Prepared in cooperation with the Maine Department of Transportation

Regression Equations for Monthly and Annual 

Mean and Selected Percentile Streamflows for 

Ungaged Rivers in Maine

Scientific Investigations Report 2015–5151

Version 1.1, December 21, 2015

U.S. Department of the Interior

U.S. Geological Survey
Cover. Unnamed stream at Ferry Beach State Park, Saco, Maine. Photograph courtesy of Melissa Williams of McLean, Virginia.
Regression Equations for Monthly and 

Annual Mean and Selected Percentile 

Streamflows for Ungaged Rivers in Maine

By Robert W. Dudley

Prepared in cooperation with the Maine Department of Transportation

Scientific Investigations Report 2015–5151

Version 1.1, December 21, 2015

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Director

U.S. Geological Survey, Reston, Virginia

First release: December 2015

Revised: December 21, 2015 (ver. 1.1)

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as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Dudley, R.W., 2015, Regression equations for monthly and annual mean and selected percentile streamflows for 

ungaged rivers in Maine (ver. 1.1, December 21, 2015): U.S. Geological Survey Scientific Investigations Report 2015–

5151, 35 p., http://dx.doi.org/10.3133/sir20155151.

ISSN 2328-0328 (online)
iii

Acknowledgments

The author thanks the Maine Department of Transportation for providing support for this study. 

Thanks also are given to Luke Sturtevant of the U.S. Geological Survey for geographic information system support and assistance. Reviews by Gardner Bent, Pam Lombard, and Anna Glover 

of the U.S. Geological Survey resulted in scientific and editorial improvements in this report.

v

Contents

Acknowledgments........................................................................................................................................iii

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

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

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

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

Data Used For This Study .............................................................................................................................2

Streamflow.............................................................................................................................................2

Basin and Climatic Characteristics ...................................................................................................5

Regression Analyses.....................................................................................................................................5

Drainage Area .......................................................................................................................................6

Distance From the Coast .....................................................................................................................6

Mean Basin Elevation ..........................................................................................................................6

Maximum Basin Elevation...................................................................................................................6

Mean Basin Slope.................................................................................................................................6

Mean Basin Percent Hydrologic Soil Group A ................................................................................8

Fraction Sand and Gravel Aquifer......................................................................................................8

Percent Open Water.............................................................................................................................8

Regression Equations....................................................................................................................................8

Summary........................................................................................................................................................22

References Cited..........................................................................................................................................23

Appendix 1.....................................................................................................................................................25

Figures

1. Map showing locations of U.S. Geological Survey streamgages and basins in

Maine and northern New Hampshire used in this study. ......................................................3

2. Map showing distribution of hydrologic soil group A in Maine and New Hampshire......9

3. Map showing distribution of sand and gravel aquifers in Maine and New Hampshire. 10

4. Map showing distribution of land cover classified as open water in the 2006

National Land Cover Dataset (NLCD) in Maine and New Hampshire................................11

5. Two-dimensional ranges of explanatory variables used in regression equations for

estimating annual and July, August, September, and October mean and selected

percentile streamflows for ungaged, unregulated streams in rural drainage basins

in Maine and northern New Hampshire .................................................................................20

6. Two-dimensional range of explanatory variables used in regression equations for

estimating January and December mean and selected percentile streamflows for

ungaged, unregulated streams in rural drainage basins in Maine and northern 

New Hampshire ..........................................................................................................................20

7. Two-dimensional ranges of explanatory variables used in regression equations for

estimating February, March, April, May, and June mean and selected percentile

streamflows for ungaged, unregulated streams in rural drainage basins in Maine

and northern New Hampshire ..................................................................................................21
vi

8. Two-dimensional range of explanatory variables used in regression equations for

estimating November mean and selected percentile streamflows for ungaged,

unregulated streams in rural drainage basins in Maine and northern

New Hampshire ..........................................................................................................................21

Tables

1. Selected U.S. Geological Survey streamgages in Maine and northern

New Hampshire ............................................................................................................................4

2. Basin characteristics for selected U.S. Geological Survey streamgages in Maine

and northern New Hampshire ....................................................................................................7

3. Point coordinates defining the Gulf of Maine Line .................................................................8

4. Regression equations for estimating annual streamflows for ungaged, unregulated

streams in rural drainage basins in Maine and northern New Hampshire ......................12

5. Regression equations for estimating January streamflows for ungaged,

unregulated streams in rural drainage basins in Maine and northern

New Hampshire ..........................................................................................................................13

6. Regression equations for estimating February streamflows for ungaged,

unregulated streams in rural drainage basins in Maine and northern

New Hampshire ..........................................................................................................................14

7. Regression equations for estimating March streamflows for ungaged, unregulated

streams in rural drainage basins in Maine and northern New Hampshire ......................14

8. Regression equations for estimating April streamflows for ungaged, unregulated

streams in rural drainage basins in Maine and northern New Hampshire ......................15

9. Regression equations for estimating May streamflows for ungaged, unregulated

streams in rural drainage basins in Maine and northern New Hampshire ......................15

10. Regression equations for estimating June streamflows for ungaged, unregulated

streams in rural drainage basins in Maine and northern New Hampshire ......................16

11. Regression equations for estimating July streamflows for ungaged, unregulated

streams in rural drainage basins in Maine and northern New Hampshire ......................16

12. Regression equations for estimating August streamflows for ungaged, unregulated

streams in rural drainage basins in Maine and northern New Hampshire ......................17

13. Regression equations for estimating September streamflows for ungaged,

unregulated streams in rural drainage basins in Maine and northern

New Hampshire ..........................................................................................................................17

14. Regression equations for estimating October streamflows for ungaged,

unregulated streams in rural drainage basins in Maine and northern

New Hampshire ..........................................................................................................................18

15. Regression equations for estimating November streamflows for ungaged,

unregulated streams in rural drainage basins in Maine and northern

New Hampshire ..........................................................................................................................18

16. Regression equations for estimating December streamflows for ungaged,

unregulated streams in rural drainage basins in Maine and northern

New Hampshire ..........................................................................................................................19
vii

Conversion Factors

International System of Units to Inch/Pound

Multiply By To obtain

Length

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2

) 0.3861 square mile (mi2)

Flow rate

cubic meter per second (m3

/s) 35.31 cubic foot per second (ft3/s) 

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

(°F) as °F = (1.8 × °C) + 32.

Datum

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).

Elevation, as used in this report, refers to distance above the vertical datum.
viii

Abbreviations

ASEP average standard error of prediction

GAGES II Geospatial Attributes of Gages for Evaluating Streamflow version II

GIS geographic information system

MDOT Maine Department of Transportation

MEGIS Maine Office of GIS

NED National Elevation Dataset

NRCS Natural Resources Conservation Service

NWIS National Water Information System

PRESS prediction error sum of squares

STATSGO State Soil Geographic database

USGS U.S. Geological Survey

VIF variance inflation factor

WLS weighted least squares

WY water year
Regression Equations for Monthly and Annual Mean and 

Selected Monthly Percentile Streamflows for Ungaged 

Rivers in Maine

By Robert W. Dudley

Abstract

In an effort to delineate hydrologic conditions in Maine, 

the U.S. Geological Survey, in cooperation with the Maine 

Department of Transportation, used streamflow data to 

develop dependent variables for 130 regression equations for 

estimating monthly and annual mean and 1, 5, 10, 25, 50, 75, 

90, 95, and 99 percentile streamflows for ungaged, unregulated rivers in Maine. Daily streamflow data from 24 rural 

unregulated basins with drainage areas between 14.9 and 

1,419 square miles in Maine and northern New Hampshire 

were used in the derivation of the equations. Streamflow data 

collected from October 1, 1982, through September 30, 2012, 

were used to derive the dependent variables for this study to 

represent current [2015] hydrologic conditions in Maine and 

northern New Hampshire. Weighted least squares regression 

techniques were used to derive the final coefficients and measures of uncertainty for the regression equations. Eight basin 

characteristics serve as the explanatory variables: drainage 

area, distance from the coast, mean and maximum basin elevation, mean basin slope, mean basin percentage of hydrologic 

soil group A, fraction of sand and gravel aquifers, and percentage of open water.

The largest average errors of prediction are associated 

with regression equations for the lowest streamflows derived 

for months during which the lowest streamflows of the year 

occur (such as the 5 and 1 monthly percentiles for August 

and September). The regression equations have been derived 

on the basis of streamflow and basin characteristics data for 

unregulated, rural drainage basins without substantial streamflow or drainage modifications (for example, diversions and 

(or) regulation by dams or reservoirs, tile drainage, irrigation, 

channelization, and impervious paved surfaces), therefore 

using the equations for regulated or urbanized basins with substantial streamflow or drainage modifications will yield results 

of unknown error. Input basin characteristics derived using 

techniques or datasets other than those documented in this 

report or using values outside the ranges used to develop these 

regression equations also will yield results of unknown error.

Introduction

Water- and natural-resources professionals routinely need 

to be able to estimate various streamflow statistics to manage 

resources, plan projects, and permit regulated uses of surface 

waters. For example, quantifying streamflows at a given location on a stream may be necessary for determining adequate 

dilution of waste load to a stream during low-flow conditions (typical of dry conditions during summer), evaluating a 

hydraulic structure’s conveyance during high-flow conditions 

(typical of wet conditions during spring snowmelt or during large rain events), and evaluating or planning hydraulic 

connectivity and fish passage efficacy over a range of seasonal flows ranging from low to high. Although estimation 

of streamflow statistics at or near locations where streamflow 

data are routinely collected is straightforward, only a small 

fraction of all the streams in Maine are gaged.

Regression equations offer a statistical method for estimating streamflows at ungaged locations. The U.S. Geological 

Survey (USGS) has derived a variety of statewide and regional 

regression equations for estimating a range of streamflow 

statistics for ungaged streams in Maine. Hodgkins (1999) 

documents statewide regression equations for estimating peak 

flows with probabilities of annual exceedances of 0.2, 1, 2, 

4, 10, 20, and 50 percent. Dudley (2004) derived statewide 

equations for estimating monthly and annual mean and median 

streamflows as well as the 7-day low flow with a 10 percent 

annual exceedance probability, superseding similar equations 

derived by Parker (1977). A few regional studies within Maine 

have produced regression equations for specific months: June 

and August median streamflows in southern Maine (Lombard, 

2010), August median streamflows in eastern coastal Maine 

(Lombard, 2004), and August median streamflows in eastern 

Aroostook County (Lombard and others, 2003). In 2012, 

the USGS began a cooperative investigation with the Maine 

Department of Transportation (MDOT) to derive statewide 

regression equations that can be used to estimate monthly and 

annual mean and 1, 5, 10, 25, 50, 75, 90, 95, and 99 percentile 

streamflows for ungaged rivers in Maine.
2 Regression Equations for Ungaged Rivers in Maine

Purpose and Scope

This report documents regression equations developed 

for estimating monthly and annual mean and 1, 5, 10, 25, 50, 

75, 90, 95, and 99 percentile streamflows for ungaged, unregulated rivers in Maine and northern New Hampshire along with 

the data and methods used to derive them. Statistics derived 

from streamflow data from 24 USGS streamgages on unregulated, rural rivers in Maine and northern New Hampshire 

were used as the dependent variables in the equations. Data 

describing various basin and climate characteristics, such as 

geology, land cover, land use, precipitation, and temperature, 

derived using geographic information systems (GIS) were 

used as explanatory variables in the equations. The regression equations presented in this report can be used to estimate 

streamflows for unregulated, rural basins in Maine and supersede those derived by Dudley (2004) because of the updated 

streamflow and basin characteristics data used.

Description of the Study Area

The State of Maine (fig. 1), in the northeastern 

United States, has a land area of 79,883 square kilometers (km2

; 30,843 square miles [mi2]) with a population of 

1.33 million people (U.S. Census Bureau, 2012). Maine is 

largely rural and forested with rolling topography of moderate 

to low relief throughout the State except for the high relief of 

the Appalachian Mountain Range in west-central Maine. Land 

elevation ranges from sea level (0 meters [m]; 0 feet [ft]) at 

the Atlantic coast (Gulf of Maine) to 1,606 m (5,268 ft) at the 

peak of Mount Katahdin (U.S. Geological Survey, 2001). The 

physiographic characteristics of west-central Maine extend 

into northernmost New Hampshire.

Basin characteristics and streamflow data from 

24 streamgages on rural, unregulated basins in Maine and 

northern New Hampshire (fig. 1) were used to derive the 

regression equations for estimating selected streamflow 

statistics. The study basins have no substantial streamflow or 

drainage modifications (that is, diversions and (or) regulation 

by dams or reservoirs, tile drainage, irrigation, channelization, and impervious paved surfaces large enough to affect the 

computation of monthly statistics). The study basins range in 

size from 38.6 to 3,675 km2 (14.9 to 1,419 mi2), with mean 

basin elevations ranging from 73 m (240 ft) at the coast in 

southern Maine to 646 m (2,120 ft) in mountainous northern 

New Hampshire (Gesch and others, 2009; U.S. Geological 

Survey, 2014a).

The study basins are mostly forested, with deciduous or 

evergreen growth or a mix thereof (including shrub growth), 

covering from 67.6 to 99.2 percent (mean of 85.2 percent) 

of the study basin areas. Open water and wetlands compose 

0.4 to 18.6 percent (mean of 8.3 percent) of the study basin 

areas. Land cover in the basins also includes developed land 

(residential housing, commercial and industrial development, 

and transportation; where impervious surfaces account for 20 

to 100 percent of total cover) ranging from 0 to 3.7 percent 

(mean of 0.7 percent) and pasture and cultivated crop areas 

ranging from 0 to 11.6 percent (mean of 2.4 percent; Fry 

and others, 2011). Although the rural character of Maine has 

changed little since the beginning of the 20th century, the 

greatest changes in land use in Maine has been the replacement of agriculture and pasture lands by forest. The overall 

forest cover in the State is estimated to have been at its lowest 

around 1900 at about 70 percent. Forest cover increased to 

about 90 percent by 1995 (Irland, 1998).

