 32.11 31.35 31.65 33.51 32.63 32.38 31.11 

20 -- 32.36 32.13 31.18 31.68 33.56 32.60 32.38 30.83 

21 -- 32.40 32.12 31.08 31.73 33.57 31.82 32.37 30.71 

22 -- 32.37 32.02 31.03 31.79 33.54 31.82 32.41 30.70 

23 -- 32.25 31.95 30.99 31.87 33.47 31.82 32.45 30.72 

24 -- 32.14 31.93 31.00 31.94 33.43 31.87 32.50 30.68 

25 -- 32.07 31.98 31.04 32.02 33.39 31.90 32.46 30.66 

26 -- 31.99 32.03 31.06 32.10 33.37 31.94 32.38 30.69 

27 -- 31.96 32.09 31.12 32.17 33.36 31.98 32.38 30.72 

28 -- 31.94 32.14 31.20 32.26 33.35 32.02 32.41 30.76 

29 -- 31.98 32.17 31.26 32.33 33.37 32.09 32.39 30.81 

30 31.91 -- 32.23 31.28 32.41 33.42 32.14 32.37 30.87 

31 31.81 -- 32.28 -- 32.49 -- 32.20 32.39 -- 

Mean -- 32.00 32.09 31.87 31.60 33.19 32.80 32.29 31.52 

Maximum -- 32.40 32.28 32.60 32.49 33.57 33.62 32.50 32.63 

Minimum -- 31.75 31.93 30.99 30.99 32.57 31.82 31.97 30.66 

APPENDIX B:

Streamflow at Partial-Record Sites, 1995–96

Appen

Table B1. Instantaneous streamflow at partial-record sites in the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer 

Rhode Island, 1995–96

[Site identifiers and locations are shown on figure 6. Streamflow measurements are in cubic feet per second. --, not measured]

Stream Site

identifier

Date of streamflow measurement

8/16/95 9/20/95 10/18/95 11/21/95 1/17/96 2/14/96 3/13/96 4/19/96 

Hunt River Basin

Scrabbletown Brook...... A 0.17 0.13 0.10 2.09 2.91 3.33 3.98 6.24 

Hunt River Tributary ..... B .36 .24 .27 2.63 3.84 4.06 4.77 7.15 

Hunt River..................... C -- 1.52 -- -- -- -- -- -- 

Hunt River..................... D -- 4.73 -- -- -- -- -- -- 

Frenchtown Brook......... E .73 1.24 1.76 11.60 14.90 16.20 19.00 31.40 

Frenchtown Brook......... F -- 1.75 -- -- -- -- -- -- 

Hunt River..................... G -- 7.57 -- -- -- -- -- -- 

Fry Brook ...................... H .05 .04 .19 5.32 13.80 6.00 9.07 16.50 

Hunt River..................... I -- 5.65 -- -- -- -- -- -- 

Hunt River..................... J -- 5.43 -- -- -- -- -- -- 

Hunt River..................... K -- 5.14 -- -- -- -- -- -- 

Sandhill Brook .............. L -- -- -- -- -- -- -- -- 

Sandhill Brook .............. M -- .08 -- -- -- -- -- -- 

Sandhill Brook .............. N -- .78 -- -- -- -- -- -- 

Sandhill Brook .............. O -- .71 -- -- -- -- -- -- 

Cocumcossuc Brook Basin

Cocumcossuc Brook ..... Q .11 .35 .60 3.55 5.24 3.82 4.88 6.98 

Annaquatucket River Basin

Annaquatucket River..... R -- -- -- -- -- -- -- -- 

Annaquatucket River..... S -- -- -- -- -- -- -- -- 

Annaquatucket River..... T 4.72 7.44 7.76 14.90 15.90 19.00 19.10 26.50 

Pettaquamscutt River Basin

Mattatuxet River............ U -- 1.36 -- -- -- -- -- -- 

Mattatuxet River............ V 2.65 2.68 2.08 3.74 19.70 14.30 18.10 15.20 
76 Numerical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer Syst

Table B1. Instantaneous streamflow at partial-record sites in the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer 

1995–96—Continued

Stream Site 

identifier

Date of streamflow measurement

5/15/96 6/19/96 7/24/96 8/21/96 9/7/96 9/25/96 10/8/96 1

Hunt River Basin

Scrabbletown Brook...... A 2.73 0.65 1.40 0.16 0.50 1.43 0.54 

Hunt River Tributary ..... B 3.38 1.48 1.28 .51 .69 1.41 .98 

Hunt River..................... C -- -- -- -- -- -- 3.07 

Hunt River..................... D -- -- -- -- 4.00 -- 4.81 

Frenchtown Brook......... E 13.50 3.36 6.74 1.84 1.80 5.77 2.78 

Frenchtown Brook......... F -- -- -- -- 2.06 -- 2.95 

Hunt River..................... G -- -- -- -- 5.79 -- 10.20 

Fry Brook ...................... H 5.57 1.02 1.63 .21 1.76 1.28 

Hunt River..................... I -- -- -- -- 9.20 -- 7.13 

Hunt River..................... J -- -- -- -- 6.90 -- 7.71 

Hunt River..................... K -- -- -- -- 8.74 -- 10.60 

Sandhill Brook .............. L -- -- -- -- .21 -- .18 

Sandhill Brook .............. M -- -- -- -- -- -- .90 

Sandhill Brook .............. N -- -- -- -- 1.33 -- 1.82 

Sandhill Brook .............. O -- -- -- -- 2.55 -- 2.15 

Cocumcossuc Brook Basin

Cocumcossuc Brook ..... Q 3.11 0.83 1.19 0.50 1.16 2.90 1.14 

Annaquatucket River Basin

Annaquatucket River..... R -- -- -- -- -- -- 1.95 

Annaquatucket River..... S -- -- -- -- 1.16 -- 1.36 

Annaquatucket River..... T 17.50 9.61 15.20 7.33 11.10 30.00 11.70 

Pettaquamscutt River Basin

Mattatuxet River............ U -- -- -- -- 15.70 -- 2.39 

Mattatuxet River............ V 12.20 5.51 4.12 3.73 11.80 8.42 4.00 
APPENDIX C:

