Simulation of Streamflow in the Pleasant,

Narraguagus, Sheepscot, and Royal Rivers, Maine,

using Watershed Models

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5221

1038000

Sheepscot River

Chisholm

Pond
Cover. Illustration shows watershed model area, stream network, and model response unit boundaries for the Sheepscot River, Maine.
Simulation of Streamflow in the Pleasant, 

Narraguagus, Sheepscot, and Royal Rivers, 

Maine, using Watershed Models

By Robert W. Dudley and Martha G. Nielsen

Scientific Investigations Report 2010–5221

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Dudley, R.W., and Nielsen, M.G., 2011, Simulation of streamflow in the Pleasant, Narraguagus, Sheepscot, and 

Royal Rivers, Maine, using watershed models: U.S. Geological Survey Scientific Investigations Report 2010–5221, 

31 p., at http://pubs.usgs.gov/sir/2010/5221/.
iii

Contents

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

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

Description of the Study River Basins...............................................................................................3

Physiography, Land Cover and Use, and Surficial Geology..................................................3

Climate..................................................................................................................................5

Streamflow...........................................................................................................................5

Methods of Study...........................................................................................................................................7

Data Used...............................................................................................................................................7

Watershed Model .................................................................................................................................8

Characterization of the Basins and Initial Parameterization..............................................12

Meteorological Data Input .......................................................................................................13

Calibration of the Watershed Models ....................................................................................20

Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine...21

Results, Uncertainties, and Limitations of the Watershed Models ............................................25

Summary........................................................................................................................................................27

Acknowledgments.......................................................................................................................................28

References Cited..........................................................................................................................................28

Figures

1–3. Maps showing—

1. Location of selected Atlantic salmon rivers in coastal Maine.....................................2

2. The study basins for the Pleasant, Narraguagus, Sheepscot, and Royal 

Rivers, Maine........................................................................................................................4

3. Network of Maine meteorological stations supplying precipitation and air 

temperature data used in this investigation....................................................................6

4. Graph showing median monthly streamflows measured at U.S. Geological Survey streamgages on the Pleasant (01022260), Narraguagus (01022500), Sheepscot 

(01038000), and Royal Rivers (01060000), Maine......................................................................7

5. Schematic diagram of the operational design of the Precipitation Runoff Modeling 

System (PRMS) ...........................................................................................................................11

6. Maps showing Model Response Units and drainage networks for the watershed 

models of the (A) Pleasant, (B) Narraguagus, (C) Sheepscot, and (D) Royal Rivers.......14

7–10. Graphs showing—

7. Solar radiation data for (A) Pleasant River Basin, (B) Narraguagus River Basin, 

(C) Sheepscot River Basin, and (D) Royal River Basin................................................22

8. Potential evapotranspiration data for (A) Pleasant River Basin, (B) Narraguagus 

River Basin, (C) Sheepscot River Basin, and for (D) Royal River Basin....................23
iv

9. (A) Pleasant River Basin calibrated model output for mean seasonal and annual 

outflow volumes simulating the measured period from August 1, 1980, through 

September 30, 1991; (B) Pleasant River Basin evaluation model output simulating 

the measured period from October 1, 2000, through September 30, 2007; 

(C) Narraguagus River Basin calibrated model output for mean seasonal and 

annual outflow volumes simulating the measured period from August 1, 1980, 

through September 30, 1997; (D) Narraguagus River Basin evaluation model 

output simulating the measured period from October 1, 1997, through September 

30, 2007; (E) Sheepscot River Basin calibrated model output for mean seasonal 

and annual outflow volumes simulating the measured period from August 1, 1980, 

through September 30, 1997; (F) Sheepscot River Basin evaluation model output 

simulating the measured period from October 1, 1997, through September 30, 

2007; (G) Royal River Basin calibrated model output for mean seasonal and annual 

outflow volumes simulating the measured period from August 1, 1980, through 

September 30, 1997; and (H) Royal River Basin evaluation model output simulating 

the measured period from October 1, 1997, through September 30, 2004................24

10. Calibration and evaluation model output for all daily streamflow for the Pleasant 

River Basin (A, B), Narraguagus River Basin (C, D), Sheepscot River Basin (E, F), 

and Royal River Basin (G, H)............................................................................................26

Tables

1. U.S. Geological Survey streamgages used in this study, coastal Maine............................8

2. National Oceanic and Atmospheric Administration’s National Weather Service 

Cooperative Observer Program meteorological stations used in this investigation 

in the vicinity of the coastal study basins, Maine ...................................................................9

3. Modular Modeling System (MMS) Modules used in the Precipitation-Runoff 

Modeling System for this investigation...................................................................................12

4. Model Response Units (MRUs) per study basin, ranges of size, and mean size, 

Maine............................................................................................................................................13

5. Sources of values for selected Model Response Unit (MRU) (distributed) and wholemodel (nondistributed) Precipitation Runoff Modeling System (PRMS) parameters 

for the study basins, Maine.......................................................................................................18

6. Meteorological stations (National Oceanic and Atmospheric Administration’s 

National Weather Service Cooperative Observer Program (NOAA COOP)) in the 

vicinity of the study basins from whose meteorological data (precipitation and 

maximum and minimum air temperature) multiple linear regressions (MLR) were 

derived to be spatially distributed within each study basin................................................20

7. Interquartile ranges (IQR) defining the threshold streamflow values delineating low 

(below the IQR), high (above the IQR), and intermediate (within the IQR, inclusive) 

streamflow regimes for each study basin ..............................................................................21

8. Nash-Sutcliffe efficiency (NSE) statistics for calibration and evaluation model runs 

for each study basin, coastal Maine .......................................................................................27
v

Conversion Factors and Datum

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2)

Volume

cubic foot (ft3) 28.32 cubic decimeter (dm3)

cubic foot (ft3) 0.02832 cubic meter (m3)

Flow rate

foot per second (ft/s) 0.3048 meter per second (m/s)

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

cubic foot per second per square 

mile [(ft3/s)/mi2]

 0.01093 cubic meter per second per square 

kilometer [(m3/s)/km2]

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

million gallons per day per square 

mile [(Mgal/d)/mi2]

1,461 cubic meter per day per square 

kilometer [(m3/d)/km2]

Hydraulic conductivity

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

Transmissivity*

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

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

 °F=(1.8×°C)+32

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

 °C=(°F–32)/1.8

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

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

Altitude, as used in this report, refers to distance above the vertical datum.
THIS PAGE INTENTIONALLY LEFT BLANK
Simulation of Streamflow in the Pleasant, Narraguagus, 

Sheepscot, and Royal Rivers, Maine, using 

Watershed Models

By Robert W. Dudley and Martha G. Nielsen

Abstract

The U.S. Geological Survey (USGS) began a study 

in 2008 to investigate anticipated changes in summer 

streamflows and stream temperatures in four coastal Maine 

river basins and the potential effects of those changes on 

populations of endangered Atlantic salmon. To achieve 

this purpose, it was necessary to characterize the quantity 

and timing of streamflow in these rivers by developing and 

evaluating a distributed-parameter watershed model for a part 

of each river basin by using the USGS Precipitation-Runoff 

Modeling System (PRMS). The GIS (geographic information 

system) Weasel, a USGS software application, was used to 

delineate the four study basins and their many subbasins, and 

to derive parameters for their geographic features. The models 

were calibrated using a four-step optimization procedure 

in which model output was evaluated against four datasets 

for calibrating solar radiation, potential evapotranspiration, 

annual and seasonal water balances, and daily streamflows. 

The calibration procedure involved thousands of model 

runs that used the USGS software application Luca (Let us 

calibrate). Luca uses the Shuffled Complex Evolution (SCE) 

global search algorithm to calibrate the model parameters. 

The calibrated watershed models performed satisfactorily, 

in that Nash-Sutcliffe efficiency (NSE) statistic values for 

the calibration periods ranged from 0.59 to 0.75 (on a scale 

of negative infinity to 1) and NSE statistic values for the 

evaluation periods ranged from 0.55 to 0.73.

The calibrated watershed models simulate daily streamflow at many locations in each study basin. These models 

enable natural resources managers to characterize the timing 

and amount of streamflow in order to support a variety of 

water-resources efforts including water-quality calculations, 

assessments of water use, modeling of population dynamics 

and migration of Atlantic salmon, modeling and assessment of 

habitat, and simulation of anticipated changes to streamflow 

and water temperature resulting from changes forecast for air 

temperature and precipitation. 

Introduction

The Gulf of Maine Distinct Population Segment (GOM 

DPS) of Atlantic salmon (Salmo salar) was classified as 

endangered, and therefore protected, under the Federal 

Endangered Species Act (ESA) in November 2007. In June 

2009, the geographic scope of the listing was expanded to 

include larger river systems; at present, the listing incorporates historically accessible freshwater habitat between the 

Androscoggin and Dennys Rivers, inclusive (fig. 1) (National 

Oceanic and Atmospheric Administration, 2009). All waters 

designated in the associated critical habitat drain to the Gulf of 

Maine. The proximity of these waters to the southern extent of 

the Atlantic salmon’s geographical range makes these populations potentially sensitive to changes in climate. State and Federal fisheries biologists are concerned about past, current, and 

future influences of changing climate and varying hydrologic 

conditions on the survival of Atlantic salmon in these rivers. 

Recent studies have demonstrated strong evidence 

of hydrologic changes during the last 30 to 150 years in 

the northeastern United States. These changes, which are 

consistent with warming air temperatures during winter 

through spring, include significant changes in snowmelt 

runoff earlier each spring; decreasing duration of ice on rivers 

and lakes; decreasing ratio of snowfall to total precipitation; 

and denser and thinner late-winter snowpack (Hodgkins 

and Dudley, 2006a, 2006b; Hodgkins and others, 2005; 

Huntington and others, 2004; Hodgkins and others, 2002; 

Dudley and Hodgkins, 2002). The combined area Maine, 

New Hampshire, Vermont, and the Canadian province of 

New Brunswick exhibit the strongest and most consistent 

changes and drains into the Gulf of Maine. Projections from 

climate models for the northeastern United States indicate 

air-temperature warming, earlier snowmelt runoff, increases 

in annual evaporation, and decreased low streamflows for the 

future (Hayhoe and others, 2007). These “model projections” 

are herein termed projected changes.
2 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

SOMERSET PENOBSCOT

OXFORD

FRANKLIN

WASHINGTON

YORK

PISCATAQUIS

HANCOCK

WALDO

KENNEBEC

CUMBERLAND

KNOX LINCOLN

ANDROSCOGGIN

AROOSTOOK

SAGADAHOC

Base from U.S. Geological Survey and Maine Office of

Geographic Information Systems digital files,

North American Datum of 1983,

Universal Transverse Mercator projection, Zone 19

Scale: 1:1,500,000

0 10 20 30 40 MILES

0 20 30 40 KILOMETERS 10

ATLANTIC OCEAN

Gulf of Maine

Androscoggin River

Narraguagus

River

Sheepscot River

Royal

River

Pleasant River

Dennys

River

UNITED STATES

CANADA

STATES

CANADA

UNITED

45°

44°

70° 69° 68°

ATLANTIC OCEAN

Gulf of Maine

CANADA

UNITED STATES

NEW QUEBEC BRUNSWICK

NEW HAMPSHIRE

VERMONT

MAINE

NEW YORK

MASSACHUSETTS

LOCATION MAP

Area enlarged

Figure 1. Location of selected Atlantic salmon rivers in coastal Maine.
Introduction 3

The Pleasant, Narraguagus, Sheepscot, and Royal Rivers 

(fig. 1) provide important habitat for wild Atlantic salmon. A 

comprehensive recovery program has been designed to protect 

and recover the species so that it can remain viable with 

minimal ongoing management and investment of resources 

(National Marine Fisheries Service and U.S. Fish and Wildlife 

Service, 2004). In 1997, the State of Maine developed 

conservation plans, updated in 2005, for these Atlantic salmon 

rivers in Maine (the Pleasant, Narraguagus, Sheepscot, and 

Royal Rivers, among others) (Maine Atlantic Salmon Task 

Force, 1997; Maine Atlantic Salmon Commission, 2005). 

