U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5179

Prepared in cooperation with the Maine Department of Environmental Protection

June and August Median Streamflows Estimated 

for Ungaged Streams in Southern Maine
Cover. Map shows location of study area.
June and August Median Streamflows 

Estimated for Ungaged Streams in 

Southern Maine

By Pamela J. Lombard

Prepared in cooperation with the Maine Department of Environmental Protection

Scientific Investigations Report 2010–5179

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: 2010

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

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

reproduce any copyrighted materials contained within this report.

Suggested citation:

Lombard, P.J., 2010, June and August median streamflows estimated for ungaged streams in southern Maine: 

U.S. Geological Survey Scientific Investigations Report 2010–5179, 16 p., at http://pubs.usgs.gov/sir/2010/5179/.
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................2

Description of Study Area ...................................................................................................................2

Data Collection and Analysis.......................................................................................................................2

Station Selection and Streamflow Measurements.........................................................................5

Basin Characteristics...........................................................................................................................5

Computation of June and August Median Streamflows at Long-Term 

Continuous-Record Stations .................................................................................................8

Estimation of June and August Median Streamflows at Partial-Record Stations.....................9

June and August Median Streamflows Estimated for Ungaged Streams .........................................10

Statistical Methods.............................................................................................................................10

Ordinary Least-Squares Regression ......................................................................................12

Weighted Least-Squares Regression.....................................................................................12

Average Standard Error of Prediction....................................................................................12

Three-Variable Models ......................................................................................................................12

One-Variable Models .........................................................................................................................13

Summary and Conclusions.........................................................................................................................14

Acknowledgments.......................................................................................................................................15

References Cited..........................................................................................................................................15

Figures

1. Map showing location of study area, Gulf of Maine line, and streamgage stations 

used as index stations in Maine, New Hampshire, and Massachusetts ............................3

2. Map showing location of partial-record and continuous-record streamgage stations 

used in regression analyses for southern Maine....................................................................4

3. Graph showing relation of base-flow measurements at partial-record station Wescott 

Brook near Gorham, Maine, USGS station number 010641125, and concurrent daily 

mean streamflow at index station Little Androscoggin River near South Paris, Maine, 

USGS station number 01057000, 2006–08..................................................................................9

4. Graph showing two-dimensional range of explanatory variables drainage area and 

percentage of basin underlain by sand and gravel aquifers used in regression 

equations for predicting June and August median streamflows on ungaged streams 

in southern Maine.......................................................................................................................13

5. Graph showing two-dimensional range of explanatory variables drainage area and 

distance from the basin centroid to the Gulf of Maine line used in regression 

equations for predicting June and August median streamflows on ungaged streams 

in southern Maine.......................................................................................................................14
iv

Conversion Factors and Datum

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square foot (ft2) 929.0 square centimeter (cm2)

square foot (ft2) 0.09290 square meter (m2)

square mile (mi2) 2.590 square kilometer (km2)

Flow rate

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]

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).

Tables

1. Partial-record streamgage stations and selected basin characteristics used in 

regression analyses, southern Maine.......................................................................................6

2. Long-term continuous-record streamgage stations and selected basin characteristics 

used in regression analyses, southern Maine.........................................................................7

3. Long-term continuous-record streamgage stations in Maine, New Hampshire, and 

Massachusetts used as index stations.....................................................................................8

4. Point coordinates that define the Gulf of Maine line..............................................................8

5. Weighted June and August median streamflows at partial-record streamgage 

stations in southern Maine .......................................................................................................11
Abstract

Methods for estimating June and August median 

streamflows were developed for ungaged, unregulated 

streams in southern Maine. The methods were developed 

using streams with drainage areas ranging in size from 0.4 to 

74 square miles, with percentage of basin underlain by a sand 

and gravel aquifer ranging from 0 to 84 percent, and with 

distance from the centroid of the basin to a Gulf of Maine line 

paralleling the coast ranging from 14 to 94 miles. Equations 

were developed with data from 4 long-term continuous-record 

streamgage stations and 27 partial-record streamgage stations. 

Estimates of median streamflows at the continuous-record and 

partial-record stations are presented. A mathematical technique 

for estimating standard low-flow statistics, such as June and 

August median streamflows, at partial-record streamgage 

stations was applied by relating base-flow measurements 

at these stations to concurrent daily streamflows at nearby 

long-term (at least 10 years of record) continuous-record 

streamgage stations (index stations). Weighted least-squares 

regression analysis (WLS) was used to relate estimates of 

June and August median streamflows at streamgage stations 

to basin characteristics at these same stations to develop 

equations that can be used to estimate June and August median 

streamflows on ungaged streams. WLS accounts for different 

periods of record at the gaging stations. 

Three basin characteristics—drainage area, percentage 

of basin underlain by a sand and gravel aquifer, and distance 

from the centroid of the basin to a Gulf of Maine line 

paralleling the coast—are used in the final regression equation 

to estimate June and August median streamflows for ungaged 

streams. The three-variable equation to estimate June median 

streamflow has an average standard error of prediction from 

-35 to 54 percent. The three-variable equation to estimate 

August median streamflow has an average standard error 

of prediction from -45 to 83 percent. Simpler one-variable 

equations that use only drainage area to estimate June and 

August median streamflows were developed for use when less 

accuracy is acceptable. These equations have average standard 

errors of prediction from -46 to 87 percent and from -57 to 

133 percent, respectively. 

Introduction

The State of Maine recently adopted In-stream Flow 

Standards (Maine State Legislature, 2007) to maintain 

streamflows according to the natural variations of flows and 

water levels. Maine’s In-stream Flow Standards are based 

on six seasonal base flows—winter, spring, early summer, 

summer, fall, and early winter—and are intended to be 

protective of natural aquatic life and designated water uses. 

Early summer and summer seasonal flows have been defined 

in the In-stream Flow Standards to be equivalent to June 

and August median flows, respectively. Currently (2010) 

few streamgage stations on small streams in southern Maine 

(drainage areas less than 100 mi2) have sufficient long-term 

records (at least 10 years) to estimate low-flow statistics in 

this region. For sites without a streamgage station, equations 

used to estimate streamflow statistics on the basis of basin 

characteristics are critical tools for estimating low-flow 

statistics and for monitoring and maintaining Maine’s flow 

standards. Streamflow statistics, such as monthly median 

streamflows, are used to evaluate water availability and the 

adequacy of streamflow at a site for the development of 

water supplies, disposal of wastes, generation of electricity, 

irrigation of agricultural land, maintenance and restoration of 

aquatic habitat, and conservation of watersheds. Equations 

are not yet available to estimate monthly median flows for 

ungaged basins of all sizes throughout the state of Maine. 

