August Median Streamflow on Ungaged Streams in 

Eastern Coastal Maine

Scientific Investigations Report 2004-5157

In cooperation with the

Maine Geological Survey,

Department of Environmental Protection,

Maine State Planning Office,

Maine Department of Agriculture,

Maine Department of Transportation

U.S. Department of the Interior

U.S. Geological Survey
August Median Streamflow on Ungaged Streams in 

Eastern Coastal Maine

By Pamela J. Lombard

In cooperation with the 

Maine Geological Survey, 

Department of Environmental Protection, 

Maine State Planning Office, 

Maine Department of Agriculture, 

Maine Department of Transportation

Scientific Investigations Report 2004-5157

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

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

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

Box 25286, Denver Federal Center

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 iii

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

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

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

Previous Studies ....................................................................................................................................................................2

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

Data Collection and Analysis............................................................................................................................................................4

Station Selection and Streamflow Measurements...............................................................................................................4

Basin Characteristics.............................................................................................................................................................8

August Median Streamflows at Streamflow-Gaging Stations ........................................................................................................8

Computation of August Median Steamflow at Long-Term Continuous-Record Stations including Index Stations............ 8

Estimation of August Median Streamflows at Partial-Record Stations and Short-Term Continuous-Record Stations...... 8

Estimation of August Median Streamflow on Ungaged Streams...................................................................................................10

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

Ordinary Least-Squares Regression............................................................................................................................ 10

Generalized Least-Squares Regression ...................................................................................................................... 10

Equations for Estimating August Median Streamflow on Ungaged Streams.................................................................................11

Two-Variable Model.............................................................................................................................................................11

One-Variable Model .............................................................................................................................................................12

Weighted Estimates of August Median Streamflow at Partial- and Short-Term Continuous-Record 

Streamflow-Gaging Stations.....................................................................................................................................................12

Summary and Conclusions.............................................................................................................................................................. 12

Acknowledgments ............................................................................................................................................................... 14

References Cited............................................................................................................................................................................. 14

Figures

1. Map showing location of study area and continuous-record streamflow-gaging stations used 

as index stations, eastern coastal Maine.................................................................................................................... 3

2. Map showing location of partial-record and continuous-record streamflow-gaging stations used in 

regression analyses in eastern coastal Maine ............................................................................................................ 5

3. Graph showing relation of base-flow measurements at partial-record station, Pleasant River near

Crebo Flat, Maine, and concurrent daily mean flow measurements at index station,

Narraguagus River at Cherryfield, Maine, 2000-2003................................................................................................. 9

4. Graph showing two-dimensional range of explanatory variables used in regression equation for

predicting August median streamflows on ungaged streams in eastern coastal Maine ...........................................11

Tables

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

analyses, eastern coastal Maine ................................................................................................................................. 6

2. Long-term continuous-record streamflow-gaging stations in Maine used as index stations........................................... 7

3. Weighted August median streamflows at partial-record and short-term continuous-record streamflowgaging stations, eastern coastal Maine ......................................................................................................................13

CONTENTS
iv 

Conversion Factors

Inch/Pound to SI

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

°C = (°F - 32) / 1.8

Multiply By To obtain

inch (in.) 2.54 centimeter (cm)

square mile (mi2) 2.590 square kilometer (km2)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)
August Median Streamflow on Ungaged Streams in 

Eastern Coastal Maine

by Pamela J. Lombard

Abstract

 Methods for estimating August median streamflow were 

developed for ungaged, unregulated streams in eastern coastal 

Maine. The methods apply to streams with drainage areas ranging in size from 0.04 to 73.2 square miles and fraction of basin 

underlain by a sand and gravel aquifer ranging from 0 to 71 percent. The equations were developed with data from three longterm (greater than or equal to 10 years of record) continuousrecord streamflow-gaging stations, 23 partial-record streamflow-gaging stations, and 5 short-term (less than 10 years of 

record) continuous-record streamflow-gaging stations. A mathematical technique for estimating a standard low-flow statistic, 

August median streamflow, at partial-record streamflow-gaging stations and short-term continuous-record streamflow-gaging stations was applied by relating base-flow measurements at 

these stations to concurrent daily streamflows at nearby longterm continuous-record streamflow-gaging stations (index stations). Generalized least-squares regression analysis (GLS) 

was used to relate estimates of August median streamflow at 

streamflow-gaging stations to basin characteristics at these 

same stations to develop equations that can be applied to estimate August median streamflow on ungaged streams. GLS 

accounts for different periods of record at the gaging stations 

and the cross correlation of concurrent streamflows among gaging stations. Thirty-one stations were used for the final regression equations.

 Two basin characteristics—drainage area and fraction of 

basin underlain by a sand and gravel aquifer—are used in the 

calculated regression equation to estimate August median 

streamflow for ungaged streams. The equation has an average 

standard error of prediction from -27 to 38 percent. A one-variable equation uses only drainage area to estimate August 

median streamflow when less accuracy is acceptable. This 

equation has an average standard error of prediction from -30 to 

43 percent. Model error is larger than sampling error for both 

equations, indicating that additional or improved estimates of 

basin characteristics could be important to improved estimates 

of low-flow statistics. 

 Weighted estimates of August median streamflow at partial-record or continuous-record gaging stations range from 

0.003 to 31.0 cubic feet per second or from 0.1 to 0.6 cubic feet 

per second per square mile. Estimates of August median streamflow on ungaged streams in eastern coastal Maine, within the 

range of acceptable explanatory variables, range from 0.003 to 

45 cubic feet per second or 0.1 to 0.6 cubic feet per second per 

square mile. Estimates of August median streamflow per square 

mile of drainage area generally increase as drainage area and 

fraction of basin underlain by a sand and gravel aquifer 

increase.

