Conjunctive-management models were developed for 

selected areas in the Pawcatuck River Basin to evaluate 

relations between streamflow-depletion criteria and waterwithdrawal volumes for several different withdrawal-well 

networks. The term “conjunctive-management model” 

commonly is used in the hydrologic literature to refer to 

the combined use of numerical simulation and optimization 

techniques to evaluate alternative strategies for balancing 

water withdrawals with aquatic-habitat protection goals 

(Barlow and Dickerman 2001a,b; Granato and Barlow, 2005). 

A conjunctive-management model consists of a mathematical 

formulation (statement) of the groundwater-development 

goals for the model area and a set of constraints that limit 

those goals. This part of the report describes information 

provided by the models that can be used for planning purposes 

by water-resource managers. The details of the mathematical 

formulation of the conjunctive-management models and the 

response-matrix technique used to solve the linear models are 

described in Appendix Part 4.

The conjunctive-management models described in this 

report were based on quantitative descriptions of groundwater/

surface-water interactions and were used to maximize water 

withdrawals within a given set of constraints. Simulations 

made with the transient numerical groundwater (MODFLOW) 

models developed for the eastern Pawcatuck and lower Wood 

River groundwater-model areas were used to quantify relations 

between withdrawals and associated streamflow depletions at 

one or more sites. Allowable streamflow depletions calculated 

from streamflow statistics were the primary constraints on the 

solution of the conjunctive-management models. The results 

of a simulation made with the basinwide HSPF model without 

any withdrawals during the 1960–2004 simulation period were 

used to formulate streamflow constraints. Water-use patterns 

were also used to constrain management-model results. The 

water-use patterns used in the formulation of the conjunctivemanagement models were estimated from statistical analyses 

of water-use data.

The surface-water (HSPF) and groundwater 

(MODFLOW) models for these conjunctive-management 

model areas were developed, calibrated, and tested on the 

basis of local information. The models, however, are idealized 

mathematical representations of complex and dynamic hydrogeological systems. The conjunctive-management models are 

subject to some of the same uncertainties and limitations of 

the HSPF and MODFLOW models because the conjunctivemanagement model inputs were based on the results of the 

surface-water and groundwater modeling efforts. Furthermore, 

the 1960–2004 study period includes a substantial amount of 

variability in climatic conditions affecting streamflow, including the 1963–1967 drought of record for the New England 

area (Walker and Lautzenheiser, 1991). Walker and 

Lautzenheiser (1991) indicate that the total precipitation 

(25.4 in.) measured in Providence, R.I., in 1965 was the lowest precipitation measured in the last 185 years. Although the 

1960–2004 period included this historical extreme, this period 

may or may not fully reflect future conditions; thus, risks for 

extreme low-flow events indicated by the duration curves can 

be regarded as planning-level estimates. 

Information from the results of the conjunctivemanagement-modeling effort can be used as a generalized 

water-resource planning tool to help balance withdrawals 

needed for water supply with aquatic-habitat protection goals. 

The models developed and tested for the eastern Pawcatuck 

River conjunctive-management-model (EPRCMM) area 

and lower Wood River conjunctive-management model 

(LWRCMM) area represent different combinations of network 

design, withdrawal patterns, withdrawal rates, and streamflowdepletion criteria. With unlimited time and resources, an 

almost infinite number of combinations and permutations of 

these factors could be tested to evaluate different conditions. 

The purpose of this analysis, however, is to provide waterresource managers with an understanding of the hydrologic 

concepts necessary to make informed decisions about the 

current and future status of water withdrawals and streamflow 

depletions in selected areas of the Pawcatuck River Basin. 

Streamflow-Response Coefficients

Streamflow-response coefficients are relations between 

groundwater withdrawals and streamflow depletions at 

selected surface-water constraint sites. A one-month unit 

withdrawal is simulated for each well to calculate the response 

coefficients caused by the withdrawal (Appendix Part 4). 

Each response coefficient is equal to the fraction of the unit 

withdrawal that is evident as a streamflow depletion in each 

month after the unit withdrawal. The sum of the response 

coefficients will be about one if the entire water withdrawal 

is accounted for in the stream (Barlow and Dickerman 

Part 4. Conjunctive-Management Models as Tools for 

Water-Resources Planning

By Gregory E. Granato and Donald A. Walter
86 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

2001a,b; Granato and Barlow, 2005). The areas of interest 

in both conjunctive-management model areas are bounded 

on three sides by different streams (figs. 4–1, 4–2). The 

response coefficients for each stream indicate the fractions 

of withdrawals that appear as streamflow depletions in each 

of the bounding streams. In each management-model area, a 

streamflow-constraint site was selected along the Pawcatuck 

River near the outlet of the active groundwater-model area 

(PAWCD in figure 4–1 and PAWC4 in figure 4–2) to ensure 

that response coefficients sum to about 1.0 within each 

management-model area. The response coefficients are used 

within the conjunctive-management model to maximize 

withdrawals while meeting streamflow-depletion criteria. 

However, examination of the response coefficients also 

provides useful water-resources planning information. 

The groundwater models developed for each area were 

modified to calculate the response coefficients for each well 

by use of the dynamic-equilibrium technique (Barlow and 

Dickerman 2001a,b; Granato and Barlow, 2005) described in 

Appendix Part 4. Nineteen proposed and existing groundwater 

withdrawal sites in the EPRCMM area and nine proposed 

and existing groundwater withdrawal sites in the LWRCMM 

area were simulated with the groundwater models (table 

4–1). The groundwater models can be used to simulate the 

effect of withdrawals throughout the model area. However, 

three sites in the EPRCMM area (fig. 4–1) and four sites 

in the LWRCMM area (fig. 4–2) were selected to analyze 

potential effects of withdrawals on streamflow depletions 

(table 4–2). These sites are at or near the HSPF model nodes 

in each conjunctive-management model area. A total of 224 

groundwater-model runs were made to calculate response 

coefficients for each groundwater-withdrawal site at four 

withdrawal rates (0.1, 0.5, 1.0, and 2.0 Mgal/d) in January 

and June to ensure that response coefficients would be 

representative of different hydrological conditions.

Examination of the streamflow-response coefficients 

provides insights about the possible effects of withdrawals 

from potential well sites. Graphs of the response coefficients 

for groundwater-withdrawal sites in these management-model 

areas indicate that the response times between withdrawals 

and associated streamflow depletions are on the order of 

several months to a year (figs. 4–3A, B). Table 4–1 provides 

a list of figures in Appendix Part 4 that document response 

coefficients for each groundwater-withdrawal site in each 

management-model area. It was necessary to include one 

surface-water withdrawal site in the EPRCMM area and 

three surface-water withdrawal sites in the LWRCMM area 

to account for management of surface-water withdrawals. 

Surface-water-withdrawal sites are listed with a response 

coefficient of 1.0 because the entire withdrawal occurs 

instantly as a streamflow depletion as water is pumped from 

the stream. Limitations on the use of monthly withdrawal rates 

for irrigation supplies from surface-water-withdrawal sites are 

discussed in Appendix Part 4. 

Response-coefficient graphs for the hypothetical well 

sites in the EPRCMM area (fig. 4–3A) illustrate the effect 

of well distance on the temporal distribution of streamflow 

depletion. For example, withdrawals from hypothetical 

well RIW–385 along the banks of Beaver River (fig. 4–1) 

have a substantial effect on streamflow in the Beaver River, 

but do not cause streamflow depletion in the UsquepaugQueen River. Response coefficients for the Pawcatuck River 

(PAWCD) represent the sum of the depletions in the tributary 

rivers; and occur on the same time scale because depletions 

from tributaries appear as depletions at downstream sites 

within a few hours or days. The initial response coefficient 

for this well is 0.93, indicating that about 93 percent of the 

streamflow depletion occurs in the Beaver River during the 

first month after a groundwater withdrawal is made from this 

hypothetical well. The response-coefficient graph indicates 

that depletions decrease exponentially to zero during the 

4 months after a groundwater withdrawal is made. The rate of 

decrease is greater for this well than for depletions from 

wells farther from the stream, but slower than for a surfacewater withdrawal. 

