U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5060

Prepared in cooperation with the

Rhode Island Department of Health

Delineation and Prediction Uncertainty of

Areas Contributing Recharge to Selected

Well Fields in Wetland and Coastal Settings, 

Southern Rhode Island
This page has been left blank intentionally.
Delineation and Prediction Uncertainty of 

Areas Contributing Recharge to Selected 

Well Fields in Wetland and Coastal Settings, 

Southern Rhode Island

By Paul J. Friesz

Prepared in cooperation with the Rhode Island Department of Health

Scientific Investigations Report 2010–5060

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Friesz, P.J., 2010, Delineation and prediction uncertainty of areas contributing recharge to selected well fields in wetland and coastal settings, southern Rhode Island: U.S. Geological Survey Scientific Investigations Report 2010–5060, 

69 p. (Also available online at http://pubs.usgs.gov/sir/2010/5060.) 
iii

Contents

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

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................4

Overview of Study Site Settings and Previous Investigations ......................................................4

Numerical Modeling......................................................................................................................................5

Hydraulic Properties.............................................................................................................................5

Recharge Rates.....................................................................................................................................6

South Kingstown Study Site.........................................................................................................................7

Geology...................................................................................................................................................9

Hydrology .............................................................................................................................................11

Simulation of Groundwater Flow and Areas Contributing Recharge.........................................14

Model Extent and Spatial Discretization................................................................................14

Boundary Conditions and Model Parameters.......................................................................19

Observations...............................................................................................................................22

Estimation of Parameters .........................................................................................................23

Simulated Water-Table Contours and Water Budget ..........................................................27

Deterministic Areas Contributing Recharge .........................................................................27

Probabilistic Areas Contributing Recharge...........................................................................30

Charlestown Study Site...............................................................................................................................39

Geology.................................................................................................................................................39

Hydrology .............................................................................................................................................39

Simulation of Groundwater Flow and Areas Contributing Recharge.........................................42

Model Extent and Spatial Discretization................................................................................42

Boundary Conditions and Model Parameters.......................................................................43

Observations...............................................................................................................................43

Estimation of Parameters .........................................................................................................46

Simulated Water-Table Contours and Water Budget ..........................................................50

Deterministic Areas Contributing Recharge .........................................................................50

Probabilistic Areas Contributing Recharge...........................................................................54

Summary and Conclusions.........................................................................................................................60

Acknowledgments.......................................................................................................................................62

References Cited..........................................................................................................................................62

Appendix 1. Water depth, and thickness of peat and organic-rich sediment (location of

profiles shown on figures 3 and 20), South Kingstown and Charlestown study

sites, southern Rhode Island ...................................................................................................66

Appendix 2. A, Stage of Worden Pond and B, stage of Tucker Pond and water levels in a

pond-bottom piezometer, 2006–2008 (location of measurement sites shown on

figure 3), South Kingstown study site, southern Rhode Island ...........................................68

Appendix 3. Streamflow measurements made at partial-record sites (location of 

partial-record sites shown on figures 3 and 20), South Kingstown and 

Charlestown study sites, southern Rhode Island..................................................................69
iv

Figures

1. Map showing study site well fields in South Kingstown and Charlestown, Rhode

Island, and selected water-supply districts, U.S. Geological Survey (USGS)

long-term network streamgages and observation wells, and a National Oceanic 

and Atmospheric Administration (NOAA) climatological station.........................................3

2. Map showing production wells, section line, selected borings, model extent,

bedrock-surface contours, and surficial geology, South Kingstown study site,

southern Rhode Island. Bedrock-surface contours from Masterson and 

others (2007) ..................................................................................................................................8

3. Map showing data-collection network near production wells, South Kingstown

study site, southern Rhode Island............................................................................................10

4. Diagram showing geologic cross section, South Kingstown study site, southern

Rhode Island................................................................................................................................12

5. Graph showing streamflow for the Beaver River streamgage (01117468) near 

Usquepaug, Rhode Island, during 1999–2008 (streamgage location shown 

on figure 1)...................................................................................................................................14

6. Graphs showing water levels measured in observation well CHW18 during

1951–60, 1988–92, and 1999–2008, Charlestown, Rhode Island (well location shown

in figure 1) ....................................................................................................................................15

7. Graph showing stage of wetland and water levels in piezometers screened in

peat, and in sand and gravel near A, west well field and B, east well field,

2007–2008, South Kingstown study site, southern Rhode Island........................................16

8. Graph showing plot of drawdown with time compared to a Theis type curve and a

leaky-aquifer type curve for a piezometer screened beneath the wetland near the

east well field, March14–April 3, 2008, South Kingstown study site, southern

Rhode Island................................................................................................................................18

9. Map showing model-boundary types and observations, South Kingstown study

site, southern Rhode Island ......................................................................................................20

10. Graph showing composite scaled sensitivities for model parameters (parameter

information is provided on table 2), South Kingstown study site, southern 

Rhode Island................................................................................................................................23

11. Graphs showing relation of A, weighted residual to weighted simulated equivalent

and of B, weighted observation to weighted simulated equivalent, South

Kingstown study site, southern Rhode Island........................................................................25

12. Map showing spatial distribution of weighted residuals and simulated water-table

contours for calibrated, steady-state conditions, South Kingstown study site,

southern Rhode Island...............................................................................................................26

13. Map showing simulated areas contributing recharge to the United Water Rhode

Island east and west well fields at their total average pumping rate of 2,138

gallons per minute, South Kingstown study site, southern Rhode Island.........................28

14. Map showing simulated areas contributing recharge to the United Water Rhode

Island east and west well fields at their total maximum pumping rate of 5,100

gallons per minute, South Kingstown study site, southern Rhode Island.........................29

15. Map showing simulated traveltimes to the United Water Rhode Island well fields

at their maximum pumping rate of 5,100 gallons per minute, South Kingstown

study site, southern Rhode Island............................................................................................31
v

16. Graphs showing frequency distribution of A, hydraulic parameters, and of B,

recharge parameters, before acceptance criteria were applied to determine the

probabilistic areas contributing recharge to the United Water Rhode Island well

fields (parameter information is provided on table 2), South Kingstown study site,

southern Rhode Island...............................................................................................................33

17. Graphs showing frequency distribution of A, hydraulic parameters, and of B,

recharge parameters, after acceptance criteria were applied to determine the

probabilistic areas contributing recharge to the United Water Rhode Island well

fields (parameter information is provided on table 2), South Kingstown study site,

southern Rhode Island...............................................................................................................35

18. Map showing simulated probabilistic areas contributing recharge to the United

Water Rhode Island well fields at their total average pumping rate of 2,138 gallons

per minute, South Kingstown study site, southern Rhode Island.......................................36

19. Map showing simulated probabilistic areas contributing recharge to the United

Water Rhode Island well fields at their total maximum pumping rate of 5,100

gallons per minute, South Kingstown study site, southern Rhode Island.........................37

20. Map showing production wells, section lines, selected borings, streamflow

partial-record sites, model extent, bedrock-surface contours, and surficial

geology, Charlestown study site, southern Rhode Island....................................................40

21. Diagram showing geologic cross section, Charlestown study site, southern 

Rhode Island................................................................................................................................41

22. Map showing model-boundary types and observations, Charlestown study site,

southern Rhode Island. .............................................................................................................44

23. Graph showing composite scaled sensitivities for model parameters (parameter

information is provided on table 4), Charlestown study site, southern Rhode Island.....46

24. Graphs showing relation of A, weighted residual to weighted simulated

equivalent, and of B, weighted observation to weighted simulated equivalent,

Charlestown study site, southern Rhode Island....................................................................48

25. Map showing spatial distribution of weighted residuals and simulated water-table

contours for calibrated, steady-state conditions, Charlestown study site, southern

Rhode Island................................................................................................................................49

26. Map showing simulated areas contributing recharge to the Central Beach Fire

District and East Beach Water Association well fields, at their total average

pumping rate of 16 gallons per minute, Charlestown study site, southern 

Rhode Island................................................................................................................................51

27. Map showing simulated areas contributing recharge to the Central Beach Fire

District and East Beach Water Association well fields, at their total maximum

pumping rate of 230 gallons per minute, Charlestown study site, southern 

Rhode Island................................................................................................................................52

28. Map showing simulated traveltimes to the Central Beach Fire District and East

Beach Water Association well fields at their maximum pumping rate of 230 gallons

per minute, Charlestown study site, southern Rhode Island...............................................53

29. Graphs showing frequency distribution of A, hydraulic parameters, and of B,

recharge parameters, before acceptance criteria were applied to determine the

probabilistic areas contributing recharge to the Central Beach Fire District and

East Beach Water Association well fields (parameter information is provided on

table 4), Charlestown study site, southern Rhode Island.....................................................55
vi

Tables

1. Characteristics of the production wells for the South Kingstown and Charlestown

study sites, southern Rhode Island............................................................................................9

2. Definition of model parameters, optimal parameter value or specified value, and

parameter-estimation statistics for the South Kingstown study site, southern 

Rhode Island................................................................................................................................21

3. Summary of the Monte Carlo analysis for the South Kingstown study site,

southern Rhode Island...............................................................................................................34

4. Definition of model parameters, optimal parameter value or specified value, and

parameter-estimation statistics for the Charlestown study site, southern Rhode

Island ............................................................................................................................................45

5. Summary of the Monte Carlo analysis for the Charlestown study site, southern

Rhode Island................................................................................................................................56

30. Map showing frequency distribution of A, hydraulic parameters, and of B,

recharge parameters, after acceptance criteria were applied to determine the

probabilistic areas contributing recharge to the Central Beach Fire District and

East Beach Water Association well fields (parameter information is provided on

table 4), Charlestown study site, southern Rhode Island.....................................................57

31. Map showing simulated probabilistic areas contributing recharge to the Central

Beach Fire District and East Beach Water Association well fields at their total

average pumping rate of 16 gallons per minute, Charlestown study site, southern

Rhode Island................................................................................................................................58

32. Map showing simulated probabilistic areas contributing recharge to the Central

Beach Fire District and East Beach Water Association well fields at their total

maximum pumping rate of 230 gallons per minute, Charlestown study site,

southern Rhode Island...............................................................................................................59
vii

Conversion Factors, Datums, and Acronyms

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

gallon per minute (gal/min) 0.06309 liter per second (L/s)

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

Hydraulic conductivity

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

Transmissivity

foot squared per day (ft2/d) 0.09290 meter squared per day (m2/d) 

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F-32)/1.8

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 (NGVD 29).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (μS/cm at 25°C)

ACRONYMS

CBFD Central Beach Fire District

EBWA East Beach Water Association

RIDEM Rhode Island Department of Environmental Management

RIDOH Rhode Island Department of Health

USGS U.S. Geological Survey

UWRI United Water Rhode Island
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Delineation and Prediction Uncertainty of Areas 

Contributing Recharge to Selected Well Fields in 

Wetland and Coastal Settings, Southern Rhode Island

By Paul J. Friesz

Abstract

Areas contributing recharge to four well fields in two 

study sites in southern Rhode Island were delineated on the 

basis of steady-state groundwater-flow models representing 

average hydrologic conditions. The wells are screened in 

sand and gravel deposits in wetland and coastal settings. 

The groundwater-flow models were calibrated by inverse 

modeling using nonlinear regression. Summary statistics from 

nonlinear regression were used to evaluate the uncertainty 

associated with the predicted areas contributing recharge to the 

well fields.

In South Kingstown, two United Water Rhode Island 

well fields are in Mink Brook watershed and near Worden 

Pond and extensive wetlands. Wetland deposits of peat near 

the well fields generally range in thickness from 5 to 8 feet. 

Analysis of water-level drawdowns in a piezometer screened 

beneath the peat during a 20-day pumping period indicated 

vertical leakage and a vertical hydraulic conductivity for the 

peat of roughly 0.01 ft/d. The simulated area contributing 

recharge for average withdrawals of 2,138 gallons per minute 

during 2003–07 extended to groundwater divides in mostly 

till and morainal deposits, and it encompassed 2.30 square 

miles. Most of a sand and gravel mining operation between 

the well fields was in the simulated contributing area. For the 

maximum pumping capacity (5,100 gallons per minute), the 

simulated area contributing recharge expanded to 5.54 square 

miles. The well fields intercepted most of the precipitation 

recharge in Mink Brook watershed and in an adjacent 

small watershed, and simulated streams ceased to flow. The 

simulated contributing area to the well fields included an area 

beneath Worden Pond and a remote, isolated area in upland 

till on the opposite side of Worden Pond from the well fields. 

About 12 percent of the pumped water was derived from 

Worden Pond.

In Charlestown, the Central Beach Fire District and 

the East Beach Water Association well fields are on a small 

(0.85 square mile) peninsula in a coastal setting. The wells 

are screened in a coarse-grained, ice-proximal part of a 

morphosequence with saturated thicknesses generally less 

than 30 feet on the peninsula. The simulated area contributing 

recharge for the average withdrawal (16 gallons per minute) 

during 2003–07 was 0.018 square mile. The contributing area 

extended southwestward from the well fields to a simulated 

groundwater mound; it underlay part of a small nearby 

wetland, and it included isolated areas on the side of the 

wetland opposite the well fields. For the maximum pumping 

rate (230 gallons per minute), the simulated area contributing 

recharge (0.26 square mile) expanded in all directions; it 

included a till area on the peninsula, and it underlay part of 

a nearby pond. Because the well fields are screened in a thin 

aquifer, simulated groundwater traveltimes from recharge 

locations to the discharging wells were short: 94 percent 

of the traveltimes were 10 years or less, and the median 

traveltime was 1.3 years.

Model-prediction uncertainty was evaluated using a 

Monte Carlo analysis; the parameter variance–covariance 

matrix from nonlinear regression was used to create parameter 

sets for the analysis. Important parameters for model 

prediction that could not be estimated by nonlinear regression 

were incorporated into the variance–covariance matrix. For 

the South Kingstown study site, observations provided enough 

information to constrain the uncertainty of these parameters 

within realistic ranges, but for the Charlestown study site, 

prior information on parameters was required. Thus, the 

uncertainty analysis for the South Kingstown study site was 

an outcome of calibrating the model to available observations, 

but the Charlestown study site was also dependent on 

information provided by the modeler. A water budget and 

model-fit statistical criteria were used to assess parameter sets 

so that prediction uncertainty was not overestimated. For the 

scenarios using maximum pumping rates at both study sites 

where the well fields intercepted most of the precipitation 

recharge that would otherwise have discharged to nearby 

small streams, results from the probabilistic contributing area 

indicated that, generally, areas closer to the well fields with 

shorter traveltimes are associated with higher probabilities and 

are more likely to coincide with the deterministic contributing 

area than are areas farther from the well fields with longer 
2 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

traveltimes and associated with lower probabilities. For both 

the maximum pumping rates and for the average pumping 

rate at the South Kingstown study site, the deterministic 

contributing areas generally corresponded to areas associated 

with high probabilities (greater than 50 percent). For the 

average pumping rate in the South Kingstown study site, areas 

associated with low probabilities were not only distant from 

the well fields but were located where simulated streams in 

the calibrated model intercepted precipitation recharge, thus 

indicating that this recharge may instead go directly to a well. 

That part of the sand and gravel mining operation between 

the well fields that was not in the deterministic contributing 

area was in the probabilistic contributing area, including some 

areas associated with high probabilities. For the maximum 

pumping rate in the South Kingstown study site, some areas 

on the opposite side of Worden Pond from the well fields that 

were not in the deterministic contributing area were in the 

probabilistic contributing area, but mostly low probabilities 

were associated with such areas. For the average pumping 

rate in the Charlestown study site, areas associated with high 

probabilities were limited to the well-field side of a nearby 

wetland; the deterministic contributing area on this side of 

the wetland coincided with this area of high probabilities. For 

both pumping rates, areas associated with low probabilities 

extended through the middle of the peninsula toward the 

mainland; for the maximum pumping rate, the low probability 

areas included small, isolated areas on the mainland.

Introduction

Accurate delineation of areas contributing recharge to 

production wells is an important component of Federal, State, 

and local strategies for protecting drinking-water supplies 

from contamination (U.S. Environmental Protection Agency, 

1991). The Source Water Assessment Program of the Rhode 

Island Department of Health (RIDOH), Office of Drinking 

Water Quality, was established by the 1996 Amendments to 

the Federal Safe Drinking Water Act. Since that time, RIDOH 

has assessed the susceptibility and risk of public-water 

supplies to contamination, and the agency encourages land-use 

planning within the areas contributing recharge to a production 

well. The Rhode Island Department of Environmental 

Management (RIDEM), Office of Water Resources, has 

determined areas contributing recharge to most production 

wells in Rhode Island, but RIDEM and RIDOH want to more 

accurately delineate areas contributing recharge to wells in 

complex hydrologic settings. Numerical groundwater-flow 

modeling, coupled with a particle-tracking technique, is a 

more advanced method for delineating areas contributing 

recharge than the analytical methods that have previously been 

used for this purpose.

The United Water Rhode Island (UWRI) well fields, in 

the Town of South Kingstown and near extensive wetlands, 

are an important groundwater supply in southern Rhode 

Island (fig. 1). The UWRI well fields supply the second 

largest quantity of groundwater in the State (Emily Wild, 

U.S. Geological Survey, written commun. 2008). UWRI 

supplies water to about 30,000 people, more than half the 

combined population of the Towns of South Kingstown and 

Narragansett, either directly or indirectly, through South 

Kingstown Water District and Narragansett Water Division 

(fig. 1). Narragansett Water Division receives all of its water 

from UWRI. In 2005, a South Kingstown Water District well 

field was removed from service because of water-quality 

concerns, requiring this district also to receive all its water 

from UWRI and thereby increasing the demand for water from 

the enlarged population served. In the past, the UWRI wells 

have also been susceptible to water-quality issues. Pesticides 

from agriculture were detected in several of the UWRI wells, 

including a well that was removed from service from 1982 to 

1988. Land use near the well fields includes a sand and gravel 

mining operation.

The well fields of the Central Beach Fire District (CBFD) 

and the East Beach Water Association (EBWA) are in a coastal 

setting in the Town of Charlestown, southern Rhode Island 

(fig. 1). The EBWA well field was reclassified as community 

wells in 2001. Both well fields are on a small peninsula 

where options for alternate supplies are limited. Water usage 

is expected to increase because of increased year-round 

residency and continued housing development. The well fields 

are screened in a shallow, unconfined aquifer generally less 

than 30-ft thick where groundwater is relatively susceptible to 

contamination from activities on the land surface. 

The U.S. Geological Survey (USGS), in cooperation 

with the RIDOH, began a 2-year study in 2006 to increase 

understanding of groundwater flow and of wetland-aquifer 

hydraulic connection at the South Kingstown and Charlestown 

study sites as part of an effort to protect the source of water 

to the well fields. This information also may be useful in 

delineation of areas contributing recharge to wells in other 

wetland and coastal settings in Rhode Island and other areas 

with similar geohydrologic settings. A numerical groundwaterflow model was designed for each study site and calibrated 

to hydrologic data by inverse modeling using nonlinear 

regression. Nonlinear regression estimates the optimal 

set of model-parameter values. In contrast to calibrating 

parameter values manually, summary statistics from 

nonlinear regression can be used to provide a quantitative 

measure of the uncertainty of the predictions, in this case, 

of its predictions for the size, location, and shape of the area 

contributing recharge to the well fields. The uncertainty that 

this study considers is from the observation dataset used 

for this calibration and not from the model design. Model 

design remains an unexplored source of uncertainty. Results 

of the calibrated model (used for a deterministic contributing 

area) and the uncertainty analysis (used for a probabilistic 

contributing area) in these complex settings could be useful 

to water-resource managers when they assess the risk of 

contamination and implement land-use plans. In addition, 

without an evaluation of the uncertainty associated with 
Introduction 3

EXPLANATION

Watershed boundaryStudy site well fieldsNOAA climatological station and identifierUSGS observation well and identifier

USGS streamgage and identifier (some sites off map)

R A N G A R S N A T T E

Y A B

B

L

O

C

K

I

S

L

A

N

D

S

O

U

N

D

P t e at mauq ucs R tt revi

revae B revi R

River

River

Wood

Chickasheen Brook

P t e at mauq ucs R tt revi

Pawca

ut ck

A

T

L

A

N

T

I

C

O

C

E

A

N

Mink

Brook Pasquiset Brook

hC pi uxet R vi re

guaS t a cu ek t

i R rev

qs U peu gua eu Q- revi Rne

95

1

Hopkinton Richmond

South

Kingstown

Narragansett

Charlestown Westerly

Exeter North Kingstown

Watchaug

Pond

Worden

Pond

Winnapaug Pond

Quonochon at

ug

Pond

Ninigret Pond

Green Hill

Pond

Trustom

Pond

Potters

Pond

Point

Judith

Pond

Maschaug Pond

Cards

 Pond

Base from U.S. Geological Survey,Rhode Island state plane projection, 1:24,000, NAD 83Sites off-map are generalized (not to scale)

41°30'

71°45' 71°54' 71°36' 71°27'

41°21'

0 5 KILOMETERS0 5 MILES

Narragansett Water Division

South Kingstown 

Water District

United Water

Rhode Island

Central Beach 

Fire District

East Beach 

Water Association

41°45'

71°45' 71°30'

42°00'41°30'

10 MILES 0

0 10 KILOMETERS

RHODE ISLAND

Block Island

PAWCATUCK

RIVER

WATERSHED

AN RR GA NA ES TT AB WY TA RE HS DE

SOUTH COASTAL WATERSHED

CHIPUXET

RIVER

WATERSHED

CHW18

CHW18

SNW6

374266

RHODE ISLAND

CONNECTICUT

01117500

01117350

01118500

01117500

374266

01117420

01117468

01118000

01117000

01117800

(latitude=41°34’26”, longitude=71°43’16”)

(latitude=41°38’28”, longitude=71°26’42”)

Figure 1. Study site well fields in South Kingstown and Charlestown, Rhode Island, and selected water-supply districts, U.S. Geological Survey (USGS) long-term network streamgages and observation wells, and a National Oceanic and Atmospheric Administration (NOAA)climatological station.
4 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

the model predictions, the area contributing recharge to a 

well may be underestimated, thereby leaving well fields 

inadequately protected.

The area contributing recharge to a well field based on 

the optimal set of parameter values from the calibrated model 

provides the best representation of the contributing area with 

the available observations. However, the parameter values 

are estimated with different levels of precision, and some 

important parameters for model predictions cannot always 

be estimated with available observations. An evaluation of 

uncertainty associated with the predicted contributing area 

was done using a stochastic Monte Carlo analysis. Multiple 

parameter sets for the Monte Carlo analysis were created using 

the parameter variance–covariance matrix from nonlinear 

regression, a method described and applied by Starn and 

others (2000). The present study applies the uncertainty 

analysis in different settings and with multiple well fields, 

exploring issues such as incorporating unestimated parameters 

into the analysis and assessing parameter sets so prediction 

uncertainty would not be overestimated.

Purpose and Scope

This report describes the geohydrology and the areas 

contributing recharge to 11 production wells in the two 

study sites of South Kingstown and Charlestown. The South 

Kingstown study site includes two UWRI well fields (7 wells), 

and the Charlestown study site includes the CBFD well field 

(2 wells) and the EBWA well field (2 wells). Numerical 

groundwater-flow models were developed and calibrated 

for each study site on the basis of geologic and hydrologic 

data collected during this and previous investigations. The 

groundwater-flow models were calibrated by inverse modeling 

using nonlinear regression to estimate the optimal set of 

parameter values. Simulated areas contributing recharge to 

the well fields based on the optimal set of parameter values 

(the deterministic contributing area) are shown on maps for 

selected pumping rates and average, steady-state hydrologic 

conditions. Summary statistics from nonlinear regression were 

used to evaluate the uncertainty associated with the predicted 

areas contributing recharge to the well fields. Issues such as 

incorporating unestimated parameters into the analysis and 

assessing parameter sets so prediction uncertainty would not 

be overestimated were explored. Maps depict the results of 

the uncertainty analysis of the simulated area contributing 

recharge expressed as a probability distribution.

Selected pumping rates include average withdrawals 

during 2003–07 and maximum-rated capacity of the 

production-well pumps. Maximum pumping rates used in the 

model simulations are not proposed, long-term (continuous) 

withdrawal rates. Instead, the simulated areas contributing 

recharge at these maximum rates are used by RIDOH for 

implementing land-use planning that protects the quality of the 

water that the production wells supply. Average withdrawals 

may change because of changes in water usage or changes 

in State policies. In addition, areas contributing recharge for 

the maximum pumping rate represent conservative, or larger, 

areas for land-use planning than for lower pumping rates.