Withdrawals from Public-Supply Wells, 1943–98

Appendix C 79

194398Continued

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)

Hunt River Basin

EDC 9A (began pumping in February 1943)

1943 -- 29.4 35.7 24.5 39.4 35.8 35.7 44.6 62.5 35.4 28.0 33.0 1.11

1944 32.5 30.6 58.8 36.8 39.5 40.1 40.9 38.4 34.3 36.1 38.0 36.9 1.27

1945 38.0 33.3 41.8 39.4 40.8 39.8 41.8 43.4 41.6 50.8 13.4 19.3 1.21

1946 37.9 29.1 32.0 21.9 24.4 26.3 25.6 31.9 28.1 36.5 23.0 21.0 .93

1947 25.1 20.8 25.3 13.6 16.7 18.9 23.6 22.4 22.7 20.0 13.6 15.3 .65

1948 14.5 12.2 12.3 12.1 18.6 20.6 23.6 29.9 33.8 32.2 25.1 30.9 .73

1949 25.1 6.5 21.2 18.1 23.6 29.4 23.2 18.2 22.6 35.6 33.3 34.3 .80

1950 35.4 29.1 35.2 28.5 2.7 9.6 9.8 11.2 4.8 2.8 2.9 2.1 .48

1951 2.4 1.5 3.6 4.9 6.5 9.7 21.5 16.8 9.6 9.6 7.1 6.6 .27

1952 6.9 8.1 7.1 8.4 8.5 17.7 29.8 17.4 14.3 10.0 7.5 9.9 .40

1953 10.1 9.4 7.7 11.1 13.5 29.4 24.7 24.5 22.9 17.3 44.0 47.9 .72

1954 48.3 43.4 16.7 14.0 11.6 21.3 20.8 18.8 12.7 19.5 11.1 17.9 .70

1955 10.9 7.0 9.3 8.8 13.3 19.0 24.9 20.9 33.2 42.8 15.5 16.9 .61

1956 17.0 15.5 11.7 14.2 18.5 22.1 27.8 32.9 25.4 19.7 14.1 23.2 .66

1957 21.5 21.9 36.3 44.7 43.4 41.0 31.9 32.8 25.8 24.8 18.8 23.9 1.00

1958 21.0 22.7 21.6 21.3 26.0 25.9 33.9 26.7 27.3 16.5 9.8 11.8 .72

1959 14.4 17.1 12.4 18.3 27.5 30.4 33.1 22.0 23.6 26.8 27.0 27.2 .77

1960 24.8 27.3 26.5 20.2 27.9 26.3 19.2 20.7 20.5 19.7 23.3 23.4 .77

1961 20.2 27 27.3 21.8 16.5 25.7 37.0 30.4 31.3 30.3 25.8 22.6 .87

1970 24.8 23.8 32.6 31.5 26.4 21.0 26.4 24.8 24.0 24.8 25.5 34.1 .88

1971 29.5 25.2 37.2 25.5 29.5 33.0 34.1 24.8 21.0 12.4 12.4 15.5 .82

1972 24.8 25.2 32.6 22.5 15.5 9.0 18.6 21.0 9.0 12.4 9.0 10.9 .58

1973 12.4 9.8 14.0 16.5 14.0 12.0 10.9 0 0 0 0 0 .25

1974 0 0 0 0 0 0 1.6 3.1 6.2 4.7 4.5 6.2 .07

1975 7.8 15.4 20.2 21.0 17.1 12.0 15.5 0 0 0 0 0 .30

1993 0 0 0 0 0 0 5.8 6.0 6.3 5.3 5.3 5.7 .09

1994 0 0 0 0 0 0 .1 12.5 23.9 6.2 0 0 .12

1995 0 4.6 5.8 3.2 5.2 7.0 3.8 7.3 7.0 7.5 2.8 7.4 .17

1996 3.2 5.8 4.5 6.4 6.0 5.7 5.7 4.2 5.2 5.0 4.5 4.9 .17

1997 5.2 12.9 4.4 5.2 2.1 0 0 4.5 8.3 6.5 6.2 5.3 .17

1998 4.9 4.5 4.9 6.2 5.7 6.6 19.4 19.3 8.3 7.9 5.2 5.8 .27

[Withdrawals are in million gallons. Record incomplete for years not shown. EDC, Rhode Island Economic Development Corporation; KCWA, Kent County Water Authority; NK, North Kingstown; 

Mgal/d, million gallons per day; --, before pumping began]
erical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer System, RI

Hunt River Basin—Continued

EDC 14A (began pumping in February 1943)