In 2008, the USGS, through its National Climate Change 

and Wildlife Science Center, began a study of anticipated 

changes in summer streamflows and stream temperatures and 

the potential effects of such changes on endangered Atlantic 

salmon populations (Dudley and others, 2008). To characterize 

the amount and timing of streamflow in these rivers, the study 

developed a distributed-parameter watershed model for each 

river basin. These watershed models could, in turn, support 

follow-on modeling of the effects of climate change on basin 

hydrology. Modeled streamflow output also could provide 

input to survival models for Atlantic salmon populations. This 

report documents the construction, calibration, and evaluation 

of distributed-parameter watershed models for parts of the 

Pleasant, Narraguagus, Sheepscot, and Royal River Basins that 

can inform subsequent survival modeling of Atlantic salmon.

Calibrated watershed models of the study basins provide simulated daily streamflow time series for many subbasin locations through each basin. This enables managers 

of natural resources to characterize the timing and quantity 

of water moving through each basin to support a variety of 

water-resources efforts, including water-quality calculations 

(for example, Ahearn and others, 2005), assessments of wateruse, modeling of Atlantic salmon population dynamics and 

migration, modeling and assessment of habitat, and testing 

scenarios—such as changes to streamflows and water temperature that are anticipated to result from forecasted changes in 

climate. Calibrated models representative of current conditions 

can be used to simulate future traces of streamflow driven by 

downscaled global climate model information. In this manner, 

the watershed models can be used to output an ensemble of 

future streamflow hydrographs representing a range of emissions scenarios simulated by several different global climate 

models. This methodology is currently (2010) being used to 

investigate anticipated changes in summer streamflows and 

stream temperatures and the potential effects of those changes 

on endangered Atlantic salmon populations.

Description of the Study River Basins

The basins of the four coastal rivers were chosen for 

study because the rivers are home to Atlantic salmon, have 

minimal or no regulation of streamflows, and have at least 

15 years of continuous streamgage data. The study basins 

(fig. 2) are representative of the geographic and climatic 

variability of coastal Maine: the Pleasant and Narraguagus 

River Basins are in the eastern coastal climate-response 

region, and the Sheepscot and Royal River Basins are in the 

southern coastal climate-response region as defined by the 

framework for a USGS hydrologic climate-response network 

in Maine (Hodgkins and others, 2009). PRMS models were 

developed for the area draining to a USGS streamgage station 

in each of the four basins.

Draining an area of 126 square miles (mi2

) (Fontaine, 

1982a), the Pleasant River flows predominantly northwest to 

southeast from its headwaters near Pleasant River Lake (altitude, 317 feet (ft)), through a bog named Great Heath (7 mi2

)

in the middle of the basin, to the Atlantic Ocean in the Gulf of 

Maine. The USGS streamgage 01022260 (altitude, 127 ft) on 

the main stem of the Pleasant River near Epping streamgage is 

about 12 mi upstream from the mouth of the river and it gages 

streamflow from a 60.6-mi2

 drainage area at the outlet of the 

Great Heath (Fontaine, 1982a). The Pleasant and Narraguagus 

River Basins share a watershed boundary along the western 

perimeter of the Pleasant River Basin.

The Narraguagus River drains an area of 243 mi2

(Fontaine, 1982a) and flows predominantly northwest to 

southeast from Eagle Lake (altitude, 406 ft) to the Atlantic 

Ocean in the Gulf of Maine (Fontaine, 1982a). The USGS 

streamgage 01022500 (altitude 44 ft) on the main stem of the 

Narraguagus River at Cherryfield is about 6 mi upstream from 

the mouth of the river and it gages streamflow from a 227-mi2

drainage area. 

The Sheepscot River drains an area of 350 mi2

 (Fontaine, 

1982b) and flows predominantly northeast to southwest from 

its headwater near Chisolm Pond (altitude, 348 ft) to the 

Atlantic Ocean in the Gulf of Maine. The USGS streamgage 

01038000 (altitude 101 ft) on the main stem of the Sheepscot 

River at North Whitefield is about 21 mi upstream from the 

mouth of the river, and it gages streamflow from a 145-mi2

drainage area (Fontaine, 1982b). 

The Royal River drains an area of 143 mi2

 (Fontaine, 

1978) and flows predominantly north to south from 

headwaters near Sabbathday Lake (altitude, 299 ft) to the 

Atlantic Ocean in the Gulf of Maine. The discontinued USGS 

streamgage 01060000 (altitude 10 ft) on the main stem of the 

Royal River at Yarmouth was less than 2 mi upstream from the 

mouth of the river, gaging streamflow from a drainage area of 

141 mi2

 (Fontaine, 1978). 

Physiography, Land Cover and Use, and Surficial 

Geology

Rolling topography with little development characterizes 

the parts of the study basins included in the watershed models. 

The peak altitudes in the hilly topography of the basins range 

from about 610 ft in the Royal River Basin and 1,100 ft in 

the Sheepscot River Basin to about 1,450 ft along the basin 

boundaries of the Pleasant and Narraguagus Rivers. Landcover data for Maine derived from Landsat Thematic Mapper 
4 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

45°

44°

70° 69° 68°

Base from U.S. Geological Survey and Maine Office of Geographic Information Systems digital files,

North American Datum of 1983, Universal Transverse Mercator projection, Zone 19

Scale 1:1,320,000

0 10 20 40 MILES

0 20 30

30

10 40 KILOMETERS

01038000

Study basin boundary

Climate-response region boundary

Inland post-glacial marine limit

U.S. Geological Survey streamflow-gaging station and number

Geographic location

EXPLANATION

EASTERN COASTAL

CLIMATE-RESPONSE

 REGION

SOUTHERN COASTAL CLIMATE-RESPONSE REGION

INLAND POST-GLACIAL MARINE LIMIT

ATLANTIC OCEAN

Gulf of Maine

Pleasant River Lake

Pleasant

 River

Eagle

 Lake

Chisholm Pond

Sabbathday

Lake

West Branch

Sheepscot River

Narraguagus River

Sheepscot River

Royal River

Great Heath

Epping

Cherryfield

North Whitefield

Yarmouth

Shaker Hill

Hogback Mountain

Pleasant Mountain

Lead

Mountain

01060000

01038000

01022500

01022260

CANADA UNITED STATES CANADA

Figure 2. The study basins for the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine.
Introduction 5

5 and 7 imagery during the years 1999–2001 (U.S. Geological 

Survey, 2005) indicate that all of the four basins are rural 

and predominantly forested with deciduous, evergreen, and 

mixed-forest types or vegetated with scrub. Other prominent 

classifications of land-cover include forested wetlands and 

open water (lakes and ponds), pastures, and hay fields in 

the Sheepscot and the Royal River Basins, and blueberry 

barrens in the Narraguagus and the Pleasant River Basins. 

Otherwise, all of the study basins have sparsely scattered areas 

of cultivated land, light and heavy forest cuts, regenerating 

forest, and light residential development and road networks. 

The largest change in land use that has occurred in these 

basins is the regeneration of forest in formerly clear-cut or 

agricultural lands. Since around 1880, when the maximum 

extent of the clearing of farmland and the harvesting of forests 

in Maine occurred, statewide forest cover has risen from about 

70 to 90 percent. Irland (1998) estimated that as of 1995, 

about 90 percent of eastern coastal Maine (Washington 

and Hancock Counties, fig. 3) was forested, and that about 

70 to 81 percent of southern coastal Maine (Waldo, Knox, 

Lincoln, Sagadahoc, Cumberland, and York Counties, fig. 3) 

was forested. About 22 percent of the forest land in Maine 

is composed of secondary forest on lands that were formerly 

farmed or pastured (Irland, 1998). Between 1880 and 1995, 

forest cover is estimated to have increased 18 percent in 

Washington County, 22 percent in Hancock County, 

186 percent in Waldo County, 100 percent in Knox, Lincoln, 

Sagadahoc, and Cumberland Counties, and 150 percent 

in York County (Irland, 1998). Though a large amount of 

growth in forest cover has taken place since 1880, estimates 

of statewide forest cover have been stable for the last several 

decades (U.S. Department of Agriculture, 2005).

The study basins lie in a region of broad lowlands that 

the ocean inundated during deglaciation approximately 

12,500 to 14,000 years ago as the margin of glacial ice 

retreated generally parallel to the present-day coastline 

(Randall, 2000; Hunter and Smith, 2001). The inland limit of 

marine inundation (fig. 2) has been determined on the basis of 

marine-limit altitude data and of the distribution of glaciomarine sediments (Thompson and Borns, 1985; Thompson and 

others, 1983). As a consequence of glacial retreat and marine 

inundation, most surficial geologic materials in the basins are 

compact glacial sediment (till), and the remainder of the materials are fine-grained glaciomarine deposits (typically silt, clay, 

and sand), marsh and bog deposits (typically peat, muck, clay, 

silt, and sand), and eskers (sand and gravel ridges deposited by 

glacial meltwater streams) (Thompson and Borns, 1985). 

The Pleasant and Narraguagus River Basins were 

partially inundated during the glacial marine submergence; 

approximately the lower third of the gaged Narraguagus 

River Basin and the lower half of the gaged Pleasant River 

Basin were inundated. In the inundated regions of the basins, 

fine- and coarse-grained glaciomarine deposits (silt, clay, and 

sand) are characteristic of the main-channel corridors, and 

marsh and bog deposits characterize the Great Heath in the 

Pleasant River Basin. The remaining portions of the basins are 

predominantly composed of till interspersed with ice-contact 

glaciofluvial deposits of sand and gravel. The Sheepscot 

River Basin was entirely inundated during the glacial marine 

submergence. Fine- and coarse-grained glaciomarine deposits 

are characteristic of the West Branch Sheepscot corridor, with 

the remainder of the basin composed of till and a few eskers. 