Hypothetical well PR–AB3B is farther from the Beaver 

River than hypothetical well RIW–385 (fig. 4–1), and the 

response coefficients for hypothetical well PR–AB3B indicate a slower streamflow response to withdrawals than for 

hypothetical well RIW–385. The initial response coefficient 

for well PR–AB3B is 0.43, indicating that about 43 percent 

of the streamflow depletion occurs in the Beaver River during 

the first month after a groundwater withdrawal is made from 

this hypothetical well (fig. 4–3A). Depletions caused by the 

withdrawal from this hypothetical well decrease exponentially during the 12 months after a groundwater withdrawal is 

made. Withdrawals from this well do not cause depletions in 

the Usquepaug-Queen River because of the proximity of this 

hypothetical well site to the Beaver River. 

Hypothetical well PR–AB4A is distant from and roughly 

midway between the Beaver and the Usquepaug-Queen Rivers 

(fig. 4–1). Accordingly, the response coefficients for this well 

are approximately equal for each month at the mouth of the 

Beaver (BEAVM) and Usquepaug-Queen River (QUEENM). 

The initial response coefficients for this well are about 0.08, 

indicating that about 8 percent of the streamflow depletion 

from this hypothetical well occurs from each river during 

the first month after a groundwater withdrawal is made 

(fig. 4–3A). The peak response (about 0.13) occurs in the 

second month, and depletions continue for about 11 more 

months, after a groundwater withdrawal is made. About 8, 21, 

and 31 percent of the total streamflow depletion have been 

made at each constraint site by the ends of the first, second, 

and third months after a groundwater withdrawal, respectively. 

Response coefficients for the Pawcatuck River constraint 

site (PAWCD) represent the total monthly depletion from 

hypothetical well PR–AB4A because they are the summation 

of depletions in the tributaries upstream of PAWCD. About 

16, 42, and 62 percent of the total streamflow depletions at this 

constraint site have been made by the ends of the first, second, 

and third months after a groundwater withdrawal, respectively 

(fig. 4–3A). 
Streamflow-Response Coefficients 87

PAWCD

QUEENM

BEAVM

RIW-385

RIW-336A

PR-AB8A

PR-AUQ9A

PR-AUQ11A

PR-AUQ8A

PR-AB5A

PR-AB3B PR-AB2B

PR-AB4A

PR-AB3A

PR-AB2A

PR-AB1A

PR-GB1A

PR-AUQ10B

PR-AUQ10A

PR-GUQ2AB

PR-AUQ7A

+$AUQ6A

PR-AUQ10C

71°38' 71°36'

41°28'

41°30'

Surface-water withdrawals

Groundwater withdrawals

EXPLANATION

Proposed irrigation-well 

location and identifier

Proposed irrigation-pond

location and identifier

Proposed production-well 

location and identifier

Stream-withdrawal location

and identifier

PR-AUQ8A

PR-AUQ8A

RIW-385

AUQ6A

Streamflow constraint

Stream cells

Streamflow-constraint 

site location and identifier

Streams simulated

in model 

QUEENM

Pawcatuck River

Beaver River

Usquepaug-Queen River

0

1 KILOMETER

1 MILE

0

0.5

0.5

Base from U.S. Geological Survey digital data, 1:24,000

North American datum of 1983

Rhode Island state plane projection

Figure 4–1. The eastern Pawcatuck River conjunctive-management model (EPRCMM) area with three streamflow-constraint 

sites (defined in table 4–2) and 20 existing or potential water-withdrawal sites (defined in table 4–1) in the Pawcatuck River 

Basin, southwestern Rhode Island.
88 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

Pawcatuck River

Wood River

Meadow Brook

Wood River

Cedar Swamp Brook

Model 

Boundary

Model 

Boundary

Pawcatuck River

71°44' 71°42'

41°26'

41°28'

GW4C

GW4B

GW4A

GW3A

GW1A

PR-AW1A

RIW-458

RIW-458B

RIW-458A

GW2A

AP1A

AW2A

MEAD2

PAWC4

WOOD6

WOOD5

Surface-water withdrawals

Groundwater withdrawals

EXPLANATION

Proposed irrigation-well 

location and identifier

Proposed irrigation-pond

location and identifier

Proposed production-well

location and identifier

Stream-withdrawal location

and identifier

PR-AW1A

GW1A

RIW-458

GW2A

Streamflow constraint

Streamflow-constraint site

location and identifier

WOOD6

AW1A

0

1 KILOMETER

1 MILE

0

0.5

0.5

Base from U.S. Geological Survey digital data, 1:24,000

North American datum of 1983

Rhode Island state plane projection

Stream cells

Streams simulated

in model 

Figure 4–2. The lower Wood River conjunctive-management model (LWRCMM) area with four streamflowconstraint sites (defined in table 4–2) and 12 existing or potential water-withdrawal sites (defined in table 4–1) in the 

Pawcatuck River Basin, southwestern Rhode Island.
Streamflow-Response Coefficients 89

Table 4–1. Characteristics of existing and potential water-withdrawal sites in the eastern Pawcatuck and lower Wood River 

conjunctive-management model areas, Pawcatuck River Basin, southwestern Rhode Island.

[ID, identifier. Index: Conjunctive-management model index number. Site type: GW, groundwater; GW–P, groundwater-pond; SW, surface water. Water 

use: IT, irrigation turf; IG, irrigation golf; MS, potential municipal supply; IV, irrigation vegetable. Response coefficient information: the number of the 

appendix which shows a graph of the response coefficients for the withdrawal site (response coefficient information equal to 1 indicates a surface-water 

site where streamflow depletion occurs simultaneously with withdrawals)]

Eastern Pawcatuck River conjunctive-management model (EPRCMM) area

Index Site ID

(Site locations shown in figure 4–1) Site type Water use MODFLOW row MODFLOW column

Response coefficient 

information

1 AUQ6A SW IT 166 82 1

2 PR–AUQ8A GW IT 175 91 A4–15

3 PR–AUQ9A GW–P IT 185 80 A4–15

4 PR–AUQ11A GW–P IT 236 74 A4–15

5 PR–AB8A GW–P IT 231 69 A4–15

6 PR–GB1A GW IG 193 48 A4–18

7 RIW–336A GW MS 205 70 A4–18

8 RIW–385 GW MS 239 56 A4–14

9 PR–AUQ7A GW IT 178 88 A4–18

10 PR–AUQ10A GW IT 215 69 A4–17

11 PR–AUQ10B GW IT 221 83 A4–17

12 PR–AUQ10C GW IT 220 76 A4–17

13 PR–AB1A GW IT 207 67 A4–16

14 PR–AB2A GW IT 213 67 A4–16

15 PR–AB2B GW IT 224 68 A4–16

16 PR–AB3A GW IT 216 69 A4–16

17 PR–AB3B GW IT 225 54 A4–14

18 PR–AB4A GW IT 219 69 A4–14

19 PR–AB5A GW IV 231 54 A4–17

20 PR–GUQ2AB GW IG 204 82 A4–18

Lower Wood River conjunctive-management model (LWRCMM) area

Index Site ID

(Site locations shown in figure 4–2) Site type Water use MODFLOW row MODFLOW column

Response coefficient 

information

1 AW2A SW IT 165 138 1

2 AP1A SW IT 196 220 1

3 GW1A GW–P IG 22 111 A4–20

4 GW2A SW IG 80 82 1

5 GW3A GW–P IG 100 138 A4–20

6 GW4A GW IG 183 120 A4–20

7 GW4B GW IG 185 111 A4–21

8 GW4C GW IG 181 91 A4–21

9 RIW–458 GW MS 158 164 A4–19

10 RIW–458A GW MS 162 152 A4–19

11 RIW–458B GW MS 165 141 A4–19

12 PR–AW1A GW IT 129 155 A4–21
90 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning Table 4–2. Characteristics of selected streamflow constraint sites in the eastern Pawcatuck and lower Wood River conjunctive-management model areas, Pawcatuck River Basin, southwestern Rhode Island. [Estimates of the minimum monthly one-day streamflow values without withdrawals are derived from the output of the basinwide surface-water model. ID, identifier; mi2, square miles; *, HSPF subbasin outlets. Site locations for EPRCMM shown in figure 4–1 and site locations for LWRCMM shown in figure 4–2 and described in table A2–4.] Management- model site designation River MOD- FLOW row MOD- FLOW column Drain- age area (mi2

)

Description

Minimum monthly one-day streamflow without withdrawals during 1960–2004, in cubic feet per second 

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

Eastern Pawcatuck River conjunctive-management model (EPRCMM) area

BEAVM Beaver River 261 50 12.47 Model cell at confluence of 

the Beaver and Pawcatuck Rivers.