Overview of Study Site Settings and 

Previous Investigations

The study sites in the Towns of South Kingstown and 

Charlestown are in southern Rhode Island (fig. 1) where the 

climate is humid and temperate. According to records from 

1960 through 2007 for the Kingston (374266), Rhode Island, 

climatological station (National Oceanic and Atmospheric 

Administration, 2008) (fig. 1), average annual temperature is 

50° F and average annual precipitation is 51 inches.

Groundwater at the study sites is stored and transmitted 

in surficial sediments of glacial origin—till, stratified, and 

morainal deposits—and in the underlying bedrock. A thin, 

discontinuous layer of till deposited directly on the bedrock 

by glacial ice is composed of a poorly sorted mixture of 

sediments ranging in size from clay to boulders. Stratified 

deposits consisting of well-sorted, layered sediments ranging 

in size from clay to gravel were deposited by glacial meltwater 

and overlie the till in the valleys and lowlands in coastal 

areas. Mixed sediments of till and stratified deposits are 

present in moraines, which formed at the ice margin when 

the retreating glacier paused for a period of time. Postglacial deposits of peat and alluvium locally overlie glacial 

deposits. The production wells are screened in coarse-grained 

stratified deposits composed of sand and gravel. Sand and 

gravel deposits, which have higher storage and transmissive 

properties than other geologic units, are the primary aquifers 

in Rhode Island.

The South Kingstown study site is characterized by 

wetlands, including Great Swamp, one of the largest wetlands 

in New England. The two UWRI well fields, about 0.8 miles 

apart and north of the Charlestown Moraine, are adjacent 

to a brook and associated wetlands in a small watershed 

of Worden Pond and Chipuxet River. These well fields are 

screened in thick saturated stratified deposits. Hydrologic and 

geologic information for this study site was available from 

regional USGS investigations. Bierschenk (1956) completed 

a reconnaissance study of groundwater conditions in the area 

that the USGS Kingston quadrangle covers, which includes 

the study site. The first comprehensive investigation of 

the groundwater and surface-water resources of the upper 

Pawcatuck River watershed, which includes the Chipuxet 

River watershed, was done by Allen and others (1966). An 

associated data report (Allen and others, 1963) compiled 

hydrologic and geologic data from this and the earlier study. 

Site-specific information from these regional investigations 

was available for the older production wells at the study site. 

Detailed mapping of the surficial deposits (Kaye, 1960) and of 

bedrock geology (Moore, 1964) has been done for the USGS 

Kingston quadrangle.
Numerical Modeling 5

The Charlestown study site is in a coastal setting. 

CBFD and EBWA well fields are south of the Charlestown 

Moraine near the center of a small (0.85 mi2) peninsula 

bounded by Block Island Sound and by large saltwater ponds 

in the South Coastal watershed. The well fields are screened 

in thin and shallow saturated stratified deposits. Previous 

USGS investigations in the area covered by the USGS 

Quonochontaug and Carolina quadrangles, which include 

the study site, include reconnaissance of the groundwater 

conditions (LaSala, Jr., and Johnson, 1960; LaSala, Jr., and 

Hahn, 1960) and mapping of the bedrock geology (Moore, 

1959). More recently, Masterson and others (2007) completed 

a regional study of geology and groundwater flow to saltwater 

ponds in the South Coastal watershed. This regional study 

included a manually calibrated groundwater-flow model. 

Relevant studies by other organizations include detailed 

mapping of the surficial deposits for the Quonochontaug and 

Carolina quadrangles (Boothroyd, 2001) and of groundwater 

conditions near the well fields (Urish, 1992, 2000).

Numerical Modeling

Many hydrologic features and processes may affect the 

size, shape, and location of the area contributing recharge 

to a well; this area is defined as the surface area where 

water recharges the groundwater and then flows toward and 

discharges to the well (Reilly and Pollock, 1993). Features 

and processes, such as groundwater systems with irregular 

geometry and complex lithology, or the interaction between 

individual pumping wells and hydrologic features such as 

surface-water bodies, are difficult to represent with analytical 

methods. Three-dimensional finite-difference numerical 

groundwater-flow models, however, can represent these 

and other geologic and hydrologic features and processes. 

Information provided by a numerical model on the source of 

water to a well can also be useful in protecting public health in 

Rhode Island.

Groundwater-flow models based on the finite-difference 

computer code MODFLOW-2000 (McDonald and Harbaugh, 

1988; Harbaugh and others, 2000) and capable of simulating 

the response of the groundwater system to production-well 

withdrawals were developed for each of the two study sites. 

Model layers were simulated by using a fixed transmissivity, 

including the top layer, to linearize and thereby simplify the 

numerical calculations and to increase numerical stability. 

Fixed transmissivity was used because simulating thin 

layers on the sides of steeply sloping hills, such as near the 

upland-valley contact and the uplands themselves presents 

convergence difficulties for the model, as does the calibration 

by inverse modeling when using nonlinear regression. 

Another advantage of using a fixed transmissivity is that it 

increases the number of model simulations that converge for 

the analysis of the probabilistic contributing area. Simplifying 

the numerical calculations by using a fixed transmissivity is 

described by DeSimone (2004) and Hill and Tiedeman (2007). 

A disadvantage of using fixed transmissivity for all model 

layers is that the simulated transmissivity of the aquifer does 

not change with drawdowns caused by different pumping rates 

than rates used in the calibrated model. Differences between 

using a fixed transmissivity and a variable transmissivity 

may include differences in hydraulic gradients, which may 

affect groundwater traveltimes and the response of surfacewater bodies to pumping, and thus potentially may affect the 

simulated area contributing recharge to a well. 

Areas contributing recharge to the production wells 

were determined on the basis of model simulations of 

average, steady-state hydrologic conditions and by use of 

the particle-tracking program MODPATH (Pollock, 1994). 

The particle-tracking program calculates groundwater-flow 

paths and traveltimes on the basis of the head distribution 

computed by the groundwater-flow simulation. Areas 

contributing recharge were delineated by forward tracking 

of particles from recharging areas to the discharging wells. 

Particles were allowed to pass through model cells with weak 

sinks, which remove only a part of the water that flows into 

the cell. Pass-through weak-sink option was used because 

simulated contributing areas to a well may be larger and 

thus more conservative in terms of land-use protection than 

if the particles were stopped at weak sinks. Traveltimes in 

the groundwater-flow simulation do not take into account 

traveltime in the unsaturated zone between the land surface 

and the water table.

Development of a groundwater-flow model required that 

the geometry and hydraulic properties of the groundwater 

system and the fluxes into and out of the model be quantified. 

Each model was calibrated with the Parameter Estimation 

(inverse modeling) process of MODFLOW-2000 (Hill and 

others, 2000; Hill and Tiedeman, 2007) using nonlinear 

regression that minimizes the differences, or residuals, 

between field (observed) and simulated water levels and 

streamflows to obtain an optimal set of parameter values. 

Parameter values that nonlinear regression estimated for the 

model were compared to values reported in the literature 

in order to determine the reasonableness of the calibration. 

Literature values also were used to specify parameter values 

that could not be estimated by nonlinear regression, and in 

some cases, for prior information on model parameters to 

constrain uncertainty about the specified parameter values 

to reasonable ranges for model-prediction uncertainty. 

Reported values for hydraulic properties and recharge rates are 

summarized in two subsequent sections.

Hydraulic Properties

Glacial Deposits: The hydraulic properties of glacial till 

are highly variable. Aquifer tests and laboratory measurements 

indicated that hydraulic conductivity values for till in southern 

Rhode Island range from 0.07 to 41 ft/d with a median of 

0.7 ft/d (Allen and others, 1966). Melvin and others (1992) 
6 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

summarized the hydraulic properties of till from previous 

studies in southern New England: for till derived from 

crystalline bedrock, horizontal hydraulic conductivities ranged 

from 0.004 to 65 ft/d, and vertical hydraulic conductivities 

ranged from 0.013 to 96 ft/d. Porosity values determined 

from a limited number of measurements in southern Rhode 

Island by Allen and others (1963) ranged from 0.23 to 0.50 

and averaged 0.30. Porosity values from a limited number of 

measurements in southern New England ranged from 0.22 to 

0.41 and averaged 0.33 (Melvin and others, 1992).

Hydraulic conductivity values of glacial stratified 

deposits have been estimated from lithology and from aquifertest results. Values determined from lithology were based on 

the relation between horizontal hydraulic conductivity and 

grain size as determined by Rosenshein and others (1968) 

and modified by Dickerman (1984) from aquifer-test results 

in central Rhode Island. These values are 20 ft/d for very 

fine sand, 50 ft/d for fine sand, 100 ft/d for sand, 200 ft/d 

for sand and gravel, and 500 ft/d for gravel. The ratios 

of horizontal hydraulic conductivity to vertical hydraulic 

conductivity ranged from 2 to 80 on the basis of aquifer-test 

analyses in southern Rhode Island by Dickerman (1984) 

and by Dickerman and others (1990), averaging 6 and 10 

in these studies, respectively. The porosities of 24 stratified 

sediment samples in southern Rhode Island reported by Allen 

and others (1963) ranged from 0.26 to 0.42 with an average 

value of 0.34. LeBlanc (1987) reported a range of porosities 

from 0.35 to 0.40 for stratified deposits in western Cape Cod, 

Massachusetts.

Few data are available for hydraulic properties of 

morainal deposits. Because morainal deposits in southern 

Rhode Island are composed of a mix of sandy ablation till 

and stratified deposits, bulk hydraulic properties most likely 

lie between properties of these two materials. Laboratory 

measurements indicated that hydraulic-conductivity values 

for morainal deposits in southern Rhode Island range from 

0.1 to 13 ft/d (Allen and others, 1966). Values determined by 

manual calibration of groundwater-flow models ranged from 

5 to 30 ft/d (Friesz, 2004; Masterson and others, 2007).

Post-glacial deposits: The interaction between streams 

and groundwater requires a conductance term that incorporates 

the geometry and the vertical hydraulic conductivity of the 

streambed. Bed sediments are typically alluvial deposits. 

Reported values for vertical hydraulic conductivity ranged 

from 0.1 to 17 ft/d for bed sediments in Rhode Island 

(Rosenshein and others, 1968; Gonthier and others, 1974; 

Johnston and Dickerman, 1974) and Massachusetts (Lapham, 

1989; de Lima, 1991; Friesz, 1996; Friesz and Church, 

2001). The vertical hydraulic conductivity of coarse-grained 

sediments in these studies typically ranged from 1 to 3 ft/d and 

from 0.1 to 0.7 ft/d for fine-grained sediments.

Wetland deposits consist of peat—organic matter in 

various stages of decomposition. Verry and Boelter (1979) 

reported hydraulic-conductivity values for peat from an 

extensive study in Minnesota that varied over several orders 

of magnitude, from less than 0.03 ft/d to more than 4 ft/d, and 

with depth; in general, shallow, loose peat consisting of recent 

deposits with large interconnected pore spaces had higher 

values of hydraulic conductivity, and highly decomposed 

compact peat with small pore spaces at greater depths had 

lower values. For wetlands in eastern Massachusetts, O’Brien 

(1977) reported hydraulic-conductivity values ranging from 

0.2 to 58 ft/d. In a large wetland in southwestern Rhode Island, 

peat deposits averaged 0.3 ft/d (Friesz, 2004). Conceptually, 

most water in a wetland moves over the surface and through 

permeable shallow peat, whereas decomposed peat at depth 

impedes vertical flow. Peat generally has at least 80 percent 

porosity (Verry and Boelter, 1979).

Bedrock: Hydraulic conductivity and porosity of 

crystalline bedrock are generally low. Analysis of specificcapacity data from bedrock wells in eastern Connecticut 

indicated an average hydraulic conductivity of 0.5 ft/d 

(Randall and others, 1966). Lower values of 0.02 and 

0.09 ft/d for crystalline bedrock in northern New Hampshire 

were determined through model calibration (Tiedeman and 

others, 1997). Porosity values for crystalline rock summarized 

in Meinzer (1923) range from 0.0002 to 0.02. 

Recharge Rates

Glacial deposits: Recharge in upland till areas is 

primarily from direct infiltration of precipitation, but it may 

also include leakage from streams, ponds, and wetlands. 

Recharge rates in upland settings are not well understood 

and conceptually are highly variable, ranging from near zero 

in low-permeability tills on steep topography, where the 

water table is near the land surface, to values approaching 

mean annual runoff (precipitation minus evapotranspiration) 

in sandy tills on moderate slopes, where the water table is 

perennially below the land surface. The application of a 

mathematical relation derived from Connecticut streamflow 

records and geology indicated that groundwater discharge, a 

measure of effective recharge (groundwater recharge minus 

groundwater evapotranspiration), is about 35 percent of mean 

annual runoff for till areas (Mazzaferro and others, 1979). 

Computerized hydrograph-separation techniques for longterm streamflow records from southeastern Rhode Island and 

Connecticut and from western Massachusetts for watersheds 

covered predominantly by till (90 percent or greater) indicated 

effective recharge rates ranging from 16 to 24 in/yr when 

mean annual runoff ranged from 27 to 31 in/yr (Bent, 1995, 

1999; Friesz and Stone, 2007).

Sources of recharge to stratified deposits in a valleyfill setting include direct infiltration of precipitation, runoff 

from adjacent upland hillslopes, and natural infiltration from 

streams, ponds, and wetlands. In some cases, pumping by 

wells may also induce water from surface-water bodies. 

Conceptually, overland runoff is minimal in areas of stratified 

deposits, and recharge rates from direct infiltration of 

precipitation should approximate mean annual runoff rates 

(Lyford and Cohen, 1988). Mean annual streamflow from 
South Kingstown Study Site 7

eight USGS long-term streamgages in southern Rhode Island 

(fig. 1) ranges from 26.8 to 32.8 in/yr over their watersheds. 

These rates are an average over the entire watershed, 

including areas of mostly stratified deposits but also areas 

of till, morainal deposits, surface-water bodies, wetlands, 

and a variety of land uses. The average and median of the 

mean annual streamflow for the eight streamgages are both 

29.1 in/yr. No studies have been done on recharge rates to 

morainal deposits in southern Rhode Island, but recharge rates 

may be nearly the same as recharge rates to stratified deposits 

because morainal deposits consist of mostly permeable coarsegrained sediments.

Wetlands: The role of wetlands in the hydrologic cycle 

is complex (Mitsch and Gosselink, 1993). Surface water in 

a wetland may be year-round or intermittent. Wetlands may 

serve as groundwater discharge areas or as recharge areas, or 

vary seasonally. Under pumping conditions, water that may 

have flowed across the surface may be induced to flow into 

the aquifer and then be withdrawn by the well. To account 

for all the water potentially available to the production 

wells under various pumping scenarios, water available for 

recharge (precipitation minus evapotranspiration) was applied 

to the wetlands. Evapotranspiration rates in wetlands are 

poorly defined. Some studies indicate that evapotranspiration 

rates from wetlands are higher than evaporation rates 

from open-water bodies, but other studies indicate that 

evapotranspiration rates are lower (Mitsch and Gosselink, 

1993). Evapotranspiration rates measured in wetlands in 

eastern Massachusetts range from 21 to 40 in/yr (O’Brien, 

1977; Hemond, 1980). For a precipitation rate of 51 in/yr 

in southern Rhode Island, the estimated water available for 

recharge over the wetlands would range from 11 to 30 in/yr 

using these evapotranspiration rates. 

South Kingstown Study Site

UWRI production wells are clustered in two well fields 

in Mink Brook watershed, a small subbasin of Worden Pond 

and the Chipuxet River in the Town of South Kingstown, 

southern Rhode Island (figs. 1 and 2). The production wells 

are in the southeast part of Chipuxet River watershed near 

the boundary with the South Coastal watershed; most of this 

watershed boundary is in relatively transmissive materials 

where groundwater divides may not coincide with surfacewater divides. The study area extends to features that serve 

as hydrologic boundaries in the numerical model and which 

minimize the effects of model boundaries on simulated heads 

near any groundwater divides. These boundaries include rivers 

and streams in the north and northeast and coastal ponds and 

Block Island Sound in the southeast and south. In the west, 

the study area extends to topographical divides in upland till 

where groundwater and surface-water divides are most likely 

the same and in small areas of stratified deposits between 

upland till, where topographical divides are assumed to be the 

same, and northward from Factory Pond to upland till parallel 

to groundwater flow, based on a water-table map drawn 

by Bierschenk (1956) with water-level accuracies of about 

±5 ft. The production wells adjoin wetlands, with additional 

wetlands south and southwest of the wells, and with Great 

Swamp north of Worden Pond. Additional land uses in and 

near Mink Brook watershed include forest, agriculture, rural 

residential, developed recreation, and sand and gravel mining 

operations, one of which is midway between the well fields. 

The UWRI well fields consist of seven wells; 

characteristics of the production wells are listed in table 1. The 

production wells are screened in a coarse-grained sediment 

unit with saturated thicknesses of about 70 ft at the east 

well field and greater than 100 ft at the west well field. The 

east well field consists of four wells, three of which have 

been withdrawing water since the 1940s. Areas contributing 

recharge for this well field were determined for the 2003–07 

average well-field withdrawal rate (658 gal/min) and the 

maximum well-field pumping capacity (2,700 gal/min). The 

west well field, which began withdrawing water in 1966, 

consists of three wells. The third well, approved for operation 

by the State during this study in 2006, was installed to 

complement operation of the existing two wells rather than 

to increase total withdrawals from the well field (Richard 

Amirault, Rhode Island Department of Health, written 

commun., 2007). Areas contributing recharge for this well 

field were determined for the 2003–07 average well-field 

pumping rate (1,480 gal/min) and for the maximum rate of 

the two highest maximum pumping capacities of the three 

wells (2,400 gal/min). Maximum pumping rates for each well 

were determined by distributing that maximum rate sum of 

2,400 gal/min equally among the three wells composing the 

well field.

Most water withdrawn by the UWRI well fields 

is exported out of the Chipuxet River watershed to the 

South Coastal and Narragansett Bay watersheds (Wild and 

Nimiroski, 2005) (fig. 1). Most of this exported water is 

either used in sewered areas and then is treated at wastewater 

facilities before discharging to Narragansett Bay or it is 

returned to groundwater through private septic systems outside 

of the modeled area. Both the remaining exported water and 

the water used in the Chipuxet River watershed are returned to 

groundwater through private septic systems. In the Chipuxet 

River watershed, this is a small, mostly rural, residential area. 

About 85 percent of the water used by domestic population on 

septic systems is returned to groundwater, and 15 percent is 

consumed (Wild and Nimiroski, 2005).

Water levels and streamflows were measured periodically 

from October 2006 to October 2008 to increase understanding 

of interactions between surface water and groundwater and 

to provide information about average hydrologic conditions. 

The data-collection network (fig. 3) included a nest of vertical 

piezometers installed in the peat and in underlying sediments 

in the vicinity of each well field, a pond-bottom piezometer 

in Tucker Pond, five existing observation wells, and six pondand stream-stage sites. Streamflow measurements were made 
8 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

1

0

-50

50

100

150

250

200

150

0

0

-100

50

100

50

0

-50

0

-100

50

-100 100

100

-50

200

100

200

0

100

150

-50

-50

50

-50

0

0

-50

50

50

0

50

50

150

-50

50

50

100

-100

-100

-50

50

50

100

0

100

A

A’

71°36' 71°34' 71°32' 71°30'

41°28'

41°26'

41°24'

41°22'

East well field

West well field

Worden Pond

Tucker Pond

Chipuxet River

Mink Brook

Alewife Brook

Block Island Sound

Great Swamp

Management Area

White Horn Brook

Genesee Brook

Factory

Pond

Saugatucket River

Point Judith Pond

Potter Pond

Card Pond

Trustom Pond

Green Hill Pond

White Pond

South Kingstown

Narragansett

Charlestown

SNW869

SNW870 SNW895

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

Model boundary

Sand and gravel operation Production well

Mink Brook and Alewife Brook watershed boundaries

Bedrock-surface contours—Interval 50 feet 

Line of geologic cross section

Boring and identifier

Bedrock-surface contours from Masterson and others (2007)

EXPLANATION

A A’

-50

0 .5 1 KILOMETER

0 .5 1 MILE 

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

Figure 2. Production wells, section line, selected borings, model extent, bedrock-surface contours, and surficial 

geology, South Kingstown study site, southern Rhode Island. Bedrock-surface contours from Masterson and 

others (2007).
South Kingstown Study Site 9

at five sites in the Mink Brook watershed and at five sites in 

adjacent watersheds. Peat thickness profiles were measured 

with a hand-held steel rod at each well field, and lithologic 

logs from USGS reports and from those of other organizations 

were compiled to define grain size of the stratified deposits 

and of post-glacial deposits.

Geology

In the South Kingstown study area, glacial and postglacial deposits overlie igneous and metamorphic bedrock of 

predominately granitic composition (Moore, 1964). Bedrock 

valleys generally trend north-south (Masterson and others, 

2007) (fig. 2). The axis of a main preglacial river valley trends 

southward beneath Great Swamp and Worden Pond, continues 

southeastward near the west well field, and then passes 

beneath Charlestown Moraine and Point Judith Moraine into 

Block Island Sound. Surficial deposits thicker than 250 ft fill 

this preglacial valley near the kettle ponds in the Charlestown 

Moraine. Thickness of surficial deposits ranges from more 

than 120 ft at the west well field to about 80 ft at the east 

well field.

Glacial sediments consist of stratified deposits, till, and 

morainal deposits (fig. 2). Glacial stratified deposits south of 

the Charlestown Moraine were deposited by glacial meltwater 

in broad flood plains away from the ice, whereas stratified 

deposits were laid down near the ice (ice-contact deposits) 

north of the moraine within the study area (Kaye, 1960). 

Till covers the bedrock surface in most places and is about 

20 ft thick in upland areas and generally more than 10 ft thick 

in lowlands beneath stratified deposits. Numerous bedrock 

outcrops are present on the isolated upland hills directly 

northwest and southwest of Worden Pond. The Charlestown 

Table 1. Characteristics of the production wells for the South Kingstown and Charlestown study sites, southern Rhode Island.

[Altitudes in feet relative to NGVD 29. USGS, U.S. Geological Survey; ft, foot; in., inch; gal/min, gallons per minute; UWRI, United Water Rhode Island; 

CBFD, Central Beach Fire District; EBWA, East Beach Water Association; --, unknown]

Name

Water 

supplier

Year Altitude 

of land 

surface 

(ft)

Screen 

diameter 

(in.)

Depth of 

screen top and 

bottom below 

land surface 

(ft)

Screen 

altitude top 

and bottom 

(ft)

1

Average 

pumping 

rate 

(gal/min)

2

Maximum 

pumping 

rate 

(gal/min)

USGS Local Drilled Inservice

South Kingstown

SNW81 PW1 UWRI 1942 1944 106 12 45 to 75 61 to 31 51 400

SNW84 PW2 UWRI 1945 1946 99 12 33.6 to 55 65.4 to 44 223 550

SNW91 PW3 UWRI 1949 1949 95 12 34 to 54 61 to 41 45 400

SNW887 PW4 UWRI 1958 1958 103 18 36 to 51 67 to 52 339 1,350

Total east well field 658 2,700

SNW1063 PW5 UWRI 1966 1966 101.9 18 78.5 to 98.5 23.4 to 3.4 670 1,000

SNW1156 PW6 UWRI 1971 1972 101.8 18 53.5 to 84 48.3 to 17.8 810 1,300

SNW1226 PW7 UWRI 2001 2006 113.9 18 80 to 105 33.9 to 8.9 0 1,100

Total west well field 1,480 3

2,400

Total UWRI well fields 2,138 5,100

Charlestown

CHW36 PW1 CBFD 1946 -- 10 8 18 to 28 -8 to -18 5 50

CHW580 PW2 CBFD 1965 -- 10 8 12.5 to 21.5 -2.5 to -11.5 5 50

Total 10 100

CHW591 PW1 EBWA 1953 1953 10 8 17.5 to 27 -7.5 to -17 3 100

CHW592 PW2 EBWA 1965 1965 10 8 18.5 to 28 -8.5 to -18 3 30

Total 6 130

Total CBFD and EBWA 16 230

1

 Average pumping rate for years 2003–2007.

2

 Maximum-rated capacity of pump.

3

 Sum of two largest maximum pumping rates.
10 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Worden Pond

Mink Brook

Alewife Brook

Browns Brook

Tucker Pond

West well field

East well field

PW2

PW4

White Pond

EXPLANATION

Peat thickness survey

Production well

Observation wells

Wetland and pond-bottom piezometers

Streamflow partial-record site

Stage measurement site

Watershed boundaries

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

0 .5 1 KILOMETER

Base from U.S. Geological Survey, 0 .5 1 MILE 

Rhode Island state plane projection, 1:24,000, NAD 83

Figure 3. Data-collection network near production wells, South Kingstown study site, southern Rhode Island.
South Kingstown Study Site 11

Moraine and the Point Judith Moraine represent long-term 

recessional positions of the retreating glacier; they consist of 

interstratified till and sorted deposits (Kaye, 1960).