Maine has a temperate climate with mild summers 

and cold winters. Climatological averages computed for the 

30-year period from 1981 to 2010 indicate a mean annual 

air temperature for Maine of 5.8 degrees Celsius (°C; 

42.5 degrees Fahrenheit [°F]). Mean annual air temperature 

ranged from 2.9 °C (37.3 °F) at Allagash to 8.8 °C (47.8 °F) 

at Sanford. For the same period, the statewide mean minimum 

air temperature was 0.1 °C (32.1 °F) and the mean maximum was 11.6 °C (52.9 °F). Precipitation in Maine is fairly 

evenly distributed throughout the year with a mean annual 

of 1,153 millimeters (mm; 45.4 inches [in.]) for the 30-year 

period from 1981 to 2010, ranging from 853 mm (33.6 in.) at 

Frenchville to 1,440 mm (56.7 in.) at Acadia National Park 

(National Climatic Data Center, 2015).

Data Used For This Study

Streamflow

Daily streamflow data collected at USGS streamgages 

(Rantz and others, 1982) on 24 rural, unregulated river basins 

in Maine and northern New Hampshire (fig. 1) were used to 

compute the statistics to serve as dependent variables for the 

regression equations developed. Candidate streamgages for 

this study needed to be located in Maine or in New Hampshire within 25 mi of the Maine border, in predominantly 

rural basins, and have more than 10 years of streamflow data 

substantially unaffected by diversions and (or) regulation 

by dams or reservoirs (table 1). The data were daily values 

derived and published from continuously collected data (typically in 15-minute intervals). Daily streamflow data were 

retrieved from the National Water Information System (NWIS; 

U.S. Geological Survey, 2014c) for the streamgages meeting 

the study criteria. Only a 6-day period of irregular low-flow 

regulation during September 20–25, 1985, for the Narraguagus River at Cherryfield, Maine (01022500) streamgage was 

censored from use in this study.

Recent studies of climate variability and its effect on 

hydrology in Maine and New England have documented 

various trends over time. Many changes have been observed 

in the winter and spring seasons, during which high snowmelt-related streamflows have trended to earlier dates during the course of the 20th century (Dudley and Hodgkins, 

2002; Hodgkins and others, 2003; Hodgkins and Dudley, 
Data Used For This Study 3

Mount Katahdin

Sanford

Allagash

Frenchville

ACADIA NATIONAL

PARK

Gulf of Maine line

72° 70° 68°

46°

44°

01130000

01064801

01064500

01060000

01057000

01055500

01055000

01054300

01054200

01052500

01048000

01047000

01044550

01038000

01037380

01031500

01031450

01031300

01030500

01029200

01027200

01022500

01021480

01013500

0 25 50 75 100 MILES

0 50 100 KILOMETERS

MAINE

NEW HAMPSHIRE

EXPLANATION

U.S. Geological Survey streamgage

Study basin

Basin centroid

VERMONT

Base map from Esri Inc. data, 2012

North American Datum 1983

Universal Transverse Mercator, zone 19N

ATLANTIC OCEAN

CANADA

CANADA

0 100 MILES

0 100 KILOMETERS

CANADA

MAINE

VERMONT

NEW HAMPSHIRE

MASSACHUSETTS

RHODE ISLAND

CONNECTICUT

Atlantic Ocean

Figure 1. Locations of U.S. Geological Survey streamgages and basins in Maine and northern New Hampshire used in this 

study. The Gulf of Maine line is a line in the Gulf of Maine defined by end points 71W, 42.75N and 65.5W, 45N, referenced to the 

North American Datum of 1983 for measuring the distance from the coast for each of the basins.
4 Regression Equations for Ungaged Rivers in Maine

Table 1. Selected U.S. Geological Survey streamgages in Maine and northern New Hampshire.

[mi2, square mile; WY, water year which begins October 1 and ends September 30 and is designated by the calendar year in which it ends]

U.S. Geological Survey streamgage Drainage area

(mi2

)

Period of record used in 

this study

(WY)

Number of 

Number Name complete WY

01013500 Fish River near Fort Kent, Maine 866 1983–2012 30

01021480 Old Stream near Wesley, Maine 29.8 1998–2012 14

01022500 Narraguagus River at Cherryfield, Maine 228 1983–2012 29

01027200 North Branch Penobscot River near Pittston Farm, Maine 223 2001–2012 11

01029200 Seboeis River near Shin Pond, Maine 173 1998–2012 14

01030500 Mattawamkeag River near Mattawamkeag, Maine 1,419 1983–2012 30

01031300 Piscataquis River at Blanchard, Maine 117 1997–2012 16

01031450 Kingsbury Stream at Abbot Village, Maine 95.1 1997–2012 15

01031500 Piscataquis River near Dover-Foxcroft, Maine 297 1983–2012 30

01037380 Ducktrap River near Lincolnville, Maine 14.9 1998–2012 14

01038000 Sheepscot River at North Whitefield, Maine 145 1983–2012 30

01044550 Spencer Stream near Grand Falls, Maine 194 1999–2012 13

01047000 Carrabassett River near North Anson, Maine 352 1983–2012 30

01048000 Sandy River near Mercer, Maine 516 1987–2012 25

01052500 Diamond River near Wentworth Location, New Hampshire 153 1983–2012 30

01054200 Wild River at Gilead, Maine 69.9 1983–2012 30

01054300 Ellis River at South Andover, Maine 130 2001–2012 11

01055000 Swift River near Roxbury, Maine 96.8 1983–2012 30

01055500 Nezinscot River at Turner Center, Maine 168 1983–1996, 2001–2012 25

01057000 Little Androscoggin River near South Paris, Maine 73.9 1983–2012 30

01060000 Royal River at Yarmouth, Maine 141 1983–2004 21

01064500 Saco River near Conway, New Hampshire 385 1983–2012 30

01064801 Bearcamp River at South Tamworth, New Hampshire 67.0 1993–2012 19

01130000 Upper Ammonoosuc River near Groveton, New Hampshire 231 1983–2004, 2009–2012 25

2006b). These winter and spring streamflow trends have been 

accompanied by earlier lake ice-out dates (Hodgkins, 2013), 

decreases in late-winter snowpack depth or increases in snowpack density (Hodgkins and Dudley, 2006a), and a decreased 

ratio of snowfall to total precipitation at sites in northern 

New England (Huntington and others, 2004).

Precipitation in New England has increased across all 

seasons (Karl and Knight, 1998; Douglas and Fairbank, 2011; 

Hodgkins and Dudley, 2011). Annual low streamflows at several streamgages in northern New England have increased during the 20th century (Hodgkins and Dudley, 2005) and annual 

peak flows have increased during the past 50 to 100 years 

at several streamgages across New England (Hodgkins and 

Dudley, 2005; Collins, 2009; Hodgkins, 2010; Armstrong and 

others, 2012).

The regression equations by Dudley (2004) integrated 

all historical streamflow and precipitation data available at 

the time. However, given the evidence of hydrologic trends, 

future investigations of this kind might benefit from being 

done at regular intervals using a moving temporal window of 

contemporary data or considering methods for incorporating 

these large-scale hydrologic trends into the statistical models. 

Therefore, to best represent contemporary hydrologic conditions in Maine, streamflow data collected during the 30-year 

period from October 1, 1982, through September 30, 2012 

(water years1

 1983–2012), are used to derive the dependent 

variables for the study in this report (table 1).

Monthly and annual streamflow.—Mean annual streamflow 

was computed as the mean of all available daily mean streamflow data for the period of record during water years 1983 to 

2012 for each station (appendix 1). Mean monthly streamflows were computed as the mean of all daily mean streamflow values parsed by month. The 1, 5, 10, 25, 50, 75, 90, 

95, and 99 monthly and annual percentile streamflows were 

1

The water year begins October 1 and ends September 30 and is designated 

by the calendar year in which it ends.
Regression Analyses 5

computed in the manner defined by Helsel and Hirsh (2002); 

for example, they define the 75th percentile, as “a value which 

exceeds no more than 75 percent of the data and is exceeded 

by no more than 25 percent of the data.” The computations 

were done using the quantile function (type=2) in the 

R programming language. Annual percentiles were computed 

on the basis of all available daily mean streamflow data for 

the period of record during water years 1983 to 2012 for each 

station (appendix 1), and monthly percentiles were computed 

on the basis of the same daily mean streamflow values parsed 

by month.

Basin and Climatic Characteristics

For the study detailed in this report, 68 GIS-derived basin 

characteristics were tested to serve as explanatory variables 

for the dependent variables of monthly and annual mean and 

1, 5, 10, 25, 50, 75, 90, 95, and 99 percentile streamflows. 

Most of the basin characteristics were retrieved from the 

Geospatial Attributes of Gages for Evaluating Streamflow 

version II (GAGES II) dataset (Falcone, 2011)—an updated 

version of the original Geospatial Attributes of Gages for 

Evaluating Streamflow dataset published in 2010 (Falcone and 

others, 2010). The GAGES II dataset includes several hundred 

watershed characteristics derived from national data sources, 

including environmental features and anthropogenic influences 

for more than 9,000 streamgages maintained by the USGS. 

The dataset also includes comments pertaining to hydrologic 

modifications published in USGS annual data reports (U.S. 

Geological Survey, 2014b).

The 68 basin characteristics comprise the following 

parameters (and variations thereof): drainage area; latitude and 

longitude; land surface elevation, shape, aspect, and slope; 

precipitation; air temperature; days of first and last freeze; 

snow percent of total precipitation; ratio of base flow to total 

streamflow; various land-cover classifications from the 2006 

National Land Cover Dataset (NLCD; Fry and others, 2011); 

population density; hydrologic soil group types; area of sand 

and gravel aquifers; and distance from the coast. These candidate explanatory variables included the five explanatory variables derived by Dudley (2004) for estimating mean monthly, 

mean annual, and 7-day, 10-year low-flow frequency (7Q10) 

streamflows: drainage area, area of sand and gravel aquifers, 

distance from the coast, mean annual precipitation, and mean 

winter precipitation. Distance from the coast and area of sand 

and gravel aquifers are not available in the GAGES II dataset 

and were computed by using GIS; details describing the computation of these basin characteristics is provided in the “Final 

Explanatory Variables” section.

Regression Analyses

Ordinary least squares (OLS) regression techniques (Helsel and Hirsch, 2002) of all possible subsets of 68 explanatory 

variables for each of 130 dependent variables were used to 

select the explanatory variables that would appear in the 

final regression equations. For the exploratory OLS regression analyses, all subset regressions were evaluated on the 

basis of adjusted coefficient of determination (R2

) values and 

significance of explanatory variables. In general, explanatory 

variables needed to have statistically significant explanatory 

power (p-values less than 0.01) for several percentile regressions in order to be retained in any model set. In most cases, 

explanatory variables rarely exhibited statistical significance 

over the entire range of percentiles, from low to high streamflows, for any given monthly or annual equation set with the 

exception of drainage area. Explanatory variables other than 

drainage area often had high statistical significance at either 

mid-to-high streamflows or mid-to-low streamflows and 

decreased in significance for the other equations; such variables were nevertheless retained in model sets in the interest 

of coherence. In the instance of three-variable models, the two 

explanatory variables other than drainage area often provided 

complementary statistical significance but were not always 

both significant for any given percentile model.

For the monthly and annual 1, 5, 10, 25, 50, 75, 90, 

95, and 99 percentile streamflows, emphasis was placed on 

developing a coherent set of equations in which each monthly 

or annual set of regression equations uses the same set of 

explanatory variables; only the coefficients vary for each percentile equation. This approach of building coherent monthly 

and annual regression equation sets reduced the possibility 

of discontinuities in the percentile estimates (for example, 

equations that yield a 5 percentile streamflow estimate that is 

greater than the 10 percentile streamflow estimate).

A variety of regression diagnostics was used to evaluate 

the capacity of the explanatory variables to explain the variability of the dependent variables and the overall robustness 

of the derived regression equations. The Cook’s D statistic 

(Helsel and Hirsch, 2002) was used to investigate any problems with leverage influence on the regression equations. 

Cook’s D indicated that basins with small drainage areas (of 

approximately 26 km2 [10 mi2] or less) and (or) mountainous 

character exerted high leverage; for this reason, 5 candidate 

streamgage study basins (2 in Maine and 3 in New Hampshire) 

were culled from an original set of 29 streamgages, reducing 

the final number of streamgage study basins to 24. Residual 

plots against predicted values, and partial residuals plots, were 

used to check for linearity, constant variance, normality, and 

the presence of outliers. Residuals were plotted and correlated 

against latitude and longitude to check for geographic bias. 

All correlation values were less than ±0.60 and no monthly 

or annual model sets indicated any systematic geographic 

bias. Residuals from 4 of 130 models indicated (strong, 

p<0.01) positive correlation with latitude: the May 90, 95 

and 99 percentile models and the July 50th percentile model. 

Residuals from 2 models indicated (strong, p<0.01) positive 

correlation with longitude: the December 50 and 75 percentile 

models. Multicollinearity among the explanatory variables 

was measured using the variance inflation factor (VIF). The 
6 Regression Equations for Ungaged Rivers in Maine

final explanatory variables (described in the “Final Explanatory Variables” section) had VIF values of 1.87 or lower, 

indicating no problems with multicollinearity. 

Weighted least squares (WLS) regression techniques 

were used to derive the final coefficients and measures of 

uncertainty for the regression equations. Where OLS simply 

minimizes the squares of the residuals, WLS regression techniques minimize the squares of weighted residuals. The weight 

factors are determined such that observations with greater 

variance have less of an influence on the derivation of the 

regression model. A common application of this is to derive 

the weights as a function of record length base on the assumption that longer records will have lower variance (are more 

reliable) than for stations with less data (Helsel and Hirsch, 

2002). Weights used in the study detailed in this report were 

computed as a function of record length, that is, the number 

of complete water years of record from water years 1983 to 

2012 divided by the mean record length (23 years) for all the 

streamgages used in the analysis; the sum of the weights is 

therefore equal to the number of streamgages used.

