Prepared in cooperation with the Rhode Island Water Resources Board

Numerical Simulation of Groundwater and Surface-Water

Interactions in the Big River Management Area,

Central Rhode Island

Scientific Investigations Report 2012–5077

U.S. Department of the Interior

U.S. Geological Survey
Cover Big River at Harkney Hill Road in Coventry, Rhode Island in February 2010 when the stage in the Flat River Reservoir was low 

and streamflow was limited to the river channel.
Numerical Simulation of Groundwater and 

Surface-Water Interactions in the Big River 

Management Area, Central Rhode Island

By John P. Masterson and Gregory E. Granato

Prepared in cooperation with the Rhode Island Water Resources Board

Scientific Investigations Report 2012–5077

U.S. Department of the Interior

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

Sally Jewell, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Masterson, J.P., and Granato, G.E., 2013, Numerical simulation of groundwater and surface-water interactions in the 

Big River Management Area, central Rhode Island: U.S. Geological Survey Scientific Investigations Report 2012–5077, 

53 p., http://pubs.usgs/sir/2012/5077/.
iii

Contents

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

Introduction.....................................................................................................................................................1

Hydrogeology..................................................................................................................................................3

Simulation of Groundwater and Surface-Water Interactions................................................................4

Development of the Groundwater Model .........................................................................................5

Model Discretization and Boundary Conditions.....................................................................5

Spatial Discretization .........................................................................................................5

Temporal Discretization.....................................................................................................5

Hydrologic Boundary Conditions .....................................................................................5

Hydraulic Properties .................................................................................................................10

Hydrologic Stresses ..................................................................................................................10

Recharge............................................................................................................................10

Pumping..............................................................................................................................14

Model Calibration ......................................................................................................................14

Simulation of Groundwater Withdrawals .......................................................................................16

Simulation of Short-Term Pumping.........................................................................................23

Effects of Model Discretization ......................................................................................27

Effects of Storage in Till Deposits ..................................................................................27

Effects of Changes in Reservoir Stage..........................................................................30

Simulation of Long-Term Pumping..........................................................................................31

Effect of Increased Pumping Time.................................................................................31

Effect of Changes in Reservoir Stage............................................................................31

Simulated Effects of Groundwater Withdrawals on Wetlands ...................................................36

Limitations of Analysis .......................................................................................................................36

Summary and Conclusions.........................................................................................................................38

References Cited..........................................................................................................................................39

Appendix 1. Methods for Estimating Long-Term Hydrologic Conditions.........................................43

Figures

1. Map showing location of Big River Management Area, central Rhode Island, and

model-calculated water levels for long-term average conditions.......................................2

2. Schematic diagram of a hypothetical aquifer showing groundwater discharge to a

surface-water body with A, no pumping; B, pumping at a rate (Q1) such that the

well would capture water that otherwise would discharge to the surface-water

body; and C, pumping at a higher rate (Q2) so that the flow direction is reversed

and the well pumps water from the surface-water body ......................................................4

3. Map showing model extent and distribution of simulated boundary conditions of

groundwater-flow model of Big River Management Area, central Rhode Island .............6

4. Sections showing vertical layering and model representation of geologic sections

A–A’ and B–B’ ...............................................................................................................................7

5. Photographs showing Big River at Harkney Hill Road, Coventry, Rhode Island................9
iv

6. Map showing surficial geology of the Big River Management Area, central 

Rhode Island................................................................................................................................11

7. Geologic sections (A–A’ and B–B’) showing the distribution of stratified glacial

deposits in the Big River Management Area, central Rhode Island..................................12

8. Graph showing monthly values of precipitation and calculated aquifer recharge 

at the T.F. Green Airport weather station, Providence, Rhode Island, from 1960 

through 2006 ................................................................................................................................14

9. Map showing locations of water-level and streamflow sites used for model

calibration and model-calculated water-level contours for long-term average

conditions, Big River Management Area, central Rhode Island ........................................15

10. Graphs showing comparison of A, model-calculated and estimated water levels,

and B, residual (estimated minus model calculated) water levels as a function of

estimated water levels for long-term average conditions...................................................17

11. Graphs showing comparison of monthly departure from average conditions for

model-calculated and estimated water levels for observation wells A, WGW285;

B, WGW286; C, WGW 287; D, WGW 290; E, WGW291; F, WGW293; G, WGW303; H,

WGW304; I, WGW305; J, WGW313; and K, WGW320 in the Big River Management

Area, central Rhode Island .......................................................................................................18

12. Graph showing comparison of changes in model-calculated and estimated 

vertical gradients with time at A, Reynolds Pond Swamp (WGW427); B, Cedar 

Swamp (WGW428); and C, Scarborough Swamp (WGW426), Big River 

Management Area, central Rhode Island ..............................................................................24

13. Graphs showing comparison of model-calculated and estimated streamflows for

long-term average monthly conditions from 1960 through 2006 in the Big River

Management Area, central Rhode Island ..............................................................................25

14. Map showing location of test wells WGW443 and WGW444 and monitoring wells

measured during the aquifer test conducted from December 16 to 21, 2009, and

model-calculated water-level changes in response to 5 days of simulated pumping

in the Big River Management Area, central Rhode Island..................................................26

15 . Graph showing comparison between measured and model-calculated water-level

changes with distance at monitoring wells measured at the end of the 5-day

aquifer test conducted from December 16 to 21, 2009, Big River Management Area,

central Rhode Island ..................................................................................................................27

16. Graph showing comparison between measured and model-calculated waterlevel changes with distance at monitoring wells measured at the end of the 

5-day aquifer test conducted from December 16 to 21, 2009, Big River Management 

Area, central Rhode Island. A, WGW445; B, WGW412; C, WGW413; D, WGW371; 

E, WGW416; and

F, WGW427 ...................................................................................................................................28

17. Maps showing model-calculated water-level declines A, after 5 days of continuous 

pumping for December conditions when reservoir area is drained and B, in response 

to continuous pumping for long-term average December conditions when reservoir 

area is drained, Big River Management Area, central Rhode Island................................32

18. Maps showing model-calculated water-level declines in response to continuous 

pumping for A, long-term average December conditions when reservoir area is 

drained and for B, long-term average August conditions when reservoir area is 

flooded, the Big River Management Area, central Rhode Island.......................................34
v

Tables

1. Horizontal hydraulic conductivity and horizontal to vertical anisotropy values of the

lithologic units used in the groundwater-flow model of the Big River Management

Area, central Rhode Island .......................................................................................................13

2. Measured and model-calculated water-level declines in response to 5 days of

continuous pumping at pumping test sites WGW443 and WGW444, Big River

Management Area, central Rhode Island ..............................................................................30

3. Source of water to pumping wells at a total pumping rate of 1.5 Mgal/d after 5 days

of pumping and for long-term monthly conditions ................................................................30

4. Model-calculated water-level declines at the priority wetland sites in response to 

continuous pumping at aquifer test sites WGW443 and WGW444 for short-term 

(5 days) and average monthly conditions, Big River Management Area, central 

Rhode Island................................................................................................................................36
vi

Conversion Factors, Datum, 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) 

Volume

gallon (gal) 0.003785 cubic meter (m3

) 

million gallons (Mgal) 3,785 cubic meter (m3

)

cubic foot (ft3

) 0.02832 cubic meter (m3) 

Flow rate

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

cubic foot per second (ft3

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

cubic foot per second per square mile 

[(ft3

/s)/mi2]

 0.01093 cubic meter per second per square 

kilometer [(m3/s)/km2]

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

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3

/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)

Hydraulic gradient

foot per mile (ft/mi) 0.1894 meter per kilometer

Transmissivity*

foot squared per day (ft2

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

Leakance

foot per day per foot [(ft/d)/ft] 1 meter per day per meter

inch per year per foot [(in/yr)/ft] 83.33 millimeter per year per meter [(mm/yr)/m]

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

(NGVD 29), formerly called Sea Level Datum of 1929.

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

Altitude, as used in this report, refers to distance above the vertical datum.

List of Acronyms

BRMA Big River Management Area

MODFLOW modular three-dimensional finite-difference groundwater model

MOVE maintenance of variance

RIWRB Rhode Island Water Resources Board

URI University of Rhode Island 

USGS U.S. Geological Survey
Simulation of Groundwater and Surface-Water 

Interactions in the Big River Management Area, 

Central Rhode Island

By John P. Masterson and Gregory E. Granato

Abstract 

The Rhode Island Water Resources Board is considering 

use of groundwater resources from the Big River Management 

Area in central Rhode Island because increasing water 

demands in Rhode Island may exceed the capacity of current 

sources. Previous water-resources investigations in this 

glacially derived, valley-fill aquifer system have focused 

primarily on the effects of potential groundwater-pumping 

scenarios on streamflow depletion; however, the effects of 

groundwater withdrawals on wetlands have not been assessed, 

and such assessments are a requirement of the State’s 

permitting process to develop a water supply in this area. 

A need for an assessment of the potential effects of 

pumping on wetlands in the Big River Management Area 

led to a cooperative agreement in 2008 between the Rhode 

Island Water Resources Board, the U.S. Geological Survey, 

and the University of Rhode Island. This partnership was 

formed with the goal of developing methods for characterizing 

wetland vegetation, soil type, and hydrologic conditions, 

and monitoring and modeling water levels for pre- and 

post-water-supply development to assess potential effects 

of groundwater withdrawals on wetlands. This report 

describes the hydrogeology of the area and the numerical 

simulations that were used to analyze the interaction between 

groundwater and surface water in response to simulated 

groundwater withdrawals.

The results of this analysis suggest that, given the 

hydrogeologic conditions in the Big River Management 

Area, a standard 5-day aquifer test may not be sufficient to 

determine the effects of pumping on water levels in nearby 

wetlands. Model simulations showed water levels beneath 

Reynolds Swamp declined by about 0.1 foot after 5 days of 

continuous pumping, but continued to decline by an additional 

4 to 6 feet as pumping times were increased from a 5-day 

simulation period to a simulation period representative 

of long-term average monthly conditions. This continued 

decline in water levels with increased pumping time is 

related to the shift from the primary source of water to the 

pumped wells being derived from aquifer storage during the 

early-time (5 days) simulation to being derived more from 

induced infiltration from the flooded portion of the Big River 

(southernmost extent of the Flat River Reservoir) during 

the months of March through October or from captured 

groundwater discharge to this portion of the Big River when 

the downstream Flat River Reservoir is drained for weed 

control during the months of November through February, as 

was the case for the long-term monthly conditions. 

Introduction

Water demand is increasing throughout Rhode Island, and 

the Rhode Island Water Resources Board (RIWRB), which 

is responsible for developing and protecting the State’s water 

resources, is concerned that increasing demand may exceed 

the capacity of current sources. In the early 1960s, the State 

proposed construction of a surface-water reservoir south of the 

Flat River Reservoir in the Big River Basin in central Rhode 

Island to meet these growing demands. At that time, the Big 

River Management Area (BRMA) (fig. 1), which covers about 

13.4 mi2

, was established under the responsibility of the Water 

Resources Coordinating Board, the precursor to the RIWRB. 

To date (2012), the U.S. Environmental Protection Agency 

has not given approval for construction of this reservoir. In 

the meantime, the RIWRB would like to develop the largely 

untapped groundwater resources of the basin as a possible

interim alternative to a surface-water reservoir.

In an effort to better understand the hydrogeology and 

groundwater-development options for the BRMA, the U.S. 

Geological Survey (USGS) and RIWRB began a series of 

cooperative studies of the area in 1995. Four reports were 

published as part of this cooperative effort: the first report 

provided hydrogeologic data collected in the area from July 

1996 through October 1998 (Craft, 2001); the second report 

described the glacial geology and hydraulic properties of 

the glacial sediments within the area (Stone and Dickerman, 

2002); the third report (Granato and others, 2003) described 

the hydrogeology of the area and simulated effects of 

selected groundwater-development options on streamflow 

in the area and provided the basis for a fourth report by 

Granato and Barlow (2005), who described the development 
2 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

255

255

255

260

270

260

270

270

265

265

325

340

330

320

315

305 310

300

290

280

270

285

280

290

300

310

320

340

350

360

270

280

290

275

260

380

370

WGW444

WGW443

WGW426

WGW4298

WGW427

WGW4362

COW484

WGW429

EXPLANATION

Active model area

Inactive model area

Pond

Wetland

Stream

Model-calculated water-level

 contour—Shows altitude at which

 water level would have stood in

 tightly cased wells. Contour interval

 5 feet. Datum is NGVD 29

Big River Management Area boundary

250

WGW444

WGW426 Monitoring well site and identifier 

Test well and site identifier

Mishnock River

Lake

Mishnock

Sweet

Pond

Capwell

Mill

Pond 

Reynolds Pond

Flat River

Reservoir

Congdon

tributar y

Big Rive

U

r

nnamed tributary

Bear Brook

Nooseneck Riv erNooseneck Riv er

Congdon River

Carr River

Reynolds Swamp Cedar Swamp

Scarborough Swamp

Congdon Swamp

0

0

2,600 5,200 FEET

500 1,000 METERS

71°39'00" 71°37'30" 71°36' 71°34'30"

41°39'00"

41°37'30"

41°36'00"

Bear Brook Swamp

RHODE ISLAND

CONNECTICUT

MASSACHUSETTS

Area enlarged

Wood RiverWood River

PawcatuckRiver

Streamgage

01118000

Hope

 Valley

Coventry

Providence

Nooseneck

 Big River

 Management

 Area

Long-term network

well SNW6

Base from Rhode Island Geographic Information System (RIGIS) digital data, 1:24,000

Lambert conformal conic projection, North American Datum of 1927

x

Hungry Hill

Figure 1. Location of Big River Management Area, central Rhode Island, and model-calculated water levels for long-term 

average conditions)
Hydrogeology 3

of a conjunctive-management model to determine timevarying monthly groundwater-pumping scenarios that meet 

groundwater-development goals and instream-flow criteria.

The report by Granato and Barlow (2005) documents 

a transient-simulation groundwater model coupled with a 

linear-optimization model to determine the groundwaterwithdrawal patterns that could provide water supplies and 

sustain streamflows in the BRMA to maintain aquatic and 

riparian ecosystems; however, the wetlands areas within the 

BRMA were not explicitly represented in the model, and the 

potential effects from pumping on these wetland areas were 

not considered in that analysis.

A need for an assessment of the potential effects of 

pumping on wetlands in the BRMA led to a cooperative 

agreement in 2008 between the RIWRB, the U.S. USGS, 

and the University of Rhode Island (URI). As part of this 

study, five wetlands areas in the BRMA were instrumented to 

measure water levels in the streams, at the wetland surface, in 

wetland sediments, and in the aquifer underlying the wetland 

areas from 2008 through 2009 to characterize the hydrological 

connection between surface waters and groundwater under 

natural conditions in this area (Borenstein and others, 2012).

This report describes the groundwater-flow model 

development component of this investigation and the analysis 

conducted to assess the effects of proposed groundwater 

withdrawals on surface waters, including wetland water levels 

in the BRMA. The groundwater-flow model used for this 

analysis was developed as a subregional model of the larger 

model developed in Granato and others (2003) to focus only 

on the BRMA and, in particular, on areas that included the 

proposed well locations in the northern part of the BRMA 

near an impoundment of the Big River (Flat River Reservoir) 

(fig. 1).

 The results of this study will benefit the development 

of field and modeling methods to improve the understanding 

of the effects of pumping on wetlands in stream-dominated, 

valley-fill aquifers commonly found throughout the glaciated 

regions of the northeastern United States. The study also 

provides information about the potential adequacy of shortterm (5 days or less) aquifer tests for evaluating long-term 

effects of groundwater withdrawals on water levels in 

wetlands; as such, the results of this study may be used to 

assist in the development of guidelines for assessing potential 

effects of water-supply development in wetland areas. The 

study also supports the RIWRB in its mission to develop, 

protect, conserve, and use the State’s water resources 

while balancing economic development and environmental 

protection for the State of Rhode Island.

Hydrogeology

The sand, gravels, silts, and clays that compose the Big 

River aquifer system were deposited by the advance and 

retreat of the last two continental ice sheets that covered 

New England during the middle and late Pleistocene about 

17,000 years ago (Stone and Borns, 1986; Boothroyd and 

others, 1998; Stone and Dickerman, 2002). These glacial 

deposits are divided into two broad categories—glacial till 

and glacial meltwater deposits. Till was deposited directly 

by glacier ice and is characterized as a nonsorted matrix 

of sand, silt, and clay with variable amounts of pebbles, 

cobbles, and large boulders. Glacial meltwater deposits were 

laid down by meltwater in lakes and streams in front of the 

retreating ice margin during deglaciation. These materials, 

also referred to as glacial stratified deposits, consist of wellsorted to poorly sorted layers of gravel, sand, silt, and clay. 

Postglacial sediments, primarily flood-plain alluvium and 

swamp deposits, are thin surface units and make up a lesser 

proportion of the surficial materials in the study area (Stone 

and Dickerman, 2002).

The aquifer system in the BRMA is unconfined and, 

for the most part, hydraulically connected with the streams, 

ponds, and wetlands throughout the area. The sources of 

water to this aquifer system include precipitation, natural 

stream and reservoir leakage, and groundwater inflow 

from adjacent till and bedrock uplands. Recharge from 

precipitation is estimated in this investigation to average 

about 27.7 inches per year (in/yr) resulting in about 

20 cubic feet per second (ft3/s) ft3/s of inflow into the study 

area. Average monthly rates ranged from 0.08 inches (in.) for 

July to 4.26 in. for March for the period of 1960 through 2006. 

Groundwater leaves the aquifer by direct discharge to streams, 

ponds, and wetlands; by evapotranspiration; and by underflow 

to adjacent flow systems. Groundwater discharge to surface 

waters is estimated in this investigation to be about 24 ft3/s for 

average annual conditions.