Glacial meltwater deposited the stratified sediments in 

morphosequences during temporary standstills of the last 

retreating glacial ice sheet (Stone and others, 2005; Masterson 

and others, 2007). Sediment size generally decreases and 

sorting increases with distance from the ice margin. The 

vertical distribution and thickness of surficial deposits along a 

generalized west-east geologic section through the production 

well fields are shown in figure 4. The geologic section shows 

a profile through a depositional sequence trending northeastsouthwest. Glacial stratified deposits were grouped into three 

units on the basis of the dominant grain sizes: sand and 

gravel; sand; and fine-grained sediment composed of very fine 

sand, silt, and clay. All seven production wells are screened in 

sand and gravel deposits at medium depth or near the bottom 

of this coarse-grained unit. A limited number of lithologic logs 

collected by Allen and others (1963) and Boothroyd and others 

(1998) were available from beneath Great Swamp and Worden 

Pond. These logs indicated a younger morphosequence north 

of the sequence shown in figure 4 trending north-south with 

sands covering lacustrine deposits of Glacial Lake Worden. 

These lacustrine deposits represent the majority of the known 

fine-grained sediments in the study area.

Post-glacial wetland deposits consist of peat in various 

stages of decomposition. Manual probing of the peat near 

both well fields (fig. 3) indicated that the thickness of the peat 

and organic-rich sediment ranged from less than 1 ft near the 

edge of the wetlands to greater than 11 ft in the center of the 

wetlands near the east well field; peat thickness generally 

ranged from 5 to 8 ft near the well fields. Peat deposits also 

extend beneath Worden Pond (fig. 4). Core samples of the 

pond bottom that Boothroyd and others (1998) collected 

indicated an average thickness of about 3 ft for the peat and 

organic-rich sediment.

Hydrology

The study area includes parts of two large watersheds 

in southern Rhode Island—the Chipuxet River and the South 

Coastal watersheds (figs. 1 and 2). The Charlestown Moraine, 

deposited across the pre-glacial river valleys, forms a ridge of 

as much as 150 ft above the land surface surrounding Worden 

Pond, and it forms most of the surface-water divide between 

these two watersheds in the southern part of the Chipuxet 

River watershed. According to Tiner (1989), the Charlestown 

Moraine promoted wetland formation by blocking surface 

drainage from the north; these wetlands are generally densely 

vegetated and are considered palustrine forested and scrubshrub wetlands. The Chipuxet River flows southward through 

Great Swamp and into Worden Pond; west of Worden Pond, 

the Chipuxet River becomes the Pawcatuck River.

The water-table map drawn by Bierschenk (1956) 

indicated a groundwater divide between the Chipuxet River 

and Block Island Sound located in the Charlestown Moraine. 

Because of minimal water-level data in the moraine, however, 

the location of the groundwater divide in the moraine and its 

proximity to the surface-water divide is unknown. Kettlepond altitudes listed on the USGS Kingston quadrangle 

along the axis of the main pre-glacial valley indicate that 

the groundwater divide is most likely between Tucker Pond 

and White Pond in this area of the moraine. The manually 

calibrated regional model (Masterson and others, 2007) 

simulated a groundwater divide between the Chipuxet and 

South Coastal watersheds that is mostly within the moraine.

The production well fields are in a small subbasin of 

the Chipuxet River, Mink Brook, which drains 1.82 mi2 at its 

confluence with Worden Pond (fig. 2). The production wells 

are screened in transmissive sand and gravel deposits adjacent 

to Mink Brook and wetlands. The vertical placements of the 

production well screens in relation to Worden Pond and to 

nearby wetlands are shown in figure 4. Transmissivity values 

ranging from 8,000 to 21,000 ft2/d were calculated for the sand 

and gravel deposits from short-duration (24 hrs) aquifer tests 

at the east well field (Allen and others, 1966); the associated 

hydraulic conductivities ranged from 100 to 400 ft/d, and the 

median value was 150 ft/d. 

The source of all water in the study area is 

precipitation. Mean annual streamflow (precipitation minus 

evapotranspiration) from long-term streamgages in southern 

Rhode Island provides an estimate of water available for 

recharge (see section “Recharge Rates”). Even though 

surface-water and groundwater divides may not coincide 

in transmissive materials, estimates of water available for 

recharge in watersheds when compared to pumping rates 

provide insights into the hydrology. A recharge rate of 29 in/yr 

over the Mink Brook watershed (1.82 mi2) is equivalent 

to 3.9 ft3/s or 1,750 gal/min. The total average well field 

withdrawal rate of 2,138 gal/min and the total maximum 

well field withdrawal rate of 5,100 gal/min exceed the water 

potentially available in this small watershed; therefore, for the 

steady-state model simulations, the well fields must derive part 

of their pumped water from outside Mink Brook watershed. If 

Alewife Brook watershed (2.08 mi2), which shares a nearby 

common boundary in transmissive stratified deposits with 

Mink Brook watershed, is included in the calculation, the total 

water available is 8.3 ft3/s or 3,730 gal/min. The total average 

well field withdrawal rate is about 60 percent of the water 

available for these two watersheds. To sustain withdrawals 

at the maximum pumping rate scenario, sources of water 

outside of these two watersheds must be withdrawn from the 

well fields.

Streams, wetlands, and ponds are potential sources 

of water to the well fields through natural infiltration, 

induced infiltration caused by pumping, or both. Streamflow 

measurements at five partial-record sites and water levels at 

two wetland-piezometer sites provide insights into surfacewater and groundwater interactions in the Mink Brook 

watershed (fig. 3). 
12 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island EXPLANATION Peat Sand and gravel Sand Fines Till BedrockVERTICAL EXAGGERATION X 20 200 100

0

-100-200

ALTITUDE, IN FEET RELATIVE TO NGVD29

SNW 869

SNW 870

SNW 895

PW6

PW5 (projected)

PW7

PW3

PW2

PW4

BEND IN SECTION

PW1

East West

Worden Pond

Screened well, and number

Well or borehole, and number

A A’

250 500 METERS

2,000 FEET 0

0

1,000

Figure 4. Geologic cross section, South Kingstown study site, southern Rhode Island.
South Kingstown Study Site 13

A set of instantaneous streamflow measurements was 

made on June 15, 2007, near mean annual streamflow and 

groundwater-level conditions (figs. 5 and 6). Small southwardflowing tributaries to Mink Brook drain a hillslope before 

entering the valley, which is underlain by thick wetland 

deposits. Limited field observations in this densely vegetated 

part of the wetland indicated small, separate pools of surface 

water but no visible channels entering Mink Brook from 

the north, in contrast to the stream network delineated 

at the 1:5,000 scale. Flow in three streams near the base 

of this hillslope ranged from 0.01 to 0.03 ft3/s, totaling 

0.05 ft3/s or 22 gal/min. This streamflow most likely infiltrates 

the groundwater system in the valley because shallow peat 

generally consists of recent, slightly decomposed permeable 

deposits. Streamflow measurements made at culverts in 

the main stem of Mink Brook between the well fields and 

downstream of the west well field indicated a slight net loss of 

0.04 ft3/s (18 gal/min), which was within the accuracy of the 

measurements. Infiltration, evapotranspiration, measurement 

error, or any combination of these may cause this loss.

Groundwater and surface-water levels were measured 

at a vertical nest of piezometers installed in the peat and in 

the underlying stratified deposits in the vicinity of each well 

field. Peat and organic-rich sediment are 6 ft thick at each 

wetland-piezometer site. A small-diameter piezometer with 

0.5-ft-length screen was installed near the middle of the peat, 

and a piezometer with a 3-ft-length screen was installed 3 to 

6 ft beneath the peat in the sand and gravel deposits at each 

site. The wetland-piezometer site near the west well field was 

installed in the channel of Mink Brook 500 ft from PW5, 

whereas the wetland-piezometer site near the east well field 

was installed in a wetland with no defined channel 200 ft 

from PW2. Water levels were measured periodically from 

November 2006 to October 2008, most of them between 

April 2007 and October 2008, either manually or by a 

recorder at 30-minute intervals (fig. 7). The production wells 

were operated on a varied pumping schedule. Well-field 

withdrawals were highest during the summer months, a period 

of generally minimal recharge from precipitation.

Water levels and field observations indicated that surface 

water in Mink Brook and in wetlands was intermittent under 

the climatic and pumping conditions during 2006–2008. 

Groundwater levels and streamflows in southern Rhode Island 

were below monthly normals (in the lowest 25 percentile of 

long-term monthly data) during August 2007 to January 2008 

(U.S. Geological Survey, 2008). Mink Brook ceased to flow 

and wetlands ceased to be covered with water beginning in 

midsummer; for 2007 and 2008, the cessation continued into 

the fall, and for 2008, persisted most of the winter. As water 

levels continued to drop, the peat became dry by late summer. 

Annual water-level fluctuations in the sand and gravel deposits 

were about 10 ft, which compared with variations of 5 to 6 ft 

at USGS long-term observation wells (CHW18 and SNW6; 

fig. 1) that are not influenced by pumping. A comparison of 

surface-water and groundwater levels indicates a generally 

downward vertical gradient and the potential for surface water 

in the wetlands and groundwater in the peat to infiltrate the 

underlying aquifer. Water levels at the wetland-piezometer site 

near the west well field indicated a downward gradient except 

for the April 2007 measurement, which was made after two 

days of no pumping at the west well field. Groundwater levels 

in the sand and gravel at this site showed minimal response 

to cycles of on-and-off pumping because of the distance 

between the piezometer site and the production wells. Because 

the wetland-piezometer site near the east well field is closer 

to pumping wells, groundwater levels in the sand and gravel 

respond to the cyclical nature of the well-field operation, 

including reversals of the vertical gradient.

Water levels at the wetland-piezometer site near 

the east well field during a period of prolonged pumping 

(March 14–April 3, 2008) (figs. 7B and 8) were analyzed 

to determine hydraulic properties at the well-field site, 

specifically the vertical hydraulic conductivity of peat, 

which controls vertical flow between the wetlands and 

the aquifer. PW2 and PW4 were pumped at a combined 

rate of 1,350 gal/min for 90 percent of this 20-day, 3-hour 

period; the average withdrawal rate during this period was 

equivalent to 1,220 gal/min. This prolonged pumping period 

was preceded by 24 hours of no pumping, during which 

water levels returned to an upward gradient before pumping 

commenced again.

Water-level drawdown in the sand and gravel piezometer 

was analyzed by means of an analytical method described by 

Hantush and Jacob (1955) and by Hantush (1956) for leaky 

aquifers. The analytical method includes several simplifying 

assumptions, such as horizontal flow in the sand and gravel 

aquifer, vertical flow through the semi-confining layer (peat), 

constant water level in the layer supplying leakage (surface 

water in the wetlands), and homogenous hydraulic properties 

in individual layers (sand and gravel, peat, and surface water). 

This method also assumes no release of water from storage 

in the peat. Water-level trends were assumed negligible 

during the aquifer test. This assumption was supported by a 

leveling of trends in the peat piezometer before and during the 

aquifer test and general trends in the sand and gravel parallel 

trends in the peat (fig. 7B). Because of these simplifying 

assumptions and because pumping was not continuous, 

the analytical solution provides only a rough estimate of 

hydraulic properties.

Curve matching showed that the shape of the drawdown 

curve from the sand and gravel deviated from the Theis 

(1935) type curve, thereby indicating vertical leakage from 

the wetlands (fig. 8). Transmissivity of the sand and gravel 

and vertical hydraulic conductivity of the peat were calculated 

from the drawdown curve and a leaky aquifer type curve 

(fig. 8). A calculated transmissivity value of 18,900 ft2/d is 

within the range of transmissivity values that Allen and others 

(1966) determined at the well field. The vertical hydraulic 

conductivity of peat, which uses the transmissivity value in its 

estimate, was calculated as 0.01 ft/d. This vertical hydraulic 

conductivity value determined from the drawdown data was 

comparable to a hydraulic conductivity value of 0.3 ft/d for 
14 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

the peat, which had been determined from a relation between 

hydraulic conductivity and 20 samples tested for bulk density 

in southwest Rhode Island (Friesz, 2004).

Worden Pond is also a potential source of water to the 

well fields, especially in the maximum pumping rate scenario. 

Worden Pond is a shallow (mean depth 4 ft; Guthrie and 

Stolgitis, 1977) but large (surface area 1.7 mi2) pond. Chipuxet 

River enters the pond in the northeast and the river outlet is 

in the west; numerous small streams flow into the pond in 

the south and east. At the Chipuxet River streamgage, 2.3 mi. 

north of Worden Pond, mean annual streamflow is 21.8 ft3/s 

(U.S. Geological Survey, 2007). On the basis of streamflow 

characteristics at this streamgage, mean annual streamflow of 

the Chipuxet River at its confluence with White Horn Brook 

a mile north of Worden Pond is estimated to be 34 ft3/s. This 

flow rate, which does not include all water that enters Worden 

Pond, is three times the combined maximum pumping rate for 

the two well fields, 5,100 gal/min or 11.4 ft3/s.

Simulation of Groundwater Flow and Areas 

Contributing Recharge

The groundwater-flow model for the South Kingstown 

study site was designed to simulate long-term, steady-state 

groundwater levels, flow paths, and traveltimes. The model 

was calibrated to 2003–07 average annual pumping conditions 

based on historical observations and on observations made 

during this study. Deterministic areas contributing recharge to 

the well fields for different pumping-rate scenarios are based 

on the optimal set of parameters. An uncertainty analysis 

provided insights into the effects of the uncertainty in these 

estimated parameter values on the delineated contributing 

area to the well fields. Wastewater return flow through private 

septic systems was not simulated in the model. Simulated 

contributing areas to the well fields, however, are mostly in the 

rural, residential area of the Chipuxet River watershed where 

total return flow is minimal. The areas contributing recharge 

to the well fields, therefore, represent slightly larger, more 

conservative areas than if return flow had been included in 

the model.

Model Extent and Spatial Discretization

Groundwater flow in the surficial deposits and the 

underlying bedrock was simulated by a five-layer numerical 

model with a uniformly spaced finite-difference grid. The 

model extended to natural hydrologic boundaries beyond 

the likely area contributing recharge to the well fields. This 

extent also allowed the location of the simulated groundwater 

divides near the well fields to shift, depending on the hydraulic 

properties, recharge rates, and pumping rates used in the 

model. The lateral model boundaries included streams in 

the north and northeast (Chipuxet River and its tributaries 

Genesee and White Horn Brooks, Saugatucket River, and an 

unnamed tributary), Block Island Sound and numerous coastal 

ponds in the southeast and south (Point Judith, Potter, Card, 

Trustom, and Green Hill Ponds), and in the west, presumed 

groundwater divides in the till uplands and small areas of 

stratified deposits and a segment drawn from Factory Pond 

northward where groundwater flow is assumed to be parallel. 

The active model represented an area of 29.2 mi2, consisted 

of 263 rows and 209 columns, and included a total of 

180,710 cells with each 150 ft on a side.

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

100

101

102

103

DAILY MEAN DISCHARGE,

IN CUBIC FEET PER SECOND

Beaver River near Usquepaug, Rhode Island (01117468)

Mean streamflow for years 1975–2008

Date of streamflow observation

EXPLANATION

Figure 5. Streamflow for the Beaver River streamgage (01117468) near Usquepaug, Rhode 

Island, during 1999–2008 (streamgage location shown on figure 1).
South Kingstown Study Site 15

25

23

21

19

17

15

13

11

Mean water level for years 1946–2008

1951 1952 1953 1954

1988 1989 1990 1991 1992

1955 1956 1957 1958 1959 1960

25

23

21

19

17

15

13

11

WATER LEVEL, IN FEET BELOW LAND SURFACE

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

25

23

21

19

17

15

13

11

Observation period or day

CHW18

YEAR

EXPLANATION

Figure 6. Water levels measured in observation well CHW18 during 1951–60, 1988–92, and 1999–2008, 

Charlestown, Rhode Island (well location shown in figure 1).
16 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

EXPLANATION

Surface water drySurface water drySurface water dry and peatwater level below screenSurface water dry and peat water level below screenSurface water drySurface water drySurface water dry and peatwater level below screenSurface water dry

Wetland piezometer site near west well field

81

82

83

84

85

86

87

88

89

90

91

92

93

WATER LEVELS, IN FEET RELATIVE TO NGVD 29

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

2007–2008

Surface water

Sand and gravel piezometer

Peat piezometer

Altitude of screened interval,

in feet relative to NGVD 29 Depth of screen interval below top of peat, in feet

80.23−77.23

85.31−84.81

9−12, in sand and gravel, or 3−6 below peat layer

3.9−4.4, in peat

Dry

A

Figure 7. Stage of wetland and water levels in piezometers screened in peat, and in sand and gravel near 

A, west well field and B, east well field, 2007–2008, South Kingstown study site, southern Rhode Island.
South Kingstown Study Site 17

EXPLANATION

Wetland piezometer site near east well field

Altitude of screened interval,

in feet relative to NGVD 29 Depth of screen interval below top of peat, in feet

B

Surface water dry

Surface water dry and peat water level below screenSurface water dry and peat

Surface water dry and peat water level below screen

water level below screen

Surface water dry and peat water level below screen

Surface water dry

Surface water dry and peat water level below screen

85

86

87

88

89

90

91

92

93

94

95

96

97

WATER LEVELS, IN FEET RELATIVE TO NGVD 29

2007–2008

Surface water

Sand and gravel piezometer

Peat piezometer 2.5−3.0, in peat

85.86−82.86

91.98−91.48

9−12, in sand and gravel, or 3−6 below peat layer

Dry

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

Figure 7. Stage of wetland and water levels in piezometers screened in peat, and in sand and gravel near 

A, west well field and B, east well field, 2007–2008, South Kingstown study site, southern Rhode Island.—Continued
18 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Theis type curve

Leaky-aquifer type curve

r/

B = 0.1

0.01

0.10

1.00

10.00

10 100 1,000 10,000 100,000

DRAWDOWN, IN FEET BELOW INITIAL WATER LEVEL

TIME SINCE START OF PUMPING, IN MINUTES

T =

K’ =

K’ = Vertical hydraulic conductivity of peat, in feet per day (ft/d)

b’ = Thickness of peat, in feet (ft)

r/B = Leaky-aquifer type curve

r = Average distance from pumping wells to piezometer, in feet (ft)

 =

T = Transmissivity of sand and gravel, in feet squared per day (ft2

/d)

Q = Average pumping rate, in gallons per minute (gal/min)

ho-h = Drawdown, in feet (ft)

W (u, r/B) = Leaky well function

15.3 Q

ho-h

(15.3) (1,220 gal/min) (1)

0.99 ft

W (u, r/B) = 1 

18,900 ft2

/d

0.015 ft/d

Tb’ (r/B)

2

r

2

(18,900 ft2/d) (6 ft) (0.12)2

(330 ft)2

Measured drawdown

Leaky-aquifer type curve

Theis type curve

EXPLANATION

1/u = 1

Drawdown = 0.99 feet

Time = 40 minutes

Match point

W (u, r/B) =

Figure 8. Plot of drawdown with time compared to a Theis type curve and a leaky-aquifer type curve for a piezometer screened 

beneath the wetland near the east well field, March14–April 3, 2008, South Kingstown study site, southern Rhode Island.
South Kingstown Study Site 19

Model layers were simulated by using a fixed 

transmissivity, including layer 1, the top layer. The model was 

first set up by representing surficial deposits in one layer (the 

top layer) and bedrock in a second layer (the bottom layer). 

The unevenness of the bedrock surface (fig. 2) resulted in 

surficial deposits of variable thickness. The top of the model 

grid, which is used to determine transmissivity of the top 

layer, was initially set at land-surface altitude. The top of the 

model grid was reset by running the basic model, temporarily 

adjusting hydraulic properties until the simulated water table 

compared favorably to available water levels and land-surface 

altitudes, and then the simulated water-table altitude was 

used as the top of the model in subsequent simulations. The 

top layer was then subdivided into four layers (layers 1 to 4) 

based on surface-water features, lithology, and placements of 

the production well screens. Layer 1 is generally 2 ft thick to 

represent surface water in the ponds and wetlands, and layer 2 

is generally 5 ft thick to represent peat deposits. Organic-rich 

pond-bottom sediments are 3 ft thick for Worden Pond and 1 ft 

thick for ponds elsewhere. Layers 3 and 4 represented 40 and 

60 percent of the remaining deposits; the production wells are 

screened in layer 4. Stratified deposits, till, and the moraine 

are represented in all four layers. Shallow bedrock areas less 

than 8 ft from the top of the model were incorporated into 

surrounding surficial materials. The bottom layer (now layer 5) 

represented bedrock with a constant thickness of 200 ft.

Boundary Conditions and Model Parameters

Several types of boundary conditions were specified 

in the model to represent areas of discharge and sources of 

recharge (fig. 9). Stream-aquifer interactions were simulated 

as head-dependent flux boundaries in layer 1 primarily by 

using the stream-routing package (Prudic, 1989) developed 

for MODFLOW. The stream-routing package accounts 

for gains and losses of water in each stream cell, and it 

routes streamflow from upstream cells to downstream cells. 

Streamflow loss to the aquifer, either naturally or from 

infiltration induced by pumping, would cease if simulated 

streamflow also ceases. Some streams that define the perimeter 

of the model were simulated by using the MODFLOW drain 

package, which only allows for a gain of water in the drain 

cell. Streams that flow into and out of ponds, except Worden 

Pond, were simulated as flowing through these water bodies. 

The model contained a total of 1,148 stream-routing cells and 

243 drain cells. Surface-water altitudes for the head-dependent 

flux boundaries were determined from, or interpolated 

between, topographical contours intersecting streams and 

from pond altitudes listed on the USGS Kingston quadrangle. 

In addition, stage measurements made during this study on 

June 15, 2007, at seven stream and pond sites in Mink and 

Alewife Brooks and Worden and Tucker Ponds were used 

(fig. 3). Water depths and bed thicknesses of 1 ft were used to 

determine the top and bottom bed altitudes from surface-water 

altitudes. Simulated streams were assigned 10-ft widths and 

150-ft lengths, which is the model cell dimension.

Most streambed materials were assumed to consist of 

coarse-grained sediments. Field observations and manual 

probing with a steel rod indicated that bed materials in 

Mink Brook consisted of peat deposits; a vertical hydraulic 

conductivity of one-tenth the value of that of the other streams 

was therefore used. For this study, a dimensionless parameter 

(SB_MULT) was defined that multiplied the vertical hydraulic 

conductivity of the streams that the stream-routing package 

simulated. A dimensionless multiplier of 1 is equivalent 

to 1 ft/d for bed materials of sediment and 0.1 ft/d for bed 

materials of peat. A parameter value of 1 would also be 

equivalent to conductances of 1,500 ft2/d and 150 ft2/d for 

bed materials of sediment and peat, respectively. The final 

drain conductance was set equivalent to the stream-routing 

conductance calculated by parameter estimation.

A constant-head boundary was used to simulate large 

bodies of surface water such as Block Island Sound, coastal 

ponds that are connected to the Sound, and Worden Pond. 

The stage of Block Island Sound and the coastal ponds was 

assumed to be 0 ft NGVD29, and the stage of Worden Pond 

was 90.3 ft NGVD29 as measured June 15, 2007. Organicrich deposits beneath Worden Pond were simulated as a 

3-ft-thick layer based on the average thickness determined 

from coring (Boothroyd and others, 1998). By using a constant 

head for Worden Pond and a 3-ft-thick layer to represent peat 

deposits beneath the pond, a single parameter could be used 

to represent peat throughout the model. The head-dependent 

river boundary with a 3-ft bed thickness showed similar model 

results. The model contained 3,050 constant-head cells. 

Recharge parameters were distributed based on surficial 

geology and on surface-water features (table 2). Recharge 

values used in the model are effective rates, which account for 

the effects of groundwater evapotranspiration. One recharge 

parameter represented both the stratified deposits and the 

morainal deposits (R_SDM); conceptually, recharge rates 

should be similar for both surficial materials because the 

morainal deposits consist of permeable materials. A second 

recharge parameter was defined for upland till (R_TILL). 