The Royal River Basin was almost entirely inundated during 

the late glacial marine submergence. Fine- and coarse-grained 

glaciomarine deposits (silt, clay, and sand) are characteristic 

of the main-channel corridors, with the remainder of the basin 

largely composed of till (Thompson and Borns, 1985). 

Climate

The climate of coastal Maine is temperate, with mild 

summers and cold winters. The mean annual air temperature in 

eastern coastal Maine, from 1971 to 2000, ranged from 42.8°F 

(at Jonesboro, altitude 185 ft) to 45.2°F (at Belfast, altitude 

30 ft) with mean monthly air temperatures ranging from 

18.2°F in January (at Jonesboro) to 68.2°F in July (at Belfast) 

(National Oceanic and Atmospheric Administration, 2002) 

(fig. 3). The mean annual air temperature in southern coastal 

Maine during the same 30-year period ranged from 44.1°F 

(at West Buxton, altitude 150 ft) to 45.7°F (at Portland 

International Airport, altitude 45 ft) with mean monthly air 

temperatures ranging from 18.3°F in January (at West Buxton) 

to 68.7°F in July (at Portland International Airport) (National 

Oceanic and Atmospheric Administration, 2002). 

Precipitation is fairly evenly distributed during the year 

throughout coastal Maine. Annual mean precipitation in eastern coastal Maine, from 1971 to 2000, ranged from 47.6 in. (at 

Belfast) to 51.3 in. (at Jonesboro); Annual mean precipitation 

in southern coastal Maine ranged from 44.7 in. (at Port Clyde, 

altitude 30 ft) to 48.0 in. (at Brunswick Naval Air Station, 

altitude 70 ft) (National Oceanic and Atmospheric Administration, 2002) (fig. 3). Mean annual evapotranspiration (loss 

of water to the atmosphere by evaporation from the soil and 

transpiration from plants) from 1951 through 1980 ranged 

from about 18 in. in eastern coastal Maine to 19 in. in southern 

coastal Maine (Randall, 1996). 

Streamflow

Flow in rivers in coastal Maine is maintained by a 

combination of groundwater inflow and surface runoff. The 

proportions are not consistent through time and depend on 

climate, seasonal weather conditions, surficial geology, and 

land cover. Median monthly streamflows in the four study 

basins, recorded at USGS streamgages 01022260, 01022500, 

01038000, and 01060000 show a seasonal variation that is 

common in Maine (fig. 4). The largest streamflows in coastal 

Maine typically occur in the spring (March, April, and May), 

when rain falls on dense (ripe) snowpack or on saturated 

soils. Streamflow then recedes as snowmelt ends and evapotranspiration increases. The recession of streamflow typically persists into late summer and early autumn (August and 

September) because of high evapotranspiration. Streamflow in 
6 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

SOMERSET PENOBSCOT

OXFORD

FRANKLIN WASHINGTON

YORK

PISCATAQUIS

HANCOCK

WALDO

KENNEBEC

CUMBERLAND

KNOX LINCOLN

ANDROSCOGGIN

AROOSTOOK

SAGADAHOC

Base from U.S. Geological Survey and Maine Office of Geographic Information Systems digital files,

North American Datum of 1983, Universal Transverse Mercator projection, Zone 19

Scale: 1:1,500,000

0 10 20 30 40 MILES

0 20 30 40 KILOMETERS 10

Orono Corinna

Belfast

Barnard

Woodland

Lewiston

Gardiner

Newcastle

Jonesboro

Port Clyde

Farmington

East Hiram

Springfield

Bridgton 3 NW

Dover-Foxcroft

West Buxton 2 NNW

Grand Lake Stream

West Rockport 1 NNW

Augusta State Airport

Waterville Treatment Plant

Brunswick Naval Air Station

Bangor International Airport

Portland International Airport

Newcastle

01060000

Study basin boundary

U.S. Geological Survey streamflow-gaging station and number

Meteorological station and name

EXPLANATION

01060000

01038000

01022500

01022260

UNITED STATES

CANADA

STATES

CANADA

UNITED

45°

44°

70° 69° 68°

ATLANTIC OCEAN

Gulf of Maine

Figure 3. Network of Maine meteorological stations supplying precipitation and air temperature data used in this investigation.
Methods of Study 7

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

MONTH (FOR PERIODS SPECIFIED FOR EACH STREAMGAGE)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

STREAMFLOW PER SQUARE MILE OF DRAINAGE AREA, 

IN CUBIC FEET PER SECOND 

01022260

01022500

01038000

01060000

Figure 4. Median monthly streamflows measured at U.S. Geological Survey streamgages on the Pleasant (01022260), 

Narraguagus (01022500), Sheepscot (01038000), and Royal Rivers (01060000), Maine. Statistics for Pleasant River were computed 

on the basis of daily mean streamflow data collected during calendar years 1980–91 and 2001–08; for the Narraguagus River on 

the basis of data during 1948–2008; for the Sheepscot River on the basis of data during 1938–2008; and for the Royal River on the 

basis of data during 1949–2004.

late summer is often dominated by groundwater discharge or 

storage release from lakes and wetlands and is frequently augmented by runoff from rainfall events. As evapotranspiration 

decreases in the autumn (October and November), streamflow 

increases. Repeated rainfall events and the occasional contribution of precipitation related to a tropical system can result 

in high streamflow during the autumn. Low streamflow can 

occur during the winter (December, January, and February) if 

precipitation and surface water are frozen for extended periods 

of time. 

Methods of Study

The following sections document the data used for analyses, limitations of those data, and the analyses performed, 

including a description of the watershed modeling application 

used and its input requirements.

Data Used

Streamflow data were collected by the USGS using 

techniques described by Rantz and others (1982). Streamflow 

data have been continuously collected at the streamgage on 

the Pleasant River (01022260) since 1980, at the Narraguagus 

River streamgage (01022500) since 1948, at the Sheepscot 

River streamgage (01038000) since 1938, and at the Royal 

River streamgage (01060000) since 1949 (figs. 2 and 4; 

table 1). Continuous streamflow data used in this study were 

retrieved from the National Water Information System (NWIS, 

http://waterdata.usgs.gov/nwis/, accessed April 2010). Since 

1980, data are common to all four study basins and were 

therefore used for this study for calibrating and evaluating 

the watershed models. The same time period 1980–2007 also 

was chosen to be congruent with the National Climate Change 

Modeling Project (Markstrom and Hay, 2009) in order to more 

effectively compare between projects, and also in case these 

models are to be included in future national modeling efforts.
8 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

Table 1. U.S. Geological Survey streamgages used in this study, coastal Maine.

[Location of streamgages shown in figure 2. USGS, U.S. Geological Survey; Latitude and longitude in degrees, minutes, and seconds; mi2, square miles]

USGS streamgage Latitude 

(north)

Longitude 

(west)

Altitude 

(feet)

Drainage area 

measured at gage

(mi2

)

Period of record 

Number Name used

01022260 Pleasant River near Epping 44° 41′ 52′′ 67° 47′ 14′′ 127 60.6 1980–91, 2000–07

01022500 Narraguagus River at Cherryfield 44° 36′ 29′′ 67° 56′ 7′′ 44 227 1980–2007

01038000 Sheepscot River at North Whitefield 44° 13′ 22′′ 69° 35′ 38′′ 101 145 1980–2007

01060000 Royal River at Yarmouth 43° 47′ 57′′ 70° 10′ 42′′ 10 141 1980–2004

Daily precipitation and minimum and maximum air 

temperature data were used from 23 meteorological stations 

(fig. 3; table 2) in the National Oceanic and Atmospheric 

Administration’s National Weather Service Cooperative 

Observer Program (National Oceanic and Atmospheric 

Administration Cooperative Observer Program, U.S. National 

Weather Service database accessed April 2010, at http://www.

nws.noaa.gov/om/coop/). Streamflow data from the NWIS 

network and meteorological data from the NOAA COOP 

network were both retrieved using the USGS Downsizer 

computer application (Ward-Garrison and others, 2009) 

written in the Java programming language (http://java.sun.

com, accessed April 2010), and designed for selecting, 

downloading, and verifying station-based time-series data for 

modeling environmental resources. 

A 1:24,000-scale USGS digital elevation model (DEM) 

of the study basins was used to describe physical attributes of 

the basins. This 32.8-ft (10 m) DEM is a geographic information system (GIS) dataset containing a spatial grid of data, 

32.8 ft on center, with altitude reported at each grid point. 

DEM data were downloaded from the USGS National Map 

Seamless Server (U.S. Geological Survey, 2008).

Additional physical attributes of the basins were 

described using data on soil, land cover, and forest speciation 

and density. The U.S. General Soil Map (STATSGO) (U.S. 

Department of Agriculture, 1994) delineates general soil units 

and was derived by the National Cooperative Soil Survey 

using 1:250,000-scale topographic quadrangles. This investigation used STATSGO to broadly describe surficial soils and 

soil profile properties in the basins. Quality assurance and 

refinements of soil characteristics were made using a surficial 

geologic map of Maine (Thompson and Borns, 1985). 

Types of land cover were characterized using version 2.0 

of the North American Land Cover Characteristics Data Base 

(NALCC); data which the USGS derived in cooperation with 

the University of Nebraska and the European Commission’s 

Joint Research Centre from satellite imagery collected during 

1992–93 (Loveland and others, 1991). These data were used 

to broadly classify land-cover types in the basins. Quality 

assurance and refinement of land-cover types were achieved 

using a digital land-cover dataset for the State of Maine 

derived from satellite imagery from the years 1999–2001 

and panchromatic imagery from 2004 (Maine Office of 

Geographic Information Systems (MEGIS), Maine LandCover Dataset (MELCD), accessed June 21, 2006, at 

http://megis.maine.gov/catalog/).

The U.S. Forest Type Groups and U.S. Forest Density 

maps were used to broadly characterize dominant forest 

speciation and vegetation density in the basins. Both 

datasets are published by the U.S. Forest Service (Zhu and 

Evans, 1994; Zhu, 1994). Solar radiation data were spatially 

interpolated using regression analysis of a nationwide climate 

network of Natural Resources Conservation Service snowpack 

telemetry stations and NWS climate stations (Hay and others, 

2006). Mean monthly potential evapotranspiration (PET) data 

were interpolated from maps produced by the NWS derived 

from the free water evaporation atlas of Farnsworth and 

others (1982).

Watershed Model

In general, watershed models simulate the generation 

of runoff from a basin when rain reaches the surface of the 

ground and meltwater forms on the surface of the ground. 

Typical input to a watershed model may include precipitation, air temperature, solar radiation, wind, and parameters 

describing the physical characteristics of the basin, including 

slope, aspect, elevation, and soil types. The models use various algorithms and methods of approximation to describe the 

physical processes that affect the movement of water over and 

through the soil. Runoff processes simulated by a watershed 

model may include overland flow, shallow subsurface flow, 

and groundwater flow. Typical output from a watershed model 

is a data time-series of the rate of runoff for a point of interest 

(on a hillside or in a channel) that represents the integrated 

hydrologic response of the upstream drainage area to precipitation input on the basis of a basin’s climatic, hydrologic, and 

physical characteristics.