The general direction of groundwater flow in the Big 

River Valley is eastward from the till and bedrock uplands 

on the western side of the basin toward the Big River and 

northward toward the Flat River Reservoir. Groundwater 

moves through the surficial aquifer in the direction of 

decreasing water levels. Within the study area, groundwater 

levels range from a maximum of about 380 feet (ft) above 

National Geodetic Vertical Datum of 1929 (NVGD 1929) in 

the southern part of the study area to a minimum of about 

245 ft above NVGD 1929 along the Flat River Reservoir 

(fig. 1). Water-level contours (fig. 1) were calculated for 

average hydrologic conditions with the model developed 

for the area in this study and are similar to those drawn on 

the basis of field measurements and reported in Granato and 

others (2003). Water-table contours presented in Granato and 

others (2003) indicate groundwater flow in the Big River 

Valley is largely independent of flow in the adjacent Carr 

River and Mishnock River Valleys to the east because of the 

presence of a northwest-to-southeast-trending bedrock ridge 

that extends from Hungry Hill towards Capwell Mill Pond and 

continues southward through the unnamed hill south of the 

pond (fig. 1). 

The largest surface-water feature in the BRMA is the 

Big River, which drains to the north and is a major tributary 
4 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

to the east-flowing Flat River. The primary tributaries to the 

Big River are the Congdon, Nooseneck, and Carr Rivers and 

Bear Brook (fig. 1). The Big River flows into the Flat River 

Reservoir, which is controlled by a dam that maintains the 

reservoir’s water level at an altitude of about 248 ft from 

March through October and is often lowered by several feet 

from November through February for the purpose of managing 

invasive weeds.

A more detailed discussion of the geologic setting and 

hydrogeologic conditions of the BRMA can be found in Stone 

and Dickerman (2002) and Granato and others (2003).

Simulation of Groundwater and 

Surface-Water Interactions

Groundwater and surface water serve as a single resource 

that sustains the aquatic habitat of streams, ponds, and 

wetlands in the valley-fill aquifer systems found throughout 

the glaciated northeastern United States. Because of the 

hydraulic connection between groundwater and surface 

water in the BRMA, there are concerns of potential effects of 

future groundwater withdrawals on nearby surface waters and 

wetland vegetation.

Groundwater withdrawals can affect surface-water 

features in several ways (fig. 2). A pumped well may capture 

groundwater that would otherwise discharge to wetlands, 

ponds, and rivers (fig. 2B). Induced infiltration may occur if 

groundwater withdrawals are large enough and the water level 

in wetlands and nearby surface-water bodies is greater than the 

water level in the underlying aquifer (fig. 2C). This can result 

in wetlands, ponds, and rivers becoming a direct source of 

water to the pumped well. Regardless of whether groundwater 

pumping results in captured groundwater or induced 

infiltration, the amount of water lost from wetlands and nearby 

surface-water bodies is directly related to the amount of water 

removed from the aquifer by pumping. 

Lowering of water levels may reduce the amount of 

time that wetlands are inundated and (or) saturated each year 

(the hydroperiod), potentially causing detrimental impacts to 

wetland functions and values. Water-level reductions caused 

by groundwater withdrawals have been shown to increase 

invasive upland plant species, destructive fires, treefall, soil 

subsidence, and the disappearance of wetland wildlife swamps 

and marshes (Rochow and Rhinesmith, 1991; Mortellaro 

and others, 1995; Skidds and Golet, 2005). Other studies 

have determined that over time, upland woody vegetation 

replaces wetland herbaceous vegetation in areas affected 

by groundwater withdrawals because of changes in the 

hydroperiod (Sonenshein and Hofstetter, 1990). 

A groundwater-flow model was developed as part of 

this investigation to synthesize the hydrologic data collected 

at selected wetlands sites (Borenstein and others, 2012) into 

the context of the surrounding groundwater-flow system to 

better understand the interaction between surface waters and 

groundwater in the BRMA. Numerical models were developed 

previously for this area (Granato and others, 2003; Granato 

and Barlow, 2005) to assess the effects of proposed minimum 

streamflow requirements on the maximum amount of 

allowable pumping. The wetland areas within the BRMA were 

not explicitly represented in those models because the focus of 

those studies was on conjunctive management of streamflows 

to balance water-supply needs and aquatic habitat protection 

goals; therefore, the potential effects from pumping on these 

wetland areas were not considered for these analyses.

Renewed interest in the BRMA as a source for 

groundwater supply has created concerns about the potential 

effects of pumping on wetlands in the area and initiated 

Schematic diagram, not to scale

Unconfined aquifer

Unconfined aquifer

Q1

Q2

Recharge area

Land surface

Water table

C

B

A

Land surface

Land surface

Surface-water

body

Surface-water

body

Surface-water

body

Unconfined aquifer

Water table

Water table

Bedrock

Bedrock

Bedrock

Recharge area

Recharge area

Figure 2. Schematic diagram of a hypothetical aquifer showing 

groundwater discharge to a surface-water body with A, no 

pumping; B, pumping at a rate (Q1) such that the well would 

capture water that otherwise would discharge to the surfacewater body; and C, pumping at a higher rate (Q2) so that the flow 

direction is reversed and the well pumps water from the surfacewater body. Figure modified from Alley and others, 1999.
Simulation of Groundwater and Surface-Water Interactions 5

the need for a better understanding of the interaction 

between groundwater and surface water beneath wetlands. 

An understanding of this groundwater and surface-water 

interaction in the BRMA will help water-resources managers 

and regulatory agencies to meet water-supply demands while 

minimizing unacceptable effects on natural resources.

Development of the Groundwater Model

Numerical models provide a means to synthesize existing 

hydrogeologic information into an internally consistent 

mathematical representation of a real system or process and 

thus are useful tools for testing and improving conceptual 

models or hypotheses of groundwater-flow systems (Konikow 

and Reilly, 1999). A groundwater-flow model was developed 

for the BRMA by creating a local-scale model of the previous 

larger scale model of the BRMA (Granato and others, 2003).

The numerical model developed for this analysis was 

based on the USGS computer program MODFLOW–2005, 

which numerically solves the three-dimensional groundwaterflow equation by finite-difference methods (Harbaugh, 2005). 

The finite-difference grid developed for the modeled area was 

aligned with the finite-difference grid of the model developed 

by Granato and others (2003) so that the boundary conditions 

for the local-scale model could be obtained from the results 

of the larger-scale model. The purpose of this model was to 

(1) refine grid spacing to better represent the geometry of 

surface-water features, (2) use the data collected as part of the 

previously described field effort (Borenstein and others, 2012 

to simulate the groundwater and surface-water interaction 

at selected wetland sites, and (3) assess potential long-term 

effects of proposed pumping scenarios on water levels and 

streamflows in the BRMA.

This local-scale model (fig. 3) was used for steady-state 

simulations representative of long-term average hydrologic 

conditions and for transient simulations of dynamic changes 

in hydrologic conditions in response to time-varying 

recharge and pumping stresses. The distribution of aquifer 

characteristics incorporated into the model was derived from 

available hydrologic data and geologic descriptions (Craft, 

2001; Stone and Dickerman, 2002). The model then was 

calibrated to estimates of groundwater levels and streamflows 

that are representative of the period of 1960 through 2006.

Model Discretization and Boundary Conditions

The finite-difference model grid consists of a series of 

orthogonal model cells in which user-specified hydraulic 

parameters, model stresses, and boundary conditions are 

varied spatially. The conceptualization of how and where 

water enters, moves through, and leaves the aquifer is critical 

to the development of an accurate flow model (Reilly, 2001). 

Model inputs include intrinsic aquifer characteristics in 

each model cell, such as hydraulic conductivity. Boundary 

conditions are applied at some model cells to simulate 

hydrologic features, including streams and reservoirs. 

A detailed discussion of grid discretization, boundary 

conditions, and the use of finite-difference equations to 

simulate groundwater flow is presented in McDonald and 

Harbaugh (1988).

Spatial Discretization

The total active modeled area of the BRMA system is 

about 5 mi2

 (fig. 3). The finite-difference grid for the numerical 

model consists of 512 rows and 232 columns of uniformly 

spaced model cells that are 50 ft on each side. The aquifer was 

subdivided vertically into seven layers of variable thickness 

that extend from the water table into shallow bedrock to allow 

for the detail necessary to represent vertical changes in the 

lithology, proposed pumping well screen zones, and the depth 

and thickness of streambed and wetland sediments (fig. 4).

Temporal Discretization

Hydrologic stresses were simulated for average annual 

and monthly conditions. In these simulations, time is 

subdivided or discretized into stress periods and time steps. 

Stress periods refer to periods of time in which specified 

model stresses, such as pumping and recharge, are constant; 

changing stresses over time are simulated by using sequential 

stress periods. Stress periods are further divided into time 

steps, which are units of time for which water levels and flows 

are calculated.

Average monthly variations in hydrologic stresses 

were simulated by dividing the annual hydrologic cycle into 

12 monthly stress periods, representing average pumping and 

recharge rates during each month. Each stress period consisted 

of daily time steps to increase model stability. 

A total of 25 stress periods was simulated for this 

analysis. The first stress period was specified as steady state, 

followed by 2 years of monthly stress periods (24 stress 

periods). The water levels produced in the initial steady-state 

stress period were used as initial conditions for subsequent 

simulations of monthly stress periods. The 2 years of monthly 

stress periods were simulated to ensure that enough time 

had elapsed in the simulation to achieve a state of dynamic 

equilibrium, defined as a condition in which simulated water 

levels and flows do not change year to year for a given stress 

period and time step. The second year of simulated time (stress 

periods 13 through 25) was used to represent hydrologic 

conditions over an average year.

Hydrologic Boundary Conditions

The hydrologic boundaries, or boundary conditions, in 

the groundwater-flow model are the areas from which, and the 

method by which, all the water entering and leaving the model 

is specified.

The upper boundary of the model is the water table, 

which is a free-surface boundary that receives spatially 

variable recharge from precipitation. The lower boundary of 
6 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

EXPLANATION

Focused recharge cell

No flow cell

Inactive model area

Pond

Wetland

Stream cell

River cell

Stream

Specified inflow

0

0

2,600 5,200 FEET

500 1,000 METERS

Base from Rhode Island Geographic Information System (RIGIS) digital data, 1:24,000

Lambert conformal conic projection, North American Datum of 1927

71°39'00" 71°37'30" 71°36' 71°34'30"

41°39'00"

41°37'30"

41°36'00"

Bear Brook Swamp

x

Hungry Hill

Flat River

Reservoir area

drained

Flat River

Reservoir area

flooded

Nooseneck Riv er

Mishnock River

Lake

Mishnock

Sweet

Pond

Capwell

Mill

Pond 

Reynolds Pond

Flat River

Reservoir

Congdon

tributar y

Big Rive

U

r

nnamed tributary

Bear Brook

Nooseneck Riv er

Congdon River

Carr River

Reynolds Swamp

Cedar Swamp

Scarborough Swamp

Congdon Swamp

Figure 3. Model extent and distribution of simulated boundary conditions of groundwater-flow model of Big River 

Management Area, central Rhode Island.
Simulation of Groundwater and Surface-Water Interactions 7

NORTH SOUTH

WEST EAST

1

2

3

4

5

6

7

Model layer Model layer

1

2

3

4

5

6

7

250

300

230

215

200

160

130

100

Altitude, in feet

relative to NGVD 29

Altitude, in feet

relative to NGVD 29250

270

230

215

200

160

130

100

A A'

B B'

EXPLANATION

Sand and gravel

Fine/medium sand

Silt and clay

Till

Bedrock

Peat

Pond

Wetland

Inactive

Hydrogeologic units

0 550 1,100 FEET

0 150 300 METERS

0 550 1,100 FEET

0 150 300 METERS

Figure 4. Sections showing vertical layering and model representation of geologic sections A–A’ and B–B’. Section lines 

are shown on figure 6.

the model is the contact between glacial stratified deposits 

and the glacial till and bedrock that underlie the entire study 

area. This boundary was represented as a no-flow boundary 

condition. The altitude of the bedrock surface ranges from 

about 340 ft to about 100 ft above NGVD 29 (Stone and 

Dickerman, 2002). 

The lateral boundaries of the model are represented as 

no-flow boundaries or head-dependent flux boundaries. In 

this valley-fill aquifer system, the upland till, bedrock, and 

thinly saturated glacial stratified deposits are represented as 

no-flow boundaries. The contact between the stratified glacial 

deposits and till upland areas is simulated as locations of 

focused recharge to account for the flow from areas outside 

of the model area that contribute water to the margins of the 

active area of the model. Recharge rates at these locations 

were derived from the previous larger scale model of the area 

(Granato and others, 2003). Part of the eastern boundary also 

includes a no-flow condition east of Sweet Pond (fig. 1) that 

represents a groundwater divide in the larger model (Granato 

and others, 2003).

Specified inflows into the model also include streamflow 

that enters the active modeled area at five locations along 

the western boundary of the study area. The five streams are 

the Congdon River, Nooseneck River, unnamed tributary, 

the Carr River at the outlet of Capwell Mill Pond, and 

Bear Brook (fig. 3). The specified flow rates for these five 

streams were estimated using the “maintenance of variance 

type 1 (MOVE.1) method (described in the appendix) with 

USGS streamgage data as originally reported in Granato and 

others (2003). 
8 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

 Flow leaves the aquifer system at the northern 

(downgradient) extent of the active model area at the Flat 

River Reservoir, which was simulated in the model by a 

combination of head-dependent flux boundaries including 

the MODFLOW River (RIV), Drain (DRN), and Streamflow 

Routing (SFR2) packages (McDonald and Harbaugh, 1988; 

Niswonger and Prudic, 2005). In this area, the downstream 

part of the Big River drains into the Flat River Reservoir 

(fig. 1). The reservoir stage is manually controlled by a 

sluiceway where releases are made periodically to drain 

the reservoir for the management of invasive weeds. These 

releases typically occur in late fall through early winter to 

expose weeds to the open air during cold months. During this 

period of lower reservoir stage, the remaining area of open 

water in the upper portion of the reservoir above Harkney Hill 

Road is reduced to only the stream channel that runs through 

the center of the once flooded area (fig. 5A).

Representation in the groundwater model of the 

manipulation of reservoir stage and the resulting change in 

the flooded area were accomplished by simulating the flooded 

area from March through October using the RIV package, and 

the drained or exposed area from November through February 

using the DRN package. When the reservoir stage is high 

from March through October (fig. 5B), the RIV package is 

used to simulate the open water of the reservoir at a constant 

stage that will be unaffected by groundwater pumping. The 

use of the RIV package is based on the assumption that an 

“infinite” supply of water potentially could be available to 

the aquifer and to wells pumping from the aquifer given the 

pumping rates assumed for this investigation compared to 

the volume of the reservoir and amount of flow entering from 

the Big River (50 ft3

/s on an average basis); this assumption 

appears reasonable.

When the reservoir stage is lowered from November 

through February, the DRN package replaced the RIV package 

to simulate groundwater discharge at seepage faces along the 

exposed pond-bottom sediments that occurs when the lower 

reservoir stage exposes these pond-bottom sediments to open 

air (fig. 5A). The DRN package assumes the same hydraulic 

conductance or leakance term as the RIV package; however, 

because the DRN package only allows water to flow from the 

aquifer to the simulated stream, the DRN package prevents 

this area from becoming a source of water to the aquifer 

or nearby pumping wells. The stage in DRN package was 

lowered from 248 ft to 245 ft above NGVD 1929 to represent 

the change in the reservoir stage.

In addition to the RIV and DRN packages, the SFR2 

package was used to simulate flow from the Big River to the 

reservoir and through the reservoir area when the reservoir is 

drained. This boundary condition was applied to model cells 

down the centerline of the reservoir (fig. 3), and this boundary 

was active throughout the simulation period. 

The SFR2 boundary condition also was used to simulate 

the remaining rivers present in the active modeled area. The 

SFR2 package allows for groundwater discharge to streams 

(gaining stream reaches) as well as streamflow seepage into 

the aquifer (losing stream reaches). The use of the SFR2 

package to represent streams allows for the simulation of 

losing conditions downgradient from pond outlets or near 

pumping wells, but unlike the RIV package, the SFR2 package 

will not allow surface-water features to become infinite 

sources of water to the aquifer after the water level falls below 

the specified streambed bottom (Niswonger and Prudic, 2005). 

The groundwater model simulates discharge to 

the streams for average conditions and, as a result, will 

underpredict peak streamflow conditions resulting from 

overland runoff. Most streams in the aquifer are gaining; 

however, losing conditions can develop adjacent to upland 

areas, downstream from pond outlets, and near pumping 

wells. The SFR2 package also accounts for water that is 

routed through stream networks. This routing capability is 

used in the models to route water from pond outlets into 

receiving streams.

The simulated discharge at head-dependent boundaries 

is a function of the hydraulic conductance, which represents 

resistance to flow across the streambed from fine-grained 

sediments. The hydraulic conductance was calculated for each 

model cell containing a stream as

 (1)

where 

C is hydraulic conductance of the streambed, in 

square feet per day; 

K is vertical hydraulic conductivity of streambed 

deposits, in feet per day; 

W is the width of the streambed within the model 

cell, in feet; 

L is the length of the streambed within the 

model cell, in feet; and 

M is the thickness of the streambed, in feet.

The simulated vertical hydraulic conductivity of the 

streambed deposits (K) was 30 feet per day (ft/d); it was 

assumed that the permeability of the streambed is similar 

to that of the surrounding aquifer. A width (W) of 10 ft, a 

thickness (M) of 5 ft, and a length (L) of 50 ft were assumed 

for all the streams simulated in the flow model. Streambed 

altitudes represented in the model were estimated from the 

digital elevation data for the study area described previously in 

Granato and others (2003). 