1943 -- 7.2 17.5 20.5 24.0 26.1 32.8 45.4 73.0 40.1 37.1 37.9 0.99

1944 64.6 38.5 68.9 37.6 40.1 39.9 40.5 59.0 36.0 37.5 38.8 43.7 1.49

1945 44.2 36.9 46.2 43.8 45.5 44.5 63.5 46.7 45.2 58.6 44.4 28.2 1.50

1946 6.9 9.7 13.2 9.2 6.3 7.1 24.7 7.1 12.2 5.9 4.0 4.1 .30

1947 3.4 2.9 3.9 10.4 11.4 12.2 18.5 22.1 19.4 16.9 15.9 17.7 .42

1948 13.7 14.9 15.6 15.5 20.5 26.2 34.8 39.7 25.0 18.6 20.7 30.1 .75

1949 28.5 41.4 33.5 32.2 21.9 37.9 44.1 48.0 29.4 9.7 9.4 10.0 .95

1950 8.5 12.9 7.2 13.9 38.5 37.4 46.2 47.8 44.5 40.1 40.6 40.8 1.04

1951 41.5 37.3 41.6 40.9 44.4 45.9 47.7 48.8 43.8 44.7 39.6 44.3 1.43

1952 45.0 40.0 47.0 40.9 44.0 45.2 46.6 43.6 42.0 44.0 41.8 45.4 1.44

1953 46.2 41.3 43.5 44.9 48.1 47.2 48.7 49.2 47.1 45.3 15.3 14.7 1.35

1954 16.0 15.2 45.1 42.9 45.2 40.1 46.2 43.5 40.8 37.6 44.6 49.4 1.28

1955 46.2 41.7 42.5 42.2 44.7 44.5 48.6 51.1 24.0 14.7 40.7 45.2 1.33

1956 48.1 48.7 52.9 50.0 49.2 50.9 52.8 52.6 49.2 50.0 49.2 43.0 1.63

1957 52.1 44.8 31.7 25.7 40.4 42.1 50.2 49.8 48.1 47.0 47.4 49.8 1.45

1958 50.1 46.3 49.5 47.2 38.5 34.9 26.7 34.7 38.0 50.2 44.7 49.4 1.40

1959 50.2 45.2 47.4 41.7 34.6 32.4 39.9 45.5 40.1 37.3 33.0 30.0 1.31

1960 32.3 26.1 23.9 26.6 30.8 30.1 42.5 50.2 40.0 34.6 27.3 38.1 1.10

1961 47.9 31.5 41.8 35.0 46.9 43.4 38.7 48.6 42.5 41.9 44.4 43.5 1.39

1970 18.6 15.4 14.0 24.0 15.5 28.5 34.1 38.8 33.0 24.8 12.0 6.2 .73

1971 21.7 19.6 31.0 21.0 20.2 27.0 38.8 38.8 37.5 37.2 40.5 38.8 1.02

1972 37.2 30.8 37.2 25.5 34.1 37.5 37.2 34.5 37.5 23.3 25.5 21.7 1.05

1973 21.7 18.2 24.8 24.0 24.8 25.5 26.4 0 0 0 0 0 .45

1974 0 0 0 0 0 0 3.1 6.2 19.5 23.3 22.5 20.2 .26

1975 18.6 16.8 7.8 1.5 6.2 4.5 6.2 0 0 0 0 0 .17

1993 0 0 0 0 0 0 10.0 12.1 9.7 5.8 8.8 4.5 .14

1994 0 0 0 0 0 0 .1 11.3 1.8 9.0 14.0 11.2 .13

1995 11.9 12.1 10.0 5.8 11.2 10.9 18.9 16.3 12.0 12.0 9.2 6.6 .38

1996 11.5 10.2 9.8 10.1 9.6 11.5 12.4 17.2 10.8 12.0 11.3 9.4 .37

1997 8.9 23.0 9.5 8.0 11.1 14.0 15.6 12.2 12.7 6.9 9.6 10.5 .39

1998 9.4 8.5 10.4 12.0 13.9 16.4 16.3 13.1 12.7 13.6 14.2 11.3 .42

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)
Appendix C 81

Hunt River Basin—Continued

EDC 3A (began pumping in July 1993)

1993 -- -- -- -- -- -- 9.3 9.0 7.5 7.9 5.9 1.6 0.11

1994 19.6 17.8 18.5 16.6 19.1 23.0 24.8 6.0 .1 5.4 6.3 9.1 .46

1995 10.8 4.7 5.8 9.4 6.3 7.3 6.1 4.6 3.5 .6 6.5 6.0 .20

1996 8.0 5.2 5.5 5.0 5.7 6.1 7.4 7.3 8.7 7.0 6.5 7.1 .22

1997 8.5 9.8 6.5 6.5 6.6 11.8 16.3 11.1 6.4 10.0 6.2 6.8 .29

1998 6.3 5.8 7.0 5.8 5.7 4.4 1.2 .2 6.9 3.0 4.2 5.6 .15

KCWA 1 (began pumping in February 1965)