In most cases a central value of a distribution of 

streamflows, such as the median, is preferable to a value that 

may be skewed by a few extreme observations, such as the 

mean (Helsel and Hirsch, 1992). The median streamflows 

referred to in this report are based on the mean of the monthly 

medians of the annual series of flows for June and August, 

respectively. Not only does this computational method provide 

an estimate of expected flows in June or August, but it also 

allows for an estimation of the error of this estimate. Methods 

for estimating low-flow statistics at partial-record stations on 

the basis of correlations between daily mean discharges at the 

partial-record streamgage stations and concurrent daily mean 

discharges at nearby continuous-record streamgage stations 

are presented by Riggs (1972). Riggs also outlines a technique 

June and August Median Streamflows Estimated for 

Ungaged Streams in Southern Maine

By Pamela J. Lombard
2 June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine

of regionalizing low-flow characteristics of rivers by multiple 

regression of basin characteristics, such as drainage area and 

surficial geology. 

Equations are currently available to estimate monthly 

median flows throughout the State for basins ranging in size 

from 10 to 1,400 mi2 (Dudley, 2004). Statewide equations use 

basin characteristics such as drainage area, percentage of basin 

underlain by a sand and gravel aquifer, and distance to a Gulf 

of Maine line that parallels the coast to estimate the annual 

7-day low flow with a 10-year recurrence interval (7Q10) and 

monthly mean and median flows in Maine. 

The equations in this report add to the set of Maine 

regression equations used to estimate streamflows of all magnitudes at all locations and basin sizes within the state. This 

is the third in a series of reports developing regional equations for estimating August median flows on small basins in 

Maine. The southern Maine equations presented here complement equations previously developed for northern and eastern 

Maine. The regional studies of small basins on ungaged 

streams in eastern Aroostook County, Maine, (Lombard and 

others, 2003) and August median streamflows on ungaged 

streams in eastern coastal Maine (Lombard, 2004b) have demonstrated that estimates of August median streamflow developed from statewide equations designed for basins with large 

drainage areas (greater than 10 mi2) and small percentages of 

sand and gravel aquifers (less than 30 percent) are not applicable to all small basins (less than 10 mi2

) in Maine, especially 

those basins underlain by greater than 30 percent sand and 

gravel aquifers. The percentage of the basin underlain by sand 

and gravel aquifers and the drainage area were used in the 

equation to estimate August median streamflows for small 

basins in eastern coastal Maine (Lombard, 2004b). Mean basin 

elevation and drainage area were used in the equation to estimate August median streamflows for small basins in eastern 

Aroostook County, Maine (Lombard and others, 2003). A fact 

sheet developed to provide guidance for selecting and applying Maine streamflow regression equations can be accessed at 

http://pubs.usgs.gov/fs/2004/3001/ (Lombard, 2004a).

Management and effective use of water resources in 

southern Maine could benefit from low-flow estimation 

techniques developed specifically for small streams in this 

region. Thus in 2006, the U.S. Geological Survey (USGS) 

began a 5-year cooperative study with the Maine Department 

of Environmental Protection (MDEP) to develop regression 

equations that could be used to improve estimates of June and 

August median streamflows for ungaged, unregulated streams 

in southern Maine. 

Purpose and Scope

This report presents equations to be used for the estimation of June and August median streamflows for streams in 

York, Cumberland, and southwestern Oxford Counties in 

southern Maine, as well as an estimate of the accuracy of 

these equations. The report describes (1) how instantaneous 

streamflow measurements at 27 partial-record streamgage stations were correlated to daily mean streamflows at long-term 

continuous-record streamgage stations to estimate June and 

August median streamflows at the partial-record stations and 

(2) how regression equations were developed to predict June 

and August median streamflows on small, ungaged streams by 

using data from 4 long-term continuous-record and 27 partialrecord streamgage stations.

Description of Study Area

This study includes sites in York, Cumberland, and 

southern Oxford Counties in southern Maine (fig. 1). York 

and Cumberland counties encompass 991 and 835 mi2, 

respectively, and as of 2007, had populations of 201,000 and 

275,000, respectively (U.S. Census Bureau, 2009). This is the 

most heavily populated region of Maine. The surficial geologic 

materials of the basins in these counties are predominantly 

crystalline and sedimentary rocks overlain by glacial deposits. 

Localized, discontinuous sand and gravel aquifers are scattered throughout the region (Thompson and Borns, 1985).

The major river basins in southern Maine are the 

Piscataqua River Basin, which drains 1,018 mi2 and includes 

the Salmon Falls River Basin (these rivers form Maine’s 

southern border with New Hampshire); the Saco River Basin, 

which drains 1,700 mi2 at the mouth; and the Presumpscot 

River Basin, which drains 647 mi2 at the mouth and includes 

Sebago Lake. In addition, there are many small coastal river 

basins that drain directly to the Atlantic Ocean, including the 

Royal River, the Mousam River, the Kennebunk River, and the 

York River Basins (fig. 2).

Cold winters and cool summers typify the climate in 

southern Maine. The average annual temperature based on 

the 30-year period from 1971 to 2000 in Portland is 45.7°F; 

mean monthly temperatures ranged from 21.7°F in January 

to 68.7°F in July. The mean annual precipitation is 45.8 in. 

in Portland. Precipitation is uniformly distributed throughout 

the year (National Oceanic and Atmospheric Administration, 

2002). High streamflows typically occur in spring and late 

fall, and low streamflows generally occur in the summer and 

early fall. During the summer months, streamflow comes from 

groundwater discharged from aquifers (base flow) and rainfall 

from summer storms. 

Data Collection and Analysis

A continuous-record streamgage station (continuousrecord station) is a station that records data with sufficient 

frequency to define daily mean streamflows. A partial-record 

streamgage station (partial-record station) is a station at which 

discrete measurements are made over a period of time without 

continuous data being recorded or computed. For the purposes 

of this report, continuous-record stations are divided into 

those with less than 10 years of record (short-term stations) 
Data Collection and Analysis 3

Figure 1. Location of study area, Gulf of Maine line, and streamgage stations used as index stations in Maine, New Hampshire, 

and Massachusetts.

Gulf of Maine line

B

A

70° 68° 66°

48°

46°

44°

Maine

0 20 40 MILES

EXPLANATION

Study area

Major rivers and tributaries

County boundary

Streamgage used as index station,

and number

National boundary United States and Canada 

Gulf of Maine line and 

location of endpoints A and B

0 20 40 KILOMETERS

Base from U.S. Geological Survey digital files, scale 1:2,000,000

projection Universal Transverse Mercator, zone 19

York

Co.

Cumberland Co.

Oxford

Co.Maine

Maine

Atlantic Ocean

Quebec

New Brunswick

Nova Scotia

New Hampshire

Massachusetts

01038000

01101000

01073000

01037380 01054200

01054200

01057000

01064801

UNITED STATES

CANADA
4 June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine

Figure 2. Location of partial-record and continuous-record streamgage stations used in regression analyses for southern Maine.