The USGS Precipitation-Runoff Modeling System 

(PRMS) (Leavesley and others, 2005; Leavesley and others, 1983) was used in this investigation to simulate daily 
Methods of Study 9

Table 2. National Oceanic and Atmospheric Administration’s National Weather Service 

Cooperative Observer Program meteorological stations used in this investigation in the vicinity of 

the coastal study basins, Maine.

[Latitude and longitude in degrees, minutes, and seconds; NW, northwest; NNW, north, northwest]

Meteorological station Latitude 

(north)

Longitude 

(west)

Altitude 

(feet) Period of record used

Number Name

170275 Augusta State Airport 44° 19′ 69° 48′ 350 1980–2007

170355 Bangor International Airport 44° 48′ 68° 49′ 148 1980–95, 1999–2007

170398 Barnard 45° 17′ 69° 9′ 545 1990–2007

170480 Belfast 44° 26′ 68° 59′ 30 1980–2007

170844 Bridgton 3 NW 44° 4′ 70° 45′ 560 1980–2007

170934 Brunswick Naval Air Station 43° 54′ 69° 56′ 70 1980–2007

171628 Corinna 44° 55′ 69° 15′ 297 1980–2007

171975 Dover–Foxcroft 45° 11′ 69° 15′ 460 1980–2007

172238 East Hiram 43° 53′ 70° 45′ 528 1980–2007

172765 Farmington 44° 41′ 70° 9′ 420 1980–2007

173046 Gardiner 44° 13′ 69° 47′ 140 1980–2007

173261 Grand Lake Stream 45° 11′ 67° 47′ 290 1980–2007

174183 Jonesboro 44° 39′ 67° 39′ 185 1980–2007

174566 Lewiston 44° 6′ 70° 13′ 180 1980–2007

175675 Newcastle 44° 3′ 69° 32′ 190 1980–2007

176430 Orono 44° 54′ 68° 40′ 115 1980–2001, 2003–05

176881 Port Clyde 43° 55′ 69° 16′ 30 1989–2007

176905 Portland International Airport 43° 39′ 70° 18′ 45 1980–2007

178353 Springfield 45° 24′ 68° 10′ 440 1980–1998

179151 Waterville Treatment Plant 44° 32′ 69° 39′ 73 1980–2007

179314 West Buxton 2 NNW 43° 41′ 70° 37′ 150 1980–2007

179593 West Rockport 1 NNW 44° 12′ 69° 9′ 380 1980–2007

179891 Woodland 45° 9′ 67° 24′ 140 1980–2007

streamflows for the study basins. PRMS is well-suited for 

modeling runoff from rural basins and has been applied to 

many basins in the United States including the Dennys River 

Basin (Dudley, 2008), Willamette River Basin, Oregon (Laenen and Risley, 1997), Methow River Basin, Washington (Ely 

and Risley, 2001; Ely 2003), Yakima River Basin, Washington 

(Mastin and Vaccaro, 2002), Feather River Basin, California 

(Koczot and others, 2004), Yampa River Basin, Colorado 

(Parker and Norris, 1989), Ah-Shi-Sle-Pah Wash Basin, New 

Mexico (Hejl, 1989), Lake Tahoe and Truckee River Basins, 

California and Nevada (Jeton, 1999a, b), Williams Draw and 

Bush Draw Basins, Colorado (Kuhn, 1989), Tug Fork River 

Basin of Kentucky, Virginia, and West Virginia (Scott, 1984), 

10 basins in Vermont (Olson, 2002), and Bald Mountain and 

Bishop Mountain Brook Basins, Maine (Fontaine, 1987).

PRMS is a deterministic, distributed-parameter modeling 

system. The model is deterministic in that it computationally 

incorporates multiple components of the hydrologic cycle as 

understood through known physical laws or empirical relations in hydrologic science. The modeled hydrologic relations 

are typically governed by quantifiable physical characteristics of the basin. Parameters describing these characteristics 

are assigned in a distributed fashion, representing the spatial 

variation (heterogeneity) in basin characteristics. In this manner, the deterministic, distributed-parameter model is designed 

to simulate the hydrologic system as explicitly as possible. 

Parameters describing the physical characteristics of a 

basin are distributed among subbasins that are referred to as 

Hydrologic Response Units (HRUs), or Model Response Units 

(MRUs) (this report refers to the units as MRUs). The size 

of an MRU is determined on the basis of spatial variation of 

physical characteristics across the basin; MRUs are intended 

to encompass regions with approximately homogeneous 

characteristics of a basin such as slope, aspect, soil type, and 
10 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

vegetation type, among others. A lake or wetland is commonly 

represented by a single MRU because of its homogeneous 

characteristics, for example. Other regions within the basin 

may be represented by one, two, or more MRUs, depending 

on the degree of variability in topography, soils, and other 

basin characteristics.

The following paragraphs from Leavesley and others 

(1983, p. 7–9) provide a good summary of the operational 

design of PRMS (fig. 5).

“System inputs are precipitation, air temperature, 

and solar radiation. Precipitation in the form 

of rain, snow, or a mixture of both is reduced 

by interception [precipitation intercepted by 

vegetation] and becomes net precipitation delivered 

to the watershed surface. The energy inputs of 

temperature and solar radiation drive the processes 

of evaporation [vaporization of water at the water’s 

surface], transpiration [evaporation of water through 

vegetation], sublimation [vaporization of water 

from the solid snow/ice phase], and snowmelt. The 

watershed system is conceptualized as a series of 

reservoirs whose outputs combine to produce the 

total system response. 

The impervious-zone reservoir represents an area 

with no infiltration capacity. The reservoir has a 

maximum retention storage capacity which must be 

satisfied before surface runoff will occur. Retention 

storage is depleted by evaporation when the area is 

snow free. 

The soil-zone reservoir represents that part of the 

soil mantle that can lose water through the processes 

of evaporation and transpiration. Average rooting 

depth of the predominant vegetation covering the 

soil surface defines the depth of this zone. Water 

storage in the soil zone is increased by infiltration 

of rainfall and snowmelt and depleted by evapotranspiration. Maximum retention storage occurs 

at field capacity; minimum storage (assumed to be 

zero) occurs at wilting point. The soil zone is treated 

as a two-layered system. The upper layer is termed 

the recharge zone and is user-defined as to depth 

and water-storage characteristics. Losses from the 

recharge zone are assumed to occur from evaporation and transpiration; losses from the lower zone 

occur only through transpiration. 

The computation of infiltration into the soil zone 

is dependent on whether the input source is rain or 

snowmelt. All snowmelt is assumed to infiltrate until 

field capacity is reached. At field capacity, any additional snowmelt is apportioned between infiltration 

and surface runoff. At field capacity, the soil zone is 

assumed to have a maximum daily snowmelt infiltration capacity. All snowmelt in excess of this capacity 

contributes to surface runoff. Infiltration in excess 

of field capacity first is used to satisfy recharge to 

the groundwater reservoir [deep reservoir], having a 

maximum daily limit. Excess infiltration, above this 

limit, becomes recharge to the subsurface reservoir 

[shallow reservoir]. Water available for infiltration 

as the result of a rain-on-snow event is treated as 

snowmelt if the snowpack is not depleted and as 

rainfall if the snowpack is depleted. 

For rainfall with no snowcover, the volume infiltrating the soil zone is computed as a function of soil 

characteristics, antecedent soil-moisture conditions, 

and storm size. For daily-flow computations, the 

volume of rain that becomes surface runoff is computed using a contributing-area concept [defining 

areas in the basin that contribute to runoff]. Daily 

infiltration is computed as net precipitation less 

surface runoff. 

The subsurface reservoir performs the routing of 

soil-water excess that percolates to shallow groundwater zones near stream channels or that moves 

downslope from point of infiltration to some point of 

discharge above the water table. Subsurface flow is 

considered to be water in the saturated-unsaturated 

and groundwater zones that is available for relatively rapid movement to a channel system. The 

subsurface reservoir can be defined either as linear 

or nonlinear. 

Recharge to the groundwater reservoir can occur 

from the soil zone and the subsurface reservoir. Soil 

zone recharge has a daily upper limit and occurs 

only when field capacity is exceeded in the soil 

zone. Subsurface reservoir recharge is computed 

daily as a function of a recharge rate coefficient and 

the volume of water stored in the subsurface reservoir. The groundwater reservoir is a linear reservoir 

and is the source of all baseflow. Streamflow is the 

sum of direct surface runoff, subsurface flow, and 

baseflow from each [MRU].”

The Modular Modeling System (MMS), developed by 

Leavesley, Markstrom, and others (1996; Leavesley, Restrepo, 

and others, 1996), is a software application that provides 

a framework for developing and integrating algorithms 

for physical-process models (Leavesley and others, 2005). 

Process-specific algorithms for PRMS are stored in MMS in a 

module library from which the algorithms can be selected to 

construct models that simulate a variety of water, energy, and 

biogeochemical processes. This modular approach to modeling enables users to construct custom models using existing 

modules or to develop custom modules for specific applications. The 15 PRMS-specific modules included in the watershed models used in this investigation are described in table 3.
Methods of Study 11

INPUTS

Air temperature Precipitation Solar radiation

Evaporation

Evaporation

Sublimation

Sublimation

Transpiration

Transpiration

Interception

Snowpack

Snowmelt

Evapotranspiration

Groundwater

recharge

recharge

Groundwater flow Streamflow

Surface runoff 

Surface Impervious zone

reservoir

Groundwater reservoir

Recharge zone

Lower zone

Evaporation

Subsurface

Subsurface

reservoir

Soil zone excess 

Throughfall

runoff

Groundwater recharge

Soil zone

reservoir

Subsurface runoff

Groundwater

sink

Figure 5. Schematic diagram of the operational design of the Precipitation Runoff Modeling System 

(PRMS). Modified from figure 2 in Leavesley and others (1983, p. 8).
12 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

Table 3. Modular Modeling System (MMS) Modules used in the Precipitation-Runoff Modeling System for this investigation.