Any surface runoff from till hillslopes that may recharge 

permeable stratified and morainal deposits at the upland-valley 

contact was not included in model simulations. Hillslope 

runoff is most likely not a major component of recharge in 

the study site compared with other valley-fill settings because 

of the size of the valley in comparison to the size of the 

upland area. A recharge parameter was also defined for the 

wetlands (R_WETLD). Conceptually, this recharge parameter 

represents water available for recharge. Some or all of this 

water may infiltrate, particularly under pumping conditions, or 

it may move across the surface as overland flow. R_WETLD 

was therefore set at a fixed value for model calibration, but 

the uncertainty in the specified value was included in the 

probabilistic contributing area analysis. Pond recharge, which 

was specified for all model simulations, was important only 

for the small ponds because constant heads were used to 

simulate the large ponds. The same value of 22 in/yr was 

applied to pond water and to wetland areas by subtracting 
20 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

K_MIX

71°36' 71°34' 71°32' 71°30'

41°28'

41°26'

41°24'

41°22'

East well field

West well field

Tucker Pond

Chipuxet River

Mink Brook

Alewife Brook

Block Island Sound

Great Swamp

Management Area

White Horn Brook

Genesee Brook

Factory Pond

Saugatucket River

Point Judith Pond

Potter Pond

Card Pond

Trustom Pond

Green Hill Pond

White Pond

Narragansett

South Kingstown

Charlestown

Worden Pond

EXPLANATION

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

Sand and gravel operation

Production well

Constant-head cell

Drain cell

Stream cell

Model boundary

K_MIX Model parameter representing 

horizontal hydraulic conductivity of

stratified, morainal, and till deposits 

northeast of well fields

Water-level observations

Group A

Group B

Group C

Streamflow partial-record site

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

0 .5 1 KILOMETER

0 .5 1 MILE 

Figure 9. Model-boundary types and observations, South Kingstown study site, southern Rhode Island.
South Kingstown Study Site 21

Table 2. Definition of model parameters, optimal parameter value or specified value, and parameter-estimation statistics for the South Kingstown study site, southern Rhode Island.[ft/d, feet per day; in/yr, inches per year; --, dimensionless or not applicable; optimal value (bold); specified value (italics)]

Parameter 

name Parameter description Units

Value 

(optimal or 

specified)

95-percent confidence interval - 

Optimal value or specified value

Coefficient of 

variation 

(dimensionless)

Reported ranges for selected 

parameters Lower value Upper value

SB_MULT Multiplier of streambed vertical hydraulic conductivity 

(X 0.1 ft/d & 1 ft/d for peat and coarse sediments)

-- 1.8 1.0–3.1 0.30 0.1–17

R_SDM Recharge rate on stratified and morainal deposits in/yr 29.0 25.8–32.0 0.05 26–33R_TILL Recharge rate on till deposits in/yr 23.1 19.8–26.4 0.07 9–33R_WETLD Water available for recharge rate on wetlands in/yr 22 10.1–33.8 -- 11–30K_SDN Horizontal hydraulic conductivity of coarse stratified deposits 

north of Charlestown Moraine

ft/d 137 110–170 0.11 50–500

K_SDL Horizontal hydraulic conductivity of lacustrine deposits ft/d 20 -- -- --K_SDS Horizontal hydraulic conductivity of coarse stratified deposits 

south of Charlestown Moraine

ft/d 332 240–460 0.17 50–500

K_TILL1 Horizontal hydraulic conductivity of till deposits south of 

Charlestown Moraine

ft/d 7.9 5.5–11.4 0.19 0.004–65

K_TILL2 Horizontal hydraulic conductivity of till deposits north of 

Charlestown Moraine

ft/d 3.8 2.4–5.9 0.23 0.004–65

K_MOR Horizontal hydraulic conductivity of Charlestown and 

Point Judith Moraine

ft/d 16 12–19 0.11 0.1–30

K_MIX Horizontal hydraulic conductivity of stratified, morainal, and 

till deposits northeast of well fields

ft/d 26 22–29 0.07 0.004–500

K_WETLD Horizontal hydraulic conductivity of surface water in wetlands 

and top of peat deposits

ft/d 1,000 and 20,000 -- -- --

K_ROCK Horizontal hydraulic conductivity of bedrock ft/d 0.1 -- -- --KV_SD Ratio of horizontal to vertical hydraulic conductivity of 

stratified deposits

-- 10 -- -- --

KV_TILL Ratio of horizontal to vertical hydraulic conductivity of till 

deposits

-- 10 -- -- --

KV_MOR Ratio of horizontal to vertical hydraulic conductivity of 

morainal deposits

-- 10 -- -- --

KV_PEAT Ratio of horizontal to vertical hydraulic conductivity of peat 

deposits (or in relation to horizontal hydraulic conductivity of 1 ft/d)

-- 10 153–0.66 (0.006–1.5 ft/d) -- (<0.03–>4 ft/d)

KV_ROCK Ratio of horizontal to vertical hydraulic conductivity of bedrock -- 1 -- -- --
22 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

the evaporation rate from a free-water surface (29 in/yr) 

(Farnsworth and others, 1982) from the rate of precipitation 

for southern Rhode Island (51 in/yr).

Hydraulic conductivity parameters were assigned 

on the basis of lithology (table 2). Initially, the horizontal 

hydraulic conductivity of the stratified deposits was 

represented by three parameters: K_SDN, K_SDL, and 

K_SDS. K_SDN represented most of the stratified deposits 

north of the Charlestown Moraine and included the well 

fields. K_SDL represented the remaining stratified deposits 

north of the moraine, lacustrine deposits at depth (layer 4) 

beneath Worden Pond and Great Swamp. K_SDS was the 

stratified deposits south of the Charlestown Moraine, much 

of which is coarse-grained sediments. Initially, till and 

morainal deposits were represented by parameters K_TILL1 

and K_MOR1, respectively. Manual calibration and initial 

parameter-estimation results indicated that glacial deposits 

in the northeast part of the model—undifferentiated morainal 

deposits, till northeast of the east well field, and a small area 

of stratified deposits northeast of these morainal and till 

deposits (fig. 9)—had different transmissive characteristics 

than other areas represented by their respective parameters. 

The extent of the undifferentiated morainal deposits is not 

well known and may include areas of stratified deposits (Janet 

Stone, USGS, oral commun., 2007). In addition few data 

were available to define the bedrock surface in this part of the 

model. The bedrock-surface altitude also varied substantially 

between data points when assigning model cell values. These 

three areas were subdivided into additional parameters, and 

because optimal values and associated confidence intervals 

determined by parameter estimation resulted in similar values, 

these three small areas were combined into one parameter 

(K_MIX) (fig. 9). Finally, initial model simulations indicated 

that remaining till north of the Charlestown Moraine would 

more accurately be represented by subdividing it (K_TILL2) 

from till south of the moraine.

Horizontal hydraulic conductivity of bedrock was 

represented by parameter K_ROCK, and wetlands were 

defined by parameter K_WETLD. Conceptually, K_WETLD 

can represent overland flow in the wetlands and groundwater 

flow through any large interconnected pores in poorly 

decomposed peat in the top part of the peat. Model cells 

containing freshwater ponds, excluding Worden Pond, were 

assigned a high hydraulic conductivity value of 50,000 ft/d to 

simulate the flat gradient across these water bodies.

The ratio of horizontal hydraulic conductivity to vertical 

hydraulic conductivity for stratified deposits, morainal 

deposits, till, bedrock, and peat was each represented by one 

parameter, KV_SD, KV_MOR, KV_TILL, KV_ROCK, and 

KV_PEAT, respectively. The horizontal hydraulic conductivity 

of peat was held constant in the model at 1 ft/d; the ratio 

is therefore always in relation to this value. KV_PEAT 

represented the medium and highly decomposed peat at depth 

that controls the connection between the wetland and the 

underlying aquifer.

Observations

The groundwater-flow model was calibrated to 135 

water-level observations and 5 streamflow observations. 

Observations were weighted based on methods described 

by Hill and Tiedeman (2007); the weights account for 

measurement error and for the difference in units as between 

water levels and streamflows. More accurate observations 

are given larger weights than less accurate observations, and 

thus have more influence in the regression and estimating 

parameters. Observation weights are equal to the inverse 

of the variance (square of the standard deviation) of the 

measurement. The standard deviation of the measurement 

error is equal to the accuracy of the measurement divided 

by the 95-percent confidence interval (1.96) for a normal 

distribution for surveyed measuring-point altitudes and 

streamflows or divided by the 90 percent confidence interval 

(1.65) for a normal distribution for measuring-point altitudes 

determined from land-surface contours on the USGS 

Kingston quadrangle.

Water-level observations were divided into three groups 

(A, B, and C) depending on their estimated accuracy (fig. 9). 

Group A included two groundwater levels measured on June 

15, 2007, and on March 7, 2008, during this study and four 

groundwater levels made August 20–25, 1959, by Allen and 

others (1963). The water levels measured on March 7, 2008, 

and during August 1959 were at average annual groundwater 

conditions, and the June 15, 2007, water level was near 

average annual groundwater conditions, according to USGS 

long-term observation well CHW18 (fig. 6). Accuracy of 

Group A observations was estimated to be 0.5 ft because 

altitude datums available from two agencies differed and 

because a measuring-point altitude common to this study 

and to Allen and others (1963) also differed. This group of 

water-level observations was generally evenly distributed over 

the north half of the modeled area, and they are screened in 

layer 1 and layer 4.

 Group B included 105 groundwater levels measured 

from July 1954 to February 1955 (Bierschenk, 1956) and 

6 measured from 1957 to 1958 (Allen and others, 1963) 

at various hydrologic conditions (fig. 6). Water levels 

measured in summer and early fall are typically at belowaverage levels. During 5 of 8 months when measurements 

were made during 1954–55, however, water levels at USGS 

long-term observation well CHW18 were within 1 ft of 

long-term average because precipitation had been above 

average during the preceding months. Historical water levels 

from these studies near the well fields were not included in 

model calibration because of increased pumping withdrawals 

since the 1950s; remaining water levels were assumed to be 

unaffected or minimally affected by the increased pumping 

rates. Accuracy of Group B groundwater levels, whose 

measuring-point altitudes were based on land-surface altitude 

determined from the USGS Kingston quadrangle, is about 

5 ft (U.S. Geological Survey, 1980). Because most of these 

groundwater levels were measured in shallow dug wells, 
South Kingstown Study Site 23

they were included in layer 1. In addition to groundwater 

levels, 11 pond altitudes listed on the USGS Kingston 

quadrangle, primarily in the Charlestown Moraine, were 

used in model calibration. These ponds were assumed to be 

in direct hydraulic connection with the surrounding aquifer 

and to represent a surface-water expression of the water table. 

Accuracy of these pond altitudes was also 5 ft.

Group C included seven groundwater levels measured 

at the well-field sites during this study on June 15, 2007, near 

average groundwater conditions (fig. 6). Four water levels are 

from the wetland piezometers—two in the peat (layer 2) and 

two in the stratified deposits (layer 3)—and the remaining 

water levels are from observation wells in layers 3 and 4. In 

addition to discrepancies in elevation that are common with 

Group A water levels, it is unknown how representative Group 

C water levels represent the steady-state pumping conditions, 

measured near pumping wells that cycle off and on, and with 

the spatial discretization used in the model. Accuracy of Group 

C observations was estimated to be 1 ft.

Five streamflow observations were measured on June 15, 

2007, and March 7, 2008, near average streamflow conditions 

(fig. 5). The accuracy of these streamflows is about 10 percent. 

For the Mink Brook observation that represents loss between 

two sites on the main stem, the total variance was determined 

by adding the measurement variances. Four small tributary 

discharges (0.01 to 0.03 ft3/s) were not used in model 

calibration because most of the stream cells upstream of the 

measuring site were simulated as dry cells.

Estimation of Parameters

Model parameters included three for recharge, nine for 

horizontal hydraulic conductivity, five for vertical anisotropy, 

and one for streambed hydraulic conductivity (multiplier of 

streambed conductivity) (table 2). Parameter R_WETLD, 

which represented water available for recharge in the 

wetlands, was specified in the model at the beginning of model 

calibration, but the uncertainty in the parameter value was 

included in the uncertainty analysis.

Parameter sensitivities, shown by their composite scaled 

sensitivities in figure 10, indicate whether water level and 

streamflow observations provided sufficient information to 

estimate a given parameter (Hill and Tiedeman, 2007). In 

addition, parameters with higher sensitivities generally can 

be more precisely estimated than can parameters with lower 

sensitivities. Parameters with composite scaled sensitivities 

that are about two orders of magnitude lower than that of 

the parameter with the highest value indicate that nonlinear 

regression may not be able to estimate the parameter (Hill and 

Tiedeman, 2007). Low sensitivities were associated with all 

the parameters for vertical anisotropy and thus were assigned 

values from the literature. The ratios of horizontal to vertical 

hydraulic conductivity of glacial deposits (KV_SD, KV_TILL, 

PARAMETER NAME

R_SDM

K_MIX

K_MOR

R_TILL

K_SDN

K_SDS

K_TILL1K_TILL2

SB_MULT

K_WETLD

K_ROCK

KV_MOR

KV_SD

KV_PEAT

KV_TILL

K_SDL

KV_ROCK

COMPOSITE SCALED SENSITIVITY

11

10

9

8

7

6

5

4

3

2

1

0

Figure 10. Composite scaled sensitivities for model parameters (parameter information is provided on table 2), South 

Kingstown study site, southern Rhode Island.
24 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

KV_MOR) and of peat (KV_PEAT) were set to 10; because 

the horizontal hydraulic conductivity of peat was set to 1 ft/d, 

the resulting vertical hydraulic conductivity was equivalent 

to 0.1 ft/d, which lies between peat values determined from 

field measurements in southern Rhode Island. KV_ROCK was 

specified a ratio of 1. Low sensitivities were also associated 

with three of the parameters for horizontal hydraulic 

conductivity (K_SDL, K_ROCK, and K_WETLD). K_SDL 

was set to 20 ft/d, representative of very fine sand sediments, 

and K_ROCK was set to a low value of 0.1 ft/d. The wetlands 

were subdivided into two areas. Great Swamp was set to 

20,000 ft/d based on manual calibration so as to flatten the 

hydraulic gradient across this wetland. The remaining smaller 

wetland areas were fixed at 1,000 ft/d, a value at the low end 

of a range of hydraulic conductivities that Masterson and 

others (2007) determined by manual calibration for wetlands 

in southern Rhode Island. Conceptually, Great Swamp 

may have more open water and less resistance to flow than 

smaller wetland areas. None of the remaining nine recharge 

and hydraulic parameters was highly correlated (parameter 

correlation coefficient greater than 0.95), and thus these 

parameters were estimated by nonlinear regression.

The quality of model calibration can be determined 

through analysis of the weighted residuals, both numerically 

and graphically; Hill and Tiedeman (2007) describe this 

analysis in detail. Weighted residuals should be randomly 

distributed and close to zero. The average weighted residual 

was -0.17 ft for the model and ranged from a minimum of 

-9.5 ft to a maximum of 5.9 ft. The sum of squared weighted 

residuals was 696 for the calibrated model. The calculated 

error variance and the standard error of the regression (square 

root of the calculated error variance), which are measures of 

the overall magnitude of the weighted residuals, were 5.32 and 

2.31, respectively; theoretically, these values should be equal 

to one, but commonly that is not the case for groundwater 

models (Hill and Tiedeman, 2007).

Weighted residuals and weighted simulated values for 

both water level and streamflow observations are shown in 

figure 11A. A comparison of weighted residuals indicated that 

residuals are generally evenly distributed above and below a 

value of zero for all weighted simulated values. Furthermore, 

131 of 140 observations are within two standard errors of 

the regression. The relation between weighted observed 

values and weighted simulated values is shown in figure 11B. 

Most values plot near a line with a 1:1 slope; the correlation 

between weighted observed values and weighted simulated 

values was 0.99. The spatial distribution of weighted water 

level and streamflow residuals is shown in figure 12. Weighted 

residuals are generally distributed randomly throughout most 

of the modeled area. In the southeast part of the modeled area, 

however, there are areas with clusters of negative residuals 

(simulated water levels are greater than observed water levels) 

near boundaries represented by a constant head of zero feet. 

Insights into observations most important to the 

parameter estimates were calculated from influence statistics 

Cook’s D and DFBeta using the RESAN-2000 program 

(Hill and others, 2000). Observations with the most overall 

influence in the regression and the resulting set of estimated 

parameters were determined from Cook’s D statistics. Thirteen 

observations (9 water levels and 4 streamflows) had a Cook’s 

D value greater than the critical value of 0.028 (4 divided by 

the number of observations); these influential observations are 

shown in figure 12. The observations with the most overall 

influence in the parameter estimation are generally distributed 

throughout the northern half of the model, which is the area 

of greatest interest. Four of the five streamflow observations 

were considered influential, thus indicating the importance of 

streamflows in model calibration. The Mink Brook seepage 

observation, although important to a few individual estimated 

parameters according to DFBeta statistics, was not among the 

13 most influential observations. Because the accuracy of the 

Mink Brook streamflow measurements was small compared to 

the measured loss, the weight on this seepage observation was 

small and thus did not affect the regression as much as did the 

other streamflow observations.

Optimal values for the nine recharge and hydraulic 

parameters that were estimated using nonlinear regression are 

listed in table 2. The optimal values are within the range of 

values reported in the literature, as discussed in the sections 

“Hydraulic Properties” and “Recharge Rates.” Recharge to 

stratified deposits and morainal deposits (R_SDM), 29.0 in/yr, 

is within the range of mean annual runoff rates determined 

from long-term USGS streamgages in southern Rhode Island. 

Recharge to till uplands (R_TILL), 23.1 in/yr, is within the 

range of recharge rates from till-dominated watersheds in 

southern New England, as calculated from computerized 

hydrograph-separation methods. Parameter K_SD1 represents 

most stratified deposits north of the Charlestown Moraine and 

is close to the median value determined from aquifer tests at 

the east well field. Optimal values for the remaining horizontal 

hydraulic conductivities are close to expected values, except 

for K_MIX, which represents undifferentiated morainal 

deposits, till, and stratified deposits in the northeast part of 

the model. The optimal value of 26 ft/d is at the high end of 

the acceptable range for till, and indicated additional data to 

define the bedrock surface may be needed to more accurately 

simulate this area. The dimensionless multiplier of streambed 

vertical hydraulic conductivity, SB_MULT, is equivalent to 

1.8 ft/d for coarse-grained bed sediments and to 0.18 ft/d for 

Mink Brook organic-rich bed sediments.

The precision or uncertainty of the parameter estimate is 

indicated by the 95-percent linear confidence interval for each 

optimal value (table 2). For these linear confidence intervals 

to be valid, weighted residuals should be normally distributed 

and the model linear near the estimated optimal values (Hill 

and Tiedeman, 2007). If weighted residuals are independent 

and normally distributed, they plot on an approximately 

straight line on a normal probability graph. The correlation 

between weighted residuals and the normal order statistics 

for the calibrated model was 0.962. This value is less than 

the critical value for 140 observations, 0.981, at the 5 percent 

significance level. Weighted residuals can be normally 
South Kingstown Study Site 25

WEIGHTED RESIDUAL, (2.31 EQUALS STANDARD

ERROR OF THE REGRESSION)

WEIGHTED SIMULATED EQUIVALENT

0 50 100 150 200 250 300 350 400

WEIGHTED OBSERV

ATION

400

350

300

250

200

150

100

50

-50

0

B (1 point at 533.0, 534.6)

Water-level observation

Streamflow observation

0 50 100 150 200 250 300 350 400 450 500 550

6.92

4.61

2.31

0

-2.31

-4.61

-6.92

-9.22

A

Water-level observation

Streamflow observation

-11.53

Figure 11. Relation of A, weighted residual to weighted simulated equivalent and of B, weighted observation to weighted 

simulated equivalent, South Kingstown study site, southern Rhode Island.
26 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

50

35

65

80

95

125

140

155

110

110

155

110

125

20

95

155

5

125

95

110

95

125

110

95

95

125

5

140

140

110

20

65

50

35

95

80

71°36' 71°34' 71°32' 71°30'

41°28'

41°26'

41°24'

41°22'

East well field

West well field

Worden Pond

Tucker Pond

Chipuxet River

Mink Brook

Alewife Brook

Block Island Sound

Great Swamp

Management Area

White Horn Brook

Genesee Brook

Factory

Pond

Saugatucket River

Point Judith Pond

Potter Pond

Card Pond

Trustom

Pond

Green Hill

Pond

White Pond

Narragansett

South Kingstown

Charlestown

EXPLANATION

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

Sand and gravel operation

Production well

Weighted residual

-9.50 to -3.00

-2.99 to -1.50

-1.49 to 0.00

0.01 to 1.50

1.51 to 3.00

3.01 to 5.91

Cook's D > critical value

Model boundary

Simulated water table—contour interval is 15 feet

5

0 .5 1 KILOMETER

0 .5 1 MILE 

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

Figure 12. Spatial distribution of weighted residuals and simulated water-table contours for calibrated, steadystate conditions, South Kingstown study site, southern Rhode Island.
South Kingstown Study Site 27

distributed, but they are correlated because of the fitting of 

the regression (Hill and Tiedeman, 2007). Weighted residuals 

can be compared to sets of randomly generated weighted 

residuals with the same degree of correlation as expected for 

the model using the RESAN-2000 program (Hill and others, 

2000). The calibrated model did produce weighted residuals 

that are normally distributed based on this comparison with 

the generated residuals. The degree of model linearity can be 

quantified using the modified Beale’s measure, calculated with 

the BEALE-2000 program (Hill and others, 2000). The model 

is considered effectively linear if the modified Beale’s measure 

is less than 0.046 and nonlinear if it is greater than 0.51. 

The modified Beale’s measure for the model was 0.249 and 

indicated that the model is moderately linear. The confidence 

intervals listed in table 2 are thus approximate values.

The 95-percent confidence intervals for the parameter 

estimates are all within the ranges of reasonable values 

reported in the literature. A comparison of the relative 

precision of different parameter estimates can be made using 

the coefficient of variation (standard deviation of the estimate 

divided by the optimal value) (table 2); a smaller coefficient 

of variance indicates a more precisely estimated parameter. 

The coefficient of variations ranged from 0.05 to 0.30. 

Recharge parameters R_SDM and R_TILL and horizontal 

hydraulic conductivity parameter K_MIX, all with coefficient 

of variation values less than 0.1, were the most precisely 

estimated, whereas the streambed multiplier SB_MULT, 

with a coefficient of variation of 0.30, was the least precisely 

estimated. Of the remaining parameters, K_SDN and K_MOR 

were more precisely estimated than K_SDS, K_Till1, and 

K_TILL2. The order of the most to least precisely estimated 

parameter values generally follows the same order as that of 

the parameter sensitivities (fig. 10) because of the information 

provided by the observations in the regression.

Simulated Water-Table Contours and 

Water Budget

The altitude and configuration of the simulated water 

table for the calibrated model are shown in figure 12 at 15-ft 

contour intervals. The simulated water-table contours and 

flow directions are consistent with the conceptual model 

of groundwater flow in the study area and with simplified 

water-table maps drawn by Bierschenk (1956) and Allen and 

others (1966). Groundwater flows from topographically high 

areas and discharges to streams and surface-water bodies. The 

water-table gradient is steepest in the till uplands and morainal 

deposits, and then it flattens in the more transmissive valleyfill areas of stratified deposits and wetlands. In the till uplands 

and morainal deposits, simulated groundwater divides are in 

the general area of topographically defined watershed divides. 

 The simulated groundwater budget for the calibrated 

model indicated that recharge from direct precipitation 

provides 52.4 ft3/s, which constitutes 95 percent of the 

inflow. Streamflow loss accounts for the remaining inflow, 

2.8 ft3/s or 5 percent. Most of this streamflow loss occurs 

near abrupt changes in transmissivity, such as at the contact 

between upland till and stratified deposits. Of the total inflow, 

14.8 ft3/s (27 percent) eventually discharges to streams and 

Worden Pond in the Chipuxet River watershed, and 4.8 ft3/s 

(9 percent) is withdrawn by the UWRI production wells. 

The remaining outflow, 35.6 ft3/s (64 percent) discharges to 

streams, coastal ponds, and Block Island Sound in the South 

Coastal watershed.

Deterministic Areas Contributing Recharge

Simulated deterministic areas contributing recharge 

and groundwater traveltimes to the UWRI well fields were 

determined on the basis of the calibrated steady-state model, 

for simulated pumping conditions, and tracking of pathlines 

with the MODPATH particle-tracking program. The areas 

contributing recharge to the well fields are based on both well 

fields pumping simultaneously. If one of the well fields stops 

pumping, or if withdrawal rates change, then the contributing 

area to the well fields would also change. The locations and 

extents of the simulated areas contributing recharge to each 

well field pumping at the 2003–07 average annual rate and the 

maximum rate (table 1) are shown in figures 13 and 14. The 

total maximum pumping rate for the well fields, 5,100 gal/min, 

is about 2.4 times greater than the 2003–07 average rate of 

2,138 gal/min.

