Evaluation of Strategies for Balancing 

Water Use and Streamflow Reductions in 

the Upper Charles River Basin, Eastern 

Massachusetts

By Jack R. Eggleston

Prepared in cooperation with the

MASSACHUSETTS EXECUTIVE OFFICE OF ENVIRONMENTAL AFFAIRS,

THE MASSACHUSETTS WATERSHED INITIATIVE

Water-Resources Investigations Report 03-4330

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2004

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

Box 25286, Denver Federal Center

Denver, CO 80225

For more information about the USGS and its products:

Telephone: 1-888-ASK-USGS

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

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

endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.
 iii

Contents

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

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

Purpose and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Previous Investigations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Description of Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Basin Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Ground Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Streamflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Estimation of Base Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Water Use and Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Modifications to the Original Flow Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Combining East and West Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Modifications to Model Parameters and Boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Modifications to Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Model Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Model Errors and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Hydrologic Response Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Water-Management Objectives and Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Response Coefficient Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Analysis of Management Alternatives Using Simulation-Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Maximize Pumping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Maximize Streamflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Proposed Wells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Wastewater Management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

New Sewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Holliston. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Bellingham . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Siting of Recharge Basins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Adding Wastewater Recharge to an Existing Wastewater Facility. . . . . . . . . . . . . . . . . . . . . 44

Injection Wells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Moving Wastewater Effluent Upstream. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Stormwater Recharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Recharge of Flood Waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Water Conservation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Drinking Water Transfers Between Towns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Drinking Water Discharge to Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Other Management Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Limitations of this Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Summary and Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

References Cited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
iv 

Appendix 1: Historic Average Monthly Stress Rates (1989–98), Upper Charles River Basin,

Eastern Massachusetts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Appendix 2: Hydrologic Response Coefficients for Withdrawal and Return Stresses

Analyzed, Upper Charles River Basin, Eastern Massachusetts. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Figures

1. Map showing location and surficial geology of the study area, upper Charles River 

basin, eastern Massachusetts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Graph showing monthly average precipitation (1957–2000) and temperature 

(National Oceanic and Atmospheric Administration, 2001) for climate station 

199316 in Medway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3, 4. Maps showing: 

3. Streamflow measurement sites and constraint points, upper Charles River 

basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4. Ground-water and surface-water withdrawals analyzed, upper Charles River 

basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5. Graph showing average monthly municipal water withdrawals (1989–98) and 

wastewater discharges in the upper Charles River basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6. Map showing water-return sites analyzed, upper Charles River basin . . . . . . . . . . . . . . . . . . . 15

7. Graph showing monthly average recharge and withdrawals (1989–98), upper 

Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

8. Map showing model grid and locations of streamflow and water-level 

calibration points, upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

9–11. Graphs showing:

9. Simulated and observed water levels for selected observation wells in the 

upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

10. Simulated and observed base-flow values for selected locations in the 

upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

11. Response coefficients for streamflow depletions at the Charles River exit 

from the study area in response to pumping during month 1 at Wrentham 

well 2 (WR-02G in table 5 and figure 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

12–15. Maps showing:

12. Proposed Bellingham wastewater facility location, upper Charles River basin . . . . . . 41

13. Hypothetical wastewater recharge and discharge facility, Franklin, upper 

Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

14. The existing Charles River Pollution Control District discharge location and a 

hypothetical upstream discharge location (CRPCD-P), upper Charles River 

basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

15. Proposed detention basin (BL-SWP), Bellingham . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

16, 17. Graphs showing:

16. Daily and average streamflow for October 1998 at the Medway streamflowgaging station (01103280) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

17. Daily streamflow variability by month at the Medway streamflow-gaging 

station (01103280) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
 v

TABLES

1. Base flow under average climatic conditions and average water-use conditions 

(1989–98), upper Charles River basin, eastern Massachusetts . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

2. Base flow under dry (90-percent low flow) climatic conditions and average 

water-use conditions (1989–98), upper Charles River basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

3. Base flow under average climatic conditions and no water-supply or 

wastewater pumping, upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

4. Base flow under dry (90-percent low flow) climatic conditions and no watersupply or wastewater pumping, upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

5. Water withdrawals in the upper Charles River basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

6. Population characteristics of towns with greater than 10,000,000 square feet of 

area within the study area, upper Charles River basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

7. Water-discharge stresses as used in the optimization analysis for the upper 

Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

8. Water withdrawals and regulatory limits by town, upper Charles River basin . . . . . . . . . . . . .17

9. Model calculated steady-state water levels and observed average water levels, 

upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

10. Modeled steady-state base flow and observed base flow, upper Charles River 

basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

11. Constraint points, upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

12. Summary of water-resource management scenarios analyzed, upper Charles 

River basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

13. Base flow under Scenario 1A, average climatic conditions and maximum 

permitted pumping, upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31

14. Base flow under Scenario 1B, dry (90-percent low flow) climatic conditions and 

maximum permitted pumping, upper Charles River basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

15. Low flows at the 10 constraint points under different pumping stresses, upper 

Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

16. Pumping rates to maximize summertime base flow, Scenario 2B, average 

climatic conditions, no proposed or hypothetical stresses, upper Charles River 

basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

17. Base flow under optimal pumping to maximize base flow, Scenario 2B, average

climatic conditions, no proposed or hypothetical stresses, upper Charles River 

basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35

18. Base flow with all wells including proposed municipal supply wells pumping at 

maximum permitted rates, Scenario 3A, average climatic conditions, upper 

Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36

19. Base flow maximized under optimal pumping with proposed wells active, 

Scenario 3C, average climatic conditions, towns receive average (1989–98) 

water supplies, upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37

20. Base flow maximized under optimal pumping with proposed wells active, 

Scenario 3D, dry (90-percent low flow) conditions, upper Charles River basin. . . . . . . . . . . . .38

21. Base flow with Holliston wastewater routed to the Charles River Pollution 

Control District treatment plant, Scenario 4A, average climatic conditions, 

average withdrawals (1989–98) and return stresses (except for Holliston 

wastewater), upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39

22. Base flow with Holliston wastewater routed to local recharge basins, Scenario 4B, 

average climatic conditions, average withdrawals (1989–98) and return stresses 

(except for Holliston wastewater), upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . .40
vi 

23. Base flow with Bellingham wastewater routed to BL-WRP recharge basin, 

Scenario 4C, average climatic conditions, average withdrawals (1989–98) and 

return stresses (except for Bellingham wastewater), upper Charles River basin. . . . . . . . . . 42

24. Response coefficients for hypothetical recharge basins west of Miscoe Brook in 

Franklin, upper Charles River basin, eastern Massachusetts. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

25. Optimal wastewater-flow schedule, Miscoe Brook hypothetical recharge-discharge 

facility, Scenario 4D, Franklin, upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

26. Pumping rates for wastewater discharge and recharge at Charles River 

Pollution Control District to optimize base flow, Scenario 4E, upper Charles 

River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

27. Base-flow changes at outflow constraint point CR4 resulting from the addition 

of a recharge basin to the Charles River Pollution Control District, Scenario 4E, 

upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

28. Base-flow changes at CR3 resulting from relocating Charles River Pollution 

Control District effluent upstream, Scenario 5A, upper Charles River basin. . . . . . . . . . . . . . . 47

29. Base flow under water conservation measures, Scenario 7A, municipal water 

use limited to 90 percent of average during June through September, average 

climatic conditions (1989–98), upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

30. Base flow at constraint points under basin-wide water-supply sharing, Scenario 8A, 

average climatic conditions, each town receives its average water supplies 

(1989–98), upper Charles River basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

31. Base flow at constraint points under dry conditions (90-percent low flow) and 

basin-wide water-supply sharing, Scenario 8B, each town receives its average 

water supplies (1989–98) , upper Charles River basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

32. Base flow under direct drinking-water discharge to streams, Scenario 9A, each

town receives its average water supplies (1989–98), average climatic conditions, 

upper Charles River basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

33. Benefits of potential water-management actions, upper Charles River basin. . . . . . . . . . . . . 53
 vii

Conversion Factors, Datums, and Abbreviations

Vertical coordinate information is referenced to the North American Vertical Datum of 1929 

(NGVD 29).

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

ABF Aquatic Base Flow

CRPCD Charles River Pollution Control District Treatment Facility

CRWA Charles River Watershed Association

EOEA Massachusetts Executive Office of Environmental Affairs

MADEM Massachusetts Department of Environmental Management

MADEP Massachusetts Department of Environmental Protection

MOVE.1 Maintenance of Variance Extension, type 1, method of correlation

MODFLOW Modular Three-Dimensional Finite-Difference Ground-Water Flow Model

MWRA Massachusetts Water Resources Authority

PCG2 Preconditioned Conjugate-Gradient 2

TAC Technical Advisory Committee

USFWS U.S. Fish and Wildlife Service

USGS U.S. Geological Survey

WMA Water Management Act 

Multiply By To obtain

acre 0.004047 square kilometer (km2)

acre-foot (acre-ft) 1,233.5 cubic meter (m3)

cubic foot per second (ft3/s) 0.0283 cubic meter per second (cm/s)

cubic foot per second per square mile 

[(ft3/s)/mi2] 0.01093

cubic meter per second per square 

kilometer (m3/s/km2)

foot (ft) 0.3048 meter (m)

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

gallons per minute (gal/min) 0.0038 cubic meters per minute (m3/min)

inch (in.) 2.54 centimeter (cm)

inch per year (in/yr) 2.54 centimeter per year (cm/yr)

mile (mi) 1.609 kilometer (km)

square mile (mi2) 2.590 square kilometer (km2)

square foot (ft2) 0.0929 square meter (m2)

Evaluation of Strategies for Balancing Water 

Use and Streamflow Reductions in the Upper 

Charles River Basin, Eastern Massachusetts

By Jack R. Eggleston

Abstract

The upper Charles River basin, located 30 miles southwest 

of Boston, Massachusetts, is experiencing water shortages 

during the summer. Towns in the basin have instituted 

water-conservation programs and water-use bans to reduce 

summertime water use. During July through October, 

streamflow in the Charles River and its tributaries regularly 

falls below 0.50 cubic foot per second per square mile, the 

minimum streamflow used by the U.S. Fish and Wildlife 

Service as its Aquatic Base Flow standard for maintaining 

healthy freshwater ecosystems. 

To examine how human water use could be changed to 

mitigate these water shortages, a numerical ground-water flow 

model was modified and used in conjunction with response 

coefficients and optimization techniques. Streamflows at 10 

locations on the Charles River and its tributaries were 

determined under various water-use scenarios and climatic 

conditions. A variety of engineered solutions to the water 

shortages were examined for their ability to increase water 

supplies and summertime streamflows. 

Results indicate that although human water use contributes 

to the problem of low summertime streamflows, human water 

use is not the only, or even the primary, cause of low flows in 

the basin. The lowest summertime streamflows increase by 12 

percent but remain below the Aquatic Base Flow standard when 

all public water-supply pumpage and wastewater flows in the 

basin are eliminated in a simulation under average climatic 

conditions. Under dry climatic conditions, the same measures 

increase the lowest average monthly streamflow by 95 percent 

but do not increase it above the Aquatic Base Flow standard.

The most promising water-management strategies to 

increase streamflows and water supplies, based on the study 

results, include wastewater recharge to the aquifer, altered 

management of pumping well schedules, regional water-supply 

sharing, and water conservation. In a scenario that simulated 

towns sharing water supplies, streamflow in the Charles River 

as it exits the basin increased by 18 percent during July through 

September and an excess water-supply capacity of 13.4 cubic 

feet per second, above and beyond average use, would be 

available to all towns in the basin. These study results could 

help water suppliers and regulators evaluate strategies for 

balancing ground-water development and streamflow 

reductions in the basin.

Introduction

The upper Charles River basin, which is 30 mi southwest 

of Boston (fig. 1), is undergoing increasing demand on its water 

resources caused by population growth of 15 percent from 1990 

to 2000. As populations have grown, communities in the basin 

have withdrawn more ground water, lowering pond levels and 

depleting streamflow in the upper Charles River and its 

tributaries (Bouck, 1998). Future water demands are likely to 

increase as development continues. The hydrologic system will 

be further altered if proposed water projects, including new 

supply wells, a surface-water withdrawal, and sewers, are built. 

Streamflow in the summertime throughout the basin 

commonly falls below the Aquatic Base Flow (ABF) criteria for 

a healthy aquatic ecosystem (U.S. Fish and Wildlife Service, 

1981). During times of low rainfall, streamflow is even lower 

and some smaller tributary streams go dry. Ecological concerns 

about low streamflow and poor water quality in the upper 

Charles River basin are associated with the perception that 

human influences, primarily ground-water pumping and 

land-use change, are to blame for the water problems. 

Water managers for towns in the upper Charles River basin 

have increased pumping, imposed water restrictions, and in 

some instances trucked in water from outside the basin, to 

meet increasing water demands. Compared to water imported 

from outside the basin, water from local supplies is typically 

less expensive and is not affected by the same regulatory 

constraints. There currently (2003) is little sharing of drinkingwater supplies between towns, and each town in the basin 

obtains the bulk of its water from within its town boundaries. 

The lack of a regional water-management approach is likely 

contributing to water-supply shortages in many towns, 

including Milford, Norfolk, Holliston, and Franklin (fig. 1). 
2 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

42o00'

42o30'

73o

00' 72o

00'

71o

00'

70o

00'

41o

30'

CAPE COD 

BAY

ATLANTIC OCEAN

NANTUCKET

SOUND

AREA SHOWN

MAJOR BASIN BOUNDARIES

MASSACHUSETTS

0 50 KILOMETERS

0 50 MILES

From U.S. Geological Survey and MassGIS data sources, Geographic Projection, Spheroid GRS 1980, Datum NAD 83 

0

0 1 2 

1 2 MILES

3 KILOMETERS

71o22'30"

42o

15'

00"

42o

07'

30"

71o

30'00"

Echo 

Lake Lake 

Winthrop

Populatic

Pond

Kingsbury

Pond

Milford 

Pond Louisa 

Lake

Box 

Pond

Lake 

Pearl

City Mills

Pond

Spring 

Pond

Charles River

Charles River

Charles

Mine Brook

Beaver Brook

Charles River

Stall Brook

Hopping Brook

Chicken Brook

Jar Brook

Dopping Brook

Dirty Meadow Brook

Bogastow Brook

Mill River

Eagle Brook

Miscoe Brook

TOWN BOUNDARY

TILL AND BEDROCK

STRATIFIED GLACIAL DEPOSITS

MEDWAY

HOLLISTON

MILFORD

BELLINGHAM

FRANKLIN

HOPKINTON

MILLIS

NORFOLK

WRENTHAM

Bush

Pond

Lake 

Archer

Great Black Swamp

EXPLANATION

Shepards Brook

Miller Brook

Cress Brook

SHERBORN

HOPEDALEHOPEDALE HOPEDALE

SURFACE WATER 

MENDON

MILFORD

ASHLAND

WRENTHAM

Charles

River

River

Figure 1. Location and surficial geology of the study area, upper Charles River basin, eastern Massachusetts.
Basin Hydrology 3

Purpose and Scope

This project was initiated by the U.S. Geological 

Survey (USGS) and the Massachusetts Executive Office of 

Environmental Affairs (EOEA) to improve understanding of 

the hydrologic system and explore strategies for mitigating 

water shortages in the upper Charles River basin. The study was 

carried out during 2002–03. This report demonstrates how 

optimization methods and hydrologic response coefficients can 

be used to solve complex water-resource management problems 

involving competing needs for water from multiple users and 

sensitive aquatic ecosystems. The methods and analysis 

presented should provide new hydrologic analysis tools for 

water-resource managers and regulators. To address the issues 

of water-supply shortages and low streamflow in the upper 

Charles basin, this report includes hydrologic analysis of 

regional water-management scenarios under dry climatic 

conditions and a variety of engineered modifications to human 

water use in the basin.

In this study, a numerical flow model that was developed 

by DeSimone and others (2002) using the USGS ground-water 

modeling code MODFLOW-2000 (Harbaugh and others, 

2000), was updated and modified. Hydrologic response 

coefficients derived from the updated numerical ground-water 

model were used to simulate the combined stream-aquifer 

system and to analyze a variety of water-resource management 

scenarios. Optimization methods were used for more complex 

scenarios to determine the best management practices for 

meeting water demand and minimum streamflow requirements.

Previous Investigations

Bouck (1998) provides a summary of water-supply issues 

faced by towns in the basin. In a comprehensive hydrologic 

study, DeSimone and others (2002) developed a numerical 

model to simulate ground-water flow and stream base flow in 

the upper Charles River basin. The comprehensive hydrologic 

study included compilation and analysis of data describing 

climate, land use, streamflow, base flow, ground-water levels, 

pond levels, water withdrawals, water use, septic discharge, 

wastewater discharge, hydrogeology, and interactions between 

ground water and surface water. The numerical flow model 

developed in that study is modified for use in this study. 

Joint simulation-optimization methods have previously 

been used to analyze water-resource management alternatives 

for shallow stream-aquifer systems (Reichard, 1995; Barlow 

and Dickerman, 2001; Barlow and others, 2003). An extensive 

body of literature describes other applications of optimization 

methods to water-resource management (for example, 

Gorelick, 1983; Mays, 1997; Heathcote, 1998; Nishikawa, 

1998). The hydrologic study of the upper Charles River basin 

by DeSimone and others (2002) included an optimization 

analysis of a small portion of the study area. This study extends 

the optimization study to the entire basin and addresses a greater 

variety of water-resource management questions.

Description of Study Area

The upper Charles River basin is 30 mi southwest of 

Boston, MA, and has an area of 105 mi2

 consisting mostly of 

suburban communities (fig. 1). Thirteen towns (Ashland, 

Bellingham, Franklin, Holliston, Hopedale, Hopkinton, 

Milford, Medway, Mendon, Millis, Norfolk, Sherborn, and 

Wrentham) are at least partially within the study area. Seven of 

the towns (Bellingham, Franklin, Holliston, Medford, Medway, 

Norfolk, and Wrentham) withdraw ground water within the 

basin for municipal drinking-water supplies. The population of 

the study area increased 15 percent, from approximately 80,500 

to 93,000, between 1990 and 2000. The basin has moderate 

topographic relief, with land elevations ranging from about 120 

to 550 ft (NGVD29). More descriptive information about the 

basin can be found in DeSimone and others (2002). 

Acknowledgments

The author thanks the members of this project’s technical 

advisory committee, composed of town water officials, 

engineering consultants, conservation group members, state 

environmental officials, and USGS employees, who met 

regularly and provided assistance to this project. In addition, 

Nigel Pickering of the Charles River Watershed Association 

(CRWA) provided code for constructing optimization 

equations and assisted with analysis of land use and recharge. 

Town water officials, particularly Donald DiMartino of 

Bellingham, William Fitzgerald of Franklin, Steven Davis of 

Walpole, and Carolyn Dykema and Jane Pierce of Holliston, 

provided useful information about town water management. 

Leslie DeSimone of the USGS generously helped with 

modeling, analysis, and logistics of the project. Donald Walter 

of the USGS provided valuable assistance with the numerical 

flow model. This report was improved by the careful attention 

of reviewers. 

Basin Hydrology

Mean monthly precipitation in the upper Charles River 

basin shows little seasonal variation (fig. 2) based on data from 

a climate station in Medway (fig. 3). From 1957 to 2000, 

precipitation in the basin averaged 46.6 in/yr, and daily average 

temperatures ranged from 24.5°F in January to 70.5°F in July, 

also based on Medway climate data (National Oceanic and 

Atmospheric Administration, 2001). 
4 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

10.0

0.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC.

0.0

2.0

4.0

6.0

8.0

PRECIPITATION

TEMPERATURE

MEAN MONTHLY TEMPERATURE, IN DEGREES FAHRENHEIT

MEAN MONTHLY PRECIPITATION, IN INCHES

Figure 2. Monthly average precipitation (1957–2000) and temperature (National Oceanic and 

Atmospheric Administration, 2001) for climate station 199316 in Medway, eastern Massachusetts.

Ground Water 

Ground water is the primary source of drinking water for 

towns in the basin. Aquifers in the study area comprise thin 

discontinuous sand and gravel units, primarily stratified glacial 

deposits (fig. 1). The aquifers, which occupy shallow valleys 

that trend northwest to southeast, are generally less than 70 ft 

thick with a maximum thickness of 130 ft. The aquifers are 

mostly unconfined and overlie bedrock or low-permeability 

glacial till. Hydraulic conductivity of the aquifers is high, 

ranging from 68 to 247 ft/d (DeSimone and others, 2002, 

table 1). The streams and underlying aquifers in the upper 

Charles River basin are in close connection and form a system 

that supplies nearly all drinking water to towns and residents. 

The high conductivity of aquifers and streambeds allows rapid 

exchange of water between aquifers and streams, and thus 

streamflow responds quickly to ground-water pumping. The 

aquifers have low storage capacity because they are thin, 

unconfined, highly conductive, and sparsely distributed.

Input to the ground-water system is primarily from 

recharging precipitation, with minor contributions from septic 

systems and recharging streams. A small amount of runoff 

infiltrates to ground water through detention basins, which are 

generally required in new residential developments. No 

wastewater recharge facilities, either infiltration basins or 

injection wells, are in the basin, but several such projects have 

been proposed. In a few areas, streams recharge to the aquifers; 

but overall, stream leakage into aquifers is only 5 percent of 

ground-water discharge to streams (DeSimone and others 

2002). 

Streamflow

The northeast portion of the study area is drained by 

Bogastow Brook and its tributaries, and the rest of the study 

area is drained by the Charles River and its tributaries (fig. 1). 

Bogastow Brook flows into the Charles River downstream of 

the study area. The only actively managed surface-water 

reservoir is Echo Lake at the headwaters of the Charles River in 

Milford and Hopkinton. During winter and spring, Echo Lake 

receives water pumped from the Charles River just upstream of 

Milford Pond, a dammed lake on the Charles River about 3 mi 

downstream from Echo Lake. During summer months water is 

drawn from Echo Lake for Milford’s water supplies. Other 

dams in the study area create impoundments that are not 

actively managed for water supply. An Army Corp of Engineers 

(1994) inventory of dams lists 17 dams in the basin that are at 

least 6 ft high and impound at least 50 acre-ft of water.
Basin Hydrology 5

Figure 3. Streamflow measurement sites and constraint points, upper Charles River basin, eastern Massachusetts. (Modified from

fig. 7, DeSimone and others, 2002.)

From U.S. Geological Survey and MassGIS data sources, Geographic Projection, Spheroid GRS 1980, Datum NAD 83

0

0 1 2

1 2 MILES

3 KILOMETERS

71o22'30" 42o

15'

00"

42o

07'

30"

71o

30'00"

TILL AND BEDROCK

STRATIFIED GLACIAL DEPOSITS

STREAMFLOW-MEASUREMENT SITE

AND IDENTIFIER

REAL-TIME STREAMFLOW-MEASUREMENT

SITE AND IDENTIFIER

CONSTRAINT POINT AND IDENTIFIER

CR4

CR4

CR3

CR2 HB2

HB1

CR1

MB1

MB2

BB1

MR1

WEATHER STATION AND IDENTIFIER

EXPLANATION

Beaver Brook

Charles River

Charles River

Hopping B

S

rook

tall Brook

Charles River

M iscoe Brook

Bogastow

Bro ok

Dirty Mead owBrook

Dopping

Brook

Jar Brook

Chicken Brook

Cress Brook

Ea gle Brook

Miller Brook

Shepards Brook

Charles River

Mill

River

Great Black Swamp

Mine Brook

Dix Brook

Echo

Lake Lake

Winthrop

City Mills

Pond

Milford

Pond

Louisa

Lake

Populatic

Pond

Kingsbury

Pond

Box

Pond

Lake

Pearl

Spring

Pond

Bush

Pond

Lake

Archer

01103140

01103393

01103300

01103305

01103120 01103280 01103217

01103240

01103206

01103235

01103110

01103140

011032056

01103260

01103210

01103225

01103234

011032515

01103292

01103295

01103381

01103386

01103389

01103280

199316

199316
6 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 1. Base flow under average climatic conditions and average water-use conditions (1989–98), upper Charles River basin, eastern 

Massachusetts.

[Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 9.6 10.4 13.3 13.5 9.0 4.1 1.7 1.8 1.7 3.9 6.2 9.4

CR2 42.5 45.0 55.3 54.0 39.3 23.5 12.4 12.6 12.5 21.8 32.3 41.2

CR3 118.8 134.4 174.1 174.9 110.4 62.0 27.9 24.2 22.7 45.5 82.6 115.6

CR4 157.6 167.4 200.4 198.1 146.4 88.4 50.7 51.7 49.8 84.1 120.3 155.1

BB1 38.6 41.1 56.5 56.4 35.4 15.4 5.9 6.2 5.8 14.5 25.3 37.4

HB1 18.3 22.6 31.3 30.5 15.6 4.1 1.0 1.1 1.1 4.1 8.7 17.7

HB2 27.0 33.4 46.3 45.2 23.1 6.1 1.5 1.7 1.7 6.0 12.9 26.2

MB1 19.1 20.9 24.0 23.7 17.9 10.4 5.8 6.0 6.0 10.1 14.0 18.8

MB2 34.6 38.6 46.0 45.7 31.9 18.0 9.2 8.6 8.4 15.6 23.8 33.6

MR1 35.4 38.0 42.5 42.3 33.5 23.2 15.0 14.2 14.0 21.0 27.7 34.6

Base flow per drainage area (ft3/s/mi2)

CR1 0.85 0.93 1.18 1.20 0.80 0.36 0.15 0.16 0.15 0.35 0.55 0.84

CR2 1.67 1.77 2.17 2.13 1.55 .92 .49 .50 .49 .86 1.27 1.62

CR3 1.82 2.06 2.67 2.68 1.69 .95 .43 .37 .35 .70 1.27 1.77

CR4 1.88 2.00 2.39 2.36 1.75 1.05 .61 .62 .59 1.00 1.43 1.85

BB1 1.85 1.98 2.72 2.71 1.70 .74 .29 .30 .28 .70 1.22 1.80

HB1 2.45 3.03 4.20 4.10 2.09 .55 .14 .15 .15 .55 1.17 2.38

HB2 2.45 3.03 4.20 4.10 2.09 .55 .14 .15 .15 .55 1.17 2.38

MB1 1.90 2.08 2.39 2.37 1.78 1.03 .58 .60 .60 1.01 1.40 1.88

MB2 2.17 2.43 2.89 2.88 2.01 1.13 .58 .54 .53 .98 1.50 2.11

MR1 2.21 2.37 2.66 2.65 2.10 1.45 .94 .89 .88 1.32 1.73 2.16

Low streamflow during summer months is a problem 

in the study area. The months of July through September, 

when streamflow is typically at its lowest, are the most critical 

months of concern and are the focus of analysis in this study. 

Some tributary streams go dry during summer months and 

periods of low rainfall. There are no long-term surface-water 

records for the upper Charles River basin, but daily streamflow 

records are available from a streamflow-gaging station in 

Medway (01103280) that was installed in 1997 (fig. 3). In each 

of the four summers (1998–2001) for which records are 

available from the Medway station, streamflow dropped below 

not only the U.S. Fish and Wildlife Service (USFWS) ABF 

standard of 0.50 ft3/s/mi2 but also below the 0.21 ft3/s/mi2

low-flow standard used by the Massachusetts Department of 

Environmental Protection (MADEP) in wastewater-discharge 

and ground-water-withdrawal permits within the Charles River 

basin. In the summers of 1998–2001, daily flow at the Medway 

station had low values of 0.20, 0.03, 0.12, and 0.12 ft3/s/mi2

, 

respectively.

Base flow, rather than streamflow, is the focus of this study 

because base flow is the portion of streamflow originating from 

ground-water discharge to streams. Base flow does not include 

surface runoff and quickflow, the portion of streamflow that 

increases quickly in response to precipitation (Hornberger and 

others, 1998). The numerical flow model computes base flow 

but does not calculate surface runoff or quickflow. Wastewater 

discharge to streams is included in the base-flow numbers in 

this study. For the water year 2000, DeSimone and others 

(2002) estimate that 88 percent of flow in the Charles River is 

base flow and, during periods of drought, the base-flow portion 

is 100 percent if wastewater effluent is not included.

Estimation of Base Flow

Information about average base-flow conditions is needed 

as a starting point for this study’s analysis of water-resource 

management alternatives. The lack of long-term streamflow 

data in the basin requires that base-flow statistics be estimated. 

Because uncertainty associated with base-flow values produced 

by the numerical flow model was high, base-flow statistics were 

estimated by the Maintenance of Variance Extension, type 1 

(MOVE.1) method (Ries and Friesz, 2000). The MOVE.1 

method relates base-flow statistics at stations with relatively 

short-term streamflow records to relatively long-term base-flow 

statistics from nearby stations. Base flow at long-term stations 

is calculated by means of hydrograph separation (DeSimone 

and others, 2002). The same partial-record streamflow data, 
Basin Hydrology 7

long-term data, and averaging weights were used in this study 

as were used by DeSimone and others (2002). Uncertainty in 

the MOVE.1 estimated base-flow values is low and is given in 

table 8 of DeSimone and others (2002). 

Several options for water withdrawal and wastewater 

disposal are analyzed in this study to determine how they 

affect base flow. The response of base flow to pumping and 

wastewater disposal is calculated by the response coefficient 

method. The response coefficient method allows base-flow 

changes caused by pumping and other hydrologic stresses 

to be calculated with linear equations. This method is used 

throughout the study because it gives more reliable results than 

the numerical flow model and because it can easily be 

implemented in conjunction with the optimization analysis.

Two flow statistics, monthly average base flow and 90-

percent duration low flow (base flow exceeded 90 percent of the 

time), were estimated for the streamflow-measurement sites 

shown in fig. 3. The same statistics were then calculated for 

sites where no partial-record streamflow data were available 

by use of equation 1 (Ries and Friesz, 2000).

, (1)

where

Equation 1 was used to estimate flow statistics at 10 constraint 

points (fig. 3), which are locations used to impose minimum 

flow standards in this study.

The values in table 1 show that, under average water use 

and average precipitation conditions, base flow drops to low 

levels during the summer in some streams. Base flow is 

especially low from July to September and on small tributary 

streams. Flow is lower in streams in the northern portion of the 

study area, Hopping Brook (HB1 and HB2) and Bogastow 

Brook (BB1), most likely because the aquifer there is more 

limited in extent and has less ground-water storage available to 

augment summertime base flow. To characterize low-flow 

conditions at a particular location, this study uses the lowest 

monthly flow out of the 12 months. The low monthly flow 

values at the 10 constraint points range from 0.14 ft3/s/mi2

in July on Hopping Brook at HB1 and HB2 to 0.88 ft3/s/mi2

in September on the Mill River at MR1. Taking the lowest 

monthly base flow value from each of the 10 constraint points 

and averaging gives a mean value of 0.41 ft3/s/mi2

. The lowest 

flows at the 10 constraint points all occur either in July or 

September, with 4 points having the lowest flows in July and 

6 points having the lowest flows in September.

The 90-percent duration monthly base-flow values 

represent dry climatic conditions (table 2). Monthly base flow 

has been lower than these values once out of every 10 months 

on average. The lowest average monthly base flow under 

average pumping and dry climatic conditions (90-percent flow 

duration) occurs in September at all 10 constraint points and 

ranges from 0.00 ft3

/s/mi2 on Hopping Brook (HB1 and HB2 ) 

to 0.32 ft3

/s/mi2 on the Mill River (MR1). For all 10 constraint 

points under dry climatic conditions, the lowest monthly flows 

average 0.10 ft3

/s/mi2. 

