Cover photo:

Crew races on the lower Charles River looking 

upstream toward the Larz Anderson Bridge.

Courtesy of: Philip Greenspun 

http://philip.greenspun.com
U.S. Department of the Interior

U.S. Geological Survey

Measured and Simulated 

Runoff to the Lower Charles 

River, Massachusetts, 

October 1999–September 2000

By PHILLIP J. ZARRIELLO and LORA K. BARLOW 

Water-Resources Investigations Report 02-4129 

In cooperation with the 

U.S. ENVIRONMENTAL PROTECTION AGENCY,

MASSACHUSETTS DEPARTMENT OF 

ENVIRONMENTAL PROTECTION, and the

MASSACHUSETTS WATER RESOURCES AUTHORITY

Northborough, Massachusetts

2002
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary 

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director 

The use of trade or product names in this report is for identification purposes only 

and does not constitute endorsement by the U.S. Government.

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

Chief, Massachusetts-Rhode Island District U.S. Geological Survey

U.S. Geological Survey Branch of Information Services

10 Bearfoot Road Box 25286

Northborough, MA 01532 Denver, CO 80225-0286

or visit our Web site at

http://ma.water.usgs.gov
Contents III

CONTENTS

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

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

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

Description of the Lower Charles River and its Watershed ........................................................................................ 3

Climate .............................................................................................................................................................. 3

Land Use ........................................................................................................................................................... 5

Soils................................................................................................................................................................... 5

Topography........................................................................................................................................................ 8

Hydrology.......................................................................................................................................................... 8

Previous Investigations................................................................................................................................................ 8

Acknowledgments....................................................................................................................................................... 11

Gaged Subbasins ................................................................................................................................................................... 12

Discharge..................................................................................................................................................................... 12

Charles River at Watertown Station—01104615 .............................................................................................. 12

Single-Family Land-Use Station—01104630................................................................................................... 14

Laundry Brook Station—01104640 .................................................................................................................. 15

Faneuil Brook Station—01104660.................................................................................................................... 15

Multifamily Land-Use Station—01104673 ...................................................................................................... 16

Commercial Land-Use Station—01104677...................................................................................................... 16

Muddy River Station—01104683 ..................................................................................................................... 17

Stony Brook Station—01104687 ...................................................................................................................... 18

Data Management ....................................................................................................................................................... 18

Precipitation-Runoff Model .................................................................................................................................................. 19

Functional Description of SWMM.............................................................................................................................. 19

Model Development .................................................................................................................................................... 20

Data ................................................................................................................................................................... 22

Spatial Data ............................................................................................................................................. 22

Time-Series Data..................................................................................................................................... 22

Representation of Overland Runoff .................................................................................................................. 23

Assignment of Subcatchments to Precipitation Gages............................................................................ 23

Subcatchment Parameterization .............................................................................................................. 24

Representation of the Drainage Network .......................................................................................................... 27

Drainage Network Parameterization ....................................................................................................... 28

Pond Storage ........................................................................................................................................... 29

Model Calibration ....................................................................................................................................................... 29

Model Fit ..................................................................................................................................................................... 29

Land-Use Subbasin Models .............................................................................................................................. 30

Single-Family Residential ....................................................................................................................... 30

Multifamily Residential........................................................................................................................... 34

Commercial ............................................................................................................................................. 36

Tributary Subbasin Models ............................................................................................................................... 39

Laundry Brook ........................................................................................................................................ 39

Faneuil Brook.......................................................................................................................................... 42

Stony Brook............................................................................................................................................. 45

Relative Model Fit............................................................................................................................................. 48

Design Storms ................................................................................................................................................... 51

Sensitivity Analysis..................................................................................................................................................... 52

Model Limitations ....................................................................................................................................................... 52
IV Contents

Runoff to the Lower Charles River ....................................................................................................................................... 55

Annual and Monthly Water Budget............................................................................................................................. 55

Single-Family Land-use Subbasin .................................................................................................................... 55

Multifamily Land-Use Subbasin ....................................................................................................................... 56

Commercial Land-Use Subbasin....................................................................................................................... 56

Laundry Brook Subbasin................................................................................................................................... 58

Faneuil Brook Subbasin .................................................................................................................................... 58

Stony Brook Subbasin....................................................................................................................................... 58

Total inflows to the Lower Charles River.......................................................................................................... 60

Design Storms ............................................................................................................................................................. 60

Summary ............................................................................................................................................................................... 61

References Cited ................................................................................................................................................................... 63

Appendix 1A-G: Model Areas and Schematics of the StormWater Management 

Model (SWMM) Elements used to Represent the Model Areas............................................................................. 65

Appendix 2: Rainfall Characteristics of Storms at BWSC-CS4, Lower Charles River Watershed, 2000 water year .......... 79

Appendix 3: Observed and Simulated Runoff Volume and Peak Discharge for Calibration Storms ................................... 83

FIGURES

1. Map showing principal geographic features, streamgage stations, and precipitation stations, 

lower Charles River Watershed, Massachusetts .................................................................................................... 4

2. Graph showing climate characteristics in the lower Charles River Watershed, (A) total monthly 

precipitation averaged from six gages in and near the watershed during the 2000 water year and the

average total monthly precipitation from January 1, 1920, to December 31, 2000, at Logan Airport in 

Boston, and (B) average monthly air temperature and snowfall during the 2000 water year and for the 

1920–2000 period at Logan Airport ...................................................................................................................... 5

3–6. Maps of the lower Charles River Watershed showing:

3. Generalized 1991 land use ............................................................................................................................ 6

4. Generalized soil types ................................................................................................................................... 7

5. Geomorphic districts and land-surface elevations......................................................................................... 9

6. Outfalls .......................................................................................................................................................... 10

7-9. Graphs showing:

7. Relation of hourly discharge of Charles River at Waltham (01104500) to Charles River at 

Watertown Dam (01104615), 2000 water year ............................................................................................. 14

8. December 6–8, 1999, storm hydrographs at Faneuil Brook streamgaging station (01104660), 

lower Charles River Watershed, determined by three methods (A) area-velocity measurements, 

(B) stage-discharge relation, and (C) simulated by the StormWater Management Model (SWMM)........... 16

9. Relation of stage at the Muddy River streamgaging station to water levels in the lower Charles 

River and Boston Harbor............................................................................................................................... 17

10. Map showing areas of the StormWater Management Models (SWMM) developed for the lower Charles 

River Watershed..................................................................................................................................................... 21

11–29. Graphs showing:

11. Rainfall-runoff relations for small storms from May through September 2000 at gaged subbasins 

in the lower Charles River Watershed ........................................................................................................... 26

12. Simulated and observed peak discharge and runoff volume at the single-family land-use subbasin, 

lower Charles River Watershed, for the 2000 water year: (A) calibration storms, and (B) all storms .......... 31

13. Percent difference between simulated and observed storm-peak discharge and runoff volume for the 

single-family land-use subbasin, lower Charles River Watershed, for 49 storms in the 2000 water 

year: (A) by month, and in relation to (B) precipitation volume, (C) precipitation intensity, and 

(D) antecedent precipitation .......................................................................................................................... 33

14. Simulated and observed peak discharge and runoff volume at the multifamily land-use subbasin, 

lower Charles River Watershed, for the 2000 water year: (A) calibration storms, and (B) all storms .......... 35
Contents V

15. Percent difference between simulated and observed storm-peak discharge and runoff volume for the 

multifamily land-use subbasin, lower Charles River Watershed, for 36 storms in the 2000 water year: 

(A) by month, and in relation to (B) precipitation volume, (C) precipitation intensity, and 

(D) antecedent precipitation .......................................................................................................................... 37

16. Simulated and observed peak discharge and runoff volume at the commercial land-use subbasin, 

lower Charles River Watershed, for the 2000 water year: (A) calibration storms, and (B) all storms .......... 38

17. Percent difference between simulated and observed storm-peak discharge and runoff volume for the 

commercial land-use subbasin, lower Charles River Watershed, for 31 storms in the 2000 water 

year: (A) by month, and in relation to (B) precipitation volume, (C) precipitation intensity, and 

(D) antecedent precipitation .......................................................................................................................... 40

18. Simulated and observed discharge and runoff volume at the Laundry Brook Subbasin, lower 

Charles River Watershed, for the 2000 water year: (A) calibration storms, and (B) all storms .................... 41

19. Percent difference between simulated and observed storm-peak discharge and runoff volume for 

the Laundry Brook Subbasin, lower Charles River Watershed, for 48 storms in the 2000 water 

year: (A) by month, and in relation to (B) precipitation volume, (C) precipitation intensity, and 

(D) antecedent precipitation .......................................................................................................................... 43

20. Simulated and observed peak discharge and runoff volume at the Faneuil Brook Subbasin, lower 

Charles River Watershed, for the 2000 water year: (A) calibration storms, and (B) all storms .................... 44

21. Percent difference between simulated and observed storm-peak discharge and runoff volume for 

the Faneuil Brook Subbasin, lower Charles River Watershed, for 48 storms in the 2000 water 

year: (A) by month, and in relation to (B) precipitation volume, (C) precipitation intensity, and 

(D) antecedent precipitation .......................................................................................................................... 46

22. Simulated and observed peak discharge and runoff volume at the Stony Brook Subbasin, lower

Charles River Watershed, for the 2000 water year: (A) calibration storms, and (B) all storms .................... 47

23. Percent difference between simulated and observed storm-peak discharge and runoff volume at 

the Stony Brook Subbasin, lower Charles River Watershed, for 28 storms in the 2000 water 

year: (A) by month, and in relation to (B) precipitation volume, (C) precipitation intensity, and 

(D) antecedent precipitation .......................................................................................................................... 49

24. Relative measures of model fit calculated by the index of agreement and coefficient of efficiency 

at three land-use and three tributary subbasin models in the lower Charles River Watershed for 

the (A) peak discharge and (B) runoff volumes............................................................................................. 50

25. Simulated and observed (A) peak discharge and (B) runoff volume at Laundry Brook, Faneuil 

Brook, and Stony Brook, lower Charles River Watershed, for 2000 water-year storms with total 

precipitation within 20 percent of the 3-month and 1-year design-storm precipitation volume................... 51

26. Peak-discharge sensitivity gradients for hypothetical storms of varying duration and intensity for 

selected subcatchment variable values, lower Charles River Watershed ...................................................... 53

27. Runoff-volume sensitivity gradients for hypothetical storms of varying duration and intensity for 

selected subcatchment variable values, lower Charles River Watershed ...................................................... 54

28. Simulated and observed monthly runoff volume at the three land-use subbasin sites in the lower 

Charles River Watershed, 2000 water year: (A) single family, (B) multifamily, and (C) commercial.......... 57

29. Simulated and observed monthly runoff volume at the three tributary subbasin sites in the lower 

Charles River Watershed, 2000 water year; (A) Laundry Brook, (B) Faneuil Brook, and 

(C) Stony Brook ............................................................................................................................................ 59

TABLES

1. Physical characteristics at gaged and ungaged subbasins in the lower Charles River Watershed, 

Massachusetts ......................................................................................................................................................... 13

2. Precipitation gages in and near the lower Charles River Watershed....................................................................... 23

3. First and second digit numbers of the six-digit subcatchment model number used to identify 

subbasins and municipalities in the lower Charles River Watershed...................................................................... 24

4. StormWater Management Model (SWMM) RUNOFF module subcatchment variables and methods 

used to obtain their initial values in the models of the lower Charles River Watershed......................................... 24
VI Contents

5. Estimated percent effective impervious area applied to the StormWater Management Models (SWMM) 

of the lower Charles River Watershed..................................................................................................................... 25

6. StormWater Management Model (SWMM) TRANSPORT module variable values used in the lower 

Charles River Watershed......................................................................................................................................... 28

7. StormWater Management Model (SWMM) RUNOFF module subcatchment variable values used in 

the land-use subbasins of the lower Charles River Watershed................................................................................ 28

8. Summary of StormWater Management Model (SWMM) fit statistics for storm-peak discharge and stormrunoff volume, lower Charles River Watershed...................................................................................................... 32

9. Annual runoff observed at Charles River at Watertown Dam and simulated at land-use and tributary 

subbasins to the lower Charles River, Water Year 2000, October 1, 1999, through September 30, 2000.............. 55

10. Storm runoff volumes simulated for the 3-month and 1-year design storms to the lower Charles River .............. 60

CONVERSION FACTORS AND VERTICAL DATUM

CONVERSION FACTORS

VERTICAL DATUM

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD 

of 1929)—a geodetic datum derived from a general adjustment of the first-order level nets of the 

United States and Canada, formerly called Sea Level Datum of 1929. 

Multiply By To obtain

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

foot (ft) 0.3048 meter

inch (in) 2.54 centimeter

inch (in) 25.4 millimeter

inch per hour (in/h) 0.0254 meter per hour

mile (mi) 1.609 kilometer

square mile (mi2) 259.0 hectare

square mile (mi2) 2.590 square kilometer 

Temperature in degrees Celsius (°C) may be converted to

degrees Fahrenheit (°F) as follows:

°F=1.8 °C+32
Abstract 1

Measured and Simulated 

Runoff to the Lower Charles 

River, Massachusetts, 

October 1999–September 2000

By Phillip J. Zarriello and Lora K. Barlow

Abstract

The lower Charles River, the water body 

between the Watertown Dam and the New Charles 

River Dam, is an important recreational resource 

for the Boston, Massachusetts, metropolitan area, 

but impaired water quality has affected its use. The 

goal of making this resource fishable and swimmable requires a better understanding of combinedsewer-overflow discharges, non-combined-seweroverflow stormwater runoff, and constituent loads. 

This report documents the modeling effort used to 

calculate non-combined-sewer-overflow runoff to 

the lower Charles River.

During the 2000 water year, October 1, 

1999–September 30, 2000, the U.S. Geological 

Survey collected precipitation data at Watertown 

Dam and compiled data from five other precipitation gages in or near the watershed. In addition, 

surface-water discharge data were collected at eight 

sites—three relatively homogenous land-use sites, 

four major tributary sites, and the Charles River at 

Watertown Dam, which is the divide between the 

upper and lower watersheds. The precipitation and 

discharge data were used to run and calibrate 

Stormwater Management Models developed for 

the three land-use subbasins (single-family, multifamily, and commercial), and the two tributary 

subbasins (Laundry and Faneuil Brooks). These 

calibrated models were used to develop a sixth 

model to simulate 54 ungaged outfalls to the lower 

Charles River. Models developed by the U.S. 

Geological Survey at gaged sites were calibrated 

with up to 24 storms. Each model was evaluated 

by comparing simulated discharge against measured discharge for all storms with appreciable 

precipitation and reliable discharge data. The 

model-fit statistics indicated that the models generally were well calibrated to peak discharge and 

runoff volumes. The model fit of the commercial 

land-use subbasin was not as well calibrated 

compared to the other models because the measured flows appear to be affected by variable conditions not represented in the model. A separate 

Stormwater Management Model of the Stony 

Brook Subbasin previously developed by others 

was evaluated with the newly collected data from 

this study; this model had a model fit comparable to 

the models developed by the U.S. Geological 

Survey.

The total annual runoff to the lower 

Charles River during the 2000 water year, not 

including contributions from combined-seweroverflows except from the Stony Brook Subbasin, 

was 16,500 million cubic feet; 92 percent of 

the inflow was from the Charles River above 

Watertown Dam, 3 percent was from the Stony 

Brook Subbasin, 2 percent was from the Muddy 

River Subbasin, and less than 1 percent was from 

the combined inflows of Laundry and Faneuil 

Brooks. The remaining ungaged drainage area contributed about 2 percent of the total annual inflow 

to the lower Charles River. Excluding discharge 

from the Charles River above Watertown Dam, 

total annual runoff to the lower Charles River was 

1,240 million cubic feet; 39 percent was from the 

Stony Brook Subbasin, 27 percent was from the 

Muddy River, which includes runoff that drains to 

the Muddy River conduit, 7 percent was from the 

Laundry Brook Subbasin, and 4 percent was from 

the Faneuil Brook Subbasin. Flow from the 
2 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

ungaged areas composed about 23 percent of the 

total annual inflow to the lower Charles River, 

excluding discharge from the Charles River above 

Watertown Dam.

Runoff to the lower Charles River was calculated for two design storms representing a 3-month 

and a 1-year event, 1.84 and 2.79 inches of total 

rainfall, respectively. These simulated discharges 

were provided to the Massachusetts Water 

Resources Authority for use in a receiving-water 

model of the lower Charles River. Total storm 

runoff to the lower Charles River was 111 and 

257 million cubic feet for the 3-month and 1-year 

storms, respectively. Excluding discharge from the 

Charles River above Watertown Dam, total runoff 

to the lower Charles River was 30 and 53 million 

cubic feet for the 3-month and 1-year storms, 

respectively. Runoff from the various tributary 

areas for the design storms was about in the same 

proportion as that for the annual runoff.

INTRODUCTION

The lower Charles River, which flows between 

the Watertown Dam and the New Charles River Dam, 

has long been recognized as an asset to the surrounding 

metropolitan area of Boston, Massachusetts, but 

impaired water quality has adversely affected this 

resource. As early as 1859, parts of the lower Charles 

River were described as “practically a cesspool” 

(Pritchett and others, 1903), and discussions began 

regarding construction of a dam to flood the tidal mud 

flats. In 1870, the Metropolitan Parks Commission, 

predecessor to the Metropolitan District Commission 

(MDC), was created to improve conditions in the lower 

Charles River. Nathan Matthews, a former Mayor of 

Boston, recommended creating a water park and 

appointed the Charles River Improvement Commission 

to develop this concept. In 1892, Charles Eliot, a prominent landscape architect, transformed the concept of a 

water park into a grander vision of a metropolitan-park 

system centered on the Charles River waterfront area. 

Much of the land surrounding the lower Charles 

River was acquired in the late 1800s as part of the 

metropolitan-park system. In 1901, engineering studies 

were undertaken to investigate the extent of sewage 

contamination and to assess the feasibility and costs of 

constructing a dam to mitigate the noxious odors and 

adverse health effects associated with the polluted tidal 

flats (Pritchett and others, 1903). The Old Charles 

River Dam, constructed by 1908, resolved many of 

these problems and created a recreational resource for 

the Boston metropolitan area (Jobin, 1998).

The lower Charles River continues to serve as a 

recreational resource for thousands of boaters and 

many thousands more who enjoy the parks along its 

embankments. The largest 1-day rowing regatta in the 

world, the Head of the Charles, brings over 5,400 

rowers and 300,000 spectators to the lower Charles 

River each fall. In addition, annual Fourth of July festivities attract more than 500,000 people (Massachusetts District Commission, 2000). Unfortunately, 

Charles River water can pose a health risk at times 

because of excessive levels of fecal bacteria, which can 

exceed Massachusetts water-quality standards, even for 

secondary-contact recreation (such as boating). 

Just as citizens and organizations in the past have 

identified and resolved environmental hazards associated with the lower Charles River, work to resolve 

water-quality issues that affect its recreational use continues today. The U.S. Environmental Protection 

Agency (USEPA) has led the effort to improve water 

quality by setting a goal of making this resource safe 

for fishing and swimming by Earth Day 2005. To meet 

this goal, accurate assessments of inflows and constituent loads from combined-sewer overflows (CSOs) and 

non-CSO stormwater are needed to develop sound 

management plans.

The Massachusetts Water Resources Authority 

(MWRA) has monitored and worked toward the elimination or treatment of CSO discharges to the lower 

Charles River for more than a decade. These efforts 

have substantially improved water quality, but a better 

understanding of non-CSO stormwater loads would 

enhance efforts to improve water quality. In 1999, the 

USGS, in cooperation with the Massachusetts Water 

Resources Authority (MWRA), the USEPA, and 

the Massachusetts Department of Environmental 

Protection (MADEP), initiated a study to quantify nonCSO stormwater runoff loads to the lower Charles 

River. This cooperative study was designed to provide 

information to regulatory agencies and others on how 

stormwater affects water quality in the lower Charles 

River.
Introduction 3

Purpose and Scope

This report describes the five StormWater Management Models (SWMM) developed to simulate 

runoff to the lower Charles River, Massachusetts. The 

modeling effort described supports a companion study 

conducted by the USGS to calculate non-CSO contaminant loads to the lower Charles River (Breault and 

others, 2002). Runoff models were used to (1) simulate 

discharge at ungaged sites during the 2000 water year, 

(2) simulate discharge at gaged sites where data are 

missing or suspect during the 2000 water year, (3) simulate discharge at all outfalls for the July 15–18 and the 

July 26–31, 2000, storms for the MWRA and (4) simulate discharge at all outfalls for two design storms. Data 

and results obtained from this study and the companion 

USGS loads study will be used by the MWRA, the 

USEPA, and the MADEP to address the transport and 

fate of contaminants within the river. 

This report describes hydrologic and meteorologic data collected at the three small relatively 

homogeneous land-use subbasins (single-family, multifamily, and commercial), four tributary subbasins 

(Laundry Brook, Faneuil Brook, Muddy River, and 

Stony Brook), and the Charles River at Watertown 

Dam; the development and calibration of the SWMM 

at the three land-use subbasins and at two tributary subbasins (Laundry and Faneuil Brook); and the model fit 

at these sites. The report also describes the model 

(SWMM) fit to the newly collected discharge data for 

the Stony Brook Subbasin previously developed by 

Metcalf and Eddy, Inc., consultants to the MWRA. 

Description of the Lower 

Charles River and Its 

Watershed

The lower Charles River is the 9-mi long 

water body between the Watertown Dam and the 

New Charles River Dam in Boston where it empties 

into Boston Harbor (fig. 1). This part of the river is 

known locally as the “basin.” The drainage area to 

the lower Charles River is located within Middlesex, 

Norfolk, and Suffolk Counties, Massachusetts. 

Native Americans aptly named its sinuous course 

“Quinobequin” for “Meandering River” (Brickford and 

Dymon, 1990). The drainage area to the lower river 

below Watertown Dam is estimated as 36.6 mi2, but 

drainage divides are complicated by a highly altered, 

man-made drainage system. The lower Charles River 

Watershed is one of the oldest urban areas in the 

Nation; its natural drainage system has been modified 

for more than three centuries. Municipalities within 

the lower Charles River Watershed include parts 

of Cambridge, Boston, Brookline, Newton, and 

Watertown. The modeled area covers the lower Charles 

River Watershed, but does not include CSO drainage 

areas except for those in the Stony Brook Subbasin. 

The Charles River Watershed above the Watertown 

Dam drains an area of 268 mi2; runoff from this area 

was measured directly or estimated from discharge 

records from the upstream gaging station at Waltham.

Climate

The climate of eastern Massachusetts is characterized as humid temperate (Gadoury and Wandle, 

1986). Precipitation generally is distributed evenly 

throughout the year, although variations can be large 

from month to month (fig. 2) and from year to year 

(Trombley, 1991). Precipitation at Logan Airport in 

Boston averaged 41.8 in. for the 1920–2000 period. 

Precipitation at six gages in and near the lower Charles 

River Watershed averaged 42.8 in. for water year 2000, 

but total precipitation at each of the gages varied from 

50.7 to 40.1 in. Precipitation during the 2000 water 

year was above the long-term average during the 

months of April and June (1.02) because of a single 

large storm in each of these months; precipitation also 

was above normal during July because of a greater than 

usual number of small storms. Precipitation from 

November 1999 through February 2000, and during 

August 2000 were below the long-term average.

Air temperature reported for Boston by the 

Northeast Regional Climate Center for the 80-year 

period 1920–2000 ranged from a low of 29.3°F in 

January to a high of 73.2°F in July and averaged 51.2°F 

annually. During the 2000 water year, the mean 

monthly air temperature reported at Logan Airport in 

Boston was similar to the long-term monthly mean air 

temperature; from a low of 27.5°F in January to a high 

of 70.3°F in August, it averaged 51.6°F in the 2000 

water year. The Boston area receives an average of 

42.4 in. of snow each year; the 24.9 in. of snowfall 

during the 2000 water year was considerably below 

average.
4 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 1. Principal geographic features, stream-gage stations, and precipitation stations, lower Charles River Watershed, Massachusetts.

0 1 2 MILES

0 1 2 KILOMETERS

STREAM GAGE AND NUMBER

SURFACE WATER

CITY BOUNDARY

N BOUNDARYÑNamed

of color

EXPLANATION

AGED DRAINAGE AREA

PRECIPITATION GAGE

AND NUMBER

BWSC-WS6

01104687

LOWER CHARLES

RIVER

WATERSHED

ATLANTIC

OCEAN

Logan

Airport

EASTERN

MASSACHUSETTS

UPPER

CHARLES

RIVER

WATERSHED

CAMBRIDGE

NEWTON

STON

BROOKLINE

01104630

(SINGLE FAMILY)

MUDDY

RIVER

STONY BROOK

LAUNDRY

BROOK

CWD-PP1

BWSC-WS6

NEW CHARLES

RIVER DAM

Base map coverages from:

Boston Water and Sewer Commission,

Beta Engineering,

City of Cambridge Department of Public Works,

City of Newton MIS Department, and

City of Watertown Department of Public Works.

Massachusetts State Plane Projection, NAD 1983

71o08' 71o06' 71o

04'

42o16'

42o18'

42o20'

42o22'

71o10'
Introduction 5

Land Use

The lower Charles River Watershed is within a 

major metropolitan area and is highly urbanized. The 

majority of land use in the watershed (fig. 3) is represented by single-family residential (38 percent) and 

multifamily residential (13 percent) uses. Other land 

uses include urban open space, such as athletic fields, 

cemeteries, parks and institutional green space (12 percent), commercial (9 percent), forest (7 percent), open 

water (4 percent), transportation (3 percent), spectator 

recreation (3 percent), and industrial (2 percent). Other 

land-use types each compose less than 1 percent of the 

watershed area. Most new development in recent years 

can be classified as redevelopment; hence, the 1991 

land-use conditions represented in figure 3 had not 

changed appreciably at the time of this study.

Soils

Soil surveys for Middlesex (U.S. Department of 

Agriculture, 1995), Norfolk and Suffolk Counties 

(Peragallo, 1989) indicate (fig. 4) that most soils in the 

watershed are derived from till (48 percent) or are disturbed urban land (35 percent). Soils classified as disturbed urban are found mostly near the river in areas 

filled to eliminate tidal marshes and mud flats. The 

remaining soil types are derived from glacial outwash 

(16 percent), post-glacial alluvium (1.4 percent) and 

aeolian sand and silt (0.4 percent). 

Figure 2. Climate characteristics in the lower Charles River Watershed, (A) total monthly precipitation averaged from six gages in and near the 

watershed during the 2000 water year and the average total monthly precipitation from January 1, 1920, to December 31, 2000, at Logan Airport in 

Boston, Massachusetts, and (B) average monthly air temperature and snowfall during the 2000 water year and for the 1920–2000 period at Logan 

Airport. [Locations are shown in fig. 1.]

AVERAGE SNOWFALL

0

2

4

6

8

10

12

14

16

1999–2000

1920–2000

AVERAGE AIR TEMPERATURE

0

10

20

30

40

50

60

70

80

1999–2000

1920–2000

AIR TEMPERATURE,

 IN DEGREES FAHRENHEIT

SNOWFALL, IN INCHES

0

1

2

3

4

5

6

7

8

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

PRECIPITATION, IN INCHES

AVERAGE FROM SIX GAGES (2000 WATER YEAR)

AVERAGE 1920–2000 LOGAN AIRPORT

B. Air Temperature and Snowfall

A. Precipitation
6 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 3. Generalized 1991 land use in the lower Charles River Watershed, Massachusetts. 