7.02 9.74 13.93 10.68 9.84 6.18 2.93 2.30 1.99 2.20 2.20 3.14

QUEENM UsquepaugQueen River 240 87 36.57 Model cell at confluence of the Usquepaug-Queen and 

Pawcatuck Rivers.

19.6 26.1 36.8 28.1 26.5 17.0 9.13 7.10 6.09 6.80 7.00 9.03

PAWCD Pawcatuck 

River

261 49 90.91 Model cell downstream of 

the confluence of the Usquepaug-Queen and Pawcatuck Rivers.

56.5 79.1 106 87.1 81.2 54.4 30.3 23.0 19.5 23.7 27.6 34.7

Lower Wood River conjunctive-management model (LWRCMM) area

MEAD2*(RCHRES 48)

Meadow Brook 241 186 7.21 Model cell at confluence of 

the Meadow Brook and the Pawcatuck River.

3.00 4.40 6.50 5.10 5.30 3.40 2.00 1.60 1.40 1.50 1.40 1.70

WOOD5*(RCHRES 63)

Wood River 144 118 85.13 Model cell downstream of the 

confluence of Canonchet Brook and the Wood River.

41.9 55.1 79.5 60.9 58.2 36.3 17.5 12.9 10.8 13.1 12.1 18.6

WOOD6*(RCHRES 65)

Wood River 232 111 88.31 Model cell downstream of the 

confluence of an unnamed tributary and the Wood River.

46.9 62.0 89.3 68.3 65.3 40.9 20.0 14.9 12.6 13.8 13.9 21.1

PAWC4*(RCHRES 50)

Pawcatuck 

River

281 98 204.33 Model cell on the Pawcatuck 

River at the outlet of the MODFLOW model below the confluence with the Wood River.

118 160 223 177 170 112 60.8 45.8 39.0 44.8 46.9 65.6
Streamflow-Response Coefficients 91

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

 PR-AB4A

 PR-AB3B

RIW-385

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Pawcatuck River at PAWCD (no RCHRES)

Beaver River at BEAVM (no RCHRES) Usquepaug River at QUEENM (no RCHRES)

RESPONSE COEFFICIENT (CHANGE IN STREAMFLOW FOR UNIT WITHDRAWAL RATE AT WELL), DIMENSIONLESS

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

EXPLANATION

END OF MONTH

END OF MONTH

A

Figure 4–3A. Selected examples of simulated response coefficients for streamflow-constraint sites on the Beaver 

(at BEAVM), Usquepaug-Queen (at QUEENM), and Pawcatuck (at PAWCD) Rivers, in the eastern Pawcatuck River 

conjunctive-management model (EPRCMM) area in the Pawcatuck River Basin, southwestern Rhode Island, for three 

hypothetical wells at different distances between the rivers. Graphs show the fraction of the unit withdrawal from each 

well that is evident as streamflow depletion at the end of each month after the withdrawal. (Site locations shown in 

figure 4–1 and described in tables 4–1 and 4–2.)
92 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

RIW-458 - furthest

RIW-458A

RIW-458B - closest

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Meadow Brook at MEAD2 (RCHRES 48) Pawcatuck River at PAWC4 (RCHRES 50)

Wood River at WOOD5 (RCHRES 63) Wood River at WOOD6 (RCHRES 65)

RESPONSE COEFFICIENT (CHANGE IN STREAMFLOW FOR UNIT WITHDRAWAL RATE AT WELL), DIMENSIONLESS

END OF MONTH

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

B

Figure 4–3B. Selected examples of simulated response coefficients for streamflow-constraint sites on the Wood 

River (at WOOD5 and WOOD6), Meadow Brook (at MEAD2), and Pawcatuck (at PAWC4) Rivers, in the lower Wood 

River conjunctive-management model (LWRCMM) area in the Pawcatuck River Basin, southwestern Rhode Island, 

for three hypothetical wells at different distances between the rivers. Graphs show the fraction of the unit withdrawal 

from each well that is evident as streamflow depletion at the end of each month after the withdrawal. (Site locations 

shown in figure 4–2 and described in tables 4–1 and 4–2.)
Streamflow-Response Coefficients 93

Response-coefficient graphs for three hypothetical well 

sites in the LWRCMM area (fig. 4–3B) also illustrate the 

effect of well distance on the temporal distribution of streamflow depletions. The three hypothetical well sites (RIW–458, 

RIW–458A, and RIW–458B) are at different distances 

between the Wood River and Meadow Brook (fig. 4–2). A 

comparison of the response-coefficient graphs for the streamflow-constraint sites WOOD5 (RCHRES 63) and WOOD6 

(RCHRES 65) indicates that all depletions in the Wood River 

from these hypothetical well sites occur downstream of the 

WOOD5 constraint site. Depletions at WOOD6 peak in the 

second month after each unit withdrawal from hypothetical well RIW–458 because this site is farther from the Wood 

River (within about 2,000 ft) than the other wells. Depletions 

at WOOD6 peak in the first month after each withdrawal 

from hypothetical wells RIW–458A and RIW–458B because 

these sites are closer to the Wood River (about 1,000 and 

300 ft away from the Wood River, respectively). About 8, 

24, and 62 percent of the total depletions caused by withdrawals from wells RIW–458, RIW–458A, and RIW–458B, 

respectively, occur in the first month after a unit withdrawal 

at each hypothetical well site. Total streamflow depletions at 

WOOD6 caused by withdrawals from these wells do not equal 

the amounts withdrawn. This is because withdrawals at these 

sites cause a shift in the location of the groundwater divides 

in the aquifer so that each well also intercepts groundwater 

that otherwise would flow toward the Meadow Brook or the 

Pawcatuck River.

Response coefficients from the groundwater model 

indicate that withdrawals from potential well sites RIW–458, 

RIW–458A, and RIW–458B have a small but sustained effect 

on streamflow depletions in Meadow Brook at constraint 

site MEAD2 (RCHRES 48) (fig. 4–3B). The amount of 

depletion at MEAD2 increases as the withdrawal location 

is shifted to the east away from the Wood River and toward 

Meadow Brook (fig. 4–3B). Although the fraction of depletion 

during each individual month is low (less than or equal to a 

maximum of about 5 percent of the unit withdrawals), the 

annual sum of the depletions could be substantial, especially 

if withdrawals were to be made at these wells throughout the 

year. In addition, the response coefficients (fig. 4–3B) indicate 

that withdrawals from these potential well sites may intercept 

a small amount of groundwater that would otherwise flow 

southward toward the Pawcatuck River and a small unnamed 

tributary in the area between Meadow Brook and the Wood 

River (fig. 4–2). The calculated depletions are caused by small 

shifts in the natural groundwater divides. These depletions 

are small, are sustained for many months, and have a pattern 

similar to depletions from Meadow Brook at MEAD2. The 

depletions caused by intercepting groundwater discharge from 

these areas are calculated by subtracting the total streamflow 

depletions at WOOD6 and MEAD2 from the total depletion in 

the Pawcatuck River at PAWC4 (RCHRES 50). 

The response coefficients in figure 4–3B also may be 

used to guide the well-site selection process. Granato and 

Barlow (2005) noted that groundwater-supply systems in 

Rhode Island substantially increase withdrawals during the 

months of May through September with a peak monthly 

withdrawal rate in July (see Appendix Part 4). This annual 

withdrawal pattern is shown in figure 4–4 with the fraction 

of the total annual depletions that would occur in each 

month if well RIW–458, RIW–458A, or RIW–458B were 

pumped according to this Rhode Island demand pattern. 

These monthly streamflow-depletion patterns indicate that 

the monthly depletion rate from well RIW–458, which is 

farthest from the Wood River, would peak in September. 

The peak monthly depletion rate from well RIW–458A, 

which is at the intermediate location, would occur in August. 

The monthly depletion rate from well RIW–458B, which is 

closest to the Wood River, would peak concurrently with peak 

withdrawal rates in July. The delay between peak withdrawals 

and peak depletions from RIW–458 and RIW–458A may 

not be advantageous because the maximum depletions occur 

in August or September concurrently with the lowest daily 

streamflows in the Wood River (see Appendix Part 4). In 

this hypothetical case, if all three wells were available, well 

RIW–458B could be used during the early summer through 

July to minimize residual depletions in August and September 

and well RIW–458 could be used in July and August to delay 

peak depletions from these withdrawals until later in the fall. 