To examine how human activities affect low-flow 

conditions, base flow under "no-pumping" conditions (tables 3 

and 4) is calculated. The effects of water withdrawals and 

wastewater and septic discharges are subtracted from average 

base flow to arrive at no-pumping base flow. This flow might 

be termed "natural" except that other human influences such as 

dams, land-use changes, infiltration to sewer lines, and 

anthropogenic climatic changes (Huff and Changnon, 1986), 

are still affecting flow. Overall, base flow increases under nopumping conditions, but the change is not uniform, varying 

with month and stream location. The percentage change is 

largest during summer months and for smaller streams. For 

example, at location CR1 on the upper Charles River, August 

monthly base flow increases by 65 percent under no-pumping 

conditions. A few of the constraint points have less flow under 

no-pumping conditions. This occurs in the Mill River (MR1) 

and Hopping Brook (HB2) because these subbasins do not 

receive their normal septic discharge under no-pumping 

conditions.

Under no-pumping conditions and dry climatic conditions 

(90-percent flow duration), Hopping Brook (HB1 and HB2)

is essentially dry (flow less than or equal to 0.02 ft3/s) from 

July through October. Base flow falls below 0.21 ft3/s/mi2

during at least 1 month at 7 of the 10 constraint points (table 4). 

Removing water withdrawals and wastewater and septic 

discharges causes large percentage flow increases in some of 

the tributary streams. For example, at constraint point CR1 

on the upper Charles River, August monthly flow increases by 

500 percent when no-pumping conditions are imposed under 

90-percent low-flow conditions.

There is ongoing discussion by state officials, town 

officials, and conservationists about setting minimum flow 

standards for streams in the upper Charles River basin. 

The MADEP has previously used a low-flow standard of 

0.21 ft3/s/mi2 to regulate wastewater disposal and ground-water 

withdrawals in the upper Charles River basin (Bruce Bouck, 

MADEP, written commun., 2002). The USFWS uses the ABF 

method for New England (U.S. Fish and Wildlife Service, 

1981), to set minimum streamflows for maintaining healthy 

streams downstream of controlled dams. The default ABF 

value, 0.50 ft3/s/mi2, is applied if no streamflow data are 

available. On the basis of streamflow data from the nearest 

long-term flow station on the Charles River at Dover, about 

7 mi downstream from the study area, a more site-specific ABF 

value, calculated as the median of the monthly mean flows for 

August (U.S. Fish and Wildlife Service, 1981), is 0.41 ft3/s/mi2. 

= base-flow statistic at constraint point;

= base-flow statistic at nearby partial-record station;

Aj = drainage area of the constraint point; and

Ai = drainage area of the partial-record station.

Y

ˆ

j Y

ˆ

i

Aj

Ai

= ----

Y

ˆ

j

Y

ˆ

i
8 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 2. Base flow under dry (90-percent low flow) climatic conditions and average water-use conditions (1989–98), upper Charles 

River basin, eastern Massachusetts.

[Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 3.56 4.97 9.63 6.62 4.23 1.41 0.42 0.24 0.21 0.47 1.38 2.63

CR2 21.88 28.01 41.91 31.68 23.25 11.27 4.90 3.61 3.37 5.97 13.22 19.44

CR3 33.79 47.78 80.55 53.94 36.34 14.66 4.73 3.45 3.37 6.02 15.99 25.99

CR4 81.76 104.87 156.25 120.31 86.90 44.73 20.35 14.71 13.94 22.06 49.95 72.67

BB1 13.11 19.34 37.88 25.67 15.11 5.32 1.44 .67 .72 1.71 5.86 11.49

HB1 4.23 6.95 18.95 9.33 5.12 0.66 .09 .05 .03 .13 .86 2.08

HB2 6.26 10.28 28.04 13.80 7.57 0.98 .13 .07 .05 .20 1.27 3.08

MB1 10.32 12.74 19.37 14.42 11.21 4.81 2.11 1.63 1.43 2.48 5.26 7.64

MB2 16.08 21.02 34.82 24.51 18.04 6.72 2.62 1.96 1.81 3.11 6.85 10.91

MR1 21.50 25.60 35.48 28.28 23.16 12.21 6.60 5.45 5.19 7.38 12.31 16.69

Base flow per drainage area (ft3/s/mi2)

CR1 0.32 0.44 0.86 0.59 0.38 0.13 0.04 0.02 0.02 0.04 0.12 0.23

CR2 .86 1.10 1.65 1.25 .91 .44 .19 .14 .13 .23 .52 .76

CR3 .52 .73 1.24 .83 .56 .23 .07 .05 .05 .09 .25 .40

CR4 .98 1.25 1.86 1.44 1.04 .53 .24 .18 .17 .26 .60 .87

BB1 .63 .93 1.82 1.23 .73 .26 .07 .03 .03 .08 .28 .55

HB1 .57 .93 2.54 1.25 .69 .09 .01 .01 .00 .02 .12 .28

HB2 .57 .93 2.54 1.25 .69 .09 .01 .01 .00 .02 .12 .28

MB1 1.03 1.27 1.93 1.44 1.12 .48 .21 .16 .14 .25 .53 .76

MB2 1.01 1.32 2.19 1.54 1.14 .42 .16 .12 .11 .20 .43 .69

MR1 1.34 1.60 2.22 1.77 1.45 .76 .41 .34 .32 .46 .77 1.04

If the median of daily mean flows for August is used to calculate 

the ABF to remove the effects of infrequent storm events, a 

lower flow value of 0.32 ft3/s/mi2

 results (Kulik, 1990; Ries and 

Friesz, 2000). Low-flow standards other than the ABF, such as 

the wetted-perimeter method or R2Cross method could also 

potentially be used to set regulatory flow criteria (Armstrong 

and others, 2001). 

Current average base flow in the basin, shown in table 1, 

falls below even the lowest of these standards, 0.21 ft3

/s/mi2, 

at 3 of the 10 constraint points (CR1, HB1, HB2) from July 

to September. Under dry climatic conditions (90-percent 

flow duration) base flow is at or below 0.21 ft3/s/mi2 on every 

stream but the Mill River (MR1) during August and September 

(table 2). Where streams exit the model, at constraint points 

CR4 and BB1, average September base flow is 0.59 and 

0.28 ft3/s/mi2, respectively, and in dry years (90-percent 

low-flow conditions) is 0.17 and 0.03 ft3/s/mi2.

A potential option for water-resources managers of 

the upper Charles River basin is to maintain base flow 

above a standard such as the ones discussed above. The baseflow numbers in tables 1–4, however, indicate that this will 

require more water than is currently in the streams. For instance, 

under no-pumping conditions and dry climatic conditions 

(90-percent duration flow), base flow at CR4 during September 

averages 0.18 ft3/s/mi2, and in this case the towns receive no 

water supplies.
Basin Hydrology 9

Table 3. Base flow under average climatic conditions and no water-supply or wastewater pumping, upper Charles River basin, eastern 

Massachusetts.

[Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 10.8 11.6 14.3 14.5 10.0 5.0 2.8 2.9 2.8 5.1 7.5 10.7

CR2 43.4 46.1 56.4 55.1 40.8 24.9 13.7 13.9 13.2 22.6 33.2 42.3

CR3 120.4 136.1 175.8 176.6 112.8 63.3 30.4 26.8 24.3 47.2 84.3 117.4

CR4 158.5 168.3 201.3 198.8 148.4 90.6 53.2 54.6 51.0 85.4 121.6 156.4

BB1 39.0 41.6 57.0 56.9 36.0 16.2 6.8 7.1 6.5 15.0 25.8 37.9

HB1 18.2 22.6 31.2 30.4 15.6 4.0 1.0 1.1 1.1 4.1 8.7 17.7

HB2 26.8 33.3 46.1 45.0 22.9 5.9 1.3 1.5 1.5 5.9 12.7 26.1

MB1 20.6 22.4 25.5 25.3 19.6 12.1 7.6 7.8 7.6 11.8 15.6 20.3

MB2 36.3 40.3 47.7 47.4 33.8 20.0 11.3 10.8 10.5 17.7 25.7 35.3

MR1 34.8 37.3 41.8 41.6 33.1 22.9 14.9 14.3 13.9 20.7 27.3 34.1

Base flow per drainage area (ft3/s/mi2)

CR1 0.96 1.03 1.27 1.29 0.89 0.45 0.25 0.26 0.25 0.45 0.66 0.95

CR2 1.71 1.81 2.22 2.17 1.60 .98 .54 .55 .52 .89 1.31 1.66

CR3 1.85 2.09 2.70 2.71 1.73 .97 .47 .41 .37 .72 1.29 1.80

CR4 1.89 2.01 2.40 2.37 1.77 1.08 .63 .65 .61 1.02 1.45 1.87

BB1 1.87 2.00 2.74 2.73 1.73 .78 .33 .34 .31 .72 1.24 1.82

HB1 2.44 3.03 4.19 4.09 2.09 .54 .13 .15 .15 .55 1.17 2.38

HB2 2.43 3.02 4.18 4.08 2.08 .53 .12 .14 .14 .53 1.15 2.36

MB1 2.06 2.23 2.54 2.52 1.95 1.21 .76 .78 .76 1.18 1.55 2.03

MB2 2.29 2.54 3.00 2.99 2.13 1.26 .71 .68 .66 1.11 1.62 2.22

MR1 2.17 2.34 2.62 2.61 2.07 1.43 .93 .90 .87 1.30 1.71 2.14

Water Use and Budget

Water is redistributed within the basin by municipal watersupply and wastewater-disposal systems (fig. 4 and table 5). 

In addition, golf clubs, power plants, farms, businesses, and 

private households withdraw ground water from wells. There is 

little transfer of drinking water across the upper Charles River 

basin boundaries, and net transfer is estimated to be zero 

(DeSimone and others, 2002). Between 1989 and 1998, publicsupply water withdrawals from the sources listed in table 5 

increased by 8 percent from 10.4 to 11.2 ft3

/s and averaged 

10.7 ft3/s for the period. The increase in water use coincides 

with a population increase of 15 percent in the basin from 

1990 to 2000 (DeSimone and others, 2002). Ground-water 

withdrawals vary seasonally, with higher withdrawals in 

the late spring and early summer (fig. 5). Monthly average 

(1989–98) rates for all stresses are given in Appendix 1. In 

the year 2000, 85 percent of the basin’s population had public 

water supply, with the remaining 15 percent on private wells 

(table 6).
10 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 4. Base flow under dry (90-percent low flow) climatic conditions and no water-supply or wastewater pumping, upper Charles 

River basin, eastern Massachusetts.

[Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 4.8 6.2 10.7 7.6 5.3 2.4 1.5 1.4 1.4 1.7 2.7 3.9

CR2 22.8 29.0 43.0 32.7 24.7 12.7 6.2 4.9 4.1 6.7 14.1 20.5

CR3 35.4 49.4 82.3 55.6 38.8 16.0 7.3 6.1 5.0 7.8 17.7 27.8

CR4 82.7 105.7 157.2 121.0 89.0 47.0 22.9 17.7 15.2 23.4 51.3 74.0

BB1 13.5 19.8 38.4 26.1 15.7 6.0 2.3 1.5 1.4 2.3 6.4 11.9

HB1 4.2 6.9 18.9 9.3 5.1 .6 .1 .1 .0 .1 .9 2.1

HB2 6.1 10.1 27.9 13.6 7.4 .8 .0 .0 .0 .1 1.1 2.9

MB1 11.9 14.3 20.9 16.0 12.9 6.6 3.9 3.4 3.1 4.2 6.8 9.2

MB2 17.8 22.7 36.5 26.3 19.9 8.7 4.8 4.1 3.9 5.2 8.7 12.7

MR1 20.9 25.0 34.8 27.6 22.7 11.9 6.6 5.5 5.1 7.1 11.9 16.2

Base flow per drainage area (ft3/s/mi2)

CR1 0.43 0.55 0.95 0.67 0.47 0.21 0.13 0.12 0.12 0.15 0.24 0.35

CR2 .90 1.14 1.69 1.29 .97 .50 .24 .19 .16 .27 .55 .81

CR3 .54 .76 1.26 .85 .60 .24 .11 .09 .08 .12 .27 .43

CR4 .99 1.26 1.87 1.44 1.06 .56 .27 .21 .18 .28 .61 .88

BB1 .65 .95 1.84 1.26 .76 .29 .11 .07 .07 .11 .31 .57

HB1 .56 .93 2.54 1.24 .68 .08 .01 .01 .00 .02 .12 .28

HB2 .55 .92 2.53 1.23 .67 .07 .00 .00 .00 .00 .10 .27

MB1 1.18 1.42 2.08 1.59 1.28 .66 .39 .34 .31 .42 .68 .91

MB2 1.12 1.43 2.30 1.65 1.25 .55 .30 .26 .25 .33 .55 .80

MR1 1.31 1.56 2.18 1.73 1.42 .75 .41 .35 .32 .44 .74 1.01
Basin Hydrology 11

TILL AND BEDROCK

STRATIFIED GLACIAL DEPOSITS

GROUND-WATER OR SURFACE-WATER

 WITHDRAWAL AND IDENTIFIER—The

 identifier ends in "G" for existing

 ground-water withdrawal, "P" for proposed

 or hypothetical, and "S" for surface-water

 withdrawal. See table 5 for details.

CONSTRAINT POINT AND IDENTIFIER

EXPLANATION

0

0 1 2 

1 2 MILES

3 KILOMETERS

Echo 

Lake Lake 

Winthrop

City Mills

Pond

Milford 

Pond

Louisa 

Lake

Populatic

Pond

Kingsbury

Pond

Box 

Pond

Lake 

Pearl

Spring 

Pond

Bush

Pond

Lake 

Archer

Beaver Brook

Charles River

Charles River

Hopping B

S

rook

tall Brook

Charles River

M iscoe Brook

Bogastow

Brook

Dirty Mead owBrook

Dopping

Brook

Jar Brook

Chicken Brook

Cress Brook

Ea gle Brook

Miller Brook

Shepards Brook

Charles River

Mill River

Great Black Swamp

Mine Brook

Dix Brook

71o30'00" 71o

22'30" 42o

15'

00"

42o

07'

30"

From U.S. Geological Survey and MassGIS data sources, Geographic Projection, Spheroid GRS 1980, Datum NAD 83 

HL-02G HL-01P

HL-06G

HL-01G GECC-01S

HL-05G

MD-01G

MD-02G

MD-03G FR-08G

FR-02P

NF-01G

NF-01P

FR-05G

FR-04G

WR-02G

WR-03G

WR-01P

FR-10G

FR-01P

FR-01G

FR-02G

FR-03G FR-06G

FR-07G

MGCC-01G

BL-07G BL-08G

BL-05G BL-12G

NEA-01G,

 02G, 03G

NEA-04G,

 05G

MF-05G

MF-01G

HL-04G

MF-03G

MF-04G

MF-02G

MD-01P

FR-01P

CR4

CR3

HB2 CR2

HB1

CR1

MB1

MB2

BB1

MR1

CR2

Figure 4. Ground-water and surface-water withdrawals analyzed, upper Charles River basin, eastern Massachusetts. (Modified 

from fig. 3, DeSimone and others, 2002.)
12 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 5. Water withdrawals in the upper Charles River basin, eastern Massachusetts.

[Site locations shown in figure 4. Optimization variables: --, Each optimization variable represents a stress value for a particular month and is used in 

optimization formulations. Type: GW, ground water; SW, surface water. Maximum permitted (Zone II) monthly withdrawal: Zone II limits are State-imposed 

maximum withdrawal rates for individual wells. No., number; ft3

/s, cubic foot per second]

Well identifier Town Source name Optimization 

variables Type

Mean annual

withdrawal

1989–98

(ft3

/s)

Maximum permitted

(Zone II) monthly

withdrawal 

(ft3

/s)

Municipal Withdrawals

BL-05G Bellingham Well No. 5 Q--B5 GW 0.30 0.45

BL-07G Bellingham Well No. 7 Q--B7 GW .16 .65

BL-08G Bellingham Well No. 8 Q--B8 GW .42 1.05

BL-12G Bellingham Well No. 12 Q--B9 GW .03 .85

FR-01G Franklin Well No. 1 Q--F1 GW .18 .73

FR-02G Franklin Well No. 2 Q--F2 GW .18 1.11

FR-03G Franklin Well No. 3 Q--F3 GW .47 .50

FR-04G Franklin Well No. 4 Q--F4 GW 1.03 1.42

FR-05G Franklin Well No. 5 Q--F5 GW .26 .77

FR-06G Franklin Well No. 6 Q--F6 GW .53 .82

FR-07G Franklin Well No. 7 Q--F7 GW .44 .90

FR-08G Franklin Well No. 8 Q--F8 GW .47 .40

FR-10G Franklin Well No. 10 Q--FT GW .34 .77

HL-01G Holliston Well No. 1 Lake Winthrop Q--H1 GW .08 .50

HL-02G Holliston Well No. 2 Maple Street Q--H2 GW .09 .48

HL-04G Holliston Well No. 4 Washington Street Q--H4 GW .22 .74

HL-05G Holliston Well No. 5 Central Street Q--H5 GW .69 1.10

HL-06G Holliston Well No. 6 Brook Street Q--H6 GW .70 1.33

MD-01G Medway Well No. 1 Populatic Street Q--D1 GW .64 .59

MD-02G Medway Well No. 2 Oakland Street Q--D2 GW .21 .91

MD-03G Medway Well No. 3 Village Street Q--D3 GW .52 .93

MF-01G Milford Dilla St. wells 1 and 2 Q--M1, 

Q--M2

GW .02 1.05

MF-02G Milford Clark Island wellfield Q--M6 GW .66 1.24

MF-03G, -04G, -05G Milford Godfrey Brook wells Q--M3, 

Q--M4, 

Q--M5

GW .56 1.22

NF-01G Norfolk Well No. 1 Gold Street Q--N1 GW .38 .67

WR-02G Wrentham Well No. 2 Q--W2 GW .49 1.11

WR-03G Wrentham Well No. 3 Q--W3 GW .65 1.47

Large Nonmunicipal Withdrawals

NEA-01G, -02G, -03G Bellingham Northeast Energy Association 

wells No. 1, 2, 3

Q--B1 GW 0.83 11.02

NEA-04G, -05G Bellingham Northeast Energy Association 

wells 4 and 5

Q--B4 GW .02 11.02

GECC-01S Holliston Glen Ellen Country Club Q--HG SW .06 .25

MGCC-01G Holliston Maplegate Country Club well Q--HM GW .05 .23
Basin Hydrology 13

1Maximum permitted withdrawal rate includes Northeast Energy Association wells No. 1 through 5.

Proposed or Hypothetical Withdrawals

FR-01P Franklin Well No. 11 Q--FE GW -- 0.72

FR-02P Franklin Populatic Pond well Q--FP GW -- .47

HL-01P Holliston Well No. 7 Q--H7 GW -- .86

MD-01P Medway Proposed well Q--DP GW -- .43

NF-01P Norfolk Mill River well Q--NP GW -- 1.08

WR-01P Wrentham Proposed well Q--W1 GW -- 1.01

Table 5. Water withdrawals in the upper Charles River basin, eastern Massachusetts.—Continued

[Site locations shown in figure 4. Optimization variables: --, Each optimization variable represents a stress value for a particular month and is used in 

optimization formulations. Type: GW, ground water; SW, surface water. Maximum permitted (Zone II) monthly withdrawal: Zone II limits are State-imposed 

maximum withdrawal rates for individual wells. No., number; ft3

/s, cubic foot per second]

Well identifier Town Source name Optimization 

variables Type

Mean annual

withdrawal

1989–98

(ft3

/s)

Maximum permitted

(Zone II) monthly

withdrawal 

(ft3/s)

J F MA MJ J A S OND

4

8

12

16

20

0

FLOW, IN CUBIC FEET PER SECOND

MONTH

TOTAL MUNICIPAL WATER WITHDRAWALS

WASTEWATER DISCHARGES FROM THE CHARLES RIVER 

POLLUTION CONTROL DISTRICT FACILITY

WASTEWATER DISCHARGES FROM THE MILFORD TREATMENT FACILITY

EXPLANATION

Figure 5. Average monthly municipal water withdrawals (1989–98) and wastewater discharges in 

the upper Charles River basin, eastern Massachusetts. (Modified from fig. 5, DeSimone and others, 

2002.)
14 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 6. Population characteristics of towns with greater than 10,000,000 square feet of area within the study area, upper Charles River

basin, eastern Massachusetts.

[Town locations shown in figure 1. Adapted from table 3 of DeSimone and others, 2002]

Town

Proportion 

of town in 

study area 

(in percent)

Total population in basin Total population on public water

(in percent)

Total population on public sewer

(in percent)

1990 2000 1990 2000 1990 2000

Bellingham 52 14,877 15,314 96 96 5 29

Franklin 91 22,095 29,560 76 80 51 61

Holliston 100 12,926 13,801 97 98 0 0

Medway 100 9,931 12,448 79 73 37 45

Milford 86 25,355 26,799 99 94 75 80

Millis 46 7,613 7,902 85 85 40 60

Norfolk 31 9,270 10,460 40 58 0 0

Wrentham 18 9,006 10,554 80 80 0 0

Total 111,073 126,838 85 85 34 43

Wastewater is discharged at sewage treatment plants (38 

percent), infiltrated to aquifers through private septic discharge 

(52 percent), or lost to evapotranspiration (10 percent); these 

percentages are based on annual average estimates. Private 

septic systems are widely distributed in the basin. Two facilities 

in the basin discharge treated wastewater to the Charles River: 

the Milford Water Treatment Facility (MTF), which serves 

Milford, and the Charles River Pollution Control District 

facility (CRPCD), which serves Bellingham, Franklin, 

Medway, and Millis (fig. 6). The greatest monthly wastewater 

discharge is in April and the smallest is in August (fig. 5). 

Wastewater discharge from the two facilities averages 11.5 ft3

/s 

annually. At the MTF, annual wastewater flow equals 75 

percent of base flow coming from upstream in the Charles 

River.

 In 2000, 43 percent of the basin’s population had sewer 

service, with the remaining 57 percent on private septic disposal 

(table 6). Details on wastewater returns for existing conditions 

and hypothetical scenarios are given in table 7.

Consumptive loss, that portion of water supply lost to 

evapotranspiration, averages 10 percent annually in New 

England (Solley and others, 1998, table 1) and is highest during 

summer months. Monthly consumptive use in the study area 

may rise as high as 42 percent in July; this estimate is based 

on differences between pumping in March (9.4 ft3/s) and July 

(13.4 ft3/s) (fig. 5) and an assumption that the additional 

pumped water is for highly consumptive uses such as filling 

swimming pools, washing cars, and gardening. 

All drinking-water withdrawals are subject to daily 

maximum pumping limits established by MADEP and referred 

to as "Zone II" limits. Regulation also comes from the 

Massachusetts Watershed Management Act (WMA), which 

covers water withdrawals of more than 100,000 gal/d and 

sets maximum annual rates for combined ground-water and 

surface-water withdrawals. Individual limits (Zone II) on wells 

listed in tables 5 and 8 total 23.8 ft3

/s, whereas the separately 

administered WMA limits total 15.5 ft3

/s. Both of these limits 

are higher than average annual municipal withdrawals of 

10.7 ft3/s (table 8). 

Input to the stream-aquifer system in the study area, 

excluding precipitation that runs off quickly to streams 

or is intercepted by vegetation, is as follows: precipitation, 

154–200 ft3/s (assumes 20–26 in. recharge per year); septic 

return flow, 4.8 ft3

/s; and wastewater discharge to streams, 

11.5 ft3/s. Outflows consist of base-flow discharge from the 

basin, 150.7 ft3/s (from MOVE.1 estimates); ground-water and 

surface water withdrawals, 14.5 ft3

/s; and evapotranspiration 

from wetlands and surface water, 7.7 ft3/s.

Total annual water use is 9 percent of annual recharge, 

calculated on the basis of 1989–98 average total municipal, 

industrial, and private water withdrawals of 14.5 ft3/s and 

annual average recharge of 164.2 ft3/s. On a monthly basis, 

however, this proportion can be much higher (fig. 7). In 

September, withdrawals are 35 percent of average recharge. 

High rates of ground-water withdrawal relative to short-term 

recharge rates are important to the hydrologic budget of the 

basin because the high permeability and low storage capacity of 

aquifers can, within a short time, lead to reduced ground-water 

discharge to streams. 
Basin Hydrology 15

CONSTRAINT POINT AND IDENTIFIER

DIRECT DRINKING WATER 

 DISCHARGE SITE 

 AND IDENTIFIER—Identifier 

 ends in "P" for proposed or hypothetical

WASTEWATER DISCHARGE FACILITY

 AND IDENTIFIER—Identifier 

 ends in "P" for proposed or hypothetical 

STORMWATER RECHARGE FACILITY

 AND IDENTIFIER—Identifier 

 ends in "P" for proposed or hypothetical

WASTEWATER RECHARGE FACILITY

 AND IDENTIFIER—Identifier 

 ends in "P" for proposed or hypothetical 

TILL AND BEDROCK

STRATIFIED 

 GLACIAL DEPOSITS

EXPLANATION

0

0 1 2 

1 2 MILES

3 KILOMETERS

Echo 

Lake Lake 

Winthrop

City Mills

Pond

Milford 

Pond

Louisa 

Lake

Populatic Pond

Kingsbury

Pond

Box 

Pond

Lake 

Pearl

Spring 

Pond

Bush

Pond

Lake 

Archer

Beaver Brook

Charles River

Charles River

Hopping B

S

rook

tall Brook

Charles River

Miscoe Brook

Bogastow

Bro ok

Dirty Mead owBrook

Dopping

Brook

Jar Brook

Chicken Brook

Cress Brook

Ea gle Brook

Miller Brook

Shepards Brook

Charles River

Mill River

Great Black Swamp

Mine Brook

Di x Brook

71o30'00" 71o

22'30" 42o

15'

00"

42o

07'

30"

DWD-MBP

MTF

BL-SWP

CR4

CR3

CR2

HB2

HB1

CR1

MB1

MB2

BB1

MR1

CR4

HL-E1P

From U.S. Geological Survey and MassGIS data sources, Geographic Projection, Spheroid GRS 1980, Datum NAD 83 

DWD-MBP

DWD-HBP

DWD-UCP

CRPCD

MTF

CRPCD-P

WDMBP

WDMP

BL-SWP

FR-W1P

BL-WRP

HL-E1P

HL-E2P

HL-WGP

FR-INP

FR-W2P

FR-W3P

FR-W4P

CR-RBP

Figure 6. Water-return sites analyzed, upper Charles River basin, eastern Massachusetts. Names and abbreviations for facilities 

are given in table 7.
16 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

1Summer months are May–August, winter months are September–April.

Table 7. Water-discharge stresses as used in the optimization analysis for the upper Charles River basin, eastern Massachusetts.

[Site locations shown in figure 6. Optimization variables: --, Each optimization variable represents a stress value for a particular month and is used in 

optimization formulations. Map identifier: P, at the end of the map identifier denotes a proposed or hypothetical facility. CRPCD, Charles River Pollution 

Control District; ft, foot]

Map 

identifier Town Source name Optimizationvariables Status

Annual

average flow

(1989–98)

Wastewater Direct Discharge to Streams

WDMP Bellingham Bellingham proposed wastewater plant W--BL -- --

CRPCD Medway CRPCD W--CR Existing 6.07

CRPCD-P Medway CRPCD upstream proposed discharge point W--CP -- --

MTF Milford Milford wastewater-treatment plant W--MF Existing 5.41

WDMBP Franklin Miscoe Brook hypothetical recharge site W--FM -- --

Drinking Water (DW) Direct Discharge to Streams

DWD-UCP Milford DW discharge to upper Charles River D--CR -- --

DWD-HBP Holliston DW discharge to upper Hopping Brook D--HB -- --

DWD-MBP Franklin DW discharge to upper Miscoe Brook D--MB -- --

Wastewater (WW) Recharge to Aquifers (infiltration basins or injection wells)

FR-INP Franklin Franklin WW injection well Q--FI -- --

FR-W4P Franklin WW recharge basin 200 ft southwest of Miscoe Brook W--M4 -- --

FR-W3P Franklin WW recharge basin 894 ft southwest of Miscoe Brook W--M3 -- --

FR-W2P Franklin WW recharge basin 1,720 ft southwest of Miscoe Brook W--M2 -- --

FR-W1P Franklin WW recharge basin 2,608 ft southwest of Miscoe Brook W--M1 -- --

HL-WGP Holliston Holliston–Gorwin Drive site W--HG -- --

HL-E1P Holliston Holliston–EHIP-1 Site W--H1 -- --

HL-E2P Holliston Holliston–EHIP-2 Site W--H2 -- --

BL-WRP Bellingham Bellingham proposed WW recharge facility Q--BR -- --

CR-RBP Medway WW recharge at CRPCD W--C1 -- --

Storm Water Recharge to Aquifers 

BL-SWP Bellingham Bellingham Proposed Recharge Facility–Maple Street 

BL-02I

Q--BS -- --

Town Wastewater Discharge (combined septic and wastewater discharge in basin)1

- Bellingham Bellingham summer wastewater return R--BS Existing 0.42

- Bellingham Bellingham winter wastewater return R--BW Existing .49

- Franklin Franklin summer wastewater return R--FS Existing 1.63

- Franklin Franklin winter wastewater return R--FW Existing 2.66

- Holliston Holliston summer wastewater return R--HS Existing .75

- Holliston Holliston winter wastewater return R--HW Existing 1.03

- Medway Medway summer wastewater return R--DS Existing .52

- Medway Medway winter wastewater return R--DW Existing .85

- Milford Milford summer wastewater return R--MS Existing .39

- Milford Milford winter wastewater return R--MW Existing .86

- Norfolk Norfolk summer wastewater return R--NS Existing .15

- Norfolk Norfolk winter wastewater return R--NW Existing .23

- Wrentham Wrentham summer wastewater return R--WS Existing .45

- Wrentham Wrentham winter wastewater return R--WW Existing .69
Basin Hydrology 17

Table 8. Water withdrawals and regulatory limits by town, upper Charles River basin, eastern Massachusetts.

[Town locations shown in figure 1. Total monthly zone II limits: Zone II limits are State-imposed withdrawal rates for individual wells. Annual WMA limits:

WMA, Watershed Management Act, WMA limits are State-imposed maximum withdrawal rates for a group of water sources controlled by a water supplier. ft3/s, 

cubic foot per second; Mgal/d, million gallons per day]

Town

Average yearly withdrawals,

1989–98 Total monthly zone II limits Annual WMA limits

(Mgal/d) (ft3/s) (Mgal/d) (ft3/s) (Mgal/d) (ft3/s)

Bellingham 0.6 0.9 1.9 3.0 1.4 2.1

Franklin 2.7 3.9 4.8 7.4 4.1 6.3

Holliston 1.2 1.8 2.7 4.1 1.1 1.8

Medway .9 1.4 1.6 2.4 .7 1.1

Milford .1 1.3 2.3 3.5 1.4 2.2

Norfolk .2 .4 .4 .7 .4 .6

Wrentham .7 1.1 1.7 2.6 .9 1.4

Totals 6.5 10.7 15.4 23.8 10.0 15.5

5%

4%

3% 4%

6%

14% 31%

32%

35%

19% 7% 5%

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC.

TOTAL WATER WITHDRAWALS, IN CUBIC FEET PER SECOND

0

50

100

150

200

250

300

350

400

RECHARGE TO BASIN, IN CUBIC FEET PER SECOND

WITHDRAWALS

RECHARGE

MONTH

Figure 7. Monthly average recharge and withdrawals (1989–98), upper Charles River basin, eastern Massachusetts. 

Numbers at top of columns are total withdrawals in basin as a percentage of recharge. Recharge values are those 

used in the transient numerical model under average climatic conditions.
18 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Modifications to the Original 

Flow Model

The numerical flow model developed by DeSimone and 

others (2002) was modified for use in this study. The modified 

numerical model has similar grid dimensions as the original 

model, with 2 layers, 420 rows, 325 columns, uniformly spaced 

cells 200 ft on a side, and grid axes coincident with north-south 

and east-west directions (fig. 8). The model cells are inactive 

over about 50 percent of the study area, where bedrock or till 

outcrops or where the sand and gravel deposits are thin or 

absent.