A previous analysis in a similar hydrogeologic setting in 

coastal Rhode Island (Masterson and others, 2007) determined 

that large changes in simulated hydraulic conductance and 

streambed altitudes can affect the location and amount of 

groundwater discharge to surface-water bodies. However, 

obtaining the information necessary to measure these 

properties throughout the study area would require a larger 

and more detailed hydrologic data-collection effort than was 

possible for this analysis.

Ponds in the Big River aquifer system are assumed to 

be generally in direct hydraulic connection with the aquifer 

C K W L

M = ( )( )( )( ) ,
Simulation of Groundwater and Surface-Water Interactions 9

A

B

Figure 5. Big River at Harkney Hill Road, Coventry, Rhode Island A, conditions in the river in 

February 2010 when the stage in the Flat River Reservoir was relatively low and streamflow 

was limited to the channel of the river. B, conditions in March 2010 when the stage of the 

reservoir was relatively high and the river overflowed its channel.
10 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

and are regions of the aquifer with no effective resistance to 

flow. As a result, groundwater-flow lines converge towards 

ponds in upgradient areas, where water discharges to ponds, 

and diverge in downgradient areas, where ponds recharge 

the aquifer. In the models, ponds are simulated as areas of 

high horizontal hydraulic conductivity (5,000 ft/d), more 

than an order of magnitude higher than the horizontal 

hydraulic conductivity values simulated in the surrounding 

aquifer. This difference in horizontal hydraulic conductivity 

causes preferential flow through the pond and simulates the 

observed effects that ponds have on groundwater flow in the 

aquifer system.

Wetlands were simulated in the top model layer as 

areas of high horizontal hydraulic conductivity (1,000 ft/d) 

to account for the effects of standing water on hydraulic 

gradients in wetlands. The underlying wetland peat deposits 

were represented as areas of low hydraulic conductivity in 

layer 2.

Hydraulic Properties

The water-transmitting properties of the aquifer 

sediments, as represented by horizontal hydraulic conductivity 

(K) and vertical anisotropy, are functions of lithology and 

differ according to grain size and the degree of sorting of the 

sediments. The four major hydrogeologic units in the study 

area are glacial stratified deposits, glacial till, wetlands’ peat, 

and bedrock. The surficial geology of the study area is shown 

on figure 6.

The stratified glacial deposits are composed of gravel, 

sand, silt, and clay that were carried away from the glacial ice 

front by meltwater streams. Thick, coarse-grained, stratified 

sediments that consist of highly transmissive fine sand to 

coarse gravel have the capacity to yield large quantities of 

water to wells and form the principal (or surficial) aquifer 

in the study area. General trends in the geologic framework 

include thick deposits of glaciolacustrine sediments beneath 

the Flat River Reservoir part of the BRMA overlying more 

permeable sands and gravels. These fine-grained deposits were 

not present in the southern part of the study area where the 

aquifer decreases in thickness (fig. 7A). 

The relation between lithology and aquifer characteristics 

(horizontal hydraulic conductivity and vertical anisotropy) 

was based on reviews of hydrogeologic information from 

previous investigations in the BRMA (Craft, 2001; Stone 

and Dickerman, 2002; Granato and others, 2003). Previous 

hydrogeologic investigations in southern Rhode Island (Friesz 

and Stone, 2007; Masterson and others, 2007; Friesz, 2010; 

Masterson, 2011) also were used to better understand the 

relation between lithology and aquifer characteristics in the 

study area.

Horizontal hydraulic conductivity values from these 

previous investigations ranged from 70 to 350 ft/d for fine 

to coarse sands and gravel to 10 to 30 ft/d for fine sand and 

silt (table 1). These estimates of hydraulic properties values 

were distributed throughout the model domain based on the 

hydrogeologic framework developed by Stone and Dickerman 

(2002) and the results of aquifer tests conducted in the 

northern part of the study area in the late 1990s (Craft, 2001; 

Stone and Dickerman, 2002), and more recently (December 

2009) as part of ongoing groundwater-resources investigations 

in the area (Blake Martin, Weston and Sampson, Inc, written 

commun., 2010). The largest difference in horizontal hydraulic 

conductivity values between the current and previous model 

(Granato and others, 2003) is the representation of wetland 

hydraulic properties and the thick glaciolacustrine deposits 

that underlie the northern part of the study area near the Flat 

River Reservoir (fig. 7A,B). The hydraulic properties of the 

wetland peat deposits were obtained from sediment core 

analyses from selected wetlands in the study area (Borenstein 

and others, 2012).

Vertical anisotropy (VA), which is the ratio of horizontal 

to vertical hydraulic conductivity, generally increases with 

decreasing horizontal hydraulic conductivity; anisotropy 

values for glacial sediments range from about 3:1 for sand and 

gravel to 100:1 for silt and clay (Granato and others, 2003; 

Masterson and others, 2007; Masterson, 2011). The values of 

VA and the corresponding range in K used in the calibrated 

model are presented in table 1.

For transient simulations, a uniform specific-yield 

value of 0.25 was used for the uppermost active layers, and 

a uniform storage coefficient value of 1×10-5 was used for 

the lower confined layers. These values were based on the 

values used in the previous model (Granato and others, 2003) 

and were consistent with previous investigations in similar 

hydrogeologic settings (Friesz and Stone, 2007; Masterson 

and others, 2007; Masterson and others, 2009). In the model 

cells representing ponds, the specific yield was set to a value 

of 1.0 to account for the high storage capacity assumed for the 

ponds. All of the surface-water features in the study area were 

represented in the top layer of the model.

Hydrologic Stresses

The hydrologic stresses simulated in the model include 

recharge from precipitation, reservoir-stage management, and 

the proposed groundwater withdrawal scenarios developed as 

part of the ongoing water resources investigation. Currently, 

there are no large-capacity groundwater withdrawals in 

the BRMA.

Recharge

The primary source of water to the BRMA aquifer is 

recharge derived from precipitation. Precipitation at T.F. Green 

Airport Weather Station in Providence, R.I., has averaged 

48 in/yr from 1960 through 2006 (National Oceanic and 

Atmospheric Administration, 2007). Some precipitation is 

lost to evapotranspiration and overland runoff to streams; 

the remainder recharges the aquifer at the water table or on 

the surface of ponds and wetlands. Therefore, the simulated 

recharge to the groundwater system consists of three separate 
Simulation of Groundwater and Surface-Water Interactions 11

Coventry Center QuadrangleCrompton Quadrangle

Hungry

Hill

Fish

Hill

WGW361

WGW366

WGW363

WGW272

WGW347

WGW314

WGW373

COW479

COW101

WGW356

WGW350

WGW30

WGW94

WGW82

WGW101

A

A'

B

B'

Surficial materials mapped by J. R. Stone, 1997–98

Locations of bedrock outcrops and contacts between

till and stratified deposits modified from

Feininger (1962), Smith (1956), and Power (1957)

Base compiled from digitized U.S. Geological Survey topographic

quadrangle maps: Coventry Center, R.I., Crompton, R.I., 1970

Polyconic projection

EXPLANATION

Artificial fill

Alluvium

Swamp deposits

Sand and gravel 

 deposits

Sand deposits

Fine deposits

Till

Bedrock outcrops

Line of section

Well or test boring 

 and identifier

A A'

Sand and gravel

 underlying sand

Sand and gravel overlying

 sand overlying fines

Sand overlying fines

Sand and gravel underlying

 sand or fines WGW361

0 0.5 1 MILE

0 0.5 1 KILOMETER

41°39'00"

41°38'45"

71°38'45" 71°37'30" 71°36'15"

RHODE

ISLAND

CONNECTICUT

MASSACHUSETTS

Area

enlarged

Big River

Management

Area

Figure 6. Surficial geology of the Big River Management Area, central Rhode Island (modified from Stone and 

Dickerman, 2002).
12 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

0 500

VERTICAL EXAGGERATION x10

1,000 METERS

0 2,000 4,000 FEET

SECTION

B–B'

Flat River Reservoir

COW479WGW373

Flat River Reservoir

Big River

WGW314

WGW347

Big River

COW101

INTERSTATE 95

WGW272

Route 3

WGW366

WGW361

WGW363—Projected

100

150

200

250

300

350

Altitude, in feet above NGVD 29

50

NORTH SOUTH

A A'

EXPLANATION

Artificial fill

Alluvium

Swamp deposits

Sand and gravel deposits

Sand deposits

Fine deposits

Till

Bedrock

Well or test boring and identifier—Length 

 of line respresents vertical extent of well

 or test boring; dashed line respresents well

 projected onto line of section

WGW366

0 500

VERTICAL EXAGGERATION x10

1,000 METERS

0 2,000 4,000 FEET

50

100

150

200

250

300

350

400

450

FEET Altitude, in feet above NGVD 29

WGW347—Projected

WGW350

WGW356

WGW94

WGW30

WGW101

WGW82

Unnamed brook

SECTION

A–A'

Big River

WEST EAST

B B' BEND IN SECTION BEND IN SECTION BEND IN SECTION BEND IN SECTION

Hungry

Hill

EXPLANATION

Artificial fill

Alluvium

Swamp deposits

Sand and gravel deposits

Sand deposits

Fine deposits

Till

Bedrock

Well or test boring and identifier—Length 

 of line respresents vertical extent of well

 or test boring; dashed line respresents well

 projected onto line of section

WGW356

Figure 7. Geologic sections (A–A’ and B–B’) showing the distribution of stratified glacial deposits in the Big River Management Area, 

central Rhode Island (modified from Stone and Dickerman, 2002; NGVD 29.
Simulation of Groundwater and Surface-Water Interactions 13

Table 1. Horizontal hydraulic conductivity and horizontal to 

vertical anisotropy values of the lithologic units used in the 

groundwater-flow model of the Big River Management Area, 

central Rhode Island.

Lithologic deposit

Horizontal 

hydraulic 

conductivity

(feet per day)

Horizontal to 

vertical

anisotropy

Stratified glacial deposits

Sand and gravel 250–350 3:1 to 5:1

Fine/medium sand 70–125 10:1 to 30:1

Fine sand and silt 10–30 30:1 to 100:1

Silt and clay 0.1–10 100:1 to 1:1

Peat 0.1 1000:1

Till 1–5 10:1

Bedrock 0.01 1:1

components: (1) areal recharge to land surface overlying 

stratified glacial deposits, (2) recharge to land surface 

overlying upland till deposits, and (3) recharge to open-water 

bodies and wetlands.

An average annual recharge rate of 27.7 in/yr was 

calculated by the climatic water-budget computer program 

WATBUG (Wilmott, 1977). WATBUG uses the Thornthwaite 

method (Chow, 1964) to compute climatic water budgets on 

a daily or monthly time scale based on daily temperature and 

precipitation data from the Providence weather station from 

1960 through 2006 and an estimate of soil-moisture capacity. 

Required data input for WATBUG include the latitude of the 

weather station, measured daily temperature and precipitation 

values, and an estimate of ambient soil-moisture capacity. 

Output values include actual and potential evapotranspiration 

rates and the change in soil-moisture storage (water available 

for recharge). The soil-moisture capacity (moisture retained 

in the soil after excess moisture is drained through gravity 

drainage) was assumed to be 6 in/yr based on the previous 

work of Carlson and Lyford (2005).

Average monthly recharge rates from 1960 through 2006 

for the stratified glacial deposits ranged from a low of 0.08 in. 

for July to a high of 4.26 in. for March with an average of 

2.3 inches per month (in/mo) (fig. 8). The variation in monthly 

recharge rates is the result of changes in monthly precipitation 

and evapotranspiration rates. Evapotranspiration rates increase 

over the summer and early fall months; as a consequence, a 

greater percentage of precipitation that occurs during these 

months is lost to evapotranspiration compared to the winter 

and spring months, resulting in a reduced amount of recharge 

to the aquifer in the summer and fall months.

Inflow to the modeled area from the surrounding upland 

till areas (fig. 6) was based on the same spatial distribution of 

inflow from the analysis of Granato and others (2003). The 

method for apportioning this inflow was based on seasonal 

patterns of streamflow in a till-dominated environment. In the 

previous study, this inflow was simulated as a specified flux 

by use of injection wells along the contact between the upland 

till and adjacent stratified glacial deposits, whereas in this 

investigation the inflow was simulated as specified recharge in 

these areas. This method resulted in the same amount of inflow 

entering the active model area while helping avoid numerical 

instability issues with the model simulations. Overall, the 

total recharge from the upland till areas was similar to the 

glacial stratified deposits; however, the timing of this recharge 

differed over the year because of differences in topography 

and aquifer storage and hydraulic conductivity properties of 

the till sediments (Granato and others, 2003).

Surface-water bodies such as ponds and wetlands were 

determined to be, on an annual basis, areas of net recharge to 

the aquifer. The simulated recharge for ponds was determined 

by the free-water-surface potential evaporation rate calculated 

by the Jensen-Haise method (Jensen and Haise, 1963). This 

method uses air-temperature and solar-radiation data to 

estimate free-water-surface evaporation obtained from the 

weather station at T.F. Green Airport, Providence, R.I. 

The estimated free-water-surface potential evaporation 

rate was determined to be 28 in/yr, similar to the rate 

determined by Farnsworth and others (1982) for the 

northeastern United States, resulting in a net recharge rate of 

20 in/yr for ponds for average annual conditions from 1960 

through 2006. Average monthly recharge rates for the ponds 

varied from a low of -2.08 in. for July to a high of 4.07 in. for 

March with an average of about 1.7 in/month (fig. 8). Negative 

recharge rates calculated for the summer months indicate 

that the estimated free-water-surface potential evaporation 

rate is higher than the average monthly precipitation rate 

for those months resulting in a lowering in pond levels from 

increased evaporation.

In wetlands, evapotranspiration is assumed to account 

for a substantial loss of water, which can be as large, or larger, 

than the evaporation loss from ponds because of the combined 

effect of evaporation and transpiration in these flooded, 

vegetated areas. Therefore, a uniform recharge rate of about 

8.4 in/yr was specified for all the wetlands in the study area, 

which is about 40 percent of the recharge rate specified for 

ponds and about 30 percent of the rate for the surrounding 

aquifer. This value was based on previous analyses in the New 

England wetland systems (Hemond, 1980; Zarriello and Bent, 

2004). Average monthly recharge rates from 1960 through 

2006 for the wetlands varied from a low of -8.12 in. for July 

to a high of 4.58 in. for December with an average of about 

0.7 in/month (fig. 8). 

It should be noted, however, that recharge in wetlands 

can vary greatly depending on the extent of open water, 

amount and type of vegetation, location of the wetland in the 

flow system, and whether the wetlands have surface-water 

outflows (Masterson and others, 2009). Negative recharge 

rates calculated for the summer months indicate that the 

estimated evapotranspiration rate is higher than the average 

monthly precipitation rate for those months resulting in a 

lowering of water levels in wetlands.
14 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

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

Month

Precipitation and recharge, in inches 

-10

-8

-6

-4

-2

0

2

4

6

Precipitation

Recharge—Aquifer

Recharge—Ponds

Recharge—Wetlands

EXPLANATION

Figure 8. Monthly values of precipitation and calculated aquifer recharge at the T.F. Green Airport 

weather station, Providence, Rhode Island, from 1960 through 2006. 

Pumping

Currently, there are no groundwater withdrawals in 

BRMA; however, plans have been proposed to withdraw as 

much as 7.0 million gallons per day (Mgal/d) from this area 

in the future (Granato and Barlow, 2005). Recently, waterresources investigations conducted by the RIWRB (Blake 

Martin, Weston and Sampson, Inc., written commun., 2009) 

have identified two test sites (WGW443 and WGW444; fig.1) 

and conducted an aquifer test from December 16 to 21, 2009, 

at rates of 550 gallons per minute (gal/min) and 490 gal/min at 

WGW443 and WGW444, respectively. These pumping wells 

were simulated by the MODFLOW Well (WEL) package 

(McDonald and Harbaugh, 1988), which is a specified-flux 

boundary condition. Pumping rates were simulated for the 

5-day period of the aquifer test to provide additional modelcalibration data. These pumping rates also were simulated for 

long-term average conditions to assess the long-term effect of 

pumping on water levels and streamflows in the BRMA.

Model Calibration

Model calibration is the process by which modifications 

are made to the initial model-input parameters for the purpose 

of making the model output more closely match measured 

water levels and streamflows (Reilly and Harbaugh, 2004). 

Because numerical models synthesize existing hydrogeologic 

information into an internally consistent mathematical 

representation of a real system, the numerical representation is 

a much simpler, generalized representation of the real system. 

Hydraulic properties are represented in the model as parameter 

values assigned to multiple cells within a region of the model.

For this analysis, calibration was achieved for this 

analysis through trial-and-error manipulation of model input 

parameters within reasonable limits and comparing the 

resulting model-calculated long-term hydraulic heads and 

flows to measured and estimated values. These calibration 

targets included estimates of long-term average monthly 

water levels and streamflows (fig. 9) from 1960 through 2006, 

along with the water levels measured during the aquifer test 

conducted in December 2009 (Blake Martin, Weston and 

Sampson, Inc., written commun., 2010). 