1965 -- -- -- 10.3 33.1 34.9 46.0 37.7 9.9 3.2 .2 16.3 .52

1966 16.1 13.5 11.8 15.3 22.4 37.8 44.2 44.3 22.4 16.4 19.1 17.4 .77

1967 19.9 16.3 9.1 25.3 11.1 41.4 39.3 33.3 38.6 25.5 11.7 22.4 .81

1968 18.3 15.4 14.3 18.1 35.6 42.8 44.9 46.9 58.7 33.8 21.3 25.5 1.03

1969 22.4 24.7 32.2 29.8 36.1 55.2 44.1 53.3 38.4 23.7 18.5 0 1.04

1970 0 0 0 20.1 25.5 25.0 54.9 54.1 48.3 35.1 18.0 37.7 .87

1971 35.4 31.6 30.9 37.4 36.8 62.1 58.2 49.8 58.4 38.7 30.3 39.6 1.40

1972 31.8 27.3 36.2 33.2 43.6 43.9 44.2 47.4 12.9 8.2 44.7 42.0 1.14

1973 49.7 54.5 55.0 44.6 57.0 58.9 56.2 67.1 47.4 43.6 34.9 34.2 1.65

1974 40.8 33.1 35.8 45.7 52.1 53.1 60.2 59.5 42.0 38.2 30.6 31.9 1.43

1975 32.0 30.2 31.1 31.6 43.5 43.2 49.5 68.7 36.3 33.8 29.0 28.2 1.25

1976 27.4 23.9 29.8 37.1 40.0 46.5 50.3 51.2 46.8 38.0 25.0 18.8 1.19

1977 14.1 11.7 12.8 17.2 43.1 33.7 23.7 20.2 15.9 12.7 12.3 40.0 .71

1978 44.6 38.7 46.1 42.9 41.0 32.0 27.8 38.7 35.5 29.6 20.9 18.7 1.14

1979 25.4 30.7 31.0 32.7 32.7 32.5 30.1 26.3 29.3 29.8 21.8 11.1 .91

1980 3.8 28.4 19.6 19.1 29.8 28.2 29.2 32.4 30.7 27.2 18.6 14.6 .77

1981 13.6 11.6 14.4 20.7 28.8 38.6 35.2 35.0 32.1 25.4 19.3 20.3 .81

1982 17.6 18.7 25.3 26.3 39.1 29.9 34.0 38.2 37.3 39.0 37.0 38.2 1.04

1983 35.5 31.6 33.4 36.3 24.7 7.4 18.7 13.0 13.4 24.4 18.3 20.9 .76

1984 21.2 15.2 25.6 23.9 28.4 27.7 30.4 30.7 26.1 19.0 13.3 14.3 .75

1985 8.6 23.3 29.4 26.9 31.1 31.0 33.0 30.0 28.4 14.3 0 0 .70

1986 2.2 17.5 18.6 19.7 24.1 26.4 28.1 21.7 17.8 16.3 16.5 12.9 .61

1987 13.4 9.9 13.2 10.6 12.2 23.7 34.3 24.3 11.4 13.4 11.9 13.7 .53

1988 11.0 10.2 9.9 10.0 14.3 26.0 24.3 28.0 6.8 0 7.9 6.3 .42

1989 7.7 7.6 7.0 4.9 10.9 10.2 14.7 12.7 7.6 .19 .18 .34 .23

1990 .32 .55 .27 .73 .73 13.4 11.2 9.6 5.6 .23 0 0 .12

1991 .26 0 .16 0 9.6 23.7 18.8 9.3 2.8 .2 0 0 .18

1992 0 .08 0 0 4.1 8.4 8.1 2.3 0 0 0 0 .06

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)
erical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer System, RI

Hunt River Basin—Continued

KCWA 1—Continued

1993 0 0 0 0 10.8 26.0 20.9 19.6 3.1 0.5 0 0 0.22

1994 0 0 0 0 .7 22.7 18.5 2.8 .6 0 0 .3 .12

1995 .3 0 0 0 0 3.4 34.1 42.2 17.2 0 0 0 .27

1996 1.8 2.8 1.4 1.0 1.6 12.5 1.1 3.2 0 0 26.0 67.5 .32

1997 46.6 .5 .4 .3 4.8 28.4 43.9 27.8 23.6 14.7 1.9 .6 .53

1998 1.2 9.8 13.3 27.7 41.0 51.2 56.4 52.9 50.9 36.9 30.2 31.3 1.10

NK 9 (began pumping in August 1944)