Final explanatory variables.—Eight basin characteristics were 

identified from the initial set of the 68 to serve as explanatory variables for estimating monthly and annual mean and 1, 

5, 10, 25, 50, 75, 90, 95, and 99 percentile streamflows. The 

eight basin characteristics are drainage area, distance from the 

coast, mean and maximum basin elevation, mean basin slope, 

mean basin percentage of hydrologic soil group A, fraction 

of sand and gravel aquifers, and percentage of open water 

(lakes and ponds; table 2). These basin characteristics were 

recomputed in GIS to check the GAGES II values; the newly 

derived values were used in the derivation of the final WLS 

regression equations.

Drainage Area

The drainage area, in square miles, of each study basin 

was computed in GIS by measuring the horizontal planar 

area enclosed by the topographic divide (drainage-basin 

boundary) inside which surface runoff drains by gravity to a 

common outlet point (point of interest). The drainage basin 

boundary was delineated using the National Elevation Dataset 

(NED) for Maine and northern New Hampshire derived from 

a 10-m (1⁄3 arc-second) resolution digital elevation model 

(DEM; Gesch and others, 2009; U.S. Geological Survey, 

2014a). The 24 streamgage basin drainage areas range from 

14.9 mi2 (38.6 km2; Ducktrap River near Lincolnville, Maine 

[01037380] streamgage) to 1,419 mi2 (3,675 km2; Mattawamkeag River near Mattawamkeag, Maine [01030500] 

streamgage), with a mean of 258 mi2 (668 km2; fig. 1; 

tables 1 and 2).

Distance From the Coast

Distance from the coast is an explanatory variable introduced by Dudley (2004) in regression equations for estimating 

January, February, March, and May mean and median 

streamflows. Distance from the coast is the distance, in miles, 

measured as the shortest distance from the drainage basin 

centroid to a line in the Gulf of Maine (GOM line) defined by 

end points 71W, 42.75N and 65.5W, 45N, referenced to the 

North American Datum of 1983 (NAD 83; Dudley, 2004). 

The shortest line of measure between a basin centroid point 

and the GOM line is a perpendicular intersector of the GOM 

line. For this study, all distance measurements were made in 

GIS using NAD 83, Universal Transverse Mercator zone 19 

coordinate system (table 3). Distances from the GOM line to 

the centroid of streamgage drainage basins used in this study 

range from 46.6 miles (mi; 75 kilometers [km]; Narraguagus 

River at Cherryfield, Maine [01022500] streamgage) to 193 mi 

(310.6 km; Fish River near Fort Kent, Maine [01013500] 

streamgage), with a mean of 102 mi (164.2 km; table 2).

Mean Basin Elevation

Mean basin elevation, in thousands of meters, was computed in GIS by arithmetically averaging all 10-m NED grid 

point elevations, in meters, within the drainage basin boundaries and dividing the mean by 1,000. The mean basin elevation 

was computed in meters because it is the native vertical unit in 

the NED. Mean elevations of streamgage drainage basins used 

in this study range from 73 m (239.5 ft; Royal River at Yarmouth, Maine streamgage [01060000]) to 646 m (2,119.4 ft; 

Diamond River near Wentworth Location, NH streamgage 

[01052500]), with a mean of 339 m (1,112.2 ft; table 2).

Maximum Basin Elevation

Maximum basin elevation, in thousands of meters, was 

computed in GIS by identifying the maximum 10-m NED grid 

point elevation, in meters, within the drainage basin boundaries (typically at the basin boundary), and dividing it by 

1,000. The maximum basin elevation is computed in meters 

because it is the native vertical unit in the NED. Maximum 

elevations of streamgage drainage basins used in this study 

range from 193 m (633.2 ft; Royal River at Yarmouth, Maine 

[01060000] streamgage) to 1,916 m (6,286 ft; Saco River near 

Conway, NH [01064500] streamgage), with a mean of 860 m 

(2,821.5 ft; table 2).

Mean Basin Slope

Mean basin slope, in percent, was computed in GIS by 

arithmetically averaging all 10-m slope grid points (steepest 

gradient identified between a cell and its neighboring cells 

derived from the 10-m NED) within the drainage basin boundaries. The slope grid was computed as the change in elevation 

between grid points divided by the distance between grid 

points and multiplied by 100 to obtain units in percent. Mean 

basin slopes of streamgage drainage basins used in this study 
Regression Analyses 

7

Table 2. Basin characteristics for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire.[Basin elevations are from the U.S. Geological Survey National Elevation Dataset and are reported in meters (m) in the original source; to convert to feet, multiply by 3.281. mi2, square mile; mi, mile; m, 

meter; HGA, hydrologic soil group A; S&G, sand and gravel]

U.S. Geological Survey streamgage Drainage 

area

(mi2)

Distance from 

the coast

(mi)

Basin elevation

(m)

Mean basin 

slope

(percent rise)

Mean basin 

HGA

(percent)

Fraction 

of S&G 

aquifer

Open 

water

(percent) Number Name Mean Maximum

01013500 Fish River near Fort Kent, Maine 866 193 274 609 8.8 0.7 0.008 6.2

01021480 Old Stream near Wesley, Maine 29.8 52.5 98 196 5.2 22.3 0.212 3.0

01022500 Narraguagus River at Cherryfield, Maine 228 46.6 99 452 5.6 24.8 0.150 2.1

01027200 North Branch Penobscot River near Pittston Farm, Maine 223 173 476 727 7.2 0.1 0.000 0.9

01029200 Seboeis River near Shin Pond, Maine 173 148 247 517 5.5 1.2 0.009 5.3

01030500 Mattawamkeag River near Mattawamkeag, Maine 1,419 110 172 742 4.5 2.5 0.020 2.7

01031300 Piscataquis River at Blanchard, Maine 117 119 378 799 9.1 2.5 0.012 2.1

01031450 Kingsbury Stream at Abbot Village, Maine 95.1 106 301 668 8.5 3.8 0.009 2.7

01031500 Piscataquis River near Dover-Foxcroft, Maine 297 111 302 799 8.6 4.5 0.018 2.1

01037380 Ducktrap River near Lincolnville, Maine 14.9 46.8 101 257 6.3 0.0 0.010 3.7

01038000 Sheepscot River at North Whitefield, Maine 145 55.3 109 336 6.9 0.2 0.044 3.5

01044550 Spencer Stream near Grand Falls, Maine 194 140 540 1,110 13.9 10.0 0.044 2.6

01047000 Carrabassett River near North Anson, Maine 352 111 376 1,292 13.7 9.6 0.084 0.9

01048000 Sandy River near Mercer, Maine 516 98.0 305 1,259 12.2 7.5 0.050 1.2

01052500 Diamond River near Wentworth Location, New Hampshire 153 135 646 1,107 18.7 5.4 0.057 0.3

01054200 Wild River at Gilead, Maine 69.9 93.5 625 1,472 26.6 6.7 0.006 0.0

01054300 Ellis River at South Andover, Maine 130 107 441 1,155 16.4 16.2 0.057 1.5

01055000 Swift River near Roxbury, Maine 96.8 108 566 1,148 18.9 7.8 0.012 0.1

01055500 Nezinscot River at Turner Center, Maine 168 77.2 190 667 11.9 16.4 0.088 1.4

01057000 Little Androscoggin River near South Paris, Maine 73.9 83.7 283 734 15.0 15.3 0.029 1.6

01060000 Royal River at Yarmouth, Maine 141 50.3 73 193 6.7 11.0 0.127 0.8

01064500 Saco River near Conway, New Hampshire 385 85.7 550 1,916 23.5 24.5 0.091 0.3

01064801 Bearcamp River at South Tamworth, New Hampshire 67.0 75.6 412 1,221 16.6 31.5 0.098 0.4

01130000 Upper Ammonoosuc River near Groveton, New Hampshire 231 119 579 1,269 17.6 15.2 0.048 0.5

Minimum 14.9 46.6 73 193 4.5 0.0 0.000 0.0

Maximum 1,419 193 646 1,916 26.6 31.5 0.212 6.2

Mean 258 102 339 860 12.0 10.0 0.053 1.9
8 Regression Equations for Ungaged Rivers in Maine

Table 3. Point coordinates defining the Gulf of Maine Line.

[Point coordinates are in meters, referenced to Universal Transverse Mercator zone 19 datum (fig. 1)]

X coordinate Y coordinate

Point A 336321.28 4734992.89

Point B 775853.75 4988911.83

range from 4.5 percent (Mattawamkeag River near Mattawamkeag, Maine [01030500] streamgage) to 26.6 percent (Wild 

River at Gilead, Maine [01054200] streamgage), with a mean 

of 12 percent (table 2).

Mean Basin Percent Hydrologic Soil Group A

Wolock (1997) aggregated data from the national Natural 

Resources Conservation Service’s (NRCS) State Soil Geographic (STATSGO) database (U.S. Department of Agriculture, 1994) to compute 1-km (0.6-mi) grids of percentages of 

each hydrologic soil type (A, B, C, and D; U.S. Department 

of Agriculture, 1986). The gridded datasets of hydrologic soil 

types have a percentage of each soil type assigned to each 

grid. The percentages were computed as averages of multiple 

soil components and layers, weighted on the basis of soil layer 

thickness and component area quantified in the STATSGO 

database. Soils classified as hydrologic group A (HGA; fig. 2) 

are well drained with high infiltration rates (minimum infiltration rate of 8 to 12 millimeters per hour [mm/h] or 0.3 to 

0.5 inches per hour [in/h]) and high rates of water transmission (greater than 7.6 mm/h or 0.3 in/h; Dunne and Leopold, 

1978; U.S. Department of Agriculture, 1986). For use in this 

report, mean basin percent HGA was computed in GIS by 

arithmetically averaging all 1-km (0.6-mi) HGA grid points 

within the drainage basin boundaries. The mean basin percentages of soils classified HGA for streamgage drainage basins 

used in this study range from 0 percent (Ducktrap River near 

Lincolnville, Maine [01037380] streamgage) to 31.5 percent 

(Bearcamp River at South Tamworth, NH [01064801] 

streamgage), with a mean of 10 percent (table 2).

Fraction Sand and Gravel Aquifer

The Maine Office of GIS (MEGIS) serves a GIS dataset comprising the polygonal boundaries of significant 

aquifers as delineated by the Maine Geological Survey at a 

1:24,000 scale throughout the State of Maine (Maine Office 

of GIS, 2015). Significant aquifers are sand and gravel glacial 

deposits having the potential to yield 38 liters per minute 

(L/min; 10 gallons per minute [gal/min]) or more to a properly 

constructed well. The aquifers are differentiated by yield in 

the GIS dataset, denoted by the stored value in the attribute 

ATYPE. A high-yield aquifer with an estimated yield greater 

than 189 L/min (50 gal/min) is denoted ATYPE = 1, and an 

aquifer with an estimated yield of 38 to 189 L/min (10 to 

50 gal/min) is denoted ATYPE = 2.

The University of New Hampshire’s Geographically 

Referenced Analysis and Information Transfer (NH GRANIT) 

Web site, a GIS clearinghouse for the State of New Hampshire, serves a GIS dataset comprising the polygonal boundaries of stratified drift aquifers as delineated by the USGS and 

the New Hampshire Department of Environmental Services, 

Water Resources Division (New Hampshire Geographically 

Referenced Analysis and Information Transfer, 2014). For the 

purposes of this report, the stratified drift aquifers mapped in 

northern New Hampshire are considered to be comparable to 

the significant sand and gravel aquifers mapped in Maine.

The fraction of sand and gravel aquifer was computed 

as the sum of polygon areas of the mapped sand and gravel 

aquifers for Maine (ATYPE = 1 and 2; fig. 3) and (or) the 

stratified drift aquifers in northern New Hampshire divided 

by the total basin drainage area. Fractions of sand and gravel 

aquifer in streamgage drainage basins used in this report 

range from 0 (North Branch Penobscot River nr Pittston 

Farm, ME [01027200] streamgage) to 0.212 (Old Stream 

near Wesley, Maine [01021480] streamgage), with a mean of 

0.053 (table 2).

Percent Open Water

The 2006 NLCD (Multi-Resolution Land Characteristics 

Consortium, 2014) is a GIS 30-m (98.4-ft) gridded dataset for 

the conterminous United States where each grid is assigned 

a single value from 16 possible classes of land cover classification (Fry and others, 2011). Land cover class code 11 

is designated open water and is defined as areas of open 

water, generally with less than 25 percent cover of vegetation 

or soil—such as lakes and ponds. Percent open water was 

computed as the sum of the area of all 30-m (98.4-ft) grids 

designated with land-classification code 11 divided by the 

total basin drainage area and multiplied by 100. Percentages 

of NLCD-classified open water in streamgage drainage basins 

used in this study (fig. 4) range from 0 percent (Wild River at 

Gilead, Maine [01054200] streamgage) to 6.2 percent (Fish 

River near Fort Kent, Maine [01013500] streamgage), with a 

mean of 1.9 percent (table 2).

Regression Equations

Regression equations for estimating monthly and 

annual mean and 1, 5, 10, 25, 50, 75, 90, 95, and 99 percentile streamflows for ungaged rivers in Maine are presented 

in tables 4 through 16. Drainage area is a highly significant 

explanatory variable (basin characteristic) for all percentile 

streamflows and for all monthly and annual mean streamflows; 

larger drainage basins contribute greater streamflows.