[MRU, model response unit; (U.S. Geological Survey, 2009)]

Module Description

basin_prms.f Declares basin and MRU physical parameters.

basin_sum_prms.f Computes daily, monthly, yearly, and total flow summaries of volumes and flows for all MRUs 

(basin scale).

ddsolrad_hru_prms.f Procedures for distributing solar radiation to each MRU and for estimating missing solar radiation data 

using a relation between maximum temperature and degree-day.

gwflow_casc_prms.f Sums inflow to groundwater reservoirs and computes outflow to streamflow and to a groundwater sink 

if specified.

hru_sum_prms.f Computes daily, monthly, yearly, and total flow summaries of volumes and flows for each MRU.

intcp_prms.f Computes amount of intercepted rain and snow, evaporation from intercepted rain and snow, and net rain 

and snow that reaches the soil or snowpack.

obs_prms.f Reads input variables from the designated data file.

potet_jh_prms.f Determines whether current time period is one of active transpiration and computes the potential 

evapotranspiration for each MRU using the Jensen-Haise formulation.

snowcomp_prms.f Initiates development of a snowpack and simulates snow accumulation and depletion processes using an 

energy-budget approach.

soilzone_prms.f Computes inflows to and outflows from soil zone of each MRU and includes inflows from infiltration, 

groundwater, and upslope MRUs, and outflows to gravity drainage, interflow, and surface runoff to 

downslope MRUs.

soltab_hru_prms.f Computes the potential solar radiation and the sunrise and sunset times for a horizontal surface and for any 

combination of slope and aspect.

srunoff_smidx_casc.f Computes surface runoff and infiltration for each MRU using a nonlinear variable-source-area method.

strmflow_prms.f Calculates daily streamflow, individual storm flows, and daily reservoir routing.

subbasin_prms.f Calculates daily streamflow at basin outlet and at internal subbasins.

xyz_dist.f Distributes meteorological variables (precipitation, and maximum and minimum air temperature) to MRUs.

Characterization of the Basins and Initial 

Parameterization

The GIS Weasel (Viger and Leavesley, 2007), a geographic information system (GIS) interface, was used to 

subdivide the basin into MRUs and to calculate parameters 

for each of the watershed models. The GIS Weasel provides 

a suite of tools to help prepare spatial information, lumped 

or distributed, for input to watershed or other environmental 

models. Using this set of tools provides objective and reproducible methods for generating input parameters for a model. 

In this investigation, the GIS Weasel was used to delineate the 

basins, subdivide the basins into MRUs, and characterize the 

basins’ physical features into the requisite sets of parameters 

for input to PRMS.

The GIS Weasel requires as input a hydrocorrected DEM 

of the basin to be modeled. The ArcHydro data model and 

tools (Djokic, 2008) were used to pre-process and hydrocorrect the raw DEM (for example, topographical sinks need to 

be filled so that all water is routed downstream). Using the 

DEM, the GIS Weasel generates a flow-direction surface, 

which in turn, is used to derive a flow-accumulation surface. 

Each point on the flow-accumulation surface designates the 

upstream drainage area. A drainage network is extracted from 

this surface by finding all points at which the flow accumulation is equal to or greater than a user-specified threshold 

(Viger and Leavesley, 2007). In this investigation, the threshold was calculated as a function of the size of the basin. A 

threshold of 0.096 mi2

 was used for the smallest subbasin (an 

interior drainage basin that contributes to the overall drainage basin) (Pleasant River), up to a threshold of 0.38 mi2

 for 

the largest subbasin (Narraguagus River). These thresholds 

generated a stream network of suitable density for each basin. 

Using the flow-direction surface, the GIS Weasel delineated 

basin boundaries on the basis of user-specified pour points, or 

basin outlets. The pour point for each basin was identified as 

the location of the USGS streamgage (01022260, 01022500, 

01038000, or 01060000) on each of the four rivers.
Methods of Study 13

Next, the GIS Weasel was used to derive MRUs for 

each basin. Initial MRUs were defined by determining the 

contributing area associated with the stream segment for each 

subbasin in the drainage network and splitting these areas with 

the same drainage network into “left-bank” and “right-bank” 

units. Additional MRUs were formed on the basis of specific 

geologic or hydrologic features including significant sand 

and gravel deposits, wetlands (such as the Great Heath), and 

bodies of water for which specific model parameters would 

later be defined to describe the features’ unique hydrologic 

properties. The process resulted in the delineation of 99 MRUs 

for the Pleasant River Basin, 198 MRUs for the Narraguagus 

River Basin, 138 MRUs for the Sheepscot River Basin, and 

140 MRUs for the Royal River Basin (fig. 6; table 4). 

The GIS Weasel was used to derive parameter values 

for the physical geographic features of the study basins 

(parameterization) using the U.S. General Soil Map, North 

American Land Cover Characteristics Data Base, U.S. Forest 

Type Groups, and U.S. Forest Density maps, and the DEM and 

its aforementioned derivative surfaces. Parameters derived for 

each MRU included area, elevation, slope, aspect, vegetation 

type and density, capacities for intercepting precipitation, and 

soil types (table 5). During parameterization, the GIS Weasel 

also determined MRU-specific indices describing connectivity 

of MRUs with the drainage network and with surface-water 

and groundwater reservoirs. The MRU responses were 

grouped by subbasins, enabling output from the models to 

provide estimates of streamflow at any subbasin within 

each basin.

Meteorological Data Input

Daily meteorological data (precipitation, and minimum 

and maximum air temperature) were provided as input to each 

watershed model. A multiple linear regression (MLR) method 

was used to spatially assign daily meteorological data, measured at NOAA cooperative observer program (COOP) stations proximal to each study basin, among the MRUs for each 

basin model. Explanatory variables for each MLR equation are 

longitude (x), latitude (y), and elevation (z) (Hay and others, 

2000). 

For each meteorological variable (MV) and basin, an 

MLR equation was derived for each month to explain the 

spatial variability of precipitation and of air temperature across 

the study basins. Each monthly MLR equation thereby provided the means to compute the daily MV at each MRU in a 

watershed model as a function of each MRU centroid location 

in space (x, y, and z). The derivation of each MLR required the 

computation of coefficients b0, b1, b2, and b3 (equation 1) for 

each MV for each month, on the basis of meteorological station data in or near each study basin:

MV = + b b x b + +y b z 0 1 2 3 , (1)

where

MV is the meteorological variable: daily 

precipitation, in inches, or daily minimum 

temperature, in degrees Fahrenheit, or 

daily maximum temperature, in degrees 

Fahrenheit;

b0 is the regression equation intercept;

b1, b2, b3 are coefficients;

x is the geographic x coordinate for the 

meteorological station, in feet;

y is the geographic y coordinate for the 

meteorological station, in feet; and

z is the elevation for the meteorological station, 

in feet.

Proximal meteorological stations were iteratively included and 

excluded in the MLR derivation procedure until a satisfactory 

regression for each MV was obtained (table 6). Satisfactory 

regression equations included multiple meteorological stations 

(table 6) and were evaluated on the basis of linearity, homogeneity of variance, and normality of the distribution of residuals 

(Helsel and Hirsch, 1992). The PRMS module xyz_dist.f

(table 3) applied the derived MLRs to distribute the meteorological variables to MRUs when the models were run.

Table 4. Model Response Units (MRUs) per study basin, ranges of size, and mean size, Maine.

[USGS, U.S. Geological Survey; mi2, square miles]

USGS streamgages Number of MRUs MRU size (mi2)

Number Name Minimum Maximum Mean

01022260 Pleasant River near Epping 99 0.1 2.5 0.6

01022500 Narraguagus River at Cherryfield 198 0.4 5.2 1.1

01038000 Sheepscot River at North Whitefield 138 0.1 3.5 1.0

01060000 Royal River at Yarmouth 140 0.2 4.2 1.0
14 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

Base from U.S. Geological Survey and Maine Office of Geographic Information Systems digital files,

North American Datum of 1983, Universal Transverse Mercator projection, Zone 19

Scale: 1:110,500

0 1 2 4 MILES

0 2 4 KILOMETERS 1

3

3

68°00' 67°55' 67°50'

44°55'

44°50'

44°45'

44°40'

01022260

Pleasant River

Pleasant

 River

 Lake

Basin boundary

Model stream network

Model response unit

Marine inundation limit

U.S. Geological Survey streamflow-gaging

station and number

01022260

EXPLANATION

A

Figure 6. Model Response Units and drainage networks for the watershed models of the (A) Pleasant, (B) Narraguagus, 

(C) Sheepscot, and (D) Royal Rivers.
Methods of Study 15

Figure 6. Model Response Units and drainage networks for the watershed models of the (A) Pleasant, (B) Narraguagus, 

(C) Sheepscot, and (D) Royal Rivers.—Continued

Base from U.S. Geological Survey and Maine Office of Geographic Information Systems digital files,

North American Datum of 1983, Universal Transverse Mercator projection, Zone 19

Scale: 1:190,750

0 3 6 MILES

0 3 6 KILOMETERS

68°15' 68°10' 68°05' 68°00' 67°55' 67°50'

45°00'

44°55'

44°50'

44°45'

44°40'

44°35'

01022500

Narraguagus

River

Eagle

 Lake

Basin boundary

Model stream network

Model response unit

Marine inundation limit

U.S. Geological Survey streamflow-gaging

station and number

01022500

EXPLANATION

B
16 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

Base from U.S. Geological Survey and Maine Office of Geographic Information Systems digital files,

North American Datum of 1983, Universal Transverse Mercator projection, Zone 19

Scale: 1:150,000

0 2.5 5 MILES

0 2.5 5 KILOMETERS

69°35' 69°30' 69°25' 69°20'

44°30'

44°25'

44°20'

44°15'

44°10'

1038000

Sheepscot River

Chisholm

Pond

Basin boundary

Model stream network

Model response unit U.S. Geological Survey streamflow-gaging

station and number

01038000

EXPLANATION

C

Figure 6. Model Response Units and drainage networks for the watershed models of the (A) Pleasant, (B) Narraguagus, 

(C) Sheepscot, and (D) Royal Rivers.—Continued
Methods of Study 17

0 2.5 5 MILES

0 2.5 5 KILOMETERS

Base from U.S. Geological Survey and Maine Office of Geographic Information Systems digital files,

North American Datum of 1983, Universal Transverse Mercator projection, Zone 19

Scale: 1:155,000

01060000

70°25' 70°20' 70°15' 70°10' 70°05'

44°05'

44°00'

43°55'

43°50'

43°45'

Royal River

Basin boundary

Model stream network

Model response unit

Marine inundation limit

U.S. Geological Survey streamflow-gaging

station and number

01060000

EXPLANATION

D

Figure 6. Model Response Units and drainage networks for the watershed models of the (A) Pleasant, (B) Narraguagus, 

(C) Sheepscot, and (D) Royal Rivers.—Continued
18 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

Table 5. Sources of values for selected Model Response Unit (MRU) (distributed) and whole-model (nondistributed) Precipitation 

Runoff Modeling System (PRMS) parameters for the study basins, Maine.—Continued

[GIS, derived from digital data sources using geographic information systems; Com., computed or estimated on the basis of climatological or hydrologic data 

or other related observations; Def., values as provided by Leavesley and others (1983); Cal., final value determined by way of calibration; MRU, modeling 

response unit; terms between parentheses indicate units of the value; day-1, per day; F-1, per degree Fahrenheit; inch-1, per inch; F, Fahrenheit; PET, potential 

evapotranspiration]

Parameter Description (in [units of measure])

Source

GIS Com. Def. Cal.