Industrial

Agriculture

Commercial

Forest

Multifamily residential

Open land

Other

Participation recreation

Single-family residential

Spectator recreation

Transportation

Urban open

Waste disposal

Open water

Wetland

EXPLANATION

BASIN BOUNDARY

0 1 2 MILES

0 1 2 KILOMETERS

LAND USE

MUDDY

STONY

BROOK

LAUNDRY LAUNDR

BROOK

SINGLE

FAMILY

COMMERCIAL

MULTIFAMILY

STREAM-GAGE STATION

Land use was reclassified from MassGIS, 1991

Massachusetts State Plane Projection

North American Datum, 1983, 1:25,000

Massachusetts Executive Office of

Environmental Affairs
Introduction 7

Figure 4. Generalized soil types in the lower Charles River Watershed, Massachusetts. 

0 1 2 MILES

0 1 2 KILOMETERS

Base map coverages from MassGIS, 1:5,000

BASIN BOUNDARY

SURFACE WATER

Till

Disturbed urban

Glacial outwash

Post-glacial alluvium

Aeolian sand and silt

EXPLANATION

STREAM-GAGE STATION

CLASSIFICATION STONY

BROOK

LAUNDRY LAUNDRY

BROOK

MUDDY

SINGLE

FAMILY

COMMERCIAL

MULTIFAMILY

71o12'

71o08'

71o04'

42o16'

42o18'

42o20'

42o22'

Soil coverages digitized from National

Resource Conservation Service soil maps

Massachusetts State Plane Projection

North American Datum 1983

Charles River
8 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Soil permeability ranges from 0.6 to more than 

6.0 in/h Highly permeable soils derived from wellsorted glacial outwash often exceed 2.0 in/h. Tillderived soils typically are less permeable than glacially 

outwash soils and range in permeability from 0.6 to 

2.0 in/h. Permeability may be less in till soils that contain fragipans (U.S. Department of Agriculture, 1995; 

Peragallo, 1989).

Topography

Skehan (1979) describes two geomorphic districts in the watershed: the Boston Lowland, and the 

Needham Upland (fig. 5). Most of the watershed is in 

the Boston Lowland, which generally is less than 50 ft 

above sea level and historically comprised large areas 

of mudflats and tidal marsh. Tidal marshes were filled 

or flooded largely by 1910 when the Old Charles River 

Dam was completed (Seasholes, 1999). The Boston 

Lowland also contains small elongated hills or drumlins that range from 50 to 140 ft above sea level. The 

Needham Upland is in the southwestern part of the 

watershed and is characterized by greater relief than the 

Boston Lowland. Drumlins also are common in the 

Needham Upland and some of them exceed 300 ft 

above sea level (Skehan, 1979). 

Hydrology

The lower Charles River Watershed has many 

named tributaries that appear on early maps of the area, 

such as the 1893 USGS 15-minute topographic map of 

Boston (Seasholes, 1999). The four largest tributaries 

to the lower Charles River, excluding the watershed 

above Watertown Dam (upper watershed) are Laundry 

Brook, Faneuil Brook, Muddy River, and Stony Brook 

(fig. 1). Most of the stream channels in these tributaries, with the exception of parts of the Muddy River, are 

enclosed in conduits. The underground storm-drain 

system of the watershed includes about 585 mi of conduit that varies in size, shape, and building material. 

The storm-drain systems were compiled into a 

common geographic information system (GIS) from 

digital engineering drawings supplied by the municipalities of Boston, Cambridge, Brookline, Newton, and 

Watertown. 

Ninety-eight major outfalls have been identified 

that discharge to the lower Charles River (fig. 6); 72 

outfalls are upstream of the Museum of Science. Sixteen of these outfalls are CSOs; 3 were closed and 13 

were still active as of the year 2000. Discharges from 

the CSO outfalls are not included as part of this study, 

but the outfalls are shown on figure 6 for reference. 

Areas tributary to the CSOs of Boston and Cambridge 

are excluded from the study area (figs. 1 and 6); these 

areas are being modeled separately by the MWRA. 

Various small outfalls are not included in the above 

count; these outfalls typically drain small street or 

parkway areas. 

Outfall identification numbers are ordered from 

upstream to downstream; outfall 1 is just below 

Watertown Dam and outfall 81 is below the Museum of 

Science. Areas that drain by direct sheet runoff or from 

small unnumbered outfalls to the lower Charles River 

were assigned the same outfall number as the next closest known upstream outfall with an added letter suffix. 

For example, three drainage areas downstream of outfall number 41 drain by sheet runoff. These drainage 

areas were identified as 41a, 41b, and 41c, and are 

labeled at the midpoint between drainage divides at the 

shoreline. Seventeen areas that drain by sheet runoff 

are identified in figure 6.

Previous Investigations

Quantification of runoff to the lower Charles 

River began during the engineering studies for the Old 

Charles River Dam in the early 1890s (Pritchett and 

others, 1903). Recent studies, summarized below, have 

focused primarily on quantifying runoff from the 

Muddy River and Stony Brook tributaries for the purpose of separating combined sewer areas. Measured 

discharge records from these studies are limited to specific events or short time periods, generally less than 

2 months duration. 

To assess the water quality of the Muddy River 

Subbasin, a model (SWMM) was developed in 1989 by 

Metcalf and Eddy, Inc. (M&E), for the Massachusetts 

Executive Office of Environmental Affairs (Metcalf 

and Eddy, Inc., 1989). The report describes the physical 

hydrologic features of the Muddy River Subbasin. 

Model simulations were limited to a synthetic 1-year, 

6-hour design storm. 
Introduction 9

Figure 5. Geomorphic districts and land-surface elevations of the lower Charles River Watershed, Massachusetts.

GEOMORPHIC BOUNDARY

STREAM-GAGE STATION

ELEVATION, IN FEET

SURFACE WATER

Base map developed using MassGIS (Massachusetts

Executive Office of Environmental Affairs) DTMs and 

Topogrid (ArcInfo 7.1) 

Massachusetts State Plane Projection

North American Datum 1983; 1:5,000

EXPLANATION

BASIN BOUNDARY

0 to 29

30 to 69 

70 to 119

120 to 159 

160 to 199 

200 to 249 

250 to 289 

290 to 329 

330 to 379 

0 1 2 MILES

0 1 2 KILOMETERS

STONY

BROOK

LAUNDRY

BROOK FANEUIL

BROOK

MUDDY

RIVER

COMMERCIAL

MULTIFAMILY

SINGLE FAMILY

NEEDHAM 

UPLAND

BOSTON

LOWLAND

71o12'

71o

08'

71o

04'

42o

16'

42o

18'

42o

20'

42o

22'

Charles River
10 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 6. Outfalls to the lower Charles River, Massachusetts. 

1 3

6

37

42

23

66

19 65 45

62

60

61

13

10

13a

12

9

8

4

11

11a

14

19a 21 20

18

22

15 16 7

5

2

27 26

28

25

43

48 49 49a

53

52 50

55 57

59

59a

47 4

41

44

6

c

27a

29

41a

41b

41

37a

30 31

32

38b

4

4

0a

0 39

38a

38

36

35

33a

34 33

58 56 54

68

69 67a

67

6

64

4a

63

70

81

77

75 73

7

72

8

76

80

77

74

17 24

Watertown Dam

Laundry Brook

Faneuil Brook

Muddy RIver

Stony Brook

Boston

arbor H

18a

Muddy RIver conduit

Hyde Brook

Salt Creek

Shepard Brook

New 

Charles

River Dam

41a

60

STREAM 

OR 

S

T

ORM-DRAIN OUTFALL AND IDENTIFI

CATI

ON N

UMBE

R

– Bold number indicates outfall is simulated by one– Alphanumeric number indicates sheet runoff, location is center point

 of the overland flow plane 

21

EXPLANATION

1 2 MILE

S

1 2 KIL

OMETER

S

0

0 CSO OUTFALL

– Not simulated

STONY BROOK SUBBASIN OUTFALL (includes CSO discharge)

Information from Boston Water and Sewer Commission,City of Cambridge Department of Public Works,City of Newton MIS Department,City of Watertown Department of Public Works,Massachusetts State Plane Projection, North American Datum 1983

Longfellow Bridge

Harvard Bridge 7

River Street 

Bridge

EliotBridge

Arsenal Street Bridge

71o12'

71o08'

71o

04'

42o22'

42o21'
Introduction 11

In 1992, a SWMM application was developed for 

the North System of the Massachusetts Water 

Resources Authority (MWRA) by M&E (Metcalf and 

Eddy, Inc., 1994). The North System includes all of the 

lower Charles River Watershed and portions of the 

Mystic and Neponset River Watersheds. The model 

was used to calculate CSO volumes in support of 

MWRA CSO facilities planning. The MWRA’s recommended CSO control plan included a screening and 

disinfection facility to remove floatables and disinfect 

discharges from the Stony Brook conduit. The model 

was discretized coarsely to represent runoff because of 

the large geographic area represented and because it 

was intended for use as a planning tool. For example, 

the model represented the entire Stony Brook Subbasin 

as a single subcatchment with no channel routing. 

Models simulated (1) four actual storms that ranged 

from 0.73 to 0.95 in., with data collected from November 1992 to November 1993, (2) design storms for 3- 

and 6-month, and 1-, 2-, and 5-year storms, and 

(3) continuous simulation for 1992. 

The U.S. Army Corps of Engineers (USACE) 

developed a new SWMM application of the Muddy 

River Subbasin following the October 1996 flood that 

caused damage to lower parts of the subbasin. The 

USACE used the SWMM RUNOFF module for subbasin runoff, SWMM TRANSPORT module for channel 

routing, and the USACE UNET model for unsteadyflow routing and to calculate floodwater elevations.

In 1997, MWRA provided the Boston Water and 

Sewer Commission (BWSC) a SWMM of the Stony 

Brook Subbasin. The BWSC Stony Brook model was 

based on the MWRA North System model and was 

used by Camp, Dresser, and McKee (CDM) and BWSC 

to develop alternatives to the MWRA plan of 

a screening and disinfection facility (Camp, Dresser, 

and McKee, 1997). From these analyses, BWSC identified sewer separation as a potential cost-effective 

alternative to the proposed screening and disinfection 

facility. MWRA and M&E conducted further evaluations that resulted in revising the CSO control plan to 

include separation of the 12 active regulators in the 

Stony Brook System. The CDM study included continuous discharge monitoring from April 22 to June 16, 

1996, at 34 locations through the subbasin. During the 

monitoring period, discharge data were collected for 

eight storms that ranged in size from 0.26 to 1.72 in.; 

the largest was about a 3-month storm.

The BWSC Stony Brook model subsequently 

was expanded by CDM to include additional detail of 

the Stony Brook System (Camp, Dresser, and McKee, 

1998). For example, the area upstream of Forest Hills, 

tributary to the Stony Brook conduit, which originally 

was modeled as a single 5,091-acre subcatchment, was 

discretized into 20 subcatchments. In addition, CDM 

further analyzed the flow capacity of the Muddy River 

by modifying the USACE SWMM model for the 

BWSC. CDM replaced the UNET model with the 

SWMM EXTRAN module for unsteady-flow routing 

and incorporated the physical characteristics of the 

Muddy River conduit into the model to split flow into 

separate outfalls to the lower Charles River (fig. 6). 

Model simulations of the Muddy River included hyetographs from actual storms that represent 1-, 2-, and 

100-year storms and a synthetic hyetograph of a 25-

year storm. CDM combined the Stony Brook and 

Muddy River models into one SWMM model, which is 

referred to herein as the Muddy River-Stony Brook 

model.

The Muddy River-Stony Brook model was 

refined further by M&E in 1998 for use in the design 

of the Stony Brook sewer-separation project (Metcalf 

and Eddy, Inc., 1999). Additional detail included an 

extensive representation of building and roof drains 

connected to the combined-sewer system to evaluate 

the effects of disconnecting roof drains on CSOs. This 

version of the Muddy River-Stony Brook model was 

provided to the USGS for use in this study.

Other information on storm runoff was collected 

in parts of the lower Charles River by other consultants. 

CH2M Hill (1990) collected discharge data at Electric 

Avenue in Brighton for two storms in May and July 

1988 for the MWRA CSO facilities plan; however, it 

was noted that these data had a high degree of uncertainty because of instrument fouling from debris. Rizzo 

Associates (1993) monitored discharge at a low-density 

residential area in West Roxbury and at an industrial 

area in Brighton for nine storms from April through 

July 1992 for the BWSC. 

Acknowledgments

The authors would like to thank the following 

municipalities and local agencies for allowing access 

to their geographic information: BWSC, Brookline 

Information Technologies Department, Cambridge 

MIS Department, Cambridge Department of Public 
12 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Works, Newton MIS Department, and Watertown 

Department of Public Works. Lawrence Soucie and 

Sharon Ho of Metcalf & Eddy, Inc., provided the latest 

SWMM of the Muddy River–Stony Brook Subbasins 

and assistance on running this model. Mark Voorhees 

of the USEPA, and Jay Brolin, formerly of the USEPA, 

provided data and reports of previous stormwatermodel investigations. Peter Weiskel of the USGS coordinated field and office work, managed meetings 

between USGS staff and the project Technical 

Advisory Committee (TAC), and carefully scrutinized 

all aspects of the study. The project TAC included 

William Walsh-Rogalski and Mark Voorhees of 

USEPA, Lise Marx of the MWRA, Kevin Brander of 

the MADEP, Kathleen Baskin of the Charles River 

Watershed Association (CRWA), and Dominique 

Brocard of Metcalf and Eddy, Inc.

GAGED SUBBASINS

The gaged subbasins include three relatively 

homogenous land-use subbasins and the four largest 

tributary subbasins to the lower Charles River, and 

Charles River at Watertown Dam (table 1, fig. 1). The 

upper watershed (Charles River above Watertown 

Dam) represents about 88 percent of the total drainage 

area to the lower Charles River. The gages on the tributaries, excluding the upper watershed, collectively measured runoff from about 66 percent of the drainage area 

to the lower Charles River. 

The land-use subbasins are 0.36 mi2 or less in 

size and drain areas that predominantly are (1) singlefamily residential—01104630, (2) multifamily residential—01104673, and (3) commercial—01104677 

(table 1). The gaged areas of the four tributary subbasins range in size from 1.42 to 11.8 mi2. Land use in 

the tributary subbasins predominantly is single-family 

residential, but generally is less residential in the eastern subbasins than in the western subbasins (table 1). 

The eastern subbasins and the areas nearer to the river 

tend to have more commercial land use than other 

areas. Gaged tributary subbasins included (1) Laundry 

Brook—01104640, (2) Faneuil Brook—01104660, 

(3) Muddy River—0110483, and (4) Stony Brook—

01104687. 

Roads often are coincident with the stormdrainage system and have a large effect upon the 

hydrologic response of a drainage basin. Road density 

is similar among land-use subbasins and averages 

about 30 mi of road per square mile of drainage area; 

storm-drain density averages 25 mi/mi2 and is slightly 

higher in the multifamily subbasin than in the commercial and single-family subbasins (table 1). Road densities are similar among the tributary subbasins, which 

average about 21 mi/mi2; storm-drain densities average 

18 mi/mi2 and are slightly higher in Laundry and 

Faneuil Brooks than in Muddy River and Stony Brook. 

The characteristics of the gaged tributary subbasins are 

similar to the characteristics of the ungaged areas.

Discharge

Discharge data were collected during the 2000 

water year (October 1, 1999, to September 30, 2000) 

unless otherwise noted. These data were used to compute contaminant loads described in a companion 

report (Breault and others, 2002), to calibrate the runoff 

models, and to evaluate the model fit described in this 

report. Specific information about the measurement 

and development of the discharge data collected at each 

station is reported in downstream order. 

Charles River at Watertown 

Station—01104615

The upper Charles River Watershed drains an 

area of 268 mi2. River stage was measured in the pool 

above the dam by a bubble gage and pressure sensor at 

15-minute intervals. A stage-discharge relation was 

developed with the use of standard techniques (Carter 

and Davidian, 1965; Buchanan and Somers 1965; 

Kennedy, 1983, 1984). Four discharge measurements 

that ranged from 30 to 1,230 ft3/s were used to define 

the rating during the water year; the computed discharge ranged from 24 to 1,350 ft3/s during the water 

year. Discharge records are considered excellent 

(meaning that measurement error is within 5 percent) 

except for a short period of missing record (August 18 

through September 1, 2000). The missing record estimated from the upstream USGS gage at Waltham is 

considered fair (the error is between 10 and 15 percent). Records for discharges below 200 ft3/s are considered poor (measurement error is greater than 15 

percent) because the Watertown Dam, which is flat and 

wide (190 ft), causes a large percent change in discharge for small change in stage at lower discharges. 

Daily mean discharge for the 2000 water year was published in the USGS MA–RI Water Resources Data 

Report (Socolow and others, 2001).
Gaged Subbasins 13 *Includes the 0.54 mi2 drainage area that drains to the Muddy River conduit. 1Aggregate of all ungaged areas not associated with a tributary subbasin. 

Table 1. Physical characteristics at gaged and ungaged subbasins in the lower Charles River Watershed, Massachusetts [Subbasin characteristics apply to the gaged drainage areas. Location of gaged basins shown in fig. 1. Latitude and longitude: In °, degrees; ′, minutes; and ′′, seconds. Commercial: Commercial also 

includes industrial, spectator recreation, transportation, and waste disposal. Urban open: Urban open also includes participation recreation, open, cemeteries, parks, institutional green space, cropland, 

and pasture. Other: Other includes open water and wetlands. mi/mi2, miles per square mile; mi2, square miles; --, not applicable; -, negligible amount] 

Station name Station No. Latitude ° ′ ′′ Longitude ° ′ ′′

Drainage 

area to 

gage

(mi2)

Drainage 

area to 

mouth

(mi2)

Average 

slope

(percent)

Land-use subbasins

Singlefamily

residential

Multifamily 

residential

Commercial Urban open Forest Other

Gaged

Land-use subbasins

Single family............................. 01104630 42 19 59 71 11 49 0.356 -- 4.3 97 - 1 2 - -Multifamily ............................... 01104673 42 22 28 71 06 49 .038 -- 2.0 - 78 - 22 - -Commercial............................... 01104677 42 22 14 71 06 53 .023 -- 3.1 - 24 76 - - -

Tributary Subbasins

Laundry Brook.......................... 01104640 42 21 53 71 11 21 4.70 4.70 5.4 66 - 12 9 11 2Faneuil Brook ........................... 01104660 42 21 21 70 09 20 1.42 1.78 8.9 53 12 8 20 4 3Muddy River ............................. 01104830 42 20 14 76 06 41 5.44 *6.32 7.2 46 14 10 16 7 7Stony Brook .............................. 01104687 42 19 04 71 06 12 11.8 12.8 6.5 35 14 13 26 12 -

Charles River at Watertown ... 01104615 42 21 54 71 11 25 268 268 -- -- -- -- -- -- --

Ungaged area1............................ -- -- -- -- 9.68 3.6 25 17 29 20 - 9

Station name Road miles Road density (mi/mi2) Storm drain (mi) Storm drain density (mi/mi2) Soils (percent) Till Sand and gravel Urban Alluvium and aeolian

Gaged

Land-use subbasins

Single family............................. 9.8 28 8.6 24 51 2 47 -Multifamily ............................... 1.1 28 1.0 27 - 75 25 -Commercial............................... 0.7 29 0.5 23 - 75 25 -

Tributary Subbasins

Laundry Brook.......................... 97 20 86 18 40 33 23 4Faneuil Brook ........................... 30 21 29 20 76 8 16 -Muddy River ............................. 115 21 87 16 61 13 25 1Stony Brook .............................. 252 21 191 16 62 13 23 2

Charles River at Watertown ... -- -- -- -- -- -- -- --

Ungaged area1............................ 290 23 192 15 26 13 60 1
14 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Discharge at the Charles River at Watertown station for the 

two design storms, based on actual storms of July 20, 1982, and 

September 20, 1961, were calculated from discharge data available from the upstream gage at Waltham, Massachusetts 

(01104500). Hourly data were obtained from the original strip 

chart record for September 20, 1961 (1-year design storm), and 

from primary computation printouts for July 20, 1982 (3-month 

design storm). Concurrent hourly discharge data collected during 

the 2000 water year at the Waltham and Watertown Dam stations 

were related (fig. 7) by two non-linear power functions:

QWatertown Dam = 6.8097QWaltham0.7334, (1)

when discharge is at or below 450 ft3/s at Waltham;

QWatertown Dam = 3.6605QWaltham0.8341, (2)

when discharge is above 450 ft3/s at Waltham;

where 

QWatertown Dam is the discharge at Watertown Dam in 

cubic feet per second, and 

QWaltham is the discharge at Waltham in cubic 

feet per second.

The difference between the discharge computed from the 

equations and the observed discharge had a root mean square 

error (RMSE) of 24 ft3/s for hourly values and 16 ft3/s for daily 

values. Discharge equations (1 and 2) reflect 

the total drainage area to the Watertown gage. 

Part of the drainage area, 23.6 mi2, usually 

does not contribute to the Waltham and 

Watertown streamgaging stations because 

discharge from it is usually diverted into 

the Cambridge water-supply reservoirs. 

However, during the 2000 water year, runoff 

from this drainage area was not diverted from 

the watershed because of construction in the 

Cambridge reservoir system. 

Single-Family Land-Use 

Station—01104630 

Runoff from a single-family land-use 

area was measured in the headwaters of 

Laundry Brook Subbasin at Newton Center. 

Stage was measured at 2-minute intervals by a 

submersible pressure transducer mounted near 

the bottom of a brick-lined 5.5-ft diameter 

pipe about 0.2 ft upstream from where it discharges into an open rectangular mortared 

field-stone channel. A shallow, 3.32-ft long 

v-notch weir was used at this site for a lowwater control. The bottom of the v-notch was 

0.29 ft above the bottom of the pipe, and the 

top of the weir was 0.66 ft above the bottom of 

the pipe. 

The stage-discharge relation was developed from eight discharge measurements and 

continuous velocity measurements made with 

an electromagnetic sensor over a period of 22 

days. Combined, these data provide a good 

stage-discharge relation between 0.14 and 

13 ft3/s. Above 13 ft3/s (0.53 ft), Manning’s 

equation was used to develop a theoretical 

rating from measured channel slopes and 

roughness coefficients estimated from field 

observations and the literature. The roughness 

coefficient was adjusted slightly until the theoretical rating matched the highest measured 

discharges. An iron security gate at the pipe 

exit, which is prone to blockage by debris, has 

an unknown effect on the hydraulics of the 

channel at high discharges. 

The computed 2-minute discharges 

ranged from 0 to 428 ft3/s. For discharges 

below 13 ft3/s, discharge is considered good 

except for a short period of missing record 

from August 14 through 23, 2000. The 

Figure 7. Relation of hourly discharge of Charles River at Waltham (01104500) to 

Charles River at Watertown Dam (01104615), Massachusetts, 2000 water year.

y = 6.8097x0.7334

400

600

800

1,000

1,200

1,400

0 200 400 600 800 1,000 1,200 1,400

CHARLES RIVER AT WALTHAM,

DISCHARGE, IN CUBIC FEET PER SECOND

CHARLES RIVER AT WATERTOWN,

DISCHARGE, IN CUBIC FEET PER SECOND

y = 3.6605x

0.8341
Gaged Subbasins 15

accuracy of the discharge above 13 ft3/s is unknown 

because the theoretical stage-discharge relation could 

not be verified above this discharge. Therefore, the 

higher the computed discharge is above the verified 

part of the theoretical rating, the greater the uncertainty 

of its value. Duration analysis of the 2-minute data 

indicates that 13 ft3/s is exceeded 0.31 percent of the 

time, 50 ft3/s is exceeded about 0.02 percent of the 

time, and 100 ft3/s is exceeded less than 0.01 percent of 

the time; however, flows greater than 13 ft3/s represent 

about 25 percent of the measured runoff volume.

At least one high-intensity storm, on July 18, 

2000 (maximum rainfall exceeded 0.5 in. in a 15-

minute interval measured at several rain gages), 

appears to have generated full-pipe flow (pressurized 

flow). Full-pipe flow may have been caused by surcharging or backwater due to debris on the security 

grate. Debris was found lodged in the transducer 

mountings at the top of the pipe after the storm. The 

stage-discharge rating does not account for pressurized 

flow or backwater; thus, the peak discharge computed 

for this storm could be overestimated.

Laundry Brook 

Station—01104640

Laundry Brook streamflow was measured near 

the confluence with the lower Charles River. Stage was 

measured at 2-minute intervals by an ultrasonic transducer mounted in the roof of a 7-ft-high by 10-ft-wide 

concrete-box culvert about 50 ft upstream of the culvert 

outlet. The culvert discharges into an open channel 

about 50 ft from its confluence with the lower Charles 

River. A shallow v-notch weir about 4 ft downstream of 

the transducer was used for a low-water control. The 

bottom of the v-notch was 0.2 ft above the bottom of 

the culvert. The top of the weir was 1.0 ft above the 

bottom of the culvert.

A theoretical rating was developed by use of the 

HEC-RAS steady-state hydraulics model for open 

channels (Brunner, 2001). The friction slope was 

assumed to be equal to the culvert slope. Fifteen channel cross sections, positioned from 60 ft downstream of 

the v-notch weir to about 100 ft upstream of the weir, 

were used to describe the conduit geometry. Cross sections were spaced closely near the weir and near the 

stage sensor. A roughness coefficient of 0.011 was used 

for the sides of the culvert and 0.013 was used for the 

bottom of the culvert. 

Water-surface elevations were computed at each 

cross section for discharges of 1, 5, 10, 50, 100, 200, 

400, 500, and 600 ft3/s. At the cross section that corresponds to the transducer location, the computed Froude 

number changes from 0.52 at 200 ft3/s to 1.98 at 

400 ft3/s, which indicates a transition from critical to 

supercritical flow. Stage-discharge relations between 

200 and 400 ft3/s are, therefore, unstable. Five discharge measurements were made at this site that ranged 

from 0.41 to 75 ft3/s. The hydraulic model rating 

agrees with the highest measured discharge (76 ft3/s) to 

within 1 percent and generally agrees with the measured stage-discharge values at low flows. However, 

measured stage-discharge values were used solely for 

developing the rating below 20 ft3/s. 

Discharge records began October 28, 1999, and 

are considered good. The computed discharge ranged 

from 0.10 to 216 ft3/s and likely was not high enough 

to become supercritical flow. Discharge at the station 

can be affected by the regulation of Bulloughs Pond, 

which at times is partially drained by the City of 

Newton in anticipation of large storms.

Faneuil Brook 

Station—01104660

Faneuil Brook streamflow was measured at 

Brighton about 0.3 mi upstream from its confluence 

with the lower Charles River; the drainage area to this 

point composes about 80 percent of the total Faneuil 

Brook drainage area. Stage and velocity were measured 

at 2-minute intervals by a submersible pressure transducer and electromagnetic-velocity sensor, respectively. Sensors were mounted near the bottom of a 9-ftdiameter concrete pipe. Discharge was computed 

directly from stage and velocity measurements; the 

data logger converted the stage to an area and adjusted 

the point velocity taken near the bottom of the pipe to a 

theoretical average velocity for a given stage. The computed discharge during base-flow periods (generally 

about 1 ft3/s or less) was erratic because of insufficient 

water depth over the velocity sensor. During base 

flow, a stage-discharge relation was developed from 

velocity-stage readings and from three cross-sectional 

discharge measurements. 

Suspect velocity measurements were observed 

during some storms, particularly during the recession, 

as indicated by an inconsistency in discharge values 

obtained by a stage-dischargeS relation and the velocity measurements. For example, the area-velocity 

discharge was consistent with the discharge computed 

from a stage-discharge relation during the first part of a 
16 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

storm on December 6, 1999 (fig. 8), but during the later part 

of the storm the area-velocity discharge quickly dropped 

while the computed stage discharge oscillated and recessed 

over about a 10-hour period. Fouling of the velocity sensor 

by debris carried during storms is believed to cause this 

problem. Site visits during non-storm periods indicate the 

presence of trash in the conduit, such as plastic bags, that 

could easily foul the transducer. For this reason, the stagevelocity discharge measurements were compared against the 

computed discharge made from the stage-discharge relation. 