Mean basin elevation is a significant explanatory variable 

for nearly all percentile streamflows for the annual period and 
Regression Equations 9

72° 70° 68°

46°

44°

0 25 50 75 100 MILES

0 50 100 KILOMETERS

MAINE

NEW HAMPSHIRE

VERMONT

Soil data mapped by D.M. Wolock, 1997

EXPLANATION

Study basin

Hydrologic soil group A

Value, in percent

High : 100

Low : 0

ATLANTIC OCEAN

CANADA

CANADA

Base map from Esri Inc. data, 2012

North American Datum 1983

Universal Transverse Mercator, zone 19N

Figure 2. Distribution of hydrologic soil group A in Maine and New Hampshire.
10 Regression Equations for Ungaged Rivers in Maine

72° 70° 68°

46°

44°

0 25 50 75 100 MILES

0 50 100 KILOMETERS

MAINE

NEW HAMPSHIRE

VERMONT

EXPLANATION

Study basin

Sand and gravel aquifer

ATLANTIC OCEAN

CANADA

CANADA

Base map from Esri Inc. data, 2012

North American Datum 1983

Universal Transverse Mercator, zone 19N

Aquifers in Maine mapped by the

Maine Geological Survey, 1:24,000, 2014

Aquifers in New Hampshire mapped by the

U.S. Geological Survey and the

New Hampshire Department of

Environmental Services, 1:24,000, 2014

Figure 3. Distribution of sand and gravel aquifers in Maine and New Hampshire. Maine aquifers from Maine Office 

of GIS (2015) and New Hampshire aquifers from New Hampshire Geographically Referenced Analysis and Information 

Transfer (2015).
Regression Equations 11

72° 70° 68°

46°

44°

0 25 50 75 100 MILES

0 50 100 KILOMETERS

MAINE

NEW HAMPSHIRE

VERMONT

Base map from Esri Inc. data, 2012

North American Datum 1983

Universal Transverse Mercator, zone 19N

Open water that is mapped by the

Multi-Resolution Land Characteristics

Consortium, 2014

EXPLANATION

Open water

Study basin

ATLANTIC OCEAN

CANADA

CANADA

Figure 4. Distribution of land cover classified as open water (land cover code 11) in the 2006 National Land Cover Dataset 

(NLCD) in Maine and New Hampshire.
12 Regression Equations for Ungaged Rivers in Maine

the months of July, August, September, and October. For these 

periods, the fraction of sand and gravel aquifer provides additional explanatory power for the low-streamflow percentiles 

(generally median and lower). Discharge from sand and gravel 

aquifers (groundwater discharge, also often referred to as base 

flow) typically composes a substantial component of the total 

streamflow during low-flow periods. The distance from the 

coast for the drainage basin provides significant explanatory 

power for the variability in flows during February, March, 

and April. Heat in the Atlantic Ocean has a warming effect on 

winter air temperatures near the coast; milder temperatures in 

basins closer to the coast generally result in less accumulated 

snowpack over the winter, greater occurrence of rain during 

winter, and earlier snowpack melt and runoff in late winter 

and early spring. For February, mean basin slope provides 

additional, significant explanatory power for median and 

lower streamflows with steeper slopes contributing to higher 

streamflows. Percent open water is a measure of storage and 

provides significant explanatory power for median and higher 

streamflows in March and for all percentiles in April.

Percent open water continues to provide significant 

explanatory power for percentiles in May and June; the signs 

of the coefficients indicate increased amounts of open water 

increase low flows and decrease the highest flows. This is 

consistent with regression equations for estimating flood 

flows of various annual exceedance probabilities by Hodgkins 

(1999), whose equations indicate basin storage has an attenuating effect on the magnitude of flood flows. Mean basin slope 

provides significant explanatory power for all percentiles in 

May and for 25 and lower percentiles (lower flows) in June.

November, December, and January have two-variable 

regression equations. Maximum basin elevation adds significant explanatory power for all percentiles in November, with 

higher elevations corresponding with higher streamflows. The 

mean basin percent of HGA (well-drained soils) adds significant explanatory power for 25 and lower percentiles (lower 

flows) in December and 90 and lower percentiles (lower 

flows) in January; in all equations, higher percentages of HGA 

correspond with higher streamflows.

Accuracy and limitations of the equations.—The 90 percent prediction interval is a measure of uncertainty for the 

regression equations; it was computed by first computing the 

average standard error of prediction (ASEP) by taking the 

arithmetic mean of the standard errors of prediction for all n

observations (in the case of this study, n = 24) for each regression equation. ASEP was then converted to a percentage for 

the 90 percent confidence interval, thereby representing an 

approximately 90 percent probability that the true value of the 

flow statistic at a location of interest is between the negativeand positive percent prediction intervals (tables 4–16). For 

example, suppose application of the annual 10 percentile flow 

equation (Q10, table 4) for a basin of interest yields 30 ft3

/s; 

there would be an approximate 90 percent probability that the 

true value of the annual 10 percentile streamflow is between 

-32.5 and +48.3 percent of 30 ft3

/s (20.2 to 44.5 ft3/s). 

Table 4. Regression equations for estimating annual streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation 

derivation; R2, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the 

mean streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; EAVG, mean basin elevation, in thousand 

meters; SGAQ, fraction of drainage basin area underlain by sand and gravel aquifer]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.000913DA1.54101.42EAVG105.19SGAQ -65.3 to 188 -57.2 to 134 0.87

Q5

 = 0.00828DA1.35101.07EAVG103.21SGAQ -43.6 to 77.2 -34.7 to 53.3 0.94

Q10 = 0.0288DA1.24100.850EAVG102.26SGAQ -32.5 to 48.3 -25.0 to 33.4 0.97

Q25 = 0.210DA1.07100.456EAVG101.15SGAQ -19.2 to 23.7 -13.2 to 15.2 0.99

Q50 = 0.865DA0.993100.204EAVG100.715SGAQ -17.7 to 21.6 -12.4 to 14.2 0.99

Q75 = 2.34DA0.984100.108EAVG100.341SGAQ -15.4 to 18.3 -10.9 to 12.2 0.99

Q90 = 5.40DA0.969100.135EAVG100.046SGAQ -15.3 to 18.0 -10.1 to 11.3 0.99

Q95 = 8.61DA0.956100.188EAVG10-0.055SGAQ -16.3 to 19.5 -10.4 to 11.6 0.99

Q99 = 23.4DA0.879100.349EAVG10-0.048SGAQ -24.8 to 32.9 -16.3 to 19.5 0.97

Qmean = 2.20DA0.960100.217EAVG100.253SGAQ -14.4 to 16.9 -9.90 to 10.9 0.99
Regression Equations 13

The prediction error sum of squares (PRESS) estimator 

of error is a measure of validation for the regression equations. 

PRESS is computed by summing the squares of the prediction residuals for the full set of n observations. A prediction 

residual for the ith observation is computed as the difference 

between the observed value of the dependent variable and the 

regression estimate of that variable on the basis of a regression 

equation derived by leaving out the ith observation (therefore 

using n–1 observations to develop the equation). The prediction residuals are computed for each observation, squared and 

summed, yielding the PRESS statistic. The ratio PRESS/n

is analogous to the average variance of prediction, and the 

square root of PRESS/n (converted to percent in tables 4–16) 

is analogous to the average standard error of prediction.

The R2 statistic is a measure of a regression model’s 

goodness of fit to the observations; its value ranges from 0 

through 1, where 1 indicates a perfect match between the 

regression model estimates and the observations. An adjusted 

R2

 (tables 4–16) is a coefficient of determination adjusted 

for the degrees of freedom in the model, thereby enabling 

direct comparison between models with differing numbers of 

explanatory variables.

The largest prediction intervals and PRESS percentages are associated with regression equations for the lowest 

streamflows derived for months during which the lowest 

streamflows of the year occur (such as the 1 and 5 percentiles for August and September). Large prediction intervals 

for a regression equation represent large uncertainty in the 

regression estimate. Because of the large uncertainty in 

regression estimates for these lowest streamflows, there is 

the possibility of discontinuities to arise during application 

of those equations. An example of a discontinuity would be 

a 1 percentile regression estimate larger in magnitude that 

the 5 percentile estimate for the same month; this does not 

mean either estimate is wrong, rather, the results are simply 

a function of the large uncertainty in the estimates of those 

low flows.

The regression equations presented in this report have 

been derived on the basis of streamflow and basin characteristics data for unregulated, rural drainage basins without 

substantial streamflow or drainage modifications (for example, 

diversions and (or) regulation by dams or reservoirs, tile drainage, irrigation, channelization, and impervious paved surfaces). Using these equations for regulated or urbanized basins 

with substantial streamflow or drainage modifications will 

yield results of unknown error. For the study detailed in this 

report, regulation needed to be completely absent or deemed 

small enough so as to have a negligible effect on the computation of monthly statistics using daily mean streamflows. For 

the 24 streamgage study basins, the sum of percentages of 

land cover classified by the NLCD as either developed open 

space (land-classification code 21) or low- (code 22), medium- 

(code 23), or high-intensity development (code 24) ranged 

from than 0.1 to 9.3 percent (mean of 2.3 percent). Not including developed open space, which commonly includes large-lot 

single-family housing units, parks, and golf courses (Fry and 

Table 5. Regression equations for estimating January streamflows for ungaged, unregulated streams in 

rural drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression 

equation derivation; R2, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in 

percent; Qmean, the mean streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; HGA, mean 

basin percentage of hydrologic soil group A]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.271DA0.971100.0068HGA -37.4 to 59.7 -24.3 to 32.1 0.92

Q5

 = 0.430DA0.946100.0048HGA -30.4 to 43.7 -20.2 to 25.3 0.95

Q10 = 0.555DA0.932100.0055HGA -28.8 to 40.5 -19.3 to 23.8 0.95

Q25 = 0.793DA0.931100.0059HGA -24.4 to 32.2 -16.3 to 19.5 0.97

Q50 = 1.06DA0.946100.0052HGA -28.6 to 40.0 -19.1 to 23.7 0.96

Q75 = 1.88DA0.925100.0048HGA -31.1 to 45.2 -20.8 to 26.3 0.94

Q90 = 4.01DA0.885100.0059HGA -31.9 to 46.8 -21.6 to 27.5 0.94

Q95 = 9.21DA0.824100.0049HGA -35.0 to 54.0 -24.2 to 32.0 0.91

Q99 = 27.6DA0.799100.0018HGA -50.4 to 101 -35.1 to 54.1 0.78

Qmean = 2.40DA0.882100.0047HGA -26.8 to 36.6 -18.0 to 21.9 0.96
14 Regression Equations for Ungaged Rivers in Maine

Table 6. Regression equations for estimating February streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation 

derivation; R2, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the 

mean streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; SLOPE, mean basin slope, in percent; 

DIST, distance from the coast, in miles, measured as the shortest distance from the drainage basin centroid to a line in the Gulf of 

Maine defined by end points 71W, 42.75N and 65.5W, 45N, referenced to North American Datum of 1983]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 1.16DA0.961100.0142SLOPEDIST-0.384 -37.4 to 59.8 -25.5 to 34.3 0.91

Q5

 = 1.80DA1.03100.0120SLOPEDIST-0.489 -29.8 to 42.5 -21.5 to 27.4 0.95

Q10 = 3.92DA1.06100.0107SLOPEDIST-0.641 -27.4 to 37.7 -19.6 to 24.4 0.96

Q25 = 7.06DA1.09100.0086SLOPEDIST-0.718 -23.6 to 30.9 -17.2 to 20.8 0.97

Q50 = 12.8DA1.09100.0058SLOPEDIST-0.762 -20.0 to 25.1 -13.9 to 16.1 0.98

Q75 = 30.8DA1.05100.0020SLOPEDIST-0.785 -14.5 to 16.9 -9.90 to 11.0 0.99

Q90 = 87.1DA1.04100.0001SLOPEDIST-0.879 -19.7 to 24.5 -14.1 to 16.4 0.98

Q95 = 244DA0.96810-0.0002SLOPEDIST-0.923 -25.9 to 34.9 -18.5 to 22.7 0.96

Q99 = 647DA0.880100.0057SLOPEDIST-0.902 -35.5 to 55.1 -26.4 to 35.8 0.90

Qmean = 35.9DA1.02100.0041SLOPEDIST-0.814 -15.9 to 18.8 -11.4 to 12.9 0.99

Table 7. Regression equations for estimating March streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation derivation; R2

, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the mean 

streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; WATER, percent of drainage basin land cover 

classified as open water (National Land Cover Data land-classification code 11); DIST, distance from the coast, in miles, measured as 

the shortest distance from the drainage basin centroid to a line in the Gulf of Maine defined by end points 71W, 42.75N and 65.5W, 

45N, referenced to North American Datum of 1983]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 5.83DA1.0210-0.0034WATERDIST-0.676 -36.5 to 57.4 -27.5 to 37.9 0.92

Q5

 = 8.42DA1.0310-0.0122WATERDIST-0.698 -32.3 to 47.7 -23.8 to 31.2 0.94

Q10 = 13.4DA1.0010-0.0129WATERDIST-0.720 -26.3 to 35.7 -19.2 to 23.8 0.96

Q25 = 36.2DA0.99010-0.0117WATERDIST-0.829 -20.7 to 26.0 -14.5 to 17.0 0.98

Q50 = 159DA1.0110-0.0116WATERDIST-1.02 -17.7 to 21.5 -11.7 to 13.3 0.98

Q75 = 274DA0.99210-0.0286WATERDIST-0.958 -21.5 to 27.4 -15.5 to 18.4 0.97

Q90 = 259DA0.93010-0.0427WATERDIST-0.721 -24.8 to 32.9 -18.6 to 22.8 0.96

Q95 = 225DA0.91310-0.0540WATERDIST-0.583 -30.0 to 42.8 -22.1 to 28.3 0.94

Q99 = 109DA0.80710-0.0744WATERDIST-0.126 -27.6 to 38.1 -20.3 to 25.5 0.94

Qmean = 103DA0.94010-0.0392WATERDIST-0.706 -18.9 to 23.3 -13.7 to 15.8 0.98
Regression Equations 15

Table 8. Regression equations for estimating April streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation derivation; R2

, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the mean 

streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; WATER, percent of drainage basin land cover 

classified as open water (National Land Cover Data land-classification code 11); DIST, distance from the coast, in miles, measured as 

the shortest distance from the drainage basin centroid to a line in the Gulf of Maine defined by end points 71W, 42.75N and 65.5W, 45N, 

referenced to North American Datum of 1983]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 3.92DA1.1210-0.0468WATERDIST-0.432 -31.0 to 44.8 -22.1 to 28.4 0.96