The estimates of long-term average monthly water levels 

and streamflows were based on the MOVE.1 regression 

method with USGS index-station data. Regression equations 

for groundwater-level data were calculated manually and 

regression equations for streamflow data were calculated 

with the Streamflow Record Extension Facilitator program 

(Granato, 2009). The equations were developed by assessing 

correlations between data from the index sites with data from 

each site of interest, graphing the data to assess the regressionmodel fit, and using monthly statistics from the long-term 

index sites to estimate values at the site of interest. A more 

detailed description of the MOVE.1 method can be found in 

appendix 1.
Simulation of Groundwater and Surface-Water Interactions 15

255

255

255

260

270

260

270

270

265

265

325

340

330

320

315

305 310

300

290

280

270

285

280

290

300

310

320

340

350

360370

380

270

280

290

275

260

EXPLANATION

Active model area

Inactive model area

Pond

Wetland

Stream

Model-calculated water-level

 contour—Shows altitude at which

 water level would have stood in

 tightly cased wells. Contour interval

 5 feet. Datum is NGVD 29

Monitoring well site

Streamflow site

250

Nooseneck Riv er

Mishnock River

Sweet

Pond

Capwell

Mill

Pond 

Reynolds Pond

Flat River

Reservoir

Congdon

tributar y

Big Rive

U

r

nnamed tributary

Bear Brook

Nooseneck Riv er

Congdon River

Carr River

Reynolds Swamp

Cedar Swamp

Scarborough Swamp

Congdon Swamp

Bear Brook Swamp

Mishnock River

Lake

Mishnock

Sweet

Pond

Capwell

Mill

Pond 

Reynolds Pond

Flat River

Reservoir

Congdon

tributar y

Big Rive

U

r

nnamed tributary

Bear Brook

Nooseneck Riv er

Congdon River

Carr River

Reynolds Swamp

Cedar Swamp

Scarborough Swamp

Congdon Swamp

Bear Brook Swamp

WGW304

WGW305

WGW303

WGW291 WGW290

WGW285

01115800

01115670

01115700

WGW320

WGW287

WGW429

WGW286

WGW293

WGW427

WGW428

WGW436

WGW304

WGW305

WGW303

WGW291 WGW290

WGW285

01115800

01115670

01115700

WGW320

WGW287

WGW429

WGW286

WGW293

WGW427

WGW428

WGW426

WGW313

0

0

2,600 5,200 FEET

500 1,000 METERS

Base from Rhode Island Geographic Information System (RIGIS) digital data, 1:24,000

Lambert conformal conic projection, North American Datum of 1927

71°39'00" 71°37'30" 71°36' 71°34'30"

41°39'00"

41°37'30"

41°36'00"

x

Hungry Hill

COW484

Figure 9. Locations of water-level and streamflow sites used for model calibration and model-calculated water-level 

contours for long-term average conditions, Big River Management Area, central Rhode Island.
16 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

The comparison between model-calculated and the 

estimated water levels for long-term average conditions 

included a determination of the mean of the residuals (the 

difference between estimated and model-calculated water 

levels) and the absolute mean of the residuals. Ideally, the 

mean of the residuals will be randomly distributed and close 

to zero, indicating no bias in the results, and the mean of the 

absolute residuals will be less than 5 percent of the total range 

in head for the water-level measurements used for model 

calibration (Anderson and Woessner, 1992). The absolute 

mean of the residual for the monthly average conditions was 

1.31 ft. These values correspond to about 3.4 percent of the 

total range (38 ft) in measured (estimated) water levels for the 

study area and indicate the model-calculated water levels were 

in reasonable agreement with the estimated data. 

The mean of the residuals (estimated minus model 

calculated) for the long-term average conditions and average 

monthly conditions was 0.05 ft, indicating that the residuals 

have a near random distribution around zero. Comparisons of 

model-calculated and estimated water levels (fig. 10A) and of 

the residual water levels as a function of the estimated water 

levels (fig. 10B) illustrate the model provides a reasonable 

match to estimated water levels for long-term average 

conditions and the residuals generally are unbiased throughout 

the range of estimated water levels in the aquifer system 

(fig. 10B).

In addition to using the mean of the residuals and the 

absolute mean of the residuals as metrics for determining 

the goodness of fit between estimated and model-calculated 

water levels, simulated changes in monthly water levels were 

compared to estimated average monthly measurements in 

long-term monitoring wells to assess the capacity of the model 

to predict the effects of changing stresses on the hydrologic 

system. The model-calculated values are, for the most part, in 

agreement with the estimated average monthly water levels 

calculated by MOVE.1, indicating that the model provides a 

reasonable representation of monthly changes in water levels 

in this analysis (fig. 11), especially in the northern part of the 

study area near the proposed water-supply sites (fig. 9). 

The estimated and model-calculated water levels did not 

match well in the southeastern part of the study area (fig. 9) 

near wells WGW285–287 and WGW320 (fig. 11A–C, K). 

Possible explanations for the difference between modelcalculated and estimated water levels in this area include 

(1) the influence of simulated changes in monthly flows in 

the nearby streams, (2) the specified inflows along the eastern 

boundary in this area of the model, or (3) the inadequate 

representation of the hydrogeologic framework in the 

southeastern part of the study area.

Another measure of how well the model matched the 

estimated water levels was to assess the match of changes in 

vertical gradient at the wetland sites that were instrumented 

to measure water levels above and below the wetland 

peat materials. The three sites selected were the Reynolds 

Pond Swamp (WGW427), Cedar Swamp (WGW428), and 

Scarborough Swamp (WGW426) (fig. 1). A comparison of 

the change in vertical gradients (head difference between 

the surface water and the deep well) indicates an acceptable 

agreement between the model-calculated and estimated water 

levels (fig. 12) with the exception of the Cedar Swamp site 

(fig. 12B). 

The estimated changes in vertical gradient at Cedar 

Swamp indicate a near constant upward gradient of about 

0.2 ft throughout the year compared to the model-calculated 

range in upward gradients of 0.3 to 0.6 ft, with the highest 

rates occurring in late winter and spring when simulated 

recharge rates are high. The difference between estimated 

and model-calculated vertical gradients may be the result of 

a local-scale hydrogeologic feature specific to Cedar Swamp 

that is not adequately represented in the flow model, such 

as the permeability of the underlying peat sediment. Local 

variations in the permeability of the peat layer separating the 

shallow, flooded part of Cedar Swamp from the underlying 

aquifer system can affect the hydrologic gradient estimated 

between the shallow (WGW429) and deeper (WGW431) 

wells that would not be accounted for in the flow model 

given the lack of hydrogeologic data available on changes in 

permeability of the peat sediments.

The MOVE.1 analysis also was used to estimate longterm average monthly streamflow values from 1960 through 

2006. Data from the long-term streamgage 01118000 on 

the Wood River at Hope Valley in the nearby Pawcatuck 

River Basin were selected to represent long-term conditions 

in the BRMA because correlations among streamflow 

measurements in these areas are very strong (greater than 

0.91; see appendix table 1–2). This streamgage has a long, 

uninterrupted period of record that includes 1960–2006, and 

water use in the Wood River Basin is a small percentage of 

average monthly streamflows (Masterson and others, 2009). 

A comparison of model-calculated and estimated streamflows 

indicates that the model-calculated streamflows generally are 

in agreement with estimated long-term average conditions 

at the USGS streamgages (fig. 13) with the exception of the 

unnamed tributary to the Congdon River in the southern part 

of the study area (fig. 13C), which may be a result of the 

explanations described previously for the differences in the 

match between estimated and model-calculated water levels in 

this area.

Simulation of Groundwater Withdrawals

Previous studies in the BRMA were designed to assess 

the effects of pumping on streamflow; changes in water levels 

in the aquifer and in wetlands were not considered (Granato 

and others, 2003; Granato and Barlow, 2005). As part of the 

previous studies, several possible well sites were identified 

for withdrawals of as much as 7.0 Mgal/d of groundwater; 

however, this proposed pumping scenario required multiple 

well sites to limit pumping during summer months when 

streamflows are typically at their lowest flows in any 

given year. 
Simulation of Groundwater and Surface-Water Interactions 17

245 250 255 260 265 270 275 280 285 290

Estimated water level, in feet

245 250 255 260 265 270 275 280 285 290

Estimated water level, in feet

245

250

255

260

265

270

275

280

285

290

Model-calculated water level, in feet Water-level residual, in feet

-4

-3

-2

-1

0

1

2

3

Line of perfect agreement

Line of perfect agreement

B

A

Figure 10. Comparison of A, model-calculated and estimated water levels, and B, residual 

(estimated minus model calculated) water levels as a function of estimated water levels for 

long-term average conditions.
18 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

A. WGW285

B. WGW286

Estimated

Model calculated

Estimated

Model calculated

EXPLANATION

EXPLANATION

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

Month

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

Month

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Change in water level from average, in feet Change in water level from average, in feet

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Figure 11. Comparison of monthly departure from average conditions for model-calculated and 

estimated water levels for observation wells A, WGW285; B, WGW286; C, WGW 287; 

D, WGW 290; E, WGW291; F, WGW293; G, WGW303; H, WGW304; I, WGW305; J, WGW313; and

K, WGW320 in the Big River Management Area, central Rhode Island.
Simulation of Groundwater and Surface-Water Interactions 19

C. WGW287

D. WGW290

Estimated

Model calculated

Estimated

Model calculated

EXPLANATION

EXPLANATION

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

Month

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

Month

Change in water level from average, in feet

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Change in water level from average, in feet

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Figure 11. Comparison of monthly departure from average conditions for model-calculated and 

estimated water levels for observation wells A, WGW285; B, WGW286; C, WGW 287; D, WGW 290; 

E, WGW291; F, WGW293; G, WGW303; H, WGW304; I, WGW305; J, WGW313; and K, WGW320 in the 

Big River Management Area, central Rhode Island.
20 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

E. WGW291

F. WGW293

Estimated

Model calculated

Estimated

Model calculated

EXPLANATION

EXPLANATION

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

Month

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

Month

Change in water level from average, in feet

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Change in water level from average, in feet

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.4

0.2

0.6

0.8

1.0

Figure 11. Comparison of monthly departure from average conditions for model-calculated and 

estimated water levels for observation wells A, WGW285; B, WGW286; C, WGW 287; D, WGW 290; 

E, WGW291; F, WGW293; G, WGW303; H, WGW304; I, WGW305; J, WGW313; and K, WGW320 in the 

Big River Management Area, central Rhode Island.
Simulation of Groundwater and Surface-Water Interactions 21

G. WGW303

H. WGW304

Estimated

Model calculated

Estimated

Model calculated

EXPLANATION

EXPLANATION

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

Month

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

Month

Change in water level from average, in feet

-1.5

-2.0

-1.0

-0.5

0.0

0.5

1.0

2.0

1.5

Change in water level from average, in feet

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Figure 11. Comparison of monthly departure from average conditions for model-calculated and 

estimated water levels for observation wells A, WGW285; B, WGW286; C, WGW 287; D, WGW 290; 

E, WGW291; F, WGW293; G, WGW303; H, WGW304; I, WGW305; J, WGW313; and K, WGW320 in the 

Big River Management Area, central Rhode Island.
22 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

I. WGW305

J. WGW313

Estimated

Model calculated

Estimated

Model calculated

Estimated

Model calculated

EXPLANATION

EXPLANATION

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

Month

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

Month

Change in water level from average, in feet

-1.5

-2.0

-1.0

-0.5

0.0

0.5

1.0

2.0

1.5

Change in water level from average, in feet

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Figure 11. Comparison of monthly departure from average conditions for model-calculated and 

estimated water levels for observation wells A, WGW285; B, WGW286; C, WGW 287; D, WGW 290; 

E, WGW291; F, WGW293; G, WGW303; H, WGW304; I, WGW305; J, WGW313; and K, WGW320 in the 

Big River Management Area, central Rhode Island.
Simulation of Groundwater and Surface-Water Interactions 23

K. WGW320

Estimated

Model calculated

EXPLANATION

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

Month

Change in water level from average, in feet

-1.5

-2.5

-2.0

-1.0

-0.5

0.0

0.5

1.0

2.5

2.0

1.5

Figure 11. Comparison of monthly departure from average conditions for model-calculated and 

estimated water levels for observation wells A, WGW285; B, WGW286; C, WGW 287; D, WGW 290; 

E, WGW291; F, WGW293; G, WGW303; H, WGW304; I, WGW305; J, WGW313; and K, WGW320 in the 

Big River Management Area, central Rhode Island.

More recent studies have been conducted to develop 

water-supply sources that could be utilized on a year-round 

basis (Blake Martin, Weston and Sampson, Inc., written 

commun., 2009). As part of these more recent studies, the 

viability of two well sites in the northern part of the BRMA 

near the southern extent of the Flat River Reservoir was 

explored (WGW443 and WGW444, fig. 1). Although this 

area is the narrowest part of the productive zone of the aquifer 

(figs. 6 and 7), the assumption was that induced infiltration 

from the reservoir could potentially satisfy pumping demands 

from this part of the aquifer, thereby limiting adverse effects 

to other more ecologically sensitive surface-water features in 

the BRMA. 

Previous investigations in the BRMA did not provide 

hydrologic information on the connection between the 

reservoir and the underlying aquifer system (Craft, 2001; 

Stone and Dickerman, 2002). Water-level data collected from 

48-hour aquifer tests as part of those studies did not provide 

the necessary data for subsequent modeling analyses to 

properly determine the interaction between groundwater and 

surface water in this area (Granato and others, 2003; Granato 

and Barlow, 2005). 

Recent water-resources investigations (Weston and 

Sampson, Inc., written commun., 2010) included aquifer 

tests in similar locations as the previous study (Craft, 2001), 

but investigations were conducted for a longer time period 

(5 days instead of 2 days) to determine whether the reservoir 

could contribute water to the pumping wells by induced 

infiltration and to assess pumping effects on nearby wetlands. 

The aquifer test consisted of two 8-in. wells (WGW443 and 

WGW444, fig. 14) simultaneously pumped at 550 gal/min and 

490 gal/min, respectively, for 5 days.

Simulation of Short-Term Pumping

A comparison of measured and model-calculated water 

levels in response to 5 days of continuous pumping during the 

aquifer test conducted from December 16 to 21, 2009, was 

done to assess how well the model matched the response of 

the aquifer to a pumping stress. This information was used to 

improve the model calibration (described previously) near the 

test wells and to better understand groundwater and surfacewater interactions in nearby wetlands. Adjustments to the 

model included changes in the simulated leakance between 

the reservoir and the underlying groundwater system and 

the extent and hydraulic conductivity of the glaciolacustrine 

deposits that underlie the reservoir and are prevalent 

throughout the northern part of the BRMA (figs. 6–7). 
24 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

A. WGW427

B. WGW428

C. WGW426

EXPLANATION

EXPLANATION

EXPLANATION

Estimated

Model calculated

Estimated

Model calculated

Estimated

Model calculated

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

Month

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

Month

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

Month

Vertical gradient, in feet Vertical gradient, in feet Vertical gradient, in feet

0

0.5

1.0

1.5

2.0

2.5

3.0

0

0.1

0.2

0.3

0.4

0.5

0.6

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Figure 12. Comparison of changes in model-calculated and estimated 

vertical gradients with time at A, Reynolds Pond Swamp (WGW427); 

B, Cedar Swamp (WGW428); and C, Scarborough Swamp (WGW426), 

Big River Management Area, central Rhode Island.
Simulation of Groundwater and Surface-Water Interactions 25

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

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

Month

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

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

Month

50

40

30

20

10

0

150

120

90

60

30

0

30

24

18

12

6

0

5

4

3

2

1

0

Monthly average streamflow, in cubic feet per second

A. Congdon River B. Capwell Mill Pond

C. Congdon Tributary D. Big River at Route 3

95-percent confidence interval of estimated

 average-monthly streamflow, from 1960 through 2006

Estimated average-monthly streamflow, from 1960 through 2006

Model-calculated mid-monthly streamflow

EXPLANATION

Figure 13. Comparison of model-calculated and estimated streamflows for long-term average monthly conditions from 

1960 through 2006 in the Big River Management Area, central Rhode Island.
26 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Unnamed tributary

Reynolds

Pond

Flat River

Reservoir

Big River

Bear Brook

Reynolds

Swamp

Cedar

Swamp

EXPLANATION

Active model area

Inactive model area

Pond

Wetland

Stream

Line of equal 

 model-calculated

 water-level change—

 Interval 0.5 foot

Monitoring well site

Pumping well site 

0.5

0

0

550 1,100 FEET

150 300 METERS

Base from Rhode Island Geographic Information System (RIGIS) digital data, 1:24,000

Lambert conformal conic projection, North American Datum of 1927

WGW427

WGW445

WGW443

WGW412

WGW413

WGW371

WGW416

WGW444

COW484

WGW428

71°37'30" 71°37'00"

 41°39'30"

41°39'00"

Bear Brook

Swamp

0.5

0.5

1.0

1.5

0.5

Area enlarged

Study area

Figure 14. Location of test wells WGW443 and WGW444 and monitoring wells measured during the aquifer test 

conducted from December 16 to 21, 2009, and model-calculated water-level changes in response to 5 days of 

simulated pumping in the Big River Management Area, central Rhode Island.
Simulation of Groundwater and Surface-Water Interactions 27

0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200

Distance from pumping well, WGW443, in feet

0

1

2

3

4

5

6

7

8

9

10

11

12

13

Water-level residual, in feet

WGW445

WGW412

WGW413

WGW371 WGW416 WGW427

Figure 15 . Comparison between measured and modelcalculated water-level changes with distance at monitoring 

wells measured at the end of the 5-day aquifer test conducted 

from December 16 to 21, 2009, Big River Management Area, 

central Rhode Island.

Effects of Model Discretization

This model provided a reasonable representation of 

the change in water levels observed during the aquifer test, 

in particular, at the wells located at a distance greater than 

200 ft from the pumped wells (fig. 15). The match between 

the measured and model-calculated water levels at observation 

wells within 200 ft of the pumped well was poor despite 

adjustments made in the model to the geologic framework and 

hydraulic conductivity of these deposits. 

The differences between the observed and simulated 

water-level changes may be attributed to the model grid 

discretization rather than the model conceptualization of the 

hydrogeologic conditions. The model underpredicted water 

levels in the observation wells closest to the pumped well 

(within 200 ft) (fig. 16A–C) but appears to provide a much 

better match to measured values at distances greater than 

200 ft (fig. 16D–F). 