The computed discharge ranged from 0.33 to 

179 ft3/s. Discharge records generally are considered good 

except for occasional erratic readings and two short periods 

of missing record (October 19–27, 1999, and April 28–May 

1, 2000). To the extent possible, erratic readings were edited 

so that they were consistent with neighboring readings. 

During several storms, the discharge computed from the 

stage-velocity reading appear inconsistent with the discharge obtained from the stage-discharge relation. This 

inconsistency may be a result of debris fouling the velocity 

sensor. For example, a plastic bag caught on the velocity 

sensor could disrupt or weaken the penetration of magnetic 

field in the column and cause an erroneously low velocity 

measurement. During periods when the velocity sensor 

appeared fouled, the stage-discharge rating was used to 

compute discharge. 

Multifamily Land-Use 

Station—01104673

Runoff from a multifamily land-use area 

was measured at 2-minute intervals in a bricklined 

2.8-ft-high oval storm drain on Broadway in

Cambridge by a submersible pressure transducer 

mounted near the floor of the pipe. Manning’s 

equation was used solely to develop the stagedischarge relation. The data from the stagevelocity sensor installed at this site for 56 days was 

erratic and could not be used. Slope was determined from invert elevations supplied by the City 

of Cambridge drainage network digital data layer. 

A roughness coefficient of 0.015 was used, which 

was similar to the roughness coefficient obtained 

when Manning’s equation was applied to other 

brick-lined pipes in the study area.

The computed discharge ranged from 0 to 

26 ft3/s since the station became operational in 

November 23, 1999. The stage-discharge rating 

could not be verified, thus, discharge records are 

of unknown quality. Data are missing between 

February 3 and March 22, 2000. Erratic discharge 

was observed during storms at the beginning of 

April 2000; discharge would increase in response 

to rainfall then drop suddenly to zero. This discharge pattern would be repeated over the course 

of the storm several times for no apparent reason; 

the data are suspect during these periods. 

Commercial Land-Use 

Station—01104677

Runoff from a commercial land-use area 

was measured at 2-minute intervals in a 3.0-ftdiameter concrete storm drain on Mt. Auburn 

Street in Cambridge by a submersible pressure 

transducer mounted near the bottom of the pipe. 

A water stage and velocity sensor temporarily 

installed in the storm drain for a 2-day period provided discharge data between 0.1 and 6 ft3/s. These 

data provided a good stage-discharge relation 

below a 1.0-ft stage. A theoretical rating was 

developed for stages above 1.0 ft from Manning’s 

equation. Slope was determined from invert 

elevations supplied by the City of Cambridge 

digital coverage of the drainage network. A 

roughness coefficient of 0.019 was determined by 

slightly adjusting the literature value for a smooth 

concrete pipe until the theoretical rating matched 

the highest measured discharges. 

Figure 8. December 6–8, 1999, storm hydrographs at Faneuil Brook streamgaging 

station (01104660), lower Charles River Watershed, Massachusetts, determined by 

three methods (A) area-velocity measurements, (B) stage-discharge relation, and 

(C) simulated by the StormWater Management Model (SWMM).

6

DECEMBER 1999

7 8

0

10

20

30

40

DISCHARGE, IN CUBIC FEET PER SECOND

AREA-VELOCITY

MEASUREMENTS

SIMULATED

STAGE-DISCHARGE

RELATION
Gaged Subbasins 17

Computed discharges ranged between 0 and 

25 ft3/s since the station began operation in January 20, 

2000. Stage measurements during the first 2 months of 

operation were noisy, but appeared to respond to storm 

precipitation. Discharge records are considered good 

below 6 ft3/s, but above this discharge the accuracy of 

the theoretical rating is unknown. Hence, the larger the 

computed discharge is above the verified part of the 

theoretical rating (6 ft3/s), the greater the uncertainty of 

its value. Duration analysis of the 2-minute data indicated that 6 ft3/s was exceeded 0.42 percent of the time, 

which represented about 10 percent of the measured 

runoff volume; 10 ft3/s was exceeded 0.02 percent of 

the time; and 20 ft3/s was exceeded less than 0.004 percent of the time. Discharge records are missing from 

April 3 through 19, 2000.

Muddy River 

Station—01104683

Muddy River streamflow was measured at 

Brookline about 2.1 mi upstream from its confluence 

with the lower Charles River; the drainage area to this 

point composes about 91 percent of the total Muddy 

River drainage area. Stage was measured at 15-minute 

intervals by a bubble-gage transducer in an open channel. Muddy River is a low-gradient stream with heavily 

vegetated banks. Variable backwater can result from 

debris in and along the channel, and from blockage of a 

trash grate 0.6 mi downstream of the gage, where the 

channel enters a culverted section for 400–500 ft prior 

to its discharge point at the Charles River. In addition to 

backwater from these factors, stage at the gage is 

affected highly by the water level in the lower Charles 

River, which is regulated daily to maintain desired seasonal water levels. The relation between the stage at the 

Muddy River gage and the stage of the lower Charles 

River over a 3-day period is shown in figure 9. The 

figure also illustrates how water levels in the lower 

Charles River are dropped during low tide and how regulation prevents high tide from raising water levels in 

the lower Charles River. In addition, large pumps are 

used during some storms to maintain water levels in the 

lower Charles River even when the tidal cycle is high. 

As a result of these variable backwater conditions, discharge estimates for the Muddy River Subbasin are 

poor (more than 20-percent measurement error) and 

have a high degree of uncertainty.

A rating was developed for the Muddy River 

gage from 11 discharge measurements that ranged from 

1.8 to 230 ft3/s. The stage for each discharge 

measurement was adjusted to an estimated stage if the 

water levels in the lower Charles River were at the 

average low-water level. For example, if the stage 

during the discharge measurement was at 8.8 ft, and the 

water level in the lower Charles River was 0.4 ft above 

its average low-water level, a correction of -0.4 ft was 

applied to the measurement stage. The adjusted stage 

had less scatter around the best-fit, stage-discharge 

Figure 9. Relation of stage at the Muddy River streamgaging station to water levels in the lower Charles River and Boston Harbor, Massachusetts. 

(Stage is based on the reference to the Metropolitan District Commission datum.)

106.4

106.6

106.8

107.0

107.2

107.4

107.6

107.8

108.0

0000 0600 1200 1800 2400 0600 1200 1800 2400 0600 1200 1800

MUDDY RIVER AND LOWER 

CHARLES RIVER STAGE, IN FEET

100

102

104

106

108

110

112

BOSTON HARBOR STAGE, IN FEET

Muddy River

Lower

Charles 

River Boston Harbor

December 26 December 27 December 28

2400

2000
18 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

relation line than did the unadjusted stage; however, the 

scatter still is higher than acceptable for standard rating 

development. By use of the same technique, the 

measured storm stage was adjusted to minimize the 

effects of the backwater from the regulation of the 

lower Charles River. 

Stony Brook 

Station—01104687

Stony Brook streamflow was measured at 

Jamaica Plain about 2.4 mi upstream from its confluence with the lower Charles River; the drainage area 

to this point composes about 90 percent of the Stony 

Brook drainage area. A submersible pressure transducer mounted along the bottom arch of a 17-ft-high 

brick-lined, horseshoe-shaped conduit recorded stage 

at 15-minute intervals. An inverted siphon about a 

mile downstream of the gage probably controls flow 

during high water. However, conduit geometry and 

slope control flow rates at lower flows. Iron grates protrude about 4 to 5 in. at the bottom of the conduit near 

the gage that likely affect the Manning’s roughness 

coefficient. A small debris pile was noted above the 

gage that probably formed on one of the protruding 

grates, but, because of inaccessibility, the extent of similar obstructions downstream of the gage are unknown. 

A rating was developed on the basis of 

Manning’s equation from surveyed geometry, one 

cross-sectional discharge measurement made in the 

conduit, and seven single-point velocity measurements. 

The single-point velocity measurements were made by 

lowering a current meter through the manhole (discharge ranged from 7 to 300 ft3/s). During storm flows, 

conditions are extremely hazardous and access is prohibitive. High velocities in the conduit limit a conventional point-velocity-current-meter measurement above 

a 2-ft stage. Slope was determined from water-surface 

elevations surveyed over a distance of 156 ft (the maximum distance that could be obtained by survey crews 

tethered to safety lines). A roughness coefficient of 

0.019 was estimated by fitting the measured velocities 

to the computed velocities from Manning’s equation. 

Computed discharge ranged from 0.49 to 

856 ft3/s since the site became operational at the beginning of April 2000. A short period of record is missing 

from April 20 through 24, 2000. Discharge records are 

considered good from 6.0 to 270 ft3/s where discharge 

measurements confirmed the Manning rating. The 

accuracy of the rating above 270 ft3/s is uncertain 

because the inverted siphon could affect the rating; 

however, discharges exceeded 270 ft3/s only 0.39 percent of the time; these discharges represent about 12 

percent of the total measured volume.

Data Management

Stage and computed discharge values for the five 

tributary gaging station subbasins (Charles River at 

Watertown—01104615, Laundry Brook—01104640, 

Faneuil Brook—01104660, Muddy River—01104683, 

and Stony Brook—01104687), and precipitation data 

from the USGS-CR3, were telemetered and automatically downloaded to ASCII files on a computer at the 

USGS office in Northborough, Massachusetts. The 

computed discharges downloaded from the data loggers were based on early stage-discharge relations, 

except at Faneuil Brook, which computed discharge 

from measurements of stage-area and velocity. The 

preliminary computed discharge from the data loggers 

was for display of near-real-time data over the Internet 

only; final computed discharge values were used for 

model calibration and model-fit statistics. At the three 

land-use subbasins, data were transferred from on-site 

data loggers to field computers periodically during site 

visits. Data from the field computers were downloaded 

to a computer at the USGS office in Northborough.

The raw ASCII files were checked for erroneous 

data, corrected, and then processed with the use of a 

computer program, Device Conversion and Delivery 

System (DECODES), for entry into the USGS 

Automated Data-Processing System (ADAPS). Only 

stage data were entered into ADAPS for each site, 

except for Faneuil Brook, which also included the computed area-velocity discharge measurement. ADAPS 

provides permanent storage of the data in the USGS 

National Water Information System (NWIS). The 

ADAPS system converted stage measurements into discharge from a specified stage-discharge relation for the 

stations described previously.

The recorded data entered into NWIS had either 

a 2-minute or a 15-minute time step. Calibration and 

assessment of the SWMM were made with 15-minute 

data. The 2-minute time-step was transformed with the 

ANNIE Watershed Data Management (WDM) system 

(Lumb and others, 1990). 
Precipitation-Runoff Model 19

PRECIPITATION-RUNOFF 

MODEL

The precipitation-runoff model, SWMM (Huber 

and Dickinson, 1988), was used to simulate runoff in 

response to precipitation in the lower Charles River 

Watershed because it was not possible to measure discharge at all outfalls to the lower Charles River (fig. 6), 

and because stormwater runoff was required for two 

design storms that could not be measured directly. 

SWMM was chosen for the simulation of runoff 

because it was designed for use in highly urbanized 

areas, such as the Boston metropolitan area. The model 

is a well-documented public domain FORTRAN program developed by the USEPA that has been used 

extensively in the analysis of urban stormwater runoff. 

For this study, a proprietary interface to SWMM, 

PCSWMM 2000, developed by Computational 

Hydraulics International (CHI), was used for simulation. PCSWMM 2000 is a graphical-user interface to 

SWMM and has additional features not available with 

the SWMM public-domain software, such as simplified 

data management, model development, and streamlined model calibration. PCSWMM 2000 can use any 

available SWMM engine; SWMM version 4.4 was 

used for this study. The SWMM models can be run 

independently of the PCSWMM interface with minor 

modifications of input files to handle data transfer 

between modules.

Modeling runoff to the lower Charles River 

required the following steps: (1) collect, compile, and 

process needed data, (2) build the model run files, 

(3) calibrate the models to selected storm events, and 

(4) calculate model-fit statistics for all storms. Because 

streamflow data were collected at multiple unrelated 

drainage systems, separate models were developed for 

separate subbasins. 

Functional Description of 

SWMM

SWMM is divided into modules that simulate 

many aspects of urban runoff quantity and quality; 

however, only the simulation of runoff quantity was 

used in the study presented here. Simulation modules 

used in this study include RAIN, COMBINE, 

RUNOFF, TRANSPORT, and EXTend TRANsport 

(EXTRAN). The RAIN module is for “service” to the 

RUNOFF module; the COMBINE module “services” 

any of the other modules; RUNOFF, TRANSPORT, 

and EXTRAN are the primary computational modules 

for runoff and flow routing. User manuals by Huber 

and Dickinson (1988) and James and others (1999a; 

1999b) provide comprehensive documentation of these 

modules.

The RAIN module formats precipitation data 

from 1 to 10 gages into a single binary file for input to 

the RUNOFF module. The RAIN module also optionally provides statistical summaries of precipitation 

characteristics and antecedent conditions (WoodwardClyde Consultants, 1989). Typically, the RAIN module 

is used for continuous simulations so that the timeseries data can be called by the RUNOFF module.

The COMBINE module allows multiple interface files (filename.int) generated by the process modules to be aggregated or combined. For example, large, 

complex drainage systems may be partitioned for simulation into smaller segments and later combined. 

The RUNOFF module is one of the primary 

process modules of SWMM, and is used to simulate 

runoff from pervious and impervious areas. Runoff is 

generated from rainfall, snowmelt, or both, and can 

be simulated in either a continuous or single-event 

mode. Runoff from impervious areas is generated 

once impervious-area interception storage is satisfied. 

Runoff from pervious areas is generated once perviousarea interception storage is satisfied and after precipitation exceeds infiltration simulated by either the GreenAmpt or the Horton method. Infiltrated water from pervious areas is routed to inlets only when the groundwater subcatchment information is provided; otherwise, infiltrated water is included in the model hydrologic mass balance but is not routed from the 

subcatchment. 

One or more subcatchments can be specified in 

the RUNOFF module to simulate a watershed. Subcatchments are simulated as idealized rectangular subcatchments with a defined width and area. The width of 

the subcatchment affects the time required for precipitation to reach the outflow from the subcatchment; as 

width increases, the time required to reach the outflow 

decreases and conversely, as the width decreases the 

time it takes for precipitation to reach the outflow 

increases. Surface runoff and subsurface discharge 

from subcatchments also are affected by the percent 

effective impervious area and soil variables of a 

subcatchment. 
20 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Runoff from a subcatchment is directed to a node 

or “manhole” in the RUNOFF module. Nodes can be 

linked together with conduits to form a network of 

channels or pipes in the RUNOFF, TRANSPORT or 

EXTRAN modules. Flow routing in the RUNOFF 

module is primitive compared to that available in the 

TRANSPORT or EXTRAN modules. For this reason, 

flow routing usually is done outside of the RUNOFF 

module. 

Flow routing in the TRANSPORT module can 

be performed for a number of predefined conduit 

shapes or by a user-defined-conduit shape. The kinematic wave equations (continuity and uniform-flow 

equations) route flow through the conduit system, but 

neglect backwater effects. Unique node identification 

numbers used in the RUNOFF module provide the 

linkage to the shared node identification numbers used 

in the routing modules. Nodes can represent manholes 

(simple nodes), lift stations, flow dividers, storage 

units, or backwater elements that can flow to other 

nodes or to conduit elements (links). The assemblage 

of nodes and links forms the drainage network of a 

watershed. Model output can be specified at any node 

in the drainage system used to represent the watershed.

Complex drainage systems and drainage systems 

subject to surcharge, pressure flow, and backwater 

effects can be simulated with the EXTRAN module. 

EXTRAN is an extended version of the TRANSPORT 

module that solves the complete dynamic-flow 

equations (continuity and momentum equations), also 

known as the St. Venant equations. The assemblage of 

nodes and links described in the EXTRAN is similar to 

that in the TRANSPORT module; however, additional 

elevation information is required to solve the momentum equations. The TRANSPORT module was used to 

describe storage components in a drainage system such 

as ponds and detention basins by a volume-discharge 

relation. 

PCSWMM run files (filename.dat) are linked to 

related data files by data-aware objects. For example, 

the RUNOFF modules in the lower Charles River 

models all are linked to the binary precipitation data 

file (Rain.int) created by the RAIN module. Overland 

runoff computed by the RUNOFF module is written to 

a single binary file (filename.int) for all subcatchments. 

TRANSPORT or EXTRAN modules are linked as a 

related object to the binary file to route subcatchment 

runoff to nodes in the drainage network. Executive 

command lines for each module run file can be 

substituted for the data-object linkage provided in 

PCSWMM to run the modules in SWMM without the 

PCSWMM interface. 

Model Development

Separate models were prepared for the three 

land-use subbasins, two tributary subbasins (Laundry 

Brook and Faneuil Brook), and for the remaining 

ungaged drainage areas not included in a tributary subbasin model. Ungaged subcatchments that discharge 

downstream of a gaged tributary subbasin were 

included in the tributary subbasin models. An existing 

SWMM model for the Muddy River–Stony Brook 

Subbasins supplied by Metcalf and Eddy, Inc., was 

used “as is” (without modification) except for substituting hyetographs and evaporation data for the conditions 

under investigation. This report only describes the 

models developed by the USGS. Documentation of 

the Muddy River-Stony Brook SWMM models can 

be found in unpublished reports described in the 

“Previous Investigations” section.

Four separate models are needed to simulate 

runoff to the lower Charles River: (1) the Laundry 

Brook model, (2) the Faneuil Brook model, (3) the 

Muddy River-Stony Brook model, and (4) the ungaged 

area model. The Laundry Brook model and the 

ungaged area model include the land-use subbasin 

models that were calibrated independently; the 

Laundry Brook Subbasin includes the single-family 

residential land-use model and the ungaged-area model 

includes the multifamily and commercial land-use 

models. The ungaged area model represents about a 

third of the lower Charles River Watershed. The spatial 

coverage of the models is shown in figure 10 and 

detailed schematics of the model elements used in the 

models developed by the USGS are provided in 

appendix 1. 
Precipitation-Runoff Model 21

Figure 10. Areas of the StormWater Management Models (SWMM) developed for the lower Charles River Watershed, Massachusetts. 

71o12'

71o08'

71o04'

42o16'

42o18'

42o20'

42o22'

STREAM-GAGE STATION AND

U.S. GEOLOGICAL SURVEY

IDENTIFICATION NUMBER

PRECIPITATION GAGE AND

IDENTIFICATION NUMBER

SURFACE WATER

BASIN BOUNDARY

EXPLANATION

0 1 2 MILES

0 1 2 KILOMETERS

01104630

MWRA-WS5

CDPW-HS2

BWSC-CS4

BWSC-WS6

USGS-CR3

MWRA-WS5

Laundry

Brook

Model Faneuil 

Brook

Model

01104630

01104640

01104660

01104683

01104687

01104677 011

01104673

Ungaged Area Model ged A

Multifamily land-use

subbasin model

Commercial land-use

subbasin model

Single family land-use

subbasin model

PRECIPITATION GAGE THIESSEN

POLYGON BOUNDARY

Bulloughs

Pond

Chandler

 Pond

MUDDY

RIVER

STONY BROOK

Charles River
22 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

The model developed for the Muddy River and 

Stony Brook Subbasins differs from the models prepared for the other drainage areas. The Muddy RiverStony Brook model was prepared primarily to simulate 

CSOs and to aid in the engineering of infrastructure to 

minimize or eliminate these overflows. For this reason, 

the EXTRAN module was used to produce a detailed 

representation of the drainage system for the Muddy 

River-Stony Brook model, which requires simulations 

to run at a 5-second time-step for numerical stability. 

This model also required a modified SWMM engine 

developed by Metcalf and Eddy, Inc.

The models developed by the USGS did not 

require the same level of detail because these models 

were designed primarily to simulate stormwater volumes for calculating constituent loads. Thus, the 

TRANSPORT module was sufficient to provide stormflow routing through the drainage network in these 

models. Peak discharge, however, could be overestimated if surcharging or backwater conditions are 

present. All models of the lower Charles River tributaries developed by the USGS were run at a 15-minute 

time step. 

Data

Development of a precipitation-runoff model 

requires spatial data to characterize the physical 

aspects of the watershed. Input time-series data of 

precipitation and evapotranspiration are necessary to 

run the model. Discharge time-series data previously 

described are needed to calibrate the model and 

evaluate model fit.

Spatial Data

Spatial data were obtained to delineate subcatchments boundaries and outfall locations from soils, 

topography, and land-use data. These data were 

obtained from a variety of sources including local 

municipalities, consulting firms, the Massachusetts 

Geographic Information System (MassGIS) office of 

the Massachusetts Executive Office of Environmental 

Affairs, and the Natural Resource Conservation Service 

(NRCS). All spatial information was entered into 

ArcInfo as digital data layers. 

Subcatchment boundaries were determined from 

the drainage network coverage that was developed 

from Computer Aided Design (CAD) engineering 

drawings at the 1 in.= 100-ft or 1 in.= 400-ft scale. 

Outfalls to the lower Charles River were identified 

from the storm-drain network. The CAD-attribute 

information typically included average pipe slopes, 

diameters, and lengths. CAD data were obtained from 

local municipalities and their consultants.

Topographic and land-use data were obtained 

from MassGIS. Digital Terrain Model (DTM) 1:5,000-

scale data were converted to grids using ArcInfo GRID. 

GRID was used to calculate an average subcatchment 

slope. Land-use data were classified into 37 possible 

categories from interpretation of 1:25,000-scale 1991 

aerial photos (MassGIS, 2001). Land use was simplified into 21 categories to calculate initial effective 

impervious values and to select the land-use subbasin 

sites. 

Soils data were obtained from the NRCS 

1:25,000-scale digital SSURGO (Soils Survey 

Geographic) data for Norfolk and Suffolk Counties. 

SSURGO data were unavailable for Middlesex County, 

which had to be manually digitized from 1: 25,000-

scale county soil-survey maps. Soil units were classified by hydrologic soil groups and by soil texture. 

Time-Series Data

Precipitation data were collected by tippingbucket instrumentation at six gages (table 2, fig. 1) for 

the 2000 water year (October 1, 1999, through September 30, 2000). The USGS established one precipitation 

gage (USGS-CR3) for this study at Watertown Dam 

(fig. 1). The other five precipitation gages (CWD-PP1, 

CDPW-HS2, BWSC-CS4, MWRA-WS5, and BWSCWS) were established previously and are operated by 

others listed in table 2. Data recorded at 5-minute time 

steps were transformed to 15-minute time-steps to 

develop input time-series data sets for the RUNOFF 

modules.

The USGS-CR3 gage did not begin operation 

until November 3, 1999. Rainfall was estimated at this 

site from October 1 to November 3, 1999, by averaging 

rainfall from gages BWSC-CS4, MWRA-WS5, and 

BWSC-WS6. The CDPW-HS2 gage was not operated 

from November 12, 1999, to March 15, 2000. During 

this period, precipitation data recorded at the BWSCCS4 was substituted for precipitation data at CDPWHS2 so that the assignment of precipitation gages to 

subcatchments in the RUNOFF module did not have to 

be varied at different times of the year. 

The data from precipitation gages were formatted and read into the RAIN module of SWMM. The 

SWMM RAIN module provided information on the 

start hour, duration, volume, average intensity, and
Precipitation-Runoff Model 23

maximum intensity of each storm. In addition, the 

RAIN module reformats the data into a binary file 

read by the RUNOFF module. 

Daily potential evapotranspiration (PET) for the 

2000 water year was calculated by the Hamon method 

(Hamon, 1961) with the use of METCMP (Lumb and 

Kittle, 1995). The Hamon method was chosen because 

SWMM requires only a total monthly PET, and data 

required to compute PET by the Hamon method could 

be obtained readily over the Internet. Minimum and 

maximum daily air temperatures reported at Logan 

Airport in Boston were obtained from the Northeast 

Climate Center at Cornell University. A monthly variable coefficient (CTS) was assigned a constant value of 

0.0055, as suggested by Hamon (1961). Total PET for 

the 2000 water year was 26.19 in. and ranged from a 

monthly low of 0.46 in. in January 2000 to a high of 

4.75 in. in July 2000.

Representation of 

Overland Runoff

Drainage subbasins to each of the outfalls 

mapped in figure 6 were represented by one or more 

subcatchments in the RUNOFF module (appendix 1). 

Subcatchment boundaries were determined from the 

storm-drain maps and topography (appendix 1). 

Many outfalls were represented by a single subcatchment, others with large drainage areas had multiple 

subcatchments; the Faneuil Brook Subbasin model 

was represented by 19 subcatchments, the Laundry 

Brook Subbasin model was represented by 17 subcatchments, and the ungaged area model was represented by 90 subcatchments. Individual outfalls from 

the ungaged areas were represented by as many as five 

subcatchments, but most outfalls were represented by 

only one or two subcatchments. Each of the land-use 

subbasin models was represented by a single subcatchment. 

Each subcatchment is assigned a 6-digit number 

in the RUNOFF module that identifies the subbasin, 

town, and outfall number that the subcatchment drains 

to in the lower Charles River. The first digit of the subcatchment number identifies the major subbasin 

(table 3), the second digit identifies the municipality, 

the third and fourth digits are sequential numbers for 

subcatchments within the same subbasin and town, and 

the fifth and sixth digits identify the outfall number that 

the subcatchment drains to in the lower Charles River 

(fig. 6). Seventeen subcatchments have no known outlet 

point and were assigned 00 in the outlet identification 

field and sequentially numbered starting from 01 in the 

subbasin identification field.

Assignment of Subcatchments to

Precipitation Gages

Each subcatchment was assigned to a single precipitation gage. Assignments were made by intersecting Thiessen polygons of the gage network and the 

subcatchment coverage (fig. 10). If more than one rain 

gage was identified from the intersection of the two 

coverages, the rain gage with the largest area from the 

Thiessen polygon coverage was used. The CWD-PP1 

rain gage (fig.1) initially was used and later omitted 

from model simulations because (1) there were various 

periods of missing record, (2) the data had to be disaggregated from an hourly time step to a 15-minute time 

step, and (3) only three ungaged subcatchments were 

assigned to this gage from the intersection with the 

original Thiessen polygon. The three subcatchments 

initially assigned to CWD-PP1 were reassigned the 

USGS-CR3 gage, which was the next closest gage to 

these drainage areas. Although the CWD-PP1 gage was 

Table 2. Precipitation gages in and near the lower Charles River Watershed, Massachusetts 

[Locations shown in figure 1. Latitude and longitude: In °, degrees; ′, minutes; and ′′, seconds]

Station name Agency and location Latitude

° ′ ′′

Longitude

° ′ ′′ Heated

CWD-PP1 Cambridge Water Department, Payson Park Reservoir 42 22 59 71 10 06 yes

CDPW-HS2 Cambridge Department of Public Works, Hampshire Street 42 22 17 71 05 51 no

USGS-CR3 U.S. Geological Survey, Watertown Dam 42 21 54 71 11 26 yes

BWSC-CS4 Boston Water and Sewer Commission, Cambridge Street 42 21 08 71 08 30 yes

MWRA-WS5 Massachusetts Water Resources Authority, Ward Street 42 20 09 71 05 46 yes

BWSC-WS6 Boston Water and Sewer Commission, Washington Street 42 17 12 71 07 42 yes
24 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

not used in the final model, it was left in the binary precipitation file (rain.int) because its sequential number 

indicates the time when the precipitation time-series 

data were entered into the binary file. Thus, eliminating 

the CWD-PP1 gage from the rain.int file would have 

required renumbering the rain-gage assignment of all 

subcatchments.

Subcatchment Parameterization

Model development requires initial variable 

values that are measured to the extent possible, but 

often are modified during the model calibration. The 

variables that define subcatchment characteristics in 

the RUNOFF module, and statements of how initial 

variable values were determined and whether they were 

modified during the model calibration are given in 

table 4.