Q5

 = 3.32DA1.1410-0.0475WATERDIST-0.313 -30.2 to 43.3 -23.4 to 30.6 0.96

Q10 = 3.22DA1.1210-0.0415WATERDIST-0.233 -24.0 to 31.5 -18.7 to 23.0 0.98

Q25 = 2.13DA1.0610-0.0291WATERDIST0.011 -21.1 to 26.8 -17.1 to 20.7 0.98

Q50 = 1.14DA1.0210-0.0113WATERDIST0.292 -19.5 to 24.2 -14.4 to 16.9 0.99

Q75 = 1.59DA0.97110-0.0207WATERDIST0.404 -19.5 to 24.2 -13.7 to 15.9 0.99

Q90 = 3.39DA0.92410-0.0374WATERDIST0.412 -18.2 to 22.3 -12.4 to 14.2 0.99

Q95 = 6.51DA0.89410-0.0443WATERDIST0.370 -16.8 to 20.2 -11.2 to 12.6 0.99

Q99 = 39.5DA0.82210-0.0518WATERDIST0.170 -26.6 to 36.2 -19.0 to 23.4 0.96

Qmean = 2.33DA0.96410-0.0283WATERDIST0.286 -16.7 to 20.0 -12.0 to 13.6 0.99

Table 9. Regression equations for estimating May streamflows for ungaged, unregulated streams in rural drainage 

basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation derivation; R2

, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the mean 

streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; WATER, percent of drainage basin land cover classified as open water (National Land Cover Data land-classification code 11); SLOPE, mean basin slope, in percent]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.0913DA1.20100.0373WATER100.0233SLOPE -33.7 to 50.9 -21.9 to 28.0 0.96

Q5

 = 0.158DA1.17100.0430WATER100.0224SLOPE -28.4 to 39.7 -20.1 to 25.2 0.97

Q10 = 0.216DA1.15100.0462WATER100.0219SLOPE -26.4 to 35.9 -18.6 to 22.8 0.98

Q25 = 0.362DA1.13100.0507WATER100.0208SLOPE -22.4 to 28.8 -15.6 to 18.5 0.98

Q50 = 0.615DA1.13100.0457WATER100.0190SLOPE -19.6 to 24.4 -12.7 to 14.5 0.99

Q75 = 1.10DA1.12100.0397WATER100.0175SLOPE -21.4 to 27.3 -13.8 to 16.0 0.98

Q90 = 2.14DA1.10100.0253WATER100.0161SLOPE -25.6 to 34.4 -16.8 to 20.2 0.98

Q95 = 3.67DA1.06100.0181WATER100.0160SLOPE -26.4 to 35.8 -17.4 to 21.0 0.97

Q99 = 9.39DA1.0210-0.0039WATER100.0139SLOPE -23.4 to 30.6 -16.0 to 19.1 0.98

Qmean = 1.07DA1.10100.0323WATER100.0174SLOPE -20.4 to 25.6 -13.3 to 15.4 0.99
16 Regression Equations for Ungaged Rivers in Maine

Table 10. Regression equations for estimating June streamflows for ungaged, unregulated streams in rural drainage 

basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation derivation; 

R2, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the mean streamflow 

estimate in cubic feet per second; DA, basin drainage area, in square miles; WATER, percent of drainage basin land cover classified as open 

water (National Land Cover Data land-classification code 11); SLOPE, mean basin slope, in percent]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.0689DA1.15100.0328WATER100.0173SLOPE -46.5 to 86.8 -34.0 to 51.6 0.91

Q5

 = 0.0922DA1.13100.0405WATER100.0197SLOPE -38.9 to 63.7 -28.1 to 39.1 0.94

Q10 = 0.109DA1.14100.0394WATER100.0195SLOPE -35.2 to 54.4 -25.0 to 33.4 0.95

Q25 = 0.188DA1.13100.0312WATER100.0178SLOPE -28.1 to 39.2 -19.5 to 24.2 0.97

Q50 = 0.384DA1.10100.0258WATER100.0147SLOPE -23.3 to 30.3 -15.9 to 18.9 0.98

Q75 = 1.12DA1.04100.0165WATER100.0108SLOPE -24.1 to 31.7 -17.5 to 20.5 0.98

Q90 = 3.64DA0.97010-0.0026WATER100.0074SLOPE -27.9 to 38.8 -20.0 to 25.0 0.96

Q95 = 8.95DA0.92010-0.0253WATER100.0029SLOPE -28.3 to 39.4 -20.4 to 25.6 0.96

Q99 = 35.8DA0.88210-0.0780WATER10-0.0017SLOPE -35.8 to 55.9 -25.4 to 34.0 0.92

Qmean = 1.41DA1.00100.0006WATER100.0104SLOPE -18.6 to 22.9 -13.6 to 15.7 0.98

Table 11. Regression equations for estimating July streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation derivation; R2

, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the mean 

streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; EAVG, mean basin elevation, in thousands of 

meters; SGAQ, fraction of drainage basin area underlain by sand and gravel aquifer]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.0061DA1.38100.891EAVG103.04SGAQ -55.5 to 125 -42.9 to 75.1 0.90

Q5

 = 0.0148DA1.31100.788EAVG102.48SGAQ -49.9 to 99.6 -36.6 to 57.8 0.91

Q10 = 0.0207DA1.30100.745EAVG102.07SGAQ -44.3 to 79.5 -31.5 to 45.9 0.94

Q25 = 0.0382DA1.27100.656EAVG101.51SGAQ -37.0 to 58.8 -25.3 to 33.9 0.96

Q50 = 0.105DA1.20100.586EAVG100.781SGAQ -29.9 to 42.7 -20.1 to 25.2 0.97

Q75 = 0.363DA1.11100.499EAVG100.001SGAQ -26.3 to 35.7 -18.5 to 22.7 0.98

Q90 = 1.08DA1.05100.474EAVG10-0.070SGAQ -24.3 to 32.1 -17.8 to 21.7 0.98

Q95 = 2.11DA1.01100.463EAVG10-0.044SGAQ -27.2 to 37.3 -19.2 to 23.7 0.97

Q99 = 6.35DA0.926100.593EAVG100.048SGAQ -42.8 to 74.7 -31.0 to 44.9 0.89

Qmean = 0.432DA1.08100.508EAVG100.165SGAQ -19.8 to 24.7 -14.4 to 16.8 0.99
Regression Equations 17

Table 12. Regression equations for estimating August streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation derivation; R2

, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the mean 

streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; EAVG, mean basin elevation, in thousands of 

meters; SGAQ, fraction of drainage basin area underlain by sand and gravel aquifer]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.000136DA1.77101.66EAVG106.56SGAQ -78.8 to 373 -71.4 to 250 0.80

Q5

 = 0.000774DA1.60101.36EAVG104.87SGAQ -67.0 to 203 -58.0 to 138 0.86

Q10 = 0.00136DA1.56101.28EAVG104.46SGAQ -62.9 to 170 -53.7 to 116 0.88

Q25 = 0.0108DA1.36100.926EAVG102.80SGAQ -42.4 to 73.6 -31.3 to 45.5 0.95

Q50 = 0.0339DA1.27100.831EAVG101.87SGAQ -32.0 to 47.1 -23.0 to 29.9 0.97

Q75 = 0.157DA1.17100.720EAVG100.655SGAQ -28.5 to 39.9 -19.3 to 23.8 0.97

Q90 = 0.497DA1.12100.717EAVG100.053SGAQ -29.4 to 41.6 -20.4 to 25.6 0.97

Q95 = 0.903DA1.09100.779EAVG100.233SGAQ -28.5 to 39.8 -19.5 to 24.2 0.97

Q99 = 4.00DA0.945100.914EAVG100.780SGAQ -42.1 to 72.7 -29.8 to 42.5 0.91

Qmean = 0.206DA1.11100.811EAVG100.905SGAQ -28.0 to 38.8 -19.1 to 23.7 0.97

Table 13. Regression equations for estimating September streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation derivation; R2

, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the mean 

streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; EAVG, mean basin elevation, in thousands of 

meters; SGAQ, fraction of drainage basin area underlain by sand and gravel aquifer]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.00013DA1.72101.65EAVG106.96SGAQ -78.3 to 360 -70.5 to 238 0.80

Q5

 = 0.000199DA1.73101.71EAVG106.28SGAQ -78.7 to 369 -72.6 to 265 0.80

Q10 = 0.00217DA1.45101.29EAVG104.54SGAQ -57.9 to 138 -49.2 to 97.0 0.90

Q25 = 0.00865DA1.33101.18EAVG103.17SGAQ -44.6 to 80.6 -35.4 to 54.9 0.94

Q50 = 0.0380DA1.21100.990EAVG102.09SGAQ -29.3 to 41.5 -22.2 to 28.5 0.97

Q75 = 0.203DA1.08100.759EAVG100.901SGAQ -22.6 to 29.1 -15.2 to 17.9 0.98

Q90 = 0.575DA1.04100.711EAVG100.329SGAQ -30.9 to 44.7 -21.1 to 26.7 0.96

Q95 = 1.29DA1.01100.596EAVG10-0.067SGAQ -34.2 to 52.1 -23.3 to 30.3 0.95

Q99 = 6.84DA0.892100.522EAVG100.207SGAQ -45.5 to 83.6 -31.2 to 45.4 0.87

Qmean = 0.279DA1.04100.729EAVG100.795SGAQ -27.3 to 37.6 -18.5 to 22.7 0.97
18 Regression Equations for Ungaged Rivers in Maine

Table 14. Regression equations for estimating October streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation derivation; R2

, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, the mean 

streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; EAVG, mean basin elevation, in thousands of 

meters; SGAQ, fraction of drainage basin area underlain by sand and gravel aquifer]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.00303DA1.33101.52EAVG104.93SGAQ -62.8 to 169 -56.0 to 127 0.86

Q5

 = 0.00476DA1.36101.38EAVG103.93SGAQ -59.0 to 144 -52.2 to 109 0.88

Q10 = 0.0142DA1.27101.18EAVG102.78SGAQ -44.1 to 79.0 -37.4 to 59.8 0.94

Q25 = 0.0759DA1.13100.869EAVG101.75SGAQ -23.7 to 31.1 -17.0 to 20.5 0.98

Q50 = 0.366DA1.02100.658EAVG100.566SGAQ -27.2 to 37.3 -19.2 to 23.8 0.97

Q75 = 1.53DA0.951100.455EAVG10-0.002SGAQ -31.1 to 45.2 -22.7 to 29.4 0.95

Q90 = 4.60DA0.896100.447EAVG10-0.159SGAQ -35.9 to 56.0 -24.8 to 33.0 0.92

Q95 = 9.43DA0.841100.499EAVG10-0.082SGAQ -35.1 to 54.0 -23.1 to 30.1 0.92

Q99 = 30.8DA0.784100.578EAVG10-0.218SGAQ -42.9 to 75.2 -29.2 to 41.2 0.86

Qmean = 1.91DA0.895100.526EAVG100.083SGAQ -28.9 to 40.6 -19.6 to 24.4 0.96

Table 15. Regression equations for estimating November streamflows for ungaged, unregulated streams in 

rural drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation 

derivation; R2, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, 

the mean streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; EMAX, maximum basin elevation, in thousands of meters]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.0514DA1.13100.376EMAX -65.0 to 185 -55.1 to 123 0.80

Q5

 = 0.100DA1.10100.342EMAX -54.2 to 118 -43.2 to 76.1 0.87

Q10 = 0.290DA1.02100.246EMAX -34.7 to 53.2 -24.8 to 33.0 0.95

Q25 = 0.977DA0.937100.146EMAX -27.0 to 37.0 -17.3 to 20.9 0.96

Q50 = 1.87DA0.955100.081EMAX -21.0 to 26.6 -14.4 to 16.9 0.98

Q75 = 3.65DA0.949100.050EMAX -19.0 to 23.4 -12.6 to 14.5 0.98

Q90 = 7.74DA0.901100.064EMAX -22.5 to 29.0 -14.4 to 16.8 0.97

Q95 = 12.3DA0.867100.094EMAX -30.4 to 43.6 -19.7 to 24.6 0.94

Q99 = 33.1DA0.758100.182EMAX -41.9 to 72.0 -28.4 to 39.6 0.86

Qmean = 3.49DA0.902100.099EMAX -20.2 to 25.4 -12.9 to 14.8 0.98
Regression Equations 19

Table 16. Regression equations for estimating December streamflows for ungaged, unregulated streams in 

rural drainage basins in Maine and northern New Hampshire.

[(PRESS/n)1/2, prediction error sum of squares, in percent, where n is the number of streamgages used in the regression equation 

derivation; R2, coefficient of determination; Qx, the streamflow estimate in cubic feet per second for x percentile, in percent; Qmean, 

the mean streamflow estimate in cubic feet per second; DA, basin drainage area, in square miles; HGA, mean basin percentage of 

hydrologic soil group A]

Regression equation

90-percent 

prediction interval

(percent)

(PRESS/n)

1/2

(percent) Adjusted R2

Q1 = 0.0516DA1.28100.0132HGA -58.6 to 142 -48.7 to 95.0 0.85

Q5

 = 0.222DA1.11100.0083HGA -27.6 to 38.2 -19.9 to 24.9 0.97

Q10 = 0.573DA0.986100.0047HGA -22.7 to 29.4 -15.8 to 18.7 0.98

Q25 = 1.12DA0.935100.0036HGA -23.2 to 30.2 -15.8 to 18.7 0.97

Q50 = 1.92DA0.936100.0021HGA -28.9 to 40.6 -19.5 to 24.2 0.96

Q75 = 2.90DA0.955100.0032HGA -31.6 to 46.1 -21.9 to 28.1 0.95

Q90 = 5.46DA0.943100.0038HGA -31.6 to 46.2 -21.6 to 27.5 0.94

Q95 = 10.8DA0.888100.0037HGA -30.4 to 43.8 -20.8 to 26.3 0.94

Q99 = 27.6DA0.855100.0059HGA -43.0 to 75.5 -29.3 to 41.3 0.86

Qmean = 3.16DA0.921100.0035HGA -24.9 to 33.1 -16.6 to 20.0 0.97
20 Regression Equations for Ungaged Rivers in Maine

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

1 10 100 1,000 10,000

Mean basin hydrologic soil group A,

in percent

Drainage area, in square miles

Figure 6. Two-dimensional range of explanatory variables used 

in regression equations for estimating January and December 

mean and selected percentile streamflows for ungaged, 

unregulated streams in rural drainage basins in Maine and 

northern New Hampshire.