The total area contributing recharge for the average 

pumping rate covers about 2.30 mi2 and includes small 

isolated areas. The contributing area extends to groundwater 

divides in mostly till and morainal deposits north, east, and 

south of the well fields. Most of the sand and gravel mining 

operation between the well fields is in the contributing area 

to the wells. The well fields derive most of their water from 

direct precipitation recharge. A water-balance calculation 

(a comparison of pumping withdrawals to the size of the 

contributing area and recharge rates) indicated that infiltration 

from the narrow streams accounted for about 3 percent of the 

pumped water. Pumping withdrawals reduced groundwater 

discharge and surface water by the amount pumped.

In some areas near simulated streams in Mink and 

Alewife Brook watersheds, including part of the sand and 

gravel mining operation, precipitation recharge discharges 

to streams instead of being captured by the well fields. 

In addition, most of Tucker Pond is not in the simulated 

contributing area because of the method used to simulate 

Alewife Brook. Alewife Brook was simulated flowing through 

Tucker Pond and with a high streambed conductance in 

order to route water to downgradient cells and to minimize 

the gradient across the pond. Because the pond is part of 

the contributing area to the west well field, all areas that 

contribute water to the pond can potentially contribute water 

to this well field.

At the maximum pumping rate, the area contributing 

recharge (5.54 mi2) expands in all directions to capture 

enough water to balance the pumping rate. As was mentioned 
28 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

20

41°28'

41°26'

41°24'

71°36' 71°34' 71°32'

95

110

80

65

80

50

35

20

35

140

35

155

170

110

5

110

155

125

95

110

110

95

95

95

95

125

125

140

95

95

140

110

140

5

155

50

95

110

125

95

125

50

65

65

80

95

20

95

110

80

East well field

West well field

Worden Pond

Tucker Pond

Chipuxet River Mink Brook

Alewife Brook

Great Swamp

Management Area

White Horn Brook

Genesee Brook

Browns Brook

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

Model boundary

Sand and gravel operation Production well

Mink Brook and Alewife Brook

 watershed boundaries

EXPLANATION

Simulated water table—Contour interval is 15 feet

Simulated area contributing recharge to

 United Water Rhode Island east well field

Simulated area contributing recharge to

 United Water Rhode Island west well field

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

0 .5 1 KILOMETER

0 .5 1 MILE 

Figure 13. Simulated areas contributing recharge to the United Water Rhode Island east and west well fields at their total 

average pumping rate of 2,138 gallons per minute, South Kingstown study site, southern Rhode Island.
South Kingstown Study Site 29

80

50

35

95

20

35

110

125

140 155

170

110

155

5

95

110

95

95

65

125

95

125

125

140

95

110

125

110

125

140

140

5

110

110

50

65

20

35

50

65

80

95

65

80

95

110

80

95

110

20

80

35

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

Model boundary

Sand and gravel operation

Production well

Mink Brook and Alewife Brook watershed boundaries

EXPLANATION

Simulated water table—Contour interval is 15 feet

Simulated area contributing recharge to

United Water Rhode Island east well field

Simulated area contributing recharge to

United Water Rhode Island west well field

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

41°24'

41°26'

71°36' 71°34' 71°32'

41°28'

East well field

West

well

field

Worden Pond

Chipuxet River

Great Swamp

Management Area

White Horn Brook

Genesee Brook

Browns Brook

0 .5 1 KILOMETER

0 .5 1 MILE 

Figure 14. Simulated areas contributing recharge to the United Water Rhode Island east and west well fields at their total 

maximum pumping rate of 5,100 gallons per minute, South Kingstown study site, southern Rhode Island.
30 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

previously in the “Hydrology” section, the maximum pumping 

rate exceeds the total water available for recharge in the Mink 

and Alewife watersheds. Thus the well fields intercepted 

most of the precipitation recharge in these watersheds, and 

simulated streams ceased to flow. The entire sand and gravel 

mining operation between the well fields is in the contributing 

area. The maximum pumping rate also shifts the simulated 

groundwater divides and captures groundwater that would 

have discharged to adjacent watersheds under average 

pumping conditions. The contributing area also extends 

beneath and beyond Browns Brook in the South Coastal 

watershed east of the well fields.

The area contributing recharge extends westward or 

downvalley beneath Worden Pond and also includes an 

isolated area remote from the well fields on the opposite side 

and northwest of Worden Pond in upland till. Particle tracks 

indicate that recharge originating in these till uplands travels 

along deep groundwater-flow paths in the stratified deposits 

and, under pumping conditions, passes beneath Worden 

Pond to the west well field. Recharging water between this 

isolated contributing area and Worden Pond travels along 

shallow depth flow paths before discharging to Worden 

Pond. Similarly, particles along the southwest edge of the 

contributing area south of Worden Pond also track beneath 

the pond before discharging to the west well field. Similar to 

Tucker Pond, because Worden Pond is part of the contributing 

area to the west well field, all areas that contribute water 

to the pond can potentially contribute water to this well 

field. The well fields derived most of their water from direct 

precipitation recharge, but about 12 percent of the pumped 

water is from surface water, primarily Worden Pond. This 

surface-water infiltration is about 4 percent of the long-term 

average streamflow calculated for the Chipuxet River at its 

confluence with White Horn Brook.

Simulated traveltime estimates from recharging locations 

to the production wells for the maximum pumping rate 

are shown in figure 15. Estimated traveltimes are based on 

porosities of 0.35 for stratified, till, and morainal deposits; 

0.80 for peat deposits; 0.02 for bedrock; and 1 for surface 

water. Porosity values only affect groundwater velocity and 

do not change the contributing areas to the wells. Traveltimes 

ranged from less than 1 year to more than 500 years; 

59 percent of the traveltimes were 10 years or less, 75 percent 

were 20 years or less, 89 percent were 40 years or less, 

96 percent were 100 years or less, and about 1 percent was 

greater than 500 years. The median traveltime to the east 

well field, screened in shallower sediments and closer to 

groundwater divides than the west well field, was 6.0 years 

or about one-half the median traveltime to the west well 

field, 11 years; traveltimes to both well fields combined had 

a median value of 7.6 years. Water that recharges the aquifer 

near the well fields has the shortest traveltimes, whereas water 

originating in the southwest, in the till uplands northwest 

of Worden Pond, and at the edge of the contributing area 

beneath Worden Pond has the longest traveltimes. The shortest 

traveltimes from the nearest large ponds are 5 years for Tucker 

Pond and 8 years for Worden Pond.

Advantages and disadvantages of using a fixed 

transmissivity for all model layers were summarized in 

the “Numerical Modeling” section. A disadvantage is that 

the simulated transmissivity of the aquifer near the well 

fields does not decrease with increased drawdowns that the 

maximum pumping rates cause. Near the west well field, 

which is in thick sediments near the preglacial-valley axis, the 

difference between the simulated saturated thickness for the 

pumping rate used in the calibrated model and the maximum 

pumping rate was minimal (less than 10 percent), but in the 

vicinity of the east well field, which is near the valley-upland 

contact, saturated thickness decreased from about 70 ft to 

40 ft. Thus, groundwater traveltimes and areas contributing 

recharge to the well field may be different for a model that 

uses fixed transmissivity compared to one that uses variable 

transmissivity. However, if a variable transmissivity model 

had similar drawdowns as the fixed transmissivity model, then 

using a horizontal hydraulic conductivity value of 240 ft/d 

would have a transmissivity equivalent to that of the fixed 

transmissivity model. Although this hydraulic conductivity 

value is greater than the upper 95-percent confidence limit 

estimated by parameter estimation, it is within the range of 

values (100 to 400 ft/d) calculated from aquifer tests at the 

well field. Also, the response of nearby surface-water bodies 

to pumping would probably be the same for either a fixed 

transmissivity or a variable transmissivity because at pumping 

rates as high as the maximum rates, all the groundwater 

was intercepted by the well field before discharging to the 

nearby stream.

Probabilistic Areas Contributing Recharge

The deterministic areas contributing recharge were based 

on estimated and specified parameter values. Parameter values 

were estimated using available observations or they were 

specified from reported values in the literature. Information 

on model parameters is provided in table 2. Different degrees 

of uncertainty are associated with these estimated parameter 

values, and additional observations may increase the precision 

of these estimates. Parameter uncertainty and its associated 

effects on the simulated contributing area can be evaluated by 

a stochastic Monte Carlo analysis. The parameter variance–

covariance matrix from nonlinear regression can be used to 

create plausible parameter sets for the Monte Carlo analysis 

(Starn and others, 2000). The parameter variance–covariance 

matrix captures the uncertainty of the parameter estimates and 

the correlation among parameters from the calibrated model. 

Parameter values for the Monte Carlo analysis were created by 

the following equation (Starn and others, 2000):
South Kingstown Study Site 31

East well field

West well field

Worden Pond

Chipuxet River

Great Swamp

Management Area

White Horn Brook

Genesee Brook

Browns Brook

Simulated traveltimes

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

Model boundary

Sand and gravel operation

Production well

Mink Brook and Alewife Brook

 watershed boundaries

EXPLANATION

Greater than 0 to 1 year

Greater than 1 to 5 years

Greater than 5 to 10 years

Greater than 10 to 20 years

Greater than 20 to 40 years

Greater than 40 to 100 years

Greater than 100 years

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

0 .5 1 KILOMETER

0 .5 1 MILE 

71°36' 71°34' 71°32'

41°28'

41°26'

41°24'

Figure 15. Simulated traveltimes to the United Water Rhode Island well fields at their maximum pumping rate of 5,100 gallons per 

minute, South Kingstown study site, southern Rhode Island.
32 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

b = z σ + μ , (1) 

where 

b is a vector of parameter values,

z is a vector of normally distributed random 

numbers,

σ is the square root of the variance–covariance 

matrix, and

μ is a vector of optimal parameter values.

Parameter values that could not be estimated by nonlinear 

regression and thus were not included in the parameter 

variance–covariance matrix of the calibrated model may still 

be important for model predictions (for this study the size, 

shape, and location of the area contributing recharge to the 

production wells). Previous studies of areas contributing 

recharge to production wells in various glacial valley-fill 

settings in Rhode Island (Friesz, 2004; Friesz and Stone, 2007) 

indicated that recharge rates, the hydraulic connection between 

surface water and the underlying aquifer, and the horizontal 

hydraulic conductivity of the aquifer were the most important 

hydrologic factors that affected the simulated contributing 

area. A sensitivity analysis confirmed that unestimated 

parameters representing anisotropy of glacial deposits and 

bedrock had little or no effect on the simulated contributing 

area to the wells for a plausible range of values. In addition, 

two horizontal hydraulic conductivity parameters, K_SDL and 

K_ROCK, had little or no effect on the simulated contributing 

area. The contributing area did show various degrees of 

sensitivity to different values for R_WETLD and KV_PEAT, 

especially at the maximum pumping rate scenario. These two 

parameters were incorporated into the variance–covariance 

matrix using the specified parameter values; the observations 

provided enough information to constrain the uncertainty 

of these parameters around the specified values within a 

realistic range for these highly variable and poorly understood 

parameters. The lower and upper 95-percent confidence 

intervals were 10.1 and 33.8 in/yr for R_WETLD and 153 

and 0.66 for KV_PEAT (equivalent to vertical hydraulic 

conductivity of 0.006 and 1.5 ft/d for peat) (table 2). Thus, 

all parameter uncertainty important for model prediction was 

incorporated into the Monte Carlo analysis, and the available 

observations constrained this uncertainty.

The parameter sets created by equation 1 are shown 

in figure 16A for hydraulic parameters and in figure 16B 

for recharge parameters. The hydraulic parameters were 

log-transformed in the model. The parameter sets have a 

lognormal or normal distribution around the optimal or 

specified parameter value; the spread of these data indicates 

the certainty with which the parameter could be estimated 

with the available observations. The KV_PEAT has the least 

certainty of the hydraulic parameters, and R_WETLD has 

the least certainty of the recharge parameters. Parameter sets 

with a KV_PEAT value two orders of magnitude greater or 

less than the specified value of 10 (a vertical conductivity 

of 0.1 ft/d for peat) were considered unrealistic for the full 

vertical thickness of the peat layer and were thus removed 

(conditioned) from the parameter sets. This accounted for 

14 percent of the parameter sets.

For the Monte Carlo analysis, the model was run with 

1,000 parameter sets and the average pumping rate. The 

eleven hydraulic and recharge parameter values in each dataset 

replaced corresponding parameter values in the calibrated 

model. Three acceptance criteria were used: (1) model had 

to converge, (2) model mass balance was 0.5 percent or less, 

and (3) calculated error variance was less than a specified 

value. The third acceptance criterion was varied in order to 

evaluate model fit to observations. This model-fit statistic 

was used so that model-prediction uncertainty would not be 

overestimated by using a parameter set having an extremely 

large calculated error variance. Table 3 summarizes the Monte 

Carlo analysis with calculated error variances in increments 

of five. The number of MODFLOW runs and the total size of 

the probabilistic contributing area increased minimally from 

a calculated error variance of 15 to 20, and for this model, 

from 15 to using a water budget as the only criterion. For 

this application of the Monte Carlo analysis, the probabilistic 

contributing area with a calculated error variance of 20 (same 

area as if only using the water budget criterion) was used. Of 

the 1,000 parameter sets run with MODFLOW, 749 fit the 

acceptance criteria. The distribution of hydraulic parameters 

and recharge parameters after the acceptance criteria were 

applied (fig. 17), although slightly altered from the original 

parameter sets, indicated a generally lognormal or normal 

distribution. The probability that a recharge location would 

be in the area contributing recharge to the production wells 

was determined by dividing the number of times a particle at 

a given location was captured by a well by the total number 

of accepted particle-tracking simulations; this probability was 

expressed as a percentage.

The probabilistic contributing area to the production 

wells for the average pumping rate is illustrated in figure 18. 

The total size of the probabilistic contributing area is larger 

than the deterministic contributing area because of the effects 

of parameter uncertainty. Areas with high probabilities (greater 

than 50 percent) generally coincide with the deterministic 

contributing area. Low probabilities indicate that observations 

used in the model calibration are not sufficient for determining 

whether a location is within or outside of the contributing 

area (Starn and others, 2000). Low probabilities are in areas 

distant from the production wells and in areas where simulated 

streams intercepted precipitation recharge in the deterministic 

model. Along margins of the probabilistic contributing area 

north and east of the production wells, there is less spread 

in low probabilities than south of the wells in areas near 

groundwater divides. This is most likely because a change in 

horizontal hydraulic conductivity results in less of a change in 

transmissivity in the thinner surficial deposits north and east 

of the wells than in the southern part of the contributing area, 

which is in and near the main bedrock valley axis. Southwest 

of the wells, a large spread in low probabilities extends to an 

area that was a groundwater mound in the calibrated model; 
South Kingstown Study Site 33

-3 -2 -1 0 1 2 3 4 5

0

1

2

3

4

5

6

K_SDN

K_MIX

K_SDS

K_TILL1

K_TILL2

K_MOR

KV_PEAT

SB_MULT

LOGARITHM OF HYDRAULIC CONDUCTIVITY, IN FEET PER 

DAY, EXCEPT KV_PEAT, WHICH IS DIMENSIONLESS

FREQUENCY OF OCCURENCE

A

5 10 15 20 25 30 35 40 45 50

0.00

0.05

0.10

0.15

0.20

0.25

R_SDM

R_TILL

R_WETLAND

RECHARGE RATE, IN INCHES PER YEAR

FREQUENCY OF OCCURENCE

B

0

Figure 16. Frequency distribution of A, hydraulic parameters, and of B, recharge parameters, before 

acceptance criteria were applied to determine the probabilistic areas contributing recharge to the 

United Water Rhode Island well fields (parameter information is provided on table 2), South Kingstown 

study site, southern Rhode Island.
34 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

the deterministic contributing area in this area corresponded 

to low probabilities including 10 percent or less. The 

probabilistic contributing area indicated that precipitation 

recharge that discharged to streams in the Mink and Alewife 

watersheds in the deterministic model may go directly to a 

well. These areas include some high probabilities. That part 

of the sand and gravel mining operation between the well 

fields that is not in the deterministic contributing area is in the 

probabilistic contributing area including high probabilities.

A second Monte Carlo analysis was done with 

production wells at average pumping rates. This analysis 

included the remaining glacial hydraulic parameters in the 

parameter variance–covariance matrix in order to verify 

that these parameters have little effect on the uncertainty 

analysis. Bedrock parameter values were not changed in 

this analysis. Incorporating parameters representing glacial 

anisotropies (KV_SD, KV_Till, and KV_Mor) and K_SDL 

into the parameter variance–covariance matrix caused large 

unrealistic uncertainties around the specified parameter 

values. Prior information for these parameters (see sections 

“Hydraulic Properties” and “Recharge Rates”) was used to 

constrain this uncertainty. A prior weight was used for the 

glacial anisotropies so that the 95-percent confidence interval 

was greater than 1 and less than or equal to 80. Prior weight 

for K_SDL was ±75 percent around the specified value of 

20 ft/d. The parameter sets created with equation 1 were then 

conditioned for unrealistic KV_Peat values as before, but 

they were also conditioned to remove parameter sets with 

glacial anisotropies less than 1 or greater than 100, which were 

considered unrealistic. The results of this second Monte Carlo 

analysis (table 3; probabilistic contributing area not shown) 

confirmed that uncertainty in these four parameters had little 

effect on the results for the probabilistic contributing area. 

The general pattern in high to low probabilities was the same 

in both analyses, and the total area was also almost the same 

(4.06 mi2 compared to 4.07 mi2).

A Monte Carlo analysis with the maximum pumping 

rate was done by using the parameter sets that fit the 

acceptance criteria for the average pumping rate. The only 

criterion for the Monte Carlo analysis that used these 749 

parameter sets with the maximum pumping rate was a water 

budget of 0.5 percent or less. Of the 749 parameter sets, 

629 parameter sets (84 percent) fit this criterion and thus 

were run with the particle tracking program (table 3). Areas 

with probabilities greater than 50 percent generally coincide 

with the deterministic contributing area (fig. 19). Generally, 

areas closest to the production wells with short traveltimes 

are associated with high probabilities, whereas areas distant 

from the wells with long traveltimes are associated with low 

probabilities. The sand and gravel mining operation between 

the well fields and within the deterministic contributing area 

has a probability of 100 percent. A sand and gravel mining 

operation north of the well fields in Genesee Brook watershed 

is not within the deterministic contributing area, but the Monte 

Carlo analysis indicated that part of this sand and gravel 

mining operation may be in the contributing area (probabilities 

of 2 percent and less).

Some areas north and south of Worden Pond that 

are not in the deterministic contributing area are in the 

probabilistic contributing area. These are areas of mostly 

low probabilities. The sensitivity analysis described earlier 

showed that, by decreasing either the recharge rates or the 

Table 3. Summary of the Monte Carlo analysis for the South Kingstown study site, southern Rhode Island.

[UWRI, United Water Rhode Island; mi2, square mile; KV_Peat, ratio of horizontal to vertical hydraulic conductivity of peat deposits; K_SDL, horizontal 

hydraulic conductivity of lacustrine deposits]

Comment

Calculated 

error variance 

criterion

Number of parameter 

sets run with 

MODFLOW: 

Number of parameter 

sets that fit criteria1

Total size of probabilistic 

contributing area to 

UWRI wells

Number of 

particles or cells

Area 

(mi2)

Average pumping rate

KV_Peat conditioned 10 1,000:662 4,609 3.72

KV_Peat conditioned 15 1,000:744 4,925 3.97

KV_Peat conditioned 20 1,000:749 5,043 4.07

KV_Peat conditioned None 1,000:749 5,043 4.07

Prior information on glacial anisotropy parameters and K_SDL; 

KV_Peat and glacial anisotropy parameters conditioned

20 1,000:714 5,027 4.06

Maximum pumping rate

Parameter sets that fit selected water budget and calculated error 

variance criteria for average pumping rate

None 749:629 9,999 8.07

1

Criteria: (1) model converged, (2) mass balance 0.5 percent or less, and (3) for some cases, a calculated error variance less than a specified value.
South Kingstown Study Site 35

K_SDN

K_MIX

K_SDS

K_TILL1

K_TILL2

K_MOR

KV_PEAT

SB_MULT

A

R_SDM

R_TILL

R_WETLAND

B

-3 -2 -1 0 1 2 3 4 5

0

1

2

3

4

5

6

LOGARITHM OF HYDRAULIC CONDUCTIVITY, IN FEET PER 

DAY, EXCEPT KV_PEAT, WHICH IS DIMENSIONLESS

0.00

0.05

0.10

0.15

0.20

0.25

RECHARGE RATE, IN INCHES PER YEAR

FREQUENCY OF OCCURENCE FREQUENCY OF OCCURENCE

0 5 10 15 20 25 30 35 40 45 50

Figure 17. Frequency distribution of A, hydraulic parameters, and of B, recharge parameters, after 

acceptance criteria were applied to determine the probabilistic areas contributing recharge to the 

United Water Rhode Island well fields (parameter information is provided on table 2), South Kingstown 

study site, southern Rhode Island.
36 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Worden Pond

Chipuxet River

Great Swamp

Management Area

White Horn Brook

Genesee Brook

West well field East well field

Probablistic contributing areas to United

Water Rhode Island well fields, in percent

EXPLANATION

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

Model boundary

Sand and gravel operation

Production well

Greater than 0 to 10

Greater than 10 to 25 

Greater than 25 to 50

Greater than 50 to 100

Mink Brook and Alewife Brook

 watershed boundaries

41°28'

41°26'

41 ̊24'

71°36' 71°34' 71°32'

0 .5 1 KILOMETER

0 .5 1 MILE 

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

Figure 18. Simulated probabilistic areas contributing recharge to the United Water Rhode Island well fields at their total 

average pumping rate of 2,138 gallons per minute, South Kingstown study site, southern Rhode Island.
South Kingstown Study Site 37

Figure 19. Simulated probabilistic areas contributing recharge to the United Water Rhode Island well fields at their total 

maximum pumping rate of 5,100 gallons per minute, South Kingstown study site, southern Rhode Island.

East well field

West well field

Worden Pond

Chipuxet River

Great Swamp

Management Area

White Horn Brook

Genesee Brook

Probablistic contributing areas to United 

Water Rhode Island well fields, in percent

EXPLANATION

Till and bedrock outcrops

Wetlands

Water (ponds, ocean)

Charlestown moraine

Stratified deposits

Point Judith moraine

Undifferentiated morainal deposits

Model boundary

Sand and gravel operation

Production well

Mink Brook and Alewife Brook

 watershed boundaries Greater than 0 to 10

Greater than 10 to 25 

Greater than 25 to 50

Greater than 50 to 100

71°36' 71°34' 71°32'

41°28'

41°26'

41°24' 0 .5 1 KILOMETER

0 .5 1 MILE 

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83
38 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

hydraulic connection between Worden Pond and the aquifer, 

the simulated area contributing recharge at the maximum 

pumping rate expanded mostly north and south of the pond 

because of the groundwater divides near the well fields. Most 

of the till uplands northwest of Worden Pond and parts of 

the till uplands southwest of the pond are in the probabilistic 

contributing area. The deterministic contributing area in the till 

uplands northwest of Worden Pond corresponded to an area of 

high probabilities (greater than 50 percent) and probabilities of 

39 to 48 percent. The probabilistic contributing area extended 

to the western edge of the model including areas between 

till uplands where assumed groundwater and surface-water 

divides may not coincide.

Additional water-level and streamflow observations 

and other types of field measurements may help reduce the 

uncertainty in the simulated contributing area by increasing 

the precision of the parameter value estimates and more 

accurately representing hydrologic features in the model. 

R_WETLD and KV_PEAT, two parameters specified in 

the model, had the least certainty of the parameters used in 

the Monte Carlo analysis. Detailed information on Worden 

Pond bed sediments, such as thickness and vertical hydraulic 

conductivity, would be important for the scenario that uses the 

maximum pumping rate. Additional streamflow observations 

in the Mink and Alewife watersheds and also distant from the 

production wells, such as the northward flowing streams to 

Worden Pond, may help decrease uncertainty of the predicted 

contributing area.
Charlestown Study Site 39

Charlestown Study Site

The CBFD and EBWA well fields are on a peninsula or 

neck, called Quonochontaug Neck, a coastal setting in the 

Town of Charlestown, in southern Rhode Island (figs. 1 and 

20). Quonochontaug Neck is bordered by Quonochontaug 

Pond and Ninigret Pond to the west and east, and by Block 

Island Sound to the south. To the north where Quonochontaug 

Neck is connected to the mainland, the Charlestown 

Moraine forms the watershed divide between the South 

Coastal watershed and the Pawcatuck River watershed. The 

geographic extent of the study area extended to surfacewater bodies, streams, a watershed divide in upland till, and 

presumed groundwater-flow paths that serve as boundaries for 

the numerical model. This model extent minimizes the effects 

of model boundaries on simulated heads near the area likely to 

be within the contributing area to the well fields. Land use on 

Quonochontaug Neck is primarily high-density residential, but 

it also includes developed recreation, wetlands, and forests.