Portland

Royal Rive r

Piscataq u a Riv er Presumpscot R i v er

Saco River

Kennebunk Riv er

Mousam Rive

S

r

almon Falls River Yo r k River

Piscat aqua River

Sebago Lake

71° 70°30' 70° 69°30'

44°30'

44°

43°30'

43°

0 5 10 MILES

0 5 10 KILOMETERS

Base from U.S. Geological Survey digital files, scale 1:2,000,000

projection Universal Transverse Mercator, zone 19

Streams and brooks are not shown on this scale of map. 

York

County

Cumberland

County

Oxford

County

Gulf of Maine line

ATLANTIC OCEAN

MAINE

Study Area

01063310

01049550

01054200

01057000

01064020

01067960

01067990

01067880

01067920

01059700 01059940

01064143

01064135

01064111

01064112

01064583

01065350

01066110

01065210

01066510

01067100

01064193

01067910

01072543

01072490 01069695

01069690

01069750

01069900

01069950

010641125

EXPLANATION

Study area

County boundary

Rivers in study area

Gulf of Maine line

Continuous-record 

station and number

Partial-record 

station and number

01049550

01059700
Data Collection and Analysis 5

and those with equal to or greater than 10 years of record 

(long-term stations). Although 10 years of record is defined 

as long-term for this report due to the very few streamgage 

stations in this region, it is the minimum to be used in calculating streamflow statistics, such as monthly median streamflow 

because longer periods result in more accurate statistics. Index 

stations have long-term mean daily streamflow measurements 

that correlate well with base-flow measurements made at a 

partial-record station. 

Ideally, equations used to estimate June and August 

median streamflows on small, ungaged streams in southern 

Maine would be developed with long-term data from stations 

on small streams in the same region. Because there was only 

one continuous-record station on a small unregulated stream 

in southern Maine at the beginning of this study (2006), 

streamflow data for partial-record stations extended by using 

streamflow measurements from index stations located in 

central Maine, southeastern New Hampshire, and northeastern 

Massachusetts were used to develop the equations (fig. 1). 

Low-flow statistics at long-term stations were calculated 

directly from the data. 

Station Selection and Streamflow 

Measurements

Twenty-seven partial-record stations were established for 

this project (table 1). In addition, four long-term continuousrecord stations in Maine with drainage areas of less than 

75 mi2 and located within 30 mi of the study area were used 

in the regression analyses (table 2). Of the four long-term 

stations used (fig. 2), one is no longer in operation (Togus 

Stream at Togus, Maine, 01049550) but has sufficient 

historical record to calculate monthly median flows. Thus 

31 stations were used in the regression analyses to develop 

equations to estimate June and August median streamflows 

on ungaged streams. All 31 stations have relatively small 

drainage areas (from 0.4 to 75 mi2) and are within 30 mi 

of the study area (fig. 2). All 31 stations are unregulated, 

meaning that they are unaltered by human activities such as 

impoundments, diversions, and (or) withdrawals.

Continuous-record stations were chosen as index 

stations if their daily mean flow correlated with base-flow 

measurements made at a partial-record station and were 

used to estimate streamflow statistics at the partial-record 

stations. Ten long-term continuous-record stations were 

tested for use as index stations, including the three long-term 

stations described above that are currently in operation and 

seven additional stations—all with drainage areas of 0.73 to 

145 mi2. Stations were required to have a period of record 

concurrent with the record of a partial-record station in order 

to be used as an index station. Ideally, index stations would 

be close to partial-record stations geographically and have 

drainage areas about the same size as the drainage areas of 

the partial-record stations (less than 100 mi2). Because few 

long-term continuous-record stations in the region meet these 

criteria, stations located up to 50 mi away from the region, 

including two stations in New Hampshire and one station in 

Massachusetts, were tested for use as index stations. Seven 

long-term stations were chosen as index stations on the basis 

of streamflow correlations with at least one partial-record 

station (fig. 1; table 3). The range of the periods of record for 

the selected index stations is 10 to 94 years. All streamflow 

data for continuous-record and partial-record stations can be 

found online (U.S. Geological Survey, 2010).

Standard USGS methods were used to make all 

streamflow measurements at the partial-record stations. 

Measurements were made using wading current-meter 

methods, portable Parshall flume methods, and volumetric 

methods (Rantz and others, 1982). Streamflows at the partialrecord stations were measured during independent base flows, 

flows separated by periods of direct runoff associated with 

rainstorms. A range of flows throughout the summer months 

was needed, and flows that changed rapidly or flows that 

could be attributed directly to direct runoff were avoided. 

Measurements of independent low-flow events were made 

within a 30-hour period at all stations. 

Basin Characteristics

Basin characteristics evaluated for use as explanatory 

variables had to make hydrologic sense, be reasonably easy 

to measure, and have the potential to explain a significant 

amount of the variability of the response variable. Topographic, climatic, and geologic basin characteristics that could 

potentially explain some of the variability of June or August 

median streamflows were delineated and calculated using a 

geographic information system (GIS). All coordinates and 

distance measurements were referenced to the North American 

Datum of 1983 (NAD 83), Universal Transverse Mercator 

zone 19 coordinate system.

In all, eight categories of basin characteristics were 

evaluated. (1) Drainage area, the area of each drainage 

basin in square miles, was delineated manually in GIS 

using the best available topographic data (typically 10 to 

20-foot contour lines from USGS 1:24,000 quadrangles). 

The intersection of these drainage-basin boundaries with 

other GIS layers were used for calculating additional basin 

characteristics. (2) Minimum, maximum, and mean basin 

elevation; elevation range; and mean basin slope were 

calculated from the intersection of the drainage area boundary 

with USGS 10-meter digital elevation models (DEMs). The 

DEM was converted into a slope layer using the Spatial 

Analyst extension, and the mean basin slope (as a percent) 

was calculated for each basin. (3) The percentage of the basin 

underlain by sand and gravel aquifers was calculated from 

the intersection of the drainage area boundary with sand and 

gravel aquifer map polygons made by the Maine Department 

of Conservation, Maine Geological Survey, at a 1:24,000 scale 

accessed under aquifer polygons at http://megis.maine.gov/

catalog/ (Maine Geological Survey, 2003). (4) Percentage 
6 June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine

Table 1. Partial-record streamgage stations and selected basin characteristics used in regression analyses, southern Maine.