Modifications made to the original model include 

combining active cells in the east and west models to form a 

single model, altering the recharge array, increasing aquifer 

thickness in some areas, and changing aquifer and stream 

stresses. Once the modifications to the original model were 

completed, simulation results were compared to the calibration 

criteria documented in DeSimone and others (2002). A 

sensitivity analysis was not performed because changes to the 

model were not substantial enough to warrant it.

Combining East and West Models

The original numerical flow model (DeSimone and others, 

2002) separated the upper Charles River basin into east and 

west models to facilitate a numerical solution to the groundwater flow equations. In this study the two models were joined 

to simplify analysis of regional scenarios. There is no groundwater connection between the east and west sides of the 

combined model, only a surface-water connection through the 

Charles River. In addition to combining input files, stream 

segments were renumbered and the Preconditioned ConjugateGradient 2 (PCG2) package (Hill, 1990) was specified for 

solving linear equation systems.

Modifications to Model Parameters and 

Boundaries

To address numerical instabilities, stream-stage elevations 

and conductance values were changed in a number of stream 

segments. Stream stage was modified in approximately 20 cells 

to reduce abrupt changes in elevation. Streambed conductance 

was modified in the vicinity of Lake Pearl to allow the model to 

converge and to improve the simulated match to observed water 

levels. The number of stream cells crossing Lake Pearl was 

increased to better simulate flow between the lake and 

underlying aquifer and remove numerical instabilities in that 

area. Other changes included adding three stream segments to 

simulate discharge of wastewater effluent directly to streams. 

Numerical instabilities in the combined model were 

caused by model cells going dry, particularly near boundaries of 

inactive cells and during periods of low recharge. To prevent 

them from going dry, a large number of cells (5,421 of 19,592 

active cells) were assigned greater thickness. By trial and error 

it was found that increasing the thickness of cells by 30 ft in 

layer 1 was enough to prevent cells from going dry. 

Modifications to Stresses

Stress periods were modified in the transient model so that 

they coincided with calendar months for a total simulation time 

of 5 years (60 months). Monthly stresses were repeated in each 

year so that the model reached a state of dynamic equilibrium 

by the fifth year. The number of time steps within each stress 

period was varied from 30 to 150 with more time steps used in 

summer months to allow model convergence.

Slight modifications were made to recharge input. Because 

recharge had to be modified to address various management 

scenarios, recharge input to MODFLOW was calculated cell by 

cell by using a FORTRAN program and then was read by 

MODFLOW as an array of constants; the zone and parameter 

functions of MODFLOW2000 were no longer used to specify 

recharge as was done in DeSimone and others (2002). The 

FORTRAN program determined recharge by calculating 

separate contributions to recharge and then summing the 

contributions. Contributions were from infiltrating 

precipitation, septic-system discharge from publicly supplied 

areas that use septic fields, and infiltrating irrigation from 

communities on public water. Subtracted from these 

contributions were monthly consumptive use in areas on private 

wells and septic systems, withdrawals from major supply wells 

in upland areas, and surface-water diversions in the Echo Lake 

subbasin. Consumptive water loss was assumed to reduce septic 

recharge by 30 percent from May through August. The 30-

percent figure comes from assuming that all of a 10-percent 

annual consumptive loss (Solley, 1998, table 1) occurs from 

May through August.

As in the study by DeSimone and others (2002), recharge 

in upland till and bedrock areas was routed to active model 

areas and added to recharge of the edge cells. Recharge rates 

from natural precipitation were assigned by land use. Monthly 

variations in recharge had the same percentages as in the 

original study. A further change was to modify only natural 

precipitation and not septic-system discharge during the model 

calibration process. Several well locations and pumping rates 

were updated with new information. Injection wells were added 

to simulate wastewater-injection wells and recharge galleries, 

which are used for recharging wastewater to the ground-water 

system.
Modifications to the Original Flow Model 19

TILL AND BEDROCK

ACTIVE MODEL AREA BOUNDARY

0

0 1 2 

1 2 MILES

3 KILOMETERS

EXPLANATION

OBSERVATION WELL AND IDENTIFIER

POND-MEASUREMENT SITE 

 AND IDENTIFIER

STREAMFLOW-MEASUREMENT SITE 

 AND IDENTIFIER

MODEL STREAM CELLS

STRATIFIED 

 GLACIAL DEPOSITS

150100150200250300325last

1

50

100

150

200

250

300

350

400

413

last

A6W52

Old Mill Pond

HTW50

HTW49

MYW60

MNW20

MNW19

MYW61

MYW58

MYW59

NNW107

NNW108

NNW109

NNW104

F2W76

F2W77

NNW112

NNW103

NNW106

XUW68

XUW65

XUW64

XUW67

NNW105

F2W74

F2W73 F2W72

F2W68

F2W75 F2W69

F2W67

A6W59

A6W63

HVW40

A6W61

A6W53 A6W64

A6W57

A6W65

MWW51

HTW47

A6W62

Lake

Winthrop

Populatic Pond

Kingsbury Pond

City Mills Pond

Bush Pond

Lake Pearl

Box Pond

Milford Pond

01103389

011033885 01103381

01103393

01103300

01103305

01103295

01103292

01103280

01103110

01103120

01103140

011032053

011032056

01103217

01103240

01103225

01103234

01103260

011032515

MNW17

A6W60

A6W55

01103206

01103235

NNW110

NNW111

01103386

HTW48

HTW51

01103210

A6W63

Box Pond

01103140

COLUMN

ROW

Figure 8. Model grid and locations of streamflow and water-level calibration points, upper Charles River basin, eastern 

Massachusetts.
20 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Model Calibration

Model modifications caused minor changes in simulated 

heads and stream base flow. A complete calibration process was 

not undertaken for the updated model because the hydraulic 

changes were minor. An exception was the southeastern part of 

the model around Lake Pearl, where difficulties getting the 

model to converge indicated that more extensive changes to 

stream properties were needed; consequently, more attention 

was paid to matching simulated and observed heads and base 

flow in this area. The steady-state model and the stress periods 

in the transient model have mass-balance errors of less than 

1 percent. 

Simulated heads were compared to observed heads at the 

same 50 observation points used to calibrate the original model 

(table 9). For the steady-state model, differences between 

observed and model calculated heads averaged -0.4 ft, and 

the mean absolute difference was 2.7 ft. In the original study, 

the mean absolute difference between observed and model 

calculated heads was 2.6 ft for the west model and 2.0 ft for the 

east model (DeSimone and others, 2002). 

Water-level fluctuations over the course of the year in 

the transient model are compared to observed water-level 

fluctuations in figure 9. Water-level fluctuations are shown 

relative to average water levels for the period shown. The 

transient model heads show the same seasonal fluctuations 

exhibited by the original model and match the observed patterns 

of seasonal fluctuation reasonably well. As in the original 

model, the pattern of minimum water levels at some sites shows 

a 1- to 2-month delay relative to observed water levels 

(fig. 9).

Modeled steady-state base flow agrees approximately with 

observed base flow, as it did for the original model (table 10). 

At the model exits (station 01103305 on the Charles River and 

station 01103393 on Bogastow Brook), simulated and observed 

base flow differ by less than 3.0 percent (as compared to less 

than 4 percent in the original model). The mean absolute 

difference between simulated and observed base flow at 23 sites 

was 2.0 ft3

/s; the original model had values of 1.6 ft3/s in the 

west model and 3.4 ft3

/s in the east model. At individual 

measurement sites, mean absolute base-flow residuals ranged 

from 2 to 45 percent of observed values (3 to 60 percent in the 

original model), with larger differences occurring at sites with 

low flow, as in the original model (DeSimone and others, 2002).

Seasonal fluctuations in the updated model are similar to 

those in the original model and agree reasonably well with 

observed fluctuations, with most base-flow values within the 

90-percent confidence intervals for observed base-flow 

estimates (fig. 10). For 23 base-flow calibration points in the 

updated transient model, mean error was -15 percent and mean 

absolute error was 45 percent of observed base flow overall. At 

the Charles River (01103305) and Bogastow Brook (01103393) 

model exit points, mean error averaged 15 percent and 22 

percent, respectively, and mean absolute error averaged 19 

percent and 71 percent. As in the original model, errors were 

larger in July through October, when base flow is lowest. The 

monthly mean absolute residual for all 23 calibration points 

ranged from 3 percent in March to 126 percent in July. The 

large error in the late summer months was mostly due to a 

month delay in the modeled low-flow period. The large 

errors are more pronounced in low-flow months, when a 

comparatively small difference in volumetric flow rate can 

be a significant proportion of observed flow. 

Model Errors and Limitations

The simulated water levels and base-flow values do not 

exactly match observed data. Errors in simulated base flow for 

the summer months are more important than for other months 

because summer streamflow provides a major constraint on 

water management and directly affects solutions to watermanagement problems. Three major differences between 

simulated and observed low base flow (fig. 10) are minimum 

base flow in the model is higher than observed minimum base 

flow; the period of minimum base flow is delayed by about 

1 month in the model (August–October) as compared to 

observed base flow (July–September); and errors, measured in 

percent, are greater for small streams (low base flow) than for 

large streams.

Other errors may exist in the simulated results because 

MODFLOW is designed primarily for simulating ground-water 

flow and not for simulating ground-water/surface-water 

interactions. Model errors may result from the assumption of 

fixed stream stages when the actual stream level is rising and 

falling. Errors may also be caused by the assumption that 

modeled streams go dry if there is not enough ground-water 

discharge, whereas actual streams carry water from surface 

runoff.

The thin and discontinuous aquifers make the numerical 

model sensitive to small changes in hydraulic properties. 

Changing streambed conductance by a small amount (50 

percent for example) can cause cells to go dry in a cascade that 

prevents model convergence. Base-flow values also fluctuate 

due to numerical instabilities. Changing the convergence 

parameters in the PCG2 solver package of the model input by 

50 percent caused base flow to vary by as much as 0.06 ft3/s in 

some cases. 

The model was used only for generating response 

coefficients, which are described in the next section, and not 

for simulating base flow under the various scenarios, because 

model errors were large. After the ground-water model 

was used to generate hydrologic response coefficients, all 

hydrologic simulations were then performed by using the 

response coefficients, rather than by using the simulation 

model. This reduced errors and allowed optimization to be 

easily implemented.
Modifications to the Original Flow Model 21

Table 9. Model-calculated steady-state water levels and observed average water levels, upper Charles River basin, eastern 

Massachusetts.

Well or

pond name

Model cell location Average annual water level (feet relative to NGVD29)

Layer Row Column Model-calculated Observed

Difference 

(calculated

minus observed)

A6W52 1 269 80 225.1 229.7 -4.58

A6W53 1 289 103 214.4 212.7 +1.70

A6W55 1 261 124 209.6 208.5 +1.11

A6W59 1 272 98 216.4 215.5 +.89

A6W60 1 236 130 200.3 205.7 -5.40

A6W61 1 280 94 219.1 219.0 +.11

A6W62 1 223 116 214.6 211.0 +3.65

A6W63 1 285 94 220.4 220.3 +.11

A6W65 1 282 129 206.2 203.2 +3.04

F2W67 1 254 164 178.1 179.0 -.86

F2W72 1 354 200 285.7 286.5 -.83

F2W73 1 355 175 249.2 254.4 -5.13

F2W74 1 381 172 261.6 265.5 -3.88

F2W75 1 291 165 190.5 188.5 +1.97

HTW47 1 114 118 240.2 238.6 +1.61

HVW40 1 247 67 232.3 238.4 -6.02

MWW51 1 200 59 251.2 248.7 +2.49

MNW17 1 193 182 173.0 183.0 -10.05

Box Pond 1 290 88 221.6 221.3 +.25

Milford Pond 1 176 57 267.4 265.7 +1.70

F2W76 1 219 235 128.8 127.1 +1.72

HTW48 1 44 163 203.0 205.2 -2.17

HTW49 1 99 225 141.9 143.8 -1.93

HTW50 1 82 184 165.2 167.1 -1.85

HTW51 1 66 202 150.4 149.0 +1.41

MNW19 1 192 224 141.2 137.7 +3.51

MNW20 1 157 217 138.5 140.7 -2.16

MYW58 1 160 263 141.5 144.7 -3.21

MYW59 1 171 229 138.4 135.6 +2.80

MYW60 1 125 221 138.9 138.5 +.37

MYW61 1 141 243 126.5 131.6 -5.14

NNW103 1 237 256 129.7 130.2 -.49

NNW104 1 218 256 125.2 128.7 -3.48

NNW105 1 283 275 173.7 173.3 +.39

NNW106 1 262 260 148.7 140.4 +8.33

NNW107 1 215 241 128.2 126.5 +1.69

NNW108 1 220 243 128.1 126.9 +1.23

NNW109 1 237 247 130.4 129.3 +1.15

NNW110 1 252 253 135.2 132.5 +2.73

NNW112 1 231 237 130.7 130.8 -.11

XUW65 1 330 268 212.1 205.7 +6.44

XUW67 1 327 287 202.2 195.3 +6.89

XUW68 1 339 288 206.8 204.2 +2.56

Bush 1 282 276 173.7 173.8 -.08

City Mills 1 263 264 149.1 148.8 +.28
22 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Kingsbury 1 237 250 130.4 129.7 +.69

Pearl 1 340 278 206.8 199.6 +7.20

Winthrop 1 116 180 176.4 174.6 +1.82

Old Mill 1 330 278 203.0 194.3 +8.69

Populatic 1 219 239 128.0 127.2 +.85

Table 9. Model-calculated steady-state water levels and observed average water levels, upper Charles River basin, eastern 

Massachusetts.—Continued

Well or

pond name

Model cell location Average annual water level (feet relative to NGVD29)

Layer Row Column Model-calculated Observed

Difference 

(calculated

minus observed)

Table 10. Modeled steady-state base flow and observed base flow, upper Charles River basin, eastern Massachusetts.

[Observed values are from Desimone and others, 2002. MOVE.1 flow values are estimated from streamflow records at the station in question as well as from longterm records at neighboring stations. No., number; ft3/s, cubic foot per second]

 Station No.

Model cell location Average annual base flow (ft3/s)

Layer Row Column Model

calculated

Observed (MOVE.1 estimated) Difference 

(calculated

minus 

observed)

Flow

90-percent confidence interval

High Low

01103110 1 161 61 1.8 2.0 1.2 3.2 -0.1

01103120 1 197 58 7.0 5.6 3.0 10.5 +1.3

01103140 1 271 76 18.4 15.8 10.6 23.7 +2.6

011032056 1 282 131 28.3 24.2 14.7 27.5 +4.1

01103206 1 239 140 31.5 28.8 17.2 34.0 +2.6

01103260 1 210 186 88.3 86.9 21.4 38.9 +1.4

01103210 1 233 137 4.3 7.6 .8 71.7 -3.2

01103217 1 200 136 15.7 14.8 5.8 37.8 +.8

01103225 1 357 167 3.1 2.5 1.5 4.2 +.6

01103234 1 305 192 11.6 13.6 10.2 18.0 -1.9

01103235 1 302 175 13.4 15.0 7.9 28.6 -1.7

01103240 1 232 170 19.9 24.4 14.9 40.0 -4.5

011032515 1 182 176 8.4 8.1 5.5 12.1 +.3

01103280 1 204 226 96.4 91.0 59.7 139.0 +5.4

01103305 1 216 263 132.6 131.4 103.0 168.0 +1.2

01103292 1 326 281 6.5 11.3 8.0 16.0 -4.8

01103295 1 279 275 15.1 18.4 11.9 28.4 -3.3

01103300 1 236 258 23.4 26.0 18.3 37.0 -2.6

01103381 1 85 176 3.5 3.3 2.2 4.9 +.2

01103386 1 66 201 1.4 1.0 .5 2.0 +.4

011033885 1 79 232 1.6 1.6 1.1 2.2 +.0

01103389 1 103 223 18.1 12.8 8.0 20.5 +5.3

01103393 1 132 243 30.9 30.2 20.9 43.6 +.7
Modifications to the Original Flow Model 23

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5

-4

-3

-2

-1

0

1

2

3

4

5

WATER LEVEL, IN FEET

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

Observed

Original model

Revised model

MONTH

HTW44 HTW51

MNW19 MNW20 MYW58

NMW108 NNW109 XUW67

F2W72

A6W53 A6W60 F2W67

Figure 9. Simulated and observed water levels for selected observation wells in the upper Charles River basin, 

eastern Massachusetts. Values are deviations from average (1989–98) water levels. Original model data are from 

figure 20, DeSimone and others, 2002.
24 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

0

20

40

60

80

100

J FMAMJ J ASOND

01103217

0

20

40

60

80

100

J FMAMJ J ASOND

01103295

0

20

40

60

80

100

J FMAMJ J ASOND

01103235

0

20

40

60

80

100

J FMAMJ J ASOND

01103393

0

20

40

60

80

100

120

140

160

180

200

J FMAMJ J ASOND

01103206

0

20

40

60

80

100

120

140

160

180

200

220 220

J FMAMJ J ASOND

01103260

Observed, vertical bar shows

90 percent confidence intervals

Original Model

Revised Model

MONTHS

FLOW IN CUBIC FEET PER SECOND

Figure 10. Simulated and observed base-flow values for selected locations in the upper Charles River basin, eastern 

Massachusetts. Observed data are MOVE.1 estimated flows based on partial-record observations. Original model 

data are from figure 21, DeSimone and others (2002). MOVE.1 flows estimated from partial streamflow records at the 

station and long-term streamflow records from nearby stations. Number at top of each chart is the U.S. Geological 

Survey site identification number. (Locations are shown in fig. 3.)
Optimization Methods 25

Optimization Methods

Optimization methods are a collection of mathematical 

techniques used to solve complex resource-management 

problems. Originally developed to guide management of 

industrial systems, optimization has been applied extensively in 

the field of water-resource management (for example, Gorelick, 

1983; Wagner, 1995; Ahlfeld and Mulligan, 2000). When 

optimization methods are combined with hydrologic simulation 

models, the combined approach is termed "simulationoptimization."

The simulation-optimization approach used here relies 

on a numerical flow model to simulate the hydrologic response 

of a stream-aquifer system to applied stresses such as water 

withdrawals. Response coefficients generated from the model 

results are combined with optimization techniques to answer 

specific water-management questions. The mathematical 

representation of these questions is a "management model" 

(DeSimone and others, 2002). 

A management model has three components: decision 

variables, objective function, and constraints (Ahlfeld and 

Mulligan, 2000). The decision variables are the quantities to be 

determined, for example, pumping rates at a supply well (Qwi). 

The objective function expresses the management goal as a 

maximum or minimum. For example, maximize total pumping 

(QwT) at three supply wells (Maximize QwT = Qw1 + Qw2 + 

Qw3). Constraints set limits on what values decision variables 

may take. For example, withdrawals must exceed a specified 

value (Qw1 + Qw2 + Qw3 > 1 Mgal/d). An optimization software 

package, LINDO (Shrage, 1997), was used to solve 

management models. Solutions consist of monthly stress rates 

for the decision variables. 

Hydrologic Response Coefficients

The management model is linked to the numerical flow 

model through a matrix of response coefficients (Gorelick, 

1983). Response coefficients quantify the hydrologic response 

to a unit increase in stress (such as pumping) at one site for 

1 month. The stress locations are shown in figures 4 and 6. To 

calculate a response coefficient, a hydrologic stress is simulated 

in month 1, and the resulting hydrologic changes are entered in 

equation 2:

, (2)

where

The stress perturbations (Qw) used to calculate coefficients 

in equation 2 were selected to represent high and low ends of the 

range of possible stress values. Ground-water withdrawal 

stresses were simulated at 25 percent and 100 percent of 

state Zone II maximum pumping rates. 

Base-flow changes are the only hydrologic responses 

analyzed. Ten stream locations, called "constraint points," were 

selected for calculating base-flow response to hydrologic 

stresses (table 11 and fig. 3). Constraint points CR4 and 

BB1 are where the Charles River and Bogastow Brook exit the 

study area; all hydrologic stresses in the upper Charles River 

basin affect base flow at one or both of these points. Constraint 

points MR1, MB2, and HB2 are the downstream ends of the 

Mill River, Mine Brook, and Hopping Brook tributaries, 

respectively; base flows at these points reflect all hydrologic 

processes in their respective subbasins. Constraint points 

MB1, HB1, and CR1 represent smaller subbasins in the Charles 

River headwaters. The remaining constraint points, CR2 

and CR3, are midway along the Charles River and allow 

downstream flow patterns in the main drainage basin to be 

determined and provide better coverage for low-flow 

constraints. 

Response coefficients were generated for each hydrologic 

stress considered in this study. Tables 5 and 7 report all groundwater withdrawal and water-return stresses considered. A 

complete listing of all response coefficients is given in 

Appendix 2. Example coefficients are shown in figure 11 for 

streamflow depletions at CR4 (Charles River exit) in response 

to pumping at Wrentham well 2 (WR-02G). Because the 

numerical model operates on the assumption that flow in 

streams moves quickly, with all flow exiting the basin within 

each 1-month time period, all constraint points downstream 

of a stress will have the same response coefficients for that 

stress.

The response coefficient approach is based on an 

assumption of linear response to hydrologic stresses. Multiple 

stresses can be added together or subtracted under this 

assumption. Because linearity of hydrologic response is 

assumed with respect to the magnitudes and times of stress, 

response coefficient values do not vary under different pumping 

rates, recharge conditions, or times of year. The only exception 

is the coefficients for wastewater discharge, which are specified 

to take on different values in the summer to account for greater 

evaporative loss of water. For example, the responses to 

wastewater discharge by the town of Holliston during May 

through August are described by different response coefficients 

than are used during the rest of the year. Hydrologic stresses 

that increase base flow, such as injection wells, septic return 

flow, wastewater discharge, and wastewater-infiltration basins 

are given negative signs in equation 2, and the resulting 

coefficients are also negative.

i = index for location of hydrologic response;

j = stress location;

k = month of hydrologic response;

Qsd = hydrologic response rate (ft3/s);

Qw = stress rate (ft3/s); and r = response coefficient.

rijk , ,

Qsdj k,

Qwj

= ---------------
26 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 11. Constraint points, upper Charles River basin, eastern Massachusetts.

[Site locations are shown in figure 3. The partial record stations were used to calculate flow statistics from equation 1. No., number; mi2, square mile]

Constraint point location Identifier

Model cell location Drainage 

area (mi2)

Partial record station

Layer Row Column Station No. Area

Charles River below Godfrey Brook CR1 1 220 64 11.3 01103120 8.3

Charles River above Hopping Brook CR2 1 214 155 25.4 01103206 21.0

Charles River Medway CR3 1 204 220 65.2 01103280 65.2

Charles River Exit CR4 1 215 264 83.8 01103305 83.8

Bogastow Brook Exit BB1 1 132 243 20.8 01103393 20.9

Hopping Brook at Beaver Brook HB1 1 157 117 7.5 01103217 9.9

End of Hopping Brook HB2 1 212 155 11.0 01103217 9.9

Mine Brook 1/2 way MB1 1 296 167 10.0 01103235 9.8

End of Mine Brook MB2 1 208 173 15.9 01103240 14.2

End of Mill River MR1 1 220 262 16.0 01103300 13.8

0.0

0.1

0.2

0.3

0.4

0.5

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

MONTH

RESPONSE COEFFICIENT

Figure 11. Response coefficients for streamflow depletions at the Charles River exit from the study area in 

response to pumping during month 1 at Wrentham well 2 (WR-02G in table 5 and figure 4).
Optimization Methods 27

Because simulated flow is in dynamic equilibrium, with 

monthly flows unchanging from year to year, hydrologic 

responses beyond month 12 were added to corresponding 

earlier months. For example, base-flow depletions in months 13 

and 14 were added to base-flow depletions in months 1 and 2, 

and then equation 2 was used to calculate response coefficients 

for the summed depletions. Hydrologic responses with a 

magnitude of less than 1 percent of the stress perturbation were 

disregarded and not included in the response coefficient matrix. 

This exclusion causes small long-term responses to be ignored, 

but these small mass-balance errors are later corrected by 

scaling the coefficients.

Once the response coefficients are generated, all 

hydrologic simulations are then based on these coefficients 

rather than on the numerical model. This reduces errors and 

allows more efficient calculation of base-flow values under the 

stress conditions determined by optimization.

Wastewater disposal coefficients were set separately for 

each town by running a simulation that routed wastewater to 

septic and sewer discharge according to the proportions in 

table 6. Septic discharge was modeled as recharge in those areas 

with public-water supplies and private septic systems, with 

rates for each model cell set according to population density. 

The appropriate fraction of wastewater was discharged at the 

wastewater facility serving each town. Because the numerical 

model assumes that all stream water discharges in each stress 

period, any direct discharge of water to streams during month 1 

has a response coefficient of -1.0 in month 1. Stream response 

to septic discharge typically lasts for several months because 

the wastewater takes time to move through aquifers to streams; 

this delay is expressed by the response coefficients. Water 

losses from supply pipes and inflow and infiltration of ground 

water into wastewater pipes were not explicitly modeled 

because insufficient data were available to quantify them.

Response coefficients for wastewater discharge were set 

separately according to time of year because of seasonality in 

consumptive losses. Changes in wastewater discharge from 

May through August were assumed to be only 70 percent of 

water withdrawal changes, following the previous use of 30-

percent consumptive loss for those months. In the other 8 

months of the year, it was assumed that there was no 

consumptive loss and that a change to water withdrawals would 

cause an equal change to wastewater discharge.

Water-Management Objectives and 

Constraints

Two types of objective function are used in this study to 

formulate management models: (1) maximizing water supplies 

to communities, and (2) maximizing water to streams. To 

maximize water to communities, pumping is maximized, 

typically only during June, July, and August when water 

demand is the highest (figs. 5 and 7). For example, the 

following objective function is used to maximize pumping by 

the town of Medway during June through August from the 

town’s three supply wells (MD-01G, MD-02G, MD-03G):

Maximize: 

Q06D1+Q07D1+Q08D1+Q06D2+Q07D2

+Q08D2+Q06D3+Q07D3+Q08D3. (3)

The variables Q--D1, Q--D2, and Q--D3 represent water 

withdrawals from the three Medway public-supply wells 

(table 5, fig.4).

To maximize water to streams, objective functions are 

formulated that minimize base-flow depletions during July, 

August, and September when streamflow falls particularly low 

(fig. 10). For example, to minimize total base-flow depletions at 

constraint point HB1 during July through September, the 

following objective function is used:

Minimize: 

- 1.0(D07HB) - 1.0(D08HB) - 1.0(D09HB) 

+ 0.095(Q01H4) + 0.137(Q02H4) + 0.179(Q03H4) 

+ 0.229(Q04H4) + 0.304(Q05H4) + 0.373(Q06H4) 

+ 0.581(Q07H4) + 0.457(Q08H4) + 0.332(Q09H4) 

+ 0.054(Q10H4) + 0.061(Q11H4) + 0.075(Q12H4) 

- 0.014(R05HS) - 0.036(R06HS) - 0.122(R07HS) 

- 0.108(R08HS) - 0.110(R09HW) - 0.069(W01HG)

- 0.080(W02HG) - 0.105(W03HG) - 0.147(W04HG) 

- 0.207(W05HG) - 0.322(W06HG) - 0.735(W07HG) 

- 0.658(W08HG) - 0.512(W09HG) - 0.049(W10HG) 

- 0.055(W11HG) - 0.062(W12HG) (4)

where Q--H4 variables represent monthly water withdrawals 

from well HL-04G, the only well affecting flow at HB1 (table 

5, fig. 4), and variables beginning with D, R, and W represent 

monthly water returns (table 7, fig. 6). For example, Q01H4 

represents pumping at Holliston Well No. 4 in January, and 

R05HG represents wastewater discharge by Holliston in May. 

Equation 4 comprises all water stresses analyzed in the study 

that affect base flow at HB1 during July through September. 

After specifying constraints, a solution to the problem can be 

found that specifies values for each variable in equation 4.

The management models employ a variety of constraints. 

Constraints are placed to limit pumping rates so that individual 

wells honor State-mandated maximum pumping rates (monthly 

Zone II limits) and groups of wells honor maximum annual 

average pumping rates imposed by the WMA limits. Holliston 

and Medway are excluded from the WMA constraints because 

their annual average (1989–98) pumping rates exceed WMA 

limits (table 8); instead, they are limited to past average 

pumping rates. Constraints are placed to ensure that, for each 

town, mass balance of wastewater disposal against water 
28 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

withdrawals is achieved. Constraints are placed to ensure that 

each town receives a minimum amount of water, generally 

equal to past average monthly pumping rates. 

Constraints are also placed to limit streamflow 

depletions. The constraint levels were chosen in consultation 

with the project’s technical advisory committee and reflect 

compromises between the higher 0.50 ft3

/s/mi2 value of 

the ABF and the lower 0.21 ft3/s/mi2 value used in some 

wastewater permits for the basin. As a default condition, 

base flow is constrained to be greater than or equal to either 

0.41 ft3/s/mi2 or average flow under no-pumping conditions, 

whichever is less. For example, flow at CR1 in January would 

be constrained to be greater than or equal to 0.41 ft3/s/mi2, 

because 0.41 is less than the average flow of 0.96 ft3

/s/mi2 at 

CR1 in January under average no-pumping conditions (table 3). 

In August, however, flow at CR1 would be constrained to be 

above only 0.26 ft3/s/mi2, the average no-pumping flow, 

because it is less than 0.41. It is important to note that these 

constraints require higher than average flow during the summer, 

because average flow (tables 1 and 2) is generally lower than 

no-pumping flow (tables 3 and 4). For some management 

models, the low-flow constraints cannot be met. In some of 

these cases, a lower flow was allowed so that a solution 

to the management model could be obtained and a better 

understanding of the management alternatives would ensue. 

The low-flow constraint levels used in this study were chosen 

only for purposes of analysis. 

Response Coefficient Errors

Errors may be caused by linearity assumptions inherent to 

the response coefficient approach. For example, when a stream 

goes dry or when a flow boundary causes nonlinear head 

responses, hydrologic responses calculated with response 

coefficients will have errors. One potential source of error is the 

assumption that aquifer transmissivity remains constant as head 

changes; in unconfined aquifers however, it does not remain 

constant (Reifler and Ahlfeld, 1996). Numerical errors in 

simulation results, such as round-off errors, may also introduce 

error to the response coefficients.

Errors in the response coefficient can be classified into two 

types: (1) mass balance and (2) timing errors. Mass balance 

considerations dictate that response coefficients for a given 

stress sum to 1.0. For example, if 2.0 ft3/s is withdrawn from 

well X in month 1, then base-flow depletions downstream of 

well X sum to 2.0 ft3/s during the time it takes for ground-water 

storage to return to its pre-pumping state. If total base-flow 

depletions do not equal pumping, then the water mass is not 

balanced. To remove mass balance errors, all response 

coefficients calculated in equation 2 were scaled so that 

equation 3 was honored for all stress (j) and stream (i) locaion 

pairs:

(5)

where k is the month index and n is the number of months in 

which base-flow depletion occurs.

In a few cases, response coefficients had the wrong sign, 

as for example when base flow increased in response to groundwater withdrawals. This type of response does not have a 

plausible physical explanation and is attributable to numerical 

errors in the ground-water simulation. Other errors of this type 

include nonmonotonic changes in base-flow depletion in 

response to a single stress where, for example, base-flow 

depletions rise, then fall, and then rise again. Because groundwater flow is described by the diffusion equation, a single prior 

stress of a fixed rate cannot cause this type of nonmonotonic 

response sequence, and the response is attributable to numerical 

errors. In these cases of obvious errors in the response 

coefficients, base-flow depletions were estimated by linear 

interpolation between their values before and after the month(s) 

with spurious values. Errors for approximately 11 percent of 

response coefficients were corrected in this way, with most 

errors in later months when responses are a small fraction of 

total response.