The underpredicted match of changes in water levels 

(drawdowns) near the pumped well may be the result of the 

simulated pumping applied over the entire 50-ft by 50-ft 

model cell, rather than at the 8-in. diameter well casing that 

occurs in the aquifer. Also, model-calculated water levels 

are averaged for the entire grid cell, thereby creating the 

potential to dampen the water-level response in a model cell 

to pumping, particularly where there are large changes in 

water levels over short distances close to the pumped well. 

This grid discretization effect has been shown to diminish 

with increasing distance from the pumped well (Reilly and 

Harbaugh, 2004).

Effects of Storage in Till Deposits

Although the match between the model-calculated 

and measured water levels improves with distance from the 

pumped well, the initial simulation of the 5-day aquifer test 

showed a larger change in water level than the measured 

response ( 0.9 ft compared with 0.5 ft) at the observation well 

(WGW427) beneath the Reynolds Pond wetland site farthest 

from the pumped well (fig. 14). This model overprediction 

of the water-level changes at this site may be attributed to 

the model representation of the contact between the upland 

till areas and the adjacent glacial stratified deposits given 

the proximity of this site to that boundary. This contact is 

represented in the model as a no-flow boundary with the 

inflow from the uplands specified as a fixed rate of enhanced 

recharge at the water table along the active model area. 

The upland till area adjacent to WGW427 was mapped 

as till deposits greater than 20 ft (fig. 6) compared to the less 

than 10-ft zone mapped throughout most of the study area 

(Stone and Dickerman, 2002). To test the hypothesis that 

the model overprediction of drawdown was related to the 

upland till contact, simulations were made with an increased 

storage capacity along the upland till contact to account for 

storage effects in the till deposits not represented with no-flow 

boundary condition. When the storage coefficient value 

was increased from 0.00001 to 0.1 in this area, the match 

between the model-calculated and observed water levels 

greatly improved from initially overpredicting drawdown 

by 0.4 ft to exactly matching the measured value. A similar 

response was not calculated for the other observation wells 

located closer to the pumped wells, indicating there may be 

a localized connection between the till upland and stratified 

glacial deposits that is not properly accounted for with the 

enhanced recharge/no-flow boundary condition, but this effect 

may not extend much beyond this hydrogeologic contact. 

Therefore, for this analysis, a storage coefficient value of 0.1 

was simulated in areas where the till thickness was greater 

than 20 ft (fig. 6).

Increasing the simulated storage properties in the areas 

representing the contact between the till and the stratified 

glacial deposits does not increase the amount of water entering 

the flow system but only affects the timing of the release of 

the recharge specified along this contact to the aquifer. The 

fact that the increased storage improved the match between 

model-calculated and measured water levels after 5-days 

of pumping suggests that the timing of the release of water 

from the uplands may not be properly accounted for by 

specifying recharge along the no-flow boundary condition or 

the possibility of an additional source, or sources of water, 

not currently represented in the model, which also may 

improve the match near the upland till contact. Additional 

sources could include the contribution of water from fractured 

rock along the upland til contact or underlying the stratified 

glacial drift deposits not accounted for in the model; a 

similar response was observed in a fractured rock system in 

northeastern Massachusetts (Lyford and others, 2003). 
28 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

0 1 2 3 4 5

Day

0 1 2 3 4 5

Day

0 1 2 3 4 5

Day

0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Change in water level, in feet

0

5.0

10.0

15.0

20.0

25.0

Change in water level, in feet

0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Change in water level, in feet

Measured

Model calculated

EXPLANATION

Measured

Model calculated

EXPLANATION

Measured

Model calculated

EXPLANATION

A. WGW445 (50 feet from pumping well WGW443)

B. WGW412 (90 feet from pumping well WGW443)

C. WGW413 (190 feet from pumping well WGW443)

Figure 16. Comparison between measured and 

model-calculated water-level changes with distance 

at monitoring wells measured at the end of the 5-day 

aquifer test conducted from December 16 to 21, 2009, 

Big River Management Area, central Rhode Island. 

A, WGW445; B, WGW412; C, WGW413; D, WGW371; 

E, WGW416; and F, WGW427.
Simulation of Groundwater and Surface-Water Interactions 29

0 1 2 3 4 5

Day

0 1 2 3 4 5

Day

0 1 2 3 4 5

Day

0

Change in water level, in feet

0

Change in water level, in feet

0

Change in water level, in feet

0.1

0.2

0.3

0.4

0.5

0.6

0.5

1.0

1.5

2.0

2.5

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Measured

Model calculated

EXPLANATION

Measured

Model calculated

EXPLANATION

Measured

Model calculated

EXPLANATION

D. WGW371 (260 feet from pumping well WGW443)

E. WGW416 (690 feet from pumping well WGW443)

F. WGW427 (1,100 feet from pumping well WGW443)

Figure 16. Comparison between measured and 

model-calculated water-level changes with distance 

at monitoring wells measured at the end of the 5-day 

aquifer test conducted from December 16 to 21, 2009, 

Big River Management Area, central Rhode Island. 

A, WGW445; B, WGW412; C, WGW413; D, WGW371; 

E, WGW416; and F, WGW427.—Continued
30 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Effects of Changes in Reservoir Stage

The aquifer test was conducted in December, a time when 

the reservoir typically is lowered for weed control, but the 

reservoir was not lowered during the time that this test was 

conducted. Therefore, a comparison of the simulated changes 

in water levels under both conditions was made to determine 

if the water level in the reservoir could affect the results of the 

aquifer test. 

Results of this comparison showed that the difference 

in water-level changes after 5 days of simulated pumping 

between flooded or drained conditions in the reservoir 

area were negligible, indicating that the aquifer-test results 

would not be affected by the water level of the reservoir area 

(table 2). This result can be explained in part by an analysis 

of the water budget for these different hydrologic conditions 

(table 3). In both instances (reservoir area flooded or drained), 

most of the water (about 63 percent) discharging to the 

pumped wells was derived from aquifer storage and, therefore, 

induced infiltration from the reservoir area is not an important 

source of water in the first 5 days of pumping.

Table 2. Measured and model-calculated water-level declines in response to 5 days of continuous pumping at pumping test sites WGW443 and 

WGW444, Big River Management Area, central Rhode Island.

[Positive value indicates water-level decline from no-pumping condition. Pumping wells are located in model layer 5]

Well name Model 

row

Model 

column

Model 

layer

Distance from 

pumping well

(feet)

Water-level change 

model-calculated 

reservoir present

(feet)

Water-level change 

model-calculated 

reservoir drained

(feet)

Difference in 

model-calculated 

water levels 

(reservoir present 

minus drained)

(feet)

WGW445 47 57 5 50 9.07 8.94 0.13

WGW412 47 54 5 90 7.59 7.47 0.12

WGW413 50 52 5 190 5.29 5.19 0.10

WGW371 52 50 5 260 4.01 3.97 0.04

WGW416 54 44 5 690 2.22 2.18 0.04

WGW427-0001 61 39 1 1,100 0.07 0.07 0.00

WGW427-0023 61 39 3 1,100 0.48 0.47 0.01

Table 3. Source of water to pumping wells at a total pumping rate of 1.5 million gallons per day after 5 days of 

pumping and for long-term monthly conditions.

Source of water to pumping wells 1

B.I.–5 days 

(in percent)

August 

(in percent)

2

B.O.–5 days 

(in percent)

December 

(in percent)

Storage 63 13 64 0

Induced Infiltration from Reservoir 22 52 8 7

Captured flow to Reservoir 6 7 24 64

Reductions in streamflow away from reservoir 9 28 4 29

1

B.I. is the condition in which the control boards were in place creating the reservoir; condition that occurs typically from March 

through October.

2

B.O. is the condition in which the control boards were removed and the reservoir drained for weed control; a condition that occurs 

typically from November through February.
Simulation of Groundwater and Surface-Water Interactions 31

Simulation of Long-Term Pumping

Simulations were made to assess the effects of continuous 

(24-hr/day) pumping at WGW443 and WGW444 at rates 

of 550 gal/min and 490 gal/min, respectively, for long-term 

average monthly conditions and to determine whether the 

water-level changes observed after 5 days of pumping would 

remain stable or additional declines would occur if pumping 

continued over a longer period, as it would if these sites were 

to be developed as water-supply sources. A comparison was 

made of simulated water-level changes between long-term 

pumping and pumping for a brief period (5 days) to determine 

if this aquifer system would reach equilibrium after 5 days 

of pumping.

Effect of Increased Pumping Time

 After 5 days of pumping, measured water levels declined 

by only about 0.5 ft near Reynolds Pond (fig. 17); however, 

when pumping at the same rates was simulated for long-term 

average monthly conditions for a typical December when the 

reservoir area is drained (fig. 18A) and for a typical August 

when the reservoir area is flooded (fig. 18B), the water-level 

declines calculated at the water table were 6 ft and 5 ft, 

respectively. This continued decline in model-calculated water 

levels with time suggests that, after 5 days of pumping, this 

aquifer system has not yet reached equilibrium with respect 

to this pumping stress, and that an aquifer test conducted for 

only a 5-day period may not be sufficiently long to adequately 

assess the effects of pumping on the wetlands in the BRMA 

or on wetland systems in similar hydrogeologic settings found 

throughout Rhode Island. 

Effect of Changes in Reservoir Stage

Model simulation of nonpumping conditions, for typical 

December conditions when the reservoir area is normally 

drained, indicates the water level in the reservoir area is lower 

relative to the surrounding aquifer resulting in about 6.4 ft3

/s 

(or 4.1 Mgal/d) of groundwater discharge to the part of the 

Big River that flows through this area. During typical August 

conditions when the reservoir area is normally flooded, the 

hydraulic gradient between the groundwater system and the 

reservoir is reduced resulting in little hydrologic interaction 

between the underlying aquifer and the reservoir. As a result, 

when the reservoir area is flooded (March–October), there 

is greater potential for the reservoir to be a source of water 

to the pumped wells through induced infiltration. During the 

year when the reservoir area is drained (November–February), 

the potential source of water to nearby pumped wells is from 

a reduction in groundwater discharge from the aquifer to the 

part of the Big River that flows through the drained part of the 

reservoir (fig. 5). 

 A comparison was made of the model-calculated sources 

of water to the pumped wells during the 5-day simulation and 

for the long-term monthly conditions (table 3) to determine 

the sources of the water pumped from the wells and whether 

the sources of water changed with increased pumping times. 

Results of the model simulations indicated that after 5 days 

of continuous pumping, the resulting declines in water 

levels in the nearby wetlands were typically less than 1 ft, 

and this change in water level did not appear to differ much 

between the condition when the reservoir area was flooded or 

drained. In both instances, most (63–64 percent) of the water 

pumped from the wells was derived from aquifer storage. 

In the scenario in which the reservoir area was flooded, the 

remaining sources of water included (1) induced infiltration 

from the reservoir (22 percent), (2) reduction in discharge to 

nearby streams (9 percent), and (3) reduction in groundwater 

discharge to the reservoir (6 percent). In the scenario in 

which the reservoir area was drained, the remaining sources 

of water included (1) reduction in groundwater discharge to 

the reservoir (24 percent), (2) induced infiltration from the 

Big River in the area of the drained reservoir (8 percent), and 

(3) reduction in discharge to nearby streams (4 percent). 

When continuous pumping was simulated for long-term 

average monthly-recharge conditions, the resulting declines in 

water levels in the vicinity of the pumping wells were about 

5 to 6 ft. These changes in water levels were on average about 

1 ft greater when the reservoir area was drained compared 

to when it was flooded (fig. 18B). In the scenario in which 

the reservoir area was flooded, more than half (52 percent) 

of the water withdrawn from the wells was derived from 

induced infiltration from the reservoir, while the remaining 

sources of water included (1) reduction in discharge to 

nearby streams (28 percent), (2) aquifer storage (13 percent), 

and (3) reduction in groundwater discharge to the reservoir 

(7 percent). In the scenario in which the reservoir area was 

drained, most (64 percent) of the water pumped from the 

wells was derived from reduction in groundwater discharge 

to the reservoir area, while the remaining sources of water 

included reduction in discharge to nearby streams (29 percent) 

and induced infiltration from the Big River in the area of the 

drained reservoir (7 percent). 

Differences in drawdowns between December and 

August were about 2 ft in the vicinity of Reynolds Swamp 

(fig. 18), indicating that even if pumping rates were to remain 

constant throughout the year, the long-term effect of pumping 

on this aquifer system appears to vary depending on whether 

or not the reservoir area is flooded. 

This analysis suggests that the differences in both waterlevel declines and the sources of water to the pumped wells 

varied with time and were dependent on whether the reservoir 

area was drained or flooded. After water levels have declined 

so that the hydraulic gradient between the nearby surface 

waters and the underlying aquifer is sufficiently large, the 

reservoir becomes a primary source of water; the contribution 

of water from storage during early pumping times would be 

replaced by increased induced infiltration from the reservoir 

and by reductions in groundwater discharge to the reservoir 

and nearby streams (table 3). 

These results also suggest that the differences between 

drawdowns for 5 days of pumping and under long-term 
32 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Reynolds

Pond

Unnamed tributary

Flat River

Reservoir

Big River

Bear Brook

Reynolds

Swamp

Cedar

Swamp

Base from Rhode Island Geographic Information System (RIGIS) digital data, 1:24,000

Lambert conformal conic projection, North American Datum of 1927

0

0

550 1,100 FEET

150 300 METERS

EXPLANATION

Active model area

Inactive model area

Reservoir area

Pond

Wetland

Stream

Line of equal 

 model-calculated

 water-level change—

 Interval 0.5 foot

Monitoring well site

Pumping well site 

0.5

0.5

1.0

1.5

0.5

0.5

WGW427

WGW445

WGW443

WGW412

WGW413

WGW371

WGW416

WGW444

COW484

WGW428

71°37'30" 71°37'00"

 41°39'30"

41°39'00"

Bear Brook

Swamp

Area enlarged

Study area

A

Figure 17. Model-calculated water-level declines A, after 5 days of continuous pumping for December conditions 

when reservoir area is drained and B, in response to continuous pumping for long-term average December 

conditions when reservoir area is drained, Big River Management Area, central Rhode Island.
Simulation of Groundwater and Surface-Water Interactions 33

Figure 17. Model-calculated water-level declines A, after 5 days of continuous pumping for December conditions 

when reservoir area is drained and B, in response to continuous pumping for long-term average December 

conditions when reservoir area is drained, Big River Management Area, central Rhode Island.

Reynolds

Pond

Unnamed tributary

Flat River

Reservoir

Big River

Bear Brook

Reynolds

Swamp

Cedar

Swamp

Base from Rhode Island Geographic Information System (RIGIS) digital data, 1:24,000

Lambert conformal conic projection, North American Datum of 1927

0

0

550 1,100 FEET

150 300 METERS

EXPLANATION

Active model area

Inactive model area

Reservoir area

Pond

Wetland

Stream

Line of equal

 model-calculated

 water-level change—

 Interval 1.0 foot

Monitoring well site

Pumping well site 

1.0

2.0

3.0

4.0

5.0

6.0

2.0

1.0

1.0

5.0

6.0

WGW427

WGW445

WGW443

WGW412

WGW413

WGW371

WGW416

WGW444

Area enlarged

Study area

COW484

WGW428

71°37'30" 71°37'00"

 41°39'30"

41°39'00"

Bear Brook

Swamp

B
34 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Reynolds

Pond

Unnamed tributary

Flat River

Reservoir

Big River

Bear Brook

Reynolds

Swamp

Cedar

Swamp

Base from Rhode Island Geographic Information System (RIGIS) digital data, 1:24,000

Lambert conformal conic projection, North American Datum of 1927

0

0

550 1,100 FEET

150 300 METERS

EXPLANATION

Active model area

Inactive model area

Reservoir area

Pond

Wetland

Stream

Line of equal

 model-calculated

 water-level change—

 Interval 1.0 foot

Monitoring well site

Pumping well site 

1.0

2.0

3.0

4.0

5.0

6.0

2.0

1.0

1.0

5.0

6.0

WGW427

WGW412

WGW413

WGW371

WGW416 WGW445

WGW443

WGW444

Area enlarged

Study area

COW484

WGW428

71°37'30" 71°37'00"

 41°39'30"

41°39'00"

Bear Brook

Swamp

A

Figure 18. Model-calculated water-level declines in response to continuous pumping for A, long-term average 

December conditions when reservoir area is drained and for B, long-term average August conditions when reservoir 

area is flooded, the Big River Management Area, central Rhode Island.
Simulation of Groundwater and Surface-Water Interactions 35

Reynolds

Pond

Unnamed tributary

Flat River

Reservoir

Big River

Bear Brook

Reynolds

Swamp

Cedar

Swamp

Base from Rhode Island Geographic Information System (RIGIS) digital data, 1:24,000

Lambert conformal conic projection, North American Datum of 1927

0

0

550 1,100 FEET

150 300 METERS

EXPLANATION

Active model area

Inactive model area

Reservoir area

Pond

Wetland

Stream

Line of equal

 model-calculated

 water-level change—

 Interval 1.0 foot

Monitoring well site

Pumping well site 

5.0

COW484

WGW428

71°37'30" 71°37'00"

 41°39'30"

41°39'00"

Bear Brook

Swamp

1.0

2.0

3.0

4.0

5.0

2.0

1.0

1.0

5.0

4.0

4.0

3.0

WGW427

WGW412

WGW413

WGW371

WGW416 WGW445

WGW443

WGW444

Area enlarged

Study area

B

Figure 18. Model-calculated water-level declines in response to continuous pumping for A, long-term average 

December conditions when reservoir area is drained and for B, long-term average August conditions when reservoir 

area is flooded, the Big River Management Area, central Rhode Island.
36 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

monthly conditions (figs. 17–18) may indicate that the waterlevel changes measured as part of the aquifer test are not 

representative of a stable condition, and water levels may 

continue to decline with increased time even with constant 

pumping until the hydraulic gradient between the reservoir 

and the underlying aquifer is large enough to create enough 

groundwater flow to the pumped wells to satisfy the pumping 

rate. These model-calculated drawdowns only reflect the 

response of the aquifer to the pumping rates simulated in 

this analysis; if pumping rates were increased, it would be 

expected that drawdowns and reductions in surface-water flow 

would increase accordingly.