[USGS, U.S. Geological Survey; Latitude and longitude are referenced to the North American Datum of 1983; ° ′ ′′, degrees, minutes and seconds; mi2, square 

miles; trib, tributary; All partial-record stations had at least 10 base-flow measurements between 2006 and 2008]

USGS 

station 

number

Station name and location Latitude

(° ’ ”)

Longitude

(° ’ ”)

Index 

station 

number

Drainage 

area 

(mi2)

Percentage 

of basin 

underlain 

by sand 

and gravel 

aquifer

Distance 

from basin 

centroid 

to Gulf of 

Maine line

(miles)

01059700 Bunganuc Stream near Brunswick, Maine 43 53 14.55 70 01 10.20 01037380 3.82 1.26 42.5

01059940 Kenny Brook near Crockett Corner, Maine 43 52 21.56 70 12 51.82 01054200 27.5 8.90 46.0

01064020 Sucker Brook near Gray, Maine 43 55 36.95 70 23 53.53 01038000 2.93 0.00 55.3

01064111 Black Brook near South Windham, Maine 43 44 31.41 70 25 19.00 01057000 3.67 0.00 44.9

01064112 North Branch Little River near Gorham, Maine 43 44 31.24 70 29 34.05 01101000 4.46 16.3 46.0

01064135 Meader Brook near Falmouth, Maine 43 43 32.57 70 18 54.19 01057000 1.14 0.19 40.6

01064143 Piscataqua River near Cumberland Center, Maine 43 47 27.13 70 18 59.27 01037380 14.5 9.09 45.0

01064193 Skilley Brook near Scarborough, Maine 43 35 10.18 70 28 19.76 01101000 0.42 48.9 35.9

01064583 Shepards River near Brownfield, Maine 43 56 06.87 70 56 55.12 01054200 17.9 6.88 67.6

01065210 Great Brook near Parsonfield, Maine 43 44 58.02 70 54 36.84 01054200 2.56 5.14 55.8

01065350 Wadsworth Brook near Cornish, Maine 43 48 33.81 70 50 44.39 01057000 3.54 3.51 59.6

01066110 Back Brook near Cornish, Maine 43 47 15.34 70 44 06.92 01101000 4.84 22.4 52.9

01066510 Black Brook near Limington, Maine 43 43 02.62 70 41 09.57 01064801 6.46 5.99 49.2

01067100 Junkins Brook near Hollis Center, Maine 43 38 16.91 70 37 03.48 01054200 2.56 49.1 43.4

01067880 Little River near Goose Rocks Beach, Maine 43 25 16.27 70 24 26.69 01073000 5.40 6.13 25.3

01067910 Carlisle Brook near Days Mill, Maine 43 27 31.27 70 37 20.26 01064801 8.75 12.8 32.2

01067920 Goff Mill Brook near Kennebunk, Maine 43 24 26.67 70 29 29.73 01073000 4.88 0.00 26.8

01067960 Carl Branch Brook near Waterboro, Maine 43 32 18.00 70 43 58.46 01101000 1.72 0.00 41.2

01067990 Middle Branch Mousam River near Sanford, Maine 43 30 51.59 70 45 51.72 01064801 6.41 6.61 40.5

01069690 Branch Brook near Wells, Maine 43 23 08.81 70 36 42.92 01064801 7.64 84.1 29.1

01069695 Unnamed trib to Branch Brook near Wells, Maine 43 23 05.75 70 36 37.61 01064801 0.73 30.2 26.8

01069750 Merriland River near Wells, Maine 43 20 40.80 70 38 36.36 01073000 9.06 38.7 27.6

01069900 Clay Hill Brook near Mount Agamenticus, Maine 43 13 40.95 70 37 34.34 01073000 1.85 0.00 19.6

01069950 Dolly Gordon Brook near York Village, Maine 43 08 11.57 70 41 57.87 01064801 1.42 0.00 14.3

01072490 Great Brook near West Lebanon, Maine 43 21 24.43 70 55 40.17 01057000 9.22 0.36 36.1

01072543 Bog Brook near Lebanon, Maine 43 24 27.88 70 51 38.9 01101000 9.21 0.00 37.8

010641125 Westcott Brook near Gorham, Maine 43 44 40.61 70 28 52.79 01057000 3.02 24.3 46.4
Data Collection and Analysis 

7

Table 2. Long-term continuous-record streamgage stations and selected basin characteristics used in regression analyses, southern Maine.[USGS, U.S. Geological Survey; Latitude and longitude are referenced to the North American Datum of 1983; ° ′ ′′, degrees, minutes and seconds; water year, the 12-month period from October 1 through September 30 designated by the calendar year in which it ends; mi2, square miles; ft3/s, cubic feet per second]

USGS 

station 

number

Station name and location Latitude (° ’ ”) Longitude (° ’ ”)

Period of 

continuous 

record 

(water years)

Drainage 

area 

(mi2)

Percentage of 

basin underlain 

by sand and 

gravel aquifer

Distance from 

basin centroid to 

Gulf of Maine line 

(miles)

June 

median flow 

(ft3/s)

August 

median flow 

(ft3/s)

01049550 Togus stream at Togus 44 15 58 69 41 52 1981–1995 23.7 0.00 57.6 17.3 5.5701054200 Wild River at Gilead 44 23 25 70 58 46 1964–2008 69.9 0.48 94.0 93.5 29.501057000 Little Androscoggin River near South Paris 44 18 14 70 32 23 1913–2008 74.1 2.91 84.1 63.5 16.701063310 Stony Brook at East Sebago 43 51 19 70 38 23 1995–2008 0.73 7.20 55.7 1.02 0.20

Table 3. Long-term continuous-record streamgage stations in Maine, New Hampshire, and Massachusetts used as index stations.[USGS, U.S. Geological Survey; Latitude and longitude are referenced to the North American Datum of 1983; ° ′ ′′, degrees, minutes and seconds; water year, the 12-month period from October 1 through September 30 designated by the calendar year in which it ends; mi2, square miles; ft3/s, cubic feet per second]

USGS 

station 

number

Station name and location Latitude (° ’ ”) Longitude (° ’ ”)

Period of 

continuous 

record 

(water years)

Drainage 

area 

(mi2)

June 

median 

streamflow 

(ft3/s)

August 

median 

streamflow 

(ft3/s)

01037380 Ducktrap River near Lincolnville, Maine 44 19 45 69 03 39 1998–2008 14.4 11.7 0.51601038000 Sheepscot River at North Whitefield, Maine 44 13 22 69 35 38 1938–2008 145 121 34.801054200 Wild River at Gilead, Maine 44 23 25 70 58 46 1964–2008 69.9 93.5 29.501057000 Little Androscoggin River near South Paris, Maine 44 18 14 70 32 23 1913–2008 74.1 63.5 16.701064801 Bearcamp River at South Tamworth, New Hampshire 43 49 48 71 17 18 1993–2008 67.6 61.7 22.301073000 Oyster River near Durham, New Hampshire 43 08 55 70 57 56 1934–2008 12.1 7.16 1.7801101000 Parker River at Byfield, Massachusetts 42 45 10 70 56 46 1945–2008 21.3 18.1 2.24
8 June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine

ponds, the areal percentage of lakes, ponds, and reservoirs in 

a basin, was calculated from National Hydrography Dataset 

(NHD) waterbodies data layer (U.S. Geological Survey, 2008). 