0

100

200

300

400

500

600

700

1 10 100 1,000 10,000

Mean basin elevation, in meters

0.00

0.05

0.10

0.15

0.20

0.25

1 10 100 1,000 10,000

Fraction of drainage basin underlain by

significant sand and gravel aquifer

0.00

0.05

0.10

0.15

0.20

0.25

0 100 200 300 400 500 600 700

Fraction of drainage basin underlain by

significant sand and gravel aquifer

Mean basin elevation, in meters

A

B

C

Drainage area, in square miles

Drainage area, in square miles

Figure 5. Two-dimensional ranges of explanatory variables used in regression equations for estimating annual and July, August, 

September, and October mean and selected percentile streamflows for ungaged, unregulated streams in rural drainage basins in Maine 

and northern New Hampshire.
Regression Equations 21

D

E

F

A

B

C

0.0

5.0

10.0

15.0

20.0

25.0

30.0

1 10 100 1,000 10,000

Mean basin slope, in percent

Drainage area, in square miles

0

50

100

150

200

250

1 10 100 1,000 10,000

Basin centroid distance from the coast, in miles

Drainage area, in square miles

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1 10 100 1,000 10,000

Basin open water, in percent

Drainage area, in square miles

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0 50 100 150 200 250

Mean basin slope, in percent

Basin centroid distance from the coast, in miles

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Mean basin slope, in percent

Basin open water, in percent

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 50 100 150 200 250

Basin open water, in percent

Basin centroid distance from the coast, in miles

Figure 7. Two-dimensional ranges of explanatory variables used in regression equations for estimating February, March, April, May, 

and June mean and selected percentile streamflows for ungaged, unregulated streams in rural drainage basins in Maine and northern 

New Hampshire.

0

500

1,000

1,500

2,000

2,500

1 10 100 1,000 10,000

Maximum basin elevation, in meters

Drainage area, in square miles

Figure 8. Two-dimensional range of explanatory variables 

used in regression equations for estimating November mean 

and selected percentile streamflows for ungaged, unregulated 

streams in rural drainage basins in Maine and northern New 

Hampshire.
22 Regression Equations for Ungaged Rivers in Maine

others, 2011), maximum developed land cover is 3.7 percent 

(mean of 0.7 percent for all 24 basins). Drainage alterations 

are assumed to accompany development and are considered 

negligible for all study basins in this report.

When using the regression equations, the basin characteristics needed for the equations (explanatory variables) should 

be derived using the same or comparable methods with the 

same sets of data as those documented in this report. Basin 

characteristics derived using other techniques or datasets 

or using values outside the ranges (and combined ranges of 

multiple explanatory variables in a single equation (fig. 5–8) 

used to develop these regression equations (table 2) will yield 

results of unknown error.

Summary

Regression equations offer a statistical method for 

estimating streamflows at ungaged locations, which is useful 

for water management, project planning, and other activities 

related to monitoring and regulating surface waters. The U.S. 

Geological Survey and the Maine Department of Transportation used streamflow data to develop dependent variables 

for 130 regression equations for estimating monthly and 

annual mean and 1, 5, 10, 25, 50, 75, 90, 95, and 99 percentile streamflows for ungaged, unregulated rivers in Maine 

and northern New Hampshire along with the data and methods used to derive them in an effort to delineate hydrologic 

conditions. The regression equations presented in this report 

supersede previously published regression equations because 

of the updated streamflow and basin characteristics data used 

in this report.

Daily streamflow data from 24 streamgages in Maine and 

northern New Hampshire were used to derive the regression 

equations. Streamflow in these 24 rural, unregulated basins 

was deemed to be substantially unaffected by diversions and 

(or) regulation by dams or reservoirs. The land cover in the 

study basins was mostly forested; open water and wetlands 

composed a mean of 8.3 percent of the study basin areas, and 

developed land of any kind composed less than 10 percent of 

any study basin area. Given recent studies documenting climatic trends and their effects on hydrology in Maine and New 

England, streamflow data collected during the 30-year period 

from October 1, 1982, through September 30, 2012, were used 

to derive the dependent variables for this report, thereby representing contemporary hydrologic conditions in Maine and 

northern New Hampshire.

Sixty-eight explanatory variables comprising characteristics such as geology, land cover, land use, precipitation, 

and temperature were derived using a geographic information system and tested for use as potential explanatory 

variables for the dependent streamflow variables. Ordinary 

least squares regression of all possible subsets of 68 explanatory variables for each of 130 dependent streamflow 

variables were used to select the explanatory variables that 

would appear in the final regression equations. Emphasis 

was placed on developing a coherent set of equations in 

an effort to reduce the possibility of discontinuities in the 

percentile estimates. Weighted least squares (WLS) regression techniques were used to derive the final coefficients and 

measures of uncertainty for the regression equations. WLS 

weights were computed as a function of the number of complete water years of record from water years 1983 to 2012 

divided by the mean record length for all of the stations used 

in the analysis.

Eight basin characteristics serve as the final explanatory variables for estimating monthly and annual mean and 

1, 5, 10, 25, 50, 75, 90, 95, and 99 percentile streamflows: 

drainage area, distance from the coast, mean and maximum 

basin elevation, mean basin slope, mean basin percentage of 

hydrologic soil group A (HGA), fraction of sand and gravel 

aquifers, and percent open water. Drainage area is a highly 

significant explanatory variable for all percentile streamflows 

and for all monthly and annual mean streamflows; larger 

drainage basins contribute greater streamflows. Mean basin 

elevation and fraction of sand and gravel aquifer are both 

significant explanatory variables for the annual period and 

low flow months. Distance from the coast provides explanatory power for the variability in February, March, and April 

flows. Percent open water, which is a measure of storage, 

provides explanatory power during spring months, with 

greater amounts of open water corresponding with lower 

flows in March and April and higher flows in May and June, 

in general. Mean basin slope provides explanatory power for 

streamflows in February, May, and June, with steeper slopes 

contributing to higher streamflows, in general. Maximum 

basin elevation provides explanatory power for November, 

with higher elevations corresponding with higher streamflows. Mean basin percent of HGA (well-drained soils) 

provides explanatory power for streamflows in December 

and January, with higher percentages of HGA corresponding 

with higher streamflows.

The largest uncertainties are associated with regression equations for the lowest streamflows derived for months 

during which the lowest streamflows of the year occur (such 

as the 1 and 5 percentiles for August and September). The 

regression equations have been derived from streamflow 

and basin characteristics data for unregulated, rural drainage 

basins without substantial drainage alterations (for example, 

diversions and (or) regulation by dams or reservoirs, tile 

drainage, irrigation, channelization, and impervious paved 

surfaces); therefore, using them for regulated or urbanized 

basins with substantial drainage alterations will yield results of 

unknown error. Basin characteristics derived using techniques 

or datasets other than those documented in this report or using 

values outside the ranges (and combined ranges of multiple 

explanatory variables in a single equation) used to develop 

these regression equations will yield streamflow estimates of 

unknown error.
References Cited 23

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Appendix 1. Monthly and Annual Mean and Selected 

Percentile Streamflows for Selected U.S. Geological Survey 

Streamgages in Maine and Northern New Hampshire

Tables 1–1—1–10. Computed monthly and annual streamflow statistics for selected 

U.S. Geological Survey streamgages in Maine and northern New Hampshire

1–1. Mean

1–2. 1 percentile

1–3. 5 percentile

1–4. 10 percentile

1–5. 25 percentile

1–6. 50 percentile

1–7. 75 percentile

1–8. 90 percentile

1–9. 95 percentile

1–10. 99 percentile
26 Regression Equations for Ungaged Rivers in Maine Table 1–1. Computed monthly and annual mean streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire. [ft3/s, cubic foot per second] U.S. Geological Survey streamgage Monthly mean streamflow (ft3/s) Annual mean stream- flow (ft3/s) Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. 01013500 Fish River near Fort Kent, Maine 798 623 715 4,140 4,450 1,650 1,030 843 567 932 1,530 1,420 1,560 01021480 Old Stream near Wesley, Maine 58.6 46.1 108 151 76.7 44.6 17.5 15.5 14.3 44.2 82.1 99.2 62.5 01022500 Narraguagus River at Cherryfield, Maine 483 453 838 1,150 656 396 204 155 157 319 597 656 505 01027200 North Branch Penobscot River near Pittston Farm, Maine 258 124 365 1,720 764 437 303 293 164 540 546 422 492 01029200 Seboeis River near Shin Pond, Maine 208 125 248 1,080 599 228 129 117 126 261 403 373 326 01030500 Mattawamkeag River near Mattawamkeag, Maine 1,650 1,310 2,950 9,080 4,670 1,940 1,200 882 671 1,670 3,300 3,070 2,700 01031300 Piscataquis River at Blanchard, Maine 134 89 259 850 375 220 109 76 93.3 248 347 282 257 01031450 Kingsbury Stream at Abbot Village, Maine 120 91.1 300 712 270 211 85.4 60.7 80.3 243 317 257 227 01031500 Piscataquis River near Dover-Foxcroft, Maine 384 294 740 2,160 897 536 278 184 193 525 827 656 639 01037380 Ducktrap River near Lincolnville, Maine 34.7 32 67.9 85.2 40.7 28.8 11.7 4.01 4.99 32.1 48.3 49.3 36.1

01038000 Sheepscot River at North Whitefield, Maine 274 239 504 721 351 211 84.4 54.4 52.4 146 306 369 27601044550 Spencer Stream near Grand Falls, Maine 200 147 314 1,260 807 409 205 174 177 377 459 350 40401047000 Carrabassett River near North Anson, Maine 471 371 970 2,470 1,270 783 418 317 274 661 982 776 81301048000 Sandy River near Mercer, Maine 686 528 1,390 3,280 1,610 1,090 526 385 297 865 1,300 1,080 1,080

01052500 Diamond River near Wentworth Location, New Hampshire 200 148 352 1,200 690 346 197 175 149 321 391 261 36901054200 Wild River at Gilead, Maine 134 92.5 245 561 336 172 87.2 97.4 77.5 188 259 180 203

01054300 Ellis River at South Andover, Maine 194 103 259 841 468 329 159 147 97 320 359 414 30801055000 Swift River near Roxbury, Maine 139 94.6 238 685 394 224 119 95.7 82.6 205 266 193 22801055500 Nezinscot River at Turner Center, Maine 246 224 508 957 457 303 136 114 71 218 397 368 33101057000 Little Androscoggin River near South Paris, Maine 97.5 84.1 224 424 195 136 59.5 52.1 35.9 101 169 154 14401060000 Royal River at Yarmouth, Maine 203 224 570 650 330 203 96.8 91.3 83.1 150 290 295 26601064500 Saco River near Conway, New Hampshire 702 502 1,080 2,770 1,870 946 529 540 429 913 1,210 1,050 1,050

01064801 Bearcamp River at South Tamworth, New Hampshire 129 100 238 440 207 136 75.9 68 63 167 192 199 16801130000 Upper Ammonoosuc River near Groveton, NH 303 239 560 1,460 924 456 260 226 207 403 491 419 493
Appendix 1 27

Table 1–2. Computed monthly and annual 1 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire.[ft3/s, cubic foot per second]

U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual 

streamflow

(ft3/s)

Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

01013500 Fish River near Fort Kent, Maine 275 195 220 382 852 466 289 116 62 58 253 405 118

01021480 Old Stream near Wesley, Maine 6.7 8.3 12 30 13 9.7 3.2 1.9 1.6 2.5 4.3 6.1 2.3

01022500 Narraguagus River at Cherryfield, Maine 83 83 130 279 170 86 47 27 22 34 50.5 58 34

01027200 North Branch Penobscot River near Pittston Farm, Maine 48 32 24 91 89 67 38 12 6.7 23 57 80 19

01029200 Seboeis River near Shin Pond, Maine 51 50 39 107 103 58 31 6.8 6.3 9.5 28 65 10

01030500 Mattawamkeag River near Mattawamkeag, Maine 245 186 265 1,260 731 226 91 45 35 64 188 460 69

01031300 Piscataquis River at Blanchard, Maine 29 22 19 70 42 25 11 4.3 3.4 7.1 17 31 6.3

01031450 Kingsbury Stream at Abbot Village, Maine 21 22 21 71 29 17 4.7 1.4 2 8 18 23 2.8

01031500 Piscataquis River near Dover-Foxcroft, Maine 62 41 68 267 123 71 30 12 9.05 23 37 61 16

01037380 Ducktrap River near Lincolnville, Maine 4.1 3.9 6.5 8.8 4.4 2.1 0.15 0.001 0.001 0.02 0.11 0.25 0.01

01038000 Sheepscot River at North Whitefield, Maine 38 34 56 116 70 28.5 16 9.8 7.85 11 16.5 21 12

01044550 Spencer Stream near Grand Falls, Maine 55 50 45 110 153 85 34 19 11 29 50 71 26

01047000 Carrabassett River near North Anson, Maine 57 54 99 382 250 117 65 38 33.5 51 72.5 108 49

01048000 Sandy River near Mercer, Maine 119 112 119 495 295 140 72 44 35 61 98 129 55

01052500 Diamond River near Wentworth Location, New Hampshire 53 48 46 102 99 50.5 23 16 12 31 58.5 56 25

01054200 Wild River at Gilead, Maine 24 26 20 80 69 24 12 8.2 7.2 12 25 30 10

01054300 Ellis River at South Andover, Maine 33 33 35 75 83 43 27 11 9.2 15 32 38 12

01055000 Swift River near Roxbury, Maine 20 24 26 100 58 26.5 12 6 4.1 15 24.5 36 9

01055500 Nezinscot River at Turner Center, Maine 39 37 51 127 85 45 21 15 11 27 42 61 17

01057000 Little Androscoggin River near South Paris, Maine 21 19 22 60.5 29 9.4 4 1.5 0.76 4.7 19.5 28 3.1

01060000 Royal River at Yarmouth, Maine 42 42 58 109 63 40 24 21 20 24 38 47 23

01064500 Saco River near Conway, New Hampshire 178 175 203 542 494 212 137 98 84 132 226 216 115

01064801 Bearcamp River at South Tamworth, New Hampshire 27 29 29 61.5 29 16 7.7 3.1 3.1 10 24 39 6

01130000 Upper Ammonoosuc River near Groveton, New Hampshire 100 68 64 210 188 100 63 42 33 63 114 125 51
28 Regression Equations for Ungaged Rivers in Maine Table 1–3. Computed monthly and annual 5 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire. [ft3/s, cubic foot per second] U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual stream- flow (ft3/s) Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. 01013500 Fish River near Fort Kent, Maine 330 250 240 614 1,450 630 386 191 109 118 358 490 238 01021480 Old Stream near Wesley, Maine 10 13 16 41 22 11 5.7 2.3 2 2.8 5.55 11 3.9 01022500 Narraguagus River at Cherryfield, Maine 105 120 180 360 228 108 58 33 33 48 95 150 55 01027200 North Branch Penobscot River near Pittston Farm, Maine 54 34 31 119 159 95 59 25 13.5 28 95 99 36 01029200 Seboeis River near Shin Pond, Maine 69 55 48 140 143 75 42 11 9.5 15 44.5 86 22 01030500 Mattawamkeag River near Mattawamkeag, Maine 365 280 361 2,780 1,050 342 149 81 62 142 326 590 177 01031300 Piscataquis River at Blanchard, Maine 36 26 31 161 77 35.5 16 6.6 5.45 9.6 24 41 12 01031450 Kingsbury Stream at Abbot Village, Maine 29 26 30 108 50 28 10 2.5 3.35 12 23 36 10 01031500 Piscataquis River near Dover-Foxcroft, Maine 77 75 97 459 197 87.5 41 15 14 30 74.5 130 36 01037380 Ducktrap River near Lincolnville, Maine 6.2 4.7 8.4 14 6.4 3.2 0.39 0.01 0.001 0.04 0.47 2.9 0.17