The CBFD and EBWA well fields are each composed 

of two wells clustered near the center of Quonochontaug 

Neck; known characteristics of the production wells are listed 

in table 1. The drilled wells are completed near the top of 

the bedrock surface in a thin aquifer consisting of coarsegrained stratified deposits. Well depths range from about 22 

to 28 ft below land surface in about 20 to 25 ft of saturated 

sediments. Areas contributing recharge were determined for 

both well fields at the average pumping rate during 2003–07 

of 16 gal/min and for both well fields at the maximum 

pumping capacity of 230 gal/min. Wastewater is disposed to 

groundwater through private septic systems.

Streamflow and peat thickness were measured in 

November and December 2006 to provide information 

concerning average streamflow conditions and wetland 

characteristics (fig. 20). Two sets of streamflow measurements 

were made at two sites in an unnamed tributary that drains 

the central part of Quonochontaug Neck near the well fields. 

Peat thickness was measured along two sections by manually 

probing the peat with a steel rod. Lithologic logs from USGS 

reports and files were compiled to define the bedrock surface 

and sediment size of the stratified deposits. 

Geology

Sediments of glacial origin—stratified deposits, till, and 

morainal—overlie igneous and metamorphic bedrock (Moore, 

1959) and fill generally southward sloping bedrock valleys 

(fig. 20). Deposits of the Charlestown Moraine thicker than 

75 ft overlie the bedrock in a main valley axis along the east 

boundary of the study area. Morainal deposits in the study area 

consist of till and stratified deposits of mostly sand and gravel 

sized sediment (Boothroyd, 2001). On Quonochontaug Neck, 

surficial deposits are generally 20 to 30 ft thick, but bedrock 

outcrops are exposed, including southwest and northeast of 

the production well fields along the shoreline of Block Island 

Sound and of Ninigret Pond (shown by 0 ft contour lines in 

figure 20).

Stratified deposits south of the Charlestown Moraine 

were laid down by meltwater when the ice margin was at the 

moraine, and these deposits extended seaward into Glacial 

Lake Block Island (Boothroyd, 2001). A generalized northsouth section through Quonochontaug Neck (fig. 21) shows 

the lithology and thickness of surficial deposits and the 

vertical placement of PW1 of CBFD. The CBFD and EBWA 

well fields are screened in coarse-grained ice-proximal part 

of a morphosequence. These coarse-grained deposits consist 

of mostly sand and gravel but they also include boulders, 

which are exposed on the land surface and in the wetlands on 

Quonochontaug Neck. 

Post-glacial deposits of peat, organic-rich pond-bottom 

sediments, and beach sand locally overlie glacial deposits. 

Manual probing of the wetlands near the well fields (fig. 20) 

indicated that peat thickness ranged from 1.2 to 4.8 ft; peat 

thickness generally ranged from 2 to 4 ft. Peat deposits 

most likely extend beneath West Pond southeast of the well 

fields. Parts of the large coastal ponds developed in large 

kettle depressions (Masterson and others, 2007). That part of 

Ninigret Pond within the study area is underlain by 3 to 5 ft of 

fine-grained organic-rich sediments in the center areas and, in 

some cases, these sediments overlie former wetland deposits 

of peat (Dillion, 1970).

Hydrology

The geographic extent of the study area includes parts of 

the South Coastal watershed and Pawcatuck River watershed 

(fig. 20). The Charlestown Moraine, which forms a 120-ft 

ridge above the coast and 80 ft above Watchaug Pond in the 

Pawcatuck River watershed, forms the surface-water divide 

between the two watersheds. A map of water-table contours by 

LaSala, Jr., and Johnson (1960) shows a groundwater divide 

in the moraine between these two watersheds, but there were 

no water-level data to support this location. The manually 

calibrated regional model (Masterson and others, 2007) 

simulated a groundwater divide through most of the moraine 

in the study area.

Quonochontaug Pond and Ninigret Pond, connected to 

Block Island Sound by breachways, are saltwater ponds. These 

coastal ponds are shallow with most of Ninigret Pond less than 

6-ft deep (Dillion, 1970). Freshwater underlies these saltwater 

ponds and barrier beaches (Masterson and others, 2007). Small 

streams discharge mainly along the northern margins of the 

ponds. The average stage of the coastal ponds and locally of 

Block Island Sound relative to NGVD29 was not measured for 

this study. 

On Quonochontaug Neck a small stream drains the 

central part of the neck and one of three small freshwater 

ponds (West Pond) and associated wetlands to Quonochontaug 

Pond. The stream network delineated at the 1:5,000 scale 

routes the stream through the wetland near the well fields, but 
40 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

B

B’

B B’

CHW48

CHW47

0

50

-50

-25

-100

100

150

50

-25

0

50

-50

0

50

0

0

-100

100

50

Block Island Sound

Ninigret Pond

Quonochontaug Pond

Quonochontaug

Neck

Watchaug Pond

Foster

Cove

Perry Healy Brook Tanyard Brook

West

Pond

Garden

Pond

CBFD

EBWA

well fields

41°22'

71°43' 71°42' 71°41'

41°20'

Model boundary

Production well

Boring and identifier

Streamflow partial-record site

EXPLANATION

Bedrock-surface altitude—

 Contour interval, in feet, is variable

Line of geologic cross section

Peat thickness survey

South Coastal and Pawcatuck River

 watershed boundary

Till and bedcrock outcrops

Wetlands

Charlestown moraine

Stratified deposits

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

0 .5 1 KILOMETER

0 .5 1 MILE 

1

Figure 20. Production wells, section lines, selected borings, streamflow partial-record sites, model extent, 

bedrock-surface contours, and surficial geology, Charlestown study site, southern Rhode Island.
Charlestown Study Site 41

100

50

0

-50

-100

ALTITUDE, IN FEET RELATIVE TO NGVD29

CHW47 (projected)

PW1 (CBFD) --- BEND IN SECTION

CHW48 --- BEND IN SECTION

Block

Island

Sound

West Pond --- BEND IN SECTION

Quonochantaug 

Pond

Charlestown moraine

North South

Peat

Sand and gravel

Sand

Till

Till, sand and gravel 

Bedrock

VERTICAL EXAGGERATION X 40

EXPLANATION

Screened well, and number

Well or borehole, and number

B B’

250 500 METERS

2,000 FEET

0

0 1,000

Figure 21. Geologic cross section, Charlestown study site, southern Rhode Island.
42 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

field observations indicated no defined channel through most 

of the wetland. Two sets of streamflow measurements made 

at culverts upstream and downstream of the well fields and of 

this wetland (fig. 20) on November 7 and December 20, 2006, 

indicated a net gain of 0.02 and 0.16 ft3/s. Measurements 

were made near mean annual streamflow conditions (shown 

in figure 5 as at mean annual streamflow conditions for this 

long-term gage), but this assessment was based on multiple 

long-term streamgages with drainage areas more than an 

order of magnitude larger than the stream and wetland. The 

specific conductance of streamwater at both sites measured 

December 20, 2006, was 168 μS/cm, typical of freshwater that 

is unaffected by saltwater. Groundwater levels measured in the 

southern half of Quonochontaug Neck by Urish (1992, 2000) 

indicated that seasonal water-level fluctuations in individual 

dug wells ranged from 0.8 to 4.2 ft, and they also indicated a 

groundwater mound southwest of the well fields.

The source of freshwater in the study area is 

precipitation. If there is about 29 in/yr available for recharge, 

based on average mean annual streamflow in southern Rhode 

Island (see Introduction heading Recharge Rates), then the 

total water available for recharge on Quonochontaug Neck 

(0.85 mi2) is equivalent to 1.8 ft3/s or 810 gal/min. The total 

average well field withdrawal rate is 2 percent and the total 

maximum well field pumping rate is about 30 percent of the 

water available for recharge on the neck. This estimate of 

total water available for recharge, however, does not represent 

the amount of water that could be withdrawn from the neck 

because of potential saltwater intrusion, impacts to surfacewater bodies, and groundwater inflow from the mainland.

Simulation of Groundwater Flow and Areas 

Contributing Recharge

The groundwater-flow model for the Charlestown 

study site was designed to simulate long-term, steady-state 

groundwater levels, flow paths, and traveltimes. A model 

design similar to that used for the South Kingstown study 

site was used: two thin top layers to simulate surface-water 

features and associated bottom sediments, and a bottom layer 

to represent bedrock. One intervening layer represented most 

of the glacial deposits, which is where pumping withdrawals 

occur. Two intervening layers were used in the South 

Kingstown study site; however, the glacial deposits are thinner 

in the Charlestown study site. Simulation of the freshwater–

saltwater interface was beyond the scope of the study. The 

model was calibrated to average annual pumping conditions 

for 2003–07 based on historical water-level observations and a 

streamflow observation made during this study. Deterministic 

areas contributing recharge to the well fields for different 

pumping rate scenarios were simulated, and an uncertainty 

analysis of the contributing area was performed. Wastewater 

return flow through private septic systems was not simulated 

in the model. Simulated contributing areas to the well fields, 

therefore, represent slightly larger, more conservative areas 

than if return flow had been included in the model.

Model Extent and Spatial Discretization

Groundwater flow in the study area was simulated by a 

four-layer finite-difference numerical model with a uniformly 

spaced grid. The model extended to natural hydrologic 

boundaries beyond the likely area contributing recharge 

to the well fields. Lateral model boundaries included large 

surface-water bodies near the well fields: Block Island 

Sound in the south and Quonochontaug and Ninigret Ponds 

directly west and east. In the northeast, the edge of the model 

extended to Foster Cove and Watchuag Pond, and it paralleled 

groundwater-flow paths between these two ponds based on 

a water-table map drawn by LaSala, Jr., and Johnson (1960). 

In the north, the edge of the model coincided with streams 

that drain to Watchaug Pond (Perry Healy Brook, Tanyard 

Brook, and an unnamed tributary). In the northwest, the 

model extended to a tributary that drains into Quonochontaug 

Pond and a watershed divide in upland till. The model 

boundary between this watershed divide and nearby streams 

was drawn along presumed groundwater-flow paths based 

on the water-table map by LaSala, Jr., and Johnson (1960). 

The groundwater-flow model subdivided the study area of 

5.5 mi2 into 312 rows and 173 columns and included a total of 

169,880 active cells. Each cell was 60 ft by 60 ft square. The 

simulated area included both surficial deposits and bedrock.

All model layers were simulated by using a fixed 

transmissivity. The model initially represented surficial 

deposits in the top layer and bedrock in the bottom layer. 

The top of the model grid, which is used to determine 

transmissivity of the top layer, was first set to land-surface 

altitude. The top of the model grid was reset by running the 

initial model, temporarily adjusting hydraulic properties until 

the simulated water table compared favorably to available 

water levels and land-surface altitudes, and then the simulated 

water-table altitude was used as the top of the model. The 

top layer was then subdivided into three layers (layers 1 to 

3) based on surface-water features, lithology, and placements 

of the production well screens. Layer 1 is 2 ft thick to 

represent surface water in small ponds and wetlands. Layer 2 

is 2 ft thick to represent peat deposits beneath wetlands and 

small ponds, and 5 ft thick to represent organic-rich coastal 

pond-bottom sediments. Layer 3 represented the remaining 

surficial deposits, which is the layer in which the production 

wells are screened. Stratified deposits, till, and the moraine 

are represented in all three layers. Shallow bedrock areas 

less than 5 ft from the top of the model were incorporated 

into surrounding surficial materials. Layer 4, the bottom 

layer, represented only bedrock. Bedrock was assigned a 

constant thickness of 200 ft throughout the model beneath the 

surficial deposits.
Charlestown Study Site 43

Boundary Conditions and Model Parameters

The interaction between streamflow and groundwater 

was simulated as a head-dependent flux boundary by using 

the stream-routing package (Prudic, 1989) developed for 

MODFLOW (fig. 22). The stream-routing package accounts 

for gains and losses of water in each stream cell, and it 

routes streamflow from upstream cells to downstream cells. 

The model contained 477 stream-routing cells. Stream 

altitudes were interpolated from topographical contours 

intersecting streams and from pond altitudes listed on the 

USGS Quonochontaug quadrangle. Both water depth and bed 

thickness were set equal to 1 ft so that the top and bottom bed 

altitude could be determined from stream altitudes. Streams 

were simulated as 10 ft wide. Streambeds were assumed to 

consist of coarse-grained sediments or organic-rich finegrained materials, such as the tributary near the well fields. 

For organic-rich streambeds, a vertical hydraulic conductivity 

of one-tenth the value of that for coarse-grained beds was 

used. A dimensionless parameter (SB_MULT) (table 4) was 

defined that multiplied the vertical hydraulic conductivity 

value. A dimensionless multiplier of 1 is equivalent to 1 ft/d 

for coarse-grained beds and 0.1 ft/d for organic-rich beds. A 

parameter value of 1 would also be equivalent to streambed 

conductances of 600 ft2/d for coarse-grained beds and 60 ft2/d 

for organic-rich beds.

A constant-head boundary was used to simulate large 

surface-water bodies—Block Island Sound and the coastal 

ponds—and the two smaller ponds that form part of the 

northeast edge of the model—Foster Cove and Watchaug Pond 

(fig. 22). The average stage of the large surface-water bodies is 

unknown; for this study a stage of 0 ft NGVD29 was assumed. 

The stage of the two smaller ponds was determined from pond 

altitudes listed on the USGS Quonochontaug quadrangle. The 

model contained 9,352 constant-head cells.

Recharge parameters were distributed based on surficial 

geology and surface-water features (table 4). Recharge values 

used in the model are effective rates, which account for 

groundwater evapotranspiration. A single recharge parameter 

represented the stratified deposits and the morainal deposits 

(R_SDM); conceptually, recharge rates should be similar for 

both surficial materials because the morainal deposits consist 

of mostly permeable materials. A second recharge parameter 

was defined for upland till (R_TILL). Any surface runoff 

from till hillslopes that may recharge permeable stratified 

and morainal deposits at the upland-valley contact was not 

included in model simulations. A recharge parameter was 

defined for the wetlands (R_WETLD), and it represented 

water available for recharge. Some or all of this water may 

infiltrate, particularly under pumping conditions, or it may 

move across the surface as overland flow. R_WETLD was 

therefore set at a fixed value for model calibration, but 

the uncertainty in the specified value was included in the 

probabilistic contributing area analysis. Pond recharge was 

specified for all model simulations. The same value of 22 in/yr 

was applied to pond water and wetland areas by subtracting 

the evaporation rate from a free-water surface (29 in/yr) 

(Farnsworth and others, 1982) from the rate of precipitation 

for southern Rhode Island (51 in/yr).

Hydraulic conductivity parameters were assigned on the 

basis of lithology (table 4). Horizontal hydraulic conductivity 

of the stratified deposits was represented by parameter K_SD, 

till by parameter K_TILL, and morainal deposits by parameter 

K_MOR. Horizontal hydraulic conductivity of bedrock 

was represented by parameter K_ROCK and wetlands by 

parameter K_WETLD. Parameter K_WETLD represented 

overland flow in the wetlands and groundwater flow through 

any large interconnected pores in poorly decomposed upper 

part of the peat. Model cells containing small freshwater ponds 

were assigned a hydraulic conductivity value of 50,000 ft/d to 

simulate minimal resistance to flow and the corresponding flat 

gradient across these water bodies.

The ratio of horizontal hydraulic conductivity to vertical 

hydraulic conductivity for stratified deposits, morainal 

deposits, and till was represented by parameters KV_SD, 

KV_MOR, and KV_TILL, respectively. The ratio of 

horizontal to vertical hydraulic conductivity for bedrock was 

defined by parameter KV_ROCK and for peat by parameter 

KV_PEAT. The horizontal hydraulic conductivity for peat 

was held constant in the model at 1 ft/d; the ratio is, therefore, 

always in relation to this value. KV_PEAT represented the 

medium decomposed and highly decomposed peat at depth 

that controls the connection between the wetland and the 

underlying aquifer.

Observations

The groundwater-flow model was calibrated to 46 waterlevel observations and 1 streamflow observation. Observations 

were weighted based on methods described by Hill and 

Tiedeman (2007); the weights account for measurement 

error and for the difference in units as between water levels 

and streamflows. Water-level observations were divided into 

Groups A and B on the basis of their estimated accuracy 

(fig. 22). Group A included 20 groundwater levels and 1 pond 

level measured July 1990 and October 1999 by Urish (1992, 

2000). Water levels measured July 1990 were near average 

annual groundwater conditions based on USGS long-term 

observation well CHW18 (fig. 6). October 1999 water levels 

were made at below-average groundwater conditions (fig. 6); 

however, considerable precipitation fell in the second half 

of September 1999. A comparison of available water levels 

measured in the same wells in both years indicated that most 

water levels during October 1999 were within 0.4 to 0.6 ft, 

both above and below the July 1990 water levels. Because 

depth to the water table in Quonochontaug Neck is less 

than depth at CHW18 (about 8 ft compared to 18 ft), water 

levels in Quonochontaug Neck may respond more quickly 

to precipitation recharge or there may have been less of a 

soil moisture deficit. Datum for Group A observations was 

local approximate mean sea level determined by tide-survey 

measurements in Quonochontaug Pond (Urish 1992, 2000). 
44 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Block Island Sound

Ninigret Pond

Quonochontaug Pond

Quonochontaug

Neck

Watchaug Pond

Foster

Cove

Perry Healy Brook

Tanyard Brook

West

Pond

Garden

Pond

CBFD

EBWA

well fields

41°22'

41°20'

71°43' 71°42' 71°41'

Till and bedcrock outcrops

Wetlands

Charlestown moraine

Stratified deposits

Model boundary

Constant head cell

Stream cell

Production well

EXPLANATION

South Coastal and Pawcatuck River

watershed boundary

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

Streamflow partial-record site

0 .5 1 KILOMETER

0 .5 1 MILE 

Water-level observations

Group A

Group B

Figure 22. Model-boundary types and observations, Charlestown study site, southern Rhode Island. 
Charlestown Study Site 45

Table 4. Definition of model parameters, optimal parameter value or specified value, and parameter-estimation statistics for the Charlestown study site, southern Rhode Island.[in/yr, inches per year; ft/d, feet per day; --, dimensionless or not applicable; optimal value (bold); specified value (italic)]

Parameter 

name Parameter description Units

Value 

(optimal or 

specified)

95-percent confidence 

interval - Optimal value or 

specified value

Coefficient of 

variation 

(dimensionless)

Reported ranges 

for selected 

parameters Lower value Upper value

SB_MULT Multiplier of streambed vertical hydraulic conductivity 

(X 0.1 ft/d & 1 ft/d for peat and coarse sediments)

-- 4.3 1.9–9.8 0.47 0.1–17

R_SDM Recharge rate on stratified and morainal deposits in/yr 29 23.0–35.0 -- 26–33R_TILL Recharge rate on till deposits in/yr 23 9.5–36.5 -- 9–33R_WETLD Water available for recharge rate on wetlands in/yr 22 8.8–35.1 -- 11–33K_SD Horizontal hydraulic conductivity of stratified deposits ft/d 64 57–71 0.05 50–500K_TILL Horizontal hydraulic conductivity of till deposits ft/d 2.2 1.0–4.4 0.40 0.004–65K_MOR Horizontal hydraulic conductivity of Charlestown Moraine ft/d 14 9–23 0.25 0.1–30K_WETLD Horizontal hydraulic conductivity of surface water in wetlands and top of 

peat deposits

ft/d 4,200 2,400–7,400 0.29 --

K_ROCK Horizontal hydraulic conductivity of bedrock ft/d 0.1 -- -- --KV_SD Ratio of horizontal to vertical hydraulic conductivity of stratified deposits -- 10 -- -- --KV_TILL Ratio of horizontal to vertical hydraulic conductivity of till deposits -- 10 -- -- --KV_MOR Ratio of horizontal to vertical hydraulic conductivity of morainal deposits -- 10 -- -- --KV_PEAT Ratio of horizontal to vertical hydraulic conductivity of peat deposits 

(or in relation to horizontal hydraulic conductivity of 1 ft/d)

-- 10 148–0.67 (0.007–1.5 ft/d) -- (<0.03–>4 ft/d)

KV_ROCK Ratio of horizontal to vertical hydraulic conductivity of bedrock -- 1 -- -- --
46 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Accuracy of the observations was estimated at 0.5 ft because 

the accuracy of the survey was not reported and the accuracy 

of the local datum and its relation to NGVD29 was unknown. 

Group A observations are distributed in the southern half of 

Quonochontaug Neck and are included in layer 1 because they 

were measured in shallow dug wells.

Group B included 17 groundwater levels measured 

primarily during August and September 1955 (LaSala, Jr., and 

Hahn, 1960; LaSala, Jr., and Johnson, 1960) also near average 

annual groundwater conditions (fig. 6). Accuracy of Group 

B groundwater levels, whose measuring-point altitudes were 

based on land-surface altitudes determined from the USGS 

Quonochontaug and Carolina quadrangles, is about 5 ft (U.S. 

Geological Survey, 1980). These groundwater levels were 

distributed throughout the modeled area, except for the center 

areas of the moraine. Because most of these water levels were 

measured in shallow dug wells they were included in layer 1. 

In addition to groundwater levels, Group B included 8 pond 

altitudes determined from land-surface contours on the USGS 

Quonochontaug quadrangle, all located in the Charlestown 

Moraine. These ponds are assumed to be in good hydraulic 

connection with the surrounding aquifer. Accuracy of these 

pond altitudes was also assumed to be 5 ft.

A streamflow observation represented the average net 

gain (0.09 ft3/s) of surface flow through the wetland near 

the well fields based on the November and December 2006 

streamflow measurements. The accuracy of each streamflow 

measurement was about 10 percent. Because the streamflow 

gain was determined from an upstream and a downstream 

measurement, the variance of the errors of the two streamflow 

measurements was summed.

Estimation of Parameters

Model parameters included three for recharge, five for 

horizontal hydraulic conductivity, five for vertical anisotropy, 

and one for streambed hydraulic conductivity (table 4). 

Parameter R_WETLD, which represented water available 

for recharge in the wetlands, was specified in the model, but 

the uncertainty in the parameter value was included in the 

probabilistic contributing area analysis.

Composite scaled sensitivities indicated that the waterlevel observations and the streamflow observation provided 

insufficient information to estimate all parameters (fig. 23). 

The parameters for vertical anisotropy had low parameter 

sensitivities and thus were assigned values from the literature. 

PARAMETER NAME

R_SDM

K_SD

K_WETLD

R_TILL

K_MOR

K_TILL

SB_MULT

K_ROCK

KV_SD

KV_PEAT

KV_MOR

KV_ROCK

KV_TILL

COMPOSITE SCALED SENSITIVITY

8

7

6

5

4

3

2

1

0

Figure 23. Composite scaled sensitivities for model parameters (parameter information is provided on table 4), Charlestown 

study site, southern Rhode Island.
Charlestown Study Site 47

The ratios of horizontal to vertical hydraulic conductivity of 

glacial deposits (KV_SD, KV_TILL, KV_MOR) and of peat 

(KV_PEAT) were set to 10; because the horizontal hydraulic 

conductivity of peat was set to 1 ft/d, the resulting vertical 

hydraulic conductivity was equivalent to 0.1 ft/d. KV_ROCK 

was specified a ratio of 1. In addition to vertical anisotropies, 

the parameter for horizontal hydraulic conductivity, K_ROCK, 

had a low sensitivity and was set to 0.1 ft/d. 

Several of the parameters with high parameter 

sensitivities were highly correlated to each other and thus 

not all of the remaining parameters could be estimated 

uniquely. R_SDM and K_SD had a parameter correlation of 

0.99, and R_TILL and K_TILL had a parameter correlation 

of 0.98. Values for both recharge parameters were specified 

for model calibration. R_SDM was assigned a value of 

29 in/yr, which is the mean and median long-term annual 

runoff rate for streamgages in southern Rhode Island and 

the recharge rate determined from model calibration for the 

South Kingstown study site. R_Till was assigned a value 

of 23 in/yr, also determined from model calibration for the 

South Kingstown study site and within the reported range of 

recharge rates determined for till-dominated watersheds by 

computerized hydrograph-separation methods. The remaining 

five parameters representing hydraulic properties, K_SD, K_

TILL, K_MOR, K_WETLD, and SB_MULT, were estimated 

by nonlinear regression.