Errors in timing of response coefficients occur if base-flow 

depletions last for too many or too few months or if depletions 

are distributed incorrectly over the correct months. The 

uncertainty associated with these errors was quantified by 

measuring timing variations. For each stress (j) and stream (i) 

location pair, four sets of ri,j,k were generated, with k being the 

month index. The following conditions defined the four sets:

1. High stress imposed in August under average recharge.

2. Low stress (25 percent of high stress) imposed in August 

under average recharge.

3. High stress imposed in February under average recharge.

4. High stress imposed in August under low recharge (41 

percent of average).

Each set of ri,j,k should be the same under the assumption 

of linear response. To quantify how timing of the response 

coefficients varied, T5% was defined as the last month in which 

stream depletions are more than 5 percent of pumping. As an 

example, for the response coefficients shown in figure 11, 

T5% = month 4. Because of simulation errors, the four sets of 

ri,j,k sometimes did not yield the same T5%. The mean absolute 

departure of T5% from the group average T5% was 1.5 months. 

rijk , ,

k = 1

n

∑ = 1.0
Analysis of Management Alternatives Using Simulation-Optimization 29

This value is the uncertainty in the timing of the coefficients, 

which cannot be removed. The uncertainty is increased 

primarily by cases 2 and 4 above. In case 2, the stress 

perturbation (Qsdj,k) on the right-hand side of equation 2 is 

quite small. The number of significant digits in the numerical 

solution is thus decreased, adding to the uncertainty of ri,j,k

(Riefler and Ahlfeld, 1996). 

In case 4, low recharge causes nonlinearity because stream 

flow is smaller and some stream cells go dry. If other cases 

that imposed higher stress perturbations and precluded dry 

conditions were used instead of cases 2 and 4 above, the mean 

absolute departure of T5% would decrease.

The use of response coefficients allows base-flow changes 

to be calculated outside of the simulation model and allows 

some numerical errors to be avoided. Starting with the MOVE.1 

flow statistics (average and 90-percent low flow), changes from 

these statistical flows caused by stresses are calculated with 

response coefficients. Therefore, instead of unknown model 

errors in the base-flow values for each scenario, there are 

known MOVE.1 uncertainties and response coefficient errors. 

Errors in the response coefficients affect solutions to 

water-resource management problems. Errors of mass balance 

have been removed from the response coefficients, but some 

timing errors remain, adding uncertainty to any solution based 

on the response coefficients. In most cases, the uncertainty is 

small enough to be acceptable. In small streams and under lowflow conditions, uncertainty is more important because baseflow depletions from a single pump can be a large percentage 

(50 percent or more) of total streamflow. Additional sitespecific data collection and modeling for small streams might 

reduce uncertainty due to errors in response coefficients.

Analysis of Management Alternatives

Using Simulation-Optimization

A variety of scenarios was considered to assist waterresources managers in development of strategies for addressing 

water-supply shortages and low streamflow. All scenarios use 

response coefficients as previously discussed. Some scenarios 

additionally use optimization methods. The scenarios were 

selected in consultation with the project’s technical advisory 

committee, which is composed of State environmental officials, 

town water officials, engineering consultants to towns, and 

representatives of conservation groups. The scenarios are 

numbered from 1A to 9A and are summarized in table 12.

Maximize Pumping

Demand for drinking water in the study area is expected 

to rise. If future water demands are met by increasing groundwater withdrawals, base flow will be affected. To examine 

this possibility, base flow is calculated for the case in which 

pumping at existing municipal wells increases to maximum 

permitted levels under monthly Zone II limits (Scenario 1A). 

Under these conditions, pumping increases to 24.1 ft3

/s, 

up from the past average annual rate of 10.0 ft3/s. WMA 

limits, which cap annual average pumping at 15.5 ft3/s, were 

not considered in this analysis due to uncertainty about 

adjusting WMA limits for towns with additional supply 

wells outside the basin. Pumping at all existing municipal 

wells was increased to maximum permitted Zone II levels 

for every month of the year and septic and wastewater discharge 

were correspondingly increased. The resulting base-flow values 

were calculated by use of response coefficients and are shown 

in table 13. 

Base flow is generally lower under maximum permitted 

pumping than under average pumping (table 1); this result 

is to be expected because 30 percent of summertime pumping 

is lost to consumptive use and thus does not recharge the 

aquifer. Seven of the 10 constraint points show lower base flow 

in every month of the year, with the Charles River at CR1 

drying up from July through September. The flow is higher in 

every month at only one constraint point (MR1); this higher 

flow is caused by increased septic discharge in the Mill River 

subbasin.

Under 90-percent low-flow conditions, increasing groundwater withdrawals from average (table 2) to maximum 

permitted rates (Scenario 1B) causes the same depletions in 

base flow. The depletions have greater importance, however, 

because flow is already so low. Under average pumping only 

Hopping Brook (HB1 and HB2) goes dry; but under maximum 

permitted pumping, Bogastow Brook (BB1), Mine Brook 

(MB1, MB2), and parts of the Charles River (CR1, CR3) also 

go dry for at least 1 month (table 14).

Low flows under average, no-pumping, and maximum 

pumping conditions are summarized in table 15. The numbers 

indicate that water use contributes to low-flow problems in the 

basin; if there were no water use, however, flow would still drop 

below the 0.50 ft3/s/mi2 ABF standard for healthy freshwater 

ecosystems in New England.
30 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 12. Summary of water-resource management scenarios analyzed, upper Charles River basin, eastern Massachusetts.

[Scenario: All scenarios employ response coefficients to calculate base flow. CRPCD, Charles River Pollution Control District; =, equals; ≥, greater than or equal 

to; --, indicates optimization was not used]

Scenario Climatic 

conditions Management action Optimization to calculate pumping rates Results

Maximize Notable constraints

1A Average Increase pumping -- -- Decreased base flow, 

increased water supply

1B Dry Increase pumping -- -- Decreased base flow, 

increased water supply

2A Average Maximize summer base flow Summer base flow Water supply ≥ existing, 

base flow ≥ no-pumping flow

No feasible solution

2B Average Maximize summer base flow Summer base flow Water supply ≥ existing, 

base flow ≥ average flow

Base flow increases

3A Average Proposed wells pumping at 

maximum permitted rates

-- -- Decreased base flow, 

increased water supply

3B Average Proposed wells allowed Summer base flow Water supply = existing, 

base flow ≥ no-pumping flow

No feasible solution

3C Average Proposed wells allowed Summer base flow Water supply = existing, 

base flow ≥ average flow

Base flow increases

3D Dry Proposed wells allowed Summer base flow Water supply = existing, 

base flow ≥ dry flow

Base flow increases

4A Average Holliston sewage to CRPCD -- -- Base flow decreases

4B Average Holliston sewage to local 

recharge

-- -- Base flow unchanged

4C Average Bellingham sewage to 

recharge

-- -- Base flow unchanged

4D Average Choice of recharge basins at 

the Miscoe Brook site

Summer base flow Direct wastewater discharge to 

streams is possible

Discharge directly to stream in 

summer, to distant recharge 

basins in other months

4E Average Recharge basin added to 

CRPCD

Summer base flow Direct wastewater discharge to 

streams is possible

Base flow increases

5A Average Wastewater discharged 

upstream

-- -- Base flow increases

6A Average Stormwater recharge -- -- Base flow increases

7A Average Water conservation 

(10 percent)

-- -- Increased base flow, increased 

water supply

8A Average Towns share drinking water Summer base flow Water supply = existing, 

base flow ≥ no-pumping flow

Increased base flow, increased 

water supply

8B Dry Towns share drinking water Summer base flow Water supply = existing, 

base flow ≥ dry flow

Increased base flow, increased 

water supply

9A Average Drinking water discharge to 

streams

Summer base flow Water supply = existing Base flow increases
Analysis of Management Alternatives Using Simulation-Optimization 31

Table 13. Base flow under Scenario 1A, average climatic conditions and maximum permitted pumping, upper Charles River basin, 

eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 6.7 7.5 10.3 10.4 5.5 0.6 0.0 0.0 0.0 1.2 3.5 6.7

CR2 41.3 43.9 54.3 53.0 36.4 20.5 9.3 9.6 11.3 20.7 31.3 40.2

CR3 116.1 131.9 171.7 172.5 105.5 58.2 22.9 19.2 19.9 42.8 79.9 113.1

CR4 159.3 169.3 202.4 200.0 144.5 86.3 48.5 49.5 50.8 85.2 121.8 156.9

BB1 37.7 40.3 55.8 55.7 34.5 14.6 5.2 5.4 5.0 13.6 24.4 36.6

HB1 18.1 22.4 31.1 30.3 15.3 3.8 .8 .9 1.0 4.0 8.6 17.6

HB2 27.0 33.5 46.3 45.2 23.0 5.9 1.3 1.6 1.7 6.1 12.9 26.3

MB1 16.8 18.6 21.7 21.5 15.6 8.3 3.8 4.0 3.9 8.0 11.8 16.5

MB2 31.9 35.9 43.3 43.0 29.3 15.5 6.7 6.1 5.8 13.1 21.1 30.8

MR1 36.1 38.9 43.4 43.3 34.2 23.6 15.3 14.4 14.2 21.2 28.0 35.2

Base flow per drainage area (ft3/s/mi2)

CR1 0.60 0.67 0.91 0.92 0.49 0.05 0.00 0.00 0.00 0.10 0.31 0.59

CR2 1.63 1.73 2.14 2.09 1.43 .81 .37 .38 .44 .82 1.23 1.58

CR3 1.78 2.02 2.64 2.65 1.62 .89 .35 .29 .31 .66 1.23 1.74

CR4 1.90 2.02 2.41 2.39 1.72 1.03 .58 .59 .61 1.02 1.45 1.87

BB1 1.82 1.94 2.68 2.68 1.66 .70 .25 .26 .24 .66 1.17 1.76

HB1 2.43 3.01 4.17 4.07 2.06 .51 .10 .12 .14 .53 1.15 2.36

HB2 2.45 3.03 4.20 4.09 2.08 .53 .12 .14 .16 .55 1.17 2.38

MB1 1.68 1.86 2.16 2.14 1.56 .83 .38 .40 .39 .80 1.18 1.65

MB2 2.01 2.26 2.73 2.71 1.85 .98 .42 .38 .37 .82 1.33 1.94

MR1 2.26 2.43 2.72 2.71 2.14 1.48 .96 .90 .89 1.33 1.75 2.20

Maximize Streamflow

Although current water use decreases summertime 

streamflow, pumping schedules could potentially be changed 

to increase summer flow. In Scenario 2A, streamflow is 

maximized by specifying an objective function that minimizes 

base-flow depletions at constraint points CR4 and BB1, the 

stream outlets from the basin:

Minimize: Total streamflow depletions at CR4 and BB1, the 

exit points from the basin, during July, August, and September.

Constraints:

1. Base flow must be greater than or equal to average flow 

under no-pumping conditions or 0.41 ft3

/s/mi2, whichever 

is less.

2. Each town’s monthly water supply is equal to average 

(1989–98) rates. 

3. Towns do not share water with each other.

4. Withdrawals are at or below State-mandated maximum 

pumping limits (monthly Zone II limits and annual 

WMA limits, except in Holliston and Medway).

No future or hypothetical projects are included and July, 

August, and September all have equal weight in the objective 

function. Pumping rates at non-municipal wells and septic and 

wastewater discharges are fixed at average (1989–98) monthly 

rates.

There is no solution to the optimization problem because 

no pumping schedule can be found that allows base flow to 

meet all the constraints. A feasible solution can be found if 

constraint (1) is relaxed so that base flow can drop as low as 

average existing base flow, a less stringent condition for the 

summer months. In this case (Scenario 2B), a solution of 

optimal pumping rates is found (table 16). When these optimal 

pumping rates are imposed, the base-flow values in table 17 

result. Monthly flow during July through September increases 

by an average of 2.6 ft3

/s (0.03 ft3/s/mi2) at CR4 and 0.4 ft3/s 

(0.02 ft3

/s/mi2) at BB1 over existing flow (table 1). 
32 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 14. Base flow under Scenario 1B, dry (90-percent low flow) climatic conditions and maximum permitted pumping, upper Charles 

River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 0.8 2.1 6.6 3.5 0.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0

CR2 20.7 26.9 41.0 30.7 20.3 8.3 1.9 .6 2.2 4.9 12.1 18.5

CR3 31.1 45.2 78.2 51.5 31.4 10.8 .0 .0 .6 3.4 13.4 23.5

CR4 83.5 106.8 158.3 122.2 85.1 42.7 18.2 12.7 15.0 23.2 51.6 74.5

BB1 12.3 18.6 37.1 24.9 14.3 4.5 .7 .0 .0 .9 5.0 10.6

HB1 4.1 6.8 18.8 9.1 4.9 .4 .0 .0 .0 .0 .8 2.0

HB2 6.3 10.3 28.0 13.8 7.4 .8 .0 .0 .1 .3 1.3 3.1

MB1 8.1 10.5 17.1 12.2 9.0 2.8 .1 .0 .0 .4 3.1 5.4

MB2 13.4 18.3 32.1 21.9 15.4 4.2 .2 .0 .0 .5 4.2 8.2

MR1 22.3 26.6 36.4 29.2 23.8 12.7 6.9 5.6 5.4 7.5 12.7 17.3

Base flow per drainage area (ft3/s/mi2)

CR1 0.07 0.19 0.59 0.31 0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00

CR2 .81 1.06 1.61 1.21 .80 .33 .07 .02 .08 .19 .48 .73

CR3 .48 .69 1.20 .79 .48 .17 .00 .00 .01 .05 .21 .36

CR4 1.00 1.27 1.89 1.46 1.02 .51 .22 .15 .18 .28 .62 .89

BB1 .59 .89 1.79 1.20 .69 .22 .03 .00 .00 .04 .24 .51

HB1 .55 .91 2.52 1.23 .65 .05 .00 .00 .00 .00 .10 .26

HB2 .57 .93 2.54 1.25 .67 .07 .00 .00 .01 .02 .12 .28

MB1 .80 1.04 1.70 1.21 .89 .27 .01 .00 .00 .04 .30 .53

MB2 .85 1.15 2.02 1.38 .97 .27 .01 .00 .00 .03 .26 .52

MR1 1.39 1.66 2.28 1.83 1.49 .79 .43 .35 .34 .47 .79 1.08

Table 15. Low flows at the 10 constraint points under different pumping stresses, upper Charles River basin, eastern Massachusetts.

[Average low monthly flow: Values are the means of lowest monthly flows from each of the 10 constraint points shown in figure 3 and are based on monthly 

values in the tables indicated. ft3/s/mi2, cubic foot per second per square mile]

Climatic condition

Average low monthly flow (ft3/s/mi2)

Climatic condition

Average low monthly flow (ft3/s/mi2)

Average 

pumping

No 

pumping

Maximum 

permitted 

pumping 

(Zone II)

Average 

pumping No pumping

Maximum 

permitted 

pumping 

(Zone II)

Average climatic conditions Dry climatic conditions (90-percent flow duration)

Average low flow a0.41 b0.46 c0.33 Average low flow d0.10 e0.15 f0.05

Lowest flow a g0.14 b g0.12 c h0.00 Lowest flow d g0.00 e g.00 f i0.00

a

From table 1.

b

From table 3.

c

From table 13.

dFrom table 2.

e

From table 4.

f

From table 14.

gHopping Brook (HB1 and HB2).

hCharles River in Milford (CR1).

i

All constraint points (CR1, CR3, BB1, HB1, HB2, MB1, and MB2) except 

the Mill River (MR1) and parts of the Charles River (CR2 and CR4).
Analysis of Management Alternatives Using Simulation-Optimization 33

Table 16. Pumping rates to maximize summertime base flow, Scenario 2B, average climatic conditions, no proposed or hypothetical 

stresses, upper Charles River basin, eastern Massachusetts.

[Site locations are shown in figure 4. Scenarios are described in table 12. Town water supplies and septic and wastewater discharge are equal to average rates 

(1989–98). Nonmunicipal withdrawals were not optimized, but set equal to average rates (1989–98). Base flow was optimized only from July through September 

and only at BB1 and CR4. All rates in cubic foot per second]

 Withdrawal

stress 

 Optimal monthly withdrawal rate and change from average (1989–98) rate 

January February March April May June

Rate Change Rate Change Rate Change Rate Change Rate Change Rate Change

 Bellingham Municipal Withdrawals

Q--B5 0.45 +0.17 -0.30 -0.32 -0.32 -0.31 -0.30

Q--B7 .21 +.09 0.66 +.55 -.13 -.15 -.28 0.30 +.02

Q--B8 -.25 -.32 0.82 +.46 0.80 +.48 1.05 +.56 1.05 +.31

Q--B9 .10 +.07 -.01 -.02 .06 +.03 -.03

 Medway Municipal Withdrawals

Q--D1 .58 .58 -.04 .30 -.39 .26 -.35 .48 -.13 .58 -.13

Q--D2 -.15 -.15 -.10 -.16 -.26 .16 -.15

Q--D3 .65 +.14 .65 +.19 .94 +.50 .94 +.51 .94 +.39 .94 +.28

 Franklin Municipal Withdrawals

Q--F1 -.08 -.11 -.13 -.06 .49 +.36 .69 +.37

Q--F2 -.08 -.11 -.13 -.06 -.13 1.10 +.78

Q--F3 -.40 -.38 .50 +.07 .50 +.02 -.55 -.57

Q--F4 .75 -.21 .71 -.24 .24 -.63 -1.02 -1.14 -1.17

Q--F5 .77 +.52 .77 +.52 .77 +.51 .77 +.56 .77 +.49 -.30

Q--F6 .82 +.25 .82 +.25 .82 +.27 .82 +.21 .82 +.19 .82 +.19

Q--F7 -.43 -.42 -.42 .38 -.09 .89 +.41 .89 +.39

Q--F8 .41 -.07 .41 .41 -.03 .41 -.04 .41 -.09 .41 -.09

Q--FT .78 +.48 .78 +.49 .78 +.48 .78 +.48 .78 +.45 .78 +.40

 Holliston Municipal Withdrawals

Q--H1 -.02 .49 +.39 .49 +.31

Q--H2 .48 +.47 .48 +.46 .48 +.43 .48 +.45 .48 +.36 .48 +.26

Q--H4 -.12 -.14 -.15 -.11 -.20 .43 +.05

Q--H5 -.71 -.62 -.61 -.70 -.81 1.09 +.33

Q--H6 1.07 +.36 .99 +.29 1.01 +.32 1.08 +.38 1.00 +.27 -.95

 Milford Municipal Withdrawals

Q--M1 -.01

Q--M2 .17 +.17 .02

Q--M3 1.23 +1.04 1.23 +1.05 .91 +.75 -.15 -.18 -.17

Q--M4 -.19 -.18 -.16 .91 +.76 .94 +.77 .96 +.79

Q--M5 -.19 -.18 -.16 -.15 -.18 -.17

Q--M6 -.81 -.67 -.42 -.45 -.42 -.46

 Norfolk Municipal Withdrawals

Q--N1 .28 .28 .33 .44 .44 .52

 Wrentham Municipal Withdrawals

Q--W2 -.48 -.48 -.47 -.46 -.71 -.60

Q--W3 1.04 +.48 1.07 +.48 .99 +.47 1.23 +.46 1.21 +.71 1.42 +.60
34 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 16. Pumping rates to maximize summertime base flow, Scenario 2B, average climatic conditions, no proposed or hypothetical 

stresses, upper Charles River basin, eastern Massachusetts.—Continued

[Site locations are shown in figure 4. Scenarios are described in table 12. Town water supplies and septic and wastewater discharge are equal to average rates 

(1989–98). Nonmunicipal withdrawals were not optimized, but set equal to average rates (1989–98). Base flow was optimized only from July through September 

and only at BB1 and CR4. All rates in cubic foot per second]

 Withdrawal

stress 

 Optimal monthly withdrawal rate and change from average (1989–98) rate 

July August September October November December

Rate Change Rate Change Rate Change Rate Change Rate Change Rate Change

 Bellingham Municipal Withdrawals

Q--B5 0.45 +0.13 -0.32 0.45 +0.14 -0.31 0.45 +0.15 0.45 +0.16

Q--B7 .66 +.41 0.66 +.48 -.11 -.11 -.10 -.07

Q--B8 -.75 -.65 -.35 -.32 -.28 -.25

Q--B9 .28 +.21 .54 +.48 .37 +.33 0.76 +.73 .26 +.23 .19 +.16

 Medway Municipal Withdrawals

Q--D1 .58 -.08 .53 -.21 -.70 .42 -.12 .28 -.32 .35 -.21

Q--D2 .91 +.58 .91 +.66 .91 +.69 -.24 -.17 -.18

Q--D3 .18 -.50 -.45 .48 .94 +.36 .94 +.49 .94 +.38

 Franklin Municipal Withdrawals

Q--F1 .69 +.39 .69 +.40 .69 +.43 -.24 -.16 -.06

Q--F2 1.11 +.82 1.11 +.82 .98 +.71 -.24 -.16 -.06

Q--F3 .48 -.05 .22 -.29 -.50 -.43 -.40 -.43

Q--F4 1.43 +.28 1.43 +.32 1.43 +.38 1.43 +.44 1.43 +.45 1.43 +.45

Q--F5 -.32 -.29 -.24 .76 +.53 .77 +.52 .77 +.48

Q--F6 -.60 -.57 -.45 .82 +.38 .09 -.25 .06 -.30

Q--F7 .89 +.40 .89 +.45 .89 +.48 -.39 -.38 -.43

Q--F8 -.51 -.49 -.49 -.46 .41 -.04 .41 -.06

Q--FT -.41 -.37 -.32 .78 +.42 .78 +.41 .78 +.42

 Holliston Municipal Withdrawals

Q--H1 .49 +.26 .49 +.31 -.13 -.04 -.03

Q--H2 -.28 -.23 -.08 .48 +.45 .48 +.46 .48 +.47

Q--H4 .66 +.24 .40 +.06 -.27 -.20 -.18 -.14

Q--H5 1.09 +.35 1.09 +.40 1.09 +.46 -.64 -.66 -.72

Q--H6 .23 -.56 .14 -.55 .69 +.02 1.09 +.43 .98 +.41 1.00 +.39

 Milford Municipal Withdrawals

Q--M1 1.05 +1.03 1.05 +1.02 1.05 +1.03 .21 +.19 .24 +.21 .13 +.11

Q--M2 -.01 -.03 -.01 -.02 -.03 -.02

Q--M3 -.18 -.18 -.22 -.20 -.22 -.22

Q--M4 -.18 -.18 -.22 -.20 -.22 -.22

Q--M5 -.18 -.18 -.22 -.20 -.22 -.22

Q--M6 .28 -.47 .46 -.45 .47 -.37 1.24 +.44 1.24 +.46 1.24 +.58

 Norfolk Municipal Withdrawals

Q--N1 .48 .37 .38 .36 .35 .31

 Wrentham Municipal Withdrawals

Q--W2 1.11 +.39 1.11 +.56 1.11 +.77 -.44 -.30 -.30

Q--W3 .39 -.39 .14 -.56 .04 -.77 .91 +.44 .90 +.30 .95 +.30
Analysis of Management Alternatives Using Simulation-Optimization 35

Table 17. Base flow under optimal pumping to maximize base flow, Scenario 2B, average climatic conditions, no proposed or 

hypothetical stresses, upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 8.9 9.8 13.0 13.3 8.9 4.1 2.3 2.3 2.1 4.1 6.3 9.4

CR2 41.7 44.5 55.0 53.8 39.3 23.5 13.0 13.2 12.9 22.0 32.3 41.1

CR3 118.0 133.9 173.6 174.5 110.2 61.7 28.8 25.1 23.4 45.4 82.6 115.7

CR4 155.8 166.0 199.3 197.4 146.1 88.6 53.5 54.5 52.2 84.1 119.6 154.2

BB1 38.1 40.8 56.2 56.2 35.1 15.5 6.5 6.7 6.0 14.2 24.8 37.0

HB1 18.4 22.7 31.4 30.6 15.8 4.2 1.0 1.1 1.2 4.2 8.8 17.8

HB2 27.1 33.6 46.4 45.3 23.2 6.1 1.5 1.7 1.8 6.1 13.0 26.3

MB1 18.8 20.6 23.5 23.2 17.5 9.9 6.1 6.4 6.3 9.8 13.9 18.8

MB2 34.3 38.4 45.7 45.3 31.7 17.5 9.4 8.9 8.6 15.2 23.7 33.6

MR1 35.3 37.4 42.1 42.2 33.6 23.7 15.6 14.7 14.3 20.8 27.1 33.9

Base flow per drainage area (ft3/s/mi2)

CR1 0.79 0.87 1.15 1.18 0.79 0.36 0.21 0.20 0.19 0.37 0.56 0.84

CR2 1.64 1.75 2.16 2.12 1.55 .93 .51 .52 .51 .87 1.27 1.62

CR3 1.81 2.05 2.66 2.68 1.69 .95 .44 .39 .36 .70 1.27 1.78

CR4 1.86 1.98 2.38 2.35 1.74 1.06 .64 .65 .62 1.00 1.43 1.84

BB1 1.83 1.96 2.70 2.70 1.69 .75 .31 .32 .29 .68 1.19 1.78

HB1 2.46 3.05 4.21 4.11 2.11 .56 .14 .15 .16 .56 1.18 2.39

HB2 2.46 3.04 4.21 4.11 2.11 .56 .14 .15 .16 .55 1.18 2.39

MB1 1.87 2.05 2.34 2.31 1.75 .99 .61 .64 .63 .98 1.39 1.88

MB2 2.16 2.42 2.88 2.85 1.99 1.10 .59 .56 .54 .96 1.49 2.12

MR1 2.21 2.34 2.63 2.64 2.10 1.48 .98 .92 .89 1.30 1.70 2.12

These increases in summertime base flow are achieved by 

exploiting differences in timing of streamflow response to 

different wells. Wells close to streams with short response times 

are pumped preferentially from October through January; this 

schedule allows the resulting streamflow depletions to take 

place before the dry months arrive. Wells far from streams with 

long response times are pumped preferentially from February 

through September, when a portion of the resulting streamflow 

depletions will take place after the low-flow period has passed. 

This can be seen in the optimal pumping rates for Medway’s 

wells (table 16). Well MD-02G (stress Q--D2), the Medway 

well with the most delayed streamflow depletion effects, is 

pumped during July, August, and September at the highest rate 

allowed by Zone II limits, 0.91 ft3/s. Well MD-01G (stress 

Q--D1), which causes the most streamflow depletion of any of 

Medway’s wells when pumped in September, is assigned to be 

shut down for that month. Well MD-03G (stress Q--D3) is 

pumped in September at a rate just high enough to meet the 

remainder of Medway’s required water supply of 1.39 ft3/s for 

that month. In October, just past the period of critically low 

streamflow, wells MD-03G and MD-01G meet the watersupply demand of Medway. Well MD-02G, the only Medway 

well whose October pumping depletes streamflow during the 

following July through September period, is shut down. That 

seasonal pumping patterns can be adjusted to augment summer 

base flow is also noted by Barlow and others (2003). 

The pumping rates in table 16 indicate how pumping could 

be managed to achieve the greatest increase in base flow during 

the summer. The pumping rates from February through 

September are higher in wells that are far from streams and have 

long response times and, from October through January, are 

higher in wells that are close to streams and have short response 

times. Towns whose wells all produce similar streamflow 

response times, whether long or short, have less management 

flexibility, which could be addressed by installing new wells. 
36 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Proposed Wells

Several towns in the study area have applied for permits to 

install new municipal water-supply wells. Pumping from these 

proposed wells would increase withdrawals permitted under 

Zone II regulations from 24.1 to 31.9 ft3/s and would alter the 

current hydrologic system. To estimate how this increased 

pumping would affect base flow, the response coefficient 

approach was applied (Scenario 3A). WMA limits were not 

included in the analysis because proposed WMA changes may 

or may not be issued concurrently with Zone II changes. The 

base-flow values shown in table 18 result when all existing and 

proposed wells pump at Zone II-permitted maximum rates for 

all months and septic, and wastewater disposal is 

correspondingly increased. 

Differences between base flow in table 13 and table 18 

indicate that increasing permitted withdrawals would cause 

substantial base-flow depletions if the additional permitted 

capacity were fully utilized. Under 90-percent low-flow 

conditions, the same base-flow depletions would take place and 

would be a larger percentage of total flow.

New wells also have the potential to increase summertime 

base flow, particularly if water use does not increase. 

Optimization was used to test how proposed wells could be 

managed along with existing supply wells to increase base flow 

during critical summer months (Scenario 3B). As with earlier 

scenarios, base-flow depletions were minimized at exits from 

the basin.

Minimize: Streamflow depletions at CR4 and BB1 during 

July, August, and September.

Constraints:

1. Base flow must be greater than or equal to average flow 

under no-pumping conditions or 0.41 ft3/s/mi2, whichever 

is less.

2. Each town gets at least as much water every month as the 

average for the period 1989–98. 

3. Towns do not share water with each other.

4. Pumping from each well is at or below State-mandated 

maximum pumping limits (monthly Zone II limits only, 

no WMA limits included).

Table 18. Base flow with all wells including proposed municipal supply wells pumping at maximum permitted rates, Scenario 3A, 

average climatic conditions, upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 6.7 7.5 10.3 10.4 5.5 0.6 0.0 0.0 0.0 1.2 3.5 6.7

CR2 41.3 43.9 54.3 53.0 36.4 20.5 9.3 9.6 11.3 20.7 31.3 40.2

CR3 116.2 132.0 171.8 172.6 105.3 57.9 22.6 18.9 19.8 42.8 79.9 113.1

CR4 160.4 170.6 203.7 201.3 144.9 86.4 48.3 49.1 51.2 85.7 122.5 157.9

BB1 36.7 39.3 54.8 54.7 33.4 13.5 4.0 4.2 3.9 12.6 23.4 35.5

HB1 18.3 22.7 31.4 30.6 15.5 4.0 1.0 1.1 1.3 4.2 8.8 17.8

HB2 27.4 33.8 46.6 45.5 23.2 6.2 1.6 1.8 2.1 6.4 13.3 26.6

MB1 15.8 17.5 20.6 20.4 14.5 7.2 2.7 2.9 2.9 7.0 10.7 15.5

MB2 30.9 35.0 42.3 42.1 28.3 14.5 5.7 5.1 4.8 12.0 20.1 29.8

MR1 36.5 39.5 44.0 43.9 34.5 23.7 15.1 14.0 14.0 21.0 28.1 35.4

Base flow per drainage area (ft3/s/mi2)

CR1 0.60 0.67 0.91 0.92 0.49 0.05 0.00 0.00 0.00 0.10 0.31 0.59

CR2 1.63 1.73 2.14 2.09 1.43 .81 .37 .38 .44 .82 1.23 1.58

CR3 1.78 2.03 2.64 2.65 1.62 .89 .35 .29 .30 .66 1.23 1.74

CR4 1.91 2.03 2.43 2.40 1.73 1.03 .58 .59 .61 1.02 1.46 1.88

BB1 1.77 1.89 2.63 2.63 1.61 .65 .19 .20 .19 .60 1.12 1.71

HB1 2.46 3.04 4.21 4.10 2.09 .54 .13 .15 .17 .56 1.19 2.39

HB2 2.48 3.07 4.23 4.13 2.11 .56 .15 .17 .19 .58 1.20 2.41

MB1 1.57 1.75 2.05 2.04 1.45 .72 .27 .29 .29 .69 1.07 1.54

MB2 1.95 2.20 2.66 2.65 1.78 .91 .36 .32 .30 .76 1.26 1.88

MR1 2.28 2.47 2.76 2.75 2.16 1.48 .94 .87 .87 1.31 1.76 2.22
Analysis of Management Alternatives Using Simulation-Optimization 37

The formulation does not include future projects other than 

proposed wells. July, August, and September all have equal 

weight in the objective function. Because base flow is 

maximized only at constraint points CR4 and BB1, flow at other 

constraint points may decrease.