The response-coefficient graphs (fig. 4–3B) and the 

associated depletion graph (fig. 4–4) provide insight into the 

time frames necessary to make effective water-management 

decisions as a drought condition evolves. These graphs 

indicate that withdrawal reductions made in response to a 

developing summer drought will not have an immediate effect 

on depletions if wells are far from the stream. Responsecoefficient graphs provide information about the effects of 

individual water-withdrawal sites in an area of interest, but 

conjunctive-management models are necessary to evaluate 

complex interactions caused by various constraints, such as 

streamflow-depletion criteria, water-withdrawal patterns, and 

well-network designs.
94 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

0.00

0.05

0.10

0.15

0.00

0.05

0.10

0.15

0.00

0.05

0.10

0.15

0.00

0.05

0.10

0.15

0.00

0.05

0.10

0.15

0.00

0.05

0.10

0.15

Hypothetical Well RIW-458A 

Hypothetical Well RIW-458B

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

MONTH

A Hypothetical Well RIW-458 

B

C

MONTHLY S

TREAMFLO

W DEPLETIO

N AS

A PR

OPORTIO

N OF TOT

AL ANNUAL DEPLETIONS, DIMENSIO

NLESS

MO

N

THLY MUNICIPAL WITHDRA

W

ALS AS

A PR

OPORTIO

N OF TOTAL ANNUAL WITHDRA

W

ALS, DIMENSIO

NLESS

Monthly withdrawals as a proportion of total annual withdrawals 

Monthly streamflow depletions as a proportion of total annual depletion

Figure 4–4. The annual pattern in streamflow depletion caused by withdrawals from potential water-withdrawal sites at 

hypothetical well (A) RIW–458, (B) RIW–458A, and (C) RIW–458B indicating in the Wood River (WOOD6, RCHRES 65) in the 

lower Wood River conjunctive-management model (LWRCMM) area in the Pawcatuck River Basin, southwestern Rhode 

Island. (Site locations shown in figure 4–2 and described in tables 4–1 and 4–2.)
Potential Allowable Streamflow-Depletion Criteria 95

Potential Allowable Streamflow-Depletion 

Criteria

Knowledge of relations between streamflow criteria and 

maximum potential water withdrawals is crucial for waterresource-planning efforts. Many instream-flow criteria were 

formulated on the basis of the assumption that a substantial 

amount of water is available in storage for maintaining 

instream flows by release from an actively managed surfacewater reservoir (Granato and Barlow, 2005). Granato and 

Barlow (2005) evaluated 11 commonly referenced flow 

criteria and determined that application of such criteria 

could overrestrict (or preclude) groundwater withdrawals 

even under average hydrologic conditions. Granato and 

Barlow (2005) also determined that criteria based on centraltendency statistics (averages or medians of monthly or annual 

streamflows) may not be protective for extreme lowflows 

if differences between these local streamflow statistics and 

regional streamflow-criteria values were greater than or equal 

to the low-flow values.

Groundwater-supply system operators cannot control 

the total volume of streamflow if they do not also operate a 

surface-water reservoir that can be used to intercept and store 

high flows for later release during dry periods to maintain 

streamflows. Most groundwater-supply systems in Rhode 

Island do not have surface-water reservoirs with adequate 

capacities for public supply and streamflow maintenance. 

Groundwater-supply system operators, however, can affect 

the magnitude and timing of streamflow depletions caused 

by groundwater withdrawals within operational constraints. 

Managing groundwater withdrawals in response to short-term 

(days or weeks) streamflow variation is not possible because 

it may take one or more months for changes in groundwater 

withdrawals to have a substantial effect on streamflow depletions (Barlow and Dickerman, 2001a,b; Barlow and others, 

2003; Granato and Barlow, 2005). 

Granato and Barlow (2005) explored an alternative 

depletion-management paradigm for groundwater-supply 

systems. This approach uses potential allowable streamflowdepletion criteria rather than streamflow target criteria to 

identify a range of streamflow depletions that can be used 

by decisionmakers to balance water-supply needs with 

ecological protection goals. The objective of that effort 

was to use optimization methods to maximize withdrawals, 

control the magnitude and timing of depletions, and minimize 

the probability of reducing streamflow beyond a specified 

nonzero streamflow value. Granato and Barlow (2005) used 

an estimated streamflow record for the period 1960–2000 to 

evaluate potential-allowable depletion criteria based on the 

one-day monthly minimum streamflow for each month during 

this period. The one-day monthly minimum streamflow is the 

minimum of the daily mean streamflows for each month of 

the period of record. In that study, post-optimization analysis 

indicated that the selected potential allowable-depletion 

criteria were adequate to provide water for public supply 

while maintaining nonzero streamflows during the simulated 

1960–2000 period. This approach also resulted in a high 

degree of natural variability at higher streamflow rates because 

withdrawals were a small fraction of these flows. 

In this study, potential allowable-depletion criteria were 

formulated from the population of minimum daily-mean 

streamflow values in each month of each year during the 

1960–2004 period. The HSPF-generated record of daily-mean 

streamflows without water withdrawals was used to identify 

these minimum daily-mean streamflow values. This results 

in about 45 minimum daily mean streamflow values for each 

month of the 45-year period for each of the seven streamflow 

constraint sites. The minimum of these 45 daily-mean streamflow values for each of the seven streamflow-constraint sites 

for each month of the entire period are listed in table 4–2. 

The lowest minimum daily-mean streamflows for the 

period of record for each constraint site occurred in the month 

of September. 

The 45 one-day monthly minimum streamflow values 

were ranked for each month of the year by using the Weibull 

plotting-position values (Appendix Part 4). The Weibull 

plotting-position values indicate the percentages of minimum daily flow values that would equal or exceed a given 

streamflow value in a given month for each site. The monthly 

flow-duration curve for each site consists of about 45 points 

each of which represents one daily minimum streamflow value 

for each month of each year during the period 1960–2004. For 

example, the percentages of September months with one-day 

monthly minimum streamflows (normalized by drainage 

area to cubic feet per second per square mile) that equal or 

exceed a given value for streamflow-constraint sites in the 

EPRCMM and LWRCMM areas are shown in figures 4–5A 

and B, respectively. The minimum one-day-minimum 

September streamflow is about 0.15 ft3/s/mi2 for all streamflow-constraint sites. The flow duration (Weibull plotting 

position) for this minimum one-day September streamflow 

value for the 1960–2004 period is 98 percent. This value 

indicates that the chance that a streamflow value may be lower 

than 0.15 ft3/s/mi2 is about 2 percent, based on the 45 years of 

data. The 90th-percentile value for normalized streamflows 

at these sites is about 0.2 ft3/s/mi2; thus the chance that the 

one-day minimum September streamflow will be below this 

value is about 10-percent. As such, the use of an allowabledepletion criterion of about 0.2 ft3

/s/mi2 would have a 10-percent chance of reducing streamflow to zero for one day in any 

given year, again, based on the 45-year record. Flow-duration 

curves for the one-day monthly minimum streamflows during 

each month of the year are shown in Appendix Part 4 for each 

streamflow-constraint location. 

These streamflow-duration curves were used as the basis 

for calculating values of allowable streamflow depletions that 

represent specific risks for inducing a zero-flow condition as 

an effect of water withdrawals. Allowable streamflow depletions were based on either a flow duration (expressed as a 

percentile flow duration) or a fraction of the 45-year one-day 

minimum flow (expressed as a percentage of the minimum). 