01038000 Sheepscot River at North Whitefield, Maine 60 48 75 190 93 37.5 21 13 11 15 22 52 18

01044550 Spencer Stream near Grand Falls, Maine 61 58 71 228 231 118 55 28 22 36 64 95 45

01047000 Carrabassett River near North Anson, Maine 107 101 145 592 343 154 75 50 45 73 136 172 79

01048000 Sandy River near Mercer, Maine 143 143 220 811 418 170 102 60 45 83 162 187 96

01052500 Diamond River near Wentworth Location, New Hampshire 65 55 59 203 159 78 37 27 22.5 48 105 70 45

01054200 Wild River at Gilead, Maine 32 30 30 114 88 32 17 10 9.65 19 39 40 19

01054300 Ellis River at South Andover, Maine 39 39 46 156 134 58 32 13 10 17 45 49 31

01055000 Swift River near Roxbury, Maine 33 30 31 144 94 36.5 18 8.6 8 20 42.5 44 19

01055500 Nezinscot River at Turner Center, Maine 50 57 65 219 124 57 26 18 13 31 59 76 27

01057000 Little Androscoggin River near South Paris, Maine 27 23 32 101 52 18 5.4 3.4 2 9.3 28 35 7.1

01060000 Royal River at Yarmouth, Maine 51 48 72 159 87 45 35 24 22 29 48 61 34

01064500 Saco River near Conway, New Hampshire 205 210 255 755 616 297 169 115 104 160 276 260 181

01064801 Bearcamp River at South Tamworth, New Hampshire 34 31 34 94.5 44.5 21 10 5.8 5.6 13 32 48 13

01130000 Upper Ammonoosuc River near Groveton, New Hampshire 114 95 93 369 280 122 76 54 46 90 142 140 83
Appendix 1 29

Table 1–4. Computed monthly and annual 10 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire.[ft3/s, cubic foot per second]

U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual 

streamflow 

(ft3/s)

Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

01013500 Fish River near Fort Kent, Maine 360 270 266 809 1,780 748 440 238 146 198 450 568 305

01021480 Old Stream near Wesley, Maine 14 17 22 47.5 28 12.5 6.3 3.4 2.8 3.1 12.5 20 5.9

01022500 Narraguagus River at Cherryfield, Maine 141 167 200 457 263 128 64 41 38 63 144 179 77

01027200 North Branch Penobscot River near Pittston Farm, Maine 62 41 49 272 213 111 78 35 20 35 119 126 51

01029200 Seboeis River near Shin Pond, Maine 80 60 60 253 187 91 49 17 11 25 72.9 109 41

01030500 Mattawamkeag River near Mattawamkeag, Maine 454 355 417 3,410 1,310 452 211 120 90 205 597 710 275

01031300 Piscataquis River at Blanchard, Maine 42 31 35 196 98 41 19 7.6 7.7 16 63 57 22

01031450 Kingsbury Stream at Abbot Village, Maine 36 30 36 143 64 35 12 3.2 5.9 18 41.5 46 17

01031500 Piscataquis River near Dover-Foxcroft, Maine 95.5 88 128 628 249 105 49 22 19.5 44 126 156 58

01037380 Ducktrap River near Lincolnville, Maine 8.2 6.2 11 18.5 9.5 3.9 0.66 0.02 0.03 0.22 2.5 11 0.59

01038000 Sheepscot River at North Whitefield, Maine 72.5 59 93 259 110 48 23 15 13 16 39.5 75 24

01044550 Spencer Stream near Grand Falls, Maine 79 64 87 260 277 139 67 33 28 45 107 104 61

01047000 Carrabassett River near North Anson, Maine 138 139 170 782 395 195 92 59 59 93.5 203 210 109

01048000 Sandy River near Mercer, Maine 185 212 272 1,070 527 218 122 71 59 109 259 261 131

01052500 Diamond River near Wentworth Location, New Hampshire 75 59 69 260 202 96 45 33 30 67 132 82 59

01054200 Wild River at Gilead, Maine 43 34 35 139 104 39.5 20 13 13 24 50 51 26

01054300 Ellis River at South Andover, Maine 45 48 55 219 161 70.5 37 16 13.5 28 76.5 63 41

01055000 Swift River near Roxbury, Maine 38 34 41.5 180 115 45 21 12 10 29 63 53 29

01055500 Nezinscot River at Turner Center, Maine 65 64 99 298 151 66.5 30 21 18 38 72.5 89 39

01057000 Little Androscoggin River near South Paris, Maine 32 30 40.5 132 63 24 7.2 4.5 4 12 38 40 13

01060000 Royal River at Yarmouth, Maine 56 64 107 205 99 53 37 28 27 34 61 71 40

01064500 Saco River near Conway, New Hampshire 241 240 280 907 731 344 193 143 136 192 338 294 219

01064801 Bearcamp River at South Tamworth, New Hampshire 42 36 41 122 59.5 25 12 7.5 8.15 18 45 56 18

01130000 Upper Ammonoosuc River near Groveton, New Hampshire 127 104 105 457 338 150 88 66 59 105 179 160 104
30 Regression Equations for Ungaged Rivers in Maine Table 1–5. Computed monthly and annual 25 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire. [ft3/s, cubic foot per second] U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual stream- flow (ft3/s) Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. 01013500 Fish River near Fort Kent, Maine 451 366 345 1,510 2,600 970 626 339 233 311 787 717 470 01021480 Old Stream near Wesley, Maine 31 24 33 74 42 16 7.9 5 3.5 8.5 32 38 13 01022500 Narraguagus River at Cherryfield, Maine 222 229 304 634 355 172 88 60 55 101 265 250 148 01027200 North Branch Penobscot River near Pittston Farm, Maine 89 52 76 563 330 183 111 64 37.5 124 217 173 103 01029200 Seboeis River near Shin Pond, Maine 105 70 87 488 284 130 67 29 21 60 137 179 82 01030500 Mattawamkeag River near Mattawamkeag, Maine 704 567 765 4,950 2,130 773 382 232 170 403 1,200 1,080 570 01031300 Piscataquis River at Blanchard, Maine 59.5 41.5 57 336 145 67 26 11 12 37 113 96.5 48 01031450 Kingsbury Stream at Abbot Village, Maine 50 38 63 239 99 54 20 11 11 30 89 76 38 01031500 Piscataquis River near Dover-Foxcroft, Maine 153 129 195 926 372 166 71 40 34 87 266 212 127 01037380 Ducktrap River near Lincolnville, Maine 12 8.8 22 31.5 17 6.4 1.4 0.29 0.18 1.7 17 19 4.7

01038000 Sheepscot River at North Whitefield, Maine 108 101 157 363 184 71 29 21 18 26 77 131 51

01044550 Spencer Stream near Grand Falls, Maine 118 98.5 106 507 398 199 92 49 48 88 213 187 108

01047000 Carrabassett River near North Anson, Maine 205 190 270 1,110 586 275 136 87 85 160 319 270 199

01048000 Sandy River near Mercer, Maine 320 289 425 1,490 758 331 157 104 99 156 419 353 245

01052500 Diamond River near Wentworth Location, New Hampshire 96 74 91 461 292 145 67 46 50 97 178 115 93

01054200 Wild River at Gilead, Maine 53 43 59 209 151 60 26 20 21 37 84 70 45

01054300 Ellis River at South Andover, Maine 88.5 61 76 379 230 113 48 32 38 48 127 136 71

01055000 Swift River near Roxbury, Maine 53 46 58 274 168 70.5 31 19 23 43 95.5 77 49

01055500 Nezinscot River at Turner Center, Maine 99 103 150 423 213 101 42 29 26 56 129 132 74

01057000 Little Androscoggin River near South Paris, Maine 44 42 63 189 96 40 13 7.8 7.3 20 64 56 33

01060000 Royal River at Yarmouth, Maine 76 81 163 285 140 71 44 35 35 44 92 99 59

01064500 Saco River near Conway, New Hampshire 305 300 358 1,280 1,020 442 249 197 191 268 541 425 315

01064801 Bearcamp River at South Tamworth, New Hampshire 54 45 82 172 92.5 38 18 15 13 30 82 74 39

01130000 Upper Ammonoosuc River near Groveton, New Hampshire 155 138 170 712 459 223 116 91 91 145 262 210 156
Appendix 1 31

Table 1–6. Computed monthly and annual 50 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire.[ft3/s, cubic foot per second]

U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual 

streamflow 

(ft3/s)

Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

01013500 Fish River near Fort Kent, Maine 672 490 556 3,850 3,800 1,370 865 476 369 575 1,120 1,130 880

01021480 Old Stream near Wesley, Maine 44 31 74.5 119 62 24 11 7.5 6.45 20 63 68.5 3601022500 Narraguagus River at Cherryfield, Maine 333 307 628 905 519 268 130 94 86 175 455 433 30801027200 North Branch Penobscot River near Pittston Farm, Maine 143 79 160 1,190 506 286 184 147 69 283 416 269 23501029200 Seboeis River near Shin Pond, Maine 154 92 157 945 463 188 100 51 37.5 130 296 282 16901030500 Mattawamkeag River near Mattawamkeag, Maine 1,160 856 1,880 8,510 3,810 1,380 635 436 310 889 2,770 1,980 1,32001031300 Piscataquis River at Blanchard, Maine 81 56 127 658 239 118 55 33.5 29 99.5 207 182 112

01031450 Kingsbury Stream at Abbot Village, Maine 73 53 137 531 178 90 34 19 28 78 174 157 89

01031500 Piscataquis River near Dover-Foxcroft, Maine 210 190 365 1,570 631 291 125 73.5 70 205 530 381 27501037380 Ducktrap River near Lincolnville, Maine 19 14.0 50 55 28 13 3.4 0.94 0.865 8.85 32 34 1701038000 Sheepscot River at North Whitefield, Maine 180 161 388 550 296 122 46 28 27 52 196 283 14301044550 Spencer Stream near Grand Falls, Maine 166 127 191 926 617 312 141 77 81.5 188 368 260 21401047000 Carrabassett River near North Anson, Maine 270 270 536 1,760 906 414 207 149 152 268 618 452 36901048000 Sandy River near Mercer, Maine 445 391 928 2,350 1,170 564 251 159 170 348 866 658 51601052500 Diamond River near Wentworth Location, New Hampshire 125 95 170 859 484 224 113 79 87 177 274 175 176

01054200 Wild River at Gilead, Maine 70 57 115 353 236 91 41 32 35 66 144 104 88

01054300 Ellis River at South Andover, Maine 126 81 158 568 358 211 78 56 52 139 261 230 15401055000 Swift River near Roxbury, Maine 73 58 113 466 268 117 54 34 39 85 169 114 10001055500 Nezinscot River at Turner Center, Maine 150 151 330 672 338 162 65 49 44 91 278 221 16401057000 Little Androscoggin River near South Paris, Maine 59.5 58 137 286 147 70.5 27 17 16 44 117 90.5 7001060000 Royal River at Yarmouth, Maine 110 121 350 418 220 107 57 47 44 57.5 177 149 118

01064500 Saco River near Conway, New Hampshire 436 375 700 2,000 1,490 640 343 278 269 426 875 663 56901064801 Bearcamp River at South Tamworth, New Hampshire 76 61 159 292 151 59 31 22 23 62 128 120 8201130000 Upper Ammonoosuc River near Groveton, New Hampshire 217 180 310 1,120 740 324 165 137 138 246 386 300 275
32 Regression Equations for Ungaged Rivers in Maine Table 1–7. Computed monthly and annual 75 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire. [ft3/s, cubic foot per second] U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual stream- flow (ft3/s) Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. 01013500 Fish River near Fort Kent, Maine 1,000 679 800 6,040 5,910 2,010 1,290 962 611 1,240 2,020 1,830 1,840 01021480 Old Stream near Wesley, Maine 65 51 143 188 92 48.5 18 15 13 51 98.5 118 78 01022500 Narraguagus River at Cherryfield, Maine 524 488 1,100 1,380 754 426 214 158 158 347 724 811 630 01027200 North Branch Penobscot River near Pittston Farm, Maine 277 145 410 2,490 890 526 416 316 153 691 728 476 546 01029200 Seboeis River near Shin Pond, Maine 229 159 263 1,540 740 297 156 129 120 318 555 428 385 01030500 Mattawamkeag River near Mattawamkeag, Maine 1,790 1,440 4,030 12,300 6,120 2,210 1,280 995 701 1,890 4,290 3,780 3,370 01031300 Piscataquis River at Blanchard, Maine 132 94.5 290 1,160 467 241 127 74 77.5 250 433 289 271 01031450 Kingsbury Stream at Abbot Village, Maine 123 94 340 920 336 214 76 49 56.5 231 365 247 228 01031500 Piscataquis River near Dover-Foxcroft, Maine 326 305 820 2,690 1,100 559 282 176 163 498 1,010 682 688 01037380 Ducktrap River near Lincolnville, Maine 35 28.0 83 98.5 48 29 11 4.4 5.1 31 58 61 42