Solution 1:

With the addition of new wells, base flow cannot be 

managed to meet all the constraints. So, as in Scenario 2B, 

constraint (1) is relaxed to allow base flow to drop as low 

as average existing base flow (Scenario 3C). A feasible 

pumping schedule is found that increases base flow during the 

months of July through September (table 19) by an average of 

4.6 ft3/s (0.06 ft3/s/mi2) at CR4 and by an average of 0.5 ft3/s 

(0.02 ft3/s/mi2) at BB1 as compared to base flow under average 

pumping rates. Only about 40 percent of this flow increase 

(2.0 out of 4.6 ft3/s), however, is attributable to the addition of 

the proposed wells, with the remainder of the increase (2.6 of 

4.6 ft3

/s) attributable to optimized management of pumping 

schedules at existing wells as described for Scenario 2B.

Solution 2:

Under low-flow conditions (90-percent flow duration) 

there is no feasible solution to the optimization problem 

because low base flow violates constraint 1. To avoid this 

problem, constraint 1 is modified to allow lower base flow 

(Scenario 3D). 

Constraints:

1. Base flow must be greater than or equal to 90-percent 

low flow under no-pumping conditions or 0.21 ft3/s, 

whichever is less. 

2–4. Same as in Scenario 3B. 

The optimal solution to Scenario 3D increases base flow 

during the months of July through September at CR4 and BB1 

by nearly the same amounts (4.7 and 0.5 ft3

/s) as under average 

precipitation (Scenario 3C). As in Scenario 3C, only about 40 

percent of the base-flow increase is attributable to the addition 

of the proposed wells (table 20).

Table 19. Base flow maximized under optimal pumping with proposed wells active, Scenario 3C, average climatic conditions, towns 

receive average (1989–98) water supplies, upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 9.0 10.0 13.1 13.4 9.0 4.0 2.3 2.3 2.1 4.1 5.6 9.3

CR2 42.7 45.5 56.0 54.8 40.2 24.4 13.8 13.9 13.8 22.8 32.6 42.1

CR3 118.6 134.6 174.6 175.6 111.0 63.3 30.0 25.9 24.3 46.5 82.9 116.1

CR4 156.3 166.6 200.2 198.1 146.4 89.4 55.5 56.4 54.2 85.1 119.9 154.4

BB1 37.9 40.6 56.2 56.1 35.4 15.9 6.7 6.7 6.1 13.8 24.2 36.4

HB1 18.4 22.7 31.4 30.6 15.5 4.0 1.1 1.2 1.1 4.1 8.8 17.8

HB2 27.1 33.6 46.4 45.3 23.0 5.9 1.5 1.8 1.7 6.1 12.9 26.3

MB1 18.5 20.3 23.4 23.2 17.6 10.6 6.4 6.4 6.4 10.2 14.0 18.2

MB2 34.1 38.2 45.6 45.4 31.8 18.3 9.8 8.9 8.7 15.7 23.8 33.0

MR1 35.1 37.8 42.4 42.2 33.6 23.6 15.9 15.2 15.0 20.9 27.1 34.0

Base flow per drainage area (ft3/s/mi2)

CR1 0.80 0.89 1.17 1.19 0.80 0.36 0.21 0.20 0.19 0.37 0.50 0.83

CR2 1.68 1.79 2.20 2.16 1.58 .96 .54 .55 .54 .90 1.28 1.66

CR3 1.82 2.07 2.68 2.70 1.70 .97 .46 .40 .37 .71 1.27 1.78

CR4 1.87 1.99 2.39 2.36 1.75 1.07 .66 .67 .65 1.01 1.43 1.84

BB1 1.82 1.95 2.70 2.70 1.70 .76 .32 .32 .29 .66 1.17 1.75

HB1 2.46 3.05 4.21 4.11 2.08 .53 .14 .16 .15 .55 1.18 2.39

HB2 2.46 3.04 4.21 4.11 2.09 .54 .14 .16 .15 .55 1.17 2.39

MB1 1.84 2.02 2.34 2.32 1.75 1.06 .64 .64 .64 1.02 1.39 1.82

MB2 2.14 2.40 2.87 2.86 2.00 1.15 .61 .56 .55 .99 1.50 2.08

MR1 2.20 2.36 2.65 2.64 2.10 1.48 1.00 .95 .94 1.31 1.69 2.13
38 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 20. Base flow maximized under optimal pumping with proposed wells active, Scenario 3D, dry (90-percent low flow) conditions, 

upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 3.1 4.7 9.6 6.6 4.3 1.4 1.0 0.7 0.6 0.0 1.6 2.1

CR2 22.2 28.6 42.7 32.5 24.1 12.1 6.3 4.9 4.7 6.3 14.2 19.9

CR3 33.8 48.0 81.1 54.7 37.0 16.0 6.8 5.2 5.0 6.4 17.1 26.1

CR4 80.7 104.2 156.1 120.4 87.0 45.8 25.2 19.5 18.4 22.3 50.4 71.6

BB1 12.4 18.9 37.6 25.4 15.1 5.7 2.1 1.2 1.0 1.0 4.8 10.5

HB1 4.3 7.1 19.1 9.4 5.0 .6 .1 .1 .0 .2 .9 2.2

HB2 6.4 10.4 28.2 13.9 7.5 .9 .2 .2 .1 .3 1.4 3.2

MB1 9.7 12.1 18.8 13.9 10.9 5.0 2.7 2.1 1.9 2.6 5.2 7.1

MB2 15.6 20.6 34.5 24.3 17.9 7.0 3.2 2.3 2.1 3.2 6.9 10.4

MR1 21.3 25.5 35.4 28.2 23.2 12.6 7.6 6.4 6.2 7.4 11.8 16.2

Base flow per drainage area (ft3/s/mi2)

CR1 0.28 0.41 0.85 0.59 0.38 0.13 0.09 0.06 0.06 0.00 0.14 0.19

CR2 .87 1.13 1.68 1.28 .95 .48 .25 .19 .18 .25 .56 .78

CR3 .52 .74 1.24 .84 .57 .25 .10 .08 .08 .10 .26 .40

CR4 .96 1.24 1.86 1.44 1.04 .55 .30 .23 .22 .27 .60 .85

BB1 .60 .91 1.81 1.22 .73 .28 .10 .06 .05 .05 .23 .50

HB1 .58 .95 2.56 1.27 .68 .07 .02 .02 .00 .03 .13 .29

HB2 .58 .94 2.55 1.26 .68 .08 .02 .01 .00 .02 .12 .29

MB1 .97 1.21 1.88 1.39 1.09 .50 .27 .21 .19 .26 .52 .70

MB2 .98 1.29 2.17 1.53 1.13 .44 .20 .15 .13 .20 .43 .65

MR1 1.33 1.59 2.21 1.76 1.45 .79 .47 .40 .39 .46 .74 1.01

New wells can improve the ability of towns to manage 

pumping schedules for the purpose of increasing streamflow. 

Towns whose wells all have similar response characteristics 

have less management flexibility. Towns that have only 

wells with short response times, like Milford, could improve 

management flexibility by placing new wells farther from 

streams and pumping them preferentially from January through 

September. Towns that have only wells with long response 

times, like Wrentham, could improve management flexibility 

by placing any new wells closer to streams and pumping them 

in the fall and winter. Towns that have only one or two wells in 

the basin, like Norfolk, have little management flexibility to 

adjust pumping schedules for the purpose of increasing 

streamflow in the basin.

Wastewater Management

Through strategic management of wastewater effluent, 

summertime base flow can be increased. Although discharging 

wastewater directly to streams increases streamflow 

immediately, recharging wastewater to an aquifer augments 

base flow over longer times. There are no centralized facilities 

in the study area that recharge wastewater to aquifers, although 

private septic systems provide widespread recharge of 

wastewater. Centralized wastewater recharge can flow through 

infiltration beds or injection wells (table 7), and both methods 

have been considered for the basin (Earth Tech, 2000; Bruce 

Bouck, Massachusetts Department of Environmental 

Protection, 2002, written commun.).

New Sewers

As towns in the basin expand their wastewater 

infrastructure, typically by installing new sewer lines, baseflow patterns are altered. Optimization models for proposed 

wastewater changes in the towns of Holliston and Bellingham 

under average streamflow conditions were used to analyze the 

altered base-flow patterns. 
Analysis of Management Alternatives Using Simulation-Optimization 39

Holliston

The town of Holliston has considered building a sewer 

system (Earth Tech, 2000) to replace private septic systems, 

which are currently the only disposal method used in the town 

(table 6). The sewer system may include either:

A. transport of wastewater to the CRPCD for treatment and 

discharge, or

B. local treatment and recharge of wastewater at three 

smaller community sites. 

The two options may have different effects on streamflow and 

are considered below. 

Case A. CRPCD

For Case A (Scenario 4A), those parts of Holliston which 

currently receive public water and are on private septic systems 

had their wastewater routed to the CRPCD treatment plant 

for direct discharge (fig. 6). Ground-water withdrawal rates 

at all wells were set to average rates (table 5), and no other 

hypothetical or proposed projects were included. The resulting 

flow values (table 21) were calculated by the use of response 

coefficients and, when compared to existing flows (table 1), 

indicate that sewering reduces flow at BB1, HB1, HB2, and 

CR3 while increasing flow at CR4. The decrease in flow at BB1 

reaches 0.05 ft3

/s/mi2 in the summer months.

Case B. Local Recharge

For case B (Scenario 4B), septic-system disposal was 

rerouted to three wastewater recharge facilities HL-E1P, 

HL-E2P, and HL-WGP (fig. 6) (Scenario 4B). HL-E1P 

received 25 percent of monthly flow, HL-E2P received 60 

percent, and HL-WGP received 15 percent, following designed 

flow rates (Earth Tech, 2000). Pumping rates were again set to 

average (1989–98) rates, and no other future or proposed 

projects were included. Comparison of the resulting base flow 

(table 22) with the existing base flow (table 1) indicates that 

flow differences are quite small, with BB1 having greater flow 

and CR3, CR4, and HB2 having lower monthly flow. The 

streamflow changes do not exceed ±0.02 ft3

/s/mi2 at any 

constraint location.

Table 21. Base flow with Holliston wastewater routed to the Charles River Pollution Control District treatment plant, Scenario 4A, 

average climatic conditions, average withdrawals (1989–98) and return stresses (except for Holliston wastewater), upper Charles River 

basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile; --, indicates flow unchanged from average conditions (table 1)]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 -- -- -- -- -- -- -- -- -- -- -- --

CR2 -- -- -- -- -- -- -- -- -- -- -- --

CR3 118.1 133.8 173.4 174.2 109.9 61.4 27.3 23.6 22.0 44.8 81.9 114.9

CR4 158.4 168.2 201.2 199.0 147.2 89.5 51.8 52.5 50.9 85.0 121.1 155.9

BB1 37.7 40.3 55.7 55.6 34.5 14.5 5.0 5.3 4.9 13.6 24.4 36.6

HB1 18.0 22.4 31.1 30.3 15.4 3.8 .7 .9 .9 3.8 8.5 17.5

HB2 26.7 33.2 46.0 44.9 22.8 5.7 1.1 1.3 1.3 5.7 12.6 25.9

MB1 -- -- -- -- -- -- -- -- -- -- -- --

MB2 -- -- -- -- -- -- -- -- -- -- -- --

MR1 -- -- -- -- -- -- -- -- -- -- -- --

Base flow per drainage area (ft3/s/mi2)

CR1 -- -- -- -- -- -- -- -- -- -- -- --

CR2 -- -- -- -- -- -- -- -- -- -- -- --

CR3 1.81 2.05 2.66 2.67 1.69 0.94 0.42 0.36 0.34 0.69 1.26 1.76

CR4 1.89 2.01 2.40 2.37 1.76 1.07 .62 .63 .61 1.01 1.44 1.86

BB1 1.81 1.94 2.68 2.67 1.66 .70 .24 .25 .23 .65 1.17 1.76

HB1 2.42 3.00 4.17 4.07 2.06 .51 .10 .12 .12 .51 1.14 2.35

HB2 2.42 3.01 4.17 4.07 2.07 .52 .10 .12 .12 .52 1.14 2.35

MB1 -- -- -- -- -- -- -- -- -- -- -- --

MB2 -- -- -- -- -- -- -- -- -- -- -- --

MR1 -- -- -- -- -- -- -- -- -- -- -- --
40 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 22. Base flow with Holliston wastewater routed to local recharge basins, Scenario 4B, average climatic conditions, average 

withdrawals (1989–98) and return stresses (except for Holliston wastewater), upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile; --, indicates flow unchanged from average conditions (table 1)]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 -- -- -- -- -- -- -- -- -- -- -- --

CR2 -- -- -- -- -- -- -- -- -- -- -- --

CR3 118.4 134.0 173.6 174.5 110.1 61.7 27.6 23.9 22.2 45.0 82.1 115.2

CR4 157.1 166.9 199.9 197.7 146.0 87.9 50.2 51.2 49.2 83.6 119.8 154.6

BB1 38.8 41.3 56.7 56.6 35.6 15.5 6.1 6.4 6.0 14.7 25.5 37.7

HB1 18.3 22.6 31.3 30.5 15.6 4.1 1.0 1.1 1.1 4.1 8.7 17.7

HB2 27.0 33.4 46.2 45.1 23.0 5.9 1.4 1.6 1.6 6.0 12.8 26.2

MB1 -- -- -- -- -- -- -- -- -- -- -- --

MB2 -- -- -- -- -- -- -- -- -- -- -- --

MR1 -- -- -- -- -- -- -- -- -- -- -- --

Base flow per drainage area (ft3/s/mi2)

CR1 -- -- -- -- -- -- -- -- -- -- -- --

CR2 -- -- -- -- -- -- -- -- -- -- -- --

CR3 1.82 2.06 2.66 2.68 1.69 0.95 0.42 0.37 0.34 0.69 1.26 1.77

CR4 1.87 1.99 2.38 2.36 1.74 1.05 .60 .61 .59 1.00 1.43 1.84

BB1 1.86 1.99 2.73 2.72 1.71 .75 .29 .31 .29 .71 1.23 1.81

HB1 2.45 3.03 4.20 4.10 2.09 .54 .13 .15 .15 .54 1.17 2.38

HB2 2.45 3.03 4.19 4.09 2.09 .54 .12 .14 .14 .54 1.16 2.37

MB1 -- -- -- -- -- -- -- -- -- -- -- --

MB2 -- -- -- -- -- -- -- -- -- -- -- --

MR1 -- -- -- -- -- -- -- -- -- -- -- --

Bellingham

Bellingham has considered building a wastewater 

treatment plant (WDMP) with lagoons for wastewater recharge 

(BL-WRP) adjacent to the Charles River (figs. 6 and 12). Areas 

in Bellingham that receive public water contribute wastewater 

either to the CRPCD treatment facility (29 percent) or to local 

septic-system discharge (71 percent) (table 6). To determine 

how the proposed facility could affect streamflow, it was 

assumed that all Bellingham wastewater would be recharged to 

the aquifer at the BL-WRP recharge facility (Scenario 4C).

Response coefficients were used to calculate flows, and 

the resulting flow changes at CR3 and CR4 are small, as can be 

seen by comparing flows in table 23 to flows under average 

conditions in table 1. The changes are small because 

Bellingham is only 29 percent sewered (table 6). 

Siting of Recharge Basins

Timing of streamflow response to wastewater recharge is 

important in the design and management of recharge basins. As 

formulated in the ground-water model, timing of streamflow 

depletions depends particularly on downgradient distance of the 

stream from the recharge basin, aquifer transmissivity and 

storativity, hydraulic gradient, and width and conductance of 

the streambed, all of which are summarized in the response 

coefficients. Scenario 4D shows how the siting of a recharge 

basin affects the timing of streamflow depletions. A series of 

hypothetical recharge basins at various distances west of 

Miscoe Brook is considered for disposing wastewater from the 

town of Franklin (fig. 13). Response coefficients for the four 

hypothetical basins reflect their distances from Miscoe Brook 

(table 24).
Analysis of Management Alternatives Using Simulation-Optimization 41

Charles River

Beaver Brook

42o05'

71o

27'30"

BL-WRP BELLINGHAM

FRANKLIN

MODEL STREAM CELL

TOWN BOUNDARY

STUDY-AREA BOUNDARY

INACTIVE MODEL AREAS

OUTSIDE OF STUDY AREA

PROPOSED WASTEWATER-RECHARGE BASIN AND IDENTIFIER

WDMP

PROPOSED WASTEWATER-DISCHARGE FACILITY AND IDENTIFIER

BL-WRP

WDMP

EXPLANATION

0 550 METERS

0 1,800 FEET

Figure 12. Proposed Bellingham wastewater facility location, upper Charles River basin, eastern Massachusetts. 

See figure 6 for view of entire study area.
42 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 23. Base flow with Bellingham wastewater routed to BL-WRP recharge basin, Scenario 4C, average climatic conditions, average 

withdrawals (1989–98) and return stresses except for Bellingham wastewater, upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile; --, indicates flow unchanged from average conditions (table 1)]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 -- -- -- -- -- -- -- -- -- -- -- --

CR2 -- -- -- -- -- -- -- -- -- -- -- --

CR3 118.8 134.5 174.1 175.0 110.4 62.1 27.9 24.1 22.6 45.4 82.5 115.5

CR4 157.6 167.4 200.4 198.1 146.4 88.5 50.7 51.5 49.7 84.0 120.1 155.0

BB1 -- -- -- -- -- -- -- -- -- -- -- --

HB1 -- -- -- -- -- -- -- -- -- -- -- --

HB2 -- -- -- -- -- -- -- -- -- -- -- --

MB1 -- -- -- -- -- -- -- -- -- -- -- --

MB2 -- -- -- -- -- -- -- -- -- -- -- --

MR1 -- -- -- -- -- -- -- -- -- -- -- --

Base flow per drainage area (ft3/s/mi2)

CR1 -- -- -- -- -- -- -- -- -- -- -- --

CR2 -- -- -- -- -- -- -- -- -- -- -- --

CR3 1.82 2.06 2.67 2.69 1.69 0.95 0.43 0.37 0.35 0.70 1.27 1.77

CR4 1.88 2.00 2.39 2.36 1.75 1.06 .60 .61 .59 1.00 1.43 1.85

BB1 -- -- -- -- -- -- -- -- -- -- -- --

HB1 -- -- -- -- -- -- -- -- -- -- -- --

HB2 -- -- -- -- -- -- -- -- -- -- -- --

MB1 -- -- -- -- -- -- -- -- -- -- -- --

MB2 -- -- -- -- -- -- -- -- -- -- -- --

MR1 -- -- -- -- -- -- -- -- -- -- -- --

To allow for greater management control, wastewater 

is allowed to discharge in the simulation either entirely to 

Miscoe Brook (WDMPB) or to any of the four basins (FR-W1P, 

FR-W2P, FR-W3P, FR-W4P), in any combination. Franklin’s 

other wastewater disposals (R--FS and R--FW) are set to 

zero under the assumption that all households on municipal 

water will send effluent to the hypothetical facility. The best 

wastewater-disposal solution for increasing summertime base 

flow at MB1 is found as follows: 

Minimize: Streamflow depletions at MB1 during July, 

August, and September.

Constraints: 

1. Monthly pumping rates at wells are equal to monthly 

average (1989–98) rates.

2. Total discharge (to Miscoe Brook and to recharge basins) 

equals total Franklin pumping in each month.

Not all of the five possible disposal options are used in 

the optimal wastewater-disposal solution (table 25). Direct 

discharge to Miscoe Brook and the most distant recharge basins 

are used, whereas the two basins closest to the stream are not 

used. This result can be explained by the response coefficients 

(table 24). During July through September, the greatest 

streamflow results when all wastewater is discharged to the 

stream (WDMBP). For all other months except June, the 

greatest increase in summertime streamflow is obtained by 

using the most distant basin because it has the highest response 

coefficients for months 4–12. To build a recharge basin even 

farther from the stream is impractical because of impermeable 

bedrock outcrops. If a recharge basin were far from a stream, 

however, it would have response coefficients for every month 

close to -1/12 (-0.083). In table 24, the response coefficients of 

basin FR-W1P are closest to this value because FR-W1P is the 

most distant basin. A distant recharge basin with response 

coefficients of -0.083 would provide additional benefit to 

streamflow when recharging during the October–January 

period as compared to basin FR-W1P. 
Analysis of Management Alternatives Using Simulation-Optimization 43

FRANKLIN

WRENTHAM

FR-W1P

WDMBP

FR-W4P

FR-W3P

FR-W2P

FR-W1P

WDMBP

MODEL STREAM CELL

TOWN BOUNDARY

STUDY-AREA BOUNDARY

INACTIVE MODEL AREAS

OUTSIDE OF STUDY AREA

direction of ground-water flow

HYPOTHETICAL WASTEWATER-RECHARGE BASIN AND IDENTIFIER

HYPOTHETICAL WASTEWATER-DISCHARGE FACILITY AND IDENTIFIER

HYPOTHETICAL DIRECT DRINKING-WATER DISCHARGE SITE AND IDENTIFIER DWD-MBP

DWD-MBP

EXPLANATION

Miscoe Brook

0 305 METERS

0 1,000 FEET

71o26'

42o

02'30"

Figure 13. Hypothetical wastewater-recharge and discharge facility, Franklin, upper Charles River basin, 

eastern Massachusetts. See figure 6 for view of entire study area.
44 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 24. Response coefficients for hypothetical recharge basins west of Miscoe Brook in Franklin, upper Charles River basin, eastern 

Massachusetts.

[Response coefficients: Negative values indicate water returns. Type: DP, discharge pipe; RB, recharge basin. ID, identifier; ft, foot; --, zero]

Recharge

stress ID Type

Downgradient

distance

to stream

(ft)

Response coefficient by month

Total

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

WDMBP DP 0 -1.000 -- -- -- -- -- -- -- -- -- -- -- -1.000

FR-W4P RB 200 -.319 -0.163 -0.119 -0.097 -.0080 -0.064 -.0056 -0.044 -0.030 -0.014 -0.014 -- -1.000

FR-W3P RB 894 -.214 -.164 -.131 -.110 -.095 -.075 -.068 -.054 -.043 -.020 -.014 -0.011 -1.000

FR-W2P RB 1,720 -.115 -.148 -.137 -.123 -.108 -.095 -.082 -.068 -.052 -.032 -.023 -.017 -1.000

FR-W1P RB 2,608 -.090 -.144 -.134 -.125 -.113 -.099 -.088 -.071 -.059 -.035 -.023 -.020 -1.000

Table 25. Optimal wastewater-flow schedule, Miscoe Brook hypothetical recharge-discharge facility, Scenario 4D, Franklin, upper 

Charles River basin, eastern Massachusetts.

[Facility location is shown in figure 12. Scenarios are described in table 12. ft3/s, cubic foot per second; --, zero]

Stress

Distance 

to stream

(foot)

Monthly flow rate (ft3/s)

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

Wastewater recharge in basins

FR-W4P 200 -- -- -- -- -- -- -- -- -- -- -- --

FR-W3P 894 -- -- -- -- -- -- -- -- -- -- -- --

FR-W2P 1,720 -- -- -- -- -- 3.22 -- -- -- -- -- --

FR-W1P 2,608 3.53 3.49 3.52 3.66 4.16 -- -- -- -- 3.79 3.47 3.45

Wastewater discharge to stream

WDMBP 0 -- -- -- -- -- -- 3.04 2.79 3.99 -- -- --

If a single recharge basin receives all wastewater and 

direct discharge of wastewater is not allowed, then siting of 

basins to maximize summertime base flow requires a different 

approach. The optimal solution in this case would be to site the 

recharge basin so that the travel time from the basin to the 

nearby stream matches the time between peak wastewater 

discharge and the low-flow period of July through September. 

March and April are the typical months of peak wastewater 

discharge from the CRPCD and MTF plants (fig. 5). Based 

on this scenario, a basin constantly receiving all available 

wastewater will cause the greatest increase in summertime 

streamflow if there is a 4 to 5-month ground-water travel time 

from the basin to the downgradient receiving stream reach.

Adding Wastewater Recharge to an 

Existing Wastewater Facility

To illustrate how adding recharge basins to an existing 

wastewater facility might improve management control over 

base flow, a hypothetical recharge basin (not shown on 

map) was modeled as available for recharging discharge 

from the CRPCD facility by means of optimization methods 

(Scenario 4E). The management objective is to increase base 

flow at constraint point CR4 just downstream of the CRPCD 

outflow. It is assumed that the hypothetical recharge basin 

is distant enough from streams to have response coefficients 

of -0.0833 in all 12 months at constraint point CR4.

Minimize: Streamflow depletions at constraint point CR4 

during July, August, and September

Constraints:

1. All withdrawal and return stresses (except for CRPCD 

flow) are at monthly average (1989–98) rates.

2. Total monthly discharge at the CRPCD (direct discharge 

plus recharge to the basin) equals average (1989–98) 

monthly discharges.

The resulting optimal management solution is shown 

in table 26, and the resulting base-flow values are shown in 

table 27. As in the previous example, the optimal solution is 

to recharge wastewater every month of the year except those 

months in which it is desired to maximize base flow. In the 

optimal case, base flow at CR4 increases compared to average 

flow (table 1) by an average of 4.77 ft3/s (0.06 ft3/s/mi2) during 

July through September, which is 79 percent of annual average 

CRPCD discharge. Base flow in the other months of the year 
Analysis of Management Alternatives Using Simulation-Optimization 45

decreases by an average of 1.56 ft3/s (0.02 ft3/s/mi2) compared 

to average flows (table 1). The large increase in summertime 

flow is not achieved if wastewater is recharged in all 12 months 

of the year; this schedule gives an increase in flow of only 

0.9 ft3/s during July through September.

Injection Wells

Injection wells are formulated the same way as recharge 

basins in the numerical model because the aquifer is thin and 

horizontal discretization is limited to 200 ft by the model grid. 

Therefore, no separate analysis of injection wells was 

performed. Injection wells are expected to have the same effects 

on base flow as recharge basins with the same flow rates.

Moving Wastewater Effluent Upstream

Another management option that can increase streamflow 

is moving wastewater discharges upstream. Such projects 

increase streamflow in the reach between the old and new 

discharge locations by an amount equal to the wastewaterdischarge rate. As an example, a hypothetical case was analyzed 

in which CRPCD wastewater effluent was moved 1,200 ft 

upstream on the Charles River to CRPCD-P (fig. 14), and the 

resulting streamflow changes at constraint point CR3 were 

calculated with the response coefficient approach (Scenario 

5A). The relocation increases flow between the current and 

hypothetical discharge points by the rate of CRPCD discharge. 

Table 28 shows flow changes at CR3, the only constraint point 

lying between CRPCD and CRPCD-P; at all other locations, 

streamflow is unchanged.

Stormwater Recharge

Recharging stormwater runoff is another management 

practice with potential to increase summertime streamflow. 

Stormwater basins catch and recharge runoff, which otherwise 

would flow quickly to streams. A hypothetical case, based on a 

proposed project in Bellingham, serves as an example of how 

stormwater basins can affect base flow (fig. 15). The proposed 

project involves retrofitting an existing residential development 

with a stormwater catchment system. 

Table 26. Pumping rates for wastewater discharge and recharge at Charles River Pollution Control District to optimize base flow, 

Scenario 4E, upper Charles River basin, eastern Massachusetts.

[The sum of discharge and recharge equals average (1989–98) CRPCD discharge rates. Scenarios are described in table 12. Variable locations are shown in figure 

6. CRPCD, Charles River Pollution Control District. ft3

/s, cubic foot per second; --, zero]

 Variable 

identifier Description Optimal pumping rate (ft3

/s) 

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

CRPCD Wastewater 

discharge to 

stream

-- -- -- -- -- -- 5.23 5.17 5.12 -- -- --

CR-RBP Wastewater 

recharge to 

basin

6.35 6.40 7.15 7.48 6.55 5.93 -- -- -- 5.47 5.71 6.29

Table 27. Base-flow changes at outflow constraint point CR4 resulting from the addition of a hypothetical recharge basin to the Charles 

River Pollution Control District, Scenario 4E, upper Charles River basin, eastern Massachusetts.

[Pumping rates are given in table 26. Changes from average were calculated using average base flows shown in table 1. Scenarios are described in table 12. ft3/s, 

cubic foot per second; ft3

/s/mi2, cubic foot per second per square mile]

Flow

Month

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

Base flow (ft3/s)

Flow 156.0 165.8 198.0 195.4 144.6 87.3 55.5 56.5 54.6 83.5 119.3 153.6

Change from average -1.57 -1.62 -2.37 -2.71 -1.78 -1.15 +4.77 +4.77 +4.77 -.69 -.94 -1.52

Base flow per drainage area (ft3/s/mi2)

Flow 1.86 1.98 2.36 2.33 1.72 1.04 .66 .67 .65 1.00 1.42 1.83

Change from average -.02 -.02 -.03 -.03 -.02 -.01 +.06 +.06 +.06 -.01 -.01 -.02
46 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

CRPCD

NORFOLK

FRANKLIN

MILLIS

MEDWAY

CRPCD-P

CR3

Charles River

Charles River

0 800 FEET

0 200 METERS

CRPCD

CRPCD-P

CR3

EXISTING WASTEWATER-DISCHARGE FACILITY AND IDENTIFIER

HYPOTHETICAL WASTEWATER-DISCHARGE FACILITY AND IDENTIFIER

CONSTRAINT POINT AND IDENTIFIER

MODEL STREAM CELL

TOWN BOUNDARY

INACTIVE MODEL AREAS

EXPLANATION

direction of streamflow

71o22'30"

42o

07'

30"

Figure 14. The existing Charles River Pollution Control District discharge location and a hypothetical upstream discharge 

location (CRPCD-P), upper Charles River basin, eastern Massachusetts. See figure 6 for view of entire study area.
Analysis of Management Alternatives Using Simulation-Optimization 47

Table 28. Base-flow changes at CR3 resulting from relocating Charles River Pollution Control District effluent upstream, Scenario 5A, 

upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Flow at constraint points other than CR3 is unchanged. Changes from average were calculated by using average base flows 

shown in table 1. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic foot per second per 

square mile]

Flow

Month

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

Base flow (ft3/s)

Flow 125.2 140.8 181.2 182.4 116.9 67.9 33.1 29.3 27.8 51.0 88.3 121.9

Change from average 6.3 6.4 7.1 7.5 6.6 5.9 5.2 5.2 5.1 5.5 5.7 6.3 

Base flow per drainage area (ft3/s/mi2)

Flow 1.92 2.16 2.78 2.80 1.79 1.04 .51 .45 .43 .78 1.35 1.87

Change from average +.10 +.10 +.11 +.11 +.10 +.09 +.08 +.08 +.08 +.08 0.09 +.10

It is assumed that the retention basin will capture runoff 

from a 500,000-ft2

 area that currently routes runoff directly 

to the Charles River. The proposed basin has the capacity to 

hold runoff from a rainstorm of 0.5 in. An analysis of storm 

records (storms separated by dry periods of more than 12 hours) 

from Logan Airport in Boston during the period 1970–95 

indicates that a basin in this area with a capacity for 0.5 in. 

storms would retain 55 percent of annual runoff. Based on 55 

percent of total rainfall (47 in/yr at the site) and the assumptions 

that all rainfall makes it to the retention basin and that the 

recharge rate is constant, the annual average recharge rate for 

the basin is 0.034 ft3/s. 

Response coefficients are used in calculating changes 

to base flow that result from the hypothetical recharge basin 

(Scenario 6A). No reduction in average streamflow is made 

to account for runoff no longer reaching the stream due to 

installation of the stormwater basin because in this study it is 

assumed that surface runoff is not a large component of 

streamflow during low-flow periods. In reality, stormwater 

basins would reduce streamflow during and just after intense 

rains because surface runoff from the catchment area would no 

longer reach streams. In Scenario 6A, because the recharge rate 

is the same each month, all constraint points downstream of the 

stormwater basin (CR2, CR3, CR4) have monthly increases in 

flow equal to the recharge rate of 0.034 ft3

/s. 