Subcatchment Width, Slope, Storage, and 

Roughness: Subcatchment width initially was calculated as the average distance between the subcatchment 

boundaries perpendicular to its drainage channel; however, the widths were calibrated to obtain the best fit 

between the simulated and observed storm-peak 

discharge and time of peak. Subcatchment widths 

varied from 380 to 4,300 ft, and generally were larger 

in developed subcatchments than undeveloped 

subcatchments. The subcatchment slope was calculated 

from a 1:5,000-scale digital-elevation grid. Slopes 

ranged from 0 to 0.165 ft/ft. Interception storage on 

pervious surfaces ranged between 0.30 and 0.50 in. 

Roughness of the pervious surface varied by land use 

and ranged between 0.30 and 0.40, and was highest in 

open and forest areas.

Effective Impervious Area: Effective impervious area is the most sensitive of all model variables 

because the runoff from impervious surfaces, such as 

roads and rooftops, that drains directly to the drainage 

Table 3. First and second digit numbers of the six-digit subcatchment 

model number used to identify subbasins and municipalities in the lower 

Charles River Watershed, Massachusetts

First digit of the

subcatchment number

Second digit of the 

subcatchment number

Identifier Subbasin name Identifier Municipality

1 Laundry Brook 1 Newton

2 Muddy River 2 Watertown

3 Faneuil Brook 3 Boston

4 Hyde Brook 4 Brookline

5 Stony Brook 5 Cambridge

6 Single family

7 Multifamily

8 Commercial

9 Unnamed

Table 4. StormWater Management Model (SWMM) RUNOFF module 

subcatchment variables and method used to obtain their initial values in 

the models of the lower Charles River Watershed, Massachuscetts

[GIS indicates that a geographic information system was used to measure 

values electronically from various data layers; minor, the value was adjused 

only slightly during the model calibration. ft, foot; ft/ft, feet per foot; 

in., inches; in/hr, inches per hour] 

Variable Variable description Initial value Calibrated

WIDTH Width of overland 

flow plain (ft) 

GIS Yes

AREA Area of subcatchment (acres)GIS No

%IMP Percent impervious 

area 

RainfallRunoff 

relation

Yes

SLP Ground slope (ft/ft) GIS No

IMPN Impervious area 

Manning’s 

roughness

Literature Minor

PERVN Pervious area 

Manning’s 

roughness

Literature Minor

IDS Impervious area 

depression storage 

(in.)

Literature Minor

PDS Pervious area 

depression storage 

(in.)

Literature Yes

Soil properties—Green-Ampt infiltration method

SUCT ................ Average capillary 

suction (in.)

Literature Yes

HYCON ............ Saturated hydraulic 

conductivity 

(in/hr)

Literature Yes

SMDMAX ........ Initial soil moisture 

deficit (unitless 

fraction: volume 

air/volume voids)

Literature Yes
Precipitation-Runoff Model 25

network has little opportunity for infiltration. Therefore, runoff from effective impervious area is directly 

proportional to rainfall minus interception and depression storage. Initial estimates of effective impervious 

area were assigned by land use from values of effective 

impervious area obtained from SWMM applications 

developed for the Neponset River Watershed and for 

Haverhill, Massachusetts (Mark Voorhees, U.S. 

Environmental Protection Agency, written commun., 

1999), and are summarized in table 5. The effective 

impervious area was refined for subbasins in the lower 

Charles River Watershed with measured discharge by 

plotting the relation between rainfall and runoff in 

inches for small storms (rainfall volumes less than 

0.5 in.) between May and September with dry antecedent conditions (fig. 11). The slope of the rainfall-runoff 

line indicates the fraction of effective impervious area 

in a basin (Jennings and Doyle, 1978). The intercept of 

the rainfall-runoff relation indicates the amount of rain 

required to produce runoff, which is a measure of the 

interception storage on effective impervious areas. A 

surface roughness coefficient of 0.02 was assigned to 

all impervious surfaces in the models.

Rainfall-runoff relations for the single-family 

land-use site indicated an effective impervious area of 

18 percent (fig. 11A). The effective impervious area 

obtained from the calibrated model for this site, which 

appears to be better represented by rainfall-runoff 

values for storms less than 0.2 in., was similar (17.4 

percent). The effective impervious area in this subbasin 

is about half that determined for single-family residential land use used in the Neponset River Basin. The 

depression storage for effective impervious areas indicated by the rainfall-runoff intercept (0.013 in.) is 

considerably less than the calibrated value (0.09 in.).

Rainfall-runoff relations for the multifamily 

land-use subbasin indicated an effective impervious 

area of 63 percent (fig. 11B). The calibrated effective 

impervious area (73 percent) was greater than that 

indicated by the slope of the rainfall-runoff line, but 

the calibrated effective impervious area is within 4 percent of the value obtained for similar land use in the 

Neponset River Basin. The depression storage for 

effective impervious areas indicated by the rainfallrunoff intercept (0.03 in.) did not change in the 

calibrated model.

Rainfall-runoff relations for the commercial 

land-use subbasin indicated an effective impervious 

area of 86 percent (fig. 11C). The rainfall-runoff plot 

was developed from selected low-intensity storms with 

rainfall-runoff coefficients less than 1.0. Possible 

causes for rainfall-runoff coefficients greater than 1.0 

are explained later in the section “Model Fit.” The calibrated effective impervious area is the same as the 

slope of the rainfall-runoff line, but is about 54 percent 

larger than the effective impervious area for similar 

land use in the Neponset River Basin. The depression 

storage for effective impervious areas indicated by the 

rainfall-runoff intercept (0.03 in.) did not change in 

the calibrated model.

Rainfall-runoff relations for the Laundry Brook 

Subbasin indicated an effective impervious area of 6 

percent (fig. 11D). The wide scatter in rainfall-runoff 

values likely is caused by variations in storage at 

Bulloughs Pond. The calibrated effective impervious 

area (11 percent) is about 80 percent higher than the 

slope of the rainfall-runoff line. The effective impervious area weighted by land-use type transferred from 

values used in the Neponset and Haverhill models indicated an effective impervious area of 23 percent, or 

about twice as large the calibrated effective impervious 

area for this subbasin. The depression storage for effective impervious area, indicated by the rainfall-runoff 

intercept (0.025 in.), was considerably less than the 

calibrated storage, which averaged 0.072 in. over the 

subbasin.

Table 5. Estimated percent effective impervious area applied to the 

StormWater Management Models (SWMM) of the lower Charles River 

Watershed, Masachusetts 

[Neponset: Transferred from Neponset River and Haverhill SWMM for 

similar land uses. Rainfall-runoff: Calculated from rainfall-runoff plots for 

small summer storms. Calibrated: Final value after model calibration. 

--, value not available]

Site

Percent effective impervious

Neponset Rainfallrunoff

Calibrated

Land-use subbasins

Single family................... 33 18 17

Multifamily ..................... 76 63 73

Commercial..................... 56 86 86

Tributary subbasins

Laundry Brook................ 23 6 11

Faneuil Brook.................. 36 8 14

Muddy River ................... 30 -- 42

Stony Brook .................... 28 6 19
26 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 11. Rainfall-runoff relations for small storms from May through September 2000 at gaged subbasins in the lower Charles River 

Watershed, Massachusetts. 

RUNOFF, IN INCHES

RAINFALL, IN INCHES

86-percent slope

0

0.1

0.2

0.3

0.4

C. Commercial Land-use Subbasin

0 0.1 0.2 0.3 0.4

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4 0.5

63-percent slope

B. Multifamily Land-use Subbasin

D. Laundry Brook Subbasin

0

0.01

0.02

0.03

0.04

0 0.1 0.2 0.3 0.4 0.5

6-percent slope

18-percent slope

0

0.02

0.04

0.06

0.08

0.10

0 0.1 0.2 0.3 0.4 0.5

A. Single-Family Land-use Subbasin

F. Stony Brook Subbasin

0

0.01

0.02

0.03

0.04

0 0.1 0.2 0.3 0.4 0.5 0.6

6-percent slope

8-percent slope

0

0.01

0.02

0.03

0.04

0 0.1 0.2 0.3 0.4 0.5

E.
Precipitation-Runoff Model 27

Rainfall-runoff relations for the Faneuil Brook 

Subbasin indicated an effective impervious area of 8 

percent (fig. 11E). The calibrated effective impervious 

area (14 percent) is about 75 percent higher than effective impervious area indicated by the slope of the rainfall-runoff line. The effective impervious area weighted 

by land-use type, transferred from values used in the 

Neponset and Haverhill models, indicated an effective 

impervious area of 36 percent, or about 160 percent 

larger than the calibrated effective impervious area for 

this subbasin. The calibrated depression storage for 

effective impervious areas (0.066 in.) was slightly 

greater than that indicated by the rainfall-runoff 

intercept (0.05 in.).

Rainfall-runoff relations for the Stony Brook 

Subbasin (fig. 10F) indicate that the effective impervious area is 6 percent of the drainage area; this value is 

considerably less than the calibrated effective impervious area (19 percent) and the estimated effective impervious area for similar land uses from the Neponset 

River watershed (28 percent). The effective impervious 

area in the Muddy River model (42 percent) is somewhat higher than the estimated effective impervious 

area for similar land use types from the Neponset River 

watershed (30 percent). Although the rainfall-runoff 

derived value of the effective impervious area could not 

be calculated for the Muddy River Subbasin, the effective impervious area from the areally weighted model 

is high relative to the other tributary subbasins. The 

percent impervious values assigned in the Stony 

Brook–Muddy River model were not altered for this 

study. 

Pervious Area Infiltration and Subsurface 

Flow: Infiltration on pervious areas was simulated by 

the Green-Ampt method. The Green-Ampt equation is 

a physically based model of infiltration that requires 

values of the soil’s capillary suction (SUCT), saturated 

hydraulic conductivity (HYCON), and the initial moisture deficit (SMDMAX). Initial values for these variables were estimated from the hydrologic soil group 

and texture reported for the mapped soils in the 

Norfolk, Suffolk, and Middlesex County soil surveys 

(U.S. Department of Agriculture, 1995; Peragallo, 

1989) and literature values for different soil textures 

reported by James and others (1999a). In subcatchments with more than one soil type, areally weighted 

averages were calculated.

Values of SUCT ranged from 4.3 to 9.7 in.; 

values of SUCT are lowest in sandy soils and highest in 

silty soils. Values of HYCON ranged between 0.01 and 

0.40 in/h and values of SMDMAX ranged between 

0.30 and 0.33 (unitless); values are highest in sandy 

soils and lowest in clayey soils.

Infiltrated water is routed to the drainage 

network only when ground-water cards (H2, H3, and 

H4) are specified in the RUNOFF module. Groundwater discharge from the saturated zone was treated 

as a simple linear reservoir in which water is drained 

at a rate defined by the coefficient A1. The coefficient 

A1 varied from 10-4 in undeveloped subcatchments 

down to 10-6 in highly developed subcatchments. The 

saturated zone was allowed to vary by 10 ft in all subcatchments. Some water loss from the saturated zone 

was allowed by deep percolation and evapotranspiration. Deep percolation was assigned a rate of 0.004 in/h 

for all subcatchments. The potential ground-water

evapotranspiration was assigned a value of 40 percent 

of the potential evapotranspiration over a depth of 10 ft 

for all subcatchments. The saturated hydraulic conductivity variable for ground-water discharge was set to the 

same value as that for the soil HYCON value. Values 

for ground-water variables were consistent for similar 

soil and land-use types. Data on ground-water levels 

relative to storm-drain elevations during storms were 

not available; therefore, the ground-water variable 

values were calibrated to the observed hydrograph 

recessions. Data required for simulation of head-dependent ground-water discharge to storm drains were not 

available. 

The saturated hydraulic conductivity for the multifamily land-use subbasin was set artificially low at 

0.01 in/h to account for impervious areas that drain to 

pervious areas (non-effective impervious area). Lowering the saturated hydraulic conductivity, in effect, 

increases the response of the pervious areas to rainfall 

because the model does not simulate the inflow to 

pervious areas from non-effective impervious areas. 

Representation of the 

Drainage Network

The drainage system was represented in the 

TRANSPORT module of SWMM. The actual drainage 

system (appendix 1) was simplified in the models to 

provide sufficient connectivity between subcatchments 

and to represent travel time from the headwater subcatchments to the outfall. For instance, the Laundry 

Brook Subbasin has 85.7 mi of storm drains, but the 

modeled drainage system includes only 6.2 mi of storm 
28 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

drains that represent the storm-sewer trunk lines. Pipe 

lengths and diameters were taken from available 

geographic data supplied by the municipalities.

In the TRANSPORT module, links and nodes 

must be assigned unique identification numbers. Node 

numbers identify junctions or outfalls, and link numbers identify conduits. Node numbers at junctions in 

the TRANSPORT module were assigned in the 

RUNOFF module (NGTO) for each subcatchment. 

Junction node numbers (ranging from 1 to 163) were 

assigned in ascending order from upstream to downstream in a subbasin and from upstream to downstream 

along the Charles Basin. Nodes that represent outfalls 

were assigned a 3-digit identification number, where 

the last two digits correspond to the outfall number 

shown in figure 6. The first digit of the outfall nodeidentification number generally begins with a 2, but the 

first digit was numbered sequentially for subcatchments that drain by sheet runoff and are identified by a 

letter suffix (fig. 6). For example, nodes representing 

outfalls 41 (known pipe outfall), 41a, 41b, or 41c (sheet 

runoff) were assigned numbers of 241, 341, 441, and 

541, respectively. Links (conduits) were assigned the 

same identification number as the node that they drain 

from plus one thousand. For example, the pipe that 

drains from node 55 is numbered 1055. 

Drainage Network Parameterization

Initial variable values for the drainage network 

were obtained from spatial-coverage attribute values or 

from literature values. The TRANSPORT module variables that describe the drainage system characteristics 

(E1 line) are listed in table 6. Only the length of the 

conduit system was changed appreciably during model 

calibration to match the simulated to the observed time 

of peak. Other drainage network variable values (in the 

RUNOFF module) were fixed or only slightly modified 

during model calibration (table 7). Only single-barrel 

pipe or rectangular-box conduits were simulated in the 

models developed by the USGS.

1 Applies only to pipe diameters in small ungaged subcatchments.

2 Invert slopes at gaged locations were either measured or estimated 

from GIS data. Invert slopes at all other locations were estimated from the 

ratio of the conduit slope at the gaging station to its nearby subbasin slope 

and applying this ratio to the subbasin slope at ungaged locations. 3Manning’s roughness values were determined from ratings 

developed at gaging stations. A characteristic roughness value of 0.012 

was used at all ungaged locations.

Table 6. StormWater Management Model (SWMM) TRANSPORT module 

variable values used in the lower Charles River Watershed, 

Massachusetts

[GIS, geographic information system—values were measured or obtained 

from attribute information. Minor, the values were adjusted only slightly 

during model calibration; ft, foot; ft/ft, feet per foot]

Variable Variable

description

Initial

value

Calibrated

DIST Length of conduit (ft) GIS Yes

GEOM1 Pipe diameter or 

rectangular conduit 

height (ft)

GIS Minor1

SLOPE Invert slope of conduit 

(ft/ft)

Measured, 

GIS 2

No

ROUGH Manning’s roughness value 

of conduit

Rating3 No

GEOM2 Rectangular conduit width 

(ft)

GIS Minor

Table 7. StormWater Management Model (SWMM) RUNOFF 

subcatchment variable values used in the land-use subbasins, lower 

Charles River Watershed, Massachusetts

[“n,” Manning’s roughness coefficient; ft, foot; ft/ft, feet per foot; in, inch; 

in/hr, inch per hour]

RUNOFF variables Single

family

Multifamily  Commercial

Percent impervious area ............ 17 73 86

Subcatchment width (ft) ............ 2,100 1,200 2,500

Slope (ft/ft) ................................ .043 .02 .031

Impervious area depression 

storage (in.)............................ .08 .03 .03

Pervious area depression 

storage (in.)............................ .16 .04 .03

Impervious area roughness (n) .. .015 .02 .015

Pervious area roughness (n) ...... .040 .35 .46

Suction (in.) ............................... 8.2 8.0 5.0

Hydraulic conductivity (in/hr)... .30 .01 .06
Precipitation-Runoff Model 29

Pond Storage

Storage nodes were used in the TRANSPORT 

module to simulate discharge through Bulloughs Pond 

in the Laundry Brook Subbasin model and Chandler 

Pond in Faneuil Brook Subbasin model (fig. 10). Storage nodes are defined by the depth-storage-discharge 

relation. Chandler Pond’s storage characteristics were 

obtained from an unpublished report by Fugro East, 

Inc. (1996). The report does not include the discharge 

characteristics of the outlet, which was estimated by 

model calibration. During the 2000 water year, Chandler Pond normally was empty for restoration and was 

treated as a flow-through system (Timothy Smith, Massachusetts District Commission, personal commun., 

2000), except when the discharge exceeded the outflow 

capacity of the drainpipe and was held in temporary 

storage. 

Storage characteristics of Bulloughs Pond were 

estimated from the average depth (Jay Fink, Newton 

Public Works, written commun., 2000); the surface 

area of the pond was obtained from the land-use 

coverage. The depth-storage-discharge characteristics 

specified for Bulloughs Pond were estimated through 

model calibration. 

Model Calibration

The general approach used was to calibrate 

models at the three land-use sites (single-family 

residential, multifamily residential, and commercial), 

then transfer the calibrated variable values from these 

models (table 7) to similar subcatchments in the 

Laundry Brook and Faneuil Brook Subbasin models. 

Values were transferred by a weighted average because 

the subcatchments in the tributary subbasin models represented mixed land use. Further adjustments of the 

values in tributary subbasin models were made to minimize the difference between simulated and observed 

discharges. These adjustments were made proportionally to the initial weighted values transferred from the 

land-use subbasin models. The final calibrated values 

for individual subcatchments in the tributary subbasin 

models represented a wide mix of land uses; these 

values were transferred to the closest subcatchment 

type in the ungaged subbasin model.

Model calibration focused on selected storms (up 

to 24) with the smallest spatial variation in total storm 

rainfall volume among the 6 gages in and near the 

study area (calibration storms are listed in appendix 3). 

This approach increases the likelihood that the calibrated model variables reflect the subbasin characteristics they are intended to represent. Measured discharge 

was not available for all selected storms for some subbasins; therefore, the number of calibration storms 

varied from site to site. Model calibration emphasized 

storm-runoff volumes, but storm-peak discharge and 

base flow also were considered. The model fit was 

evaluated for the calibration storms and for all storms 

of appreciable size at each site. All storms were used to 

test or “verify” the models. Limiting the analysis to 

storms not used in the model calibration would bias the 

fit to storms with a large spatial rainfall variability. 

Unequal rainfall distribution cannot be well represented by a few rainfall gages; therefore, the model fit 

for these storms would not be a good measure of the 

model’s conceptualization or calibration.

Model Fit

Model fit is a measure of how well the simulated 

storm-peak discharge and runoff volumes match the 

observed values. Various measures of model fit are 

reported for calibration storms and for all storms 

including absolute measures of model error, relative 

measures of fit, and several supporting measures of fit. 

Absolute error is reported as the standard error of estimate (SE) and the RMSE, which were calculated by the 

SWMM calibration wizard. The relative model fit is 

measured by the coefficient of efficiency and the index 

of agreement (Legates and McCabe, 1999). 
30 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Other statistical measures and scatter plots of 

paired simulated and observed values are provided to 

assess model performance. Supporting statistics 

include the median, range, and standard deviation 

of the percent difference between simulated and 

observed values, and the percent of the time these 

values are within 10, 25, and, 50 percent. Model errors 

were examined to determine if there were systematic 

biases related to time of year or storm characteristics. 

Causes for the largest error between simulated and 

observed peak discharges and storm volumes also were 

examined for each model.

Land-Use Subbasin Models

The three land-use subbasins represent 60 percent of the land use in the lower Charles River Watershed. Variable values obtained from the calibrated 

models developed at these subbasins provided the initial values for subcatchments of similar land use in tributary subbasin models and the ungaged subbasin 

model. The calibrated subbasin-variable values at the 

three land-use subbasins are summarized in table 7.

Single-Family Residential

Calibration Storms: Twenty storms were used 

for model calibration; total rainfall during these storms 

ranged from 0.31 to 1.80 in. (mean 0.60 in.), which 

resulted in observed discharges that ranged from 1.6 to 

59 ft3/s (mean of 12 ft3/s) in peak discharge and 0.027 

to 0.302 in. (mean of 0.104 in.) in runoff volume. The 

simulated peak discharges had a SE of 7.2 ft3/s and a 

RMSE of 17 ft3/s (table 8); the difference between simulated and observed peaks ranged between -46 and 150 

percent with a median difference of -19 percent and a 

standard deviation of 47 percent. Simulated peak discharges were within 10 percent of the observed peak 25 

percent of the time, within 25 percent of the observed 

peak 35 percent of the time, and within 50 percent of 

the observed peak 90 percent of the time. The scatter 

plot (fig. 12A) and model-fit statistics (table 8) indicate 

that the simulated peak discharge is undersimulated.

The difference between the simulated and 

observed runoff volumes had a SE of 0.032 in. and a 

RMSE of 0.109 in. (table 8); the difference between 

simulated and observed runoff volumes ranged 

between -16 and 281 percent, with a median difference 

of 29 percent and a standard deviation of 67 percent. 

Simulated runoff volumes were within 10 percent of 

the observed volume 30 percent of the time, within 25 

percent of the observed volume 45 percent of the time, 

and within 50 percent of the observed volume 70 percent of the time. Good agreement between simulated 

and observed runoff volume is indicated for storms 

with more than 0.15 in. of runoff; storms with less than 

0.15 in. of runoff tend to be oversimulated (fig. 12A). 

All Storms: Forty-nine storms were used to evaluate the overall model fit; total rainfall during these 

storms ranged from 0.01 to 3.64 in. (mean 0.60 in.) that 

resulted in observed discharges that ranged in peak discharge from 1.0 to 66 ft3/s (mean of 14 ft3/s) and volumes from 0.013 to 0.862 in. (mean of 0.135 in.). The 

simulated peak discharge had a SE of 46 ft3/s and a 

RMSE of 97 ft3/s (table 8); the difference between simulated and observed peak discharges ranged between 

-90 and 493 percent with a median difference of -18 

percent and a standard deviation of 101 percent. Simulated peak discharges were within 10 percent of the 

observed peak 30 percent of the time, within 25 percent 

of the observed peak 45 percent of the time, and within 

50 percent of the observed peak 70 percent of the time 

(table 8). A large variability between simulated and 

observed peak discharge is indicated for most storms 

(fig. 12B).

The difference between the simulated and 

observed storm runoff volumes for all storms had a SE 

of 0.121 in. and a RMSE of 0.362 in. (table 8); the difference between simulated and observed runoff 

volumes ranged between –52 and 502 percent with 

a median difference of 18 percent and a standard deviation of 95 percent. Simulated storm runoff volumes 

were within 10 percent of the observed volume 28 

percent of the time, within 25 percent of the observed 

volume 51 percent of the time, and within 50 percent 

of the observed volume 72 percent of the time. Simulated runoff volume is in good agreement with the 

observed runoff volume over the entire range of storms 

(fig. 12B). 

Error: Model error, for both peak discharge and 

runoff volume, was largest in the summer months 

(fig. 13A), which tend to be dominated by convective 

storms with rainfall amounts that can vary widely over 

a watershed. Model error was not correlated with 

rainfall volume, intensity, or antecedent conditions 

(figs. 13B, C, and D), as measured by the Spearman
Precipitation-Runoff Model 31

rank test. The tendency to undersimulate storm peak 

discharges and oversimulate runoff volumes indicated 

by the plotting position of smaller calibration storms 

(fig. 12A) suggests that subcatchment width and the 

interception storage could be increased; this increase 

was not done, however, because of the good agreement 

between simulated and observed runoff volumes for 

all storms. Undersimulated peak discharge for the 

larger storms (fig. 12B) could be a result of error in 

the observed discharge resulting from debris on the 

security gate at the pipe exit causing backwater and an 

overmeasurement of the actual peak discharge.

Figure 12. Simulated and observed peak discharge and runoff volume at the single-family land-use subbasin, lower Charles River Watershed,

Massachusetts, for the 2000 water year: (A) calibration storms, and (B) all storms. SIMULATED PEAK DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED PEAK DISCHARGE, OBSERVED RUNOFF VOLUME, IN INCHES

IN CUBIC FEET PER SECOND

PEAK DISCHARGE RUNOFF VOLUME

A. Calibration storms

B. All storms 

SIMULATED RUNOFF VOLUME, IN INCHES

0

10

20

30

40

50

60

0 10 20 30 40 50 60

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4

0

20

40

60

80

0 20 40 60 80

0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0
32 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

1Subset of storms with rainfall/runoff coefficients less than 1.3.

Table 8. Summary of StormWater Management Model (SWMM) fit statistics for storm-peak discharge and storm-runoff volume, lower Charles River 

Watershed, Massachusetts

[No.: Number of storms used to compute statistics. Standard error of the estimate (SE) and root mean square error (RMSE) are in units of cubic feet per second for peak discharge and inches for runoff volume. E: Coefficient of efficiency. d: Index of agreement. ft3/s, cubic feet per second]

Site No. SE RMSE E d

Percent time simulated value is within 

observed value

10 25 50

Storm-peak discharge

Calibration Storms

Land-use subbasin models

Single family 20 7.2 17 0.69 0.88 25 35 90

Multifamily 21 2.0 6.0 .84 .96 29 62 95

Commercial 13 2.0 5.1 .81 .95 23 46 85

Tributary subbasin models

Laundry Brook 24 15 48 .73 .94 29 58 92

Faneuil Brook 21 8.9 27 .35 .87 25 50 80

Stony Brook 17 41 120 .83 .96 18 47 71

All Storms

Land-use subbasin models

Single family 49 46 97 .81 .94 30 45 70

Multifamily 36 2.6 10 .71 .93 25 58 86

Commercial 31 3.0 10 .27 .83 26 52 77

Commercial1 10 2.5 4.8 -.01 .72 22 67 78

Tributary subbasin models

Laundry Brook 48 22 85 .70 .94 21 60 81

Faneuil Brook 48 15 64 -.33 .76 19 44 65

Stony Brook 28 80 260 .84 .97 14 43 79

Storm-runoff volume

Calibration Storms

Land-use subbasin models

Single family 20 0.032 0.109 0.81 0.94 30 45 70

Multifamily 21 .088 .303 .94 .98 43 67 95

Commercial 13 .407 .794 .66 .27 31 69 92

Tributary subbasin models

Laundry Brook 24 .016 .061 .91 .97 46 67 87

Faneuil Brook 21 .029 .094 .59 .92 40 75 95

Stony Brook 17 .048 .139 .32 .74 29 53 76

All Storms

Land-use subbasin models

Single family 49 .121 .362 .83 .94 28 51 72

Multifamily 36 .220 .640 .93 .98 33 50 89

Commercial 31 .941 2.19 .40 .67 26 58 90

Commercial1 10 .548 1.02 .69 .87 22 67 100

Tributary subbasin models

Laundry Brook 48 .030 .130 .90 .97 33 65 83

Faneuil Brook 48 .125 .602 .86 .97 31 69 96

Stony Brook 28 .070 .210 .90 .98 21 54 82
Precipitation-Runoff Model 33

Figure 13. Percent difference between simulated and observed storm-peak discharge and runoff volume for the single-family land-use 

subbasin, lower Charles River Watershed, Massachusetts, for 49 storms in the 2000 water year: (A) by month, and in relation to (B) 

precipitation volume, (C) precipitation intensity, and (D) antecedent precipitation. PERCENT DIFFERENCE BETWEEN SIMULATED AND OBSERVED DISCHARGE

D. Model error in relation to antecedent precipitation

-200

0

200

400

600

0 50 100 150 200 250 300 350 400

TIME, IN HOURS SINCE LAST 0.01 INCH OF PRECIPITATION

PEAK DISCHARGE

RUNOFF VOLUME

EXPLANATION

-200

0

200

400

600

0 0.2 0.4 0.6 0.8 1.0

MAXIMUM PRECIPITATION INTENSITY, IN INCHES PER HOUR

C. Model error in relation to maximum precipitation intensity

B. Model error in relation to precipitation volume

-200

0

200

400

600

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

PRECIPITATION VOLUME, IN INCHES

WATER YEAR

-200

200

600

400

0

A. Model error in relation to time

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.
34 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

The largest model errors can be attributed to several factors. The January 31, 2000, storm had the most 

oversimulated peak discharge (493 percent) and one of 

the larger oversimulated runoff volumes (134 percent). 