Distributed (MRU-dependent) parameters

carea_max Maximum area contributing to surface runoff (decimal fraction). X

cov_type Vegetation cover type. X

covden_sum Summer vegetation cover density (decimal fraction). X

covden_win Winter vegetation cover density (decimal fraction). X

gwflow_coef Groundwater routing coefficient; contribution to streamflow (in day-1). X

gwsink_coeff Groundwater sink coefficient (in day-1). X

gwstor_init Initial storage in each groundwater reservoir (in inches). X

hru_area MRU area (in acres). X

hru_aspect MRU compass-bearing exposure (in degrees). X

hru_deplcrv Index number for snowpack depletion curve. X

hru_elev MRU mean altitude (in feet). X

hru_gwres Index of groundwater reservoir. X

hru_percent_imperv MRU percent impervious area (decimal fraction). X

hru_sfres Index of surface reservoir. X

hru_slope MRU slope (vertical feet/horizontal feet; decimal fraction). X

hru_ssres Index of subsurface reservoir. X

hru_type Index differentiating between land and lake/reservoir MRU types. X

jh_coef_hru MRU air temperature coefficient used in Jensen and Haise (1963) PET

computations (in degrees F-1).

X

rad_trncf Transmission coefficient for short-wave radiation through the winter 

vegetation canopy (decimal fraction).

X

smidx_coef Coefficient in the nonlinear computations for surface runoff from 

contributing area (decimal fraction).

X

smidx_exp Exponent in computations for surface runoff from contributing area 

(in inches-1).

X

snarea_thresh Maximum threshold water equivalent for application of the snow area 

depletion curve (in inches).

X

snow_intcp Snow interception storage capacity for major vegetation type on MRU 

(in inches).

X

snowinfil_max Maximum snow infiltration (in inches per day). X

soil_moist_init Initial value for available water in the soil profile (in inches). X

soil_moist_max Maximum water-holding capacity of the soil profile (in inches). X

soil_rechr_init Initial value for available water in the soil recharge zone (in inches). X

soil_rechr_max Maximum value for available water in the soil recharge zone (in inches). X

soil_type Index indicating MRU soil type. X

soil2gw_max Maximum value for excess soil water routed to groundwater (in inches 

per day).

X

srain_intcp Summer precipitation interception storage capacity for major vegetation 

type on MRU (in inches).

X

ssr2gw_rate Coefficient to route water from subsurface to groundwater (in days-1). X
Methods of Study 19

Table 5. Sources of values for selected Model Response Unit (MRU) (distributed) and whole-model (nondistributed) Precipitation 

Runoff Modeling System (PRMS) parameters for the study basins, Maine.—Continued

[GIS, derived from digital data sources using geographic information systems; Com., computed or estimated on the basis of climatological or hydrologic data 

or other related observations; Def., values as provided by Leavesley and others (1983); Cal., final value determined by way of calibration; MRU, modeling 

response unit; terms between parentheses indicate units of the value; day-1, per day; F-1, per degree Fahrenheit; inch-1, per inch; F, Fahrenheit; PET, potential 

evapotranspiration]

Parameter Description (in [units of measure])

Source

GIS Com. Def. Cal.

Distributed (MRU-dependent) parameters—Continued

tmax_adj MRU maximum temperature adjustment on the basis of slope and aspect 

of the MRU (in degrees F).

X

tmin_adj MRU minimum temperature adjustment on the basis of slope and aspect 

of the MRU (in degrees F).

X

transp_tmax Temperature index to determine specific date of start of transpiration 

period (in degrees F).

X

transp_beg Month to begin summing MRU maximum temperatures; transpiration 

begins when sum is greater than or equal to transp_tmax.

X

transp_end Last month for transpiration computations. X

wrain_intcp Winter rain interception storage capacity for major vegetation type on 

MRU (in inches).

X

Nondistributed (basinwide) parameters

adjmix_rain Monthly adjustment factor for the proportion of rain in a mixed rain/snow 

event (decimal fraction).

X

adjust_rain Downscaling adjustment for rain (decimal fraction). X

adjust_snow Downscaling adjustment for snow (decimal fraction). X

jh_coef Monthly air temperature coefficient used in Jensen and Haise (1963) PET

computations (in degrees F-1).

X

melt_force Julian date to force snowpack to spring snowmelt stage. X

melt_look Julian date to begin looking for spring snowmelt. X

tmax_allrain Maximum temperature above which all precipitation is simulated as rain 

(in degrees F).

X

tmax_allsnow Maximum temperature below which all precipitation is simulated as snow 

(in degrees F).

X
20 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

Table 6. Meteorological stations (National Oceanic and Atmospheric Administration’s National Weather Service Cooperative 

Observer Program (NOAA COOP)) in the vicinity of the study basins from whose meteorological data (precipitation and maximum and 

minimum air temperature) multiple linear regressions (MLR) were derived to be spatially distributed within each study basin.

[USGS, U.S. Geological Survey]

Study basin, 

USGS streamgage

NOAA COOP stations providing meteorological data 

(station identification numbers)

Dependent daily meteorological variable used for MLR

Pleasant River, 01022260 170355, 170398, 171628, 171975, 173261, 174183, 176430 Precipitation

170355, 170398, 170480, 171975, 173261, 174183, 176430, 178353, 179891 Air temperature, maximum

170355, 170398, 170480, 171975, 173261, 174183, 176430, 178353, 179891 Air temperature, minimum

Narraguagus River, 01022500 170355, 170398, 171628, 171975, 173261, 174183, 176430 Precipitation

170355, 170398, 170480, 171975, 173261, 174183, 178353, 179891 Air temperature, maximum

170355, 170398, 170480, 171975, 173261, 174183, 178353, 179891 Air temperature, minimum

Sheepscot River, 01038000 170275, 170480, 170934, 173046, 174566, 175675, 176881, 179151, 179593 Precipitation

170275, 170934, 173046, 174566, 175675, 179593 Air temperature, maximum

170275, 170480, 170934, 172765, 173046, 175675, 176881, 179151, 179593 Air temperature, minimum

Royal River, 01060000 170844, 172238, 173046, 176905, 179314 Precipitation

170275, 170934, 173046, 174566, 175675, 176905 Air temperature, maximum

170275, 170844, 170934, 172238, 173046, 175675, 176881 Air temperature, minimum

Calibration of the Watershed Models

Following initial parameterization using the GIS Weasel, 

the four watershed models were sequentially calibrated to 

determine the values of parameters that cannot be directly 

measured. Calibration used a stepwise, multiple-objective 

method; that is, calibration was carried out in a step by step 

fashion, and each step involved maximizing or minimizing 

model output values (defined by objective functions) to 

most closely match values derived from measured data. This 

stepwise, multiple-objective calibration method follows a 

procedure documented by Hay and others (2006) in their 

application of PRMS to the Yampa River Basin in Colorado; 

the same method was adopted by Dudley (2008) in applying 

PRMS to the Dennys River Basin in Maine. 

Calibration involved a four-step procedure in which 

model output was evaluated against four independent datasets 

by using computed objective functions. The objective functions enabled us to evaluate the fit between the simulated 

model output and measured values; the objective functions 

serve as criteria for the calibration. During each step, selected 

model parameters were calibrated by improving one or more 

associated objective functions. The values of the previously 

calibrated parameters were carried forward into the next 

calibration step. The four-step procedure was repeated until no 

further improvement was made in the simulation.

The four steps with associated calibration datasets and 

objective functions were (1) mean monthly solar radiation for 

the basin, with an objective function of the sum of the absolute difference in the logarithms of measured and of simulated 

solar radiation; (2) basin mean potential evapotranspiration, 

with an objective function of the sum of the absolute difference in the logarithms of measured and of simulated potential 

evapotranspiration; (3) annual and seasonal water balances, 

with multiple objective functions of the sums of the absolute 

value of the normalized residuals for each year and season; 

and (4) daily streamflow, with multiple objective functions 

of the normalized root mean square error for low streamflow 

(streamflow in the lowest quartile), high streamflow (streamflow in the highest quartile), intermediate streamflow (interquartile range), and all streamflow for the historical period of 

record (table 7). 

The four-step calibration procedure described above 

involved thousands of model runs using the software application Luca (Let us calibrate) (Hay and Umemoto, 2006; 

Umemoto and others, 2006). Luca provides a user-friendly, 

systematic method for building and executing user-defined 

calibration procedures for any model constructed with MMS. 

Luca uses the Shuffled Complex Evolution (SCE) global 

search algorithm (Duan and others, 1994) to calibrate the 

model parameters; results of experimental studies indicate 

that the SCE method reliably produces satisfactory solutions 

for large complex optimization problems (Duan and others, 

1994). Dudley (2008) used Luca to calibrate PRMS models 

of the Dennys River and Cathance River Basins, Maine, with 

satisfactory results. 
Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine 21

The Nash-Sutcliffe efficiency (NSE) statistic 

(equation 2) was used as a measure of model performance 

for the four basins in this study; it is a normalized statistic 

that provides a measure of how well simulated output 

matches measured data (Moriasi and others, 2007; Nash and 

Sutcliffe, 1970):

NSE n

Q Q

n

Q Q

obs i sim i

i

n

obs i obs i

i

n = −

( ) −

− ( )













=

=

∑

∑

1

1

1

2

1

2

1

, ,

, ,













. (2)

where

Qobs i, is the ith measurement for basin streamflow,

Qsim i, is the ith simulated basin streamflow,

Qobs i, is the mean of the measured basin streamflow, 

and

n is the total number of measurements.

NSE ranges in value from negative infinity through 1.0; a 

value of 0.0 or less indicates that the mean measured streamflow is a better predictor than the simulated streamflow; and 

values between 0.0 and 1.0 are viewed as acceptable, with 1.0 

indicating a perfect match between every measured and simulated streamflow value (Moriasi and others, 2007). 

Simulation of Streamflow in the 

Pleasant, Narraguagus, Sheepscot, and 

Royal Rivers, Maine

This section describes the results of the SCE calibration 

procedure for the watershed models of the Pleasant, 

Narraguagus, Sheepscot, and Royal Rivers. All four models 

were calibrated and evaluated using measured streamflow 

for two different historical periods. The calibration involved 

adjusting the model parameters to match measured streamflow 

during the calibration period. The evaluation involved 

comparing modeled streamflow to measured streamflow 

without any adjustment of model parameters.

The first step in the four-step Luca calibration procedure 

involved basin mean monthly solar radiation (SR). Modeled 

estimates of SR as a function of daily shortwave radiation, 

estimated from daily air temperature data and time of the solar 

year, adjusted by the slope and aspect (topography) for each 

MRU. In general, the calibrated models yielded simulated SR 

close to the calibration data (fig. 7). Evaluation values were 

satisfactory, with deviations from interpolated values being a 

function of the variability in air temperature data available for 

input for the evaluation periods.