During dry periods (90-percent low-flow conditions), the 

small increases in base flow from the proposed stormwater 

basin are comparatively more important. In the month of 

October under average climatic conditions, base flow at CR2 

increases by 0.07 percent due to the proposed stormwater basin; 

under 90-percent low-flow conditions, base flow increases by 

0.25 percent. A larger drainage area or multiple recharge basins 

would, however, produce correspondingly greater base-flow 

increases.

It is important to consider typical management 

practices when deciding where future stormwater recharge 

projects will be located. Stormwater basins are usually left 

to operate with little management other than vegetation 

control and debris cleaning. Although monthly rainfall is fairly 

consistent throughout the year, runoff is likely to be highest 

from December to March when frozen ground and lower 

evapotranspiration lead to higher runoff. To achieve the highest 

increases in base flow during the critical months of July through 

September, stormwater basins need to have high response 

coefficients in response months 5–10. The best stormwater 

basin location would therefore have a ground-water travel time 

from basin to stream of about 6 months.

Recharge of Flood Waters

During floods, water can be withdrawn from streams and 

infiltrated to aquifers to augment base flow in the summer 

months. Such systems require an intake pipe at the stream, 

pumps, controls, and either injection wells or infiltration basins 

to recharge water to the aquifer. The system would ideally have 

several infiltration basins at different distances from the stream 

and with different response coefficients. Water could be 

infiltrated at the basins in accordance with a schedule giving the 

greatest streamflow increases during July through September. 

The effects of such a project on streamflow are analogous to 

the effects from wastewater and stormwater basins. Flood 

waters can also be diverted to surface-water storage for later 

summertime release or water supply, as is done by Milford with 

Echo Lake.
48 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

MODEL STREAM CELL

TOWN BOUNDARY

INACTIVE MODEL AREA

PROPOSED STORMWATER RECHARGE BASIN AND IDENTIFIER

RUNOFF CATCHMENT AREA

BL-SWP BELLINGHAM

FRANKLIN

Charles River

Stall Brook

Charles River

BL-SWP

EXPLANATION 0 305 METERS

0 1,000 FEET

71o27'

42o

07'30"

Figure 15. Proposed detention basin (BL-SWP), Bellingham, eastern Massachusetts. See figure 6 for 

entire study area.
Analysis of Management Alternatives Using Simulation-Optimization 49

Water Conservation

In response to water-supply shortages, many towns in the 

basin have instituted water-conservation measures. These 

conservation measures commonly impose restrictions on 

outdoor water use during the summer. An example is provided 

by Walpole, a town 5 mi east of the study area. From 1999 to 

2002, Walpole restricted water use from mid-May to midSeptember, limiting outdoor water use to every other day and 

banning automatic sprinkling devices. Over 3 years, average 

water demand from June through September dropped from 3.38 

to 3.07 Mgal/d, a 9.2-percent decline which has helped the town 

avoid costly infrastructure investment (Steven Davis, Walpole 

Water Commission, written commun., 2002).

Hypothetical water conservation was simulated across the 

entire study area by reducing pumping rates to 90 percent of 

average during June through September (Scenario 7A). Other 

months of the year were assigned 100 percent of the average 

pumping rate. The 10-percent summer decrease was applied to 

all municipal and country club wells, but not to power plant 

wells (Bellingham NEA wells # 1, 2, 3, 4, and 5) or private 

wells. No proposed wells or other future projects were included 

and average streamflows were assumed. Wastewater disposal 

was not decreased, despite the decrease in pumping, because it 

was assumed that the reduction in pumping would only affect 

consumptive use and that wastewater production and hence 

wastewater disposal would remain constant. The resulting base 

flow was calculated with the response coefficient approach and 

is shown in table 29. Flow increases during July through 

September by an average of 0.17 ft3

/s at CR4 and 0.03 ft3/s at 

BB1. Under 90-percent low-flow conditions, these base-flow 

increases are the same, but the increases are proportionally 

greater. In addition to increasing base flow, water conservation 

has the additional benefit to towns of reducing water demand on 

days of peak use during the summer when the largest stress is 

placed on water-supply capacity. 

Table 29. Base flow under water conservation measures, Scenario 7A, municipal water use limited to 90 percent of average during 

June through September, average climatic conditions (1989–98), upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 9.6 10.4 13.3 13.5 9.0 4.1 1.8 1.9 1.8 4.0 6.2 9.4

CR2 42.5 45.1 55.3 54.0 39.3 23.6 12.6 12.8 12.7 21.9 32.4 41.2

CR3 118.9 134.5 174.1 175.0 110.4 62.2 28.2 24.6 23.1 45.7 82.7 115.7

CR4 157.7 167.5 200.4 198.2 146.4 88.9 51.3 52.3 50.6 84.5 120.5 155.3

BB1 38.6 41.1 56.5 56.4 35.4 15.5 6.1 6.3 5.9 14.6 25.3 37.5

HB1 18.3 22.6 31.3 30.5 15.6 4.1 1.0 1.1 1.2 4.1 8.7 17.7

HB2 27.0 33.5 46.3 45.2 23.1 6.1 1.5 1.7 1.7 6.0 12.9 26.2

MB1 19.1 20.9 24.0 23.8 17.9 10.5 6.0 6.1 6.1 10.2 14.1 18.9

MB2 34.6 38.7 46.0 45.7 32.0 18.1 9.3 8.8 8.6 15.7 23.8 33.6

MR1 35.3 38.0 42.5 42.4 33.6 23.3 15.1 14.4 14.2 21.2 27.8 34.7

Base flow per drainage area (ft3/s/mi2)

CR1 0.85 0.93 1.18 1.20 0.80 0.36 0.16 0.17 0.16 0.35 0.55 0.84

CR2 1.67 1.77 2.17 2.13 1.55 .93 .49 .50 .50 .86 1.27 1.62

CR3 1.82 2.06 2.67 2.69 1.69 .95 .43 .38 .35 .70 1.27 1.78

CR4 1.88 2.00 2.39 2.36 1.75 1.06 .61 .62 .60 1.01 1.44 1.85

BB1 1.86 1.98 2.72 2.71 1.70 .75 .29 .30 .29 .70 1.22 1.80

HB1 2.45 3.03 4.20 4.10 2.09 .55 .14 .15 .16 .55 1.17 2.38

HB2 2.45 3.03 4.20 4.10 2.09 .55 .14 .15 .15 .55 1.17 2.38

MB1 1.91 2.09 2.39 2.37 1.79 1.05 .59 .61 .61 1.02 1.40 1.88

MB2 2.18 2.43 2.90 2.88 2.01 1.14 .59 .55 .54 .99 1.50 2.12

MR1 2.21 2.38 2.66 2.65 2.10 1.46 .95 .90 .89 1.32 1.74 2.17
50 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Drinking-Water Transfers Between Towns

Transfer of drinking water between towns in the study area 

is quite limited and typically done only during emergency water 

shortages. Municipal drinking-water systems are managed on 

a town-by-town basis and state regulations are imposed on 

towns or on individual wells. Towns with excess water-supply 

capacity may be reluctant to sign long-term contracts for selling 

water to neighboring towns because they may anticipate future 

increases in their own water demand and difficulties obtaining 

permits for new withdrawals. Pipe connections are in place in 

many areas, however, to allow neighboring towns to share 

water supplies during emergency situations. To examine 

the possibility of regional cooperation in more detail, an 

optimization problem was formulated in which towns share 

water (Scenario 8A).

Minimize: Streamflow depletions at CR4 and BB1 during 

July, August, and September.

Constraints: 

1. Base flow must be greater than or equal to average flow 

under no-pumping conditions or 0.41 ft3/s, whichever is 

less.

2. Each town’s monthly water supply is equal to average 

(1989–98) rates.

3. Towns share water (any town can draw from any 

municipal well in the basin).

4. Pumping from each well is at or below State-mandated 

maximum pumping rates (monthly Zone II and annual 

WMA limits are imposed).

No future projects are included other than drinking-water 

transfers. July, August, and September have equal weight in the 

objective function. Base flow is maximized only at constraint 

points CR4 and BB1; limiting the maximization to these two 

constraint points may cause flow at other constraint points to be 

lower.

The optimal pumping schedule increases base flow 

during July through September by an average of 3.4 ft3/s 

(0.04 ft3/s/mi2) at CR4 and by an average of 0.9 ft3/s 

(0.04 ft3/s/mi2) at BB1 (table 30), as compared to base flow 

under average pumping conditions (table 1). The base-flow 

increases are achieved by preferentially pumping wells that are 

close to the river during the winter and wells that are far from 

the river during the summer, as was done in Scenario 2B. The 

base-flow increases are greater than in Scenario 2B (31 percent 

greater at CR4 and 124 percent at BB1) because allowing any 

well to supply any town gives greater management flexibility 

and allows differences in response coefficients between wells to 

be exploited. Norfolk and Franklin, which have wells with long 

response times, pump more than average in the summer and less 

than average in the winter. Holliston, Medway, and Milford, 

which have wells with mostly short response times, pump less 

than average in the summer and more than average in the 

winter. Wrentham, whose wells have long response times, 

pumps more than average in every month; and Bellingham, 

which has wells with 8- to 10-month response times, pumps less 

than average in every month except May.

When 90-percent low-flow conditions are in effect 

(Scenario 8B), constraint 1 must be modified to allow flow 

to drop as low as 0.21 ft3/s/mi2 or to its 90-percent low-flow 

value under no-pumping conditions, whichever is less. The 

optimal pumping schedule increases base flow (table 31) during 

the July through September period by an average of 

2.9 ft3/s (0.03 ft3/s/mi2) at CR4 and by an average of 0.9 ft3/s 

(0.04 ft3

/s/mi2) at BB1 as compared to base flow under average 

pumping and 90-percent low-flow conditions (table 2). 

Drinking-Water Discharge to Streams

Another management technique with potential to increase 

summertime streamflow is pumping drinking water directly to 

streams. This action is analogous to releasing water from a 

surface-water reservoir to increase streamflow, but with the 

aquifer acting as the reservoir. In scenario 9A, drinking water 

can be discharged to Hopping Brook (DWD-HBP), Mine Brook 

(DWD-MBP), and the Charles River upstream of Milford 

(DWD-UCP) as shown in figure 6. All stream reaches 

downstream of a discharge point have an increase in flow in the 

same month as the discharges. Further assumptions are made 

that water from any municipal well can be piped to any 

drinking-water discharge point without passing through septic 

or wastewater systems.

Optimization methods are used to determine pumping 

rates that most improve streamflow in the summer months. It is 

assumed that towns receive average drinking-water supplies 

and any excess pumping goes to discharge at DWD-UCP, 

DWD-HBP, or DWD-MBP (fig. 6). It is required that all 

discharge points have equal discharge rates.

Minimize: Streamflow depletions at CR1, MB1, and HB1 

from July through September.

Constraints: 

1. Base flow must be greater than or equal to average flow 

under no-pumping conditions or 0.41 ft3

/s, whichever is 

less.

2. Each town’s monthly water supply is equal to average 

(1989–98) rates.

3. Towns share water (any town can draw from any 

municipal well in the basin).

4. Pumping from each well is at or below State-mandated 

maximum pumping rates (monthly Zone II and annual 

WMA limits are imposed).

5. In each month, flows at DWD-UCP, DWD-HBP, and 

DWD-MBP are equal. 
Analysis of Management Alternatives Using Simulation-Optimization 51

Table 30. Base flow at constraint points under basin-wide water-supply sharing, Scenario 8A, average climatic conditions, each town 

receives its average water supplies (1989–98), upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 8.5 9.5 12.4 12.8 9.3 4.8 2.8 2.9 2.8 4.6 5.6 8.0

CR2 42.4 45.5 55.7 54.2 39.9 24.7 13.9 14.6 14.2 22.9 32.7 41.0

CR3 118.7 134.8 174.5 175.3 111.1 63.1 29.9 26.8 24.5 46.3 83.1 115.7

CR4 156.9 167.0 199.9 197.9 146.8 89.8 54.2 55.2 53.0 84.8 120.0 154.6

BB1 38.0 40.6 56.0 55.9 35.5 16.2 7.1 7.1 6.5 14.4 24.8 36.9

HB1 18.4 22.7 31.4 30.6 15.8 4.3 1.2 1.3 1.1 4.2 8.8 17.8

HB2 27.1 33.6 46.4 45.3 23.2 6.2 1.6 1.9 1.7 6.1 13.0 26.3

MB1 18.8 20.5 23.6 23.5 17.8 10.0 6.1 6.4 6.1 9.7 13.9 18.8

MB2 34.4 38.4 45.9 45.7 32.0 17.7 9.6 9.0 8.5 15.2 23.8 33.7

MR1 35.8 37.7 42.0 42.2 33.2 23.1 14.6 13.3 13.6 20.8 27.4 34.6

Base flow per drainage area (ft3/s/mi2)

CR1 0.75 0.84 1.10 1.13 0.83 0.43 0.25 0.26 0.25 0.41 0.50 0.71

CR2 1.67 1.79 2.19 2.13 1.57 .97 .55 .58 .56 .90 1.29 1.61

CR3 1.82 2.07 2.68 2.69 1.71 .97 .46 .41 .38 .71 1.28 1.78

CR4 1.87 1.99 2.38 2.36 1.75 1.07 .65 .66 .63 1.01 1.43 1.84

BB1 1.83 1.95 2.69 2.69 1.71 .78 .34 .34 .31 .69 1.19 1.78

HB1 2.46 3.05 4.21 4.11 2.11 .57 .15 .18 .15 .56 1.18 2.39

HB2 2.46 3.04 4.21 4.11 2.11 .57 .15 .17 .15 .55 1.17 2.39

MB1 1.87 2.05 2.36 2.34 1.77 1.00 .61 .63 .61 .97 1.39 1.88

MB2 2.16 2.42 2.89 2.87 2.01 1.11 .60 .56 .53 .96 1.50 2.12

MR1 2.24 2.36 2.63 2.64 2.07 1.45 .91 .83 .85 1.30 1.71 2.17

Base flow increases by an average of 194 percent during 

July through September at CR1, HB1, and MB1 under the 

optimal pumping schedule. Clean water is discharged to each of 

the three stream locations in July, August, and September at 

respective rates of 3.8, 4.2, and 4.6 ft3/s. These flow rates are the 

same at each discharge location as required by constraint 5 and 

no water is discharged in other months of the year. The resulting 

base flows at the 10 constraint points are given in table 32. 

Direct discharge of drinking water would be of less benefit 

to streams if done on a town-by-town basis. If towns were not 

sharing drinking water in Scenario 9A, then only those towns 

with excess supply capacity during summer months would have 

water available to discharge to streams. 

Other Management Strategies

Other strategies for addressing water shortages include 

leaky pipe detection and repair, land-use change, increased use 

of surface-water reservoirs, and importing water supplies from 

outside the basin. Loss of water from distribution pipes can 

be large. For example, investigations by the Massachusetts 

Water Resources Authority (MWRA), the water suppliers for 

Boston and many nearby towns, have detected leaks in their 

water-distribution system totaling 30 Mgal/d (Yeo and 

Estes-Smargiassi, 2000). Repairs to the pipes make more water 

available for use but also reduce the amount of leaking water 

that recharges ground water. Land-use changes, such as 

reduction of impermeable surface area, removal of ditching, 

and revegetation, can increase aquifer recharge by converting 

runoff to infiltration. New surface reservoirs, which help to 

alleviate the naturally low storage capacity of aquifers in the 

basin, can be managed either to increase municipal water 

supplies or to augment summertime streamflow. Connecting to 

outside water-supply systems, most notably the MWRA 

system, is an option that other suburban Boston towns have 

chosen. Water imported to the basin increases municipal water 

supplies and the resulting wastewater, if discharged within the 

basin, increases summertime streamflow. These other strategies 

were not analyzed in this study because a lack of supporting 

data would require major assumptions to be made and would 

increase the uncertainty of the results.

The results of this study indicate that several waterresources management options can increase municipal water 

supplies and summertime streamflows. In table 33, benefits to 

water supplies and summertime streamflows are summarized 

based on the results of this study.
52 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Table 31. Base flow at constraint points under dry conditions (90-percent low flow) and basin-wide water-supply sharing, Scenario 8B, 

each town receives its average water supplies (1989–98), upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 3.5 4.8 9.4 6.9 5.1 2.4 1.5 1.4 1.4 1.7 2.4 2.7

CR2 22.2 28.9 42.7 32.8 24.1 12.2 6.1 4.9 4.0 6.8 14.3 19.9

CR3 34.4 48.9 81.6 55.4 37.6 16.0 7.2 6.1 5.6 7.7 17.5 26.6

CR4 81.3 104.7 156.1 120.9 87.5 45.9 23.4 17.8 16.4 22.3 50.0 72.1

BB1 12.5 18.7 37.3 25.1 15.2 6.0 2.5 1.5 1.4 2.3 5.7 11.0

HB1 4.3 7.1 19.1 9.4 5.3 .9 .1 .1 .0 .2 .9 2.2

HB2 6.4 10.4 28.2 13.9 7.7 1.2 .2 .1 .0 .3 1.3 3.2

MB1 10.2 12.6 19.2 14.3 11.2 5.0 3.0 2.8 2.7 3.0 5.3 7.5

MB2 16.2 21.2 35.0 24.7 18.4 7.3 3.8 3.3 3.3 3.9 7.2 11.0

MR1 22.0 25.0 34.8 27.9 22.5 11.4 5.6 4.1 3.8 6.2 11.6 16.1

Base flow per drainage area (ft3/s/mi2)

CR1 0.31 0.43 0.83 0.62 0.45 0.21 0.13 0.12 0.12 0.15 0.21 0.24

CR2 .87 1.14 1.68 1.29 .95 .48 .24 .19 .16 .27 .56 .78

CR3 .53 .75 1.25 .85 .58 .25 .11 .09 .09 .12 .27 .41

CR4 .97 1.25 1.86 1.44 1.04 .55 .28 .21 .20 .27 .60 .86

BB1 .60 .90 1.79 1.21 .73 .29 .12 .07 .07 .11 .27 .53

HB1 .58 .95 2.56 1.27 .70 .12 .02 .01 .00 .03 .13 .29

HB2 .58 .94 2.55 1.26 .70 .11 .01 .01 .00 .02 .12 .29

MB1 1.02 1.25 1.91 1.42 1.11 .50 .30 .28 .27 .30 .53 .75

MB2 1.02 1.33 2.20 1.56 1.16 .46 .24 .21 .21 .25 .45 .70

MR1 1.38 1.56 2.18 1.74 1.41 .71 .35 .26 .24 .39 .72 1.01

Limitations of this Analysis

Although the analyses in this study focus on monthly 

average flow rates, there can be substantial streamflow 

variation within a month. A comparison of daily flow variability 

to monthly mean flow at the Medway streamflow-gaging 

station (01103280, fig. 3) in the eastern part of the study area is 

shown in figure 16. A statistical analysis was done on daily 

streamflow data collected from November 1997 to December 

2000 at the Medway station. Daily mean flow values are below 

the monthly mean flow value more than half the month because 

of short-duration high stormwater flows (fig. 17). During July 

and September at the same station, daily flow values are less 

than monthly mean flow more than 75 percent of the time.

Awareness of how flow statistics vary with length of 

averaging period is important in setting minimum flow 

standards for water-resource management goals. Because 

streamflow data are characterized by a lack of negative values 

and infrequent extreme high values, longer averaging periods 

will generally result in higher mean values. Therefore, the mean 

monthly flow values used in this study will be higher than mean 

daily flow values more than half the time. If a regulatory 

program has the goal of protecting freshwater aquatic ecology, 

then the duration of low flow that is critical to maintaining 

ecology is important. For instance, if streamflow below 

0.05 ft3/s/mi2 is fatal to fish when it lasts for more than a day, 

then a management process that uses at least daily average 

streamflow values to set management actions will be most 

effective at protecting fish. The results of this study, quantified 

as monthly average streamflow values, can be at least partially 

applied to averaging periods of less than a month by comparing 

monthly average flow-duration curves to shorter term (such as 

daily) flow-duration curves.

The results presented here are affected by errors in

the response coefficients. These errors can be important 

in the analysis of low flow, particularly in small streams, 

because errors are a higher percentage of total streamflow 

than for average and high flows. Other errors due to model
Analysis of Management Alternatives Using Simulation-Optimization 53

Table 32. Base flow under direct drinking-water discharge to streams, Scenario 9A, each town receives its average water supplies 

(1989–98), average climatic conditions, upper Charles River basin, eastern Massachusetts.

[Scenarios are described in table 12. Grey shading indicates July–September months with flow less than 0.5 ft3/s/mi2. ft3/s, cubic foot per second; ft3/s/mi2, cubic 

foot per second per square mile]

Constraint

point January February March April May June July August September October November December

Base flow (ft3/s)

CR1 8.1 9.4 12.5 14.0 9.8 5.0 4.7 4.4 4.3 1.4 4.0 7.5

CR2 40.8 44.0 54.2 54.4 39.8 23.9 14.7 14.5 14.1 19.5 30.0 39.1

CR3 117.0 133.4 173.7 176.2 112.0 63.5 37.6 33.6 32.1 42.3 79.8 113.2

CR4 155.1 166.2 200.0 199.1 147.6 89.2 58.9 59.1 56.9 80.3 117.4 152.8

BB1 39.2 41.3 56.7 56.4 35.4 15.6 5.4 5.2 4.4 14.0 25.3 37.9

HB1 18.3 22.7 31.4 30.6 15.7 4.3 4.8 5.2 5.6 4.0 8.7 17.7

HB2 27.1 33.5 46.4 45.3 23.2 6.2 5.3 5.8 6.1 6.0 12.9 26.2

MB1 19.3 21.2 24.9 24.9 19.3 12.0 9.8 9.7 9.6 9.6 13.9 18.9

MB2 34.4 38.6 46.5 46.5 32.9 19.3 12.8 12.0 11.7 14.7 23.3 33.2

MR1 34.8 37.4 42.2 41.4 32.2 22.0 13.5 12.6 12.2 20.0 27.0 33.8

Base flow per drainage area (ft3/s/mi2)

CR1 0.72 0.84 1.11 1.25 0.87 0.44 0.42 0.39 0.38 0.13 0.36 0.67

CR2 1.61 1.73 2.13 2.14 1.57 .94 .58 .57 .55 .77 1.18 1.54

CR3 1.80 2.05 2.67 2.70 1.72 .97 .58 .52 .49 .65 1.23 1.74

CR4 1.85 1.98 2.39 2.38 1.76 1.06 .70 .71 .68 .96 1.40 1.82

BB1 1.88 1.99 2.73 2.71 1.70 .75 .26 .25 .21 .67 1.22 1.82

HB1 2.46 3.04 4.21 4.11 2.11 .57 .65 .70 .75 .54 1.17 2.38

HB2 2.45 3.04 4.20 4.10 2.11 .57 .48 .52 .55 .54 1.17 2.38

MB1 1.93 2.12 2.48 2.49 1.92 1.20 .98 .97 .96 .95 1.39 1.88

MB2 2.17 2.43 2.93 2.93 2.07 1.21 .81 .76 .74 .93 1.47 2.09

MR1 2.18 2.34 2.64 2.59 2.02 1.37 .84 .79 .76 1.25 1.69 2.11

insufficiencies may be present in the results. These error 

sources include inadequate representation of surface 

topography and surface-water features. For example, if a stream 

that is close to a well is absent in the numerical flow model, the 

actual stream response times may be much faster than indicated 

by the model and derived response coefficients will contain 

inherent inaccuracies. 

This analysis only considers flow at the 10 constraint 

points shown in figure 3. In other stream reaches, particularly 

upstream of constraint points, normalized flow (cubic foot per 

second per square mile) may be lower. Water quality was not 

considered in this study. Many of the scenarios considered 

involve management of variably treated wastewater, which may 

affect surface-water quality. Changing the pumping schedules 

of wells may also be difficult due to water-quality deterioration 

associated with high pumping rates.

In some cases, gaps in the data used to describe pumping 

wells may have affected results. For example, mechanical limits 

to pumping rates for some wells were not included in the 

analysis because reliable data about such limits were not 

available.

1

If actively managed to increase base flow.

2

Only if combined with a surface-water reservoir.

Table 33. Benefits of potential water-management actions, 

upper Charles River basin, eastern Massachusetts.

Management action

Benefits

Increased 

water 

supply

Increased 

base flow

New wells 9 19

Stormwater recharge 9

Treated wastewater recharge 9

Inter-town water transfers (intra-basin) 9 19

New surface-water reservoirs 9 19

Leaky pipe repair 9

Pumping schedule management 9 9

Direct discharge of drinking water to streams 9

Import water from outside basin 9 9

Water-use restrictions 9 9

Land-use management 9

Flood skimming 29 9

Moving wastewater effluent upstream 9
54 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

0

100

200

300

400

500

0 5 10 15 20 25 30

Daily

Average for Month

DAY OF MONTH

STREAMFLOW, IN CUBIC FEET PER SECOND

Figure 16. Daily and average streamflow for October 1998 at the Medway streamflow-gaging station (01103280), eastern 

Massachusetts.

0

100

200

300

400

500

JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC.

MONTH

STREAMFLOW, IN CUBIC FEET PER SECOND

Q1

Minimum

Maximum

Q3

Median

Mean

(N)

(93)

(85) (93)

(90)

(93)

(90)

(93)

(93)

(90) (93)

(109)

(119)

Figure 17. Daily streamflow variability by month at the Medway streamflow-gaging station (01103280), eastern 

Massachusetts. The period of record is November 1997 through December 2000. N is the number of daily 

streamflow values used to calculate the statistics. Q1 is the 25th percentile, and Q3 is the 75th percentile.
Summary and Conclusions 55

Summary and Conclusions

Water shortages in the upper Charles River basin are 

evident from strained municipal water supplies and average 

stream base flow that falls below 0.50 ft3/s/mi2, the ABF lowflow value recommended to "sustain and perpetuate indigenous 

aquatic fauna" (U.S. Fish and Wildlife Service, 1981). Under 

average climatic and pumping conditions, 6 of 10 constraint 

points analyzed (BB1, HB1, HB2, CR1, CR2, CR3) have 

mean monthly flows below 0.50 ft3/s/mi2 in summer, with 

the lowest monthly flow at the 10 constraint points averaging 

0.41 ft3

/s/mi2. Under dry climatic conditions (defined as 

periods of 90-percent flow duration) and average pumping, base 

flow drops below 0.50 ft3/s/mi2 at every constraint point, 

average low monthly flow at the 10 constraint points is 

0.10 ft3/s/mi2, and Hopping Brook (at constraint points HB1 

and HB2) essentially goes dry. Dry climatic conditions magnify 

the effects of water-management actions because humancontrolled flow then constitutes a much larger percentage of 

streamflow. 

Although human water use exacerbates summertime low 

flow, study results indicate that human water use is not the only, 

or even the primary, cause of low flow in the basin. When 

no-pumping conditions are simulated, flow at 5 of the 10 

constraint points (BB1, HB1, HB2, CR1, CR3) still falls 

below 0.50 ft3/s/mi2 in the summertime. Under no-pumping 

conditions, the lowest monthly streamflow at the 10 constraint 

points increases slightly from an average of 0.41 ft3

/s/mi2 to an 

average of 0.46 ft3

/s/mi2, due to the cessation of human induced 

evaporative losses. 

New ground-water wells can certainly increase the water 

supply available to towns. If handled carefully, new wells can 

also increase the ability of towns to manage withdrawals so that 

they cause less streamflow depletion during the summer. To 

increase streamflow, however, pump locations must be chosen, 

and pumping schedules must be actively managed with that 

explicit goal.

Because the two wastewater facilities contribute such 

large flows to the Charles River, management actions at these 

facilities have important consequences for water supply and 

streamflow in the basin. The addition of a recharge basin at 

the CRPCD facility, in combination with optimal effluent 

management, can increase flow in the Charles River at its outlet 

point CR4 by 4.77 ft3/s (0.06 ft3/s/mi2) during the JulySeptember period; this increase is more than twice the flow 

increase of 2.2 ft3

/s resulting from shutting off all pumps in the 

basin. 

Sewering projects, which replace distributed septic 

systems with sewers and centralized wastewater treatment, 

have the potential to decrease summertime base flow. This is 

evident from the results of Scenario 4A, in which Holliston’s 

wastewater is routed to the CRPCD. The use of localized 

recharge facilities in Holliston negates this streamflow 

decrease. 

Aquifer recharge from construction of a storm-water basin 

could increase base flow during the summer (Scenario 6A). If 

the size of the basin and its collecting watershed in Scenario 6A 

were increased, the summertime base-flow would also increase. 

However, other limitations on the size of the basin, such as 

availability of property in an existing neighborhood without a 

stormwater recharge system, were not considered in this 

hydrologic analysis.

The use of response coefficients to describe how 

streamflow responds to water withdrawals and wastewater 

disposals can provide useful information to water-resources 

managers about the timing of streamflow changes relative to the 

timing of ground-water pumping or recharge. The results of this 

study show that considerable enhancement of summertime 

streamflow can be realized from towns strategically managing 

their pumping well schedules. The greatest benefit can be 

realized by towns that have wells with a variety of streamflow 

response times. On the basis of this study, wells that have short 

response times will cause less summertime flow depletion if 

they are pumped preferentially from October to January; wells 

that have long response times, because they are far from the 

river, can be pumped preferentially from February to 

September. 

If recharge basins are built for the purpose of increasing 

ground-water storage and base flow, the optimal location of a 

basin depends on how it is to be managed. If wastewater or 

stormwater continually flow at an approximately constant rate 

to the basin, then, on the basis of this study, a basin sited so that 

ground-water travel time from basin to stream equals the time 

between peak wastewater discharge and the low streamflow 

period will give the greatest increase to summertime flow. In 

the Charles River basin, wastewater discharge and stormwater 

flow often reach their peaks during March and April, 5 to 6 

months before the months of lowest streamflow. Based on 

this study, recharge basins receiving continuous flow will 

therefore achieve the greatest increase in August and September 

streamflow by being located so that ground-water travel-time 

from the basin to the downgradient stream is 5 to 6 months. 

However, if a recharge basin is paired with a pipe that 

discharges directly to a stream, the greatest benefit to 

summertime streamflow can be achieved by locating the basin 

as far as possible from the stream, discharging water directly 

to the stream during periods of low flow, and discharging to the 

recharge basin the rest of the year. Greater streamflow increases 

result from a basin sited far from a stream because the response 

coefficients are more likely to be uniform across all months; 

this uniformity of response yields the greatest ground-water 

discharge to the stream in the summertime. Even greater benefit 

to summertime streamflow can be realized with multiple 

recharge basins managed in conjunction with a pipe discharging 

directly to the stream. Optimization methods are useful for 

choosing optimal basin locations and discharge schedules for 

such facilities.
56 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Response coefficients can also help in the siting of 

locations for new ground-water wells. If a town plans to manage 

its well system to minimize summertime streamflow depletions, 

then the results of this study indicate that new well locations 

should be chosen to have response times unlike those of existing 

wells. A collection of wells with a variety of response times 

provides the greatest management flexibility for reducing 

pumping effects on streams. For example, if it is known that a 

new well will only be used in the summer to meet peak 

demands, then the well can be sited as far as possible from 

streams to delay the resulting streamflow depletions.

Water-conservation measures have been implemented 

by some towns in the basin to reduce peak water use in 

the summer. The results of this study indicate that water 

conservation also has the desired effect of increasing 

summertime base flow in the upper Charles River and its 

tributaries. The benefits of water conservation for water supply 

and streamflow will be greater than in Scenario 7A if more than 

a 10-percent reduction in water use is achieved.