Cold weather prior to this storm may have affected the 

stage readings. The storm of April 26, 2000, produced 

the second highest simulated runoff-volume error 

(276 percent); this storm followed a wet period 

(3.54 in. of rainfall during the previous week), which 

suggests that there was less available storage in the soil 

then the calibrated model variables allowed. The July 

22, 2000, storm produced the highest simulation runoff 

volume error (502 percent); this storm had one of the 

highest maximum rainfall intensities and the second 

highest variability in total rainfall volume among the 

six gages. The June 27 storm had one of the largest 

negative errors in the both peak discharge and runoff 

volume; total rainfall volume during this storm measured at the six gages had the largest variability during 

the 2000 water year. The USGS-CR3 gage assigned to 

this subcatchment had the lowest total rainfall among 

the six gages. Analysis of model error indicates that 

much of the difference between simulated and 

observed discharges results from variation in rainfall; 

thus, further calibration would not appreciably improve 

the model simulations.

Some of the largest model errors, for both stormpeak discharge and runoff volume, were observed in 

storms with more than one pulse of rainfall resulting in 

multiple rises in the storm hydrograph with main peak 

discharge occurring during the later part of a storm. 

During these storms (March 28, May 10–11, June 6, 

and June 11–12) the second peak discharge was undersimulated, which also resulted in an undersimulation of 

storm volumes. SWMM resets the soil moisture deficit 

if there is a sufficient period without rainfall between 

peaks; thus, more moisture is allowed to infiltrate in 

pervious areas than would infiltrate if the soil moisture 

deficit were not reset. An option in SWMM to allow a 

maximum amount of infiltration during a storm likely 

would better represent runoff during these types of 

storms; however, this option currently is not available 

for a continuous simulation using the Green-Ampt 

infiltration option.

Multifamily Residential

Calibration Storms: Twenty-one storms from 

November 25, 1999, to January 11, 2000, and from 

March 27, 2000, to September 30, 2000, were used for 

model calibration; total precipitation during these 

storms ranged from 0.27 to 1.74 in. (mean 0.69 in.), 

which resulted in observed discharges that ranged from 

1.3 to 20 ft3/s (mean of 6.5 ft3/s) in peak discharge and 

0.142 to 1.46 in. (mean of 0.515 in.) in runoff volume. 

Storms of April 4 and April 8, 2000, were not used to 

calibrate or evaluate the model fit because the observed 

measurements were erratic. The simulated peak discharge had a SE of 2.0 ft3/s and a RMSE of 6.0 ft3/s 

(table 8); the difference between simulated and 

observed peaks ranged between -41 and 90 percent 

with a median difference of -0.6 percent and a standard 

deviation of 30 percent. Simulated peak discharges 

were within 10 percent of the observed peak 29 percent 

of the time, within 25 percent of the observed peak 62 

percent of the time, and within 50 percent of the 

observed peak 95 percent of the time. Simulated peak 

discharge generally is in good agreement with the 

observed peak for most calibration storms (fig. 14A).

The difference between the simulated and 

observed runoff volumes had a SE of 0.088 in. and a 

RMSE of 0.303 in. (table 8); the difference between 

simulated and observed volumes ranged between -33 

and 100 percent with a median difference of -1.2 percent and a standard deviation of 30 percent. Simulated 

runoff volumes were within 10 percent of the observed 

volume 43 percent of the time, within 25 percent of the 

observed volume 67 percent of the time, and within 50 

percent of the observed volume 95 percent of the time.

Simulated runoff volume is in good agreement with the 

observed volume for all calibrated storms (fig. 14A).

All Storms: Thirty-six storms were used to evaluate the overall model fit. Discharge data were unavailable prior to November 25, 1999, and from January 11, 

2000, to March 27, 2000. Storms on April 4 and April 

8, 2000, had erratic observed discharge and were not 

used in the evaluation of the model fit. Total rainfall 

during these storms ranged from 0.13 to 3.58 in. (mean 

0.75 in.) that resulted in observed discharges that 

ranged from 0.9 to 20 ft3/s (mean of 5.9 ft3/s) in peak 

discharge and 0.073 to 4.44 in. (mean of 0.619 in.) in 

runoff volume. The simulated peak discharge for all 

storms had a SE of 2.6 ft3/s and a RMSE of 10 ft3/s 

(table 8); the difference between simulated and 

observed peaks as a percent ranged between -68 and 

214 and with a median difference of 7.5 percent and a 

standard deviation of 47 percent. Simulated peak discharges were within 10 percent of the observed peak 25 

percent of the time, within 25 percent of the observed 

peak 58 percent of the time, and within 50 percent of 

the observed peak 86 percent of the time. Simulated 

peak discharge generally is in good agreement with the
Precipitation-Runoff Model 35

observed peak (fig. 14B), but there is more variability 

between simulated and observed peak discharges than 

in the calibration storms (fig. 14A).

The difference between the simulated and 

observed storm-runoff volumes had a SE of 0.22 in. 

and a RMSE of 0.64 in. (table 8); the difference 

between simulated and observed volumes ranged 

between -33 and 100 percent with a median difference 

of 2.8 percent and a standard deviation of 34 percent. 

Simulated storm-runoff volumes were within 10 percent of the observed volume 33 percent of the time, 

within 25 percent of the observed volume 50 percent of 

the time, and within 50 percent of the observed volume 

89 percent of the time. Simulated runoff volume 

closely matches the observed volume for most storms 

(fig. 14B).

Figure 14. Simulated and observed peak discharge and runoff volume at the multifamily land-use subbasin, lower Charles River Watershed, 

Massachusetts, for the 2000 water year: (A) calibration storms, and (B) all storms.

0

1

2

3

4

5

 0 1 2 3 4 5

June 6, 2000

0

5

10

15

20

25

0 5 10 15 20 25

0

0.5

1.0

1.5

0 0.5 1.0 1.5

0

5

10

15

20

25

30

0 5 10 15 20 25

OBSERVED PEAK DISCHARGE, 

IN CUBIC FEET PER SECOND

OBSERVED RUNOFF VOLUME, IN INCHES

SIMULATED PEAK DISCHARGE, IN CUBIC FEET PER SECOND

B. All storms 

A. Calibration storms

PEAK DISCHARGE RUNOFF VOLUME SIMULATED RUNOFF VOLUME, IN INCHES
36 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Error: Differences between peak discharge and 

runoff volume tended to be largest during the summer 

months (fig. 15A). Model error was not correlated with 

rainfall volume, intensity, and antecedent conditions 

(figs. 15B, C, and D) as measured by the Spearman 

rank test. 

Errors, in percent, typically were largest for 

small storms with rainfall volume less than 0.40 in. 

Most model error was attributed to rainfall variability 

across the watershed; for example, the storm of June 6 

(the largest outlier in runoff volume shown of fig. 14B) 

had a simulated volume of 3.26 in. and observed 

volume of 4.44 in., and varied by ± 0.5 in. at the six 

rain gages. In addition, the drainage area, which has a 

topographic drainage divide that differs from the storm 

drain drainage divide (appendix 1), could have been 

affected by the storm magnitude. During large or highintensity storms, such as the storm of June 6, runoff 

could follow topographic divides if storm drains that 

normally discharge out of the subbasin are blocked 

or are at capacity; thus, the drainage-area size could 

increase temporarily. The storm of January 31 had the 

largest oversimulated peak discharge (214 percent). 

Reported air temperatures at Logan Airport were below 

32°F for part of this day, which likely resulted in some 

rainfall falling as snow and, therefore, less moisture 

was available for runoff. 

Commercial

Rainfall-runoff (RR) relations at the commercial 

land-use subbasin varied widely, often yielding coefficients greater than one, which are not typical because it 

means that runoff exceeded the amount of rainfall. In a 

natural flow system, runoff rarely exceeds rainfall 

except in some situations where the ground-water 

drainage area is appreciably larger than the surfacewater drainage area. Other explanations for the high 

RR coefficients include discharge or rainfall measurement error, or both, external sources of water that drain 

to the storm-sewer system, a variable drainage area not 

strictly defined by the subsurface drainage system, or a 

combination of these factors. In a highly urbanized 

area, such as this subbasin, external sources of water 

such as leakage or cross connections from the sanitarysewer system often are an additional source of water in 

storm drains. The topographic drainage area is about 50 

percent larger (drainage area increases from 0.023 to 

0.034 mi2) than the drainage area delineated from the 

storm drainage system (appendix 1). During large or 

high-intensity storms, drains that normally flow out of 

the subbasin could become blocked or at capacity; thus, 

runoff would follow the topographic drainage divides, 

which could cause the wide variation in RR coefficients. For this reason, the commercial land-use subbasin model was calibrated with preference given to 

storms with RR coefficients less than 1.0. Model-fit 

statistics are reported for all available storms regardless 

of the RR coefficient, but the effect of storms with high 

RR coefficients on the model fit are also discussed. 

Observed discharge is suspect for most storms 

during late May through June 2000 because the 

hydrograph recession is uncharacteristically gradual for 

a highly impervious small subbasin; simulated runoff 

volumes averaged 39 percent less than the observed 

runoff volume for storms during this period. Observed 

storm hydrographs during other periods of the year 

indicated a return to base-flow conditions within about 

an hour following the storm peak, which is expected 

for this type of subbasin. Furthermore, at the commercial land-use site, a nearly constant base flow of 0.2 

ft3/s was observed, which also is unlikely given the 

high percentage of effective impervious area and the 

small drainage area (0.023 mi2) This base flow may 

result because of presently unidentified discharges to 

storm drains upgradient of the gage site. 

Calibration Storms: Thirteen storms from late 

April to September 2000 were used for model calibration; total rainfall during these storms ranged from 0.31 

to 1.74 in. (mean 0.74 in.), which resulted in observed 

discharges that ranged from 1.7 to 18 ft3/s (mean of 

6.6 ft3/s) in peak discharge and from 0.475 to 1.90 in. 

(mean of 0.908 in.) in runoff volume. The simulated 

calibration storm peaks had a SE of 2.0 ft3/s and a 

RMSE of 5.1 ft3/s (table 8); the difference between 

simulated and observed peaks ranged between -39 and 

70 percent with a median difference of 2.0 percent and 

a standard deviation of 35 percent. Simulated peak discharges were within 10 percent of the observed peak 23 

percent of the time, within 25 percent of the observed 

peak 46 percent of the time, and within 50 percent of 

the observed peak 85 percent of the time. Simulated 

peak discharge generally is in good agreement with the 

observed peak discharge for most storms (fig. 16A). 
Precipitation-Runoff Model 37

Figure 15. Percent difference between simulated and observed storm-peak discharge and runoff volume for the multifamily land-use subbasin, 

lower Charles River Watershed, Massachusetts, for 36 storms in the 2000 water year: (A) by month, and in relation to (B) precipitation volume, 

(C) precipitation intensity, and (D) antecedent precipitation. PERCENT DIFFERENCE BETWEEN SIMULATED AND OBSERVED DISCHARGE

-200

0

200

400

600

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

B. Model error in relation to precipitation volume

PRECIPITATION VOLUME, IN INCHES

-200

0

200

400

600

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

A. Model error in relation to time

-200

200

400

600

0 0.2 0.4 0.6 0.8 1.0

0

C. Model error in relation to maximum precipitation intensity

MAXIMUM PRECIPITATION INTENSITY, IN INCHES PER HOUR

TIME IN HOURS SINCE LAST 0.01 INCHES OF PRECIPITATION

-200

0

200

400

600

0 50 100 150 200 250 300 350 400

D. Model error in relation to antecedent precipitation

PEAK DISCHARGE

RUNOFF VOLUME

EXPLANATION
38 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

The difference between the simulated and 

observed runoff volumes had a SE of 0.407 in. and a 

RMSE of 0.794 in. (table 8); the difference between 

simulated and observed volumes ranged between -61 

and 21 percent with a median difference of -11 percent 

and a standard deviation of 22 percent. Simulated 

runoff volumes were within 10 percent of the observed 

volume 31 percent of the time, within 25 percent of the 

observed volume 69 percent of the time, and within 50 

percent of the observed volume 92 percent of the time. 

Calibration runoff volumes with RR coefficients 

greater than 1.3 accounted for three of the four storms 

with poorly fit runoff volumes (fig. 16A).

All Storms: Thirty-one storms between February and September 2000 were used to evaluate the 

overall model fit; total rainfall during these storms 

Figure 16. Simulated and observed peak discharge and runoff volume at the commercial land-use subbasin, lower Charles River Watershed, 

Massachusetts, for the 2000 water year; (A) calibration storms, and (B) all storms. SIMULATED PEAK DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED RUNOFF VOLUME, IN INCHES OBSERVED PEAK FLOW,

IN CUBIC FEET PER SECOND

PEAK DISCHARGE RUNOFF VOLUME

A. Calibration storms

B. All storms 

0

5

10

15

20

0 5 10 15 20

0

0.5

1.0

1.5

2.0

0 0.5 1.0 1.5 2.0

Equal to or less than 1.299

Greater than 1.3

RAINFALL-RUNOFF COEFFICIENTS

0

4

8

12

16

20

0 4 8 12 16 20

Less than 0.999

1.0 to 1.299

1.3 to 1.999

Greater than 2

RAINFALL-RUNOFF COEFFICIENTS

SIMULATED RUNOFF VOLUME, IN INCHES

0 2 4 68

0

2

4

6

8
Precipitation-Runoff Model 39

ranged from 0.13 to 3.58 in. (mean of 0.80 in.), which 

resulted in observed discharges that ranged from 1.5 to 

18 ft3/s (mean of 6.4 ft3/s) in peak discharge and 0.392 

to 6.93 in. (mean of 1.17 in.) in runoff volume. The 

simulated peak discharge had a SE of 3.0 ft3/s and a 

RMSE of 10 ft3/s (table 8); the difference between simulated and observed peak discharge ranged between -

58 and 184 percent with a median difference of -4.6 

percent and a standard deviation of 47 percent. Simulated peak discharges were within 10 percent of the 

observed peak 26 percent of the time, within 25 percent 

of the observed peak 52 percent of the time, and within 

50 percent of the observed peak 77 percent of the time. 

The scatter plot generally indicates a good agreement 

between the simulated and observed peak discharge 

(fig. 16B).

The difference between the simulated and 

observed runoff volumes had a SE of 0.941 in. and a 

RMSE of 2.19 in. (table 8); the difference between simulated and observed volumes ranged from -66 and 33 

percent with a median difference of -13 percent and a 

standard deviation of 25 percent. Simulated runoff volumes were within 10 percent of the observed volume 

26 percent of the time, within 25 percent of the 

observed volume 58 percent of the time, and within 50 

percent of the observed volume 90 percent of the time. 

Simulated and observed runoff volumes were in good 

agreement for storms with RR coefficients less than 1.3 

(fig. 16B).

Error: Of the 31 possible storms, only 10 storms 

had RR coefficients less than 1.3, which were used to 

reevaluate the model fit. These storms ranged in rainfall volume from 0.59 to 3.20 in. (mean of 1.31 in.), 

which resulted in discharges that ranged from 3.6 to 8.2 

ft3/s (mean of 6.2 ft3/s) in peak discharge and from 

0.519 to 2.88 in. (mean of 1.33 in.) in runoff volume. 

The differences between the simulated and 

observed storm peak discharge for the subset of storms 

declined slightly in comparison to all storms. The simulated peak discharge for the subset of storms had a SE 

of 2.50 ft3/s and a RMSE of 4.75 ft3/s (table 8); the difference between simulated and observed volumes 

ranged between -21 and 62 percent with a median difference of -0.89 percent and a standard deviation of 30 

percent. Simulated peak discharges were within 10 percent of the observed peak 22 percent of the time, within 

25 percent of the observed peak 67 percent of the time, 

and within 50 percent of the observed peak 78 percent 

of the time.

The difference between the simulated and 

observed runoff volumes for the subset of storms substantially improved in comparison to all storms. The 

simulated runoff volume had SE of 0.548 in., and a 

RMSE of 1.021 in., which was about half the absolute 

error for all storms; the difference between simulated 

and observed runoff volumes ranged between -33 and 

33 percent with a median difference of 0.36 percent 

and a standard deviation of 22 percent. Simulated 

runoff volumes were within 10 percent of the observed 

volume 22 percent of the time, within 20 percent of the 

observed volume 67 percent of the time, and within 50 

percent of the observed volume 100 percent of the 

time. 

Differences between simulated and observed 

peak discharges were about equally scattered from February to September (fig. 17A); however, runoff volumes 

tended to be undersimulated in May and June when RR 

coefficients tended to be high. Model error was not correlated with rainfall volume, intensity, and antecedent 

conditions (figs. 17B, C, and D) as measured by the 

Spearman rank test. Model error is largely attributed to 

uncertainty in the observed discharge, or one or more 

of the other factors that could cause large RR coefficients.

Tributary Subbasin Models

The model fit is described for the tributary subbasin models at Laundry Brook and Faneuil Brook 

developed by the USGS and the Stony Brook model 

developed by others. The Muddy River portion of the 

Stony Brook model was not evaluated for model fit 

because of the high degree of uncertainty in the 

observed discharge data. 

Laundry Brook

The model fit at this site can be affected by the 

dynamic regulation of Bulloughs Pond. Bulloughs 

Pond has a surface area of 4.7 acres and an estimated 

storage volume of 0.5 to 0.75 million ft3. At times, 

measured discharge at the Laundry Brook gaging station was sustained and elevated prior to storms, possibly because water was being released from Bulloughs 

Pond. SWMM does not account for dynamic regulation 

of storage, thus, the model fit can be affected when the 

pond level is lowered in anticipation of a storm. Storms 

that are affected by regulation are noted, and the effect 

of this regulation on the model fit is described.
40 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 17. Percent difference between simulated and observed storm-peak discharge and runoff volume for the commercial land-use subbasin, 

lower Charles River Watershed, Massachusetts, for 31 storms in the 2000 water year: (A) by month, and in relation to (B) precipitation volume, 

(C) precipitation intensity, and (D) antecedent precipitation.

PER

CENT DIFFEREN

CE BETWEEN 

SIM

ULATED AND 

OBSERVED DISCHAR

GE

PEAK DISCHARGE

RUNOFF VOLUME

EXPLANATION

-200

-150

-100

-50

0

50

100

150

200

A. Model error in relation to time

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

0 0.1 0.2 0.3 0.4 0.5 -200

-150

-100

-50

0

50

100

200

150

MAXIMUM PRECPITATION INTENSITY, IN INCH PER HOUR

C. Model error in relation to maximum precipitation intensity

-200

-150

-100

-50

0

50

100

150

200

0 1.0 2.0 3.0 4.0

B.

PRECIPITATION VOLUME, IN INCHES

-200

-150

-100

-50

0

50

100

150

200

0 50 100 150 200 250 300 350

D. Model error in relation to antecedent precipitation
Precipitation-Runoff Model 41

Calibration Storms: Twenty-four storms were 

used for model calibration; total rainfall during these 

storms ranged from 0.35 to 1.83 in. (mean 0.76 in.), 

which resulted in observed discharges that ranged from 

10.9 to 100.8 ft3/s (mean of 41.7 ft3/s) in peak discharge and 0.028 to 0.231 in. (mean of 0.083 in.) in 

runoff volume. The simulated peak discharge had a SE 

of 15.2 ft3/s and a RMSE of 47.5 ft3/s (table 8); the difference between simulated and observed peak discharges ranged between –38 and 103 percent with a 

median difference of 14.6 percent and a standard deviation of 29 percent. Simulated peak discharges were 

within 10 percent of the observed peak 29 percent of 

the time, within 25 percent of the observed peak 58 

percent of the time, and within 50 percent of the 

observed peak 92 percent of the time. Simulated and 

observed peak discharges are generally in good agreement; the largest peaks were affected by regulation of 

Bulloughs Pond (fig. 18A). 

Figure 18. Simulated and observed discharge and runoff volume at the Laundry Brook Subbasin, lower Charles River Watershed, Massachusetts, for 

the 2000 water year: (A) calibration storms, and (B) all storms. SIMULATED PEAK DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED PEAK DISCHARGE, OBSERVED RUNOFF VOLUME, IN INCHES

IN CUBIC FEET PER SECOND

PEAK DISCHARGE RUNOFF VOLUME

A. Calibration storms

B. All storms 

SIMULATED RUNOFF VOLUME, IN INCHES

0

0.25

0.50

0.75

0 0.25 0.50 0.75

0

50

100

150

200

 0 50 100 150 200

Storms affected

by Bulloughs

Pond regulation

 0

 0.05

 0.10

 0.15

 0.20

 0.25

 0 0.05 0.10 0.15 0.20 0.25

 0

 50

 100

 150

 0 50 100 150

Storm affected

by Bulloughs

Pond regulation
42 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

The difference between the simulated and 

observed storm runoff volume had a SE of 0.016 in. 

and a RMSE of 0.061 in. (table 8); the difference 

between simulated and observed volumes ranged from 

–33 to 81 percent, with a median difference of 1.0 percent and a standard deviation of 30 percent. Simulated 

runoff volumes were within 10 percent of the observed 

volume 46 percent of the time, within 25 percent of the 

observed volume 67 percent of the time, and within 50 

percent of the observed volume 87 percent of the time. 

Simulated runoff volume is generally in good agreement with the observed volume for most storms 

(fig. 18A).

All Storms: Forty-eight storms were used to 

evaluate the overall model fit; total rainfall during these 

storms ranged from 0.10 to 3.64 in. (mean 0.73 in.), 

which resulted in observed discharges that ranged from 

3.3 to 153 ft3/s (mean of 53.7 ft3/s) in peak discharge 

and 0.012 to 0.437 in. (mean of 0.081 in.) in runoff volume. The simulated peak discharge had a SE of 

21.9 ft3/s and a RMSE of 85.1 ft3/s (table 8); the difference between simulated and observed peaks ranged 

from –54 to 287 percent with a median difference of 11 

percent and a standard deviation of 56 percent. Simulated peak discharges were within 10 percent of the 

observed peak 21 percent of the time, within 25 percent 

of the observed peak 60 percent of the time, and within 

50 percent of the observed peak 81 percent of the time. 

Simulated peak discharge generally is in good agreement with the observed peak, but several peaks were 

oversimulated as a result of regulation of Bulloughs 

Pond (fig. 18B).

The difference between the simulated and 

observed runoff volumes had a SE of 0.030 in. and a 

RMSE of 0.130 in. (table 8); the difference between 

simulated and observed volumes ranged from -61 to 

181 percent, with a median difference of -0.9 percent 

and a standard deviation of 44 percent. Simulated 

storm volumes were within 10 percent of the observed 

volume 33 percent of the time, within 25 percent of the 

observed volume 65 percent of the time, and within 

50 percent of the observed volume 83 percent of the 

time. Simulated runoff volume is generally in good 

agreement with the observed storm volume (fig. 18).

Error: Model performance as a function of time 

of year, rainfall volume, intensity, and antecedent conditions did not indicate systematic bias in the simulation results (fig. 19). The Spearman rank test indicates 

that the model error is not correlated with rainfall 

characteristics or antecedent conditions. 

The dates when storms discharge appeared to be 

affected by regulation of Bulloughs Pond include the 

March 16–17, April 21–26, July 18–19, July 22 and 

26–28, and September 15–16, 2000. The available storage in the pond will affect storm-peak discharges more 

than it effects storm-runoff volume if the water drained 

from the pond is included in the runoff volume. For 

example, if water drained from the pond immediately 

prior to a storm is included in the total storm volume, 

the stormwater remaining in the pond at the end of a 

storm is about equivalent to what was drained; thus, the 

total storm volume is unchanged. Conversely, storm 

volume would appear to be oversimulated by the 

volume of water drained from storage if this volume is 

not included in the measured runoff volume of the 

storm. The measured peak discharge is likely always 

affected when the pond is lowered prior to a storm to 

allow stormwater to be retained in storage.

Rainfall variability affected the model fit during 

the July 22 storm, which had one of the largest oversimulated peak discharges (110 percent) and the largest 

oversimulated runoff volume (181 percent). Measured 

rainfall at the USGS-CR3 was 0.97 in., but rainfall 

measured at other gages varied from 0.12 to 1.32 in. 

Mixed precipitation as rain and snow can also affect the 

model fit, which may have caused the January 31 storm 

to have the largest oversimulated peak discharge (287 

percent). 

Faneuil Brook

The model fit at this site was assessed with discharge data computed from stage-velocity measurements and by a stage-discharge relation during periods 

with erratic or suspect velocity measurements, as 

explained previously. If the stage-velocity discharge 

appeared erroneously low, the computed discharge 

determined by the stage-discharge relation was used 

to evaluate the model fit. The reported model-fit 

statistics do not include the storm of June 6, with a 

total rainfall of more than 4 in.; the measured volume 

of runoff during this storm (regardless of the discharge 

method used) was comparable to runoff for storms 

that ranged between 0.7 and 1.6 in. of rainfall. Therefore, this storm was excluded from the model fitstatistics because it exerted a large effect on them, 

and the volume and peak discharge appear to be 

undermeasured.
Precipitation-Runoff Model 43

Figure 19. Percent difference between simulated and observed storm-peak discharge and runoff volume for the Laundry Brook Subbasin, 

lower Charles River Watershed, Massachusetts, for 48 storms in the 2000 water year: (A) by month, and in relation to (B) precipitation volume, 

(C) precipitation intensity, and (D) antecedent precipitation. PERCENT DIFFERENCE BETWEEN SIMULATED AND OBSERVED DISCHARGE

A. Model error in relation to time

B. Model error in relation to precipitation volume

PRECIPITATION VOLUME, IN INCHES

D. Model error in relation to antecedent precipitation

TIME IN HOURS SINCE LAST 0.01 INCH OF PRECIPITATION

PEAK DISCHARGE

RUNOFF VOLUME

EXPLANATION

C. Model error in relation to maximum precipitation intensity

MAXIMUM PRECIPITATION INTENSITY, IN INCHES PER HOUR

-200

0

200

400

600

0 50 100 150 200 250 300 350 400

-200

0

200

400

600

0 0.2 0.4 0.6 0.8 1.0

-200

0

200

400

600

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

-200

0

200

400

600

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.
44 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Calibration Storms: Twenty-one storms were 

used for model calibration with total rainfall ranging 

from 0.27 to 2.10 in. (mean 0.67 in.), which resulted in 

discharges that ranged from 6.5 to 39 ft3/s (mean of 

19 ft3/s) in peak discharge and from 0.047 to 0.207 in. 

(mean of 0.091 in.) in runoff volume. The simulated 

storm peaks had a SE of 8.9 ft3/s and a RMSE of 

27 ft3/s (table 8); the difference between simulated and 

observed peaks ranged between –33 and 89 percent 

with a median difference of 5 percent and a standard 

deviation of 22 percent. Simulated peak discharges 

were within 10 percent of the observed peak 25 percent 

of the time, within 25 percent of the observed peak 

50 percent of the time, and within 50 percent of the 

observed peak 80 percent of the time. The simulated 

peak discharge is generally in good agreement with the 

observed when peaks are less than 20 ft3/s, but peaks 

above 20 ft3/s tended to be more variable (fig. 20A).

Figure 20. Simulated and observed peak discharge and runoff volume at Faneuil Brook Subbasin, lower Charles River Watershed, Massachusetts, 

for the 2000 water year: (A) calibration storms, and (B) all storms.