The second step in the SCE calibration procedure 

involved basin mean monthly potential evapotranspiration 

(PET). Modeled estimates of PET are computed using daily 

mean air temperature and daily solar radiation by following a 

procedure developed by Jensen and Haise (1963); the monthly 

variability in modeled PET results for the evaluation period 

thus closely resembles that for solar radiation. Simulated 

potential evapotranspiration values generally agreed with values calculated from PET maps (fig. 8). Simulated values from 

the evaluation period were likewise satisfactory. 

The third step in the SCE calibration procedure related 

simulated annual and seasonal water volumes to basin runoff 

volumes measured at the downstream streamgages. Seasonal 

runoff volumes were defined as total runoff for the months 

associated with the four seasons: winter—December, January, 

February; spring—March, April, May; summer—June, July, 

August; autumn—September, October, November. 

For the Pleasant River Basin, runoff for the 11-year calibration period was 0.0 percent different from measured runoff; 

9 of the 11 years were less than 10 percent different (fig. 9A). 

Total runoff for the 7-year evaluation period was -15.3 percent 

different from measured runoff (fig. 9B); 4 of the 7 years were 

within 10.2 percent different from measured runoff (fig. 9B). 

Calibrated seasonal runoff volumes ranged from 1.9 percent 

different (spring) to -13.1 percent different (winter) from 

measured runoff (fig. 9A); evaluation seasonal runoff volumes 

ranged from -8.7 percent different (autumn) to -25.0 percent 

different (summer) from measured runoff (fig. 9B).

For the Narraguagus River Basin, runoff for the 17-year 

calibration period was 0.6 percent different from measured 

runoff; 15 of the 17 years were 10 percent or better different 

Table 7. Interquartile ranges (IQR) defining the threshold 

streamflow values delineating low (below the IQR), high (above 

the IQR), and intermediate (within the IQR, inclusive) streamflow 

regimes for each study basin (step 4 of the calibration procedure 

outlined in the section, “Calibration of the Watershed Models”).

[USGS, U.S. Geological Survey; ft3/s, cubic feet per second; Statistics 

for Pleasant River, USGS station number 01022260, were computed on 

the basis of daily mean streamflow data collected during calendar years 

1980–91, 2001–08; for Narraguagus River, 01022500, on the basis of data 

during 1948–2008; for Sheepscot River, 01038000, on the basis of data during 1938–2008; and for Royal River, 01060000, on the basis of data during 

1949–2004]

USGS streamgage Interquartile 

range

(ft3

/s) Number Name

01022260 Pleasant River near Epping 53–194

01022500 Narraguagus River at Cherryfield 141–625

01038000 Sheepscot River at North Whitefield 49–322

01060000 Royal River at Yarmouth 62–280
22 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models Interpolated Calibrated Evaluated EXPLANATION JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC MONTH JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC MONTH

0

600500400300200100

0

600500400300200100

BASIN MEAN SOLAR RADIATION, 

IN LANGLEYS PER DAY

BASIN MEAN SOLAR RADIATION, 

IN LANGLEYS PER DAY

A

C

B

D

 Royal River Basin. Spatially Sheepscot River Basin, and (D) Narraguagus River Basin, (C) Pleasant River Basin, (B) Solar radiation data for (A) Figure 7.

interpolated solar radiation data computed from regression analysis of nationwide network of Natural Resources Conservation Service snowpack telemetry stations and National Weather Service climate stations. Calibrated model output for basin mean monthly solar radiation simulates the period of measured 

0, 1991). Evaluation streamflow from August 1, 1980, through September 30, 1997 (except for the Pleasant River whose measured period ends September 3

model output simulates the measured period from October 1, 1997, through September 30, 2007 (except for the Pleasant River whose measured period begins October 1, 2000, and the Royal River whose measured period ends September 30, 2004). 
Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine 23 Interpolated Calibrated Evaluated EXPLANATION JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC MONTH JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC MONTH

0.1800.1600.1400.1200.1000.0800.0600.0400.020

00

BASIN MEAN POTENTIAL EVAPOTRANSPIRATION,

IN INCHES PER DAY

BASIN MEAN POTENTIAL EVAPOTRANSPIRATION,

IN INCHES PER DAY

0.1800.1600.1400.1200.1000.0800.0600.0400.020

A

C

B

D

Figure 8. Potential evapotranspiration data for (A) Pleasant River Basin, (B) Narraguagus River Basin, (C) Sheepscot River Basin, and for (D) Royal River 

eather Service. Calibrated model output for Basin. Spatially interpolated data computed from potential evapotranspiration maps produced by the National W

basin mean monthly potential evapotranspiration simulates the period of measured streamflow from August 1, 1980, through September 30, 1997 (except for the Pleasant River whose measured period ends September 30, 1991). Evaluated model output simulates the measured period from October 1, 1997, through September 30, 2007 (except for the Pleasant River whose measured period begins October 1, 2000, and for the Royal River whose measured period ends September 30, 2004).
24 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

WINTER SPRING SUMMER AUTUMN ANNUAL

SEASON

WINTER SPRING SUMMER AUTUMN ANNUAL

SEASON

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0

50

100

150

200

250

300

350

400

450

500

BASIN RUNOFF, 

IN MILLIONS OF CUBIC FEET

BASIN RUNOFF, 

IN MILLIONS OF CUBIC FEET

0

100

200

300

400

500

600

700

800

900

BASIN RUNOFF, 

IN MILLIONS OF CUBIC FEET

0

100

200

300

400

500

600

700

800

900

BASIN RUNOFF, 

IN MILLIONS OF CUBIC FEET

Measured

Calibrated

Measured

Calibrated

Measured

Evaluated

Measured

Evaluated

Measured

Calibrated

Measured

Evaluated

Measured

Calibrated

Measured

Evaluated

A B

C D

E F

G H

EVALUATION PERIOD

(OCTOBER 1, 1997–SEPTEMBER 30, 2004) 

EVALUATION PERIOD

(OCTOBER 1, 1997–SEPTEMBER 30, 2007) 

CALIBRATION PERIOD

(AUGUST 1, 1980–SEPTEMBER 30, 1997) 

CALIBRATION PERIOD

(AUGUST 1, 1980–SEPTEMBER 30, 1997) 

EVALUATION PERIOD

(OCTOBER 1, 1997–SEPTEMBER 30, 2007) 

EVALUATION PERIOD

(OCTOBER 1, 2000–SEPTEMBER 30, 2007) 

CALIBRATION PERIOD

(AUGUST 1, 1980–SEPTEMBER 30, 1997) 

CALIBRATION PERIOD

(AUGUST 1, 1980–SEPTEMBER 30, 1991) 

Royal River 01060000

Sheepscot River 01038000

Pleasant River 01022260

Narraguagus River 01022500

Figure 9. (A) Pleasant River Basin 

calibrated model output for mean 

seasonal and annual outflow volumes 

simulating the measured period from 

August 1, 1980, through September 30, 

1991; (B) Pleasant River Basin evaluation 

model output simulating the measured 

period from October 1, 2000, through 

September 30, 2007; (C) Narraguagus 

River Basin calibrated model output 

for mean seasonal and annual outflow 

volumes simulating the measured period 

from August 1, 1980, through September 

30, 1997; (D) Narraguagus River Basin 

evaluation model output simulating 

the measured period from October 

1, 1997, through September 30, 2007; 

(E) Sheepscot River Basin calibrated 

model output for mean seasonal and 

annual outflow volumes simulating the 

measured period from August 1, 1980, 

through September 30, 1997; 

(F) Sheepscot River Basin evaluation 

model output simulating the measured 

period from October 1, 1997, through 

September 30, 2007; (G) Royal River 

Basin calibrated model output for mean 

seasonal and annual outflow volumes 

simulating the measured period from 

August 1, 1980, through September 

30, 1997; and (H) Royal River Basin 

evaluation model output simulating the 

measured period from October 1, 1997, 

through September 30, 2004.
Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine 25

from measured runoff (fig. 9C). Total runoff for the 10-year 

evaluation period was 1.0 percent different from measured 

runoff; 5 of the 10 years were 10.3 percent or better different 

from measured runoff (fig. 9D). Calibrated seasonal runoff 

volumes ranged from -0.5 percent different (spring) to 

16.7 percent different (autumn) from measured runoff 

(fig. 9C); evaluation seasonal runoff volumes ranged from 

0.5 percent different (spring) to 25.9 percent different 

(autumn) from measured runoff (fig. 9D).

For the Sheepscot River Basin, runoff for the 17-year 

calibration period was 2.0 percent different from measured 

runoff; 13 of the 17 years were 10 percent or better different 

from measured runoff (fig. 9E). Total runoff for the 10-year 

evaluation period was -1.1 percent different from measured 

runoff; 7 of the 10 years were 10 percent or better different 

from measured runoff (fig. 9F). Calibrated seasonal runoff 

volumes ranged from 1.6 percent different (winter) to 

-12.3 percent different (summer) from measured runoff 

(fig. 9E); evaluation seasonal runoff volumes ranged from 

-0.4 percent different (spring) to -4.8 percent different (winter) 

from measured runoff (fig. 9F).

For the Royal River Basin, runoff for the 17-year 

calibration period was -1.9 percent different from measured 

runoff; 13 of the 17 years were 10.5 percent or better different 

from measured runoff (fig. 9G). Total runoff for the 7-year 

evaluation period was 3.3 percent different from measured 

runoff; 6 of the 7 years were 10 percent or better different 

from measured runoff (fig. 9H). Calibrated seasonal runoff 

volumes ranged from 0.4 percent different (autumn) to 

-19.5 different (summer) from measured runoff (fig. 9G); 

evaluation seasonal runoff volumes ranged from -4.6 percent 

different (autumn) to -25.7 percent different (winter) from 

measured runoff (fig. 9H).

The fourth step in the SCE calibration procedure related 

simulated daily streamflow to basin runoff measured at the 

downstream streamgages (fig. 10). The objective of the 

calibration was to minimize differences between simulated 

and measured daily low, high, and intermediate streamflow. 

In a few cases, when several days or weeks correlated 

poorly (fig. 10) as a result of a mismatch between modeled 

meteorological inputs to the basin and what actually happened 

in the basin (see “Watershed Model Results, Uncertainties, 

and Limitations” section), NSE values for the calibration 

and evaluation periods ranged from 0.55 to 0.75, indicating 

satisfactory simulations overall (table 8).

The Pleasant River Basin (figs. 10A and B) model tended 

to underestimate low streamflow during the calibration and 

evaluation periods. This is most likely a result of inadequately 

modeling the storage effects of the Great Heath located just 

upstream from the USGS streamgage. Future work with this 

model should involve explicit modeling of the storage capacity 

of the Great Heath using the recently developed lakes module 

for PRMS (Dudley, 2008). The models for the Narraguagus 

River Basin (figs. 10C and D), Sheepscot River Basin 

(figs. 10E and F), and Royal River Basin (figs. 10G and H) 

models generally performed satisfactorily, except for a few 

cases when several days or weeks correlated poorly as a 

result of a mismatch between meteorological data inputs to 

the model and what actually meteorologically transpired in 

the basin. 