If basin-wide management of water resources were 

instituted in the upper Charles River basin, both towns and 

streams could benefit. The results of Scenarios 8A and 8B 

indicate that if drinking-water transfers between towns were 

practiced and coordinated, summertime flow could be increased 

at the basin exit points by 2.9 ft3

/s at constraint point CR4 and 

by 0.9 ft3

/s at constraint point BB1, which corresponds to 18 

percent and 95 percent of flow, respectively, under dry climatic 

conditions. If water sharing were practiced, an excess watersupply capacity of 13.4 ft3

/s would be available to any town 

because Zone II limits allow 24.1 ft3/s of pumping as compared 

to 10.7 ft3/s for current average municipal water use. This study 

focused on hydrologic analyses and did not consider factors 

such as the economic effects of current water-sharing practices 

on the availability and cost of public-water supply in the basin. 

Pumping clean water directly to streams has the potential 

to raise summertime streamflow and improve the quality of the 

water. The water can be pumped either from ground-water 

storage (aquifers) or a surface-water reservoir. The benefit to 

streams is much greater if towns share water supplies, so that 

the water can be delivered to the most stressed streams, even if 

they are in a town that does not have excess drinking-water 

supply in the summer.

Low streamflow and public water-supply shortages during 

the summer in the upper Charles River basin have caused 

concern about water supplies in the basin. In response to this 

concern, the USGS and the Massachusetts EOEA cooperated to 

prepare this study of potential alternatives for water-resources 

managers to address water shortages in the basin. A technical 

advisory committee composed of town water officials, USGS 

staff, state environmental regulators, and environmental 

advocates helped define the questions to be addressed.

The results of this study indicate that response coefficients 

and simulation-optimization methods are well suited for 

analyzing stressed stream-aquifer systems and are useful for 

analyzing water-resource management strategies to increase 

water supply and streamflow. The following strategies have 

potential benefit for addressing water shortages in the basin:

• Water conservation measures

• Strategic scheduling of ground-water pumping

• Direct discharge of water to streams

• Towns sharing drinking water

• Use of wastewater recharge basins and injection wells

• Stormwater basins

• New wells

Each of these strategies can, when properly managed, both 

increase summertime flow in streams and increase summertime 

water supply for human use. The results of this study will be 

useful to managers, planners, and regulators of water resources 

in the upper Charles River basin and in similar hydrogeologic 

settings where human water use affects shallow stream-aquifer 

systems. 

References Cited

Ahlfeld, D.P., and Mulligan, A.E., 2000, Optimal management 

of flow in ground-water systems: Academic Press, New 

York, 185 p.

Armstrong, D.S., Richards, T.A., and Parker, G.W., 2001, 

Assessment of habitat, fish communities, and streamflow 

requirements for habitat protection, Ipswich River, 

Massachusetts: U.S. Geological Survey, Water-Resources 

Investigations Report 01-4161, 72 p.

Army Corp of Engineers, 1994, The National inventory of dams 

1993–94: Troy, NY, Venture Computing Group, Inc., CDROM.

Barlow, P.M., Ahlfeld, D.P., and Dickerman, D.C., 2003, 

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Appendix 1

Appendix 1 61

Appendix 1. Historic average monthly stress rates (1989–98), upper Charles River basin, eastern Massachusetts.[CRPCD, Charles River Pollution Control District; NEA, Northeast Energy Association; --, zero]

Stress description Historic average stresses, in cubic foot per second January February March April May June July August September October November December Annual 

 Pumping 

Bellingham NEA Wells 1, 2, and 3 0.802 0.851 0.825 0.865 0.705 0.768 0.753 0.805 0.817 0.851 0.892 0.986 0.827 Bellingham NEA Wells 4 and 5 .023 .026 .023 .027 .028 .018 .016 .015 .015 .014 .016 .002 .019 Bellingham Well Number 12 .003 .028 .011 .016 .026 .032 .072 .057 .039 .029 .029 .026 .031 Bellingham Well Number 5 .280 .296 .320 .319 .313 .299 .317 .316 .306 .311 .294 .283 .304 Bellingham Well Number 7 .120 .111 .128 .148 .281 .271 .248 .172 .115 .106 .104 .072 .156 Bellingham Well Number 8 .253 .319 .356 .316 .484 .739 .746 .652 .354 .316 .279 .251 .422 Franklin Populatic Injection Well -- -- -- -- -- -- -- -- -- -- -- -- --Franklin Populatic Pond Well -- -- -- -- -- -- -- -- -- -- -- -- --Franklin Proposed Well Number 11 -- -- -- -- -- -- -- -- -- -- -- -- --Franklin Well Number 1 .075 .108 .125 .056 .129 .322 .298 .289 .265 .241 .155 .064 .177 Franklin Well Number 10 .299 .289 .295 .301 .331 .375 .407 .372 .318 .365 .366 .362 .340 Franklin Well Number 2 .075 .108 .125 .056 .129 .322 .298 .289 .265 .241 .155 .064 .177 Franklin Well Number 3 .401 .375 .430 .481 .546 .572 .529 .504 .499 .435 .405 .427 .467 Franklin Well Number 4 .961 .950 .871 1.019 1.136 1.172 1.149 1.107 1.045 .984 .977 .980 1.029 Franklin Well Number 5 .249 .250 .260 .208 .276 .304 .320 .286 .237 .228 .244 .285 .262 Franklin Well Number 6 .571 .575 .555 .618 .633 .636 .596 .565 .451 .447 .339 .360 .529 Franklin Well Number 7 .427 .418 .417 .470 .480 .504 .496 .436 .414 .386 .379 .433 .438 Franklin Well Number 8 .475 .415 .438 .446 .500 .493 .511 .491 .493 .462 .450 .472 .470 Holliston Glen Ellen Country Club -- -- -- .004 .060 .156 .189 .146 .078 .039 -- -- .056 Holliston Maplegate Country Club -- -- -- .016 .031 .064 .111 .111 .115 .077 .032 -- .046 Holliston Proposed Well Number 7 -- -- -- -- -- -- -- -- -- -- -- -- --Holliston Well Number 1 Lake Winthrop -- -- -- .018 .101 .183 .234 .176 .133 .043 .026 -- .076 Holliston Well Number 2 Maple Street .007 .011 .041 .029 .119 .219 .280 .234 .079 .022 .019 .003 .089 Holliston Well Number 4 Washington Street .123 .138 .147 .111 .203 .382 .421 .333 .266 .200 .181 .143 .221 Holliston Well Number 5 Central Street .707 .617 .612 .700 .811 .757 .746 .688 .637 .644 .661 .715 .691 Holliston Well Number 6 Brook Street .704 .701 .687 .697 .733 .947 .794 .686 .665 .652 .567 .612 .704 Medway Proposed Well -- -- -- -- -- -- -- -- -- -- -- -- --Medway Well Number 1 Populatic Street .581 .625 .694 .608 .616 .713 .665 .736 .696 .538 .597 .558 .636 Medway Well Number 2 Oakland Street .147 .147 .104 .157 .260 .301 .336 .255 .221 .240 .171 .177 .210 Medway Well Number 3 Village Street .507 .464 .437 .428 .545 .661 .677 .447 .477 .579 .443 .553 .518 
62 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA Pumping—Continued Milford Clark Island Wellfield 0.807 0.672 0.419 0.449 0.416 0.458 0.749 0.908 0.836 0.802 0.776 0.664 0.663 Milford Dilla Street Wells Number 1 .008 .011 .004 -- -- -- .014 .027 .014 .021 .025 .017 .012 Milford Dilla Street Wells Number 2 .008 .011 .004 -- -- -- .014 .027 .014 .021 .025 .017 .012 Milford Godfrey Brook Well 3 .194 .184 .162 .153 .176 .167 .181 .182 .215 .201 .217 .224 .188 Milford Godfrey Brook Well 4 .194 .184 .162 .153 .176 .167 .181 .182 .215 .201 .217 .224 .188 Milford Godfrey Brook Well 5 .194 .184 .162 .153 .176 .167 .181 .182 .215 .201 .217 .224 .188 Norfolk Proposed Mill River Well -- -- -- -- -- -- -- -- -- -- -- -- -- Norfolk Well Number 1 Gold Street .276 .279 .333 .441 .436 .524 .481 .365 .375 .356 .353 .311 .378 Wrentham Proposed Well -- -- -- -- -- -- -- -- -- -- -- -- -- Wrentham Well Number 2 .477 .477 .474 .457 .714 .598 .727 .556 .343 .443 .302 .300 .489 Wrentham Well Number 3 .559 .594 .514 .776 .499 .825 .773 .697 .806 .463 .601 .650 .646 Stormwater Recharge Bellingham SW Recharge -- -- -- -- -- -- -- -- -- -- -- -- -- Wastewater Recharge Bellingham Proposed Facility -- -- -- -- -- -- -- -- -- -- -- -- -- Holliston–Gorwin Drive Site -- -- -- -- -- -- -- -- -- -- -- -- -- Holliston–EHIP-1 Site -- -- -- -- -- -- -- -- -- -- -- -- -- Holliston–EHIP-2 Site -- -- -- -- -- -- -- -- -- -- -- -- -- Recharge 2,608 ft from Miscoe Brook -- -- -- -- -- -- -- -- -- -- -- -- -- Recharge 1,720 ft from Miscoe Boork -- -- -- -- -- -- -- -- -- -- -- -- -- Recharge 894 ft from Miscoe Brook -- -- -- -- -- -- -- -- -- -- -- -- -- Recharge 200 ft from Miscoe Brook -- -- -- -- -- -- -- -- -- -- -- -- -- Hypothetical recharge at CRPCD -- -- -- -- -- -- -- -- -- -- -- -- -- Wastewater Discharge Bellingham Proposed -- -- -- -- -- -- -- -- -- -- -- -- -- CRPCD 6.348 6.395 7.145 7.484 6.550 5.926 5.226 5.173 5.116 5.466 5.712 6.290 6.069 CRPCD Upstream Discharge -- -- -- -- -- -- -- -- -- -- -- -- -- Milford 6.440 5.611 7.244 7.001 5.908 4.591 4.005 3.872 4.076 4.576 5.247 6.332 5.408 Miscoe Brook Hypothetical -- -- -- -- -- -- -- -- -- -- -- -- -- Appendix 1. Historic average monthly stress rates (1989–98), upper Charles River basin, eastern Massachusetts.—Continued [CRPCD, Charles River Pollution Control District; NEA, Northeast Energy Association; --, zero] Stress description Historic average stresses, in cubic foot per second January February March April May June July August September October November December Annual 
Appendix 1 63

Combined Wastewater Discharge and Septic Discharge

Bellingham Summer -- -- -- -- 1.104 1.342 1.382 1.198 -- -- -- -- 0.419 Bellingham Winter 0.656 0.754 0.815 0.799 -- -- -- -- 0.813 0.762 0.706 0.631 .495 Franklin Summer -- -- -- -- 4.555 5.129 5.069 4.788 -- -- -- -- 1.628 Franklin Winter 3.857 3.837 3.836 3.997 -- -- -- -- 4.417 4.226 3.901 3.859 2.661 Holliston Summer -- -- -- -- 1.967 2.488 2.475 2.117 -- -- -- -- .754 Holliston Winter 1.542 1.467 1.487 1.555 -- -- -- -- 1.779 1.561 1.455 1.473 1.027 Medway Summer -- -- -- -- 1.420 1.675 1.678 1.438 -- -- -- -- .518 Medway Winter 1.235 1.236 1.236 1.193 -- -- -- -- 1.394 1.357 1.211 1.288 .846 Milford Summer -- -- -- -- .942 .960 1.320 1.508 -- -- -- -- .394 Milford Winter 1.404 1.246 .912 .909 -- -- -- -- 1.510 1.449 1.478 1.368 .856 Norfolk Summer -- -- -- -- .436 .524 .481 .365 -- -- -- -- .151 Norfolk Winter .276 .279 .333 .441 -- -- -- -- .375 .356 .353 .311 .227 Wrentham Summer -- -- -- -- 1.213 1.423 1.500 1.253 -- -- -- -- .449 Wrentham Winter 1.036 1.071 .987 1.233 -- -- -- -- 1.149 .905 .903 .950 .686 

 Direct Drinking-Water Discharge to Streams 

Drinking Water Discharge to Charles River -- -- -- -- -- -- -- -- -- -- -- -- --Drinking Water Discharge to Hopping Brook -- -- -- -- -- -- -- -- -- -- -- -- --Drinking Water Discharge to Mine Brook -- -- -- -- -- -- -- -- -- -- -- -- --

Appendix 1. Historic average monthly stress rates (1989–98), upper Charles River basin, eastern Massachusetts.—Continued[CRPCD, Charles River Pollution Control District; NEA, Northeast Energy Association; --, zero]

Stress description Historic average stresses, in cubic foot per second January February March April May June July August September October November December Annual 

Appendix 2

Appendix 2 67

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1

Bellingham Northeast 

Energy Association 

wells 1, 2, and 3

Q01B1 1 — 0.574 0.574 0.574 — — — — — —

Q02B1 2 — .199 .199 .199 — — — — — —

Q03B1 3 — .092 .092 .092 — — — — — —

Q04B1 4 — .063 .063 .063 — — — — — —

Q05B1 5 — .036 .036 .036 — — — — — —

Q06B1 6 — .025 .025 .025 — — — — — —

Q07B1 7 — .010 .010 .010 — — — — — —

Q08B1 8 — — — — — — — — — —

Q09B1 9 — — — — — — — — — —

Q10B1 10 — — — — — — — — — —

Q11B1 11 — — — — — — — — — —

Q12B1 12 — — — — — — — — — —

Bellingham Northeast 

Energy Association 

wells 4 and 5

Q01B4 1 — .485 .485 .485 — — — — — —

Q02B4 2 — .214 .214 .214 — — — — — —

Q03B4 3 — .119 .119 .119 — — — — — —

Q04B4 4 — .083 .083 .083 — — — — — —

Q05B4 5 — .043 .043 .043 — — — — — —

Q06B4 6 — .034 .034 .034 — — — — — —

Q07B4 7 — .013 .013 .013 — — — — — —

Q08B4 8 — .010 .010 .010 — — — — — —

Q09B4 9 — — — — — — — — — —

Q10B4 10 — — — — — — — — — —

Q11B4 11 — — — — — — — — — —

Q12B4 12 — — — — — — — — — —

Bellingham proposed 

wastewater 

recharge facility 

Q01BR 1 — -.910 -.910 -.910 — — — — — —

Q02BR 2 — -.077 -.077 -.077 — — — — — —

Q03BR 3 — -.013 -.013 -.013 — — — — — —

Q04BR 4 — — — — — — — — — —

Q05BR 5 — — — — — — — — — —

Q06BR 6 — — — — — — — — — —

Q07BR 7 — — — — — — — — — —

Q08BR 8 — — — — — — — — — —

Q09BR 9 — — — — — — — — — —

Q10BR 10 — — — — — — — — — —

Q11BR 11 — — — — — — — — — —

Q12BR 12 — — — — — — — — — —

Bellingham proposed 

stormwater 

recharge facility

Q01BS 1 — -.754 -.754 -.754 — — — — — —

Q02BS 2 — -.170 -.170 -.170 — — — — — —

Q03BS 3 — -.042 -.042 -.042 — — — — — —

Q04BS 4 — -.020 -.020 -.020 — — — — — —

Q05BS 5 — -.014 -.014 -.014 — — — — — —

Q06BS 6 — — — — — — — — — —

Q07BS 7 — — — — — — — — — —

Q08BS 8 — — — — — — — — — —

Q09BS 9 — — — — — — — — — —

Q10BS 10 — — — — — — — — — —

Q11BS 11 — — — — — — — — — —

Q12BS 12 — — — — — — — — — —
68 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Bellingham well 12 Q01B9 1 — 0.368 0.368 0.368 — — — — — —

Q02B9 2 — .235 .235 .235 — — — — — —

Q03B9 3 — .139 .139 .139 — — — — — —

Q04B9 4 — .090 .090 .090 — — — — — —

Q05B9 5 — .060 .060 .060 — — — — — —

Q06B9 6 — .038 .038 .038 — — — — — —

Q07B9 7 — .029 .029 .029 — — — — — —

Q08B9 8 — .025 .025 .025 — — — — — —

Q09B9 9 — .016 .016 .016 — — — — — —

Q10B9 10 — — — — — — — — — —

Q11B9 11 — — — — — — — — — —

Q12B9 12 — — — — — — — — — —

Bellingham well 5 Q01B5 1 — .613 .613 .613 — — — — — —

Q02B5 2 — .141 .141 .141 — — — — — —

Q03B5 3 — .073 .073 .073 — — — — — —

Q04B5 4 — .086 .086 .086 — — — — — —

Q05B5 5 — .021 .021 .021 — — — — — —

Q06B5 6 — .031 .031 .031 — — — — — —

Q07B5 7 — .021 .021 .021 — — — — — —

Q08B5 8 — .013 .013 .013 — — — — — —

Q09B5 9 — — — — — — — — — —

Q10B5 10 — — — — — — — — — —

Q11B5 11 — — — — — — — — — —

Q12B5 12 — — — — — — — — — —

Bellingham well 7 Q01B7 1 — .406 .406 .406 — — — — — —

Q02B7 2 — .188 .188 .188 — — — — — —

Q03B7 3 — .125 .125 .125 — — — — — —

Q04B7 4 — .104 .104 .104 — — — — — —

Q05B7 5 — .061 .061 .061 — — — — — —

Q06B7 6 — .039 .039 .039 — — — — — —

Q07B7 7 — .029 .029 .029 — — — — — —

Q08B7 8 — .021 .021 .021 — — — — — —

Q09B7 9 — .016 .016 .016 — — — — — —

Q10B7 10 — .012 .012 .012 — — — — — —

Q11B7 11 — — — — — — — — — —

Q12B7 12 — — — — — — — — — —

Bellingham well 8 Q01B8 1 — .480 .480 .480 — — — — — —

Q02B8 2 — .175 .175 .175 — — — — — —

Q03B8 3 — .099 .099 .099 — — — — — —

Q04B8 4 — .067 .067 .067 — — — — — —

Q05B8 5 — .047 .047 .047 — — — — — —

Q06B8 6 — .044 .044 .044 — — — — — —

Q07B8 7 — .027 .027 .027 — — — — — —

Q08B8 8 — .024 .024 .024 — — — — — —

Q09B8 9 — .020 .020 .020 — — — — — —

Q10B8 10 — .016 .016 .016 — — — — — —

Q11B8 11 — — — — — — — — — —

Q12B8 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 69

Bellingham 

wastewater return 

May–August

R01BS 1 — -0.387 -0.387 -0.387 — — — — — —

R02BS 2 — -.133 -.133 -.133 — — — — — —

R03BS 3 — -.070 -.070 -.070 — — — — — —

R04BS 4 — -.037 -.037 -.037 — — — — — —

R05BS 5 — -.037 -.037 -.037 — — — — — —

R06BS 6 — -.023 -.023 -.023 — — — — — —

R07BS 7 — -.013 -.013 -.013 — — — — — —

R08BS 8 — — — — — — — — — —

R09BS 9 — — — — — — — — — —

R10BS 10 — — — — — — — — — —

R11BS 11 — — — — — — — — — —

R12BS 12 — — — — — — — — — —

Bellingham 

wastewater return 

September–April

R01BW 1 — -.597 -.597 -.597 — — — — — —

R02BW 2 — -.159 -.159 -.159 — — — — — —

R03BW 3 — -.083 -.083 -.083 — — — — — —

R04BW 4 — -.047 -.047 -.047 — — — — — —

R05BW 5 — -.034 -.034 -.034 — — — — — —

R06BW 6 — -.032 -.032 -.032 — — — — — —

R07BW 7 — -.029 -.029 -.029 — — — — — —

R08BW 8 — -.018 -.018 -.018 — — — — — —

R09BW 9 — — — — — — — — — —

R10BW 10 — — — — — — — — — —

R11BW 11 — — — — — — — — — —

R12BW 12 — — — — — — — — — —

Franklin wastewater 

return May–August

R01FS 1 — — -.031 -.584 — — — — -0.013 -0.125

R02FS 2 — — -.023 -.050 — — — -0.013 -.016 -.052

R03FS 3 — — -.011 -.024 — — — — — -.044

R04FS 4 — — -.010 -.015 — — — — — -.037

R05FS 5 — — — -.015 — — — — — -.033

R06FS 6 — — — -.013 — — — — — -.033

R07FS 7 — — — — — — — — — —

R08FS 8 — — — — — — — — — —

R09FS 9 — — — — — — — — — —

R10FS 10 — — — — — — — — — —

R11FS 11 — — — — — — — — — —

R12FS 12 — — — — — — — — — —

Franklin wastewater 

return September–

April

R01FW 1 — — -.045 -.788 — — — -.016 -.019 -.178

R02FW 2 — — -.033 -.067 — — — — -.023 -.074

R03FW 3 — — -.016 -.053 — — — — -.011 -.063

R04FW 4 — — -.015 -.035 — — — — -.011 -.053

R05FW 5 — — -.013 -.029 — — — — -.011 -.047

R06FW 6 — — -.011 -.028 — — — — — -.047

R07FW 7 — — — — — — — — — —

R08FW 8 — — — — — — — — — —

R09FW 9 — — — — — — — — — —

R10FW 10 — — — — — — — — — —

R11FW 11 — — — — — — — — — —

R12FW 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
70 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Holliston wastewater 

return May–August

R01HS 1 — — -0.129 -0.166 -0.202 -0.085 -0.110 — — —

R02HS 2 — — -.043 -.043 -.065 -.022 -.027 — — —

R03HS 3 — — -.025 -.025 -.047 -.014 -.015 — — —

R04HS 4 — — -.015 -.015 -.035 — — — — —

R05HS 5 — — -.012 -.012 -.025 — — — — —

R06HS 6 — — -.010 -.010 -.021 — — — — —

R07HS 7 — — — — -.014 — — — — —

R08HS 8 — — — — -.011 — — — — —

R09HS 9 — — — — -.008 — — — — —

R10HS 10 — — — — — — — — — —

R11HS 11 — — — — — — — — — —

R12HS 12 — — — — — — — — — —

Holliston wastewater 

return September–

April

R01HW 1 — — -.280 -.283 -.249 -.110 -.139 — — —

R02HW 2 — — -.061 -.061 -.089 -.023 -.027 — — —

R03HW 3 — — -.038 -.038 -.063 -.012 -.014 — — —

R04HW 4 — — -.027 -.027 -.046 — — — — —

R05HW 5 — — -.022 -.022 -.034 — — — — —

R06HW 6 — — -.026 -.026 -.026 — — — — —

R07HW 7 — — — — -.018 — — — — —

R08HW 8 — — — — -.011 — — — — —

R09HW 9 — — — — -.008 — — — — —

R10HW 10 — — — — — — — — — —

R11HW 11 — — — — — — — — — —

R12HW 12 — — — — — — — — — —

Medway wastewater 

return May–August

R01DS 1 — — -.127 -.478 -.056 — -.029 — — —

R02DS 2 — — -.051 -.055 -.021 — -.014 — — —

R03DS 3 — — -.027 -.030 -.014 — — — — —

R04DS 4 — — -.017 -.018 -.011 — — — — —

R05DS 5 — — -.009 -.009 -.008 — — — — —

R06DS 6 — — — — — — — — — —

R07DS 7 — — — — — — — — — —

R08DS 8 — — — — — — — — — —

R09DS 9 — — — — — — — — — —

R10DS 10 — — — — — — — — — —

R11DS 11 — — — — — — — — — —

R12DS 12 — — — — — — — — — —

Medway wastewater 

return September–

April

R01DW 1 — — -.211 -.721 -.082 — -.052 — — —

R02DW 2 — — -.046 -.048 -.019 — -.016 — — —

R03DW 3 — — -.029 -.033 -.016 — — — — —

R04DW 4 — — -.021 -.027 -.016 — — — — —

R05DW 5 — — -.020 -.022 -.014 — — — — —

R06DW 6 — — — — — — — — — —

R07DW 7 — — — — — — — — — —

R08DW 8 — — — — — — — — — —

R09DW 9 — — — — — — — — — —

R10DW 10 — — — — — — — — — —

R11DW 11 — — — — — — — — — —

R12DW 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 71

Milford wastewater 

return May–August

R01MS 1 -0.015 -0.626 -0.626 -0.626 — — — — — —

R02MS 2 -.013 -.017 -.017 -.017 — — — — — —

R03MS 3 -.010 -.016 -.016 -.016 — — — — — —

R04MS 4 -.009 -.014 -.014 -.014 — — — — — —

R05MS 5 -.009 -.014 -.014 -.014 — — — — — —

R06MS 6 — -.012 -.012 -.012 — — — — — —

R07MS 7 — — — — — — — — — —

R08MS 8 — — — — — — — — — —

R09MS 9 — — — — — — — — — —

R10MS 10 — — — — — — — — — —

R11MS 11 — — — — — — — — — —

R12MS 12 — — — — — — — — — —

Milford wastewater 

return September–

April

R01MW 1 -.107 -1.000 -1.000 -1.000 — — — — — —

R02MW 2 — — — — — — — — — —

R03MW 3 — — — — — — — — — —

R04MW 4 — — — — — — — — — —

R05MW 5 — — — — — — — — — —

R06MW 6 — — — — — — — — — —

R07MW 7 — — — — — — — — — —

R08MW 8 — — — — — — — — — —

R09MW 9 — — — — — — — — — —

R10MW 10 — — — — — — — — — —

R11MW 11 — — — — — — — — — —

R12MW 12 — — — — — — — — — —

Norfolk wastewater 

return May–August

R01NS 1 — — — -.412 — — — — — -0.302

R02NS 2 — — — -.104 — — — — — -.067

R03NS 3 — — — -.057 — — — — — -.041

R04NS 4 — — — -.037 — — — — — -.028

R05NS 5 — — — -.026 — — — — — -.021

R06NS 6 — — — -.019 — — — — — -.016

R07NS 7 — — — -.013 — — — — — -.012

R08NS 8 — — — -.011 — — — — — -.011

R09NS 9 — — — -.011 — — — — — -.009

R10NS 10 — — — -.009 — — — — — --

R11NS 11 — — — — — — — — — --

R12NS 12 — — — — — — — — — --

Norfolk wastewater 

return September–

April

R01NW 1 — — — -.534 — — — — — -.393

R02NW 2 — — — -.150 — — — — — -.137

R03NW 3 — — — -.098 — — — — — -.103

R04NW 4 — — — -.065 — — — — — -.081

R05NW 5 — — — -.056 — — — — — -.068

R06NW 6 — — — -.046 — — — — — -.060

R07NW 7 — — — -.019 — — — — — -.014

R08NW 8 — — — -.013 — — — — — -.011

R09NW 9 — — — -.011 — — — — — -.009

R10NW 10 — — — -.010 — — — — — —

R11NW 11 — — — — — — — — — —

R12NW 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
72 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Wrentham wastewater 

return May–August

R01WS 1 — — — -0.179 — — — — — -0.179

R02WS 2 — — — -.083 — — — — — -.083

R03WS 3 — — — -.073 — — — — — -.073

R04WS 4 — — — -.067 — — — — — -.067

R05WS 5 — — — -.061 — — — — — -.061

R06WS 6 — — — -.055 — — — — — -.055

R07WS 7 — — — -.038 — — — — — -.038

R08WS 8 — — — -.035 — — — — — -.035

R09WS 9 — — — -.032 — — — — — -.032

R10WS 10 — — — -.029 — — — — — -.029

R11WS 11 — — — -.024 — — — — — -.024

R12WS 12 — — — -.025 — — — — — -.025

Wrentham wastewater 

return September–

April

R01WW 1 — — — -.204 — — — — — -.204

R02WW 2 — — — -.139 — — — — — -.139

R03WW 3 — — — -.125 — — — — — -.125

R04WW 4 — — — -.113 — — — — — -.113

R05WW 5 — — — -.101 — — — — — -.101

R06WW 6 — — — -.096 — — — — — -.096

R07WW 7 — — — -.051 — — — — — -.051

R08WW 8 — — — -.046 — — — — — -.046

R09WW 9 — — — -.041 — — — — — -.041

R10WW 10 — — — -.037 — — — — — -.037

R11WW 11 — — — -.026 — — — — — -.026

R12WW 12 — — — -.022 — — — — — -.022

Franklin hypothetical 

wastewater 

injection well 

Q01FI 1 — — — -.755 — — — — — —

Q02FI 2 — — — -.176 — — — — — —

Q03FI 3 — — — -.048 — — — — — —

Q04FI 4 — — — -.021 — — — — — —

Q05FI 5 — — — — — — — — — —

Q06FI 6 — — — — — — — — — —

Q07FI 7 — — — — — — — — — —

Q08FI 8 — — — — — — — — — —

Q09FI 9 — — — — — — — — — —

Q10FI 10 — — — — — — — — — —

Q11FI 11 — — — — — — — — — —

Q12FI 12 — — — — — — — — — —

Franklin proposed 

Populatic Pond well

Q01FP 1 — — — .776 — — — — — —

Q02FP 2 — — — .145 — — — — — —

Q03FP 3 — — — .036 — — — — — —

Q04FP 4 — — — .011 — — — — — —

Q05FP 5 — — — .016 — — — — — —

Q06FP 6 — — — .016 — — — — — —

Q07FP 7 — — — — — — — — — —

Q08FP 8 — — — — — — — — — —

Q09FP 9 — — — — — — — — — —

Q10FP 10 — — — — — — — — — —

Q11FP 11 — — — — — — — — — —

Q12FP 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 73

Franklin proposed 

well 11

Q01FE 1 — — 0.117 0.117 — — — 0.117 0.117 —

Q02FE 2 — — .110 .110 — — — .110 .110 —

Q03FE 3 — — .105 .105 — — — .105 .105 —

Q04FE 4 — — .120 .120 — — — .120 .120 —

Q05FE 5 — — .111 .111 — — — .111 .111 —

Q06FE 6 — — .105 .105 — — — .105 .105 —

Q07FE 7 — — .086 .086 — — — .086 .086 —

Q08FE 8 — — .080 .080 — — — .080 .080 —

Q09FE 9 — — .066 .066 — — — .066 .066 —

Q10FE 10 — — .046 .046 — — — .046 .046 —

Q11FE 11 — — .033 .033 — — — .033 .033 —

Q12FE 12 — — .021 .021 — — — .021 .021 —

Franklin well 1 Q01F1 1 — — .148 .148 — — — .148 .148 —

Q02F1 2 — — .143 .143 — — — .143 .143 —

Q03F1 3 — — .110 .110 — — — .110 .110 —

Q04F1 4 — — .098 .098 — — — .098 .098 —

Q05F1 5 — — .093 .093 — — — .093 .093 —

Q06F1 6 — — .076 .076 — — — .076 .076 —

Q07F1 7 — — .081 .081 — — — .081 .081 —

Q08F1 8 — — .075 .075 — — — .075 .075 —

Q09F1 9 — — .072 .072 — — — .072 .072 —

Q10F1 10 — — .054 .054 — — — .054 .054 —

Q11F1 11 — — .050 .050 — — — .050 .050 —

Q12F1 12 — — -- -- — — — — — —

Franklin well 10 Q01FT 1 — — .654 .654 — — — .654 .654 —

Q02FT 2 — — .222 .222 — — — .222 .222 —

Q03FT 3 — — .074 .074 — — — .074 .074 —

Q04FT 4 — — .034 .034 — — — .034 .034 —

Q05FT 5 — — .016 .016 — — — .016 .016 —

Q06FT 6 — — — — — — — — — —

Q07FT 7 — — — — — — — — — —

Q08FT 8 — — — — — — — — — —

Q09FT 9 — — — — — — — — — —

Q10FT 10 — — — — — — — — — —

Q11FT 11 — — — — — — — — — —

Q12FT 12 — — — — — — — — — —

Franklin well 2 Q01F2 1 — — .273 .273 — — — .273 .273 —

Q02F2 2 — — .180 .180 — — — .180 .180 —

Q03F2 3 — — .115 .115 — — — .115 .115 —

Q04F2 4 — — .102 .102 — — — .102 .102 —

Q05F2 5 — — .091 .091 — — — .091 .091 —

Q06F2 6 — — .070 .070 — — — .070 .070 —

Q07F2 7 — — .041 .041 — — — .041 .041 —

Q08F2 8 — — .036 .036 — — — .036 .036 —

Q09F2 9 — — .031 .031 — — — .031 .031 —

Q10F2 10 — — .031 .031 — — — .031 .031 —

Q11F2 11 — — .029 .029 — — — .029 .029 —

Q12F2 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
74 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Franklin well 3 Q01F3 1 — — 0.335 0.335 — — — 0.335 0.335 —