0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

0

20

40

60

80

100

0 20 40 60 80 100

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4

SIMULATED PEAK DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED PEAK DISCHARGE, OBSERVED RUNOFF VOLUME, IN INCHES

IN CUBIC FEET PER SECOND

PEAK DISCHARGE RUNOFF VOLUME

A. Calibration storms

B. All storms 

SIMULATED RUNOFF VOLUME, IN INCHES

0 10 20 30 40 50 60

0

10

20

30

40

50

60

July 18, 2000

April, 2000
Precipitation-Runoff Model 45

The difference between the simulated and 

observed runoff volumes had a SE of 0.029 in. and a 

RMSE of 0.094 in. (table 8); the difference between 

simulated and observed storm volumes ranged between 

-21 and 64 percent with a median difference of 4 percent and a standard deviation of 14 percent. Simulated 

storm volumes were within 10 percent of the observed 

volume 40 percent of the time, within 25 percent of the 

observed volume 75 percent of the time, and within 50 

percent of the observed volume 95 percent of the time. 

Simulated runoff volume in relation to the observed 

volume indicates that the model fit did not vary with 

the size of the storm (fig. 20A).

All Storms: Forty-eight storms were used to 

evaluate the overall model fit; total rainfall during these 

storms ranged from 0.10 to 3.39 in. (mean 0.69 in.), 

which resulted in observed discharges that ranged from 

2.8 to 49 ft3/s (mean of 20 ft3/s) in peak discharge and 

0.040 to 0.566 in. (mean of 0.102 in.) in runoff volume. 

The simulated peak discharge had a SE of 15 ft3/s and a 

RMSE of 64 ft3/s (table 8); the difference between simulated and observed peak discharges ranged between –

61 and 314 percent with a median difference of 11 percent and a standard deviation of 73 percent. Simulated 

peak discharges were within 10 percent of the observed 

peak 19 percent of the time, within 25 percent of the 

observed peak 44 percent of the time, and within 50 

percent of the observed peak 65 percent of the time. 

Simulated peaks varied considerably from the observed 

peaks, but, in general, the model fit did not vary with 

the peak discharge size (fig. 20B).

The difference between the simulated and 

observed runoff volumes had a SE of 0.125 in. and a 

RMSE of 0.602 in. (table 8); the difference between 

simulated and observed volumes ranged between -42 

and 65 percent with a median difference of -3 percent 

and a standard deviation of 24 percent. Simulated 

runoff volumes were within 10 percent of the observed 

volume 31 percent of the time, within 25 percent of the 

observed volume 69 percent of the time, and within 50 

percent of the observed volume 96 percent of the time. 

Simulated runoff volume is generally in good agreement with the observed volume for most storms 

(fig. 20B).

Error: The June and July storms tended to have 

larger error than the storms during other times of the 

year (fig. 21A); the storms during this period also 

tended to have the greatest spatial rainfall variability. 

Model error was not correlated with rainfall volumes, 

intensity, and antecedent conditions (figs. 21B, C, and 

D), except for a weak correlation (31 percent of the 

model error is explained) with rainfall intensity as measured by the Spearman rank test. 

Storms of April 22 and the July 18 had the largest differences between simulated and observed peak 

discharge. The April 22 storm had the second largest 

rainfall volume (3.4 in.) and the July 18 storm had the 

highest rainfall intensity (0.55 in/h) recorded during the 

2000 water year. Upstream surcharging of the drainage 

system could be a factor in limiting the observed peak 

discharge during these storms.

Stony Brook

The Stony Brook model has undergone several 

transformations. The model fit described is for the version of the model that was supplied by M&E consultants (Lawrence Soucie, Metcalf and Eddy, Inc., 

personal commun., February 28, 2001) who have made 

the most recent revisions to the model. The modelconduit number that corresponds to the gaging station 

is 3544.

Calibration Storms: Seventeen storms were 

used for model calibration; total precipitation during 

these storms ranged from 0.35 to 1.83 in. (mean 

0.76 in.), which resulted in observed discharges that 

ranged from 16 to 350 ft3/s (mean of 126 ft3/s) in peak 

discharge and 0.058 to 0.207 in. (mean of 0.118 in.) in 

runoff volume. The simulated peak discharge had a SE 

of 41 ft3/s and a RMSE of 120 ft3/s (table 8); the difference between simulated and observed peaks ranged 

between -72 and 100 percent with a median difference 

of -22 percent and a standard deviation of 44 percent. 

Simulated peak discharges were within 10 percent of 

the observed peak 18 percent of the time, within 25 

percent of the observed peak 47 percent of the time, 

and within 50 percent of the observed peak 71 percent 

of the time. The simulated peak discharge is not 

affected by the peak discharge (fig. 22A).

The difference between the simulated and 

observed runoff volumes had a SE of 0.048 in. and a 

RMSE of 0.139 in. (table 8); the difference between 

simulated and observed volumes ranged between -58 

and 81percent with a median difference of 5.3 percent

and a standard deviation of 35 percent. Simulated 

runoff volumes were within 10 percent of the observed 

volume 29 percent of the time, within 25 percent of the 

observed volume 53 percent of the time, and within 50 

percent of the observed peak 76 percent of the time. 

Simulated runoff volume tends to agree less with 

observed runoff volume than simulated with observed 

peak discharge (fig. 22A). 
46 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 21. Percent difference between simulated and observed storm-peak discharge and runoff volume for the Faneuil Brook Subbasin, lower

Charles River Watershed, Massachusetts, for 48 storms in the 2000 water year: (A) by month, and in relation to (B) precipitation volume, (C) 

precipitation intensity, and (D) antecedent precipitation.

D.

TIME IN HOURS SINCE LAST 0.01 INCH OF PRECIPITATION

PEAK DISCHARGE

RUNOFF VOLUME

EXPLANATION

0 100 200 300 400 500 600

-100

-50

0

50

100

150

200

250

300

350

0 0.1 0.2 0.3 0.4 0.5 0.6

-100

-50

0

50

100

150

200

250

300

350

MAXIMUM PRECIPITATION INTENSITY, IN INCHES PER HOUR

C. Model error in relation to maximum precipitation intensity

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

-100

-50

0

50

100

150

200

250

300

350

B.

PRECIPITATION VOLUME, IN INCHES

-100

-50

0

50

100

150

200

250

300

350

PER

CENT DIFFEREN

CE BETWEEN 

SIM

ULATED AND 

O

B

SERVED DISCHAR

G

E

A. Model error in relation to time

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.
Precipitation-Runoff Model 47

All Storms: Twenty-eight storms were used to 

evaluate the overall model fit; discharge data were not 

available prior to April 1, 2000. The April 21 storm 

was not used to assess the model fit because of a meter 

malfunction. Total precipitation during these storms 

ranged from 0.10 to 4.75 in. (mean 0.87 in.), which 

resulted in observed discharges that ranged from 16 to 

860 ft3/s (mean of 120 ft3/s) in peak discharge and 

0.048 to 1.24 in. (mean of 0.156 in.) in runoff volume. 

The simulated peak discharge had a SE of 80 ft3/s and a 

RMSE of 260 ft3/s (table 8); the difference between 

simulated and observed peaks ranged between -72 and 

430 percent with a median difference of -20 percent

and a standard deviation of 93 percent. Simulated peak 

Figure 22. Simulated and observed peak discharge and runoff volume at Stony Brook Subbasin, lower Charles River Watershed, Massachusetts, for 

the 2000 water year: (A) calibration storms, and (B) all storms. SIMULATED PEAK DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED PEAK DISCHARGE, OBSERVED RUNOFF VOLUME, IN INCHES

IN CUBIC FEET PER SECOND

PEAK DISCHARGE RUNOFF VOLUME

A. Calibration storms

B. All storms 

SIMULATED RUNOFF VOLUME, IN INCHES

 0

 0.05

 0.10

 0.15

 0.20

 0.25

0 0.05 0.10 0.15 0.20 0.25

 0

 400

 800

 1,200

 0 400 800 1,200

 0

 0.05

 0.10

 0.15

 0.20

 0.25

 0 0.05 0.10 0.15 0.20 0.25

 0

 100

 200

 300

 400

 0 100 200 300 400
48 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

discharges were within 10 percent of the observed peak 

14 percent of the time, within 25 percent of the 

observed peak 43 percent of the time, and within 50 

percent of the observed peak 79 percent of the time. 

Simulated peak discharge is in good agreement with 

the observed peak for most storms, except for the two 

largest, which are oversimulated (fig. 22B).

The difference between the simulated and 

observed runoff volume had a SE of 0.070 in. and a 

RMSE of 0.210 in. (table 8); the difference between 

simulated and observed volumes ranged between 

–58 and 117 percent with a median difference of 18 

percent and a standard deviation of 37 percent. Simulated runoff volumes were within 10 percent of the 

observed volume 21 percent of the time, within 25 

percent of the observed volume 54 percent of the time, 

and within 50 percent of the observed volume 82 percent of the time. Simulated runoff volume is generally 

in good agreement with observed runoff volume, but 

simulated and observed volumes tend to agree less well 

than simulated and observed peak discharges 

(fig. 22B).

Error: Plots of model error in relation to 

time of year, precipitation volume, intensity, and antecedent conditions did not indicate any systematic bias 

(fig. 23). The storm of July 22 had the largest oversimulated peak discharge (434 percent) and the largest 

oversimulated runoff volume (117 percent). The model 

error for this storm is largely attributed to areal variation in precipitation that ranged from 0.12 to 1.32 in. 

at the six rain gages.

In general, the Stony Brook model fit is comparable to that of the other models developed for the 

lower Charles River by the USGS. The Stony Brook 

model was developed primarily to assist in design of 

sewer-separation projects; therefore, development of 

the model focused on peak-discharge calibration. The 

models developed by the USGS are intended to calculate stormwater runoff for calculating constituent loads, 

and, thus, design and calibration of these models 

focused primarily on stormwater volume. For this reason, the USGS models tend to fit stormwater volumes 

slightly better than the Stony Brook model does, and, 

conversely, the Stony Brook model tends to fit storm 

peak discharges slightly better than the USGS models.

Relative Model Fit

The relative model fit of the models developed 

for the lower Charles River are quantified by the index 

of agreement and the coefficient of efficiency. Values 

of relative model fit can range from 0 to 1.0 for the 

index of agreement and from minus infinity to 1.0, for 

the coefficient of efficiency. Coefficient of efficiency 

values less than zero indicate that the observed mean 

provides a better predictor than the model; values 

greater than zero indicate that the model is a better predictor than the observed mean. Interpretation of the 

value of the index of agreement is similar to the coefficient of determination (R2) in a regression equation—

the closer the R2 value is to 1.0, the better the agreement between simulated and observed values. Unlike 

the coefficient of determination, the index of agreement 

does not provide a measure of the total variance 

explained by the model. Both relative measures of 

model fit are sensitive to extreme values. The relative 

model fit for storm peak discharge and runoff volume 

calculated by the index of agreement and the coefficient of efficiency for each of the models is shown in 

figure 24. James and Burgess (1982) report that an 

excellent calibration is obtained if the coefficient of 

efficiency exceeds 0.97.

Peak discharge: The index of agreement for calibration storms ranged from 0.87 to 0.96 and averaged 

0.93; the coefficient of efficiency ranged from 0.35 to 

0.84 and averaged 0.71. The index of agreement for all 

storms ranged from 0.72 to 0.97 and averaged 0.86; the 

coefficient of efficiency ranged between -0.33 and 

0.84 and averaged 0.43 (table 8). The coefficient 

of efficiency at the Faneuil Brook site indicates that 

the model is in less agreement with the observations 

than the mean value for peak discharge. Possible explanations for the relatively poor peak discharge simulation at Faneuil Brook are: (1) the storage-discharge 

characteristics of Chandler Pond are not well defined, 

(2) Chandler Pond is dynamically regulated, and 

(3) surcharging in the storm-drain system could cause 

an oversimulated peak discharge. In general, the relative model fit for peak discharge was better for calibration storms than for all storms because the precipitation 

variability was less in the calibration storms than in the 

other storms. 
Precipitation-Runoff Model 49

Figure 23. Percent difference between simulated and observed storm-peak discharge and runoff volume for the Stony Brook Subbasin, lower 

Charles River Watershed, Massachusetts, for 28 storms in the 2000 water year: (A) by month, and in relation to (B) precipitation volume, (C) 

precipitation intensity, and (D) antecedent precipitation. PERCENT DIFFERENCE BETWEEN SIMULATED AND OBSERVED DISCHARGE

PEAK DISCHARGE

RUNOFF VOLUME

EXPLANATION

-200

0

200

400

600

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

B. Model error in relation to precipitation volume

PRECIPITATION VOLUME, IN INCHES

-200

0

200

400

600 A. Model error in relation to time

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

-200

0

200

400

600

0 0.2 0.4 0.6 0.8 1.0

C. Model error in relation to precipitation intensity

MAXIMUM PRECIPITATION INTENSITY, IN INCHES PER HOUR

 -200

 0

 200

 400

 600

0 50 100 150 200 250 300 350 400

D. Model error in relation to antecedent precipitation

TIME IN HOURS SINCE LAST 0.01 INCH OF PRECIPITATION
50 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Runoff Volume: The index of agreement for calibration storms ranged from 0.27 to 0.98 and averaged 

0.80; the coefficient of efficiency ranged from 0.32 to 

0.94 and averaged 0.71. The index of agreement for all 

storms ranged from 0.67 to 0.98 and averaged 0.92; the 

coefficient of efficiency ranged between 0.40 and 0.93 

and averaged 0.80 (table 8). The index of agreement 

and the coefficient of efficiency were relatively low at 

the commercial land-use subbasin for reasons previously described. The relative model fit improved substantially for runoff volume at the commercial land-use 

subbasin for storms with rainfall-runoff coefficients 

less than 1.2. In general, the values for the coefficient 

of efficiency indicated a model fit that was good to 

excellent for all storms, and the values for the index of 

agreement indicated a model fit that was excellent for 

most sites for all storms. 

Figure 24. Relative measures of model fit calculated by the index of agreement and coefficient of efficiency at three land-use and three tributary 

subbasin models in the lower Charles River Watershed, Massachusetts, for the (A) peak discharge and (B) runoff volumes. COEFFICIENT OF EFFICIENCY, UNITLESS

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0

INDEX OF AGREEMENT,

UNITLESS

B. RUNOFF VOLUME

0

0.2

0.4

0.6

0.8

1.0

Laundry

Brook

Faneuil

Brook

Stony

Laundry

Brook

Brook

Faneuil

Brook

Stony

Brook

Single family

Multifamily

Commercial

Land-use

Subbasin

Tributary

Subbasins

A. PEAK DISCHARGE

0

0.2

0.4

0.6

0.8

1.0

CALIBRATION STORMS

ALL STORMS

SELECTED STORMS WITH RAINFALL-RUNOFF 

COEFFICIENTS LESS THAN 1.2

EXPLANATION

Single family

Multifamily

Commercial

Land-use

Subbasin

Tributary

Subbasins
Precipitation-Runoff Model 51

Design Storms

The model fit for the design storms was evaluated as a surrogate measure by the collective model fit 

at the three tributary subbasin models, Laundry Brook, 

Faneuil Brook, and Stony Brook, for measured storms 

with precipitation volumes roughly equivalent to the 

MWRA 3-month and 1-year design storms. Collectively, these three tributary models represent 49 percent 

of the total drainage area to the lower Charles River 

below Watertown Dam. 

Three storms with measured discharge and total 

precipitation within ± 20 percent of the 3-month and 1-

year design storms (1.84 and 2.79 in., respectively) 

were available. Storms with precipitation volumes 

roughly equivalent to the 3-month storm occurred on 

March 12, and July 27, 2000, with precipitation totals 

of 1.56 and 2.10 in., respectively, at BWSC-CS4 gage 

(fig. 10). Only one storm, April 22, 2000, had a total 

precipitation volume roughly equivalent to the 1-year 

storm—3.39 in. measured at BWSC-CS4 gage. 

Measured discharge was not available for the March 12 

and April 22 storms at the Stony Brook, thus, a 

combined total of seven storms were used in this 

analysis. 

The simulated storm peak discharges had a SE of 

27 ft3/s and a RMSE of 41 ft3/s; the difference between 

simulated and observed peaks ranged between -15 and 

107 percent with a median difference of 0.2 percent 

and a standard deviation of 46 percent. Simulated peak 

discharges were within 10 percent of the observed peak 

43 percent of the time, within 25 percent of the 

observed peak 71 percent of the time. Simulated peak 

discharge (fig. 25A) is generally in good agreement 

with observed peak discharge, except for one storm that 

was oversimulated (April 22 storm at Faneuil Brook). 

The difference between the simulated and 

observed runoff volumes had a SE of 0.061 in. and a 

RMSE of 0.110 in.; the difference between simulated 

and observed volumes ranged between -13 and 30 percent with a median difference of 5 percent and a standard deviation of 17 percent. Simulated runoff volumes 

were within 10 percent of the observed volume 29 percent of the time, within 25 percent of the observed 

volume 71 percent of the time, and within 50 percent of 

the observed volume 100 percent of the time. Simulated runoff volume agrees well with observed runoff 

volume (fig. 25B).

Figure 25. Simulated and observed (A) peak discharge and (B) runoff volume at Laundry Brook, Faneuil Brook, and Stony Brook, lower Charles River 

Watershed, Massachusetts, for 2000 water-year storms with total precipitation within 20 percent of the 3-month and 1-year design-storm 

precipitation volume. SIMULATED PEAK DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED PEAK DISCHARGE, IN CUBIC FEET PER SECOND OBSERVED RUNOFF VOLUME, IN INCHES

A. Peak Discharge B. Runoff Volume SIMULATED TOTAL DISCHARGE, IN INCHES

3-MONTH EQUIVALENT

1-YEAR EQUIVALENT

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

50

100

150

200

250

300

0 50 100 150 200 250 300
52 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Model-fit statistics and scatter plots for storms 

comparable to the 3-month and 1-year design storms at 

the tributary subbasins indicate that these models provide a reliable simulation of the peak discharge and 

runoff volume for the design storms. Although the 

ungaged area model fit is unknown, the variable values 

for the ungaged model are derived from the tributary 

variable values for similar land use. Thus, a reliable 

simulation model for the ungaged area can be inferred 

from the model fit of the tributary subbasin models. 

Sensitivity Analysis

Sensitivity analysis measures the response of the 

model-simulated discharge to a change in a variable 

value that represents watershed properties. Typically, a 

sensitivity analysis is an iterative process whereby the 

value of a given variable is changed while all other 

variables are held constant thus indicating the degree to 

which that variable can affect simulation results. The 

process of varying a model variable and measuring the 

effect on the simulation results is automated in the 

PCSWMM 2000 Sensitivity Wizard. Variables that 

were tested for sensitivity include: subcatchment 

width, percent effective impervious area, impervious 

area roughness, pervious area roughness, impervious 

area depression storage, pervious area depression storage, capillary suction, saturated hydraulic conductivity, 

and the initial moisture deficit. 

The Sensitivity Wizard tests the sensitivity of a 

model variable to storms of different durations and 

intensities—long, medium, and short duration (10-

hour, 1-hour, and 20-minute storms, respectively), and 

high, medium, and low intensity (varied from 3.0 to 

0.1 in/h, dependent on the duration). Sensitivity analysis was performed on peak discharge and runoff 

volume with the use of hyetographs that represent each 

of the different permutations of duration and intensity 

(only long and short durations are presented in figs. 26 

and 27) for the single-family land-use subbasin. The 

single-family land-use subbasin was chosen for the 

sensitivity analysis because (1) it represents the dominant land-use type in the lower Charles River Watershed, and (2) it is more likely to demonstrate the 

sensitivity of pervious area values than the multifamily 

and commercial subbasins, which have a higher percentage of effective impervious area. Variables were 

allowed to change by ±30 percent during the sensitivity 

testing.

Results of the sensitivity analysis (figs. 26 and 

27) indicate that the percent effective impervious area 

was the most sensitive variable affecting runoff volumes and peak discharge for most storm types. For 

storms with precipitation totals of 1 in. or more, the 

value of effective impervious area was about 50 times 

more sensitive than the next closest subcatchment 

variable—typically impervious and pervious area 

depression storage for runoff volume and subcatchment 

width for peak discharge. The sensitivity gradients of 

effective impervious area are proportional to the value 

of storm-peak discharge or runoff volume. Decreases in 

effective impervious area result in decreases in peak 

discharge and runoff volume and, conversely, increases 

in effective impervious area result in increases in peak 

discharge and runoff volume. 

Decreases in impervious and pervious area 

depression storage were the most sensitive variables 

affecting peak discharge and runoff volume for 

medium-duration, low-intensity storms. Total precipitation for this type of storm was only 0.1 in., which is 

near the interception storage starting values; thus, 

decreasing the values of interception storage has a large 

effect on both peak discharge and runoff volume for 

small storms. Other subcatchment variables have the 

greatest effect on peak discharge and runoff volume 

for short-duration storms (20 minutes) and mediumduration storms (1 hour) of low intensity. Peak discharge is affected mostly by the value of the impervious area roughness for the short-duration, low-intensity 

storm (total precipitation of 0.03 in.).

Model Limitations

SWMM was chosen to simulate runoff to the 

lower Charles River because its numerical solutions are 

well suited to this type of watershed. Still, a number of 

simplifications are made in the mathematical model 

representation of runoff process and in the structural 

representation (discretization) of the hydrologic system. The models developed by the USGS for the lower 

Charles River were conceptualized and calibrated to 

represent runoff to compute stormwater loads. For 

example, these models do not include the entire drainage network, but only a sufficient portion of the drainage system to provide subcatchment linkage, which 

allows water to be routed by the kinematic-wave 

method to its outfall. Thus, the models developed by 

the USGS are not suitable for storm-sewer design or 

other applications that require robust analysis of flow 

hydraulics of the storm-drain system. 
Precipitation-Runoff Model 53

Figure 26. Peak-discharge sensitivity gradients for hypothetical storms of varying duration and intensity for selected subcatchment variable 

values, lower Charles River Watershed, Massachusetts.

-30 -20 -10 0 10 20 30

Short duration, Low intensity - 20 min., 0.1 in/hr

0.30

0.35

0.40

0.45

0.50

0.25 80

90

100

110

120

130

140

-30 -20 -10 0 10 20 30

Short duration, High intensity - 20 min. 3 in/hr

-30 -20 -10 0 10 20 30

Medium duration, Low intensity - 1 hr, 0.1 in/hr

1.5

1.0

2.0

0.5

Medium duration, High intensity - 1hr, 1 in/hr

-30 -20 -10 0 10 20 30

30

35

40

45

50

60

20

3.0

3.5

4.0

4.5

5.0

-30 -20 -10 0 10 20 30

Long duration, Low intensity - 10 hr, 0.1 in/hr 5.5

2.5

-30 -20 -10 0 10 20 30

Long duration, High intensity - 10 hr, 0.2 in/hr

6

7

8

9

10

5

11

EXPLANATION

SUBCATCHMENT WIDTH

IMPERVIOUS AREA DEPRESSION STORAGE

EFFECTIVE PERCENT IMPERVIOUS

PERVIOUS AREA DEPRESSION STORAGE

SLOPE CAPILLARY SUCTION

SATURATED HYDRAULIC CONDUCTIVITY

IMPERVIOUS AREA ROUGHNESS

PERVIOUS AREA ROUGHNESS

INITIAL MOISTURE DEFICIT

 VARIABLE VALUE CHANGE, IN PERCENT 

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

Pervious and impervious

area depression storage
54 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 27. Runoff-volume sensitivity gradients for hypothetical storms of varying duration and intensity for selected subcatchment variable 

values, lower Charles River Watershed, Massachusetts. [hr, hours; in, inch; min, minute]

Short duration, low intensity - 20 min., 0.1 in/hr

-30 -20 -10 0 10 20 30

Long duration, low intensity - 10 hr, 0.1 in/hr 

5.0

5.1

5.2

5.3

5.4

5.5

5.6 Short duration, high intensity - 20 min., 3 in/hr

-30 -20 -10 0 10 20 30

100

120

140

160

80

Medium duration, low intensity - 1 hr, 0.1 in/hr

-30 -20 -10 0 10 20 30

7

8

9

10

11 Medium duration, high intensity - 1hr, 1 in/hr

-30 -20 -10 0 10 20 30

100

120

140

160

180

80

-30 -20 -10 0 10 20 30

100

120

140

160

180

80

Long duration, high intensity - 10 hr, 0.2 in/hr

-30 -20 -10 0 10 20 30

200

250

300

350

400

RUNOFF VOLUME, IN THOUSANDS OF CUBIC FEET 

 VARIABLE VALUE CHANGE, IN PERCENT

Pervious and impervious area

depression storage

EXPLANATION

SUBCATCHMENT WIDTH

IMPERVIOUS AREA DEPRESSION STORAGE

EFFECTIVE PERCENT IMPERVIOUS

PERVIOUS AREA DEPRESSION STORAGE

SLOPE CAPILLARY SUCTION

SATURATED HYDRAULIC CONDUCTIVITY

IMPERVIOUS AREA ROUGHNESS

PERVIOUS AREA ROUGHNESS

INITIAL MOISTURE DEFICIT
Runoff to the Lower Charles River 55

SWMM requires a single set of variable values to 

represent a subcatchment (lumped variables), but the 

physical properties of the tributary subbasin model subcatchments are spatially heterogeneous. Although simulation results obtained from the tributary subbasin 

models at the gage locations (calibration points) were 

good, the model performance of individual subcatchments is unknown. The ungaged subbasin model has an 

even larger degree of uncertainty than the gaged model 

because the variable values were obtained by transferring each value from subcatchments with similar landuse characteristics in the tributary subbasin models. 

The model performance for the aggregate of these subcatchments could not be evaluated as it was for the 

gaged subbasins. The sensitivity analysis indicates that 

even small changes in the effective imperviousness can 

produce large changes in the storm peak discharge and 

runoff volume. Ungaged areas, however, represent only 

about 4 percent of the total drainage area to the lower 

Charles River. 

The performance of the models outside of the 

range of storms evaluated in the calibration and model 

fit analysis is unknown. The models were calibrated 

and tested over a wide range of storms (0.10 to 4.4 in.), 

but the majority of these storms had less than 1 in. of 

total precipitation. The largest storm included in the 

evaluation of the model fit, June 6, 2000, had a total 

precipitation of 4.4 in. and an estimated recurrence 

interval of 2 to10 years. The simulated runoff volume 

error ranged between -27 and 23 percent, excluding the 

model performance at the commercial land-use subbasin and Faneuil Brook Subbasin, which had questionable observed discharge data as previously described. 

The median simulated runoff volume error ranged 

between –13 and 18 percent; thus, the simulated runoff 

volume for storms of this magnitude or larger is potentially greater than that reported for all storms. Flow 

conditions other than those evaluated for this study 

could affect the model results and, therefore, simulation results outside the range of conditions used to 

assess the model should be used with caution. 

RUNOFF TO THE LOWER

CHARLES RIVER

The calibrated models were used to simulate 

runoff to the lower Charles River from the watershed 

below Watertown Dam for (1) the 2000 water year, 

October 1, 1999, through September 30, 2000, (2) a 

3-month design storm, and (3) a 1-year design storm. 

SWMM results provided annual and design-storm 

hydrographs for the calculation of constituent loads to 

the lower Charles River presented in a companion 

report by Breault and others (2002). The annual (water 

year) runoff to the lower Charles River is summarized 

in table 9. 

Annual and Monthly 

Water Budget

For each of the gaged subbasins, simulated flow 

components are described for the annual water budget 

and the simulated monthly runoff volumes are compared to the measured monthly volumes. Differences 

between the simulated and the observed monthly runoff 

relative to the previously described stormwater-volume 

error indicate the potential error associated with the 

calculation of constituent loads.