Results, Uncertainties, and Limitations of the 

Watershed Models

The PRMS watershed models require data on precipitation and air temperature as input to drive the computations; 

thus, the models are highly dependent on the accuracy of those 

data. In this study, precipitation data were largely derived from 

a relatively sparse network of NWS meteorological stations. 

Precipitation records used in this investigation provided a 

point coverage in and around the basins of interest, and were 

interpolated to provide an areal distribution of precipitation 

within the modeled basins. Actual rainfall can vary greatly 

over small distances; thus, the available precipitation dataset 

used in this investigation contributed to imprecise matches 

between simulated streamflow and measured streamflow on an 

event-by-event basis.

Temperature records were similarly derived from the 

relatively sparse network of NWS meteorological stations. 

Temperature data have a significant effect on simulated runoff; 

the data are used in computations of solar radiation, and therefore, in computations of evapotranspiration. Air temperatures 

are a controlling factor in determining the form of precipitation (rain, snow, or mixture of both) and whether existing 

snowpack accumulates or melts, thereby directly affecting the 

timing and amount of precipitation released from frozen-water 

storage in the basins. Thus, just as did the precipitation dataset 

used in this investigation, the temperature dataset contributed 

to imprecise matches between simulated streamflow and measured streamflow on an event-by-event basis.

The computation of runoff by PRMS is a rudimentary 

accounting of streamflow at the MRU (subbasin) scale rather 

than a rigorous simulation of the hydraulics of water movement; the location and velocity of channelized runoff within 

any subbasin is not explicitly modeled, nor are mechanisms 

such as gains from and losses to groundwater through the 

streambed in any given reach.

The lack of groundwater data in the study basins 

introduces uncertainties in the models because there was little 

to no information available to guide the proper modeling of 

groundwater flow throughout the basin. Despite the lack of 

groundwater data and associated uncertainties, the models 

could calibrate simulated streamflow to measured streamflow 

thereby providing a first-cut estimate of the relative amounts 

of surface-water and groundwater contributions to streamflow 

throughout the basin. With more groundwater data, and 

with intensive, explicit modeling of interactions between 

groundwater and surface water by using GSFLOW, subsequent 

studies can very probably improve the performance of the 

four study basin models. GSFLOW is a coupled groundwater 

and surface-water flow model based on the integration 
26 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

1 10,000

1 100 10,000 1 100 10,000

100 1 100 10,000

MEASURED DAILY STREAMFLOW, IN CUBIC FEET PER SECOND

10 10,000

1 100 10,000 1 100 10,000

10 10,000

1

10

100

1,000

10,000

SI

MULATED DAILY STREA

MFLOW,

IN CUBIC FEET PER SECOND 

SI

MULATED DAILY STREAMFLOW,

IN CUBIC FEET PER SECOND

1

10

100

1,000

10,000

1

10

100

1,000

10,000

1

10

100

1,000

10,000

10

100

1,000

10,000

1

10

100

1,000

10,000

SI

MULATED DAILY STREA

MFLOW,

IN CUBIC FEET PER SECOND 

SI

MULATED DAILY STREAMFLOW,

IN CUBIC FEET PER SECOND

1

10

100

1,000

10,000

10

100

1,000

10,000

E F

G H

A B

C D

EVALUATION PERIOD

(OCTOBER 1, 1997–SEPTEMBER 30, 2004) 

EVALUATION PERIOD

(OCTOBER 1, 1997–SEPTEMBER 30, 2007) 

CALIBRATION PERIOD

(AUGUST 1, 1980–SEPTEMBER 30, 1997) 

CALIBRATION PERIOD

(AUGUST 1, 1980–SEPTEMBER 30, 1997) 

EVALUATION PERIOD

(OCTOBER 1, 1997–SEPTEMBER 30, 2007) 

EVALUATION PERIOD

(OCTOBER 1, 2000–SEPTEMBER 30, 2007) 

CALIBRATION PERIOD

(AUGUST 1, 1980–SEPTEMBER 30, 1997) 

CALIBRATION PERIOD

(AUGUST 1, 1980–SEPTEMBER 30, 1991) 

Royal River 01060000

Sheepscot River 01038000

Pleasant River 01022260

Narraguagus River 01022500

Figure 10. Calibration and evaluation model 

output for all daily streamflow for the Pleasant 

River Basin (A, B), Narraguagus River Basin (C, D), 

Sheepscot River Basin (E, F), and Royal River Basin 

(G, H). Calibrated model output for daily streamflow 

simulates the measured period from August 1, 

1980, through September 30, 1997 (except for the 

Pleasant River Basin whose measured period ends 

September 30, 1991. Evaluated model output simulates 

the measured period from October 1, 1997, through 

September 30, 2007 (except for the Pleasant River 

Basin whose measured period begins October 1, 2000, 

and the Royal River Basin whose measured period 

ends September 30, 2004).
Summary 27

Table 8. Nash-Sutcliffe efficiency (NSE) statistics for calibration 

and evaluation model runs for each study basin, coastal Maine.

[USGS, U.S. Geological Survey; NSE value is a measure, between negative 

infinity and 1.0, of the extent to which output simulated by the model matches 

measured data]

USGS streamgage

NSE value 

(range: negative infinity 

to 1.0)

Number Name Calibration

Evaluation

01022260 Pleasant River near Epping 0.59 0.69

01022500 Narraguagus River at Cherryfield 0.72 0.66

01038000 Sheepscot River at North Whitefield 0.75 0.73

01060000 Royal River at Yarmouth 0.74 0.55

of PRMS and the Modular Groundwater Flow Model 

(MODFLOW-2005) (Markstrom and others, 2008).

Overall, the basin models constructed in this investigation performed satisfactorily, with the weakest simulations 

occurring during periods of extremely low streamflow and 

during the winter months. Some periods of unsatisfactory 

performance of the models during winter months could be 

due to sensitivity of the models to air temperature data and 

the difficulty in properly modeling rain, snow, or mixed-phase 

precipitation events. The models may also be sensitive to the 

changing permeability of frozen soils during cold periods. 

Spatially and temporally explicit characterization of 

hydrologic conditions throughout each of the study basins will 

lead to a better understanding of water quantity and quality 

and will support the planning and execution of ongoing and 

future efforts to protect Atlantic salmon. Calibrated watershed 

models can be used as tool to support a variety of crossdiscipline and resource-management investigations and the 

decision making associated with such investigations. 

Summary

Four watersheds in coastal Maine (Pleasant, Narraguagus, 

Sheepscot, and Royal River Basins) were simulated using 

the USGS Precipitation Runoff Modeling Systems (PRMS) 

to investigate anticipated changes in summer streamflow 

and stream temperatures and the potential effects of those 

changes on endangered Atlantic salmon populations. PRMS 

is a deterministic, distributed-parameter modeling system that 

simulates daily streamflow, given inputs of daily minimum and 

maximum temperature and daily precipitation. Development 

of these models helps advance the comprehensive recovery 

programs for endangered species developed by the National 

Marine Fisheries Service and U.S. Fish and Wildlife Service. 

These models also advance the development of watermanagement plans for each of the four river basins that are 

home to protected Atlantic salmon.

Parameters for the geographic features of the study 

basins and subbasins were derived using the GIS Weasel 

and the U.S. General Soil Map, North American Land Cover 

Characteristics Data Base, U.S. Forest Type Groups, and U.S. 

Forest Density maps, and a digital elevation model (DEM) and 

its derivative surfaces. Parameters derived for each subbasin 

(modeling response unit (MRU)) include: area, elevation, 

slope, aspect, vegetation type and density, intercepting 

capacities for precipitation, and soil types.

The stepwise, multiple-objective calibration method used 

in the development of the watershed models followed a fourstep procedure in which model outputs were evaluated against 

four calibration datasets using mathematical optimization 

for solar radiation, potential evapotranspiration, annual and 

seasonal water balances, and daily streamflow. The calibration 

procedure involved thousands of model runs and was carried 

out using the software application Luca, which provides a 

user-friendly, systematic way to build and execute user-defined 

calibration procedures for any model constructed with USGS 

Modular Modeling System (MMS). Luca used the shuffled 

complex evolution global search algorithm to optimize 

model parameters.

Models for the study basins were calibrated using 

17 years of streamflow data collected from August 1, 

1980, through September 30, 1997, except for the Pleasant 

River Basin which ends September 30, 1991. Ten years of 

streamflow record from October 1, 1997, through September 

30, 2007, were used as an evaluation dataset, except for the 

Pleasant River Basin, the record for which begins October 1, 

2000, and the Royal River Basin, the record for which ends 

September 30, 2004.

The calibrated watershed models simulate daily streamflow at many locations in each study basin. These models 

enable natural-resources managers to characterize the timing and amount of streamflow to support a variety of waterresources efforts, including water-quality calculations, 

assessments of water use, modeling of population dynamics 

and migration of Atlantic salmon, modeling and assessment of 

habitat, and simulation of anticipated changes to streamflow 

and water temperature resulting from forecasted changes in 

precipitation and in air temperatures.

The watershed models performed well, with the weakest simulations occurring during periods of extremely low 

streamflow and during the winter months. Some unsatisfactory 

performance of the models during the winter months could be 

due to sensitivity of the models to air temperature data, the difficulty in properly modeling rain, snow, or mixed precipitation 

events, and possible sensitivity to the changing permeability of 

soils during cold periods.
28 Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models

PRMS watershed models require data on precipitation 

and air temperature as input to drive the computations; thus, 

the models are highly dependent on the accuracy of those data. 

In this study, precipitation and temperature data were largely 

derived from a relatively sparse National Weather Service 

(NWS) meteorological data network. The computation of 

streamflow by PRMS is a rudimentary accounting of streamflow at the subbasin scale, and not a rigorous simulation of 

the hydraulics of water movement; the location and velocity 

of channelized runoff within any subbasin is not explicitly 

modeled, nor are mechanisms such as gains from and losses to 

groundwater through the streambed in any given reach.

The lack of groundwater data in the study basins introduced uncertainties in the models because there was little to 

no information available to guide the modeling of groundwater flow throughout the basins. Nevertheless, these watershed models simulated streamflow calibrated to measured 

streamflow provide a first-cut estimate at quantifying relative 

amounts of surface-water and groundwater contributions to 

streamflow throughout the watersheds.

Acknowledgments

The authors thank the USGS watershed modeling 

group—Lauren Hay, Steve Markstrom, Steve Regan, and 

Roland Viger for helpful technical support, advice, and 

guidance. Reviews by Glenn Hodgkins, Katherine Chase, 

and Alice Koller, USGS, resulted in scientific and editorial 

improvements in this report.

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Prepared by the Pembroke and Lafayette Publishing 

Service Centers.

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Dudley and Nielsen—Simulation of Streamflow in the Pleasant, Narraguagus, Sheepscot, and Royal Rivers, Maine, using Watershed Models—SIR 2010–5221