Selected flow-duration values for each month of the year were 
96 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

 QUEENM

 BEAVM

 PAWCD

B Lower Wood River conjunctive-management model (LWRCMM) area

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

 MEAD2 (RCHRES 48)

 WOOD6 (RCHRES 65)

 PAWC4 (RCHRES 50)

A Eastern Pawcatuck River conjunctive-management model (EPRCMM) area 

PERCENTAGE OF SEPTEMBER MONTHS DURING WHICH THE ONE-DAY-MINIMUM 

MONTHLY STREAMFLOW WAS EQUALED OR EXCEEDED

ONE-DAY MINIMUM MONTHLY STREAMFLOW, IN CUBIC FEET PER SECOND PER SQUARE MILE 

1 2 5 10 20 30 40 50 60 70 80 90 95 98 99

1 2 5 10 20 30 40 50 60 70 80 90 95 98 99

Figure 4–5. Monthly streamflow-duration curves showing the percentage of one-day-minimum September streamflows that would 

equal or exceed a selected streamflow value at selected sites in the (A) eastern Pawcatuck River conjunctive-management model 

(EPRCMM) area and the (B) lower Wood River conjunctive-management model (LWRCMM) area in the Pawcatuck River Basin, 

southwestern Rhode Island. (Site locations for EPRCMM shown in figure 4–1, and site locations for LWRCMM shown in figure 4–2 and 

described in table 4–2.)
Potential Allowable Streamflow-Depletion Criteria 97

used to evaluate relations between the allowable-depletion 

criteria and the maximum water-withdrawal yield for a given 

well network with different operational constraints; these 

constraints are described in the section entitled “Formulation of the Conjunctive-Management Model” in Appendix 

Part 4. Four flow-duration values—the 80-, 90-, 95-, and 

98-percentile flow durations—were selected as examples of 

potential allowable-depletion values (fig. 4–6). As potential 

allowable depletions, these values represent 20-, 10-, 5- and 

2-percent chances of causing a zero-flow event in each year, 

respectively. Four potential allowable-depletion values that 

are equal to 75, 60, 50, and 25 percent of the 45-year minimum daily streamflow value for each month (table 4–2) also 

were selected to evaluate water-withdrawal yields that would 

further reduce the risk of a zero-flow event (fig. 4–6). These 

allowable-depletion criteria would maintain 45-year minimum 

daily mean streamflows for each month that are 25, 40, 50, 

and 75 percent of the estimated historical minimums without 

withdrawals, respectively. 

Optimization techniques can be used to estimate the 

maximum groundwater withdrawals that can be achieved 

within the allowable-depletion criteria. The relations between 

estimated maximum-withdrawal rates and the allowabledepletion criteria can be expressed visually with a conjunctivemanagement-model yield graph (for example, fig. 4–6). The 

yield graph can be used by water managers to balance watersupply needs with environmental protection goals. The x-axis 

represents the allowable depletion, which may be less than, 

equal to, or greater than the minimum daily mean streamflow. An increase in allowable depletion represents an equal 

reduction in streamflows. The streamflow-depletion criteria 

are established on the basis of historical minimum daily-mean 

streamflows in each month of the year, but the yield graphs 

that are presented are for annual total withdrawals. Rather than 

repeat the same yield curve for each of the 12 monthly allowable-depletion criteria, the allowable-depletion criteria for the 

month with the lowest minimum daily-mean streamflows were 

selected. This is because allowable depletion criteria for the 

ESTIMATED SEPTEMBER DEPLETION, AT STREAMFLOW CONSTRAINT SITE WOOD6, 

IN CUBIC FEET PER SECOND PER SQUARE MILE

0.0 0.05 0.10 0.15 0.20 0.25 0.30

0

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

1,300

1,400

1,500

1,600

1,700

TOTAL ANNUAL MUNICIPAL GROUNDWATER

WITHDRAWALS,

IN MILLIONS OF GALLONS PER YEAR

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

TOTAL ANNUAL GROUNDWATER

WITHDRAWALS,

IN MILLIONS OF GALLONS PER DAY

90th-percentile flow 

duration

95th-percentile flow 

duration

98th-percentile flow 

duration (the 

minimum flow)

80th-percentile flow 

duration

75 percent of 

minimum flow

60 percent of 

minimum flow

50 percent of minimum flow

25 percent of minimum flow

 Maximum withdrawal rate: 1.4 Mgal/d

 Maximum withdrawal rate: 2.0 Mgal/d

Figure 4–6. Conjunctive-management-model yield relations between potential allowable streamflow depletion criteria 

in the Wood River (WOOD6, RCHRES 65) and total annual groundwater withdrawals at the specified Rhode Island 

withdrawal rates from hypothetical wells RIW–458, RIW–458A, and RIW–458B in the lower Wood River conjunctivemanagement model (LWRCMM) area in the Pawcatuck River Basin, southwestern Rhode Island. Withdrawals are 

graphed with respect to potential allowable-depletion values for September because these values are the primary 

groundwater withdrawal constraints throughout the year. Each conjunctive-management model, however, is based on 

the same flow statistics for each month of the year. Mgal/d, million gallons per day. (Site locations shown in figure 4–2 

and described in tables 4–1 and 4–2.)
98 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

month with the minimum daily-mean streamflows, in this 

case September, are the binding criteria in the conjunctivemanagement models that limit total annual withdrawals. 

The shape of the curve or curves on the yield graph 

indicates the change in total annual withdrawals with a change 

in allowable depletion (fig. 4–6). A steep slope in the curve 

indicates a large change in allowable withdrawals with a 

small change in allowable depletion. If the slope is steep, 

selection of an allowable depletion criterion (and therefore 

the minimum daily mean streamflow that will occur with 

allowable withdrawals) is critical for determining available 

water supplies. A low slope in the curve indicates that a small 

change in allowable depletions will occur with a small change 

in allowable withdrawals; in this case, a compromise in the 

allowable depletion criterion may not have a large effect on 

available water supplies. A zero slope indicates that selection 

of an allowable depletion criterion will not affect the available 

water supply. In this case, another factor (for example, the 

number and capacity of available water-withdrawal sites) 

controls the amount of available water supplies. Both yield 

curves in figure 4–6 have steep slopes at small values 

of allowable depletion, intermediate slopes as allowable 

depletions increase, and a plateau with a zero slope above 

an allowable-depletion criterion that equals the maximum 

production capacity of the production-well network within the 

specified withdrawal-pattern constraint. 

Sixteen conjunctive-management models (fig. 4–6) were 

developed to demonstrate the relations between potential 

allowable-depletion criteria and maximum water yields if 

hypothetical wells RIW–458, RIW–458A, and RIW–458B 

(fig. 4–2) in the LWRCMM area were modeled according to 

the Rhode Island municipal water-demand pattern (Appendix 

Part 4). In this case, the streamflow-depletion criterion that 

is 25 percent of the minimum streamflow limits withdrawals 

to about 760 Mgal/yr, with very little difference between the 

two management models with different (1.4 and 2.0 Mgal/d) 

maximum withdrawal rates (fig. 4–6). 

As potential allowable-depletion criteria are increased, 

annual withdrawals increase until the maximum withdrawal 

rates limit the total annual water withdrawals. The management models with a maximum withdrawal rate of 1.4 Mgal/d 

reach a plateau of about 1,120 Mgal/yr when allowable depletions are about 75 percent of the minimum streamflow value 

(fig. 4–6). The total annual water withdrawals are less than the 

1,530 Mgal/yr one would expect for three wells each withdrawing 1.4 Mgal/d throughout the year because the Rhode 

Island municipal-withdrawal pattern is not constant throughout 

the year. Therefore, the wells operate at maximum capacity 

only to meet peak (monthly) July water demands. In this situation, an alternative to decisionmakers could be to consider 

specifying a maximum allowable depletion that is less than the 

historical minimum streamflow value and greater than 

75 percent of the minimum streamflow value without having a 

substantial effect on groundwater withdrawals from this well 

network under the specified constraints. 

The conjunctive-management models for the higher 

withdrawal rate (2 Mgal/d per well) indicate a similar pattern 

with a higher plateau (fig. 4–6). The management models 

with a maximum withdrawal rate of 2 Mgal/d reach a plateau 

of about 1,600 Mgal/yr when allowable depletions are about 

equal to the estimated minimum streamflow value for the 

45-year period. The total annual withdrawals are higher and 

the plateau begins at a higher potential allowable-depletion 

value as the maximum withdrawal rate becomes the binding 

criterion. Setting the potential allowable depletion to 

75 percent of the minimum streamflow value would result in a 

decrease in the total annual withdrawal of about 120 Mgal/yr; 

at 50 percent of the minimum streamflow, the decrease would 

be about 380 Mgal/yr.

Water-resource decisionmakers also may use such 

groundwater-yield curves to set different allowable-depletion 

criteria for wet and dry years. For example, if the allowabledepletion criterion is equal to the minimum daily-mean 

streamflow value in wet and normal years, the three-well 

network with a maximum withdrawal rate of 1.4 Mgal/d could 

produce 1,120 Mgal/yr. Although the allowable-depletion 

criterion equals the historical minimum daily-mean streamflow 

values, use of this criterion would not result in a zero-flow 

event in wet or normal years. If water-conservation measures 

could be expected to reduce annual withdrawals by 10 percent 

in dry years, an annual production rate of about 1,000 Mgal/yr 

might be achievable with a dry-year allowable-depletion value 

that is about 50 percent of the minimum streamflow (fig. 4–6). 