Single-Family Land-Use 

Subbasin

Annual precipitation simulated on the singlefamily land-use subbasin was 42.0 in.—simulations 

indicate about 80 percent infiltrated the ground, 14 percent became surface runoff, and 5 percent evaporated 

Table 9. Annual runoff observed at Charles River at Watertown Dam, and 

simulated at land-use and tributary subbasins to the lower Charles River, 

Massachusetts, Water Year 2000, October 1, 1999 through September 30, 

2000

[WY, water year; --, not applicable] 

Site

Annual WY 2000 volume

(Millions of cubic feet)

To stream gage To outfall

Land-use subbasins

Single family............................... 9.51 --

Multifamily ................................. 3.04 --

Commercial................................. 8.11 --

Tributaries and ungaged subbasins

Charles River at Watertown ........ 15,300 --

Laundry Brook............................ 82.3 82.3

Faneuil Brook ............................. 38.6 49.1

Muddy River ............................... 202 157

Muddy River conduit .................. -- 183

Stony Brook ............................... 478 489

Aggregate of ungaged 

subbasins.................................

-- 284
56 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

from surface storage. Of the water that infiltrated the 

ground, 46 percent entered deep ground-water storage 

and is considered lost from the subbasin, 41 percent 

was lost to evapotranspiration, and 14 percent entered 

the drainage systems as ground-water discharge. The 

simulated runoff volume for the 2000 water year was 

9.51 million ft3 (table 9), the average discharge was 

0.30 ft3/s, the minimum discharge was 0.001 ft3/s, and 

the maximum discharge was 79 ft3/s. 

Simulated monthly runoff volumes (fig. 28A) 

differed from the observed runoff volume by -37 to 

18 percent. Monthly runoff was generally undersimulated by about 12 percent, but storm-runoff volumes 

are oversimulated by 18 percent on average. Hence, 

the difference in the monthly runoff is largely attributed to differences in base flow. The observed base 

flow generally was between 0.02 and 0.05 ft3/s, 

whereas simulated base flow was typically zero. 

Therefore, constituent loads calculated from the simulated discharge values can be expected to underestimate base-flow loads by an average of 12 percent and 

overestimate storm loads by about 18 percent on 

average.

Multifamily Land-Use 

Subbasin 

Annual precipitation simulated on the multifamily land-use subbasin was 40.95 in.—simulations 

indicate about 13 percent infiltrated the ground, 77 percent became surface runoff, and 10 percent evaporated 

from surface storage. Of the 6.66 in. of water that infiltrated the ground or was lost from the subsurface storage over the simulation period, 60 percent entered deep 

ground-water storage (considered lost from the subbasin), 39 percent was lost to evapotranspiration, and 1 

percent entered the drainage systems as ground-water 

discharge. Total runoff volume for the 2000 water 

year was 3.04 million ft3, the average discharge was 

0.10 ft3/s, the minimum discharge was zero, and the 

maximum discharge was 25 ft3/s.

Simulated monthly runoff volumes differed from 

the observed volumes by -24 to 39 percent (fig. 28B). 

The model slightly undersimulated runoff in December 

and January, and slightly oversimulated runoff in May, 

July, August, and September. The month of June was 

undersimulated by 24 percent largely because of the 

undersimulation of the June 6 storm, but storm-runoff 

volumes were oversimulated by 3 percent on average. 

On average, base-flow constituent loads can be 

expected to be underestimated slightly and stormwater 

constituent loads can be expected to be oversimulated 

by 3 percent. 

Commercial Land-Use 

Subbasin 

Annual precipitation simulated on the commercial land-use subbasin was 40.95 in.—simulations indicate about 80 percent became surface runoff, about 11 

percent infiltrated the ground, and about 9 percent 

evaporated from surface storage. Of the 5.83 in. of 

water that infiltrated into the ground or drained from 

subsurface storage over the simulation period, about 24 

percent was lost to evapotranspiration, and most of the 

rest (about 76 percent) entered deep ground-water 

storage. The simulated total runoff volume for the 2000 

water year was 8.11 million ft3, the average discharge 

was 0.26 ft3/s, the minimum discharge was zero, and 

the maximum discharge was 19 ft3/s.

The constant base flow of 0.20 ft3/s that was 

added to the TRANSPORT module is not included in 

the water budget above. A base flow of this magnitude 

would require a ground-water discharge of 71 in/yr, or 

about twice the amount of annual precipitation over the 

subbasin. A small portion of the base flow (about 5 percent) could be gained by eliminating the loss to the 

deep ground-water system; however, this rate of loss is 

consistent with the calibrated ground-water loss used in 

other subbasins models. 

Simulated monthly runoff volumes differed from 

the observed runoff by -51 to 25 percent (fig. 28C); the 

month of June (-51 percent error) was appreciably 

undersimulated primarily because measured discharge 

during the June 6 storm had a prolonged elevated recession. This type of recession is atypical for this type of 

subbasin and is likely caused by measurement error or 

the possible conditions that caused high RR coefficients in this subbasin as previously explained. After 

the station was made operational in mid-January, the 

measured discharge was noisy and undersimulated 

compared to the observed discharge until early April. 

Measured discharge is missing from April 2 to 20. 

Therefore, constituent loads calculated from simulated 

discharges are expected to overestimate base-flow 

loads during the late summer and overestimate storm 

loads by -13 percent, on average; however, the error in 

the load estimate is expected to be minor if runoff is 

unaffected by the variable source area or the cross 

connections.
Runoff to the Lower Charles River 57

Figure 28. Simulated and observed monthly runoff volume at the three land-use subbasin sites in the lower Charles River Watershed, 

Massachusetts, 2000 water year: (A) single family, (B) multifamily, and (C) commercial. [Observed monthly runoff volumes are not shown for 

months with missing data.]

0

0.4

0.8

1.2

1.6

SIMULATED

OBSERVED

A. Single family

0

5

10

15

20

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

RUNOFF VOLUME, IN INCHES

WATER YEAR 2000

 0

 1

 2

 3

 4

 5

 6

 7

B. Multifamily

C. Commercial
58 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Laundry Brook Subbasin

Annual precipitation simulated on the Laundry 

Brook Subbasin was 42.05 in.—simulations indicate 

about 86 percent infiltrated into ground, about 10 percent became surface runoff, and about 4 percent evaporated from surface storage. Of the 36.06 in. of water 

that infiltrated into the ground, 47 percent entered deep 

ground-water storage, 42 percent was lost to evapotranspiration, 10 percent entered the drainage systems 

as ground-water discharge, and 1 percent was added to 

subsurface storage over the simulation period. Total 

runoff volume for the 2000 water year was 82.3 million 

ft3, the average discharge was 2.60 ft3/s, the minimum 

discharge was 0.36 ft3/s, and the maximum discharge 

was 194 ft3/s.

Simulated monthly runoff volumes differed from 

the observed volumes by -25 to 52 percent (fig. 29A). 

Monthly runoff was undersimulated by about 1.5 percent on average and storm runoff was undersimulated 

by 0.9 percent, on average. The model undersimulates 

runoff in February, March, April, May, August, and 

September; and oversimulates runoff in November, 

December, January, June, and July. Slightly underestimated annual loads and storm loads are expected 

when constituent loads are calculated from simulated 

discharges.

Faneuil Brook Subbasin

Annual precipitation simulated on the Faneuil 

Brook Subbasin was 42.2 in.—simulations indicate that 

about 81 percent infiltrated the ground, 15 percent was 

surface runoff, and 4 percent evaporated from surface 

storage. Of the 34.13 in. of water that infiltrated the 

ground, 42 percent entered deep ground-water storage, 

40 percent was lost to evapotranspiration, 17 percent 

entered the drainage systems as ground-water discharge, and 1 percent was added to the subsurface storage over the simulation period. Total annual-runoff 

volume to the gaging station for the 2000 water year 

was 38.6 million ft3, the average discharge was 

1.22 ft3/s, the minimum discharge was zero, and the 

maximum discharge was 136 ft3/s. Total runoff volume 

from Faneuil Brook to the lower Charles River for 

the 2000 water year was 49.1 million ft3, the average 

discharge was 1.55 ft3/s, the minimum discharge 

was zero, and the maximum discharge was 171 ft3/s.

Simulated monthly runoff volumes differed from 

the observed volumes by -57 to 24 percent (fig. 29B); 

the largest error is in June largely because the storm 

volume on June 6 was oversimulated. Runoff volumes 

during November through March were undersimulated; 

storm volumes were undersimulated by 3 percent on 

average. Base flow during the winter and spring generally was undersimulated because the ground water was 

treated as a linear reservoir that drained to a fixed elevation in the conduit. Therefore, constituent loads calculated from simulated discharges are expected to 

underestimate base-flow loads during the winter and 

spring and slightly underestimate storm loads.

Stony Brook Subbasin

Annual precipitation simulated on the Stony 

Brook Subbasin was 42.36 in.—simulations indicate 

that about 67 percent infiltrated the ground, about 

28 percent became surface runoff, and about 6 percent 

evaporated from surface storage. Ground water was 

not simulated in the Stony Brook model; therefore, 

infiltrated ground water in the subbasin is not routed to 

the stream. The total simulated runoff volume to the 

gage for the 2000 water year was 478 million ft3, the 

average discharge was 15.1 ft3/s, the minimum discharge was 10.1 ft3/s, and the maximum discharge was 

1,059 ft3/s. The simulated annual runoff volume to the 

mouth for the 2000 water year was 489 million ft3, the 

average discharge was 15.5 ft3/s, the minimum discharge was 10.3 ft3/s, and the maximum discharge was 

685 ft3/s.

Simulated monthly runoff volumes differed from 

the observed volumes by -3 to 63 percent (fig. 29C). 

The model undersimulates runoff in June, July, August, 

and September and oversimulates runoff in May; on 

average, monthly runoff is undersimulated by 24 percent. Storm-runoff volumes were oversimulated by 

18 percent, on average. Underestimated annual loads 

and overestimated storm loads are expected from 

constituent loads calculated from simulated 

discharges. 
Runoff to the Lower Charles River 59

Figure 29. Simulated and observed monthly runoff volume at three tributary subbasin sites in the lower Charles River Watershed, 

Massachusetts, 2000 water year: (A) Laundry Brook, (B) Faneuil Brook, and (C) Stony Brook. [Observed monthly runoff volumes are not 

shown for months with missing data.]

0

0.4

0.8

1.2

1.6

A. Laundry Brook

0

0.5

1.0

1.5

2.0

2.5

RUNOFF VOLUME, IN INCHES

B. Faneuil Brook

0

0.5

1.0

1.5

2.0

2.5

3.0

C. Stony Brook

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

Observed

Simulated

WATER YEAR 2000
60 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Total Inflows to the 

Lower Charles River

Total annual inflow to the lower Charles River 

was 16,500 million ft3; about 92 percent of the annual 

inflow was from the upper basin, 3 percent was from 

the Stony Brook Subbasin, 2 percent was from the 

Muddy River Subbasin, and less than 1 percent was 

from the combined inflows of Laundry and Faneuil 

Brooks (table 9). These inflows do not include CSO 

discharges to the river, except those entering Stony 

Brook prior to its discharge to the lower Charles River. 

The remaining ungaged drainage area contributed 

about 2 percent of the total annual inflow to the lower 

Charles River. Excluding inflows from the upper basin 

(Charles River above Watertown Dam), the total 

annual inflow to the lower Charles River was 1,320 

million ft3; about 39 percent was from the Stony Brook 

Subbasin, 27 percent was from the Muddy River Subbasin, which includes the area that drains to the Muddy 

River conduit, 7 percent was from the Laundry Brook 

Subbasin, 4 percent was from the Faneuil Brook Subbasin, and the ungaged areas not included in the tributary subbasin models contributed about 23 percent.

Design Storms

The MWRA selected two design storms for 

their river model simulations of bacterial transport and 

fate in the lower Charles River. The design storms represent a 3-month storm, based on an actual storm of 

July 20, 1982, and a 1-year storm, based on an actual 

storm of September 20, 1961. The 3-month storm 

lasted 30 hrs, had 1.84 in. total rainfall, 0.06 in/h average rainfall intensity, and 0.4 in/h maximum rainfall 

intensity. The 1-year storm lasted 26 hrs, had 2.79 in. 

total rainfall, 0.11 in/h average rainfall intensity, and 

0.65 in/h maximum rainfall intensity. Discharge from 

the upper basin (Charles River above Watertown Dam) 

was estimated from discharge recorded at the Waltham, 

Massachusetts, gage (01104500) as previously 

described. The models developed by the USGS and 

MWRA were used to calculate runoff produced by 

these storms from all other areas to the lower Charles 

River, excluding CSO discharges except those to Stony 

Brook. 

Total storm runoff for the 3-month and 1-year 

storms was 111 and 257 million ft3, respectively. The 

upper basin drainage area, the largest source of water 

to the lower Charles River, produced 21 and 46 percent 

of the total inflow for the 3-month and 1-year design 

storms, respectively (table 10). Typically, after a large 

storm the discharge at Charles River at Watertown 

Dam takes several days to return to base-flow conditions; the prolonged recession is attributed to water 

storage in upstream riparian wetlands. For this reason, 

the storm volumes for both design storms were truncated after about 3 days because discharges were 

affected by later storms. Muddy River, Stony Brook, 

and the ungaged subbasins not included in tributary 

subbasin models each make up about 5 to 7 percent of 

the total runoff volume for the 3-month storm and 

about 3 to 6 percent of the runoff volume for the 1-year 

storm. The Laundry Brook and Faneuil Brook Subbasins each made up less than 2 percent of the total runoff 

volume for both the 3-month and 1-year storms.

Excluding inflow from the upper basin the runoff 

to the lower Charles River was as follows. Total storm 

runoff for the 3-month and 1-year design storms was 

30 and 53 million ft3, respectively. The largest source 

was Muddy River Subbasin, which contributed 34 percent of the runoff for the 3-month storm and 35 percent 

of the runoff for the 1-year storm. The Stony Brook 

Subbasin and the ungaged subbasins, not included in 

the tributary subbasin models, contribute about equal 

proportions for both storms (about 26 to 30 percent of 

the total runoff, respectively). Combined, the Muddy

Table 10. Storm-runoff volumes simulated for the 3-month and 1-year 

design storms to the lower Charles River, Massachusetts

Site

Design storm volume

(millions of cubic feet)

3 month 1 year

Land-use subbasins

Single family................................... 0.278 0.443

Multifamily..................................... .120 .208

Commercial..................................... .104 .160

Tributaries and ungaged subbasins

Charles River at Watertown ............ 80.2 204

Laundry Brook................................ 2.15 3.53

Faneuil Brook ................................. .968 1.64

Muddy River conduit ..................... 5.16 8.77

Muddy River................................... 4.91 9.54

Stony Brook .................................... 7.91 14.9

Aggregate of ungaged 

subbasins .................................... 8.99 14.3

Total........................................... 111 257
Summary 61

River and Stony Brook Subbasins contributed about 60 

percent of the design-storm runoff; these inputs are 

significant because they enter the lower Charles River 

in a prime recreational area. Laundry Brook contributes 

about 7 percent and Faneuil Brook contributes about 3 

percent of the total runoff for these design storms.

SUMMARY

The lower Charles River is an important recreational resource for the Boston metropolitan area, 

but contaminated stormwater and combined-sewer 

overflows (CSOs) have impaired its use because at 

times the river is unfit for secondary contact recreation 

(boating). The U.S. Environmental Protection Agency 

(USEPA) has set a goal of making the lower Charles 

River fishable and swimmable by Earth Day 2005. 

To meet this goal, a better understanding of the nonCSO stormwater discharge and constituent loads to the 

lower Charles River is needed. The U.S. Geological 

Survey (USGS), in cooperation with the USEPA, the 

Massachusetts Water Resources Authority (MWRA), 

and the Massachusetts Department of Environmental 

Protection (MADEP), developed and calibrated StormWater Management Models (SWMM) to quantify nonCSO stormwater loads to the lower Charles River. This 

report documents the stormwater-modeling procedures 

used to calculate runoff to the lower Charles River. 

Constituent loads are described in a companion report.

During the 2000 water year (September 30, 1999, 

through October 1, 2000), surface-water discharge data 

were collected at eight sites—three relatively homogenous land-use sites, four major tributaries downstream 

of the Watertown Dam, and the Charles River where it 

enters the lower Charles River at Watertown Dam. The 

three land-use sites represent the largest land-use categories in the lower Charles River Watershed: (1) singlefamily residential, (2) multifamily residential, and 

(3) commercial. The major tributary sites included all 

of the drainage area of Laundry Brook, and 80, 84, and 

90 percent of the Faneuil Brook, Muddy River, and 

Stony Brook drainage areas, respectively. The USGS 

collected precipitation data at Watertown Dam and 

compiled precipitation data maintained by other agencies at five gages in or near the lower Charles River 

Watershed.

Precipitation and discharge data were used to run 

and calibrate models developed for the three land-use 

subbasins, and two tributary subbasins, Laundry and 

Faneuil Brook. Precipitation data were also used in a 

model that simulates discharge to the lower Charles 

River from numerous ungaged outfalls not included in 

the tributary subbasin models. The three homogeneous 

land-use subbasin models were later incorporated into 

other models; the residential land-use subbasin model 

was part of the Laundry Brook model, the multifamily 

subbasin and the commercial subbasin models were 

part of the ungaged area model. The Laundry, Faneuil, 

and ungaged area models include 126 subcatchments 

and 116 conduits. 

The SWMM of the Stony Brook Subbasin was 

developed prior to this study by others, but evaluated 

with the newly collected data from this study. The 

Stony Brook model also included the Muddy River 

Subbasin, but variable backwater conditions at the 

Muddy River stream gage resulted in poor quality discharge records; therefore, the Muddy River Subbasin 

portion of the model was not evaluated. To simulate 

runoff from the lower Charles River Watershed requires 

four separate models—(1) Laundry Brook model, 

(2) Faneuil Brook model, (3) Stony Brook model, and 

(4) the ungaged area model.

Model variable values were calculated from relations of rainfall to runoff, available spatial data, field 

measurements, and literature values. The land-use 

subbasin models were calibrated first and the variable 

values obtained from these models were used as initial 

values for similar land-use types in the tributary and 

ungaged subbasin models. Variable values were 

adjusted during model calibration to minimize the difference between simulated and observed discharges; 

particularly the value of the effective impervious area, 

which largely determines the storm-peak discharge and 

runoff volume. Models developed by the USGS were 

calibrated with up to 24 storms. This number depended 

on the availability of measured discharge data; these 

storms were selected because they had the least variability in precipitation measured over the six rain gages. 

The model fit was evaluated for each model for 

the calibration storms and for all storms with appreciable precipitation and reliable discharge data. Statistics 

reported to evaluate the model fit included the standard 

error of estimate (SE), the root mean square error 

(RMSE), the coefficient of efficiency (E), and the index 

of agreement (d) for storm-peak discharge and runoff 

volume. The first two statistics are absolute measures of 

the model fit, whereas the last two statistics are relative 

measures of the model fit. Model calibration 
62 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

emphasized minimizing the differences between simulated and observed storm-runoff volumes rather than 

storm-peak discharge, although peak discharge was 

also considered in the model calibration.

Twenty storms, on average, were used for model 

calibration; the number of calibration storms varied 

between 13 and 24. The overall runoff volume model 

fit for the models developed by the USGS for these 

storms had SE values that ranged from 0.016 to 

0.407 in. (average of 0.114 in.), RMSE that ranged 

from 0.061 to 0.794 in. (average of 0.272 in.), E that 

ranged from 0.32 to 0.94 (average of 0.78), and that 

ranged from 0.27 to 0.98 (average of 0.82). For the 

USGS models overall, the simulated runoff volume 

was within 10 percent of the observed volume from 30 

to 46 percent of the time (average 38 percent), within 

25 percent of the observed volume from 45 to 75 percent of the time (average 65 percent), and within 50 

percent of the observed volume from 70 to 95 percent 

of the time (average 88 percent). 

Forty-two storms, on average, were used to test 

the model fit; the number of storms ranged between 31 

and 48. For the USGS models, the runoff-volume 

model fit for these storms had SE that ranged from 

0.030 to 0.941 in. (average of 0.209 in.), RMSE that 

ranged from 0.130 and 2.19 in. (average of 0.551 in.), 

E that ranged from 0.40 to 0.93 (average of 0.84), and 

that ranged from 0.67 to 0.98 (average of 0.95). The 

simulated storm-runoff volume was within 10 percent 

of the observed volume between 26 and 33 percent of 

the time (average 29 percent), within 25 percent of 

the observed volume between 51 and 69 percent of the 

time (average 60 percent), and within 50 percent of 

the observed volume between 72 and 96 percent of 

the time (average 88 percent). The SE was at least 

four times larger and RMSE was at least three times 

larger for the commercial land-use subbasin model 

than for the other models, because measured discharge 

appears to be affected by variable conditions that are 

not considered in the model. 

Over all storms, the USGS model runoff volumes were, on average, oversimulated by 18 percent 

by the single-family land-use subbasin model, undersimulated by 3 percent by the multifamily land-use 

subbasin model, oversimulated by 0.4 percent by the 

commercial land-use subbasin model, undersimulated 

by 1 percent by the Laundry Brook Subbasin model, 

and undersimulated by 3 percent by the Faneuil Brook 

Subbasin model. Model-fit statistics for storm-peak 

discharges generally were comparable to the statistics 

for runoff volume. 

The Stony Brook Subbasin model generally had 

a model fit comparable to that of the USGS models. 

Twenty-eight storms were used to evaluate the model 

fit. The simulated storm-runoff volume had a SE of 

0.070 in., RMSE of 0.210 in., E of 0.90, and d of 0.98. 

The simulated storm-runoff volume was within 10 

percent of the observed volume 21 percent of the time, 

within 25 percent of the observed volume 54 percent 

of the time, and within 50 percent of the observed 

volume 82 percent of the time. Simulated storm runoff 

volumes at Stony Brook were oversimulated by 18 

percent, on average. In general, the USGS models tend 

to fit stormwater volumes slightly better than the 

Stony Brook model, and, conversely, the Stony Brook 

model tends to fit storm-peak discharges slightly 

better than the USGS models, reflecting the different 

purposes for which the models were developed.

The total annual runoff to the lower Charles 

River, not including CSOs (except those entering 

Stony Brook), during the 2000 water year was 

16,500 million ft3; 92 percent of the inflow was from 

the upper basin, 3 percent was from the Stony Brook 

Subbasin, 2 percent was from the Muddy River 

Subbasin, which includes runoff that drains to the 

Muddy River conduit, and less than 1 percent was 

from the combined inflows of Laundry and Faneuil 

Brooks. The ungaged drainage area, not included in 

the tributary models, contributed about 2 percent of 

the total annual inflow to the lower Charles River. 

Total annual runoff to the lower Charles River, which 

excludes runoff above Watertown Dam, was 

1,320 million ft3; 39 percent was from the Stony 

Brook Subbasin, 27 percent was from the Muddy 

River Subbasin, which includes runoff that drains to 

the Muddy River conduit, 7 percent was from the 

Laundry Brook Subbasin, and 4 percent was from the 

Faneuil Brook Subbasin. The ungaged areas, not 

included in the tributary subbasin models, contributed 

about 23 percent of the total annual inflow to the lower 

Charles River, excluding runoff above Watertown 

Dam.

Runoff to the lower Charles River was calculated for two design storms that represent a 3-month 

and a 1-year event. The MWRA used these storms in a 

receiving water model to simulate the transport and 

fate of bacteria in the lower Charles River. These are 

actual storms on July 20, 1982 (3-month storm), and 

September 20, 1961 (1-year storm), with total rainfall 
References Cited 63

volumes of 1.84 and 2.79 in., respectively. The models 

were used to simulate runoff for these storms from the 

lower Charles River Watershed; a relation between the 

Charles River Watertown station and the long-term 

Waltham station was developed to calculate inflow 

from the upper basin. Total storm runoff to the lower 

Charles River was 111 and 257 million ft3 for the 3-

month and 1-year storms, respectively. Total storm 

runoff to the lower Charles River excluding that from 

the upper basin was 30 and 53 million ft3 for the 3-

month and 1-year storms, respectively. Runoff from the 

various tributary areas for the design storms occurred 

in about the same proportion as the annual runoff.

Models developed and calibrated by the USGS 

were designed to estimate stormwater runoff to the 

lower Charles River. These models provide a planning 

tool for calculating stormwater runoff, for example, 

simulating runoff to compute constituent loads. The 

drainage system network, however, was not represented 

in sufficient detail for use in engineering design. 

Although the models are well calibrated to observed 

data for the 2000 water year, simulation results for 

storms larger than about 4.5 in. are untested and care 

should be exercised in the use of simulated discharges 

for storms larger than this amount.

REFERENCES CITED

Breault, R.F., Sorenson, J.R., and Weiskel, P.K., 2002, 

Streamflow, water quality, and contaminant 

loads in the lower Charles River Watershed, 

Massachusetts, 1999–2000: U.S. Geological 

Survey Water-Resource Investigations Report 02-

4137, 131 p.

Brickford, W.E. and Dymon, U.J., 1990, An atlas of 

Massachusetts River systems—Environmental 

designs for the future: Amherst, University of 

Massachusetts Press, 87 p.

Buchanan, T.J., and Somers, W.T., 1965, Stage 

measurement at gaging stations, in Hydraulic 

measurement and computation: U.S. Geological 

Survey Surface Water Techniques, book 1, 

chap. A10, p. 1–26.

Brunner, G.W, 2001, HEC-RAS, River analysis system 

hydraulics reference manual: U.S. Army Corps of 

Engineers report CDP-69, 262 p.

Camp, Dresser and McKee, Inc., 1997a, Stony Brook 

Sewer System Study: Unpublished report on file at 

Camp, Dresser and McKee, Inc., Cambridge, MA, 

variously paged. 

_____1997b, Technical Memorandum Number 3, 

Hydraulic Model of the Stony Brook System: 

Unpublished report on file at Camp, Dresser and 

McKee, Inc, Cambridge, MA, variously paged.

Carter R.W., and Davidian, J. 1965, General procedure 

for gaging stations, in Hydraulic measurement and 

computation: U.S. Geological Survey Surface 

Water Techniques, book 1, chap. 9, p. 1–13.

CH2M Hill, 1990, Final combined sewer overflow 

facilities plan and final environmental impact 

statement, Appendix E—Summaries of technical 

memoranda and errata for the draft CSO facilities 

plan: Boston, MA, CH2M Hill, Inc., variously 

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Appendix 1: Model areas and schematics of the 

StormWater Management Model (SWMM) 

elements used to represent the model areas

Appendix 1 67

Appendix 1A. Laundry Brook Subbasin, lower Charles River Watershed, Massachusetts.

Charles Rive r

121502

1017

1 2 MILES

1 2 KILOMETERS

0

0

Newton

Allston

Brighton

Brookline

Watertown

Outfall # 2

EXPLANATION

STREAM-GAGE STATION

SIMULATED DRAINAGE NETWORK

STORM-DRAIN NETWORK

SURFACE WATER

MODEL BASIN

DRAINAGE AREA OF SINGLE FAMILY LAND-USE SUBBASIN

850040

1118

NODE AND IDENTIFICATION NUMBER 

CONDUIT NUMBER

SUBCATCHMENT NUMBER

110602

110702

110202

110802

111002

110902

110102

110302

110402

111102

111202

111302

111602

111402

121702

110502

1006

1007

1005

1003

1002

1004

1008

1010

1011

1012

1013

1014

1015

1018

1016

1009

SUBCATCHMENT BOUNDARIES

Bulloughs

Pond

Information from City of Newton MIS Department and

City of Watertown Department of Public Works

Massachusetts State Plane Projection

119 North American Datum 1983

3

5 6

7

11

10

12

2

9

8

4

13

14

15

18 16

99

17

97

N
68 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Appendix 1B. Schematic of StormWater Management Model (SWMM) elements used to represent Laundry Brook Subbasin, 

lower Charles River Watershed, Massachusetts.