The quality of model calibration can be determined 

through analysis of the weighted residuals, both numerically 

and graphically (Hill and Tiedeman, 2007). Weighted residuals 

should be randomly distributed and close to zero. The average 

weighted residual was 0.02 ft and ranged from a minimum of 

-3.6 ft to a maximum of 4.8 ft. The sum of squared weighted 

residuals was 127 for the calibrated model. The calculated 

error variance and the standard error of the regression, 

measures of the overall magnitude of the weighted residuals, 

were 3.03 and 1.74, respectively. A comparison of weighted 

residuals, shown in figure 24A, indicated that residuals are 

generally randomly distributed around zero for all weighted 

simulated values. Forty-five of the 47 observations are 

within two standard errors of the regression. A comparison 

of weighted observed values and weighted simulated values 

(fig. 24B) indicated a reasonable agreement; the correlation 

between weighted observed values and weighted simulated 

values was 0.98. The spatial distribution of weighted water 

level and streamflow residuals (fig. 25) is generally distributed 

randomly throughout the modeled area except near the contact 

between the morainal and stratified deposits north of Ninigret 

Pond. In this modeled area, simulated water levels are greater 

than observed water levels for five of the six observations. 

Observations with the most overall influence in the set of 

estimated parameter values were determined from Cook’s D 

statistics. Three water-level observations and the streamflow 

observation had a Cook’s D value greater than the critical 

value of 0.085 (4 divided by number of observations). The 

observations with the most overall influence in the parameter 

estimation (fig. 25) are distributed throughout the model. The 

streamflow observation, in addition to being an influential 

observation to the set of estimated parameters, was the only 

observation important to more than two individual estimated 

parameters, according to DFBeta statistics.

Optimal values for the five hydraulic parameters that 

were estimated using nonlinear regression are listed in table 4. 

The optimal values for the glacial deposits and the streambed 

multiplier are within the range of values reported in the 

literature as discussed in the “Hydraulic Properties” section. 

The optimal value for horizontal hydraulic conductivity 

of wetlands (K_WETLD) was in the mid-range of values 

(1,000–10,000 ft/d) determined by manual calibration for 

wetlands in southern Rhode Island by Masterson and others 

(2007). The optimal value for K_SD was at the low end of 

expected values for coarse-grained stratified deposits. These 

deposits were laid down near the ice margin and may not 

be well-sorted or the bedrock surface may need to be more 

accurately defined. The optimal value for K_MOR (14 ft/d) is 

close to the simulated value for Charlestown morainal deposits 

in the South Kingstown study site (16 ft/d). The dimensionless 

multiplier of streambed vertical hydraulic conductivity, 

STR_MULT, is equivalent to 4.3 ft/d for coarse-grained bed 

sediments and to 0.43 ft/d for organic-rich bed sediments.

The precision or uncertainty of the parameter estimate is 

indicated by the 95-percent linear confidence interval for each 

optimal value (table 4). For these linear confidence intervals 

to be valid, weighted residuals should be normally distributed 

and the model linear near the estimated optimal values (Hill 

and Tiedeman, 2007). The correlation between weighted 

residuals and the normal order statistics for the calibrated 

model was 0.984. This value is greater than the critical value 

for 47 observations, 0.951, at the 5-percent significance level, 

which indicates that the weighted residuals are independent 

and normally distributed. The degree of model linearity can be 

quantified using the modified Beale’s measure. The model is 

considered effectively linear if the modified Beale’s measure 

is less than 0.037 and nonlinear if it is greater than 0.41. The 

modified Beale’s measure for the model was 0.034, indicating 

that the model is linear; thus, the linear confidence intervals 

are considered to be accurate.

The 95-percent confidence intervals for the parameter 

estimates are within the range of reasonable values reported 

in the literature. A comparison of the relative precision 

of different parameter estimates can be made using the 

coefficient of variation (standard deviation of the estimate 

divided by the optimal value) (table 4); a smaller coefficient 

of variance indicates a more precise parameter estimate. The 

covariance of variation ranged from 0.05 for K_SD to 0.47 

for SB_MULT. Of the remaining parameters, K_MOR and 

K_WETLD were more precisely estimated than K_TILL. The 

order of the most to the least precisely estimated parameter 

values generally follows the same order as that of the 

parameter sensitivities (fig. 23) because of the information 

provided by the observations in the regression.
48 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

WEIGHTED SIMULATED EQUIVALENT

-10 -5 0 5 10 15 20 25 30

WEIGHTED RESIDUAL (1.74 EQUALS STANDARD

ERROR OF THE REGRESSION)

5.22

3.48

1.74

0

-1.74

-3.48

-5.22

Water-level observation

Streamflow observation

WEIGHTED SIMULATED EQUIVALENT

-10 -5 0 5 10 15 20 25 30

WEIGHTED OBSERV

ATION

30

25

20

15

10

5

0

-5

-10

Water-level observation

Streamflow observation

A

B

Figure 24. Relation of A, weighted residual to weighted simulated equivalent, and of B, weighted observation to weighted 

simulated equivalent, Charlestown study site, southern Rhode Island.
Charlestown Study Site 49

10

20

30

40

50

60

90

80

70

110

100

140

130

80

90

10

70

60

40

40

5

4

5

3

1

2

3

3

4

50

50

40

30

20

2

1

120

5

Block Island Sound

Ninigret Pond

Quonochontaug Pond

Quonochontaug

Neck

Watchaug Pond

Foster

Cove

Perry Healy Brook

Tanyard Brook

West

Pond

Garden

Pond

CBFD

EBWA

well fields

41°22'

41°20'

71°43' 71°42' 71°41'

Till and bedcrock outcrops

Wetlands

Charlestown moraine

Stratified deposits

Model boundary

Production well

EXPLANATION

Simulated water table—Contour interval,

in feet, is variable (as shown)

South Coastal and Pawcatuck River watershed boundary

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

Weighted residual

less than -3

-3 to -1.5

-1.5 to 0

0 to 1.5

1.5 to 3

greater than 3 

Cook's D greater than critical value

0 .5 1 KILOMETER

0 .5 1 MILE 

Figure 25. Spatial distribution of weighted residuals and simulated water-table contours for calibrated, steadystate conditions, Charlestown study site, southern Rhode Island.
50 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Simulated Water-Table Contours and 

Water Budget

The altitude and configuration of the simulated water 

table for the calibrated model are shown in figure 25 at 

10-ft contour intervals except for 1-ft intervals in low-lying 

areas of Quonochontaug Neck and near the coastal ponds. 

The simulated water-table contours and flow patterns are 

consistent with the conceptual model of groundwater flow 

in the study area and with groundwater maps by LaSala, Jr., 

and Hahn (1960), LaSala, Jr., and Johnson (1960), and Urish 

(2000). Groundwater generally flows from topographically 

high areas and discharges to streams and surface-water 

bodies. A simulated groundwater divide between South 

Coastal and Pawcatuck River watersheds is in the north part 

of the Charlestown Moraine near, but generally north, of 

the watershed divide. A simulated groundwater divide on 

Quonochontaug Neck trends north-south near the center of 

the neck from the till deposits toward West Pond and Garden 

Pond. Groundwater generally enters the three freshwater 

ponds along the northern perimeters, and pond water enters 

the aquifer along the southern perimeter before discharging to 

Block Island Sound. Water in West Pond also exits through the 

small stream but toward the northwest. Southwest of the well 

fields, a groundwater mound is simulated in the center of the 

area bounded by Block Island Sound, Quonochontaug Pond, 

and West Pond.

The simulated groundwater budget for the calibrated 

model indicated that recharge from direct precipitation 

provided 8.6 ft3/s or 92 percent of the inflow. Stream leakage 

(0.7 ft3/s or 7 percent) and pond leakage (0.1 ft3/s or 1 percent) 

account for the remaining inflow. Most of the inflow, 6.6 ft3/s 

or 70 percent, discharges to streams and to the large surfacewater bodies in the South Coastal watershed; the production 

well fields withdraw about 0.04 ft3/s. The remaining outflow, 

2.8 ft3/s or 30 percent, discharges to streams and Watchaug 

Pond along the northern model boundary.

Deterministic Areas Contributing Recharge

Simulated deterministic areas contributing recharge and 

groundwater traveltimes to the CBFD and EBWA well fields 

were determined on the basis of the calibrated steady-state 

model, for simulated pumping conditions, and tracking of 

pathlines with the MODPATH particle-tracking program. The 

areas contributing recharge to the well fields are based on both 

well fields pumping simultaneously. The areas contributing 

recharge would change if one of the well fields were to 

stop pumping or if withdrawal rates changed. The locations 

and extents of the simulated areas contributing recharge 

to each well field pumping at the 2003–07 average annual 

rate (16 gal/min) and the maximum rate (230 gal/min) are 

illustrated in figures 26 and 27. 

The area contributing recharge for the average pumping 

rate is 0.018 mi2. The area contributing recharge extends 

southwestward from the well fields to the simulated watertable mound, underlies a small part of the adjoining wetland, 

and includes isolated areas on the opposite side of the wetland 

northeast of the well fields. At the maximum withdrawal 

rate, the area contributing recharge (0.26 mi2) expands in all 

directions to capture enough water to balance the increased 

pumping rate. At the lower pumping rate, the well fields 

mostly intercept groundwater that would have discharged 

to the adjoining wetland (or the stream routed through the 

wetland), but at the higher pumping rate, the well fields also 

intercept water that would have discharged directly to the 

coastal ponds and Block Island Sound. The area contributing 

recharge for the CBFD well field includes water originating 

in the till northeast of the well fields. The area contributing 

recharge for the EBWA well field includes an area underlying 

West Pond. As was mentioned previously, simulation of 

the freshwater–saltwater interface was beyond the scope of 

the study; however, model results indicated no infiltration 

from the saltwater bodies into the underlying aquifer at the 

maximum pumping rates.

Simulated traveltime estimates from recharging locations 

to the production wells for the maximum pumping rate 

are shown in figure 28. Estimated traveltimes are based on 

porosities of 0.35 for stratified deposits, till, and morainal 

deposits; 0.80 for peat deposits; 0.02 for bedrock; and 1 for 

surface water. Estimated traveltimes ranged from less than 

6 months to more than 50 years; 94 percent of the traveltimes 

were 10 years or less. The median traveltime to the well 

fields in this thin aquifer was 1.3 years. Water that recharges 

the aquifer near the well fields has the shortest traveltimes, 

whereas water originating in the till northeast of the well fields 

and in the stratified deposits along the southwest edge of the 

contributing area has the longest traveltimes.

A limitation of using a fixed transmissivity for all model 

layers, previously mentioned in the section “Numerical 

Modeling” is that the simulated transmissivity of the 

aquifer near the well fields does not decrease with increased 

drawdowns that the maximum pumping rates cause. In the 

vicinity of the well fields, the simulated saturated thickness 

for the pumping rate used in the calibrated model and the 

maximum pumping rate decreased from 23 ft to 15 ft. 

Traveltimes and areas contributing recharge to the well fields 

may be different for a model that uses fixed transmissivity 

when compared to a model that uses a variable transmissivity. 

If a variable transmissivity model had drawdowns similar 

to those of the fixed transmissivity model, then using a 

horizontal hydraulic conductivity value of 100 ft/d would have 

a transmissivity equivalent to that of the fixed transmissivity 

model. Although this hydraulic conductivity value is greater 

than the upper 95-percent confidence limit estimated by 

parameter estimation, it is within the range of reported values 

for coarse-grained deposits in Rhode Island.
Charlestown Study Site 51

Figure 26. Simulated areas contributing recharge to the Central Beach Fire District and East Beach Water 

Association well fields, at their total average pumping rate of 16 gallons per minute, Charlestown study site, 

southern Rhode Island.

5

4

1

2

3

4

30

10

40

20

50

90

80

70

60

100

110

130

120

10

1 2

3

10

20

30

140

71°43' 71°42'

41°22'

41°20'

Block Island Sound

Ninigret Pond

Quonochontaug Pond

Quonochontaug

Neck

Tanyard Brook

West

Pond

Garden

Pond

CBFD well field

EBWA well field

Model boundary

Production well

South Coastal and Pawcatuck River

 watershed boundary

Simulated water table—Contour interval is variable

EXPLANATION

Simulated area contributing recharge to

 Central Beach Fire District well field

Simulated area contributing recharge to

 East Beach Water Association well field

Till and bedcrock outcrops

Wetlands

Charlestown moraine

Stratified deposits

5

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

0 .5 1 KILOMETER

0 .5 1 MILE 
52 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

140

130

30

30

10

40

20

50

60

70

80

90

100

110

120

10

5

4

3

2

1

-1

1

-2

3

3

0

2

2

1

1

5

10

20

Block Island Sound

Ninigret Pond

Quonochontaug Pond

Quonochontaug

Neck

Tanyard Brook

West

Pond

Garden

Pond

CBFD well field

EBWA well field

71°43' 71°42'

41°22'

41°20'

Model boundary

Production well

South Coastal and Pawcatuck River

 watershed boundary

Simulated water table—Contour interval is variable

EXPLANATION

Simulated area contributing recharge to

 Central Beach Fire District well field

Simulated area contributing recharge to

 East Beach Water Association well field

Till and bedcrock outcrops

Wetlands

Charlestown moraine

Stratified deposits

5

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

0 .5 1 KILOMETER

0 .5 1 MILE 

Figure 27. Simulated areas contributing recharge to the Central Beach Fire District and East Beach Water 

Association well fields, at their total maximum pumping rate of 230 gallons per minute, Charlestown study 

site, southern Rhode Island.
Charlestown Study Site 53

71°43' 71°42'

41°22'

41°20'

Simulated traveltimes

EXPLANATION

Greater than 0 to 0.5 year

Greater than 0.5 to 1 year

Greater than 10 years

Greater than 3 to 10 years

Greater than 1 to 3 years

Model boundary

Production well

South Coastal and Pawcatuck River

 watershed boundary

Till and bedcrock outcrops

Wetlands

Charlestown moraine

Stratified deposits

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83

Block Island Sound

Ninigret Pond

Quonochontaug Pond

Quonochontaug

Neck

Tanyard Brook

West

Pond

Garden

Pond

CBFD well field

EBWA well field

0 .5 1 KILOMETER

0 .5 1 MILE 

Figure 28. Simulated traveltimes to the Central Beach Fire District and East Beach Water Association 

well fields at their maximum pumping rate of 230 gallons per minute, Charlestown study site, southern 

Rhode Island.
54 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Probabilistic Areas Contributing Recharge

The deterministic areas contributing recharge were based 

on the optimal parameter set determined from nonlinear 

regression and specified parameter values from the literature. 

Information on model parameters is provided in table 4. 

Different degrees of precision are associated with these 

estimated parameter values. A quantitative measure of the 

effects of parameter uncertainty on the simulated contributing 

area was determined by a Monte Carlo analysis. The parameter 

variance–covariance matrix from nonlinear regression can be 

used to create plausible parameter sets for the Monte Carlo 

analysis (Starn and others, 2000). The variance–covariance 

matrix incorporates the uncertainty of the parameter estimates 

and the correlation among parameters from the calibrated 

model. Parameter values for the Monte Carlo analysis were 

generated by equation 1.

In addition to the optimal parameter set estimated by 

nonlinear regression, several of the specified parameters 

were incorporated into the variance–covariance matrix. 

Uncertainty in the specified parameter values may also affect 

model predictions. A partial sensitivity analysis determined 

that unestimated parameters representing the anisotropy of 

glacial deposits and hydraulic properties of bedrock had 

little or no effect on the simulated contributing area to the 

production wells for a plausible range in values. Recharge 

parameters (R_SDM, R_TILL, and R_WETLD) and the 

hydraulic connection between surface water and the aquifer 

(KV_PEAT), important parameters that may affect the 

simulated contributing area in glacial valley-fill settings, 

were incorporated into the variance–covariance matrix. 

Incorporating these four parameters into the variance–

covariance matrix, however, caused large unrealistic 

uncertainties about the specified parameter values, most 

likely because of insufficient information provided by 

the observations and high parameter correlations. Prior 

information for these parameters (see sections “Hydraulic 

Properties” and “Recharge Rates”) was used to constrain 

uncertainty about the specified value to realistic ranges 

reported in the literature. Prior weights were used so that 

the 95-percent confidence intervals about the specified value 

(table 4) were equivalent to ±21 percent for R_SDM and to 

±59 percent for R_TILL and R_WETLD. The 95-percent 

confidence interval for KV_PEAT was equivalent to a vertical 

conductivity for peat of 0.007 to 1.5 ft/d. Thus, all parameter 

uncertainty important for model prediction was incorporated 

into the Monte Carlo analysis. In contrast with the South 

Kingstown study site, however, parameter uncertainty was 

constrained by observations as well as by prior information.

The parameter sets created by equation 1 for the 

Monte Carlo analysis are shown in figure 29A for hydraulic 

parameters and figure 29B for recharge parameters. The 

hydraulic parameters were log-transformed in the model. 

The parameter sets have a lognormal or normal distribution 

around the optimal or specified parameter value. The 

spread of these data indicates the certainty with which the 

parameter was estimated considering the observations and 

prior information. Parameter sets with a KV_PEAT value two 

orders of magnitude greater or less than the specified value 

of 10 (a vertical conductivity for of 0.1 ft/d) were considered 

unrealistic for the vertical thickness of the peat layer simulated 

in the model, and thus parameter sets having these values were 

removed from the analysis. This accounted for 13 percent of 

the parameter sets.

For the Monte Carlo analysis, the model was first run 

with 1,000 parameter sets and the average pumping rate. The 

nine hydraulic and recharge parameter values in each set 

replaced corresponding parameter values in the calibrated 

model. Three acceptance criteria were used: (1) model had 

to converge, (2) model mass balance was 0.5 percent or less, 

and (3) calculated error variance was less than a specified 

value. The third acceptance criterion was varied in order to 

evaluate model fit to observations. These criteria were used so 

that model prediction uncertainty would not be overestimated. 

Results of the Monte Carlo analysis for the average 

pumping rate, with increasing calculated error variances, 

are summarized in table 5. The total size of the probabilistic 

contributing area was about the same (673 to 677 particles) for 

calculated error variances from 12 to18, but the size increased 

substantially (677 to 725 particles) if the model-fit statistic 

was not used. For this application of the Monte Carlo analysis, 

a calculated error variance criterion of 18 was used. Of the 

1,000 parameter sets run with MODFLOW, 599 fit the selected 

criteria. The distribution of hydraulic and recharge parameters 

after the acceptance criteria were applied (fig. 30) was slightly 

altered from the original parameter sets, but a generally 

lognormal or normal distribution is indicated. The probability 

that a recharge location would be in the area contributing 

recharge to the production wells was determined by dividing 

the number of times a particle at a given location was captured 

by a well by the total number of accepted particle-tracking 

simulations. A Monte Carlo analysis with the maximum 

pumping rate was also done by using the parameter sets that fit 

the selected criteria for the average pumping rate. The criteria 

for the Monte Carlo analysis using the 599 parameter sets with 

the maximum pumping rate was a water budget of 0.5 percent 

or less. Of the 599 parameter sets, 584 sets or 97 percent fit 

these criteria and thus were run with the particle tracking 

program (table 5).

The probabilistic areas contributing recharge to the 

production wells at the average pumping rate and the 

maximum pumping rate are shown in figures 31 and 32; 

probabilities are expressed as a percentage. The sizes of 

the probabilistic contributing areas are larger than the 

deterministic contributing areas; this indicates that some areas 

not in the deterministic contributing area may actually be in 

the contributing area.

At the average pumping rate, areas with high probabilities 

(greater than 50 percent) are on the same side of the nearby 

stream as the production wells, at and near the wells. The 

deterministic contributing area on this side of the stream 

generally coincides with these high probabilities. There is 
Charlestown Study Site 55

0

1

2

3

4

K_SD

K_TILL

K_MOR

K_WETLAND

KV_PEAT

SB_MULT

FREQUENCY OF OCCURENCE

0.00

0.05

0.10

0.15

0.20

R_SDM

R_TILL

R_WETLAND

-3 -2 -1 0 1 2 3 4 5

LOGARITHM OF HYDRAULIC CONDUCTIVITY, IN FEET PER 

DAY, EXCEPT KV_PEAT, WHICH IS DIMENSIONLESS

5 10 15 20 25 30 35 40 45 50

RECHARGE RATE, IN INCHES PER YEAR

A

B

0

FREQUENCY OF OCCURENCE

Figure 29. Frequency distribution of A, hydraulic parameters, and of B, recharge parameters, before 

acceptance criteria were applied to determine the probabilistic areas contributing recharge to the 

Central Beach Fire District and East Beach Water Association well fields (parameter information is 

provided on table 4), Charlestown study site, southern Rhode Island.
56 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

less spread of low probabilities on the production-well side of 

the stream, most likely because this area is close to the wells 

and is constrained by model boundaries and the groundwater 

mound southwestward. On the side of the stream opposite the 

production wells, probabilities decrease in a radially outward 

pattern; three quarters of the deterministic contributing area 

on this side of the stream coincides with probabilities greater 

than 10 percent to 50 percent, with the remaining deterministic 

contributing area in an area associated with probabilities of 

10 percent or less. Areas associated with low probabilities 

extend northward on the west side of a simulated groundwater 

divide, and they include precipitation recharge originating in 

the till uplands.

At the maximum withdrawal rate, areas with probabilities 

greater than 50 percent generally coincide with the 

deterministic contributing area. Generally, areas with shorter 

traveltimes are associated with higher probabilities and are 

more likely to coincide with the deterministic contributing 

area than areas with longer traveltimes associated with 

lower probabilities. Areas with low probabilities extend 

north through the middle of Quonochontaug Neck to the 

mainland. These low probabilities include small isolated areas 

Table 5. Summary of the Monte Carlo analysis for the Charlestown study site, southern Rhode Island.

[CBFD, Central Beach Fire District; EBWA, East Beach Water Association; mi2, square mile; KV_Peat, ratio of horizontal to vertical hydraulic conductivity of 

peat deposits]

Comment

Calculated 

error variance 

criterion

Number of parameter sets 

run with MODFLOW: 

Number of parameter sets 

that fit criteria1

Total size of probabilistic contributing 

area to CBFD & EBWA wells

Number of particles 

or cells

Area 

(mi2)

Average pumping rate

KV_Peat conditioned 6 1,000:224 530 0.0684

KV_Peat conditioned 9 1,000:460 642 0.0829

KV_Peat conditioned 12 1,000:553 673 0.0869

KV_Peat conditioned 15 1,000:591 676 0.0873

KV_Peat conditioned 18 1,000:599 677 0.0874

KV_Peat conditioned None 1,000:620 725 0.0936

Maximum pumping rate

Parameter sets that fit selected water budget and 

calculated error variance criteria for average 

pumping rate

None 599:584 2,829 0.376

1

Criteria: (1) model converged, (2) mass balance 0.5 percent or less, and (3) for some cases, a calculated error variance less than a specified value.

remote from the production wells, and they include recharge 

originating in the Charlestown Moraine near the divide 

between the South Coastal watershed and the Pawcatuck 

River watershed.

Uncertainty in the simulated areas contributing recharge 

may be reduced by additional observations of water level 

and streamflow and by other types of field measurements. 

Additional observations may increase the precision of 

estimated parameter values. Additional observations may 

also help to increase the number of parameters that could 

be estimated using nonlinear regression by providing more 

information and (or) by reducing parameter correlations. 

Specifically, streamflow observations may reduce parameter 

correlations for recharge parameters, which conceptually are 

very important for determining contributing areas. Increasing 

the number of parameters estimated by nonlinear regression, 

thereby decreasing need for using prior information, would 

allow an uncertainty analysis based solely on objective 

model-calibration data. Knowledge of the average altitudes of 

Block Island Sound and the coastal ponds Quonochontaug and 

Ninigret would reduce model-design uncertainty.
Charlestown Study Site 57

0

1

2

3

4

FREQUENCY OF OCCURENCE

0.00

0.05

0.10

0.15

0.20

-3 -2 -1 0 1 2 3 4 5

LOGARITHM OF HYDRAULIC CONDUCTIVITY, IN FEET PER 

DAY, EXCEPT KV_PEAT, WHICH IS DIMENSIONLESS

A

B

5 10 15 20 25 30 35 40 45 50

RECHARGE RATE, IN INCHES PER YEAR

0

R_SDM

R_TILL

R_WETLAND

K_SD

K_TILL

K_MOR

K_WETLAND

KV_PEAT

SB_MULT

FREQUENCY OF OCCURENCE

Figure 30. Frequency distribution of A, hydraulic parameters, and of B, recharge parameters, after 

acceptance criteria were applied to determine the probabilistic areas contributing recharge to the 

Central Beach Fire District and East Beach Water Association well fields (parameter information is 

provided on table 4), Charlestown study site, southern Rhode Island.
58 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Figure 31. Simulated probabilistic areas contributing recharge to the Central Beach Fire District and 

East Beach Water Association well fields at their total average pumping rate of 16 gallons per minute, 

Charlestown study site, southern Rhode Island.