In this example, the probability is about 2 percent in any given 

year that this dry-year allowable-depletion criterion would 

produce a minimum daily-mean streamflow value that is 

50 percent of the minimum streamflow without withdrawals.

Well-Site Selection for Groundwater 

Withdrawals

A set of 72 conjunctive-management models for the 

LWRCMM area were formulated and tested to evaluate the 

effect of well-site selection on water withdrawals (fig. 4–7). 

These models included site-specific withdrawal patterns 

defined by site type and water use in table 4–1. The irrigationwithdrawal patterns and the municipal withdrawal patterns are 

described in Appendix Part 4. The effect of well-site selection 

was tested by using hypothetical wells RIW–458, RIW–458A, 

or RIW–458B, which are about 2,500, 1,000, and 300 ft 

east of the Wood River), respectively (fig. 4–2). Well-site 

selections for these hypothetical wells were tested because 

of differences in their response coefficients (fig. 4–3B) and 

associated depletion graphs (fig. 4–4). The additional irrigation 

withdrawals also are useful for further defining relations 

between potential allowable-depletion criteria and maximum 

water withdrawals.

Irrigation withdrawals are included in the management 

model to represent potential agricultural demands, but the 

conjunctive-management models have limited applicability 
Well-Site Selection for Groundwater Withdrawals 99

for optimizing irrigation withdrawals. Irrigation withdrawals 

are made on a daily basis in response to precipitation deficits. 

The conjunctive-management models are used to maximize 

withdrawals on a monthly time scale and are not suitable 

for daily variations in irrigation needs. For this reason, the 

monthly average irrigation-withdrawal patterns documented in 

Appendix Part 4 were used in this analysis. This time scale is 

appropriate for groundwater withdrawals because it is consistent with the response times of streamflow depletions from 

wells, which are on the order of several months to a year. Use 

of one-day monthly minimum streamflows during each month 

of the year to estimate the maximum streamflow-depletion 

constraint, however, does not preclude the potential for 

short-term surface-water withdrawals to exceed the instantaneous streamflow during the hours when the surface-water 

withdrawals are active. The potential effects of these differences in time scale between variable hourly irrigation withdrawals with instantaneous depletions from surface-water sites 

and monthly groundwater withdrawals from wells are demonstrated in the HSPF modeling results (Part 3). The monthly 

average withdrawal rates calculated by the management model 

are used to demonstrate groundwater-management concepts 

rather than the management of surface-water withdrawals. 

In the conjunctive-management models, the surface-water 

withdrawals are approximated by the use of monthly average 

withdrawal rates and a response coefficient of one. 

Streamflow depletion criteria and maximum annual 

water-withdrawal yields are shown in figure 4–7. These 

models include withdrawals from hypothetical municipal 

wells, and irrigation withdrawals from nine hypothetical or 

Figure 4–7. Conjunctive-management-model yield relations between potential allowable streamflow depletion criteria 

in the Wood River (WOOD6, RCHRES 65) and total annual groundwater withdrawals from hypothetical agricultural 

locations that follow irrigation-withdrawal patterns and groundwater withdrawals at the specified Rhode Island 

withdrawal rates from hypothetical wells RIW–458, RIW–458A, or RIW–458B in the lower Wood River conjunctivemanagement model (LWRCMM) area in the Pawcatuck River Basin, southwestern Rhode Island. Withdrawals are 

graphed with respect to potential allowable-depletion values for September because these values are the primary 

groundwater withdrawal constraints. Each conjunctive-management model, however, is based on the same flow 

statistics for each month of the year. Mgal/d, million gallons per day. (Site locations shown in figure 4–2 and described 

in tables 4–1 and 4–2.)

0

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

1,300

1,400

1,500

1,600

1,700

TOTAL ANNUAL MUNICIPAL GROUNDWATER

WITHDRAWALS,

IN MILLIONS OF GALLONS PER YEAR

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

TOTAL ANNUAL GROUNDWATER

WITHDRAWALS,

IN MILLIONS OF GALLONS PER DAY

90th-percentile flow 

duration

95th-percentile flow 

duration

98th-percentile flow 

duration (the 

minimum flow)

80th-percentile flow 

duration

75 percent of 

minimum flow

60 percent of 

minimum flow

50 percent of minimum flow

25 percent of minimum flow

 Maximum withdrawal rate: 1.4 Mgal/d

 Maximum withdrawal rate: 2.0 Mgal/d

0.00 0.50 0.10 0.15 0.20 0.25 0.30

ESTIMATED SEPTEMBER DEPLETION, AT STREAMFLOW CONSTRAINT 

SITE WOOD6, IN CUBIC FEET PER SECOND PER SQUARE MILE
100 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

existing water-withdrawal sites. The models were constrained 

by maximum withdrawal rates of 1.0, 1.4 or 2.0 Mgal/d at 

each withdrawal site. Total annual withdrawal yields increase 

from about 800 Mgal/yr with a depletion criterion that is about 

25 percent of the minimum of one-day monthly minimum 

streamflow measurements during 1960 to 2004 and diverge 

at plateaus representing the maximum yields of about 1,650, 

2,300, and 3,300 Mgal/yr for withdrawal rates of 1.0, 1.4, and 

2.0 Mgal/d, respectively. This graph indicates that, at this site, 

maximum withdrawal capacities have a greater effect on total 

annual withdrawals than distance from the stream because 

the management model results for this area are limited more 

by maximum withdrawal capacity than by withdrawal-site 

location. Differences among total annual withdrawals for the 

different hypothetical withdrawal locations are on the order 

of 2 to 4 percent until the maximum withdrawal capacity is 

reached, at which point withdrawals from the three sites are 

identical for each maximum withdrawal rate. 

There is a perception that wells next to a stream may 

have more deleterious effects on streamflow than wells that 

are farther away. However, the relative merit of different well 

locations is more complex then that because it depends on the 

characteristics of the aquifer, the water-demand pattern, the 

maximum withdrawal capacity of the well, and the effects of 

applying monthly streamflow depletion criteria in different 

areas. For example, in the LWRCMM area, the well that is 

2,500 ft away from the Wood River (RIW–458) can produce 

about 55 percent less water than the well next to the river 

(RIW–458B) at a maximum withdrawal rate of 2.0 Mgal/d 

and a streamflow depletion criterion of about 0.036 ft3/s/mi2. 

(These differences are not apparent in figure 4–7 because of 

the interplay that occurs between municipal and agricultural 

withdrawals as allowable stream-depletion criteria vary.) The 

large differences in total withdrawals between hypothetical 

well RIW–458 and RIW–458B occur because of the timing 

of minimum streamflows (in September), peak demands (in 

July), and the differences in the timing of depletions caused 

by withdrawals from each well (fig. 4–4). Differences in total 

withdrawals for these different well locations disappear as the 

allowable streamflow depletion constraints increase because 

the specified maximum withdrawal capacity of the withdrawal 

sites becomes the limiting criterion. This information is 

important for evaluating water-supply alternatives specific to 

the LWRCMM area, but the details concerning withdrawal 

capacities and distances of hypothetical wells from the stream 

may not be transferable to different locations. 

Well RIW–458 also has a greater effect on streamflow in 

the Meadow Brook than the wells that are closer to the Wood 

River. This may be of concern because monthly minimum 

streamflows in the Wood River are almost an order of magnitude higher than monthly minimum streamflows in the 

Meadow Brook (table 4–2). Depletions in the Meadow Brook 

caused by withdrawals from this well peak in the third month 

after a given withdrawal (fig. 4–3B). As a result of the threemonth lag time, peak July water demands cause depletions in 

Meadow Brook during the dry months (August to October). 

Although September depletions in Meadow Brook may be the 

binding criteria in some management models, groundwater 

yield curves are graphed with respect to normalized depletions 

(in cubic feet per second per square mile) in the Wood River to 

maintain consistency with the presentation of other results in 

this section of the report. The normalized allowable depletions 

at the two constraint sites, which were developed with the 

same statistical thresholds, are comparable because normalized streamflows in both streams are similar (fig. 4–5B).