1944 -- -- -- -- -- -- -- 57.8 51.6 29.8 18.7 40.5 .54

1945 46.5 29.7 26.7 18.7 22.8 28.7 32.3 35.7 33.6 30.4 5.7 15.1 .89

1946 34.8 35.4 30.0 36.0 36.6 18.7 12.3 14.9 13.0 13.3 25.2 30.1 .82

1947 29.2 25.3 26.9 26.5 25.6 22.4 28.1 37.5 30.7 28.0 29.0 26.9 .92

1948 29.9 32.4 28.5 24.7 27.8 22.6 30.9 34.1 20.1 18.4 15.1 19.5 .83

1949 18.4 18.8 18.3 16.1 17.0 23.1 19.8 14.8 12.5 16.6 15.5 16.5 .57

1950 17.5 15.2 16.7 14.5 15.8 17.9 21.3 19.8 16.5 18.4 17.8 18.6 .58

1951 19.4 17.7 19.9 18.6 19.3 19.0 18.2 19.9 16.7 22.0 23.7 22.6 .60

1952 21.3 16.6 17.6 17.9 19.1 20.1 23.1 19.5 17.3 19.5 18.8 18.5 .63

1953 19.3 16.9 18.1 17.9 18.6 23.6 20.3 16.5 16.7 17.5 17.6 16.7 .60

1954 16.9 15.2 16.4 16.0 17.0 20.6 20.9 16.3 14.8 14.1 14.4 15.1 .54

1955 15.9 15.0 14.9 15.5 15.2 16.6 21.6 17.6 15.4 16.9 15.7 17.7 .54

1956 17.4 21.3 25.7 16.5 18.7 21.7 23.4 24.7 15.5 16.8 22.0 19.7 .67

1957 18.6 16.6 17.4 18.6 18.5 26.5 17.7 9.2 6.1 16.2 16.1 16.6 .54

1958 15.4 17.0 19.1 19.0 19.6 15.3 21.6 15.7 16.9 16.8 16.2 18.1 .58

1959 20.1 16.9 9.8 12.1 17.9 17.1 15.5 24.6 14.5 20.7 14.4 16.5 .55

1960 19.4 15.8 18.8 15.4 21.7 23.3 22.7 29.2 23.9 18.6 20.0 22.7 .69

1961 23.0 22.3 20.1 20.6 21.3 24.5 23.9 22.2 16.1 17.0 19.8 20.5 .69

1962 21.0 18.5 15.3 14.0 17.4 19.4 21.0 24.3 15.2 21.3 17.1 22.3 .62

1963 21.6 20.5 23.6 21.2 17.9 24.2 28.4 24.5 22.1 37.7 12.0 20.7 .75

1964 20.6 21.5 16.3 18.1 26.5 31.3 28.0 25.1 25.1 17.1 19.4 21.8 .74

1965 22.9 19.5 23.1 9.0 13.2 13.2 15.5 25.3 30.4 25.1 25.5 16.2 .65

1966 20.3 19.5 18.9 17.1 17.9 15.6 29.0 11.0 19.0 16.2 16.9 18.0 .60

1967 18.1 13.0 16.1 16.4 29.1 12.1 14.2 12.5 14.6 23.5 24.7 19.6 .59

1968 18.3 22.2 23.4 18.6 17.8 16.8 17.4 11.7 10.0 16.2 21.6 21.3 .59

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)
Appendix C 83

Hunt River Basin—Continued

NK 9—Continued

1969 20.4 17.7 20.2 18.1 21.1 28.2 23.3 14.2 18.3 18.8 24.7 39.0 0.72

1970 38.8 33.0 36.4 19.6 28.0 37.1 20.1 18.0 0 11.8 16.7 6.4 .73

1971 4.7 8.4 9.7 7.9 10.2 34.1 31.4 19.3 6.9 6.2 8.8 8.6 .43

1972 5.9 10.5 8.2 3.2 1.3 0 0 0 0 0 0 0 .08

1973 0 0 0 0 0 .4 0 0 0 0 0 3.0 .01

1974 .2 0 0 0 .3 1.8 1.5 9.7 0 0 1.0 1.0 .04

1975 0 0 0 0 .7 1.8 4.0 12.0 2.4 0 1.2 .2 .06

1976 .1 0 0 .7 0 11.6 6.1 0 0 .5 0 0 .05

1977 0 0 0 .3 4.2 2.8 17.0 .9 0 0 0 0 .07

1978 0 0 0 2.6 .8 11.7 14.3 .1 0 0 0 1.4 .08

1979 0 0 0 0 0 6.6 14.8 1.8 .2 0 0 17.0 .11

1980 30.7 1.0 0 19.1 6.4 18.1 28.7 22.1 26.9 2.9 0 0 .43

1981 0 2.3 1.9 1.1 2.8 7.1 12.7 0 0 0 0 0 .08

1982 0 0 0 0 0 0 16.2 0 0 0 0 0 .04

1990 0 0 0 0 0 .3 1.0 1.5 0 0 0 0 .01

1991 0 0 0 0 0 0 2.9 .7 13.6 22.3 5.2 0 .12

1992 0 0 0 .6 0 0 0 0 0 0 0 0 .00

1993 0 0 0 0 4.1 36.6 47.3 51.4 42.6 36.3 31.2 23.1 .75

1994 0 0 0 0 0 33.6 44.8 38.1 38.7 38.9 34.7 31.6 .71

1995 31.0 32.1 30.4 0 12.2 36.8 41.8 42.9 33.5 6.0 3.9 0 .74

1996 20.0 26.5 28.0 23.8 34.4 44.2 49.8 58.7 44.0 34.6 33.0 34.2 1.18

1997 33.7 27.0 32.0 33.8 38.9 49.1 47.8 39.7 32.5 28.8 26.9 23.3 1.13

1998 23.5 21.3 31.0 27.6 12.1 0 27.6 43.5 37.2 35.7 29.5 17.6 .84

NK 10 (began pumping in June 1944)

1944 -- -- -- -- -- 18.4 42.8 32.2 17.1 30.6 35.7 10.1 .51

1945 15.3 26.1 28.3 37.6 32.1 35.6 43.2 37.5 21.4 10.5 33.4 24.9 .95

1946 6.0 1.8 11.4 4.6 5.4 25.8 35.5 22.1 20.8 20.1 19.4 18.3 .52

1947 19.7 18.3 19.7 18.8 15.8 19.4 14.9 5.9 11.1 16.0 10.1 15.1 .51

1948 10.5 7.8 14.1 17.0 5.7 6.6 2.9 .5 13.9 13.4 14.1 8.2 .31

1949 8.8 7.2 10.6 12.7 15.7 26.6 28.5 24.1 18.5 18.3 18.7 16.4 .56

1950 13.7 13.8 18.4 19.4 21.4 22.9 21.6 16.8 16.5 15.6 12.9 9.9 .56

1951 7.7 7.7 8.5 10.1 16.8 18.2 30.3 23.4 24.8 20.3 25.2 23.2 .59

1952 14.2 12.1 13.6 13.6 15.3 19.4 38.5 20.1 19.0 15.4 14.0 15.0 .58

1953 14.7 14.3 14.6 14.7 19.1 38.8 34.6 29.3 28.5 22.7 18.6 17.7 .73

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)
erical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer System, RI