Block Island Sound

Ninigret Pond

Quonochontaug Pond

Quonochontaug

Neck

Tanyard Brook

West

Pond

Garden

Pond

CBFD well field

EBWA well field

0 .5 1 KILOMETER

0 .5 1 MILE 

71°43' 71°42'

41°22'

41°20'

Probablistic contributing areas to

Central Beach Fire District and East Beach

Water Associations well fields, in percent

EXPLANATION

Greater than 0 to 10

Greater than 10 to 25

Greater than 25 to 50

Greater than 50 to 100

Model boundary

Production well

South Coastal and Pawcatuck River

 watershed boundary

Till and bedcrock outcrops

Wetlands

Charlestown moraine

Stratified deposits

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83
Charlestown Study Site 59

Figure 32. Simulated probabilistic areas contributing recharge to the Central Beach Fire District and 

East Beach Water Association well fields at their total maximum pumping rate of 230 gallons per minute, 

Charlestown study site, southern Rhode Island.

71°43' 71°42'

41°22'

41°20'

Block Island Sound

Ninigret Pond

Quonochontaug Pond

Quonochontaug Neck

Ta

ny

ard

Brk

West

Pond

Garden

Pond

CBFD well field

EBWA well field

0 .5 1 KILOMETER

0 .5 1 MILE 

Probablistic contributing areas to

Central Beach Fire District and

East Beach Water Association

well fields, in percent

Greater than 0 to 10

Greater than 10 to 25

Greater than 25 to 50

Greater than 50 to 100

EXPLANATION

Model boundary

Production well

South Coastal and Pawcatuck River

 watershed boundary

Till and bedcrock outcrops

Wetlands

Charlestown moraine

Stratified deposits

Base from U.S. Geological Survey,

Rhode Island state plane projection, 1:24,000, NAD 83
60 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Summary and Conclusions

The U.S. Geological Survey (USGS), in cooperation 

with the Rhode Island Department of Health, Office of 

Drinking Water Quality, began a 2-year investigation in 

2006 to increase understanding of groundwater flow and 

the areas contributing recharge to four well fields in South 

Kingstown and Charlestown in southern Rhode Island. The 

well fields are screened in surficial sediments of glacial origin 

in wetland and coastal settings. Areas contributing recharge 

to the well fields were determined on the basis of numerical 

steady-state groundwater-flow models representing longterm average hydrologic conditions. The groundwater-flow 

models were calibrated to field observations collected during 

this and previous studies by inverse modeling using nonlinear 

regression. Summary statistics from nonlinear regression were 

used to provide a quantitative measure of model-prediction 

uncertainty. The area contributing recharge to a well is defined 

as the surface area where water recharges the groundwater and 

then flows toward and discharges to the well.

In South Kingstown, two UWRI well fields, composed 

of seven production wells, are in Mink Brook watershed and 

near Worden Pond and wetlands of large areal extent. Mink 

Brook is a small intermittent stream that drains 1.82 mi2

at its confluence with Worden Pond in the Chipuxet River 

watershed. The wells are screened in sand and gravel deposits 

of a glacial morphosequence with saturated thicknesses greater 

than 100 ft at the well field closest to the preglacial valley axis 

and about 70 ft at the well field closest to the valley-upland 

contact. Wetland deposits of peat in the vicinity of the well 

fields range from less than 1 ft near the edges of the wetland 

to greater than 11 ft in central areas; thicknesses generally 

range from 5 to 8 ft. Stage measurements in Mink Brook and 

the wetlands and water levels in a vertical nest of piezometers 

installed in the peat and sand and gravel deposits near each 

well field indicated a downward gradient during pumping 

conditions, and thus the potential for surface water to infiltrate 

the underlying aquifer. An analytical method to determine 

hydraulic properties based on water-level drawdowns was 

used at one piezometer site when the nearby well field 

pumped 1,350 gal/min during 90 percent of a 20-day period. 

Transmissivity estimated for the sand and gravel deposits was 

18,900 ft2/d, which is within the range of previously reported 

values at the well field. The analysis indicated that the vertical 

hydraulic conductivity of the peat, which controls vertical 

flow between the surface water and the aquifer, was roughly 

0.01 ft/d.

Groundwater flow at the South Kingstown study site 

was simulated by a five-layer model representing surficial 

deposits and the underlying bedrock. The model was 

calibrated to 135 water-level observations and 5 streamflow 

observations. Boundary conditions and hydraulic properties 

were represented by18 parameters: 3 recharge parameters, 

9 horizontal hydraulic-conductivity parameters, 5 vertical 

anisotropy parameters, and 1 multiplier of streambed vertical 

hydraulic conductivity. One of the recharge parameters, which 

represented water available for recharge in the wetlands, 

was specified in the model, but it was included in modelprediction uncertainty. Nine parameters were estimated by 

nonlinear regression; observations did not provide enough 

information on the remaining parameters, most of which 

represented vertical anisotropies of the surficial deposits and 

hydraulic properties of bedrock, and these parameters were 

therefore specified in the model based on reported values. A 

model-fit statistic, the calculated error variance, which is a 

measure of the overall magnitude of the weighted residuals 

(differences between observed and simulated water levels 

and streamflows), was 5.32. Influence statistics indicated 

that nine water-level and four streamflow observations had 

the most overall influence in the regression and the set of 

estimated parameters; four of the five streamflow observations 

were influential, indicating the importance of streamflow 

observations in model calibration. The estimated optimal 

parameter value for recharge to stratified and morainal 

deposits was 29.0 in/yr and to till deposits was 23.1 in/yr. 

Estimated optimal values for horizontal hydraulic conductivity 

parameters were as follows: stratified deposits, 137 and 

332 ft/d; till deposits, 3.8 and 7.9 ft/d; Charlestown and Point 

Judith Moraines, 16 ft/d; and a small area of mixed deposits of 

stratified, till, and undifferentiated morainal deposits, 26 ft/d. 

The optimal parameter value for the streambed multiplier was 

equivalent to vertical hydraulic conductivities of 1.8 ft/d for 

coarse-grained bed sediments and 0.18 ft/d for organic-rich 

bed sediments. Optimal values for the two recharge parameters 

and the parameter representing a mix of surficial deposits were 

the most precisely estimated, whereas the streambed hydraulic 

conductivities were the least precisely estimated. 

The simulated area contributing recharge to the UWRI 

well fields at the average pumping rates during 2003–07 

(total rate of 2,138 gal/min) extended to groundwater 

divides in mostly till and morainal deposits, and it covered 

2.30 mi2. Most of a sand and gravel mining operation, which 

is between the well fields and near Mink Brook, was in the 

simulated contributing area. Precipitation recharge in some 

areas near small simulated streams in Mink Brook watershed 

and Alewife Brook watershed, which share a common 

boundary in transmissive stratified deposits, discharged to the 

streams instead of being captured by the well fields. At the 

maximum pumping capacities for the well fields (total rate 

of 5,100 gal/min), the contributing area expanded to 5.54 mi2

and intercepted additional groundwater and infiltration of 

surface water. Most of the precipitation recharge in Mink 

Brook and Alewife Brook watersheds was intercepted by 

the well fields, and simulated streams ceased to flow. The 

maximum pumping rate shifted the simulated groundwater 

divides and captured groundwater that would have discharged 

to adjacent watersheds under average pumping conditions. 

The contributing area included an area beneath Worden Pond 

and a remote, isolated area in upland till on the side of Worden 

Pond opposite the well fields. Particle tracks indicated that 

recharge originating in this upland till travels along deep 
Summary and Conclusions 61

groundwater-flow paths in the valley-fill deposits and, under 

pumping conditions, passes beneath Worden Pond to one 

of the well fields. About 12 percent of the pumped water 

was from surface water, primarily Worden Pond; this pondwater infiltration is less than four percent of the long-term 

average streamflow entering the pond. Simulated groundwater 

traveltimes from recharge locations to production wells for 

the maximum pumping rate ranged from less than 1 year to 

greater than 500 years; 59 percent of the traveltimes were 

10 years or less. 

Parameter uncertainty and associated effects on the 

simulated area contributing recharge to the well fields were 

evaluated using a Monte Carlo analysis. Optimal parameter 

values and the parameter variance–covariance matrix from 

nonlinear regression were used to create parameter sets for 

the analysis. Two unestimated parameters (water available for 

recharge in the wetlands and vertical hydraulic conductivity 

of the peat) that are important for model predictions were 

incorporated into the variance–covariance matrix. The 

observations provided enough information to constrain the 

uncertainty of these parameters within a realistic range around 

the specified values of 22 in/yr and 0.1 ft/d, respectively, for 

these highly variable and poorly understood parameters. The 

95-percent confidence intervals were 10.1 and 33.8 in/yr for 

wetland recharge and 0.006 and 1.5 ft/d for vertical hydraulic 

conductivity of the peat. Of 1,000 parameter sets, 749 that 

fit a criterion for water budget and a criterion for calculated 

error variance for the average pumping rate were used 

in the uncertainty analysis. The maximum pumping rate 

scenario used these 749 parameter sets with a water-budget 

criterion. The size of the probabilistic contributing area for 

both the average and maximum pumping rates was larger 

than the size of the deterministic contributing areas because 

of the effects of parameter uncertainty; this indicates that 

some areas not in the deterministic contributing areas may 

actually be in the contributing area. For both pumping rates, 

the deterministic contributing area generally coincides 

with areas associated with high probabilities (greater than 

50 percent). For the average pumping rate, in addition to 

areas with low probabilities distant from the well fields, areas 

where simulated streams intercepted precipitation recharge 

in the calibrated model were associated with generally low 

probabilities, indicating that this recharge may instead go 

directly to a well. That part of the sand and gravel mining 

operation between the well fields and not in the deterministic 

contributing area was in the probabilistic contributing 

area, including some areas with high probabilities. For 

the maximum pumping rate, some areas on the opposite 

side of Worden Pond from the well fields that are not in 

the deterministic contributing area are in the probabilistic 

contributing area but at mostly low probabilities. A sensitivity 

analysis showed that by decreasing recharge rates or the 

hydraulic connection between surface water and the aquifer, 

the simulated contributing area at the maximum pumping 

rate expanded primarily by intercepting groundwater that 

originated on the opposite side of Worden Pond. 

In Charlestown the CBFD and EBWA well fields, each 

composed of two production wells, are on a 0.85 mi2 peninsula 

bounded by Block Island Sound and large saltwater ponds. 

The wells are screened in a coarse-grained, ice-proximal part 

of a morphosequence with saturated thicknesses generally 

less than 30 ft on the peninsula. Streamflow measured in a 

stream and associated wetlands near the well fields indicated 

an average net gain of 0.09 ft3/s at approximately average 

hydrologic conditions. Measured peat thicknesses generally 

ranged from 2 to 4 ft.

Groundwater flow was simulated by a four-layer model 

representing surficial deposits and the bedrock. The model was 

calibrated to 46 water-level and 1 streamflow observations. 

The model was represented by 14 parameters—3 recharge 

parameters, 5 horizontal hydraulic-conductivity parameters, 

5 vertical anisotropy parameters, and a multiplier of streambed 

hydraulic conductivity. Available observations did not provide 

enough information to estimate parameters representing 

vertical anisotropies of surficial deposits and hydraulic 

properties of the bedrock. In addition, two sets of parameters 

(recharge rate to stratified and morainal deposits, and the 

horizontal hydraulic conductivity of the stratified deposits; 

recharge rate to till deposits, and the horizontal hydraulic 

conductivity of till deposits) were too highly correlated to 

be estimated uniquely. The recharge parameters, including a 

parameter that represented water available for recharge in the 

wetlands and the parameters that were insensitive to available 

observations, were specified in the model on the basis of 

reported values and parameter-estimation results from the 

South Kingstown study site. Five parameters (four horizontal 

hydraulic conductivities and the streambed multiplier) were 

estimated by nonlinear regression. The calculated error 

variance was 3.03. Influence statistics indicated that the 

streamflow observation, in addition to being one of four 

observations influential to the set of estimated parameters 

values, was the only observation important to more than two 

individual estimated parameter values. Estimated optimal 

values for glacial horizontal hydraulic-conductivity parameters 

were as follows: stratified deposits, 64 ft/d; till deposits, 

2.2 ft/d; and the Charlestown Moraine, 14 ft/d. The optimal 

value for a parameter that represented the lack of resistance 

to surface-water flow in the wetland and groundwater flow 

in poorly decomposed peat was 4,200 ft/d. The optimal 

parameter value for the streambed multiplier was equivalent 

to hydraulic conductivities of 4.3 ft/d for coarse-grained 

bed sediments and 0.43 ft/d for organic-rich bed sediments. 

The optimal parameter value for the horizontal hydraulic 

conductivity of stratified deposits was the most precisely 

estimated, and the streambed hydraulic conductivities were the 

least precisely estimated.

The simulated area contributing recharge for the 

combined average pumping rates during 2003–07 (16 gal/min) 

for the CBFD and EBWA well fields included 0.018 mi2. 

The contributing area extended southwestward from the 

well fields to a simulated groundwater mound, it underlay a 

small part of the adjacent wetlands, and it included isolated 
62 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

areas on the side of the wetland opposite to the well fields. 

For the maximum pumping rate (230 gal/min), the simulated 

contributing area (0.26 mi2) expanded in all directions to 

capture enough water to balance the increased pumping 

rate. The contributing area included precipitation recharge 

originating in a till area on the peninsula, and it underlay 

part of a nearby pond. Because the wells are screened in a 

thin aquifer, simulated traveltimes from recharge locations to 

the production wells were relatively short: 94 percent of the 

traveltimes were 10 years or less, and the median traveltime 

was 1.3 years.

Four unestimated parameters that may be important for 

quantifying prediction uncertainty (3 recharge parameters 

and a peat vertical hydraulic-conductivity parameter) 

were included in the variance–covariance matrix for the 

Monte Carlo analysis. Including these four parameters, 

however, led to unrealistic uncertainties about the specified 

parameter value because of insufficient information 

provided by the observations. Prior information was used 

to constrain parameter uncertainties to realistic ranges so 

that model-prediction uncertainty was not overestimated. Of 

1,000 parameter sets, 599 that fit a criterion for water budget 

and a criterion for calculated error variance for the average 

pumping rate were used in the analysis. The maximum 

pumping rate scenario used these 599 parameter sets with a 

water-budget criterion. For the average pumping rate, areas 

associated with high probabilities were only on the well-field 

side of the nearby wetlands; the deterministic contributing area 

on this side of the wetland corresponded to this area of high 

probability. On the opposite side of the wetland from the well 

fields, probabilities decreased in a radially outward pattern. 

Areas associated with low probabilities extended to the till 

area on the peninsula. For the maximum pumping rate, areas 

associated with high probabilities generally corresponded 

with the deterministic contributing area. Areas with low 

probabilities extended through the middle of the peninsula to 

the mainland, and they included small isolated areas remote 

from the well fields.

Acknowledgments

The author expresses appreciation to Clay Commons 

(Source Water Assessment Coordinator, RIDOH, Office of 

Drinking Water Quality) for initiating and supporting the 

study, and to Richard Amirault (RIDOH), Ernie Panciera 

(RIDEM), and Theodore Peters (RIDEM) for their suggestions 

during the study. The author thanks Jeffrey Starn (USGS, 

Connecticut Water Science Center) for providing a computer 

program to facilitate the Monte Carlo analysis and for his 

insights into the method, and Janet Stone (USGS Geologic 

Discipline, Connecticut) for her guidance in constructing the 

geologic sections. Finally, the author appreciates the assistance 

of Stanley Knox (Manager, UWRI), Neil Williamson (Chief 

Operator, UWRI), William Meyer (CBFD), and Peter Ogle 

(EBWA) for information concerning groundwater withdrawals 

and for their assistance in coordinating field activities.

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66 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

Appendix 1. Water depth, and thickness of peat and organic-rich sediment (location of profiles shown on figures 3 

and 20), South Kingstown and Charlestown study sites, southern Rhode Island.—Continued

[ft, foot; coordinates determined by global positioning system at South Kingstown study site and by 1:5,000 orthophoto at Charlestown 

study site; A, North-south profile near west well field, November 6, 2006; B, West-east profile in Mink Brook near west well field, 

November 6, 2006; C, North-south profile near east well field, November 7, 2006; D, West-east profile near east well field, November 7, 

2006; and E, West-east profile near east well field, November 7, 2006; F, West-east profile north of Sea Breeze Avenue, December 6, 

2006; and G, West-east profile south of Sea Breeze Avenue, December 6, 2006]

Profile Easting

(ft)

Northing

(ft)

Water depth

(ft)

Thickness of peat and 

organic-rich sediment

(ft)

South Kingstown study site

A 313,880 128,290 0 7.5

A 313,956 128,299 0 6.3

A 313,979 128,276 0 5.8

A 313,949 128,225 0 4.3

A 314,024 128,160 0 5.3

A 314,000 128,113 0 5.9

A 313,977 128,036 0 6.1

A 313,926 127,993 0 7.1

A 313,930 127,947 0 8.6

A 313,933 127,910 0 9.4

A 313,949 127,877 0 7.0

A 313,984 127,863 0 4.7

A 313,984 127,844 1.0 MinkBrook 4.3

A 313,998 127,832 0 4.4

A 313,995 127,806 0 5.7

A 313,971 127,781 0 6.8

A 313,978 127,748 0 8.0

A 313,984 127,719 0 7.6

A 313,982 127,689 0 6.4

A 314,014 127,658 0 5.7

A 314,021 127,615 0 4.6

A 314,025 127,593 0 3.1

A 314,012 127,577 0 2.0

A 313,992 127,540 0 0.8

B 313,852 127,808 1.2 4.7

B 313,881 127,807 1.3 5.7

B 313,929 127,819 1.4 6.3

B 314,052 127,826 0.7 4.2

B 314,101 127,797 0.7 4.8

B 314,143 127,768 0.5 4.9

C 317,861 128,228 2.1 5.0

C 317,809 128,175 0.7 5.6

C 317,834 128,122 0.4 7.6

C 317,831 128,050 0.5 5.6

C 317,814 128,009 0.6 5.6

C 317,803 127,962 0.4 5.9
References Cited 67

Appendix 1. Water depth, and thickness of peat and organic-rich sediment (location of profiles shown on figures 3 

and 20), South Kingstown and Charlestown study sites, southern Rhode Island.—Continued

[ft, foot; coordinates determined by global positioning system at South Kingstown study site and by 1:5,000 orthophoto at Charlestown 

study site; A, North-south profile near west well field, November 6, 2006; B, West-east profile in Mink Brook near west well field, 

November 6, 2006; C, North-south profile near east well field, November 7, 2006; D, West-east profile near east well field, November 7, 

2006; and E, West-east profile near east well field, November 7, 2006; F, West-east profile north of Sea Breeze Avenue, December 6, 

2006; and G, West-east profile south of Sea Breeze Avenue, December 6, 2006]

Profile Easting

(ft)

Northing

(ft)

Water depth

(ft)

Thickness of peat and 

organic-rich sediment

(ft)

South Kingstown study site—continued

C 317,715 127,894 1.0 7.9

C 317,701 127,813 2.0 7.3

C 317,706 127,756 2.2 7.3

D 317,375 128,302 1.7 6.6

D 317,559 128,260 0.3 7.2

D 317,671 128,232 0.5 3.9

D 317,728 128,245 1.1 2.4

D 317,777 128,233 0.9 2.7

D 317,862 128,220 2.2 5.8

D 317,925 128,269 1.4 5.9

D 317,956 128,321 0.4 3.6

E 317,536 127,942 0.3 11.7

E 317,569 127,915 0.2 11.0

Charlestown study site

F 271,710 94,400 0.4 1.2

F 271,740 94,410 0.4 4.8

F 271,770 94,420 0.4 4.4

F 271,820 94,430 0.4 1.9

F 271,850 94,430 0.4 2.2

F 271,880 94,440 0.4 2.1

G 271,630 93,670 0.4 4.5

G 271,680 93,690 0.8 4.0

G 271,720 93,720 0.7 3.1

G 271,760 93,740 0.5 3.8

G 271,810 93,760 0.6 4.0

G 271,850 93,780 0.6 3.6

G 271,890 93,810 0.8 3.1

G 271,940 93,830 0.5 3.3

G 271,970 93,860 0.9 2.5

G 272,020 93,870 0.7 2.8

G 272,060 93,900 0.6 2.6

G 272,100 93,930 0.8 2.0

G 272,150 93,950 0.6 2.2

G 272,190 93,980 0.6 1.2

G 272,240 94,000 0.5 2.2
68 Delineation and Prediction Uncertainty of Areas Contributing Recharge to Selected Well Fields, Southern Rhode Island

91

92

93

94

95

Tucker Pond stage

Water level in pond-bottom piezometer

WATER LEVELS, IN FEET RELATIVE TO NGVD29

2006 2007 2008

B

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

87

88

89

90

91

Worden Pond stage

WATER LEVELS, IN FEET RELATIVE TO NGVD29

2006 2007 2008

A

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

Appendix 2. A, Stage of Worden Pond and B, stage of Tucker Pond and water levels in a pond-bottom piezometer, 2006–2008 

(location of measurement sites shown on figure 3), South Kingstown study site, southern Rhode Island.
References Cited 69

Appendix 3. Streamflow measurements made at partial-record sites (location of partial-record sites shown on figures 3 and 20), 

South Kingstown and Charlestown study sites, southern Rhode Island.

[USGS, U.S. Geological Survey; latitude and longitude in degrees, minutes, and seconds; mi2, square mile; ft3/s, cubic feet per second; μS/cm, microsiemens 

per centimeter; °C, degrees Celsius; --, no data]

USGS 

streamgage 

number

Streamgage name Latitude

 ° ‘ “

Longitude

 ° ‘ “

Drainage 

area 

(mi2)

Date Discharge 

(ft3/s)

Specific 

conductance 

(μS/cm at 

25°C)

South Kingstown study site

01117235 Unnamed tributary to Peace Dale Reservoir 

at Allen Avenue near Peace Dale, RI

41 26 49 71 30 51 0.31 3/7/2008 0.33 --

01117250 Browns Brook at Wakefield, RI 41 25 56 71 31 22 0.50 6/15/2007 0.51 --

01117252 Unnamed tributary to Potter Pond at 

State Route 1 near Wakefield, RI

41 24 41 71 31 51 0.31 3/7/2008 0.30 --

01117352 Unnamed tributary to Genesee Brook at 

Curtis Corner Road near Curtis Corner, RI

41 26 54 71 32 51 0.02 6/15/2007 0.03 --

01117353 Mink Brook at Tuckertown, RI 41 25 56 71 32 35 0.58 6/15/2007 0.59 --

011173531 Unnamed tributary to Mink Brook 1.1 mi 

northeast of Tuckertown Four Corners, RI

41 26 20 71 32 42 -- 6/15/2007 0.03 --

011173532 Unnamed tributary to Mink Brook 1.0 mi 

northeast of Tuckertown Four Corners, RI

41 26 22 71 32 47 -- 6/15/2007 0.01 --

011173533 Unnamed tributary to Mink Brook 0.9 mi 

northeast of Tuckertown Four Corners, RI

41 26 21 71 33 00 -- 6/15/2007 0.01 --

011173534 Mink Brook at State Route 110 near 

Tuckertown Four Corners, RI

41 26 00 71 33 24 1.64 12/20/2006 0.93 --

6/15/2008 0.55 --

011173535 Alewife Brook upstream of Tucker Pond near 

Tuckertown Four Corners, RI

41 25 34 71 32 46 0.63 6/15/2008 0.15 --

Charlestown study site

01117290 Unnamed tributary to Quonochontaug Pond at 

Sea Breeze Avenue at Quonochontaug, RI

41 20 29 71 42 18 0.15 11/7/2006 0.15 --

12/20/2006 0.11 168

011172901 Unnamed tributary to Quonochontaug Pond at 

Quonochontaug Road at Quonochontaug, RI

41 20 37 71 42 34 0.30 11/7/2006 0.31 --

12/20/2006 0.13 168
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