01038000 Sheepscot River at North Whitefield, Maine 305 268 693 861 438 227 76 52 47 143 431 495 35801044550 Spencer Stream near Grand Falls, Maine 232 178 332 1,690 954 471 228 171 160 444 576 369 45301047000 Carrabassett River near North Anson, Maine 410 410 1,050 3,060 1,540 773 383 277 263 609 1,140 774 87601048000 Sandy River near Mercer, Maine 667 595 1,610 4,100 1,950 1,110 489 312 287 839 1,560 1,190 1,210

01052500 Diamond River near Wentworth Location, New Hampshire 178 143 350 1,520 824 386 205 169 156 317 473 278 386

01054200 Wild River at Gilead, Maine 108 87 235 674 367 151 76 72 63 152 240 164 19501054300 Ellis River at South Andover, Maine 209 115 306 1,090 596 391 143 136 98.5 366 455 408 36601055000 Swift River near Roxbury, Maine 109 93 230 828 466 217 115 76 78 182 282 180 23001055500 Nezinscot River at Turner Center, Maine 250 220 667 1,060 541 304 125 96 77 221 505 428 38701057000 Little Androscoggin River near South Paris, Maine 92 86 261 504 223 129 61 45 35 101 202 165 16201060000 Royal River at Yarmouth, Maine 178 229 768 721 358 168 90 68 61 126 320 274 27401064500 Saco River near Conway, New Hampshire 684 534 1,180 3,470 2,220 961 534 487 409 911 1,400 1,130 1,170

01064801 Bearcamp River at South Tamworth, New Hampshire 123 103 294 549 249 114 69 48 55.5 140 218 208 180

01130000 Upper Ammonoosuc River near Groveton, New Hampshire 310 240 643 1,770 1,090 504 269 241 231 423 628 480 565
Appendix 1 33

Table 1–8. Computed monthly and annual 90 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire.[ft3/s, cubic foot per second]

U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual 

streamflow 

(ft3/s)

Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

01013500 Fish River near Fort Kent, Maine 1,380 1,210 1,330 7,820 7,870 3,070 1,880 2,080 1,290 1,900 3,120 2,670 3,77001021480 Old Stream near Wesley, Maine 110 79 229 287 134 92 37 33 32 99 169 198 15001022500 Narraguagus River at Cherryfield, Maine 974 880 1,810 2,000 1,140 768 407 310 268 659 1,220 1,370 1,16001027200 North Branch Penobscot River near Pittston Farm, Maine 538 267 793 3,830 1,650 922 654 662 401 1,190 1,210 938 1,14001029200 Seboeis River near Shin Pond, Maine 355 227 587 2,100 1,140 394 239 294 342 581 852 717 78401030500 Mattawamkeag River near Mattawamkeag, Maine 3,000 2,580 6,950 15,900 9,210 3,710 2,600 2,140 1,370 4,170 6,650 6,740 7,10001031300 Piscataquis River at Blanchard, Maine 249 170 585 1,770 845 496 251 177 200 609 802 549 66101031450 Kingsbury Stream at Abbot Village, Maine 224 170 690 1,540 590 535 183 121 130 605 705 492 580

01031500 Piscataquis River near Dover-Foxcroft, Maine 612 510 1,750 4,370 1,830 1,170 651 435 405 1,210 1,750 1,280 1,560

01037380 Ducktrap River near Lincolnville, Maine 67 65.0 139 159 79 66 29 11 10.5 80 104 103 87

01038000 Sheepscot River at North Whitefield, Maine 532 475 1,120 1,360 601 475 176 122 96.5 325 678 800 676

01044550 Spencer Stream near Grand Falls, Maine 339 239 682 2,740 1,500 737 371 380 372 929 903 621 925

01047000 Carrabassett River near North Anson, Maine 700 632 2,130 5,160 2,500 1,610 881 646 476 1,600 2,110 1,510 1,910

01048000 Sandy River near Mercer, Maine 1,150 871 2,930 6,970 3,050 2,300 1,050 783 573 2,020 2,730 2,170 2,500

01052500 Diamond River near Wentworth Location, New Hampshire 353 234 754 2,520 1,340 758 425 395 292 686 783 486 858

01054200 Wild River at Gilead, Maine 185 150 568 1,230 640 307 159 189 135 359 485 283 434

01054300 Ellis River at South Andover, Maine 378 170 569 1,860 898 646 321 370 206 825 752 821 737

01055000 Swift River near Roxbury, Maine 200 148 538 1,440 779 457 247 182 152 438 528 319 53201055500 Nezinscot River at Turner Center, Maine 465 380 1,130 1,940 866 621 266 222 133 522 871 821 79101057000 Little Androscoggin River near South Paris, Maine 163 136 528 869 353 276 132 119 73.5 221 346 294 327

01060000 Royal River at Yarmouth, Maine 400 513 1,360 1,270 607 339 161 108 106 274 613 652 608

01064500 Saco River near Conway, New Hampshire 1,230 878 2,070 5,580 3,360 1,620 1,000 926 765 1,830 2,220 1,980 2,23001064801 Bearcamp River at South Tamworth, New Hampshire 250 171 511 970 377 252 170 111 136 373 396 399 38401130000 Upper Ammonoosuc River near Groveton, New Hampshire 540 420 1,200 2,850 1,660 829 537 468 397 770 933 739 1,090
34 Regression Equations for Ungaged Rivers in Maine Table 1–9. Computed monthly and annual 95 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire. [ft3/s, cubic foot per second] U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual stream- flow (ft3/s) Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. 01013500 Fish River near Fort Kent, Maine 1,670 1,680 1,800 9,420 9,160 3,630 2,280 2,770 1,940 2,710 3,860 3,200 5,610 01021480 Old Stream near Wesley, Maine 163 149 308 376 190 154 59 53 54 180 241 274 215 01022500 Narraguagus River at Cherryfield, Maine 1,530 1,380 2,210 2,860 1,480 1,180 628 497 436 947 1,660 1,810 1,630 01027200 North Branch Penobscot River near Pittston Farm, Maine 872 390 1,030 5,300 2,360 1,330 896 1,110 679 1,750 1,530 1,370 1,830 01029200 Seboeis River near Shin Pond, Maine 491 314 750 2,390 1,530 492 341 451 571 1,030 1,070 949 1,220 01030500 Mattawamkeag River near Mattawamkeag, Maine 4,620 3,750 9,540 17,900 11,500 5,360 4,010 3,620 2,540 5,500 9,450 9,020 10,300 01031300 Piscataquis River at Blanchard, Maine 461 260 910 2,230 1,110 738 399 280 349 918 1,060 832 994 01031450 Kingsbury Stream at Abbot Village, Maine 368 254 1,130 2,010 761 817 339 259 293 967 1,120 830 910 01031500 Piscataquis River near Dover-Foxcroft, Maine 1,220 794 2,750 5,730 2,400 1,720 1,070 670 735 1,970 2,630 2,010 2,450 01037380 Ducktrap River near Lincolnville, Maine 129 125.0 214 240 111 116 47 17 20 119 145 153 128

01038000 Sheepscot River at North Whitefield, Maine 852 768 1,330 1,770 821 733 320 211 193 577 966 977 974

01044550 Spencer Stream near Grand Falls, Maine 496 304 1,030 3,560 2,190 992 559 626 607 1,310 1,130 937 1,410

01047000 Carrabassett River near North Anson, Maine 1,250 917 3,460 6,660 3,140 2,640 1,500 1,010 773 2,520 3,160 2,450 3,010

01048000 Sandy River near Mercer, Maine 1,830 1,170 4,430 9,100 4,100 3,690 1,970 1,450 878 3,330 4,030 3,140 3,91001052500 Diamond River near Wentworth Location, New Hampshire 559 397 1,160 3,460 1,940 1,070 693 675 473 979 1,070 745 1,330

01054200 Wild River at Gilead, Maine 357 250 895 1,690 964 481 303 333 249 691 895 524 751

01054300 Ellis River at South Andover, Maine 564 224 807 2,350 1,190 950 571 586 325 1,310 975 1,510 1,11001055000 Swift River near Roxbury, Maine 382 244 772 2,070 1,090 751 388 359 223 798 881 545 844

01055500 Nezinscot River at Turner Center, Maine 705 648 1,440 2,600 1,150 951 487 406 198 814 1,170 1,130 1,15001057000 Little Androscoggin River near South Paris, Maine 264 225 724 1,200 488 460 198 193 120 385 491 477 52601060000 Royal River at Yarmouth, Maine 690 760 1,720 1,840 885 669 259 189 171 483 924 1,130 1,00001064500 Saco River near Conway, New Hampshire 1,850 1,200 3,360 7,330 4,260 2,370 1,470 1,780 1,190 3,250 3,170 2,870 3,43001064801 Bearcamp River at South Tamworth, New Hampshire 438 360 727 1,230 532 406 273 247 224 679 533 583 60301130000 Upper Ammonoosuc River near Groveton, New Hampshire 800 600 1,710 3,890 2,370 1,130 764 674 557 1,290 1,150 1,100 1,640
Appendix 1 35

Table 1–10. Computed monthly and annual 99 percentile streamflows for selected U.S. Geological Survey streamgages in Maine and northern New Hampshire.[ft3/s, cubic foot per second]

U.S. Geological Survey streamgage Monthly streamflow (ft3/s) Annual 

streamflow 

(ft3/s)

Number Name Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

01013500 Fish River near Fort Kent, Maine 2,510 2,300 3,810 11,900 12,000 4,760 2,650 4,060 3,170 5,230 4,780 5,360 8,95001021480 Old Stream near Wesley, Maine 270 273 511 584 336 322 109 135 135 341 437 673 40701022500 Narraguagus River at Cherryfield, Maine 2,370 2,340 3,660 4,440 2,670 2,440 1,150 1,010 1,490 2,620 2,900 3,650 2,92001027200 North Branch Penobscot River near Pittston Farm, Maine 1,770 552 4,440 7,050 4,210 2,090 1,430 2,450 1,210 4,920 1,940 2,100 4,18001029200 Seboeis River near Shin Pond, Maine 1,210 476 1,340 3,150 2,750 807 530 779 1,120 1,850 1,680 1,810 2,14001030500 Mattawamkeag River near Mattawamkeag, Maine 12,100 7,500 13,900 22,500 18,100 14,400 9,530 6,530 6,490 12,500 15,000 16,500 16,50001031300 Piscataquis River at Blanchard, Maine 954 620 2,330 3,470 1,620 1,550 854 714 1,280 2,310 1,990 2,440 2,10001031450 Kingsbury Stream at Abbot Village, Maine 828 720 2,900 3,060 1,340 1,660 801 879 1,120 2,740 2,330 2,460 2,060

01031500 Piscataquis River near Dover-Foxcroft, Maine 3,800 2,310 5,150 9,790 3,970 4,200 1,980 1,670 1,900 5,590 5,020 6,010 5,30001037380 Ducktrap River near Lincolnville, Maine 251 323.0 369 643 180 271 112 42 79 363 329 235 30601038000 Sheepscot River at North Whitefield, Maine 1,640 1,290 2,090 3,240 1,490 1,310 606 355 440 1,610 1,610 1,540 1,72001044550 Spencer Stream near Grand Falls, Maine 808 560 2,360 5,120 3,420 2,080 1,260 1,520 1,580 2,610 2,060 1,880 2,89001047000 Carrabassett River near North Anson, Maine 5,410 2,170 6,270 10,800 5,610 6,850 3,490 2,690 2,550 6,400 5,890 5,640 6,40001048000 Sandy River near Mercer, Maine 5,400 2,750 8,140 13,600 7,530 9,340 4,780 3,040 2,520 8,480 7,910 8,480 8,57001052500 Diamond River near Wentworth Location, New Hampshire 1,500 1,020 3,340 5,570 3,750 2,000 1,510 1,460 999 2,700 1,810 1,810 3,05001054200 Wild River at Gilead, Maine 1,590 710 1,980 3,440 1,880 1,480 922 1,130 876 2,580 2,480 1,770 1,870

01054300 Ellis River at South Andover, Maine 1,260 475 1,550 2,850 1,630 2,050 1,400 1,430 765 2,440 1,770 3,250 2,300

01055000 Swift River near Roxbury, Maine 1,410 738 1,990 3,250 2,000 1,980 927 982 911 2,290 1,850 1,390 2,08001055500 Nezinscot River at Turner Center, Maine 1,740 1,600 2,910 5,110 2,480 2,260 1,260 1,090 539 1,780 1,850 2,210 2,430

01057000 Little Androscoggin River near South Paris, Maine 757 676 1,410 2,070 990 1,140 555 606 312 842 923 1,160 1,13001060000 Royal River at Yarmouth, Maine 1,450 1,550 2,900 4,440 1,790 2,320 593 914 872 1,420 1,950 2,380 2,22001064500 Saco River near Conway, New Hampshire 4,360 2,340 7,120 11,600 7,440 5,100 3,200 4,510 2,900 8,130 6,860 8,340 7,37001064801 Bearcamp River at South Tamworth, New Hampshire 824 780 1,490 2,270 1,080 1,890 696 983 722 1,830 1,020 1,360 1,36001130000 Upper Ammonoosuc River near Groveton, New Hampshire 1,750 1,200 4,000 5,920 3,870 2,430 1,620 1,470 1,100 3,110 1,910 2,240 3,320

For more information concerning this report, contact:

Director, New England Water Science Center

U.S. Geological Survey 

196 Whitten Road 

Augusta, ME 04330 

dc_nweng@usgs.gov

or visit our Web site at:

http://newengland.water.usgs.gov

Publishing support by: 

The Pembroke Publishing Service Center.
Dudley—Regression Equations for Ungaged Rivers in Maine—Scientific Investigations Report 2015–5151, ver. 1.1

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20155151