Hunt River Basin—Continued

NK 10—Continued

1954 17.0 15.8 18.0 17.8 19.0 27.9 29.4 24.1 24.3 25.2 19.2 19.5 0.70

1955 20.1 17.4 18.8 16.8 29.0 25.3 33.5 33.6 25.0 22.2 20.4 21.3 .78

1956 20.6 8.8 4.5 13.5 16.9 29.2 20.1 18.9 19.8 14.3 22.7 20.4 .57

1957 12.3 9.6 9.7 12.0 27.3 34.9 37.2 29.4 26.8 15.3 11.1 15.8 .66

1958 11.0 6.4 8.4 8.5 12.2 19.5 16.9 21.7 17.4 16.7 14.3 13.7 .46

1959 11.7 11.4 24.1 21.0 21.7 19.7 24.8 21.7 24.4 21.3 17.4 15.4 .64

1960 13.6 16.5 15.9 21.2 19.6 25.3 27.1 21.6 17.8 17.1 13.6 13.6 .61

1961 13.4 12.8 16.2 13.4 14.2 20.1 27.9 25.8 24.2 18.8 14.1 13.3 .59

1962 14.8 13.4 20.9 23.4 27.3 28.6 35.4 30.9 25.1 15.3 16.9 13.7 .73

1963 15.7 14.1 14.9 20.3 27.7 29.7 38.6 32.5 21.9 6.2 24.6 17.5 .72

1964 16.9 12.7 20.7 19.2 37.5 43.6 33.4 29.1 27.6 27.7 23.8 19.2 .85

1965 18.7 18.1 17.2 19.5 8.5 18.3 22.0 14.0 14.3 17.4 17.5 7.4 .53

1966 6.6 5.9 7.3 8.7 8.5 9.1 21.9 14.3 3.3 3.7 4.1 9.3 .28

1967 6.9 12.3 5.5 6.1 6.3 10.9 3.4 3.3 5.9 4.1 6.4 7.6 .22

1968 22.6 4.9 4.9 1.0 2.0 3.1 14.2 10.3 10.5 .7 3.1 4.7 .22

1969 3.9 2.5 1.1 0 0 0 11.4 2.6 8.4 6.7 3.8 0 .11

1970 0 0 0 .6 1.8 5.1 8.0 0 0 0 0 0 .04

1971 0 0 0 .1 0 10.5 10.7 3.0 1.5 .9 .8 1.4 .08

1972 .7 1.2 .7 0 .4 .3 9.0 9.6 30.0 33.4 0 0 .23

1973 .9 0 0 .9 .9 16.6 8.1 21.5 3.7 0 0 0 .14

1974 0 .4 .8 0 .3 18.1 28.6 37.8 .2 .4 0 0 .24

1975 0 0 0 0 5.2 11.9 29.8 10.4 0 .1 0 0 .16

1976 0 0 0 1.0 2.7 35.4 30.9 12.9 1.8 .3 0 .5 .23

1977 0 0 0 1.8 24.1 24.4 40.2 21.2 8.6 1.0 0 0 .33

1978 .4 .04 0 0 5.9 22.2 38.3 11.4 .2 0 0 0 .21

1979 0 3.6 .2 .8 5.2 20.4 38.1 9.9 3.6 .6 0 0 .23

1980 .4 1.1 0 5.5 2.0 10.4 30.7 2.6 3.6 0 0 0 .15

1981 0 0 1.1 0 12.9 29.2 29.7 18.0 6.3 .3 0 0 .27

1982 0 0 0 0 12.4 2.5 30.3 8.7 4.8 0 0 0 .16

1990 25.9 25.7 28.9 29.0 34.4 41.9 34.6 40.4 29.2 21.8 30.7 35.1 1.03

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)
Appendix C 85

Hunt River Basin—Continued

NK 10—Continued

1991 34.8 32.1 36.7 39.0 45.7 62.1 65.5 49.9 22.6 0 26.7 37.1 1.24

1992 35.1 34.1 37.8 34.7 43.6 45.8 48.4 20.0 0 0 0 0 .82

1993 0 0 0 0 0 0 0 0 0 0 0 0 .00

1994 0 0 0 0 0 0 0 0 0 0 0 0 .00

1995 0 0 0 0 0 0 0 0 0 0 0 0 .00

1996 0 0 0 0 0 0 0 0 0 0 0 0 .00

1997 0 0 0 0 0 0 0 0 0 0 0 0 .00

1998 0 0 0 0 0 0 0 0 0 0 0 0 .00

NK 6 (began pumping in March 1978)