Simulated Effects of Groundwater Withdrawals 

on Wetlands

The model-calculated change in water levels at the Bear 

Brook, Cedar, Reynolds, and Scarborough Swamps were 

assessed for the short-term (5-day) pumping period and the 

long-term pumping period for average conditions for the 

months of December and August when the reservoir area 

was drained and flooded (table 4). A fifth site, the Congdon 

Swamp (fig. 1), was selected as part of the field component 

of this study (Borenstein and others, 2012) as a control site 

to compare the potential long-term ecological changes in the 

four sites listed above to one under unstressed conditions once 

large-scale withdrawal commence in the BRMA .

Model results indicate that the water-level declines at 

the Bear Brook, Cedar, Reynolds, and Scarborough Swamps 

ranged from 0 to 0.2 ft for short-term (5-day) conditions 

representative of the pump test conducted in December 2009 

(fig. 14, table 4). During that pump test, the boards had not yet 

been removed for weed control and the reservoir was flooded. 

The model-calculated water-level declines were greatest 

beneath Cedar Swamp for a maximum decline of about 0.2 ft 

(fig. 14, table 2). Simulation of the boards removed and the 

reservoir area drained resulted in the same amount of waterlevel decline as with the boards in place.

Continuous pumping rates of 550 and 490 gal/min 

were simulated at WGW443 and WGW444, respectively, 

for long-term average monthly conditions. Model-calculated 

water-level declines were determined for the wetland sites for 

average monthly August and December conditions when the 

reservoir area is typically flooded and drained. Model results 

indicate that water-level declines beneath the Bear Brook, 

Cedar, Reynolds, and Scarborough Swamps ranged from 0 to 

3.8 ft for August conditions with the greatest decline (3.8 ft) 

occurring at Reynolds Swamp. The water-level declines for 

December conditions, when the boards are typically out and 

the reservoir area is drained, ranged from 0.1 to 5.8 ft with the 

greatest declines also occurring at Reynolds Swamp (5.8 ft).

The largest change in water-level declines from August to 

December conditions occurred at Reynolds Swamp indicating 

that when the reservoir area is flooded (i.e. August conditions) 

the water-level declines in this area may be about 2 ft less than 

for December conditions when the reservoir area is drained. 

This response does not occur at the other wetland sites (fig. 18, 

table 4) and may be related to the proximity of Reynolds 

Swamp to the pumping wells and or its proximity to the 

upland till boundary (fig. 18).

Limitations of Analysis

The primary focus of this analysis was to determine 

the potential effects of pumping on surface-water features 

such as ponds, streams, and wetlands in the BRMA and to 

determine whether field methods such as aquifer tests would 

be sufficient to adequately assess the potential effects of 

pumping on surface waters in this aquifer system. A better 

understanding of the water availability in this area was needed 

to fully assess these effects. Two processes that affect water 

Table 4. Model-calculated water-level declines at the priority wetland sites in response to continuous 

pumping at aquifer test sites WGW443 and WGW444 for short-term (5 days) and average monthly 

conditions, Big River Management Area, central Rhode Island.

[Postive value indicates water-level decline from no-pumping condition.]

Wetland name Well name

B.I.1

 -5 days B.O.2 -5 days August December

(feet) (feet) (feet) (feet)

Bear Brook Swamp COW484 0 0 0.2 0.2

Scarborough Swamp WGW426 0 0 0 0.1

Reynolds Swamp WGW427 0.1 0.1 3.8 5.8

Cedar Swamp WGW428 0.2 0.2 0.4 0.5

Congdon Swamp WGW429 0 0 0 0

1

B.I. is the condition in which the control boards were in place creating the reservoir; condition that occurs typically 

from March through October.

2

B.O. is the condition in which the control boards were removed and the reservoir drained for weed control; acondition 

that occurs typically from November through February.
Simulation of Groundwater and Surface-Water Interactions 37

availability in this area are the interaction between the till 

uplands and the valley-fill aquifer system and the interaction 

between the reservoir area of the Big River and the underlying 

groundwater system. 

Because more than half (about 60 percent) of the recharge 

that enters this valley-fill aquifer system is estimated to be 

derived from inflow from the surrounding upland till areas 

(fig. 6), an understanding of how much water is available 

in these upland areas and of the timing of the release of this 

water into the adjacent aquifer system is needed to fully assess 

water availability in the BRMA. To date, flow rates from the 

uplands and how best to account for upland flow in numerical 

simulations are not very well understood.

The representation of the upland till areas in the 

groundwater model was based on the previous analysis 

conducted by Granato and other (2003) and has been a 

common approach to numerically represent these features in 

valley-fill aquifer systems in Rhode Island (Dickerman and 

Ozbilgin, 1985; Dickerman and others, 1990; Dickerman 

and Bell, 1993; Dickerman and others, 1997; Barlow and 

Dickerman, 2001; Friesz and Stone, 2007; Friesz, 2010). This 

approach has included removing the upland till region from 

the active model area and accounting for the flow from these 

areas as specified rates of streamflow for streams that drain 

upland areas or as specified recharge rates in the undrained 

areas of the uplands. 

The total flux of the water specified along the contact 

between the uplands and the stratified glacial deposits for the 

undrained upland areas was based on a similar recharge rate as 

the valley-fill system on an annual basis but was adjusted on 

a monthly basis to account for possible changes in the timing 

of the movement of groundwater from the till deposits to the 

aquifer, referred to as the “release of water from storage”. 

The adjustment made to the timing of the release of water 

from storage in the till areas was based on the distribution of 

monthly flow in gaged streams in nearby till areas as described 

in Granato and others (2003). This method was used because 

the water released from storage in the till deposits could not 

be explicitly represented in the model simulations given the 

boundary conditions used in this analysis.

Results from this analysis, as shown by the match 

between model-calculated and estimated water levels and 

streamflows (figs. 11–12), indicate that the total amount 

of recharge entering the aquifer from the till areas and the 

method of implicitly accounting for the change in the timing 

of water released from storage from the till areas appears 

adequate for this analysis on a monthly time scale. An 

exception to this includes the southern part of the BRMA 

where the model appears to be underrepresenting the release 

of water from upland storage (WGW285, fig. 11A) or not 

properly accounting for the timing of the release of water from 

storage in these areas (WGW28, fig. 11B). 

Another instance of where the release of water from 

storage in the uplands may not be properly accounted for in 

the model simulations is the analysis of the change in water 

levels during the 5-day aquifer test. A comparison of the 

model-calculated water levels to those measured after 5 days 

of pumping during the aquifer test conducted in December 

2009 indicates that differences between measured and modelcalculated water levels improve with distance from the 

pumped wells except for the area along upland till contact at 

observation well WGW427 (fig. 16F).

 The model overprediction of water-level declines at 

this monitoring well may be a function of the inability of the 

model to accurately represent the effects of water released 

from storage in the till deposits on a less than monthly time 

scale. In order to account for this, the storage coefficient 

values simulated in the stratified glacial deposits along the 

no-flow boundary representing the contact between the 

uplands and the valley-fill deposits were increased by four 

orders of magnitude (from 0.00001 to 0.1) in the areas where 

till deposits exceed 20-ft in thickness. 

Increasing the amount of storage along the no-flow 

boundary resulted in a dampening of the water-level 

declines in this area indicating there may be a local-scale 

hydrogeologic condition not properly accounted for in the 

model. This change in storage coefficient did not appear to 

affect simulated water-level declines in the other observation 

wells located away from the upland contact, suggesting this 

storage effect may be a local one and needs to be considered 

when evaluating potential effects of pumping on wetlands 

located near the till upland areas. However, given the 

current understanding of the groundwater and surface-water 

interactions between till uplands and valley-fill sediments, 

it is not possible to quantify the amount of uncertainty this 

interaction adds to this analysis.

An additional process that may warrant further analysis is 

the interaction between the reservoir part of the Big River and 

the underlying groundwater system and, more specifically, the 

extent to which the reservoir may serve as a potential source 

of water to pumped wells in the BRMA through the process 

of induced infiltration. For the purpose of this analysis, the 

reservoir bottom sediments were assumed to have a uniform 

vertical leakance of 0.1 ft/d. This value was increased by an 

order of magnitude to determine whether a better connection 

between the reservoir and the underlying aquifer would 

decrease the amount of simulated drawdowns observed as part 

of this analysis for pumping under long-term average monthly 

conditions. Results showed little change in water levels, for 

the 5-day aquifer-test period and for the long-term monthly 

conditions, indicating that the reservoir bottom sediments 

do not appear to have a substantial effect on limiting the 

interaction between groundwater and surface water in this 

aquifer system.

 Additional simulations were made to determine the 

importance of the permeability of the glaciolacustrine deposits 

that underlie the reservoir bottom sediments (cross section 

A–A′ (fig. 7A) on the interaction between groundwater and 

surface water in this area. An increase from 10 ft/d to 100 ft/d 

in the horizontal hydraulic conductivity value simulated in 

the model for these glaciolacustrine deposits resulted in a 

reduction in the simulated drawdown by as much as 3 ft in 
38 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

the vicinity of the pumping wells. This reduction indicates if 

these sediments were simulated as being more permeable there 

would be more connection between the surface waters and 

the pumped wells, thus underscoring the importance of these 

sediments on the interaction between groundwater and surface 

water in this area. 

Although the simulated drawdowns appear to be less with 

the simulation of more permeable glaciolacustrine deposits, 

the matches between measured and model-calculated water 

levels for the 5-day aquifer test were unacceptable for this 

simulated condition, indicating that the assumption of a more 

permeable glaciolacustrine deposit underlying the reservoir is 

not likely. Further examination of the distribution and extent 

of these sediments beneath the reservoir may be warranted to 

better understand the hydrogeologic control these sediments 

may have on changes in water levels in response to proposed 

groundwater withdrawals in this area. 

Finally, the use of numerical models to simulate 

groundwater flow systems such as that of the BRMA has 

inherent limitations. Proper model design and calibration can 

help reduce these limitations; however, it is important to note 

that numerical simulations such as the ones detailed in this 

report are simplified representations of real-world conditions 

and only are designed for the purpose of helping better 

understand complex hydrogeologic conditions.

Summary and Conclusions

The Rhode Island Water Resources Board (RIWRB) is 

responsible for developing and protecting the State’s water 

resources. In order to address ongoing concerns that increasing 

demand may exceed current capacity, the RIWRB has been 

exploring the largely untapped groundwater resources of 

the Big River Management Area (BRMA), an area that has 

been under consideration for development as a surface-water 

reservoir since the early 1960s. To date (2012), the U.S. 

Environmental Protection Agency has not given final approval 

for construction of this reservoir.

Since 1995, the U.S. Geological Survey (USGS), in 

cooperation with the RIWRB, has been conducting a series 

of scientific investigations of the water resources of the 

BRMA. These investigations were designed to improve the 

understanding of the hydrogeologic conditions of the area 

and the potential effects of groundwater withdrawals on 

streamflow in the area. The most recent of these investigations 

began in 2008 in response to a need for an assessment of 

the potential effects of pumping on wetlands in the BRMA. 

To address this need, a partnership was formed among the 

RIWRB, the USGS, and the University of Rhode Island 

(URI) with the goal of developing methods for characterizing 

wetland vegetation, soils, and hydrology, and monitoring 

and modeling water levels for pre- and post-watersupply development. 

As part of this analysis, a groundwater-flow model was 

developed to assess the effects of proposed groundwater 

withdrawals on wetland water levels in the BRMA. The 

groundwater-flow model used for this analysis was developed 

as a subregional model of the larger model developed by 

Granato and others (2003) to focus only on the BRMA and, 

in particular, on the area in the northern part of the BRMA 

near the Flat River Reservoir. Test sites in this area were 

selected, in part, because of the assumption that if water were 

withdrawn from these sites, it most likely would be derived 

from induced infiltration from the flooded reservoir area of 

the Big River, and, therefore, groundwater withdrawals in this 

area would have less of an impact on surrounding wetlands 

and streamflow. 

The model was calibrated to long-term average water 

levels, and streamflows estimated by the maintenance of 

variance type 1 (MOVE.1) analysis are documented in the 

appendix. The model then was used to calculate the change in 

water levels for 5 days of continuous pumping for conditions 

when the reservoir area is flooded, when the reservoir area 

is drained, and for conditions in which pumping rates are 

constant for average monthly recharge conditions in December 

when the reservoir area is typically drained and in August 

when the reservoir area is typically flooded. The model also 

was used to determine the sources of water to the pumped 

wells for these varying conditions and to assess how the 

sources of water to the pumped wells change with increasing 

pump times.

 Results of the model simulations indicated that after 

5 days of continuous pumping, the resulting declines in water 

levels in the nearby wetlands were typically less than 1 foot 

(ft), and this change in water level did not appear to differ 

much between the condition when the reservoir area was 

flooded or drained. In both instances, most (63–64 percent) 

of the water pumped from the wells was derived from 

aquifer storage. In the scenario in which the reservoir 

area was flooded, the remaining sources of water included 

(1) induced infiltration from the reservoir (22 percent), 

(2) reduction in discharge to nearby streams (9 percent), 

and (3) reduction in groundwater discharge to the reservoir 

(6 percent). In the scenario in which the reservoir area was 

drained, the remaining sources of water included (1) reduction 

in groundwater discharge to the reservoir (24 percent), 

(2) induced infiltration from the Big River in the area of the 

drained reservoir (8 percent), and (3) reduction in discharge to 

nearby streams (4 percent). 

Results of the model simulations indicated that for 

continuous pumping for long-term average monthly recharge 

conditions, the resulting declines in water levels near the 

pumping wells of about 5 to 6 ft. These changes in water 

levels were on average about 1 ft greater when the reservoir 

area was drained compared to when the area was flooded. 

The differences in water-level declines and the sources 

of water to the pumped wells varied with time and were 

dependent on whether the reservoir area was drained or 

flooded. In the scenario in which the reservoir area was 
References Cited 39

flooded, more than half (52 percent) of the water withdrawn 

from the wells was derived from induced infiltration from 

the reservoir, while the remaining sources of water included 

(1) reduction in discharge to nearby streams (28 percent), 

(2) aquifer storage (13 percent), and (3) reduction in 

groundwater discharge to the reservoir (7 percent). In 

the scenario where the reservoir area was drained, most 

(64 percent) of the water pumped from the wells was derived 

from reduction in groundwater discharge to the reservoir 

area, while the remaining sources of water included reduction 

in discharge to nearby streams (29 percent) and induced 

infiltration from the Big River in the area of the drained 

reservoir (7 percent). 

The analysis of the potential effects of groundwater 

withdrawals on wetlands in the BRMA indicates that given 

the hydrogeologic conditions of this aquifer system, a 5-day 

aquifer test may not be sufficient to adequately determine the 

effects of pumping on water levels in nearby wetlands. Model 

simulations showed that water levels continued to decline 

beneath the Reynolds Swamp wetland by an additional 4 to 

6 ft, depending on whether the reservoir area was flooded 

or drained, as pumping times were increased from a 5-day 

simulation period to a simulation period representative of 

long-term average monthly conditions, which would be more 

indicative of how the wells would be utilized as a source of 

public-water supply. 

 The primary reason for the continued decline in water 

levels with increased pumping time is related to the shift from 

the primary source of water to the pumped wells being derived 

from aquifer storage during the early-time (5 days) simulation 

to being derived from induced infiltration from the reservoir 

or captured groundwater discharge to the Big River in the 

reservoir area, as was the case for the long-term monthly 

conditions simulated for December and August. Additional 

testing for a longer period of time and a more detailed 

characterization of geologic framework and the interaction 

between the till uplands and stratified glacial deposits may 

be required to fully assess the effects of pumping on surfacewater features in this aquifer system.

References Cited

Alley, W.M., Reilly, T.E., and Franke, O.L., 1999, 

Sustainability of ground-water resources: U.S. Geological 

Survey Circular 1186, 79 p.

Anderson, M.P., and Woessner, W.W., 1992, Applied 

groundwater modeling: San Diego, Calif., Academic Press, 

Inc., 381 p.

Barlow, P.M., and Dickerman, D.C., 2001, Numericalsimulation and conjunctive-management models of the 

Hunt-Annaquatucket-Pettaquamscutt stream-aquifer system, 

Rhode Island: U.S. Geological Survey Professional Paper 

1636, 88 p.

Boothroyd, J.C., Freedman, J.H., Brenner, H.B., and Stone, 

J.R., 1998, The glacial geology of southern Rhode Island, in

Murray, D.P., ed., New England Intercollegiate Geological 

Conference, 90th annual meeting, Kingston, R.I., October 

9–11, 1998, Guidebook for fieldtrips in Rhode Island and 

adjacent regions of Connecticut and Massachusetts: trip C5, 

25 p.

Borenstein, M.S., Golet, F.C., Armstrong, D.S., Breault, 

R.F., McCobb, T.D., and Weiskel, P.K., 2012, Hydrologic, 

vegetation, and soils data collected in selected wetlands of 

the Big River Water Management Area, Rhode Island: U.S. 

Geological Survey Data Series 666, 101 p.

Carlson, C.S., and Lyford, F.P., 2005, Simulated ground-water 

flow for a pond-dominated aquifer system near Great Sandy 

Bottom Pond, Pembroke, Massachusetts: U.S. Geological 

Survey Scientific Investigations Report 2004–5269, 43 p.

Chow, V.T., 1964, Handbook of applied hydrology: New York, 

McGraw-Hill, [variously paged].

Craft, P.A., 2001, Hydrogeologic data for the Big River–

Mishnock River stream-aquifer system, central Rhode 

Island: U.S. Geological Survey Open-File Report 01–250, 

104 p.