(5) Percentage wetlands, the areal percentage of all types of 

wetlands in a basin, and (6) percentage total storage, the areal 

percentage of all types of wetlands, lakes, ponds, reservoirs 

and rivers in a basin, were calculated from the intersection 

of drainage basin polygons with digital National Wetland 

Inventory maps produced by U.S. Fish and Wildlife Service at 

a scale of 1:24,000 (U.S. Fish and Wildlife Service, 2008) in 

combination with the NHD waterbodies layer. 

The locations of the basin centroids were determined 

in GIS and were used in calculating additional basin 

characteristics. (7) Mean monthly and annual precipitation 

at the basin centroids for each basin were computed using 

Parameter-elevation Regressions on Independent Slopes 

Model (PRISM) output grids (Daly and Neilson, 1992; Daly 

and others, 1997) (accessed at http://www.wcc.nrcs.usda.gov/

climate/prism.html on March 2009) and converted to inches. 

(8) Distance from the centroid of the basin to a Gulf of Maine 

line was calculated as the shortest distance (in miles) from 

the centroid of the basin to an arbitrary Gulf of Maine line 

paralleling the coast (fig. 1). The end coordinates (points A 

and B, fig. 1) of the Gulf of Maine line are given in table 4. 

The shortest distance between a basin centroid and the Gulf 

of Maine line is a perpendicular intersector of the Gulf of 

Maine line. The Gulf of Maine line is an indicator of distance 

from the Atlantic Ocean which can affect moisture available 

during storms (Dudley, 2010). The base-10 logarithmic 

transformation of many of the basin characteristics also was 

calculated and tested for use in the equations. 

Computation of June and August Median 

Streamflows at Long-Term Continuous-Record 

Stations

June and August median streamflows for nine longterm continuous-record stations in southern Maine, New 

Hampshire, and Massachusetts were calculated from June 

and August annual monthly median streamflow series at each 

station (tables 2 and 3). Calculated medians were used for 

the regression equations, for the stations used as an index 

station, or both (USGS stations 01054200 and 01057000 are 

listed in both tables 2 and 3). Although the Mann Kendall 

trend test (Helsel and Hirsch, 1992) indicated that there was 

no evidence of trends over time in the annual series of June 

or August medians for any of the long-term stations at a 

p-value equal to 0.05 or less, several of the stations did not 

have sufficient periods of record to make such a trend test 

meaningful. The projected monthly median streamflows for 

June and August were estimated by computing the mean of 

the observed annual June and August medians, respectively. 

This method of computing the monthly median streamflows 

closely approximates the method of using the daily mean 

streamflow that is exceeded 50 percent of the time during any 

given month throughout the period of record but is preferable 

because it allows for the calculation of the variance around the 

median. The estimate of variance is essential for the weighted 

least-squares regression analyses and provides an estimate of 

error for the final regression equations.

Estimation of June and August Median 

Streamflows at Partial-Record Stations

In order to estimate June and August medians for partialrecord stations and determine standard deviations of these 

medians, the logarithm of the measured streamflows needs to 

have a linear correlation with the logarithm of the concurrent 

daily mean streamflows at an index station. An example 

of the correlation between concurrent measurements for a 

partial-record station and an index station is shown in 

figure 3. A partial-record station was required to have a correlation coefficient of 0.70 or greater with an index station in 

order to be used in this analysis. If measurements at a partialrecord station correlated well (coefficient greater than 0.70) 

with measurements from more than one index station, then the 

index station with the higher correlation coefficient was used. 

If the correlation coefficient was similar for two index stations, 

then the index station used was chosen on the basis of a visual 

observation of the graphical relation between the two stations. 

June and August median streamflows for the partialrecord stations were estimated by use of a least-squaresregression analysis of the logarithms of the flows after confirmation that the base-flow measurements at the partial-record 

station had an adequate linear relation with the concurrent 

daily streamflows at an index station. Stedinger and Thomas 

(1985) developed a technique to estimate the mean and standard deviation of an annual event such as the d-day T-year low 

flow, which is the annual, minimum d-day consecutive low 

flow that will be exceeded, on average, every T years. Using 

this technique to calculate the monthly median at a partialrecord station, as opposed to the d-day T-year low flow, is 

appropriate if the logarithms of the monthly medians at the 

index station are approximately normally distributed. For all 

Table 4. Point coordinates that define the Gulf of Maine line.

[Latitude and longitude coordinates are referenced to North American 

Datum of 1983, meter coordinates are referenced to Universal Transverse 

Mercator Zone 19 datum, Gulf of Maine line is shown in figure 1]

X-coordinate Y-coordinate

Point A

71°0′0′′ west longitude

336321.28 meters

42°45′0′′ north latitude

4734992.89 meters

Point B

65°30′0′′ west longitude

775853.75 meters

45°0′0′′ north latitude

4988911.83 meters
Data Collection and Analysis 9

index stations used in this study, except Sheepscot River at 

North Whitefield, Maine (USGS station number 01038000), 

the logarithms of the monthly medians were normally distributed during both June and August. Although the logarithms of 

the August medians were not normally distributed at Sheepscot River, the logarithms of the median of the annual series 

of August medians was equal to the logarithms of the mean of 

the annual series of August means at this station, and thus the 

Stedinger and Thomas (1985) technique was still considered 

valid. The Stedinger and Thomas (1985) technique was used 

to calculate the June and August median streamflows and the 

error of the estimates at all partial-record stations (table 5). 

Base-flow measurements at the partial-record station, 

the corresponding daily mean streamflows at an index station, 

total number of years of record at the index station, and the 

median and standard deviation of the base-10 logarithms of 

the June and August median streamflows at the index station 

were used to compute the base-10 logarithms of the median 

streamflow and its variance at the partial-record station. 

Estimates of median flows for 27 partial-record stations are 

presented in table 5.

Five partial-record stations (USGS stations 01064111, 

01067960, 01069900, 01069950, and 01072543) had one 

measurement of zero streamflow each. Ordinary least-squares 

regression is based on the assumption that the residuals from 

the regression equation are approximately normally distributed. A logarithmic transformation of streamflow is generally 

required to achieve approximate normality; however, the 

occurrence of zero flows makes the logarithmic transformation 

difficult to apply. Thus the median streamflows and standard errors for these five sites were computed using only the 

non-zero observations after determining graphically from the 

correlation with an index site that the estimates of June and 

August median flows at these sites were greater than zero. 

Figure 3. Relation of base-flow measurements at partial-record station Wescott Brook near Gorham, Maine, USGS 

station number 010641125, and concurrent daily mean streamflow at index station Little Androscoggin River near South 

Paris, Maine, USGS station number 01057000, 2006–08.