1990 19.2 16.8 15.5 19.3 20.3 19.1 19.4 18.2 17.2 17.3 4.5 0 .51

1991 0 2.7 5.9 2.1 8.5 10.5 13.1 5.4 6.1 11.1 5.1 3.1 .20

1992 1.1 1.6 1.5 .3 4.1 10.4 7.2 16.0 20.3 18.5 15.4 16.4 .31

1993 17.9 15.5 18.3 18.1 24.5 18.3 14.9 8.9 5.0 .1 0 3.5 .40

1994 16.9 15.2 17.0 15.7 18.7 20.8 18.5 8.8 7.2 1.7 .4 2.0 .39

1995 2.7 .02 1.8 15.4 11.1 8.1 17.4 17.9 11.1 16.0 13.8 16.8 .36

1996 10.1 5.9 4.6 6.7 9.5 10.8 11.7 10.2 4.9 6.4 4.0 6.1 .25

1997 6.9 8.4 7.9 7.5 .3 0 18.6 11.7 13.6 14.2 9.0 1.2 .27

1998 3.0 8.2 6.9 9.1 16.6 19.8 20.5 14.9 9.9 5.0 6.6 3.7 .34

Annaquatucket River Basin

NK 1 (began pumping in December 1944)

1945 6.5 6.0 6.8 6.5 5.9 7.4 8.5 8.9 7.8 5.8 5.6 6.5 .23

1946 7.8 7.7 7.2 7.2 7.1 7.0 8.4 7.0 6.6 6.5 6.1 6.3 .23

1947 6.3 5.7 6.5 6.4 7.1 7.5 8.7 9.0 7.8 7.7 7.2 7.2 .24

1948 7.1 6.6 7.2 6.9 7.3 7.5 9.7 10.6 9.0 7.9 7.2 7.5 .26

1949 7.6 7.1 8.1 8.2 8.2 12.2 13.1 11.8 9.1 9.1 8.1 7.8 .30

1950 8.2 7.3 8.2 7.9 8.4 9.5 11.5 10.1 9.0 8.4 7.7 8.1 .29

1951 8.1 7.4 8.4 8.0 8.6 9.0 11.7 10.1 7.9 7.7 0 4.7 .25

1952 8.7 8.1 8.7 8.7 9.4 11.7 17.0 11.2 10.3 10.6 10.8 11.5 .35

1953 10.5 9.1 10.6 10.2 11.4 17.5 16.8 15.7 15.5 12.7 10.9 11.4 .42

1954 11.6 10.6 12.2 11.9 12.9 16.0 18.4 14.9 12.3 11.5 11.5 12.0 .43

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)
erical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer System, RI

Annaquatucket River Basin—Continued

NK 1—Continued

1955 12.2 11.1 12.7 12.7 10.4 16.7 22.4 19.9 15.1 14.2 13.2 13.9 0.48

1956 13.6 13.0 14.3 14.4 16.4 21.9 20.9 21.3 17.2 15.2 0 3.4 .47

1957 15.7 14.1 15.9 16.6 21.7 27.6 27.5 21.2 18.2 18.8 14.9 15.8 .62

1958 15.8 14.9 15.8 16.1 16.6 18.4 21.5 20.8 17.7 17.4 16.2 17.3 .57

1959 12.6 16.2 4.4 4.3 5.4 7.5 6.9 5.6 7.3 7.8 8.1 8.8 .26

1960 8.2 7.8 7.7 6.8 8.3 9.1 9.5 10.4 19.4 9.6 7.5 5.9 .30

1961 21.7 20.8 22.3 21.8 25.3 25.8 38.3 32.5 24.8 24.5 22.4 22.0 .83

1962 24.1 21.3 22.7 23.1 28.7 33.7 39.8 35.5 25.9 23.4 20.1 21.2 .88

1963 21.9 19.8 23.3 25.3 28.3 35.2 27.5 27.7 28.7 25.6 22.2 24.7 .85

1990 4.2 1.5 5.4 0 .1 15.2 20.0 13.5 15.1 11.4 12.7 14.6 .31

1991 13.7 9.2 8.3 12.9 15.5 18.1 16.1 16.1 14.2 12.3 9.6 9.1 .42

1992 8.9 7.8 7.7 11.2 15.1 15.2 17.0 19.3 17.1 16.1 13.6 14.9 .45

1993 16.6 14.5 15.6 16.1 23.9 23.5 21.1 22.6 16.1 17.8 11.6 12.6 .58

1994 16.8 15.5 17.2 15.5 18.9 21.1 20.9 8.6 .3 4.4 7.4 9.7 .43

1995 9.9 8.9 10.0 16.6 15.3 15.3 19.3 18.9 13.6 14.7 0 20.5 .45

1996 .03 0 4.8 7.6 5.0 14.2 11.7 9.1 5.8 3.3 3.8 1.3 .18

1997 0 0 0 0 1.2 15.7 17.1 6.1 5.3 0 5.0 11.5 .17

1998 8.2 7.0 3.5 5.5 15.8 16.6 17.5 13.0 6.3 0 0 2.9 .26

NK 2 (began pumping in August 1956)

1959 4.6 8.9 12.6 12.5 16.3 13.1 16.2 18.9 13.9 11.1 9.4 9.2 .40

1960 10.1 9.8 10.9 12.7 14.0 18.1 21.2 20.7 14.9 12.0 12.1 14.4 .47

1990 0 0 0 .5 0 2.9 7.2 2.6 4.4 1.4 0 0 .05

1991 0 .02 .1 0 .9 8.7 7.1 2.5 .5 .1 0 0 .05

1992 .3 0 .03 .3 1.9 2.6 1.0 7.7 12.8 13.5 10.0 11.5 .17

1993 7.7 6.5 7.7 7.6 10.9 9.7 10.9 8.5 2.9 .2 .07 3.1 .21

1994 8.8 7.4 8.1 11.3 14.0 14.2 13.0 5.4 4.6 3.0 .3 .3 .25

1995 0 0 .7 9.0 11.1 2.0 13.8 11.4 5.3 10.5 18.4 0 .23

1996 9.1 5.4 3.7 4.9 4.2 4.1 2.9 1.9 4.0 4.3 2.9 2.7 .14

1997 3.6 4.2 3.9 3.7 9.7 17.7 16.8 8.4 8.5 9.1 2.6 7.4 .26

1998 7.5 .4 0 0 9.8 12.8 14.0 9.3 6.7 4.8 4.0 .09 .19

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)
Appendix C 87

Annaquatucket River Basin—Continued

NK 4 (began pumping in May 1967)