Q02F3 2 — — .212 .212 — — — .212 .212 —

Q03F3 3 — — .138 .138 — — — .138 .138 —

Q04F3 4 — — .098 .098 — — — .098 .098 —

Q05F3 5 — — .069 .069 — — — .069 .069 —

Q06F3 6 — — .050 .050 — — — .050 .050 —

Q07F3 7 — — .035 .035 — — — .035 .035 —

Q08F3 8 — — .028 .028 — — — .028 .028 —

Q09F3 9 — — .021 .021 — — — .021 .021 —

Q10F3 10 — — .013 .013 — — — .013 .013 —

Q11F3 11 — — — — — — — — — —

Q12F3 12 — — — — — — — — — —

Franklin well 4 Q01F4 1 — — — .186 — — — — — 0.191

Q02F4 2 — — — .284 — — — — — .236

Q03F4 3 — — — .205 — — — — — .149

Q04F4 4 — — — .136 — — — — — .088

Q05F4 5 — — — .097 — — — — — .050

Q06F4 6 — — — .044 — — — — — .031

Q07F4 7 — — — .030 — — — — — .019

Q08F4 8 — — — .019 — — — — — —

Q09F4 9 — — — — — — — — — —

Q10F4 10 — — — — — — — — — —

Q11F4 11 — — — — — — — — — —

Q12F4 12 — — — — — — — — — —

Franklin well 5 Q01F5 1 — — — .373 — — — — — .373

Q02F5 2 — — — .303 — — — — — .303

Q03F5 3 — — — .154 — — — — — .154

Q04F5 4 — — — .079 — — — — — .079

Q05F5 5 — — — .045 — — — — — .045

Q06F5 6 — — — .032 — — — — — .032

Q07F5 7 — — — .014 — — — — — .014

Q08F5 8 — — — — — — — — — —

Q09F5 9 — — — — — — — — — —

Q10F5 10 — — — — — — — — — —

Q11F5 11 — — — — — — — — — —

Q12F5 12 — — — — — — — — — —

Franklin well 6 Q01F6 1 — — .622 .622 — — — .622 .622 —

Q02F6 2 — — .146 .146 — — — .146 .146 —

Q03F6 3 — — .078 .078 — — — .078 .078 —

Q04F6 4 — — .054 .054 — — — .054 .054 —

Q05F6 5 — — .035 .035 — — — .035 .035 —

Q06F6 6 — — .022 .022 — — — .022 .022 —

Q07F6 7 — — .016 .016 — — — .016 .016 —

Q08F6 8 — — .014 .014 — — — .014 .014 —

Q09F6 9 — — .011 .011 — — — .011 .011 —

Q10F6 10 — — — — — — — — — —

Q11F6 11 — — — — — — — — — —

Q12F6 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 75

Franklin well 7 Q01F7 1 — — 0.165 0.165 — — — — 0.165 —

Q02F7 2 — — .151 .151 — — — — .151 —

Q03F7 3 — — .106 .106 — — — — .106 —

Q04F7 4 — — .095 .095 — — — — .095 —

Q05F7 5 — — .084 .084 — — — — .084 —

Q06F7 6 — — .079 .079 — — — — .079 —

Q07F7 7 — — .063 .063 — — — — .063 —

Q08F7 8 — — .053 .053 — — — — .053 —

Q09F7 9 — — .042 .042 — — — — .042 —

Q10F7 10 — — .040 .040 — — — — .040 —

Q11F7 11 — — .021 .021 — — — — .021 —

Q12F7 12 — — .017 .017 — — — — .017 —

Franklin well 8 Q01F8 1 — — — .732 — — — — — —

Q02F8 2 — — — .192 — — — — — —

Q03F8 3 — — — .056 — — — — — —

Q04F8 4 — — — .020 — — — — — —

Q05F8 5 — — — — — — — — — —

Q06F8 6 — — — — — — — — — —

Q07F8 7 — — — — — — — — — —

Q08F8 8 — — — — — — — — — —

Q09F8 9 — — — — — — — — — —

Q10F8 10 — — — — — — — — — —

Q11F8 11 — — — — — — — — — —

Q12F8 12 — — — — — — — — — —

Holliston Glen Ellen 

Country Club well

Q01HG 1 — — — — 0.900 — — — — —

Q02HG 2 — — — — .083 — — — — —

Q03HG 3 — — — — .017 — — — — —

Q04HG 4 — — — — — — — — — —

Q05HG 5 — — — — — — — — — —

Q06HG 6 — — — — — — — — — —

Q07HG 7 — — — — — — — — — —

Q08HG 8 — — — — — — — — — —

Q09HG 9 — — — — — — — — — —

Q10HG 10 — — — — — — — — — —

Q11HG 11 — — — — — — — — — —

Q12HG 12 — — — — — — — — — —

Holliston EHIP-1 

wastewater 

recharge site

W01H1 1 — — — — -.191 — — — — —

W02H1 2 — — — — -.194 — — — — —

W03H1 3 — — — — -.133 — — — — —

W04H1 4 — — — — -.106 — — — — —

W05H1 5 — — — — -.081 — — — — —

W06H1 6 — — — — -.073 — — — — —

W07H1 7 — — — — -.062 — — — — —

W08H1 8 — — — — -.048 — — — — —

W09H1 9 — — — — -.042 — — — — —

W10H1 10 — — — — -.034 — — — — —

W11H1 11 — — — — -.020 — — — — —

W12H1 12 — — — — -.017 — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
76 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Holliston EHIP-2 

wastewater 

recharge site

W01H2 1 — — — — -0.186 — — — — —

W02H2 2 — — — — -.223 — — — — —

W03H2 3 — — — — -.177 — — — — —

W04H2 4 — — — — -.120 — — — — —

W05H2 5 — — — — -.093 — — — — —

W06H2 6 — — — — -.062 — — — — —

W07H2 7 — — — — -.048 — — — — —

W08H2 8 — — — — -.038 — — — — —

W09H2 9 — — — — -.027 — — — — —

W10H2 10 — — — — -.014 — — — — —

W11H2 11 — — — — -.010 — — — — —

W12H2 12 — — — — — — — — — —

Holliston Gorwin 

Drive wastewater 

recharge site

W01HG 1 — — -0.480 -0.480 — -0.480 -0.480 — — —

W02HG 2 — — -.162 -.162 — -.162 -.162 — — —

W03HG 3 — — -.093 -.093 — -.093 -.093 — — —

W04HG 4 — — -.067 -.067 — -.067 -.067 — — —

W05HG 5 — — -.047 -.047 — -.047 -.047 — — —

W06HG 6 — — -.034 -.034 — -.034 -.034 — — —

W07HG 7 — — -.020 -.020 — -.020 -.020 — — —

W08HG 8 — — -.022 -.022 — -.022 -.022 — — —

W09HG 9 — — -.022 -.022 — -.022 -.022 — — —

W10HG 10 — — -.017 -.017 — -.017 -.017 — — —

W11HG 11 — — -.016 -.016 — -.016 -.016 — — —

W12HG 12 — — -.016 -.016 — -.016 -.016 — — —

Holliston Maplegate 

Country Club well

Q01HM 1 — — .347 .347 — — — — 0.347 —

Q02HM 2 — — .155 .155 — — — — .155 —

Q03HM 3 — — .109 .109 — — — — .109 —

Q04HM 4 — — .090 .090 — — — — .090 —

Q05HM 5 — — .072 .072 — — — — .072 —

Q06HM 6 — — .057 .057 — — — — .057 —

Q07HM 7 — — .050 .050 — — — — .050 —

Q08HM 8 — — .034 .034 — — — — .034 —

Q09HM 9 — — .028 .028 — — — — .028 —

Q10HM 10 — — .023 .023 — — — — .023 —

Q11HM 11 — — .019 .019 — — — — .019 —

Q12HM 12 — — .016 .016 — — — — .016 —

Holliston proposed 

well 7

Q01H7 1 — — — — .047 — — — — —

Q02H7 2 — — — — .102 — — — — —

Q03H7 3 — — — — .161 — — — — —

Q04H7 4 — — — — .339 — — — — —

Q05H7 5 — — — — .166 — — — — —

Q06H7 6 — — — — .087 — — — — —

Q07H7 7 — — — — .047 — — — — —

Q08H7 8 — — — — .025 — — — — —

Q09H7 9 — — — — .015 — — — — —

Q10H7 10 — — — — .011 — — — — —

Q11H7 11 — — — — — — — — — —

Q12H7 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 77

Holliston well 1 Q01H1 1 — — — — 0.343 — — — — —

Q02H1 2 — — — — .220 — — — — —

Q03H1 3 — — — — .144 — — — — —

Q04H1 4 — — — — .104 — — — — —

Q05H1 5 — — — — .054 — — — — —

Q06H1 6 — — — — .047 — — — — —

Q07H1 7 — — — — .033 — — — — —

Q08H1 8 — — — — .026 — — — — —

Q09H1 9 — — — — .017 — — — — —

Q10H1 10 — — — — .012 — — — — —

Q11H1 11 — — — — -- — — — — —

Q12H1 12 — — — — -- — — — — —

Holliston well 2 Q01H2 1 — — — — .760 — — — — —

Q02H2 2 — — — — .123 — — — — —

Q03H2 3 — — — — .046 — — — — —

Q04H2 4 — — — — .031 — — — — —

Q05H2 5 — — — — .026 — — — — —

Q06H2 6 — — — — .015 — — — — —

Q07H2 7 — — — — — — — — — —

Q08H2 8 — — — — — — — — — —

Q09H2 9 — — — — — — — — — —

Q10H2 10 — — — — — — — — — —

Q11H2 11 — — — — — — — — — —

Q12H2 12 — — — — — — — — — —

Holliston well 4 Q01H4 1 — — 0.300 0.300 — 0.300 0.300 — — —

Q02H4 2 — — .141 .141 — .141 .141 — — —

Q03H4 3 — — .140 .140 — .140 .140 — — —

Q04H4 4 — — .092 .092 — .092 .092 — — —

Q05H4 5 — — .072 .072 — .072 .072 — — —

Q06H4 6 — — .066 .066 — .066 .066 — — —

Q07H4 7 — — .042 .042 — .042 .042 — — —

Q08H4 8 — — .030 .030 — .030 .030 — — —

Q09H4 9 — — .023 .023 — .023 .023 — — —

Q10H4 10 — — .022 .022 — .022 .022 — — —

Q11H4 11 — — .016 .016 — .016 .016 — — —

Q12H4 12 — — .016 .016 — .016 .016 — — —

Holliston well 5 Q01H5 1 — — — — .221 — — — — —

Q02H5 2 — — — — .193 — — — — —

Q03H5 3 — — — — .149 — — — — —

Q04H5 4 — — — — .113 — — — — —

Q05H5 5 — — — — .084 — — — — —

Q06H5 6 — — — — .069 — — — — —

Q07H5 7 — — — — .045 — — — — —

Q08H5 8 — — — — .038 — — — — —

Q09H5 9 — — — — .029 — — — — —

Q10H5 10 — — — — .022 — — — — —

Q11H5 11 — — — — .013 — — — — —

Q12H5 12 — — — — .012 — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
78 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Holliston well 6 Q01H6 1 — — — — 0.323 — — — — —

Q02H6 2 — — — — .324 — — — — —

Q03H6 3 — — — — .177 — — — — —

Q04H6 4 — — — — .098 — — — — —

Q05H6 5 — — — — .041 — — — — —

Q06H6 6 — — — — .024 — — — — —

Q07H6 7 — — — — .013 — — — — —

Q08H6 8 — — — — — — — — — —

Q09H6 9 — — — — — — — — — —

Q10H6 10 — — — — — — — — — —

Q11H6 11 — — — — — — — — — —

Q12H6 12 — — — — — — — — — —

Franklin hypothetical 

recharge basin 

200 ft from Miscoe 

Brook

W01M4 1 — — -0.319 -0.319 — — — -0.319 -0.319 —

W02M4 2 — — -.163 -.163 — — — -.163 -.163 —

W03M4 3 — — -.119 -.119 — — — -.119 -.119 —

W04M4 4 — — -.097 -.097 — — — -.097 -.097 —

W05M4 5 — — -.080 -.080 — — — -.080 -.080 —

W06M4 6 — — -.064 -.064 — — — -.064 -.064 —

W07M4 7 — — -.056 -.056 — — — -.056 -.056 —

W08M4 8 — — -.044 -.044 — — — -.044 -.044 —

W09M4 9 — — -.030 -.030 — — — -.030 -.030 —

W10M4 10 — — -.014 -.014 — — — -.014 -.014 —

W11M4 11 — — -.014 -.014 — — — -.014 -.014 —

W12M4 12 — — -- -- — — — -- -- —

Franklin hypothetical 

recharge basin 

2,608 ft from 

Miscoe Brook

W01M1 1 — — -.090 -.090 — — — -.090 -.090 —

W02M1 2 — — -.144 -.144 — — — -.144 -.144 —

W03M1 3 — — -.134 -.134 — — — -.134 -.134 —

W04M1 4 — — -.125 -.125 — — — -.125 -.125 —

W05M1 5 — — -.113 -.113 — — — -.113 -.113 —

W06M1 6 — — -.099 -.099 — — — -.099 -.099 —

W07M1 7 — — -.088 -.088 — — — -.088 -.088 —

W08M1 8 — — -.071 -.071 — — — -.071 -.071 —

W09M1 9 — — -.059 -.059 — — — -.059 -.059 —

W10M1 10 — — -.035 -.035 — — — -.035 -.035 —

W11M1 11 — — -.023 -.023 — — — -.023 -.023 —

W12M1 12 — — -.020 -.020 — — — -.020 -.020 —

Franklin hypothetical 

recharge basin 

1,720 ft from 

Miscoe Brook

W01M2 1 — — -.115 -.115 — — — -.115 -.115 —

W02M2 2 — — -.148 -.148 — — — -.148 -.148 —

W03M2 3 — — -.137 -.137 — — — -.137 -.137 —

W04M2 4 — — -.123 -.123 — — — -.123 -.123 —

W05M2 5 — — -.108 -.108 — — — -.108 -.108 —

W06M2 6 — — -.095 -.095 — — — -.095 -.095 —

W07M2 7 — — -.082 -.082 — — — -.082 -.082 —

W08M2 8 — — -.068 -.068 — — — -.068 -.068 —

W09M2 9 — — -.052 -.052 — — — -.052 -.052 —

W10M2 10 — — -.032 -.032 — — — -.032 -.032 —

W11M2 11 — — -.023 -.023 — — — -.023 -.023 —

W12M2 12 — — -.017 -.017 — — — -.017 -.017 —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 79

Franklin hypothetical 

recharge basin 

894 ft from Miscoe 

Brook

W01M3 1 — — -0.214 -0.214 — — — -0.214 -0.214 —

W02M3 2 — — -.164 -.164 — — — -.164 -.164 —

W03M3 3 — — -.131 -.131 — — — -.131 -.131 —

W04M3 4 — — -.110 -.110 — — — -.110 -.110 —

W05M3 5 — — -.095 -.095 — — — -.095 -.095 —

W06M3 6 — — -.075 -.075 — — — -.075 -.075 —

W07M3 7 — — -.068 -.068 — — — -.068 -.068 —

W08M3 8 — — -.054 -.054 — — — -.054 -.054 —

W09M3 9 — — -.043 -.043 — — — -.043 -.043 —

W10M3 10 — — -.020 -.020 — — — -.020 -.020 —

W11M3 11 — — -.014 -.014 — — — -.014 -.014 —

W12M3 12 — — -.011 -.011 — — — -.011 -.011 —

Medway proposed 

well

Q01DP 1 — — — — 0.406 — — — — —

Q02DP 2 — — — — .247 — — — — —

Q03DP 3 — — — — .124 — — — — —

Q04DP 4 — — — — .071 — — — — —

Q05DP 5 — — — — .046 — — — — —

Q06DP 6 — — — — .043 — — — — —

Q07DP 7 — — — — .020 — — — — —

Q08DP 8 — — — — .017 — — — — —

Q09DP 9 — — — — .015 — — — — —

Q10DP 10 — — — — .010 — — — — —

Q11DP 11 — — — — — — — — — —

Q12DP 12 — — — — — — — — — —

Medway well 1 Q01D1 1 — — .010 .801 — — — — — —

Q02D1 2 — — — .132 — — — — — —

Q03D1 3 — — — .045 — — — — — —

Q04D1 4 — — — .022 — — — — — —

Q05D1 5 — — — — — — — — — —

Q06D1 6 — — — — — — — — — —

Q07D1 7 — — — — — — — — — —

Q08D1 8 — — — — — — — — — —

Q09D1 9 — — — — — — — — — —

Q10D1 10 — — — — — — — — — —

Q11D1 11 — — — — — — — — — —

Q12D1 12 — — — — — — — — — —

Medway well 2 Q01D2 1 — — .000 .050 .024 — — — — —

Q02D2 2 — — .010 .107 .040 — — — — —

Q03D2 3 — — — .094 .070 — — — — —

Q04D2 4 — — — .093 .065 — — — — —

Q05D2 5 — — — .065 .061 — — — — —

Q06D2 6 — — — .053 .049 — — — — —

Q07D2 7 — — — .026 .041 — — — — —

Q08D2 8 — — — .026 .036 — — — — —

Q09D2 9 — — — .013 .032 — — — — —

Q10D2 10 — — — — .028 — — — — —

Q11D2 11 — — — — .016 — — — — —

Q12D2 12 — — — — .012 — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
80 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Medway well 3 Q01D3 1 — — — 0.782 — — — — — —

Q02D3 2 — — — .156 — — — — — —

Q03D3 3 — — — .044 — — — — — —

Q04D3 4 — — — .018 — — — — — —

Q05D3 5 — — — — — — — — — —

Q06D3 6 — — — — — — — — — —

Q07D3 7 — — — — — — — — — —

Q08D3 8 — — — — — — — — — —

Q09D3 9 — — — — — — — — — —

Q10D3 10 — — — — — — — — — —

Q11D3 11 — — — — — — — — — —

Q12D3 12 — — — — — — — — — —

Milford Clark Island 

wellfield

Q01M6 1 0.303 0.303 0.303 .303 — — — — — —

Q02M6 2 .198 .198 .198 .198 — — — — — —

Q03M6 3 .154 .154 .154 .154 — — — — — —

Q04M6 4 .136 .136 .136 .136 — — — — — —

Q05M6 5 .121 .121 .121 .121 — — — — — —

Q06M6 6 .065 .065 .065 .065 — — — — — —

Q07M6 7 .023 .023 .023 .023 — — — — — —

Q08M6 8 — — — — — — — — — —

Q09M6 9 — — — — — — — — — —

Q10M6 10 — — — — — — — — — —

Q11M6 11 — — — — — — — — — —

Q12M6 12 — — — — — — — — — —

Milford Dilla Street 

well 1

Q01M1 1 .240 .240 .240 .240 — — — — — —

Q02M1 2 .199 .199 .199 .199 — — — — — —

Q03M1 3 .164 .164 .164 .164 — — — — — —

Q04M1 4 .163 .163 .163 .163 — — — — — —

Q05M1 5 .135 .135 .135 .135 — — — — — —

Q06M1 6 .073 .073 .073 .073 — — — — — —

Q07M1 7 .026 .026 .026 .026 — — — — — —

Q08M1 8 — — — — — — — — — —

Q09M1 9 — — — — — — — — — —

Q10M1 10 — — — — — — — — — —

Q11M1 11 — — — — — — — — — —

Q12M1 12 — — — — — — — — — —

Milford Dilla Street 

well 2

Q01M2 1 .311 .311 .311 .311 — — — — — —

Q02M2 2 .201 .201 .201 .201 — — — — — —

Q03M2 3 .146 .146 .146 .146 — — — — — —

Q04M2 4 .136 .136 .136 .136 — — — — — —

Q05M2 5 .119 .119 .119 .119 — — — — — —

Q06M2 6 .064 .064 .064 .064 — — — — — —

Q07M2 7 .023 .023 .023 .023 — — — — — —

Q08M2 8 — — — — — — — — — —

Q09M2 9 — — — — — — — — — —

Q10M2 10 — — — — — — — — — —

Q11M2 11 — — — — — — — — — —

Q12M2 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 81

Milford Godfrey 

Brook well 5

Q01M5 1 0.813 0.813 0.813 0.813 — — — — — —

Q02M5 2 .110 .110 .110 .110 — — — — — —

Q03M5 3 .048 .048 .048 .048 — — — — — —

Q04M5 4 .029 .029 .029 .029 — — — — — —

Q05M5 5 — — — — — — — — — —

Q06M5 6 — — — — — — — — — —

Q07M5 7 — — — — — — — — — —

Q08M5 8 — — — — — — — — — —

Q09M5 9 — — — — — — — — — —

Q10M5 10 — — — — — — — — — —

Q11M5 11 — — — — — — — — — —

Q12M5 12 — — — — — — — — — —

Milford Godfrey 

Brook well 4

Q01M4 1 .829 .829 .829 .829 — — — — — —

Q02M4 2 .096 .096 .096 .096 — — — — — —

Q03M4 3 .052 .052 .052 .052 — — — — — —

Q04M4 4 .022 .022 .022 .022 — — — — — —

Q05M4 5 — — — — — — — — — —

Q06M4 6 — — — — — — — — — —

Q07M4 7 — — — — — — — — — —

Q08M4 8 — — — — — — — — — —

Q09M4 9 — — — — — — — — — —

Q10M4 10 — — — — — — — — — —

Q11M4 11 — — — — — — — — — —

Q12M4 12 — — — — — — — — — —

Milford Godfrey 

Brook well 3

Q01M3 1 .820 .820 .820 .820 — — — — — —

Q02M3 2 .099 .099 .099 .099 — — — — — —

Q03M3 3 .050 .050 .050 .050 — — — — — —

Q04M3 4 .025 .025 .025 .025 — — — — — —

Q05M3 5 — — — — — — — — — —

Q06M3 6 — — — — — — — — — —

Q07M3 7 — — — — — — — — — —

Q08M3 8 — — — — — — — — — —

Q09M3 9 — — — — — — — — — —

Q10M3 10 — — — — — — — — — —

Q11M3 11 — — — — — — — — — —

Q12M3 12 — — — — — — — — — —

Norfolk proposed Mill 

River well

Q01NP 1 — — — .512 — — — — — 0.512

Q02NP 2 — — — .237 — — — — — .237

Q03NP 3 — — — .122 — — — — — .122

Q04NP 4 — — — .064 — — — — — .064

Q05NP 5 — — — .033 — — — — — .033

Q06NP 6 — — — .022 — — — — — .022

Q07NP 7 — — — .010 — — — — — .010

Q08NP 8 — — — — — — — — — —

Q09NP 9 — — — — — — — — — —

Q10NP 10 — — — — — — — — — —

Q11NP 11 — — — — — — — — — —

Q12NP 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
82 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Norfolk well 1 Q01N1 1 — — — 0.082 — — — — — 0.046

Q02N1 2 — — — .145 — — — — — .091

Q03N1 3 — — — .157 — — — — — .096

Q04N1 4 — — — .161 — — — — — .113

Q05N1 5 — — — .153 — — — — — .117

Q06N1 6 — — — .141 — — — — — .078

Q07N1 7 — — — .054 — — — — — .046

Q08N1 8 — — — .042 — — — — — .034

Q09N1 9 — — — .033 — — — — — .027

Q10N1 10 — — — .017 — — — — — .019

Q11N1 11 — — — .015 — — — — — .015

Q12N1 12 — — — -- — — — — — --

Wrentham proposed 

well

Q01W1 1 — — — .159 — — — — — .159

Q02W1 2 — — — .147 — — — — — .147

Q03W1 3 — — — .128 — — — — — .128

Q04W1 4 — — — .131 — — — — — .131

Q05W1 5 — — — .096 — — — — — .096

Q06W1 6 — — — .071 — — — — — .071

Q07W1 7 — — — .059 — — — — — .059

Q08W1 8 — — — .052 — — — — — .052

Q09W1 9 — — — .046 — — — — — .046

Q10W1 10 — — — .044 — — — — — .044

Q11W1 11 — — — .035 — — — — — .035

Q12W1 12 — — — .031 — — — — — .031

Wrentham well 2 Q01W2 1 — — — .400 — — — — — .400

Q02W2 2 — — — .173 — — — — — .173

Q03W2 3 — — — .103 — — — — — .103

Q04W2 4 — — — .074 — — — — — .074

Q05W2 5 — — — .047 — — — — — .047

Q06W2 6 — — — .046 — — — — — .046

Q07W2 7 — — — .035 — — — — — .035

Q08W2 8 — — — .033 — — — — — .033

Q09W2 9 — — — .027 — — — — — .027

Q10W2 10 — — — .025 — — — — — .025

Q11W2 11 — — — .019 — — — — — .019

Q12W2 12 — — — .017 — — — — — .017

Wrentham well 3 Q01W3 1 — — — .467 — — — — — .467

Q02W3 2 — — — .142 — — — — — .142

Q03W3 3 — — — .089 — — — — — .089

Q04W3 4 — — — .065 — — — — — .065

Q05W3 5 — — — .052 — — — — — .052

Q06W3 6 — — — .036 — — — — — .036

Q07W3 7 — — — .030 — — — — — .030

Q08W3 8 — — — .028 — — — — — .028

Q09W3 9 — — — .026 — — — — — .026

Q10W3 10 — — — .025 — — — — — .025

Q11W3 11 — — — .023 — — — — — .023

Q12W3 12 — — — .018 — — — — — .018

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 83

Bellingham proposed 

wastewater 

discharge

W01BL 1 — -1.000 -1.000 -1.000 — — — — — —

W02BL 2 — — — — — — — — — —

W03BL 3 — — — — — — — — — —

W04BL 4 — — — — — — — — — —

W05BL 5 — — — — — — — — — —

W06BL 6 — — — — — — — — — —

W07BL 7 — — — — — — — — — —

W08BL 8 — — — — — — — — — —

W09BL 9 — — — — — — — — — —

W10BL 10 — — — — — — — — — —

W11BL 11 — — — — — — — — — —

W12BL 12 — — — — — — — — — —

Charles River 

Pollution Control 

District discharge

W01CR 1 — — — -1.000 — — — — — —

W02CR 2 — — — — — — — — — —

W03CR 3 — — — — — — — — — —

W04CR 4 — — — — — — — — — —

W05CR 5 — — — — — — — — — —

W06CR 6 — — — — — — — — — —

W07CR 7 — — — — — — — — — —

W08CR 8 — — — — — — — — — —

W09CR 9 — — — — — — — — — —

W10CR 10 — — — — — — — — — —

W11CR 11 — — — — — — — — — —

W12CR 12 — — — — — — — — — —

Charles River 

Pollution Control 

District discharge 

hypothetical 

upstream location

W01CP 1 — — -1.000 -1.000 — — — — — —

W02CP 2 — — — — — — — — — —

W03CP 3 — — — — — — — — — —

W04CP 4 — — — — — — — — — —

W05CP 5 — — — — — — — — — —

W06CP 6 — — — — — — — — — —

W07CP 7 — — — — — — — — — —

W08CP 8 — — — — — — — — — —

W09CP 9 — — — — — — — — — —

W10CP 10 — — — — — — — — — —

W11CP 11 — — — — — — — — — —

W12CP 12 — — — — — — — — — —

Milford wastewater 

treatment plant

W01MF 1 — -1.000 -1.000 -1.000 — — — — — —

W02MF 2 — — — — — — — — — —

W03MF 3 — — — — — — — — — —

W04MF 4 — — — — — — — — — —

W05MF 5 — — — — — — — — — —

W06MF 6 — — — — — — — — — —

W07MF 7 — — — — — — — — — —

W08MF 8 — — — — — — — — — —

W09MF 9 — — — — — — — — — —

W10MF 10 — — — — — — — — — —

W11MF 11 — — — — — — — — — —

W12MF 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
84 Evaluation of Strategies for Balancing Water Use and Streamflow Reductions in the Upper Charles River Basin, Eastern MA

Miscoe Brook 

hypothetical 

wastewater 

discharge site

W01FM 1 — — -1.000 -1.000 — — — -1.000 -1.000 —

W02FM 2 — — — — — — — — — —

W03FM 3 — — — — — — — — — —

W04FM 4 — — — — — — — — — —

W05FM 5 — — — — — — — — — —

W06FM 6 — — — — — — — — — —

W07FM 7 — — — — — — — — — —

W08FM 8 — — — — — — — — — —

W09FM 9 — — — — — — — — — —

W10FM 10 — — — — — — — — — —

W11FM 11 — — — — — — — — — —

W12FM 12 — — — — — — — — — —

Drinking water direct 

discharge to Charles 

River

D01CR 1 -1.000 -1.000 -1.000 -1.000 — — — — — —

D02CR 2 — — — — — — — — — —

D03CR 3 — — — — — — — — — —

D04CR 4 — — — — — — — — — —

D05CR 5 — — — — — — — — — —

D06CR 6 — — — — — — — — — —

D07CR 7 — — — — — — — — — —

D08CR 8 — — — — — — — — — —

D09CR 9 — — — — — — — — — —

D10CR 10 — — — — — — — — — —

D11CR 11 — — — — — — — — — —

D12CR 12 — — — — — — — — — —

Drinking water direct 

discharge to 

Hopping Brook

D01HB 1 — — -1.000 -1.000 — -1.000 -1.000 — — —

D02HB 2 — — — — — — — — — —

D03HB 3 — — — — — — — — — —

D04HB 4 — — — — — — — — — —

D05HB 5 — — — — — — — — — —

D06HB 6 — — — — — — — — — —

D07HB 7 — — — — — — — — — —

D08HB 8 — — — — — — — — — —

D09HB 9 — — — — — — — — — —

D10HB 10 — — — — — — — — — —

D11HB 11 — — — — — — — — — —

D12HB 12 — — — — — — — — — —

Drinking water direct 

discharge to Miscoe 

Brook

D01MB 1 — — -1.000 -1.000 — — — -1.000 -1.000 —

D02MB 2 — — — — — — — — — —

D03MB 3 — — — — — — — — — —

D04MB 4 — — — — — — — — — —

D05MB 5 — — — — — — — — — —

D06MB 6 — — — — — — — — — —

D07MB 7 — — — — — — — — — —

D08MB 8 — — — — — — — — — —

D09MB 9 — — — — — — — — — —

D10MB 10 — — — — — — — — — —

D11MB 11 — — — — — — — — — —

D12MB 12 — — — — — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1
Appendix 2 85

Charles River 

Pollution Control 

District facility 

hypothetical 

recharge

W01C1 1 — — — -0.083 — — — — — —

W02C1 2 — — — -.083 — — — — — —

W03C1 3 — — — -.083 — — — — — —

W04C1 4 — — — -.083 — — — — — —

W05C1 5 — — — -.083 — — — — — —

W06C1 6 — — — -.083 — — — — — —

W07C1 7 — — — -.083 — — — — — —

W08C1 8 — — — -.083 — — — — — —

W09C1 9 — — — -.083 — — — — — —

W10C1 10 — — — -.083 — — — — — —

W11C1 11 — — — -.083 — — — — — —

W12C1 12 — — — -.083 — — — — — —

Appendix 2. Hydrologic response coefficients for withdrawal and return stresses analyzed, upper Charles River basin, eastern 

Massachusetts.—Continued

[See tables 5 and 7 for more information on stress variables. ft, foot; — zero]

Stress causing

streamflow change

Optimization

variable

Month

Hydrologic response coefficients for constraint-point locations

CR1 CR2 CR3 CR4 BB1 HB1 HB2 MB1 MB2 MR1