10 100

1

2.0

3.0

BASE FLOW AT WESTCOTT BROOK NEAR GORHAM, MAINE,

IN CUBIC FEET PER SECOND

CORRELATION COEFFICIENT (R) = 0.98

DAILY MEAN STREAMFLOW AT LITTLE ANDROSCOGGIN RIVER 

NEAR SOUTH PARIS, MAINE, IN CUBIC FEET PER SECOND
10 June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine

Table 5. Weighted June and August median streamflows at partial-record streamgage stations in southern Maine.

[USGS, U.S. Geological Survey; ft3/s, cubic feet per second; ft3/s/mi2, cubic feet per second per square mile; trib, tributary]

USGS 

station 

number

Partial-record station name and location

Weighted 

June median 

streamflow 

(ft3/s)

Weighted 

August median 

streamflow 

(ft3/s)

Weighted 

June median 

streamflow 

(ft3/s/mi2)

Weighted 

August median 

streamflow 

(ft3/s/mi2)

01059700 Bunganuc Stream near Brunswick 1.32 0.22 0.35 0.06

01059940 Kenny Brook near Crockett Corner 17.7 8.22 0.64 0.30

01064020 Sucker Brook near Gray 1.80 0.78 0.61 0.27

01064111 Black Brook near South Windham 1.84 0.35 0.50 0.09

01064112 North Branch Little River near Gorham 4.66 2.88 1.04 0.65

01064135 Meader Brook near Falmouth 0.73 0.23 0.64 0.20

01064143 Piscataqua River near Cumberland Center 15.2 3.57 1.05 0.25

01064193 Skilley Brook near Scarborough 0.29 0.21 0.69 0.50

01064583 Shepards River near Brownfield 25.9 11.6 1.45 0.65

01065210 Great Brook near Parsonfield 1.75 0.80 0.68 0.31

01065350 Wadsworth Brook near Cornish 2.64 0.80 0.75 0.23

01066110 Back Brook near Cornish 5.85 3.44 1.21 0.71

01066510 Black Brook near Limington 4.24 0.49 0.66 0.08

01067100 Junkins Brook near Hollis Center 3.40 2.46 1.32 0.96

01067880 Little River near Goose Rocks Beach 1.65 0.58 0.31 0.11

01067910 Carlisle Brook near Days Mill 6.43 1.91 0.74 0.22

01067920 Goff Mill Brook near Kennebunk 1.07 0.23 0.22 0.05

01067960 Carl Branch Brook near Waterboro 1.68 0.28 0.98 0.16

01067990 Middle Branch Mousam River near Sanford 5.99 0.91 0.94 0.14

01069690 Branch Brook near Wells 19.1 11.5 2.50 1.50

01069695 Unnamed trib to Branch Brook near Wells 0.80 0.23 1.10 0.32

01069750 Merriland River near Wells 5.90 2.59 0.65 0.29

01069900 Clay Hill Brook near Mount Agamenticus 0.27 0.03 0.15 0.02

01069950 Dolly Gordon Brook near York Village 0.49 0.12 0.34 0.08

01072490 Great Brook near West Lebanon 5.24 0.62 0.57 0.07

01072543 Bog Brook near Lebanon 6.37 0.74 0.69 0.08

010641125 Westcott Brook near Gorham 2.93 1.67 0.97 0.55
June and August Median Streamflows Estimated for Ungaged Streams 11

June and August Median Streamflows 

Estimated for Ungaged Streams

Multiple linear regression analyses were used to develop 

equations to estimate June and August median streamflows 

on ungaged streams. June and August median streamflows 

at the 31 partial- and continuous-record stations were related 

statistically to physical and climatic characteristics of the 

drainage basins of these stations. The explanatory variables 

drainage area, percentage of basin underlain by a sand and 

gravel aquifer, and distance from the drainage basin centroid 

to the Gulf of Maine line best explain the variability in the 

response variables June and August median streamflows and 

are included in the final regression equations. If these basin 

characteristics can be calculated, equations can be used to 

estimate June or August median streamflow on a river in the 

absence of streamflow data. 

Statistical Methods

Initially, variations in the June and August median 

streamflows were related to variations in the drainage-basin 

characteristics through ordinary least-squares regression 

analysis (OLS) (Helsel and Hirsch, 1992). Regressions of all 

possible subsets in OLS were used to reduce the number of 

drainage-basin characteristics and determine the best combination of explanatory variables for use in the final equation. 

Weighted least-squares (WLS) regression techniques were 

used to develop the final equations and estimates of accuracy 

presented in this report. Stedinger and Tasker (1985) showed 

that WLS regression techniques are more appropriate than 

OLS for regionalizing streamflow statistics where the streamflow records at the index stations are of varying lengths. 

A modified version of the Weighted Multiple Linear 

Regression Program (WREG), WREGvMedian, was 

used for the regression analysis described in this report 

(Eng and others, 2009). This program is identical to the 

standard WREG program except that weighting matrices are 

constructed to be appropriate for median flows. The WLS 

option in WREGvMedian weights each station included in the 

regression on the basis of the variance of the estimated median 

streamflow. Estimates with large variance are more uncertain, 

and hence, those stations are given smaller weight. For 

continuous-record stations, the variance is calculated based on 

Equation 2 in Lombard and others (2003, p. 14). For partialrecord stations, the variance is based on the equation provided 

in Stedinger and Thomas (1985). Regression coefficients 

are estimated using an iterative search procedure (Stedinger 

and Tasker, 1985; Eng and others, 2009). A generalized 

least-squares (GLS) option that roughly follows the methods 

described in Lombard and others (2003) also was tested 

in order to account for the cross-correlation of concurrent 

streamflows due to the fact that in some cases multiple 

partial-record stations were correlated with the same index 

station. The GLS results were comparable to the WLS results; 

therefore, the extra complexity associated with application of 

the GLS method was deemed unnecessary for this study.

Ordinary Least-Squares Regression

OLS equations were developed in a regression of all 

possible subsets. To establish linearity, logarithmic transformations of the response variables (June and August median 

streamflows) and one of the explanatory variables (drainage area) were performed. The equations with the strongest 

relations between the explanatory variables and the response 

variables were chosen on the basis of the p-values of the 

T-statistic, the adjusted R2, and Mallow’s Cp statistic (Helsel 

and Hirsch, 1992). The p-values of the T-statistic indicate 

the significance of the individual explanatory variables. The 

adjusted R2 value indicates the amount of variance in the 

response variable explained by the explanatory variable(s), 

and Mallow’s Cp statistic is a compromise between maximizing the explained variance by including all relevant variables 

and minimizing the standard error by keeping the number 

of variables as small as possible (Helsel and Hirsch, 1992). 