1990 7.6 6.5 7.8 6.4 2.8 11.1 13.8 14.4 11.4 9.2 8.3 5.2 0.29

1991 3.3 2.5 2.8 3.4 7.8 17.9 16.1 11.2 9.0 6.7 9.2 9.0 .27

1992 12.0 11.9 9.9 10.1 12.1 16.2 15.1 11.2 10.0 10.5 10.2 9.9 .38

1993 9.7 8.6 9.0 9.0 15.1 18.4 19.3 19.2 14.8 11.4 9.7 8.7 .42

1994 10.3 8.7 9.8 9.2 11.6 17.8 19.3 12.9 12.4 11.0 8.8 8.9 .39

1995 8.9 7.8 8.7 9.7 11.5 15.4 22.4 20.1 14.8 12.0 11.2 17.0 .44

1996 0 0 0 9.9 10.3 13.1 6.5 3.2 5.1 7.2 4.6 4.1 .18

1997 9.2 11.2 10.2 4.9 8.8 15.1 22.2 14.3 9.0 10.3 3.4 1.9 .33

1998 15.9 10.9 7.9 11.9 11.7 10.9 16.0 14.9 11.3 9.8 7.6 5.4 .37

NK 5 (well drilled in January 1969)

1990 6.3 5.5 5.8 7.2 11.0 14.8 9.6 8.7 6.6 3.9 4.3 8.6 .25

1991 10.9 10.0 11.2 10.4 12.9 14.4 16.9 13.0 12.1 9.9 9.2 10.7 .39

1992 8.4 7.5 10.6 8.8 15.7 16.5 14.0 12.1 11.0 12.0 10.0 10.2 .37

1993 9.8 8.7 9.9 9.9 14.4 19.5 19.0 17.5 7.6 9.0 8.3 9.5 .39

1994 11.3 9.9 11.3 10.0 12.2 19.4 19.2 12.4 12.9 11.2 9.5 9.8 .41

1995 9.7 8.4 9.6 10.5 13.1 15.9 23.4 21.6 15.2 10.6 8.7 2.9 .41

1996 15.9 13.3 16.6 9.8 16.1 21.8 24.7 23.8 12.4 8.0 9.3 9.1 .50

1997 3.8 .5 3.6 9.7 10.9 22.5 31.7 12.0 11.5 14.4 15.6 22.8 .44

1998 4.6 4.6 7.8 3.4 14.7 15.1 21.6 17.0 12.6 10.4 10.2 3.9 .34

Pettaquamscutt River Basin

NK 3 (began pumping in September 1961)

1961 -- -- -- -- -- -- -- -- 3.4 .4 .3 .3 .01

1962 0 .2 .3 .4 .8 1.4 1.9 3.9 1.1 1.7 1.1 .4 .04

1963 1.3 1.1 1.1 1.3 1.4 2.7 22.4 12.0 2.4 1.1 1.4 1.3 .14

1990 0 0 0 0 0 3.0 11.2 8.5 0 0 0 0 .06

1991 0 0 0 0 0 1.0 2.6 0.1 0 0 0 0 .01

1992 0 0 0 0 .5 1.2 .4 0 0 0 0 0 .01

1993 0 0 0 0 0 4.0 5.8 4.0 5.8 5.6 3.4 1.4 .08

1994 .3 .8 2.2 2.2 2.1 7.5 11.0 4.7 0 0 0 0 .08

1995 0 0 0 0 0 0 6.6 7.4 7.9 9.3 9.0 8.7 .13

1996 7.8 6.8 5.1 1.5 1.6 3.7 5.3 9.0 7.0 6.4 5.5 5.6 .18

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)
erical-Simulation and Conjunctive-Management Models, Hunt-Annaquatucket-Pettaquamscutt Stream-Aquifer System, RI

Pettaquamscutt River Basin—Continued

NK 3—Continued

1997 5.5 3.9 4.6 3.9 5.4 5.5 7.4 6.9 5.1 4.4 3.8 0 0.15

1998 2.7 5.2 4.7 3.6 4.6 4.3 5.1 4.6 4.0 5.0 4.3 4.0 .14

NK 7 (began pumping in August 1996)

1996 -- -- -- -- -- -- -- 1.3 1.8 2.5 .6 .8 .02

1997 .9 0 .6 .9 .2 3.1 11.0 6.1 1.7 .6 0 .1 .07

1998 .4 .1 6.1 7.6 8.2 4.7 5.7 4.4 1.5 .4 .3 .3 .11

NK 8 (began pumping in August 1996)

1996 -- -- -- -- -- -- -- .8 .5 1.0 .5 .2 .01

1997 .4 0 .4 .6 .1 2.4 7.3 3.7 1.0 .3 0 .1 .04

1998 .4 .1 3.6 5.6 7.0 7.8 9.4 9.5 5.7 .3 .3 .6 .14

Year January February March April May June July August September October November December

Average annual 

daily rate 

(Mgal/d)