As the potential allowable streamflow depletion criteria 

are reduced, total irrigation withdrawals are disproportionally 

reduced by conjunctive-management models that are designed 

to maximize total annual withdrawals from the entire withdrawal-site network within streamflow-depletion constraints 

and water-use pattern constraints. The hypothetical municipal 

supply well sites have higher withdrawal volumes because 

these wells are used throughout the year, and withdrawals in 

the fall, winter, and spring are a fixed proportion of summer 

withdrawals. If this area of Rhode Island had an alternative 

municipal water source (for example, the proposed Big River 

Reservoir) to meet nonagricultural peak-summer demand, 

then the fraction of total withdrawals for agricultural use in 

the summer could increase, and the total amount of nonagricultural withdrawals could increase in the winter months. 

For example, Granato and Barlow (2005) demonstrated that 

proposed wells in the Big River area could produce twice as 

much water per year if withdrawals were not limited by the 

municipal-demand pattern. This is because the alternative 

source would be used to meet municipal demands in the 

summer so that the wells can produce more in the winter 

and less in the summer while meeting the summer lowflow constraints. 

Use of Community Wells for Irrigation

Potential yields from individual water-withdrawal sites 

and two alternative irrigation networks were tested under 

different criteria for the EPRCMM area. The alternative 

well-network designs include community wells (irrigation 

wells that are shared by several farmers in the same area) to 

supply irrigation water for all the farms in the area. Several 

factors may favor the use of community irrigation wells 

for adjacent farms. For example, one factor is the potential 

economic benefits of community wells, which may include 

reduced infrastructure costs. Community wells also may 

provide water from more advantageous water-withdrawal sites 

if water restrictions preclude withdrawals from other sites. 

Water-withdrawal sites for the community-well scenarios 

were not selected by using optimization techniques; the NRCS 

selected 18 potential well sites for this analysis (table 4–3, 

fig. 4–1) on the basis of logistical considerations, such as 

proximity to roads and electrical power (Vicky Drew, Natural 

Resources Conservation Service, written commun., 2006). 

The conjunctive-management models for individual waterwithdrawal sites include 18 potential sites. Fourteen of the 
Use of Community Wells for Irrigation 101

sites were assigned to community-well option A, and 13 to 

community-well option B (table 4–3). 

Sixty-three management models were formulated and 

tested to evaluate the potential effects of well-network design 

on the total groundwater-withdrawal yields for different 

potential-allowable-streamflow-depletion criteria (fig. 4–8). 

Potential allowable streamflow-depletion criteria ranged from 

a fraction (25 percent) of the 45-year minimum streamflow 

to the 80-percent flow duration of monthly minimum streamflows (meaning that 80 percent of the monthly minimum 

flows exceed this value during the period 1960–2004). 

The conjunctive-management models were constrained by 

maximum withdrawal rates of 1.0, 1.4 or 2.0 Mgal/d at each 

withdrawal site. Withdrawals for golf courses, turf farms, and 

vegetable farms (table 4–1) also were constrained to match 

irrigation patterns (Appendix Part 4).

The groundwater withdrawal yields are limited by 

the potential allowable-depletion criteria in all of these 

community-well management models for the EPRCMM area 

(fig. 4–8). This is evident because the yield curves do not 

fully plateau in the range of allowable depletions that were 

tested. Estimated streamflow statistics without withdrawals 

for the Wood, Beaver, and Usquepaug-Queen Rivers in 

both management-model areas are similar if the values are 

normalized by drainage area (table 4–2, fig. 4–5A). However, 

the combined drainage area of the Beaver and UsquepaugQueen Rivers is about half of the drainage area of the 

Wood River so the tributaries to the Pawcatuck in the 

EPRCMM area have lower flows than the Wood River. The 

number of potential water-withdrawal sites in the EPRCMM 

area is larger than the number of sites in the LWRCMM area 

in all of the scenarios tested. Thus, management models for 

hypothetical well networks in EPRCMM area do not reach 

full network capacity (the number of wells multiplied by 

the maximum withdrawal rate and the withdrawal-pattern 

constraint) within the range of potential-allowable depletion 

criteria that were used. The streamflow-depletion limitation 

is evident in figure 4–8 because the total annual groundwater 

withdrawals do not substantially diverge at low potential 

allowable depletions and do not reach a plateau as in 

figures 4–6 and 4–7. 

Table 4–3. Irrigation management-model scenarios for existing and potential water-withdrawal sites in 

the eastern Pawcatuck River conjunctive-management model (EPRCMM) area, Pawcatuck River Basin, 

southwestern Rhode Island.

[Site locations shown in figure 4–1 and described in table 4–1. ID, identifier. Index: Conjunctive-management model index number]

Index Site ID

Scenarios

Individual irrigation wells Community-well option A Community-well option B

1 AUQ6A X X X

2 PR–AUQ8A X X X

3 PR–AUQ9A X X X

4 PR–AUQ11A X X X

5 PR–AB8A X X X

6 PR–GB1A X X X

7 RIW–336A

8 RIW–385 

9 PR–AUQ7A X X X

10 PR–AUQ10A X

11 PR–AUQ10B X X X

12 PR–AUQ10C X X X

13 PR–AB1A X X

14 PR–AB2A X

15 PR–AB2B X

16 PR–AB3A X

17 PR–AB3B X X X

18 PR–AB4A X X X

19 PR–AB5A X X X

20 PR–GUQ2AB X X X
102 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

Management models that have higher maximum 

withdrawal rates produce slightly more water as potential 

allowable-depletion criteria increase because higher maximum 

withdrawal rates at the more optimal withdrawal sites increase 

the total annual withdrawals for the given allowable-depletion 

criteria (fig. 4–8). Total annual withdrawals in all management 

models for the EPRCMM area are about 377 Mgal/yr if the 

depletion criterion is a fraction (25 percent) of the one-day 

monthly minimum streamflow for each month of the year. 

As the potential allowable-depletion criteria increase to 

the 98 percent flow-duration value for monthly minimum 

streamflows, differences in total annual withdrawals among 

the irrigation-withdrawal networks increase to about 

10 percent of the total annual withdrawals. If potential 

allowable depletions are increased from the 98th percentile to 

the 80th percentile one-day minimum-monthly flow duration, 

the differences between management models increase to about 

35 percent of the annual withdrawal at the 80th percentile 

flow duration. For example, the total annual withdrawals for 

the models for community-well option B with maximum 

withdrawal rates of 1.0 Mgal/d and 2.0 Mgal/d are about 

1,440 and 2,060 Mgal/yr, respectively (a 35-percent 

difference). In comparison, the maximum difference in total 

annual withdrawals is about 11 percent among the three wellnetwork designs (individual irrigation wells, community-well 

option A, and community-well option B) with a maximum 

withdrawal rate of 1.0 Mgal/d (fig. 4–8). This is because 

the maximum withdrawal rates differ by a factor of 2 but 

the number of wells differ by a factor of 1.4 among the 

conjunctive-management models.

The maximum difference among the three well-network 

designs for a given withdrawal rate occurs with the withdrawal 

rate of 1.0 Mgal/d because the maximum withdrawal capacity 

of a well network is the product of the number of wells and the 

maximum withdrawal rate of each well. Management models 

with the maximum withdrawal rates of 1.4 and 2.0 Mgal/d are 

substantially limited by the streamflow depletion criteria at 

the 80th percentile flow duration, but the management models 

with the maximum withdrawal rate of 1.0 Mgal/d have almost 

reached the network-capacity threshold (fig. 4–8). At this 

0

500

1,000

1,500

2,000

2,500

0

1

2

3

4

5

6

7

ESTIMATED SEPTEMBER DEPLETION AT STREAMFLOW CONSTRAINT SITE QUEENM, 

IN CUBIC FEET PER SECOND PER SQUARE MILE

0.0 0.05 0.10 0.15 0.20 0.25 0.30

TOTAL ANNUAL GROUNDWATER

WITHDRAWALS,

IN MILLIONS OF GALLONS PER DAY

TOTAL ANNUAL GROUNDWATER

WITHDRAWALS,

IN MILLIONS OF GALLONS PER YEAR

25 percent of minimum flow

50 percent of minimum flow

75 percent of minimum flow

98th-percentile flow duration (the minimum flow)

95th-percentile flow duration

90th-percentile flow duration

80th-percentile flow 

duration

Irrigation 1.0 Mgal/d

Individual irrigation wells

Irrigation 1.4 Mgal/d

Irrigation 2.0 Mgal/d

Option A 1.0 Mgal/d

Community-wells

Option A 1.4 Mgal/d

Option A 2.0 Mgal/d

Option B 1.0 Mgal/d

Option B 1.4 Mgal/d

Option B 2.0 Mgal/d

0.35

Figure 4–8. Conjunctive-management-model yield relations between potential allowable streamflow depletion 

criteria in the Usquepaug-Queen River (QUEENM) and total annual groundwater withdrawals from hypothetical 

agricultural locations that follow irrigation-withdrawal patterns in the eastern Pawcatuck River conjunctivemanagement model (EPRCMM) area in the Pawcatuck River Basin, southwestern Rhode Island. Withdrawals are 

graphed with respect to potential allowable-depletion values for September because these values are the primary 

groundwater withdrawal constraints. Each conjunctive-management model, however, is based on the same 

flow statistics for each month of the year. Mgal/d, million gallons per day. (Site locations shown in figure 4–1 and 

described in tables 4–2 and 4–3.)
Postoptimization Analysis 103

point, differences among these management modes with the 

same maximum withdrawal rate occur because of differences 

in the total number of wells; the individual irrigation-well 

option has 18 active wells, community-well option A has 14 

active wells, and community-well option B has 13 active wells 

(table 4–3). 