Typically the p-values of the T-statistic have been found to 

be significant at p = < 0.05, and the Cp statistic is less than 

or equal to the number of explanatory variables plus one in 

order to indicate a meaningful equation; however, there are no 

absolute cutoff points for these statistics, and results need to 

be evaluated within the context of the project. Partial residual 

plots and residuals in relation to predicted plots were examined. The best models were tested for regression assumptions 

including linearity, homoscedasticity (constant variance in the 

response variable over the range of explanatory variables), and 

normality. The best models for both June and August median 

stramflows that satisfied the above mentioned criteria had the 

following explanatory variables: the logarithm of the drainage 

area, the percentage of basin underlain by a sand and gravel 

aquifer, and the distance from the basin centroid to the Gulf of 

Maine line.

Weighted Least-Squares Regression

The final models, their coefficients, and their estimates of 

error were selected using WLS regression because WLS can 

adjust for streamflow records of different lengths. Models that 

used the explanatory variables drainage area, percentage of 

basin underlain by a sand and gravel aquifer, and the distance 

from the basin centroid to the Gulf of Maine line minimized 

the standard error and maximized the explained variance for 

the June and August median streamflows, respectively. Additional models using only drainage area were selected for both 

June and August monthly median streamflows for cases where 

use of a simplified model with reduced accuracy was considered acceptable. Residuals determined by applying the final 

models were mapped for each partial-record station, and no 

spatial patterns were found using the models for either month. 
12 June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine

Average Standard Error of Prediction

The average standard error of prediction (ASEP) is a 

measure of the uncertainty of a prediction obtained using the 

regression equation—or a measure of how well the regression 

equation estimates the response variable when it is applied 

to ungaged drainage basins that were not used to develop 

the equation. For OLS regression, the ASEP is calculated as 

the mean square error (MSE) (a measure of the variability 

of observations about the regression line) plus the sampling 

error variance of the model coefficients (a measure of the 

uncertainty in the placement of the regression line). WLS 

regression, however, allows for the partition of the MSE into 

the model error variance (the portion of the MSE that results 

from an imperfect model, and which is relevant to the ASEP) 

and the sampling error variance of the residuals (the portion 

of the MSE that can be attributed to imprecise estimates of 

the observed dependent variable due to finite record length, 

and which is not relevant for ASEP). Thus for WLS, the ASEP 

is calculated as the sum of the model error variance plus the 

sampling error variance of the model coefficients. There is a 

68-percent probability that the true value of median streamflow at a station will be within the range of the ASEP.

Three-Variable Models

The final equations using drainage area (DRNAREA) in 

square miles, percentage of basin underlain by sand and gravel 

aquifers (PCTSNDGRV), and the distance from the basin centroid to the Gulf of Maine line (GOMDIST) in miles to predict 

June (JUND50) and August (AUGD50) median streamflows 

on ungaged streams are

 JUND DRNAREA PCTSNDGRV GOM 50 0.2151( 10 10 0 9812 0 0086 0 0096 = ) . . ( ) . ( DIST) (1)

 AUGD50 = 0.0310(DRNAREA) PCTSNDGRV 10 10 0.9057 0. ( 0172 ) . 0 0155(GOMDIST), (2)

where

JUND50 is June median streamflow in cubic feet per second,

AUGD50 is August median streamflow in cubic feet per second,

DRNAREA is drainage area in square miles,

PCTSNDGRV is percentage of basin underlain by sand and gravel aquifers, and

GOMDIST is the distance from the basin centroid to the Gulf of Maine line in miles.

For June median streamflow, drainage area, percentage 

of basin underlain by a sand and gravel aquifer, and distance 

to the Gulf of Maine line are all significant (p-values less than 

0.0001, equal to 0.0001, and equal to 0.0006, respectively). 

The ASEP is from -35 to 54 percent. For August median 

streamflow, drainage area, fraction of basin underlain by a 

sand and gravel aquifer, and distance to the Gulf of Maine line 

are all significant (p-values all less than or equal to 0.0001), 

and the ASEP is from -45 to 83 percent. 

The equations listed above are appropriate for predicting 

June and August median streamflows at unregulated drainage 

basins on ungaged streams in York, Cumberland, and southern Oxford Counties within the two-dimensional ranges of 

variables shown by the shaded area in figures 4 and 5. If the 

equations are used with explanatory variables outside the twodimensional ranges shown in these figures, or if the explanatory variables are calculated with methods other than those 

outlined in this report, then the resulting estimates of June and 

August median streamflows will be of unknown accuracy.
June and August Median Streamflows Estimated for Ungaged Streams 13

One-Variable Models

Simplified equations using only drainage area 

(DRNAREA) in square miles to estimate June and August 

median streamflows on ungaged streams (JUND50 and 

AUGD50, respectively) are presented below. These equations 

are faster and easier to apply than the three-variable model 

but are to be used only when estimates of less accuracy 

are acceptable. 

For June median streamflow, drainage area is highly 

significant (p-value < 0.0001). The average standard error 

of prediction is from -46 to 87 percent. For August median 

streamflow, drainage area is also highly significant (p-value 

< 0.0001). The average standard error of prediction is from 

-57 to 133 percent.

Figure 4. Two-dimensional range (shaded area) of explanatory variables drainage area and percentage of 

basin underlain by sand and gravel aquifers used in regression equations for predicting June and August median 

streamflows on ungaged streams in southern Maine.

DRAINAGE AREA, IN SQUARE MILES

0

20

40

60

80

FRACTION OF THE DRAINAGE BASIN UNDERLAIN BY

 SIGNIFICANT SAND AND GRAVEL AQUIFERS

1 10 100

 JUND50 = 0.6566 1.081 (DRNAREA) (3)

 AUGD50 = 0.1973(DRNAREA 1.0597 ) (4)
14 June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine

Figure 5. Two-dimensional range (shaded area) of explanatory variables drainage area and distance from the basin centroid to 

the Gulf of Maine line used in regression equations for predicting June and August median streamflows on ungaged streams in 

southern Maine.

1 10 100

DRAINAGE AREA, IN SQUARE MILES

0

20

40

60

80

100

DISTANCE FROM THE BASIN CENTROID 

TO THE GULF OF MAINE LINE, IN MILES

Summary and Conclusions

In 2006, the U.S. Geological Survey began a cooperative 

study with the Maine Department of Environmental Protection 

to evaluate June and August median streamflow at existing 

continuous-record stations in southern Maine, develop 

new partial-record stations at some of the locations where 

continuous-record stations were not available, estimate June 

and August median streamflows at new partial-record stations, 

and develop equations to estimate June and August median 

streamflows on small ungaged streams in southern Maine. 

Equations with known estimates of accuracy are a critical 

part of Maine’s In-stream Flow Standards adopted in 2007; 

however, equations that are currently (2010) available for 

estimating low-flow statistics statewide in Maine were not 

designed for basins of less than 10 square miles. Currently 

there are few streamgage stations in southern Maine with 

sufficient periods of record for the calculation of long-term 

June and August medians. 