Dickerman, D.C., and Bell, R.W., 1993, Hydrogeology, water 

quality, and ground-water-development alternatives in the 

upper Wood River ground-water reservoir, Rhode Island: 

U.S. Geological Survey Water-Resources Investigations 

Report 92–4119, 87 p.

Dickerman, D.C., Kliever, J.D., and Stone, J.R., 1997, 

Hydrogeology, water quality, and simulation of 

groundwater-development alternatives in the UsquepaugQueen ground-water reservoir, southern Rhode Island: U.S. 

Geological Survey Water-Resources Investigations Report 

97–4126, 48 p.

Dickerman, D.C., and Ozbilgin, M.M., 1985, Hydrogeology, 

water quality, and ground-water development alternatives in 

the Beaver-Pasquiset ground-water reservoir, Rhode Island: 

U.S. Geological Survey Water-Resources Investigations 

Report 85–4190, 104 p.

Dickerman, D.C., Trench, E.C.T., and Russell, J.P., 

1990, Hydrogeology, water quality, and ground-water 

development alternatives in the lower Wood River 

groundwater reservoir, Rhode Island: U.S. Geological 

Survey Water-Resources Investigations Report 89–4031, 

109 p.

Farnsworth, R.K., Thompson, E.S., and Peck, E.L., 1982, 

Evaporation atlas for the contiguous 48 states: National 

Oceanic and Atmospheric Administration Technical Report 

NWS 33, 26 p. 
40 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Feininger, T.G., 1962, Surficial geology of the Hope Valley 

quadrangle, Rhode Island: U.S. Geological Survey Geologic 

Quadrangle GQ-166, scale 1:24,000.

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. 

Friesz, P.J., and Stone, J.R., 2007, Simulation of ground-water 

flow and areas contributing recharge to production wells 

in contrasting glacial valley-fill settings, Rhode Island: 

U.S. Geological Survey Scientific Investigations Report 

2007–5133, 50 p.

Granato, G.E., 2009, Streamflow Record Extension 

Facilitator (SREF version 1.0)—A program for extending 

and augmenting available streamflow data using longterm streamflow records from hydrologically similar 

sites, appendix 3 in Computer programs for obtaining 

and analyzing daily mean streamflow data from the U.S. 

Geological Survey National Water Information System Web 

site: U.S. Geological Survey Open-File Report 2008–1362, 

123 p. on CD–ROM.

Granato, G.E., and Barlow, P.M., 2005, Effects of alternative 

instream-flow criteria and water-supply demands on 

ground-water development options in the Big River 

Area, Rhode Island: U.S. Geological Survey Scientific 

Investigations Report 2004–5301, 110 p.

Granato, G.E., Barlow, P.M., and Dickerman, D.C., 2003, 

Hydrogeology and simulated effects of ground-water 

withdrawals in the Big River Area, Rhode Island: U.S. 

Geological Survey Water-Resources Investigations Report 

03–4222, 76 p.

Harbaugh, A.W., 2005, MODFLOW-2005—The U.S. 

Geological Survey modular ground-water model—the 

ground-water flow process: U.S. Geological Survey 

Techniques and Methods 6–A16, variously paged.

Hemond, H.F., 1980, Biogeochemistry of Thoreau’s bog, 

Concord, Massachusetts: Ecological Monographs, v. 50, 

no. 4, p. 507–526.

Jensen, M.E., and Haise, H.D., 1963, Estimating 

evapotranspiration from solar radiation: Journal of Irrigation 

and Drainage, v. 89, no. IR4, p. 15–41.

Konikow, L.F., and Reilly, T.E., 1999, Groundwater modeling, 

in Delleur, J.W., ed., The handbook of groundwater 

engineering: Boca Raton, Fla., CRC Press, 40 p.

Lyford, F.P., Carlson, C.S. and Hansen, B.P., 2003, Delineation 

of water sources for public-supply wells in three fracturedbedrock aquifer systems in Massachusetts: U.S. Geological 

Survey Water-Resources Investigations Report 02–4290, 

114 p.

Masterson, J.P., 2011, Simulated effects of water withdrawals 

on groundwater flow (MODFLOW models), part 3 of Bent, 

G.C., Zarriello, P.J., Granato, G.E., Masterson, J.P., Walter, 

D.A., Waite, A.M., and Church, P.E., Simulated effects of 

water withdrawals and land-use changes on streamflows 

and groundwater levels in the Pawcatuck River Basin, 

southwestern Rhode Island and southeastern Connecticut: 

U.S. Geological Survey Scientific Investigations Report 

2009–5127, 254 p.

Masterson, J.P., Sorenson, J.R., Stone, J.R., Moran, 

S.B., and Hougham, Andrea, 2007, Hydrogeology and 

simulated ground-water flow in the Salt Pond region of 

southern Rhode Island: U.S. Geological Survey Scientific 

Investigations Report 2006–5271, 56 p.

McDonald, M.G., and Harbaugh, A.W., 1988, A modular 

three-dimensional finite-difference ground-water flow 

model: U.S. Geological Survey Techniques of WaterResources Investigations, book 6, chap. A1, 586 p.

Mortellaro, S., Krupa, S., Fink, L., and Van Horn, J., 1995, 

Literature review on the effects of groundwater drawdown 

on isolated wetlands: West Palm Beach, Fla., South Florida 

Water Management District Technical Publication No. 

96–01, 44 p.

National Oceanic and Atmospheric Administration, 2007, 

accessed March 21, 2007, at http://www.cdo.ncdc.noaa.gov/

dly/DLY.

Niswonger, R.G., and Prudic, D.E., 2005, Documentation 

of the Streamflow-Routing (SFR2) package to include 

unsaturated flow beneath streams—A modification to SFR1: 

U.S. Geological Survey Techniques and Methods book 6, 

chap. A13, 50 p.

Power, W.R., Jr., 1957, Surficial geology of the Slocum 

quadrangle, Rhode Island: U.S. Geological Survey Geologic 

Quadrangle GQ-106, scale 1:31,680.

Reilly, T.E., 2001, System and boundary conceptualization 

in ground-water flow simulation: U.S. Geological Survey 

Techniques of Water-Resources Investigations, book 3, 

chap. B8, 38 p.

Reilly, T.E., and Harbaugh, A.W., 2004, Guidelines for 

evaluating ground-water flow models: U.S. Geological 

Survey Scientific Investigations Report 2004–5038, 30 p.

Rochow, T.F., and Rhinesmith P., 1991, Comparative analysis 

of biological conditions in five cypress dome wetlands at 

the Starkey and Eldridge-Wilde well fields in southwest 

Florida: Brooksville, Fla., Southwest Florida Water 

Management District Technical Report 1991–1, 67 p. 

Skidds, D.E., and Golet. F.C., 2005, Estimating hydroperiod 

suitability for breeding amphibians in southern Rhode 

Island seasonal forest ponds: Wetlands Ecology and 

Management, v. 13, p. 349–366.
References Cited 41

Smith, J.H., 1956, Surficial geology of the Crompton 

quadrangle, Rhode Island: U.S. Geological Survey Geologic 

Quadrangle GQ-94, scale 1:31,680.

Sonenshein, R.S., and Hofstetter, R.H., 1990, Hydrologic 

effects of well-field operations in a wetland, Dade 

County, Florida: U.S. Geological Survey Water-Resources 

Investigations Report 90–4143, 59 p.

Stone, B.D., and Borns, H.W., Jr., 1986, Pleistocene glacial 

and interglacial stratigraphy of New England, Long Island, 

and adjacent George’s Bank and Gulf of Maine, in Sibrava, 

V., Bowen, D.Q., and Richmond, G.M., eds., Quaternary 

glaciations in the northern hemisphere: Oxford, Pergamon 

Press, p. 39–52.

Stone, J.R., and Dickerman, D.C., 2002, Glacial geology 

and aquifer characteristics of the Big River area, central 

Rhode Island: U.S. Geological Survey Water-Resources 

Investigations Report 01–4169, 12 p.

Wilmott, C.J., 1977, WATBUG–A fortran IV algorithm for 

calculating the climatic water budget: Climatology, v. 30, 

p. 2–4.

Zarriello, P.J., and Bent, G.C., 2004, A precipitation-runoff 

model for the analysis of the effects of water withdrawals 

and land-use change on streamflow in the Usquepaug–

Queen River Basin, Rhode Island: U.S. Geological Survey 

Scientific Investigations Report 2004–5139, 86 p.
This page has been left blank intentionally.
Appendix 1. Methods for Estimating Long-Term 

Hydrologic Conditions

Contents

Methods for Estimating Long-Term Hydrologic Conditions ..................................................................44

Estimates of Long-Term Average Groundwater Level Altitudes in the Big River Area...........46

Estimates of Long-Term Average Streamflows in the Big River Area .......................................47

References Cited..........................................................................................................................................53

Figures

1–1. Example MOVE.1 regression line predicting groundwater-level altitudes at project 

well WGW305 from groundwater-level altitudes at index well SNW6. Results for 

average-monthly values from 1960 through 2006 also are shown. ....................................45

1–2. Example MOVE.1 regression line predicting streamflows at streamgage 01115800 

Big River at Route 3 near Nooseneck, Rhode Island, and from streamflows at 

streamgage 01118000 Wood River at Hope Valley, R.I. Results for monthly-average 

values from 1960 through 2006 also are shown.....................................................................46

1–3. Boxplot showing long-term variations in annual-average and monthly-average 

groundwater-level altitudes in long-term index well SNW 6 from 1960 through 2006....50

1–4. Boxplot showing long-term variations in annual-average and monthly-average 

streamflows at streamgage 01118000 Wood River at Hope Valley, Rhode Island, 

from 1960 through 2006. .............................................................................................................52

Tables

1–1. Correlation table between groundwater-level altitudes measured at U.S. Geological 

Survey long-term network wells, monitoring wells in the Big River Management 

Area, and pond levels recorded at Capwell Mill Pond.........................................................47

1–2. MOVE.1 Regression statistics for monitoring wells in the Big River Management 

Area and Capwell Mill Pond developed using U.S. Geological Survey long-term 

network well data. ......................................................................................................................48

1–3. Average-monthly groundwater-level altitudes for U.S. Geological Survey longterm network wells from 1960 through 2006 and MOVE.1 regression estimates of 

groundwater-level altitudes for monitoring wells and Capwell Mill Pond in the Big 

River Management Area. ..........................................................................................................49

1–4. MOVE.1 regression statistics for short-term streamgages and partial-record 

stations in the Big River Management Area developed using streamflow data from 

the 1960–2009 period at U.S. Geological Survey streamgage 01118000 the Wood River 

at Hope Valley, Rhode Island. ...................................................................................................51
44 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Methods for Estimating Long-Term 

Hydrologic Conditions

Long-term estimates of hydrologic conditions are needed 

to put short-term study results into a larger hydrologic context 

and to provide data for calibration of hydrologic simulation 

models. If no other data are available, it may take a decade 

or more to collect the data necessary to begin to represent 

hydrologic variability at a site of interest. However, long-term 

index data can be used with short-term data from the site of 

interest to estimate long-term values for that site. The U.S. 

Geological Survey, in cooperation with other State and Federal 

agencies, maintains an extensive network of streamgages 

and water-level monitoring wells. Data from this network 

can be used to estimate hydrologic conditions at a site of 

interest. There are several methods that are commonly used 

to estimate long-term hydrologic statistics with limited data; 

the maintenance of varance type 1 (MOVE.1) regression 

method was selected for this study (Hirsch, 1982; Hirsch and 

Gilroy, 1984; Ries and Friesz, 2000; Helsel and Hirsch, 2002; 

Granato, 2009).

The MOVE.1 regression method (also known as the line 

of organic correlation) is used to develop long-term data or 

statistics for a site of interest. Short-term data collected over 

a range of hydrologic conditions at the site of interest is used 

with concurrent data collected at one or more long-term index 

sites to develop one or more regression equations (Hirsch, 

1982; Hirsch and Gilroy, 1984; Helsel and Hirsch, 2002; 

Granato, 2009). The fundamental regression equation is

, (1)

where

i is the index value for a given measurement;

Ypi is predicted streamflow value for the ith 

measurement at the short-term-record site; 

Xi is the streamflow value for the ith 

measurement at the long-term-record site; 

m is the regression-line slope;

b is the regression-line intercept; and.

ei is the difference (or error) between the 

regression-line estimate (Ypi) and 

the measured value (Yi

) for the ith 

measurement.

The slope (m) of the MOVE.1 regression line is 

calculated as the product of the sign of the correlation 

coefficient (r) and the ratio of the standard deviation of the Y

values (Sy

) to the standard deviation of the concurrent X values 

(Sx

), and is expressed mathematically as

, (2)

Unlike ordinary least squares regression, the MOVE.1 

approach preserves the variance of the predicted Y population 

because the sign of the correlation coefficient is used rather 

than the magnitude of the correlation coefficient (Hirsch, 

1982; Hirsch and Gilroy, 1984; Helsel and Hirsch, 2002; 

Granato, 2009).

The intercept (b) of the MOVE.1 regression line is 

expressed mathematically as

, (3)

where 

is the average of concurrent values measured 

at the index site; and

is the average of concurrent values measured 

at the site of interest.

As such, the intercept is calculated so that the line with 

slope m passes through a point with Xi

 and Yi coordinates 

that equal the mean of the X and Y populations, respectively 

(Helsel and Hirsch, 2002).

Once the regression equation is formulated, the quality 

of the fit can be evaluated using residual error statistics. The 

residual error (or uncertainty) in the predicted Ypi value for 

each X,Y pair is expressed mathematically as

, (4)

Statistics of the residuals can be used to determine the 

goodness of fit and to estimate prediction-interval uncertainties 

(Hirsch, 1982; Hirsch and Gilroy, 1984).

Figure 1–1 is an example of a MOVE.1 regression 

line calculated using measured groundwater-level-altitude 

data in two wells. Concurrent monthly groundwater-levelaltitude measurements are paired and are used to estimate the 

coefficients of the regression line. In this case, 24 concurrent 

monthly groundwater measurements from USGS network 

well SNW6 and Big River Management Area (BRMA) 

well RI–WGW 305 were used to define the MOVE.1 

regression line.

Once the regression line is established, it can be used 

to estimate groundwater-level altitudes in the BRMA from 

altitudes in the index well. For example, figure 1–1 shows 

estimates of long-term average-monthly groundwater-level 

altitudes in well WGW305 that are estimated using statistics 

from USGS network well SNW6. These values fall on the line 

because the MOVE.1 regression estimate is the most probable 

value of the corresponding value for well WGW305
Methods for Estimating Long-Term Hydrologic Conditions 45

Groundwater-level altitude at well SNW6, in feet above NGVD 29

98 99 100 101 102 103

Groundwater-level altitude at well WGW305, in feet above NGVD 29

254

255

256

257

258

259

260

261

262

263

Equation: WGW305 = 131.35 + 1.26 SNW6 

MOVE.1 regression line

95-percent prediction-interval limits

Concurrent groundwater-level-altitude data

Monthly average water-table altitude

 estimates, from 1960 through 2008

EXPLANATION

Figure 1–1. Example MOVE.1 regression line predicting groundwater-level 

altitudes at project well WGW305 from groundwater-level altitudes at index well 

SNW6. Results for average-monthly values from 1960 through 2006 also are shown.

Random variations in paired measurements used to 

construct the regression line are evident by the considerable 

scatter around the regression line on the figure. The regression 

line provides the expected value, but actual values may 

vary. The 95-percent prediction intervals on figure 1–1 are 

calculated using the residual statistics from available data. 

It is inferred that there is a 95-percent chance that the actual 

long-term average-monthly groundwater-level altitude in well 

WGW305 would be within the region between the confidence 

intervals. For example, the lowest long-term average-monthly 

groundwater-level altitude in well SNW6 for the period 

1960–2006 is 98.52 feet above NGVD 29. The corresponding 

MOVE.1 estimate for well WGW305 is 255.49 feet above 

NGVD 29, and there is a 95-percent chance that the actual 

value (if it were available) would be in the range 254.24 to 

256.74 ft above NGVD 29.

MOVE.1 regression analysis of streamflow data uses 

the common (base 10) logarithms of streamflow because 

logarithmic transformation commonly helps linearize relations 

between streamflows collected at different stations and 

improves the structure of residuals (Ries and Friesz, 2000; 

Helsel and Hirsch, 2002; Granato and others, 2003; Granato, 

2009). Figure 1–2 is an example of a MOVE.1 regression 

line calculated using the logarithms of streamflow data 

measured at streamgages on the Wood River and the Big 

River. As with the previous example, figure 1–2 shows the 

data, the regression line, the 95-percent confidence limits, 

and the average-monthly estimates from 1960 through 2006. 

There are two far outliers (one on January 17, 1995, and the 

other on December 12, 2008) that are beyond the 95-percent 

confidence limits of the data (fig. 1–2). These values, which 

are stormflow measurements, occur because of differences 

between the instantaneous measurements at the Big River 

streamgage and the mean-daily streamflows reported for the 

Wood River streamgage. These two data points, however, were 

not removed from the data used to formulate the regression 

model because they reflect measurement conditions and do not 

inordinately affect the estimate of the slope or the intercept as 

indicated by the good fit to the rest of the data in figure 1–2.
46 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Streamflow at streamgage 01118000

Wood River at Hope Valley, Rhode Island, in cubic feet per second

10 100 1,000 2,000

1

10

100

1,000

Streamflow at streamgage 01115800 Big River at Route 3

near Nooseneck, Rhode Island, in cubic feet per second

01/17/1995

12/12/2008

Y = 0.23325 * X1.049

MOVE.1 estimate

95-percent prediction-interval limits

Concurrent streamflows on the Wood River and Big River

Average monthly values, from 1960 through 2008

EXPLANATION

Figure 1–2. Example MOVE.1 regression line predicting streamflows at streamgage 

01115800 Big River at Route 3 near Nooseneck, Rhode Island, and from streamflows at 

streamgage 01118000 Wood River at Hope Valley, R.I. Results for monthly-average values 

from 1960 through 2006 also are shown.