Lower Charles River 

Bulloughs Pond

(storage element)

1002 1003

1004

1007

1008 1009

1006 1005

1010

1011 1012 1013

1014

1016

1015 1017 1018

Singlefamily 

land-use 

subbasin 

Laundry Brook Subbasin

24 3 6 7 5

8 97

98

99

10

13 11

15

17

16

18

12

14

202

9

110602 110802 110702

110902

111202

111402

121502

111602

121702

110102 110202

110302 110502

111002 111102

111302

110402

EXPLANATION

2

1002

SUBCATCHMENT AND

IDENTIFICATION NUMBER

NODE AND 

IDENTIFICATION NUMBER

CONDUIT AND 

IDENTIFICATION NUMBER

110102

outfall 2 (figure 6)
Appendix 1 69

Appendix 1C. Faneuil Brook Subbasin, lower Charles River Watershed, Massachusetts.

1 MILE

1 KILOMETER

0

0

EXPLANATION

UNGAGED AREA AND BOUNDARY

STREAM-GAGE STATION

SIMULATED DRAINAGE NETWORK

STORMDRAIN NETWORK

SURFACE WATER

MODEL BASIN

850040

1118

NODE AND IDENTIFICATION NUMBER 

CONDUIT NUMBER

SUBCATCHMENT NUMBER

SUBCATCHMENT BOUNDARIES

Charles River

331922

331821

331821

331621

331521

331021

331221

310721

310421

310221

310521

331121

330921

331421

310621

310821

310321

310121

1056

1060

1066

1074

1073

1072

1071

1070

1069

1068

1059

1054

1055

1067

1056

1062

1058

1057

Outfall # 21

Newton

Allston

Brighton

Brookline

Watertown

Information from City of Newton MIS Department and

Boston Water and Sewer Commission

Massachusetts State Plane Projection

North American Datum 1983

119

66

74

63

72

71

70

62

65

68

73

69

64

67

61

60

56

58

59

57

99

N

UNGAGED
70 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Appendix 1D. Schematic of StormWater Management Model (SWMM) elements used to represent Faneuil Brook Subbasin, lower Charles River 

Watershed, Massachusetts.

62

Faneuil Brook 

stream gage station

(01104660)

1059

Chandler Pond

storage element

Faneuil Brook Subbasin

1057 1058

1062

1061 1060

1065 1064

1067 1068

1069

1070 1071

1066

1072

1073 1074

1063

1056

EXPLANATION

SUBCATCHMENT AND

IDENTIFICATION NUMBER

NODE AND 

IDENTIFICATION NUMBER

CONDUIT AND 

1058 IDENTIFICATION NUMBER

310821

58

65

64

66

67

68

69 70

71

72

73

74

57 59

56

61

60

58

63

221

99

310221

310321

331721

310121

331021

330921 331421

331521

331621

331821

331921

331121

310621 331221

310721

310521

310421

310821

331321

Lower Charles River 

 Outfall 21 (figure 6)
Appendix 1 71

Appendix 1E. Multifamily and commercial land-use subbasins, and drainage area to outfall 40 (fig. 6), lower Charles River 

Watershed, Massachusetts.

0 1,000 2,000 FEET

STREAM-GAGE STATION

SUBBASIN BOUNDARY

BOUNDARY OF DRAINAGES

TO OUTFALL 40

MULTIFAMILY LAND-USE

SUBBASIN

COMMERCIAL LAND-USE

SUBBASIN

ADDITIONAL DRAINAGE AREA TO COMMERCIAL LAND-USE SUBBASIN 

THAT COULD CONTRIBUTE TO COMMERCIAL LAND-USE SUBBASIN BASED ON TOPOGRAPHIC DIVIDE

OTHER DRAINAGE AREA 

TO OUTFALL 40

EXPLANATION

850040

1118

NODE AND IDENTIFICATION NUMBER 

CONDUIT NUMBER

SUBCATCHMENT NUMBER

TOPOGRAPHIC CONTOUR—

In 10-foot increments.

Datum is sea level. (NAD 1983)

SIMULATED STORM-DRAIN NETWORK

STORM-DRAIN NETWORK

0 500 250 METERS

Charles

River

Information from City of Cambridge MIS Department and

City of Cambridge Department of Public Works

Massachusetts State Plane Projection

North American Datum 1983

10

20

20

40

50

30

20

20

20

30

20

30

30

20

30

20

10

10

20

40

40

750040

1119

1116

1117

1118

850040

950040

950240

Outfall # 40

119

118

116

117

119

Cambridge

N
72 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Appendix 1F. Schematic of StormWater Management Model (SWMM) elements used to represent multifamily and 

commercial land-use subbasins, lower Charles River Watershed, Massachusetts.

Lower Charles River 

1116

1117

1118

1119

Multifamily 

land-use

subbasin

Commercial 

land-use

subbasin

1116 116 117 118

240

119

750040 850040 950240

950140

EXPLANATION

SUBCATCHMENT AND

IDENTIFICATION NUMBER

NODE AND 

IDENTIFICATION NUMBER

CONDUIT AND 

IDENTIFICATION

NUMBER

116

850040

outfall 40 (fig. 6)
Appendix 1 73 Figure 1G. Schematic of StormWater Management Model (SWMM) elements used to represent ungaged subbasin (outfalls 1 through 14, fig. 6), lower Charles River Watershed, Massachusetts.

Lower 

River Charles 

Last two digits of the node numbers along the lower Charles Rivercorrespond to the outfall numbers shown in figure 6.

EXPLANATION

SUBCATCHMENT ANDIDENTIFICATION NUMBER

NODE ANDIDENTIFICATION NUMBER

CONDUIT AND IDENTIFICATION NUMBER

1030

920108

30

10321031 1038 1039

Laundry

Brook

(see appendix 1B)

1035

1037

1028

1029

1036

1044

1023

1025

1026 1023 1024

1001

1020

1021

1030

1033

1040

1042

1043

920105 920405

920505 920205

920305 920306 920107 920110 920111 920100 920114

910013

910312 920309

920108 920104 920103 920101

910209 910109 910112 910212

910200

205 206 207 210 211 311 214

213 212 209 208 204 203 201

1 20 21 30 33

32 31

40

39 38

42

44 37 36 35 29 28 26

25

24 22

23

202 313

43
74 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 1G. Schematic of StormWater Management Model (SWMM) elements used to represent ungaged subbasin (outfalls 15 through 28, fig. 6), lower Charles River Watershed, Massachusetts—

Continued.

Lower River Charles 

1047 1048

1046

1045

1051

1052

1053

1054

1055

1078

1076

1077

1083

1088

1079

1080

1081

1085 1084

1087

46 45

47

48 51 52

219

53

319

54

320

55

78

322

76

323

77

226

83

88

79 80 81

85

84

227

215 216 217 218 318 224 228 225

87

327

Last two digits of the node numbers along the lower Charles Rivercorrespond to the outfall numbers shown in figure 6.

EXPLANATION

SUBCATCHMENT ANDIDENTIFICATION NUMBER

NODE AND IDENTIFICATION NUMBER

CONDUIT AND IDENTIFICATION NUMBER

1043

43

910200

920115 920116 920118 920300

930119 930400 930120

920124

930122 930523 930126

920128

920125 920225 920325

930127

930227

920217

920117

930500
Appendix 1 75

Figure 1G. Schematic of StormWater Management Model (SWMM) elements used to represent ungaged subbasin (outfalls 30 through 40, fig. 6), lower Charles River Watershed, Massachusetts—

Continued.

Lower River Charles 

1095

outfall 40

See appendix 1F

95

230 231

90 89

233

91

333

92

334

93

236

94

337

98 96

237

238

99

338

100

438

101

340

107

240

1091

1090

1089

1092

1093

1094

1098

1096

1099

1100

1101

1107

930700

930237

950130 950131 950133 950600 950134 950136 950138 950800 950900 951000

930137

Last two digits of the node numbers along the lower Charles River correspond to the outfall numbers shown in figure 6.

EXPLANATION

SUBCATCHMENT ANDIDENTIFICATION NUMBER

NODE AND IDENTIFICATION NUMBER

CONDUIT AND IDENTIFICATION NUMBER 1095

95

930137
76 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Figure 1G. Schematic of StormWater Management Model (SWMM) elements used to represent ungaged subbasin (outfalls 41 through 55, fig. 6), lower Charles River Watershed, Massachusetts—

Continued.

Lower 

River Charles 

Muddy Riveroutfall(no schematic)

1108

Muddy Riverconduit outfall(no schematic)

1112

1111

1110

1109

1114

1123

1115

1128

1132

1124

1125

1129

1126

1113

1127

1131

1122

1121

Last two digits of the node numbers along the lower Charles River correspond to the outfall numbers shown in figure 6.

EXPLANATION

SUBCATCHMENT ANDIDENTIFICATION NUMBER

NODE AND IDENTIFICATION NUMBER

CONDUIT AND IDENTIFICATION NUMBER

1030

920108

30

951100 951200

930142

951300 950144

950346

940145

950251

950155

940148 940149

950152

930143

950246

950146

950151

930154

950141

931400

341 441

242

112

110 109

541

111

244

114

246

123

245

115

251

128

255

132

248

124

249

125

252

129

349

126

243

113

127

254

131

122

121

241

108
Appendix 1 77

Figure 1G. Schematic of StormWater Management Model (SWMM) elements used to represent ungaged subbasin (outfalls 57 through 70, fig. 6), lower Charles River Watershed, Massachusetts—

Continued.

Lower River Charles 

Stony Brook

outfall

(no schematic)

1155

1154

1153

1156

1157

1161

1162

1158

1159

1163

950157 950159 951500 950161 950163 950267 951300 950164 951600 950186

257 259 359 261 263 267 367 264 364 270

154 153 155 156 157 161 162 158 159 163

1154

Last two digits of the node numbers along the lower Charles Rivercorrespond to the outfall numbers shown in figure 6.

EXPLANATION

SUBCATCHMENT ANDIDENTIFICATION NUMBER

NODE AND IDENTIFICATION NUMBER

CONDUIT AND IDENTIFICATION NUMBER

950159

154

Appendix 2: Rainfall characteristics of storms at

BWSC-CS4, lower Charles River

Watershed, 2000 water year

Appendix 2 81

Appendix 2. Precipitation characteristics of storms at BWSC-CS4 in the lower Charles River Watershed, Massachusetts, 2000 water year

Date Dura-tion (hrs)

Volume 

(inches)

Intensity 

(inches per hour)

Time since specified precipitation totals

(hours)

Antecedent precipitation amounts 

since specified

time in hours 

(inches)

Total Range Average Maxi-mum Range >0.01 >0.1 >0.2 >0.5 >1.0 24 48 72 168 

10-04-1999 19 0.74 0.67–0.82 0.04 0.42 0.30–0.47 90 90 90 407 407 0 0 0 0.4510-10-1999 7 .25 0.21–0.26 .04 .08 0.06–0.09 28 130 130 130 556 0 .06 .06 .8010-13-1999 13 .51 0.51–1.01 .04 .13 0.13–0.58 75 75 75 212 638 0 0 0 .3110-17-1999 10 1.24 1.14–1.35 .12 .28 0.22–0.28 84 84 84 84 735 0 0 0 .5110-20-1999 17 .71 0.69–0.90 .04 .18 0.15–0.24 44 44 44 44 44 0 .23 1.24 1.7510-23-1999 5 .35 0.35–0.41 .07 .15 0.14–0.18 52 52 52 52 113 0 0 .71 1.9511-02-1999 18 .80 0.74–1.27 .04 .21 0.15–0.29 246 246 246 303 364 0 0 0 011-10-1999 7 .41 0.37–0.41 .06 .14 0.12–0.14 181 181 181 181 563 0 0 0 011-12-1999 12 .14 0.12–0.14 .01 .09 0.08–0.09 42 42 42 230 612 0 .37 .41 .4111-14-1999 3 .10 0.09–0.12 .03 .06 0.06–0.08 30 30 84 272 654 0 .14 .14 .5511-20-1999 2 .15 0.13–0.20 .08 .09 0.09–0.11 147 147 234 422 804 0 0 0 .1011-25-1999 52 .93 0.81–0.93 .02 .20 0.13–0.20 105 105 341 529 911 0 0 0 .1511-27-1999 11 .52 0.40–0.52 .05 .19 0.17–0.21 4 23 31 148 387 .10 .19 .41 .5612-06-1999 21 1.12 1.02–1.33 .05 .29 0.28–0.29 46 215 215 215 1178 0 .02 .02 .0612-14-1999 34 .41 0.36–0.45 .01 .10 0.07–0.10 15 178 178 178 178 .08 .08 .08 .1012-20-1999 7 .27 0.24–0.32 .04 .10 0.10–0.15 112 112 112 324 324 0 0 0 .49

1-03-2000 33 1.06 1.02–1.30 .03 .22 0.20–0.27 30 326 326 657 657 0 .03 .03 .031-10-2000 6 .70 0.70–0.83 .12 .24 0.23–0.28 12 133 133 133 133 .06 .06 .06 1.121-31-2000 3 .31 0.29–0.64 .10 .16 0.12–0.19 16 487 487 487 626 .02 .02 .02 .022-14-2000 12 1.22 1.12–1.32 .10 .19 0.19–0.22 59 329 329 819 958 0 0 .07 .072-24-2000 50 .78 0.67–0.85 .02 .13 0.11–0.14 54 54 247 247 247 0 0 .16 .162-28-2000 11 .21 0.21–0.26 .02 .06 0.06–0.08 29 29 29 29 326 0 .10 .73 .943-11-2000 31 1.56 1.48–1.75 .05 .26 0.20–0.28 38 288 288 328 625 0 .01 .01 .063-16-2000 12 .98 0.87–1.01 .08 .23 0.21–0.24 94 94 94 94 94 0 0 0 1.573-28-2000 6 1.16 1.10–1.53 .19 .31 0.28–0.40 147 228 262 262 368 0 0 0 .01

Appendix 2. Precipitation characteristics of storms at BWSC-CS4 in the lower Charles River Watershed, Massachusetts, 2000 water year [Gage location shown in fig. 10. Shaded cells indicate storm used for model calibration. Range: Range was calculated from the 5 precipitation gages in or near the basin: CDPW-HS2, USGS-CR3, 

BWSC-CS4, MWRA-WS5, and BWSC-WS6. hrs, hours; >, actual value is greater than value shown]
82 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000 4-04-2000 32 0.31 0.16–0.35 0.01 0.08 0.07–0.12 138 139 160 164 166 0 0 0 1.35 4-08-2000 14 .74 0.62–1.01 .05 .13 0.13–0.20 35 81 81 97 97 0 .04 .04 .35 4-18-2000 16 .81 0.73–0.88 .05 .11 0.10–0.13 59 157 225 225 336 0 0 .08 .18 4-21-2000 58 3.39 3.20–3.85 .06 .34 0.34–0.45 13 49 49 49 401 .01 .01 .82 .90 4-26-2000 23 .43 0.31–0.58 .02 .08 0.06–0.09 53 53 53 53 53 0 0 .40 3.64 5-10-2000 17 .79 0.62–0.95 .05 .18 0.18–0.34 33 190 318 394 394 0 .05 .05 .11 5-13-2000 4 .24 0.20–0.46 .06 .10 0.09–0.29 70 70 70 70 481 0 0 .21 .84 5-18-2000 31 .57 0.44–0.60 .02 .11 0.08–0.14 104 104 104 178 589 0 0 0 .24 5-23-2000 5 .32 0.21–0.39 .06 .12 0.08–0.20 77 77 77 77 697 0 0 0 .57 5-24-2000 22 .80 0.71–1.05 .04 .29 0.29–0.45 20 20 20 102 722 .30 .32 .32 .89 6-02-2000 4 .56 0.30–0.96 .14 .40 0.14–0.78 199 212 212 212 956 0 0 0 0 6-06-2000 26 4.40 3.58–4.75 .17 .50 0.37–0.53 20 82 82 82 1042 .04 .04 .04 .60 6-11-2000 12 .80 0.73–0.92 .07 .37 0.28–0.55 108 108 108 108 108 0 0 0 4.44 6-18-2000 9 .14 0.13–0.22 .02 .10 0.07–0.14 20 20 20 148 268 .43 .43 .43 1.36 6-27-2000 5 .21 0.14–1.88 .04 .13 0.10–1.43 20 207 236 364 484 .02 .02 .02 .05 7-09-2000 4 .49 0.42–0.57 .12 .28 0.21–0.31 81 251 288 657 777 0 0 0 .04 7-16-2000 3 .35 0.27–0.82 .12 .21 0.16–0.42 145 145 145 806 926 0 0 0 .49 7-18-2000 3 .75 0.38–0.94 .25 .55 0.30–0.82 60 60 60 869 989 0 0 .35 .35 7-22-2000 7 .32 0.12–0.97 .05 .20 0.06–0.49 77 77 77 77 1069 0 0 0 1.10 7-26-2000 30 2.10 1.74–2.10 .07 .42 0.32–0.42 98 98 98 182 1174 0 0 0 .32

7-30-2000 18 .76 0.70–0.90 .04 .17 0.17–0.23 73 73 73 73 73 0 0 0 2.108-14-2000 12 .34 0.34–0.47 .03 .11 0.07–0.22 90 326 326 326 417 0 0 0 .068-16-2000 2 .27 0.27–0.46 .14 .22 0.22–0.42 32 45 45 383 474 0 .12 .35 .408-18-2000 8 .25 0.22–0.34 .03 .07 0.06–0.10 58 58 58 443 534 0 0 .27 .628-23-2000 3 .37 0.31–0.46 .12 .19 0.19–0.23 110 110 110 561 652 0 0 0 .259-02-2000 9 .46 0.16–0.91 .05 .30 0.11–0.58 224 224 224 788 879 0 0 0 09-15-2000 9 1.50 1.34–1.50 .17 .75 0.49–0.75 47 47 304 1101 1192 0 .02 .12 .129-19-2000 13 .52 0.46–0.80 .04 .32 0.21–0.50 99 99 99 99 99 0 0 0 1.629-26-2000 19 .42 0.42–0.69 .02 .08 0.08–0.14 141 141 141 141 253 0 0 0 .52

Appendix 2. Precipitation characteristics of storms at BWSC-CS4 in the lower Charles River Watershed, Massachusetts, 2000 water year—Continued

Date Dura-tion (hrs)

Volume 

(inches)

Intensity 

(inches per hour)

Time since specified precipitation totals

(hours)

Antecedent precipitation amounts 

since specified

time in hours 

(inches)

Total Range Average Maxi-mum Range >0.01 >0.1 >0.2 >0.5 >1.0 24 48 72 168 
Appendix 3: Observed and simulated runoff

volume and peak discharge for calibration storms

Appendix 3 85

Appendix 3A. Observed and simulated runoff volume and peak discharge for calibration storms at the single-family land-use subbasin, lower Charles River 

Watershed, Massachusetts 

[ft3/s, cubic feet per second]

Date

Runoff volume (inch) Peak discharge (ft3/s)

Observed Simulated Percent

difference Observed Simulated Percentdifference

11-10-1999 0.048 0.072 50 7.5 4.6 -39

11-25-1999 .051 .078 53 9.0 6.0 -33

12-06-1999 .147 .185 26 21.0 16.0 -24

12-15-1999 .051 .080 57 4.8 3.2 -33

12-20-1999 .037 .055 49 8.0 5.0 -38

1-04-2000 .184 .184 0 9.7 10.0 3.1

1-10-2000 .186 .156 -16 15.0 10.0 -33

4-04-2000 .038 .075 97 3.2 3.2 0

4-08-2000 .135 .140 3.7 11.0 6.2 -44

4-18-2000 .118 .161 36 4.0 4.3 7.5

4-26-2000 .027 .103 281 1.6 3.0 88

5-18-2000 .080 .106 33 3.8 3.4 -11

6-02-2000 .089 .119 34 15.0 19.0 27

6-11-2000 .196 .178 -9.2 59.0 32.0 -46

7-09-2000 .091 .088 -3.3 16.0 9.8 -39

7-26-2000 .302 .290 -4.0 17.0 16.0 -5.9

7-31-2000 .141 .142 .7 14.0 8.4 -40

8-14-2000 .047 .056 19 2.2 5.5 150

9-19-2000 .070 .079 13 25.0 28.0 12

9-26-2000 .040 .093 133 4.1 4.1 0
86 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Appendix 3B. Observed and simulated runoff volume and peak discharge for calibration storms at the multifamily land-use subbasin, lower Charles River 

Watershed, Massachusetts

[ft3/s, cubic feet per second]

Date

Runoff volume (inch) Peak discharge (ft3/s)

Observed Simulated Percent

difference Observed Simulated Percentdifference

11-25-1999 0.142 0.284 100 2.3 2.3 0

12-06-1999 .910 .994 9.2 8.5 9.9 16

12-14-1999 .436 .313 -28 2.3 1.6 -30

12-20-1999 .239 .183 -23 3.5 2.6 -26

1-04-2000 .904 .877 -3.0 4.7 4.5 -4.3

1-10-2000 .677 .642 -5.2 6.0 5.3 -12

4-18-2000 .412 .551 34 1.5 2.1 40

4-26-2000 .253 .169 -33 1.3 1.0 -23

5-10-2000 .481 .475 -1.2 5.0 5.1 2.0

5-18-2000 .252 .226 -10 2.0 1.8 -10

6-02-2000 .408 .431 5.6 12.0 10.0 -17

6-11-2000 .732 .545 -26 14.0 14.0 0

7-09-2000 .338 .455 35 5.5 7.0 27

7-26-2000 1.456 1.402 -3.7 8.5 10.0 18

7-31-2000 .419 .518 24 3.9 3.4 -13

8-14-2000 .353 .300 -15 7.0 4.2 -40

8-16-2000 .334 .319 -4.5 12.0 7.1 -41

8-23-2000 .221 .280 27 5.5 7.0 27

9-15-2000 1.258 1.261 .2 20.0 25.0 25

9-19-2000 .338 .336 -.6 8.9 9.6 7.9

9-26-2000 .235 .268 14 2.1 4.0 90

Appendix 3C. Observed and simulated runoff volume and peak discharge for calibration storms at the commercial land-use subbasin, lower Charles River 

Watershed, Massachusetts

[ft3/s, cubic feet per second]

Date

Runoff volume (inch) Peak discharge (ft3/s)

Observed Simulated Percent

difference Observed Simulated Percentdifference

4-26-2000 0.713 0.525 -26 1.7 1.1 -35

5-18-2000 .972 .568 -42 3.1 2.6 -16

6-02-2000 .769 .672 -13 7.1 9.1 28

6-11-2000 1.896 .746 -61 7.3 11.0 51

7-09-2000 .775 .668 -14 7.6 4.6 -39

7-27-2000 1.749 1.256 -28 7.6 7.2 -5.3

7-31-2000 .809 .717 -11 3.6 4.2 17

8-13-2000 .639 .603 -5.6 5.3 3.7 -30

8-16-2000 .562 .595 5.9 10.0 8.0 -20

8-23-2000 .475 .577 21 4.8 6.5 35

9-15-2000 1.275 1.145 -10 18.0 19.0 5.6

9-19-2000 .609 .616 1.1 7.4 7.6 2.7

9-26-2000 .559 .582 4.1 2.0 3.4 70
Appendix 3 87

Appendix 3D. Observed and simulated runoff volume and peak discharge for calibration storms at the Laundry Brook Subbasin, lower Charles River 

Watershed, Massachusetts

[ft3/s, cubic feet per second]

Date

Runoff volume (inch) Peak discharge (ft3/s)

Observed Simulated Percent

difference Observed Simulated Percentdifference

11-10-1999 0.028 0.050 79 15 20 33

11-25-1999 .031 .056 81 14 18 29

12-06-1999 .124 .122 -1.6 56 56 0

12-15-1999 .043 .057 33 13 15 15

12-20-1999 .035 .040 14 17 19 12

1-04-2000 .117 .122 4.3 57 48 -16

1-10-2000 .110 .103 -6.4 82 51 -38

4-04-2000 .053 .057 7.5 15 18 20

4-08-2000 .103 .095 -7.8 44 33 -25

4-18-2000 .092 .108 17 20 22 10

4-26-2000 .109 .073 -33 14 15 7.1

5-10-2000 .133 .122 -8.3 77 78 1.3

5-18-2000 .072 .074 2.8 16 16 0

6-02-2000 .059 .082 39 52 72 38

6-11-2000 .129 .121 -6.2 73 96 32

7-09-2000 .046 .061 33 30 42 40

7-26-2000 .231 .202 -13 90 83 -7.8

7-31-2000 .099 .096 -3.0 51 45 -12

8-13-2000 .029 .026 -10 11 17 55

8-16-2000 .039 .049 26 38 77 103

8-23-2000 .034 .033 -2.9 30 34 13

9-15-2000 .175 .175 0 100 130 30

9-19-2000 .062 .051 -18 72 76 5.6

9-26-2000 .036 .060 67 15 22 47
88 Measured and Simulated Runoff to the Lower Charles River, Massachusetts, October 1999–September 2000

Appendix 3E. Observed and simulated runoff volume and peak discharge for calibration storms at the Faneuil Brook Subbasin, 

lower Charles River Watershed, Massachusetts

[ft3/s, cubic feet per second; in, inch]

Date

Runoff volume (inch) Peak discharge (ft3/s)

Observed Simulated Percent

difference Observed Simulated Percentdifference

11-10-1999 0.061 0.056 -8 13.0 15.0 15

11-25-1999 .057 .059 4 15.0 11.0 -27

12-06-1999 .141 .129 -9 25.0 39.0 56

12-15-1999 .075 .068 -9 8.9 8.6 -3

12-20-1999 .049 .049 0 14.0 14.0 0

1-04-2000 .159 .126 -21 27.0 18.0 -33

1-10-2000 .130 .103 -21 30.0 22.0 -27

4-04-2000 .056 .064 14 7.6 6.6 -13

4-09-2000 .077 .108 40 12.0 15.0 25

4-18-2000 .107 .113 6 9.9 9.9 0

4-26-2000 .097 .127 31 7.6 8.2 8

5-18-2000 .075 .087 16 6.5 7.5 15

6-02-2000 .077 .091 18 19.0 36.0 89

6-11-2000 .097 .159 64 39.0 54.0 38

7-09-2000 .093 .076 -18 20.0 21.0 5

7-26-2000 .207 .269 30 30.0 50.0 67

7-31-2000 .097 .122 26 14.0 20.0 43

8-14-2000 .047 .055 17 7.4 11.0 49

8-16-2000 .059 .057 -3 36.0 29.0 -19

8-23-2000 .062 .056 -10 34.0 29.0 -15
Appendix 3 89

Appendix 3F. Observed and simulated runoff volume and peak discharge for calibration storms at the Stony Brook Subbasin, 

lower Charles River Watershed, Massachusetts

[ft3/s, cubic feet per second]

Date

Runoff volume (inch) Peak discharge (ft3/s)

Observed Simulated Percent

difference Observed Simulated Percentdifference

4-04-2000 0.087 0.078 -10 31 18 -42

4-09-2000 .159 .177 11 120 150 25

4-18-2000 .124 .098 -21 76 25 -67

4-26-2000 .192 .081 -58 65 18 -72

5-10-2000 .122 .115 -5.7 85 60 -29

5-18-2000 .098 .090 -8.2 47 31 -34

6-02-2000 .136 .136 0 260 200 -23

6-11-2000 .185 .115 -38 200 110 -45

7-09-2000 .063 .114 81 65 130 100

7-26-2000 .207 .218 5.3 250 250 0

7-31-2000 .104 .133 28 140 120 -14

8-13-2000 .058 .079 36 16 25 56

8-16-2000 .068 .102 50 89 94 5.6

8-23-2000 .071 .091 28 81 62 -23

9-15-2000 .175 .175 0 350 340 -2.9

9-19-2000 .088 .139 58 210 190 -10

9-26-2000 .069 .084 22 53 21 -60