In order to develop equations to estimate June and 

August median streamflows for small basins in southern 

Maine, 27 new partial-record stations were established to augment data from 4 long-term stations. Instantaneous streamflow 
References Cited 15

measurements at partial-record stations were correlated 

to daily mean streamflow at long-term continuous-record 

streamgage stations in southern Maine, New Hampshire, and 

Massachusetts in order to estimate June and August median 

streamflows at the partial-record stations included in this 

report. Estimates of June and August median streamflows 

at both partial-record and continuous-record stations were 

analyzed with basin characteristics determined using basin 

boundaries in order to develop regression equations to estimate selected low-flow statistics for small, ungaged streams. 

Drainage area, the percentage of the basin underlain 

by sand and gravel aquifers, and the distance from the basin 

centroid to the Gulf of Maine line are the basin characteristics 

that were best able to predict the June and August median 

streamflows on stream basins in York, Cumberland, and southwestern Oxford Counties in southern Maine. The equations 

were developed using weighted least-squares regression—in 

which each station included in the regression is weighted on 

the basis of the variance of its estimated median streamflow. 

Estimates with large variance are more uncertain, and hence, 

those stations are given smaller weight. Equations presented in 

this report can only be used for ungaged stream locations with 

basin characteristics within the range of values used in the 

development of the equations. Application of the equations to 

streams that do not meet these criteria will provide results with 

unknown accuracy. 

Estimates made using the equations are more meaningful 

if they are accompanied by estimates of the error of the 

results. The equation to estimate June median streamflow has 

an average standard error of prediction (ASEP) from -35 to 

54 percent. The equation to estimate August median streamflow has an ASEP from -45 to 83 percent. Simpler onevariable equations that use only drainage area to estimate 

June and August median streamflows were developed for 

use when less accuracy is acceptable. These equations have 

ASEPs from -46 to 87 percent and from -57 to 133 percent, 

respectively. There is a greater difference in errors between the 

one-variable equation and the 3-variable equation to estimate August mean streamflow than between the one-variable 

equation and the 3-variable equation to estimate June median 

streamflow. The equations to estimate June and August median 

streamflows with one-variable are designed to be used only in 

situations where the additional basin characteristics cannot be 

determined.

Acknowledgments

The author thanks Julie Kiang and Ken Eng of the USGS 

for providing substantial assistance in the statistical analyses 

in this report. In addition, the author thanks the following 

USGS personnel for assisting in the collection of field data for 

this report: Nick Stasulis, Martha Nielsen, Jim Caldwell and 

Josh Kempf.

References Cited

Daly, C., and Neilson, R.P., 1992, A digital topographic 

approach to modeling the distribution of precipitation in 

mountainous terrain, in Jones, M.E., and Laenen, A., eds., 

Interdisciplinary approaches in hydrology and hydrogeology: American Institute of Hydrology, p. 437–454. 

Daly, C., Taylor, G.H., and Gibson, W.P., 1997, The PRISM 

approach to mapping precipitation and temperature: 

Proceedings of the 10th AMS Conference on Applied 

Climatology, American Meteorological Society, Reno 

Nevada, October 20–23, 1997, p. 10–12. 

Dudley, R.W., 2004, Estimating monthly, annual, and low 

7-day, 10-year streamflows for ungaged rivers in Maine: 

U.S. Geological Survey Scientific Investigations Report 

2004–5026, 22 p.

Eng, Ken, Chen, Yin-Yu, and Kiang, J.E., 2009, User’s guide 

to the weighted-multiple-linear-regression program (WREG 

version 1.0): U.S. Geological Survey Techniques and 

Methods, book 4, chap. A8, 21 p. (Available at 

http://pubs.usgs.gov/tm/tm4a8).

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in 

water resources: New York, Elsevier, 522 p.

Lombard, P.J., 2004a, Methods for estimating streamflow 

statistics for ungaged streams in Maine: U.S. Geological 

Survey Fact Sheet FS–2004–3001, 2 p.

Lombard, P.J., 2004b, August median streamflow on ungaged 

streams in eastern coastal Maine: U.S. Geological Survey 

Scientific Investigations Report 2004–5157, 15 p.

Lombard, P.J., Tasker, G.D., and Nielsen, M.G., 2003, 

August median streamflow on ungaged streams in eastern 

Aroostook County, Maine: U.S. Geological Survey WaterResources Investigations Report 03–4225, 20 p.

Maine Geological Survey, 2003, Sand and gravel aquifer 

mapping, served by the Maine office of GIS, accessed 

September 2, 2003, at http://megis.maine.gov/catalog.

Maine State Legislature, 2007, In-stream flows and lake and 

pond water levels, 2007, Sec 1. 38 MRSA c.3, sub-c.I, 

article 4-B.

National Oceanic and Atmospheric Administration, 2002, 

Monthly station normals of temperature, precipitation, and 

heating and cooling degree days 1971–2000: Climatography of the United States, no. 81.

Rantz, S.E., and others, 1982, Measurements and computation 

of streamflow volume 1, measurement of stage and discharge: U.S. Geological Survey Water-Supply Paper 2175, 

284 p.
16 June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine

Riggs, H.C., 1972, Low-flow investigations: U.S. Geological 

Survey Techniques of Water-Resources Investigations, 

book 4, chap. B1, 18 p.

Stedinger, J.R., and Tasker, G.D., 1985, Regional hydrologic 

analysis 1, Ordinary, weighted, and generalized leastsquares compared: Water Resources Research, v. 21, no. 9, 

p. 1421–1432.

Stedinger, J.R., and Thomas, W.O., 1985, Low-flow frequency 

estimation using base-flow measurements: U.S. Geological 

Survey Open-File Report 85–95, 22 p.

Thompson, W.B., and Borns, H.W., Jr., 1985, Surficial 

geologic map of Maine: Maine Geological Survey, 

scale 1:500,000.

U.S. Census Bureau, 2009, State and county quick facts, 

served by the U.S. Census Bureau, accessed 

March 31, 2009, at http://quickfacts.census.gov/qfd/

states/23/23005.html.

U.S. Fish and Wildlife Service, 2008, National Wetlands 

Inventory Maps, vector digital data from Maine Office of 

Geographic Information Systems, scale 1:24,000, accessed 

March 2008, at http://megis.maine.gov/catalog/.

U.S. Geological Survey, 2008, National Hydrography Dataset, 

accessed March 2008, at http://nhd.usgs.gov/index.html.

U.S. Geological Survey, 2010, National Water Information 

System, accessed January 13, 2010, at 

http://waterdata.usgs.gov/me/nwis/sw.
Prepared by the Pembroke Publishing Service Center.

For more information concerning this report, contact:

Director

U.S. Geological Survey

Maine Water Science Center

196 Whitten Road

Augusta, ME 04330

dc_me@usgs.gov

or visit our Web site at:

http://me.water.usgs.gov
Lombard—June and August Median Streamflows Estimated for Ungaged Streams in Southern Maine—Scientific Investigations Report 2010–5179

Printed on recycled paper