Estimates of Long-Term Average GroundwaterLevel Altitudes in the Big River Area

MOVE.1 was used to estimate average monthly 

groundwater-level altitudes for 12 wells and 1 pond (Capwell 

Mill Pond) in the BRMA for the period 1960 through 2006 

Index wells COW411, EXW6, and SNW6 were evaluated 

for use. Correlations between groundwater-level-altitude 

measurements in these wells and in wells in the BRMA are 

relatively strong. Correlations are greater than 0.61 for all 

well pairs and greater than 0.79 for the selected (best fit) 

well pairs (table 1–1). Well SNW6 was the best fit for nine 

wells and well EXW6 was the best fit for three wells and 

for Capwell Mill Pond. As such, these two index wells were 

selected to represent long-term conditions in the BRMA. 

The highlighted MOVE.1 regression equations in table 1–2 

were used to estimate the long-term average-annual and 

average-monthly groundwater-level altitudes in feet above 

NVGD 1929 for the period 1960–2006, which are listed 

in table 1–3. The median 95-percent prediction intervals 

in table 1–2 provide an uncertainty range for the estimated 

groundwater-level altitudes in table 1–3. For example, the 

estimated annual-average groundwater-level altitude during 

1960–2006 at well WGW285 (264.48 ft) was estimated from 

the estimated annual-average value for EXW6 during the 

same period (127.09 ft) using equation 2 in table 1–2. The 

95-percent prediction interval for the MOVE.1 regression 

equation is about 0.82 ft; therefore, it is expected, based on 

analysis of available data, that there is a 95-percent chance 

that the actual annual-average groundwater-level altitude 

at well WGW285 is in the range from 263.66 to 265.30 ft. 

The magnitude of uncertainty represented in the MOVE.1 

prediction interval is similar to variations in the long-term 

record. Data from long-term index wells indicate substantial 

variations in the average-annual and monthly groundwaterlevel altitudes during the period of record. At index well 

SNW6, the total range in individual measurements is about 

7 ft, the range of measurements within individual months is 

about 5 ft, the range in annual-average values is about 3 ft, and 

the range in average-monthly values is about 2.5 ft (fig. 1–3). 

Groundwater-level altitude variations at other locations may 

be different from the ones shown because the variations 

depend on the hydrogeology at the screened interval of the 

observation well and the topographic setting, which indicates 

the position of the well in the hydrologic system (Frimpter, 

1981; Socolow and others, 1994; Granato and others, 2003).
Methods for Estimating Long-Term Hydrologic Conditions 47

Table 1–1. Correlation table between groundwater-level altitudes measured at 

U.S. Geological Survey (USGS) long-term network wells, monitoring wells in the 

Big River Management Area, and pond levels recorded at Capwell Mill Pond.

[Table shows Pearson’s r correlation coefficients, which are unitless; the shaded correlation coefficients were selected as the best alternative for estimating water levels in the associated well in 

the Big River Management Area]

Big River 

wells or pond

Correleations coefficients (unitless) with data from 

USGS long-term network wells

COW411 EXW6 SNW6

WGW285 0.781 0.806 0.752

WGW286 0.801 0.702 0.888

WGW87 0.887 0.793 0.932

WGW290 0.883 0.775 0.917

WGW291 0.934 0.916 0.935

WGW293 0.907 0.892 0.912

WGW294 0.702 0.809 0.707

WGW303 0.737 0.612 0.797

WGW304 0.859 0.784 0.935

WGW305 0.912 0.827 0.949

WGW313 0.901 0.841 0.915

WGW320 0.885 0.929 0.895

Capwell Mill Pond 0.913 0.939 0.913

Estimates of Long-Term Average Streamflows in 

the Big River Management Area

MOVE.1 also was used to estimate long-term averagemonthly streamflow values from 1960 through 2006. Data 

from the long-term streamgage 01118000 on the Wood River 

at Hope Valley was selected to represent long-term conditions 

in the BRMA because correlations among streamflow 

measurements in these areas are very strong (greater than 

0.91; table 1–4). This streamgage has a long, uninterrupted 

period of record from 1960 through 2006 and water use in the 

Wood River Basin is a small percentage of average-monthly 

streamflows (Zarriello, 2011).

The MOVE.1 regression equations in table 1–4 were 

developed using concurrent flow measurements from the 

1960–2009 period to increase the amount of data available 

to develop the equations. However, statistics for streamflows 

measured from 1960 through 2006 at streamgage 01118000 

were used to estimate the long-term average-annual and 

average-monthly streamflow values in cubic feet per second at 

selected locations in the Big River watershed for the modeling 

period (table 1–4). For example, the estimated annual-average 

streamflow during 1960–2009 in the Big River at Route 3 is 

estimated to be about 48.4 ft3/s (about 2.15 ft3/s/mi2

) using the 

equation in table 1–4. The logarithmic 95-percent prediction 

interval for this MOVE.1 regression equation is 0.232, 

which would yield an upper 95-percent prediction interval 

value of about 1.72 times the MOVE.1 estimate and a lower 

95-percent prediction interval value of about 0.59 times the 

MOVE.1 estimate. Therefore, based on analysis of available 

data, it is expected that there is a 95-percent chance that the 

actual annual-average flow rate in the Big River at Route 3 

is in the range from 28.3 (about 1.26 ft3/s/mi2

) to 82.6 ft3/s 

(about 3.67 ft3

/s/mi2). In comparison, the annual-average 

streamflows at streamgage 01118000 the Wood River at Hope 

Valley ranged from 1.18 to 3.51 ft3

/s/mi2 with an average value 

of 2.2 ft3

/s/mi2 from 1960 through 2006 (fig. 1–4).
48 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Table 1–2. MOVE.1 regression statistics for monitoring wells in the Big River Management Area and Capwell Mill Pond developed 

using U.S. Geological Survey long-term network well data.

[MOVE.1, maintenance of variance type 1; RMSE, root mean square error; PI, 95-percent prediction interval width (median value); the shaded statistics were 

estimated using data from well EXW6, whereas the nonshaded statistics were estimated using data from well SNW6]

Big River

wells or ponds

Network 

well

Correlation

coefficient

MOVE.1 

Slope Intercept RMSE PI

WGW285 COW411 0.781 0.54701 134.05 0.18 0.869

WGW285 EXW6 0.806 0.59517 188.84 0.16 0.819

WGW285 SNW6 0.752 0.46264 218.21 0.204 0.922

WGW286 COW411 0.801 1.10705 22.11 0.642 1.634

WGW286 EXW6 0.702 1.17919 136.13 0.963 2.005

WGW286 SNW6 0.888 0.95714 190.38 0.363 1.226

WGW287 COW411 0.887 2.11561 -231.34 1.459 2.477

WGW287 EXW6 0.793 2.345 -24.95 2.663 3.35

WGW287 SNW6 0.932 1.78672 94.41 0.879 1.916

WGW290 COW411 0.883 1.16583 -15.13 0.445 1.365

WGW290 EXW6 0.775 1.2786 100.33 0.859 1.896

WGW290 SNW6 0.917 0.97865 164.96 0.317 1.151

WGW291 COW411 0.934 0.61196 108.01 0.071 0.545

WGW291 EXW6 0.916 0.66586 169.29 0.09 0.615

WGW291 SNW6 0.935 0.51632 202.29 0.07 0.541

WGW293 COW411 0.907 0.6338 101.05 0.102 0.654

WGW293 EXW6 0.892 0.6804 165.67 0.118 0.705

WGW293 SNW6 0.912 0.54203 197.97 0.097 0.636

WGW294 COW411 0.702 0.76358 102.87 0.506 1.458

WGW294 EXW6 0.809 0.82585 179.96 0.324 1.17

WGW294 SNW6 0.707 0.64425 220.51 0.497 1.441

WGW303 COW411 0.737 1.56851 -115.87 1.799 2.746

WGW303 EXW6 0.612 1.6951 42.69 2.656 3.341

WGW303 SNW6 0.797 1.32477 125.63 1.388 2.404

WGW304 COW411 0.859 2.20168 -271.76 1.815 2.75

WGW304 EXW6 0.784 2.3518 -45.82 2.769 3.402

WGW304 SNW6 0.935 1.87582 65.59 0.832 1.857

WGW305 COW411 0.912 1.48857 -97.57 0.604 1.605

WGW305 EXW6 0.827 1.71176 39.68 1.185 2.242

WGW305 SNW6 0.949 1.26025 131.35 0.352 1.222

WGW313 COW411 0.901 0.97947 20.06 0.3 1.134

WGW313 EXW6 0.841 1.10216 113.5 0.482 1.434

WGW313 SNW6 0.915 0.8205 171.57 0.258 1.051

WGW320 COW411 0.885 1.73911 -150.28 1.124 2.214

WGW320 EXW6 0.929 2.07801 0.47 0.69 1.737

WGW320 SNW6 0.895 1.43175 121.29 1.023 2.111

Capwell Mill Pond COW411 0.913 0.12086 227.22 0.005 0.145

Capwell Mill Pond EXW6 0.939 0.14705 237.37 0.003 0.122

Capwell Mill Pond SNW6 0.913 0.10068 245.98 0.005 0.146
Methods for Estimating Long-Term Hydrologic Conditions 49

Table 1–3. Average monthly groundwater-level altitudes for U.S. Geological Survey long-term network wells during 1960 through 2006 and MOVE.1 regression estimates of groundwater-level altitudes for monitoring wells and Capwell Mill Pond in the Big River Management Area.[Altitude, in feet above National Geodetic Vertical Datum of 1929; the shaded equations were selected as the best alternative for estimating water levels in the associated well in the Big River Management Area]

Location Annual

average January February March April May June July August September October November December

Calculated average monthly water-table altitude 

EXW6 127.09 127.57 127.70 128.11 127.96 127.59 127.07 126.46 126.19 126.12 126.28 126.83 127.33

SNW6 99.71 99.98 100.32 100.82 101.00 100.49 100.02 99.37 98.93 98.65 98.52 98.84 99.43

Estimated average monthly water-table altitude 

WGW285 264.48 264.77 264.84 265.09 265.00 264.78 264.47 264.11 263.94 263.90 264.00 264.33 264.62

WGW286 285.82 286.07 286.40 286.88 287.05 286.56 286.11 285.49 285.07 284.80 284.68 284.98 285.55

WGW287 272.56 273.05 273.65 274.55 274.87 273.96 273.12 271.96 271.17 270.67 270.44 271.01 272.06

WGW290 262.54 262.81 263.14 263.63 263.80 263.30 262.84 262.21 261.78 261.50 261.38 261.69 262.27

WGW291 253.77 253.91 254.09 254.35 254.44 254.17 253.93 253.60 253.37 253.22 253.16 253.32 253.63

WGW293 252.02 252.16 252.35 252.62 252.72 252.44 252.18 251.83 251.59 251.44 251.37 251.54 251.86

WGW294 284.92 285.31 285.42 285.76 285.64 285.33 284.90 284.40 284.17 284.12 284.25 284.70 285.12

WGW303 257.72 258.08 258.53 259.19 259.43 258.76 258.13 257.27 256.69 256.32 256.15 256.57 257.35

WGW304 252.63 253.13 253.77 254.71 255.05 254.09 253.21 251.99 251.16 250.64 250.40 251.00 252.10

WGW305 257.01 257.35 257.78 258.41 258.64 257.99 257.40 256.58 256.03 255.67 255.51 255.91 256.66

WGW313 253.38 253.60 253.88 254.29 254.44 254.02 253.64 253.10 252.74 252.51 252.41 252.67 253.15

WGW320 264.56 265.56 265.83 266.68 266.37 265.60 264.52 263.26 262.69 262.55 262.88 264.02 265.06

Capwell Mill Pond 256.06 256.13 256.15 256.21 256.19 256.13 256.06 255.97 255.93 255.92 255.94 256.02 256.09
50 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

Jan. Feb. Mar. Apr. May June

Time

Annual July Aug. Sept. Oct. Nov. Dec.

96

97

98

99

100

101

102

103

104

Groundwater-level altitudes, in feet above National Geodetic Vertical Datum of 1929

Maximum

Minimum

1st Percentile

5th Percentile

25th Percentile

75th Percentile

95th Percentile

99th Percentile

Average

Median

EXPLANATION

Figure 1–3. Boxplot showing long-term variations in annual-average and monthly-average groundwater-level altitudes in 

long-term index well SNW 6 from 1960 through 2006.
Methods for Estimating Long-Term Hydrologic Conditions 51

Table 1–4. MOVE.1 regression statistics for short-term streamgages and partial-record stations in the Big River Management Area developed using streamflow data from the 1960 through 2009 period at U.S. Geological Survey streamgage 01118000 the Wood River at Hope Valley, Rhode Island.[MOVE.1 maintenance of variance type 1; BCF, Bias correction factor; LRMSE logarithmic (base 10) root mean square error; LPI, logarithmic (base 10) 95-percent prediction interval width (median value); the regression equations for streamflow were developed using the logarithms of data. The intercept values in the table have been retransformed. Thus, the streamflow at the site of interest is equal to the streamflow at the index site raised to the power of the slope then multiplied by the intercept]

Station number Station name

Period of record during 1960 through 2009 MOVE.1 regression statistics

Years Number of daily flows Correlation coefficient Slope Intercept BCF LRMSE LPI

Short-term streamgages

01115630 Nooseneck River at Nooseneck, R.I. 1963–81; 2007–09 7,175 0.958 1.0685 0.08259 1.041 0.117 0.234

01115670 Congdon River near Nooseneck, R.I. 2006–09 823 0.951 1.0121 0.04819 1.044 0.118 0.241

01115770 Carr River near Nooseneck, R.I. 1964–79; 2006–09 6,674 0.962 1.1139 0.04566 1.037 0.115 0.231

Station number Station name

Years Number of measurements Correlation coefficient Slope Intercept BCF LRMSE LPI

Partial-record sites

01115700 Congdon River Tributary near Nooseneck, R.I. 1995–98 31 0.919 0.6983 0.03416 1.035 0.12 0.28

01115800 Big River at Route 3 near Nooseneck, R.I. 1992–98; 2006–09 90 0.974 1.0491 0.23325 1.032 0.108 0.232

01115830 Bear Brook near Coventry, R.I. 1961–63; 1996–98 38 0.95 1.3409 0.00725 1.062 0.159 0.367

01115833 Big River at Harkney Hill Road near Coventry Center 2005–09 42 0.943 0.9328 0.57535 1.054 0.142 0.306
52 Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Central Rhode Island

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

Time

Streamflow at streamgage 01118000 Wood River at Hope Valley, Rhode Island,

in cubic feet per second per square mile

0.1

1

10

Maximum

Minimum

1st Percentile

5th Percentile

25th Percentile

75th Percentile

95th Percentile

99th Percentile

Average

Median

EXPLANATION

Figure 1–4. Boxplot showing long-term variations in annual-average and monthly-average streamflows at streamgage 01118000 

Wood River at Hope Valley, Rhode Island, from 1960 through 2006.
References Cited 53

References Cited

Frimpter, M.H., 1981, Probable high ground-water levels in 

Massachusetts: U.S. Geological Survey Open-File Report 

80–1205, 22 p.

Granato, G.E., 2009, Streamflow Record Extension Facilitator 

(SREF Version 1.0)—A program for extending and augmenting available streamflow data using long-term streamflow records from hydrologically similar sites, Appendix 

3 in Computer programs for obtaining and analyzing daily 

mean streamflow data from the U.S. Geological Survey 

National Water Information System Web Site: U.S. Geological Survey Open-File Report 2008–1362, 123 p. on CDROM http://pubs.usgs.gov/of/2008/1362/.

Granato, G.E., Barlow, P.M., and Dickerman, D.C., 2003, 

Hydrogeology and simulated effects of ground-water withdrawals in the Big River Area, Rhode Island: U.S. Geological Survey Water-Resources Investigations Report 03–4222, 

76 p.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in 

water resources—Hydrologic analysis and interpretation: 

Techniques of Water-Resources Investigations of the U.S. 

Geological Survey, chap. A3, book 4, 510 p.

Hirsch, R.M., 1982, A comparison of four streamflow record 

extension techniques: Water Resources Research, v. 18, no. 

4, p. 1081–1088.

Hirsch, R.M., and Gilroy, E.J., 1984, Methods of fitting a 

straight line to data—examples in water resources: Water 

Resources Bulletin, v. 20, no. 5, p. 705–711.

Ries, K.G., III, and Friesz, P.J., 2000, Methods for estimating low-flow statistics for Massachusetts streams: U.S. 

Geological Survey Water-Resources Investigations Report 

2000–4135, 81 p.

Socolow, R.S., Frimpter, M.H., Turtora, Michael, and Bell, 

R.W., 1994, A technique for estimating ground-water levels 

at sites in Rhode Island from observation-well data: U.S. 

Geological Survey Water-Resources Investigations Report 

94–4138, 43 p.

Zarriello, P.J., 2011, Simulation of water-use and land-use 

changes on streamflow with a precipitation-runoff model 

(HSPF), part 2 of Bent, G.C., Zarriello, P.J., Granato, G.E., 

Masterson, J.P., Walter, D.A., Waite, A.M., and Church, 

P.E., Simulated effects of water withdrawals and land-use 

changes on streamflows and groundwater levels in the 

Pawcatuck River Basin, southwestern Rhode Island and 

southeastern Connecticut: U.S. Geological Survey Scientific 

Investigations Report 2009–5127, 254 p.
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Masterson and Granato—Simulation of Groundwater and Surface-Water Interactions in the Big River Management Area, Rhode Island—SIR 2012–5077