Post-Optimization Analysis

Post-optimization analysis provides information that 

can be used by water-resource managers to evaluate relations 

between withdrawal plans and the potential effects of withdrawal plans on streams in the area. In the post-optimization 

analysis for this investigation, the conjunctive-management 

model results are used to estimate streamflows that might have 

occurred if the optimized withdrawal plans had been utilized 

during the period 1960–2004. These estimates were made by 

calculating monthly streamflow depletions caused by each 

management model and then interpolating the monthly depletions to estimate a record of daily depletions. These depletions 

were then subtracted from the simulated record of daily-mean 

streamflows without withdrawals that was computed with 

the basinwide surface-water model (HSPF). This information provides an estimate of the relative risks posed by each 

withdrawal plan to streamflow for future conditions under the 

assumptions that optimization methods are applicable for irrigation withdrawals, the streamflow-depletion response times 

for groundwater withdrawal sites even out daily fluctuations in 

irrigation demands, and the estimates of historical streamflows 

will represent future streamflows.

The following discussion is intended to provide examples 

of the effects of the application of allowable-depletion criteria 

on the potential distribution of instream flows. Streamflows 

discussed in the following paragraphs are not described as 

suggested instream-flow targets that may balance water withdrawals and ecological protection; instead, they are descriptive examples of potential relations between withdrawals, 

depletions, and instream flows. They also show the potential 

benefits of using a depletion-based criterion that can be related 

to withdrawals (and therefore, to water-conservation methods) 

in comparison to a minimum-flow criterion that cannot be 

explicitly addressed with demand-management efforts. 

The conjunctive-management models for individual 

irrigation wells in the EPRCMM area (table 4–3) with a 

maximum sustained withdrawal capacity of 1.4 Mgal/d were 

selected as examples. Flow-duration curves for the Usquepaug-Queen River at site QUEENM indicate the potential 

effects of the optimized withdrawal plan on daily streamflows 

during the 1960–2004 period for each of the seven streamflow-depletion criteria (fig. 4–9). Hydrographs for the 1960–

2003 period show the estimated records of streamflow without 

withdrawals and for two specific withdrawal plans (fig. 4–10). 

The period 1960–2003 was selected for presentation of the 

hydrographs in figure 4–10 to show streamflow records for 

complete calendar years. 

Streamflows are presented in cubic feet per second 

per square mile (ft3/sec/mi2) to facilitate comparison with 

streamflow-maintenance criteria, which are commonly 

normalized by drainage area. For example, the aquatic 

baseflow (ABF) criterion of 0.5 ft3/sec/mi2 has been proposed 

as a minimum-flow criterion for use in Rhode Island. 

Figure 4–9 indicates that streamflows in the UsquepaugQueen River at site QUEENM without withdrawals would 

be below this criterion about 9 percent of the time. Use of 

the withdrawal plan with allowable depletions that equal the 

estimated historical monthly minimum streamflows would 

result in daily flows that were less than 0.5 ft3/sec/mi2 about 

14 percent of the time. The hydrographs for the 1960–2003 

period (fig. 4–10) indicate that for both scenarios, streamflows 

would be equal to or below the ABF criterion in many of the 

same years.

Flow-duration curves and hydrographs are presented for 

all daily-mean streamflows rather than for one-day monthly 

minimum streamflows in this example because ecological 

streamflow criteria commonly include objectives for 

maintenance of natural flow variations as well as minimumflow targets (David Armstrong, U.S. Geological Survey, 

written commun., 2004). The flow durations for the one-day 

monthly minimum streamflows (for example fig. 4–5) are not 

equal to the flow durations for all daily mean streamflows. 

For example, daily flows are estimated to be below 

0.01 ft3/sec/mi2 about 1.4 percent of the time (the 98.6th 

percentile flow duration) if withdrawals based on the 80th 

percentile of the monthly minimum streamflows are used 

(fig. 4–9). 

Land and water managers may use information about 

the relative risk of using different depletion criteria, associated withdrawal plans, and the resultant effects on instream 

flows to select withdrawal plans for different years based on 

drought projections and water needs. For example, if a moderately dry year is predicted, then a water-withdrawal plan that 

allows depletions that are greater than the one-day monthly 

minimum streamflow may be adopted if depletions under 

this plan will meet ecological protection goals. If an extreme 

drought is projected, managers may be able to use knowledge 

about withdrawal plans and streamflow depletions to make 

informed decisions about municipal water conservation and 

crop selection to reduce the probability of extreme low-flow 

events (Vicky Drew, Natural Resources Conservation Service, 

oral commun., 2005). Such decisions are especially critical 

for agriculture because crop-irrigation needs would otherwise 

increase in the drier years. Examination of these flow-duration 

curves and historical hydrographs reinforces the concept of 

managing depletions (Granato and Barlow, 2005), which are 

under anthropogenic control, rather than attempting to manage instream flow. Water and land managers cannot effectively control streamflow in basins without a large controlled 

surface-water reservoir that can be used to augment available 

flow. However, managers can use drought projections and 

management-model information to make decisions about withdrawals and subsequent streamflow depletions.
104 Part 4. Conjunctive-Management Models as Tools for Water-Resources Planning

0.01

100

PERCENTAGE OF TIME ESTIMATED STREAMFLOW WAS EQUALED OR EXCEEDED

0.1

1

10

STREAMFLOW, IN CUBIC FEET PER SECOND PER SQUARE MILE

0.01 0.1 0.5 1 2 5 10 20 30 40 50 60 70 80 90 95 98 99 99.5 99.9 99.99

Streamflows without withdrawals

25 percent of minimum flow

50 percent of minimum flow

75 percent of minimum flow

98th-percentile flow duration (the minimum flow)

95th-percentile flow duration

90th-percentile flow duration

80th-percentile flow duration

Streamflows with potential allowable depletions 

from individual irrigation wells equal to:

Figure 4–9. Daily-mean flow-duration curves showing the percentage of time estimated streamflow was equaled or 

exceeded in the Usquepaug-Queen River in the eastern Pawcatuck River conjunctive-management model (EPRCMM) area 

in the Pawcatuck River Basin, southwestern Rhode Island at QUEENM, the streamflow constraint site for the period 1960–

2004. Estimated streamflows are shown without withdrawals and with streamflow depletions caused by the application 

of the optimized withdrawal plans for individual irrigation wells operated at a maximum withdrawal capacity of 1.4 million 

gallons per day. (Site location shown in figure 4–1 and described in table 4–2.)
Postoptimization Analysis 105

0.01

0.1

1

10

100

0.01

0.1

1

10

100

0.01

0.1

1

10

100

0.01

0.1

1

10

100

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970

1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

STREAMFLOW, IN CUBIC FEET PER SECOND PER SQUARE MILE

YEARS

Streamflows without withdrawals Streamflows with depletions from individual irrigation wells

Potential allowable depletions equal to the monthly minimum flow

Potential allowable depletions equal to the 80th-percentile flow duration

Figure 4–10. Estimated streamflow in the Usquepaug-Queen River at streamflow constraint site QUEENM in the eastern Pawcatuck 

River conjunctive-management model (EPRCMM) area in the Pawcatuck River Basin, southwestern Rhode Island for the period 1960–

2003. Estimated streamflows are shown without withdrawals and with streamflow depletions caused by the application of the optimized 

withdrawal plans for individual irrigation wells operated at a maximum withdrawal capacity of 1.4 million gallons per day. (Site location 

shown in figure 4–1 and described in table 4–2.)
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