Introduction

 The need for information to describe low-flow characteristics of streams in Maine by Federal, State, and local agencies, 

consulting engineers, commercial enterprises, and natural 

resource conservation groups is increasing. Low-flow characteristics are used to determine the adequacy of streamflow for 

development of water supplies, disposal of wastes, generation 

of electricity, irrigation of agricultural land, maintenance and 

restoration of aquatic habitat, and conservation of watersheds. 

Currently (2004), few streamflow-gaging stations on small 

streams (streams with drainage areas less than 100 mi2

 ) in eastern coastal Maine have a sufficient period of record (10 years) 

to estimate low-flow statistics in this region. New Englandwide equations used to estimate August median streamflows on 

ungaged streams with large drainage areas may not apply to 

small streams in eastern coastal Maine. Management and effective utilization of water resources could improve with low-flow 

estimation techniques developed specifically for small streams 

in this region.

 The New England Aquatic Base-Flow (ABF) policy was 

developed by the U.S. Fish and Wildlife Service (USFWS) 

(1981) to manage low streamflows for aquatic organisms while 

still allowing water withdrawals for human consumption. The 

ABF policy recommends that water not be withdrawn from 

streams when streamflow is below the August median streamflow. The USFWS estimated the August median streamflow 

per square mile of drainage area by using the median of the 

annual series of August monthly mean streamflows from 48 

streamflow-gaging stations in New England (U.S. Fish and 
2 August Median Streamflow on Ungaged Streams in Eastern Coastal Maine

Wildlife Service, 1981). In the absence of adequate streamflow 

data, the policy recommends that an ABF of 0.5 (ft3/s)/mi2

(cubic feet per second per square mile) of drainage area can be 

used to approximate August median flow. 

 The definition of August median streamflow has varied in 

previous investigations; thus, the resulting values of August 

median streamflow per square mile of drainage area also have 

varied. In cases where a central value of a distribution is preferable to one that may be skewed by a few extreme observations, the median of the monthly medians or the median of the 

daily flows is preferable to a central measure such as the mean 

or the median of the mean monthly streamflows (Helsel and 

Hirsch, 1992). Charles Ritzi and Associates (1987) and Kulik 

(1990) calculated the August median streamflow at streamflowgaging stations in New England as the median of all of the daily 

mean streamflows measured in August during the period of 

record. Charles Ritzi and Associates (1987) estimated the 

August median to be from 0.33 to 0.38 (ft3/s)/ mi2. Kulik 

(1990) determined that the August median varied by region and 

estimated it as 0.6 (ft3/s)/mi2 for mountain windward regions 

and 0.3 (ft3/s)/mi2 for non-mountain windward regions in New 

England. 

 County and statewide policies and regulations regarding 

water withdrawals and (or) instream water use are being developed with limited information on streamflows in Maine. The 

State of Maine recently adopted legislation to ensure waterwithdrawal reporting (Maine State Legislature, 2002). This legislation directs the Board of Environmental Protection to establish water-use standards for maintaining instream flows by 

2005. Standards will be based on the natural variation of flows 

and water levels. Adequate equations to estimate low-flow statistics, including August median streamflows, are a critical first 

step in establishing these standards. Additionally, one of the 

goals of the Atlantic Salmon Conservation Plan is “to ensure 

water withdrawal or impoundment does not adversely affect 

Atlantic salmon during high, medium, or low water periods” 

(Maine Atlantic Salmon Task Force, 1997). Part of this plan is 

to obtain reliable and accurate flow information for the Narraguagus, Pleasant, and Machias Rivers in eastern coastal Maine. 

To develop regression equations that could be used to better 

estimate the August median streamflow on ungaged, unregulated streams in eastern coastal Maine, the U.S. Geological Survey (USGS) began a 5-year cooperative study with the Maine 

Geological Survey in 2000. Additional support for the project 

was provided by Maine Department of Environmental Protection, Maine State Planning Office, Maine Department of Agriculture, and Maine Department of Transportation. 

 Purpose and Scope

 This report presents equations to estimate August median 

streamflow on streams in Washington and Hancock Counties in 

eastern coastal Maine (Fig.1), as well as an estimate of the accuracy of these equations. The report describes (1) how instantaneous streamflow measurements at partial-record streamflowgaging stations and short-term continuous-record streamflowgaging stations were correlated to daily mean streamflows at 

long-term continuous-record streamflow-gaging stations to 

estimate August median streamflows at the partial-record stations and short-term continuous-record stations; (2) how 

regression equations to estimate August median streamflow on 

small, ungaged streams were developed; and (3) how weighted 

estimates of August median streamflow at partial-record stations and continuous-record stations in the study area were calculated. 

 Previous Studies 

 A previous study of August median streamflow on 

ungaged streams was conducted in eastern Aroostook County, 

Maine (Lombard and others, 2003). Mean basin elevation and 

drainage area were used to estimate August median streamflow 

on basins with drainage areas from 0.38 to 43 mi2 in northern 

Maine. Additionally, statewide low-flow equations for basins 

ranging in size from 10 to 1,400 mi2

 were recently developed 

for Maine (Dudley, 2004). These statewide low-flow equations 

use drainage area and fraction of basin underlain by a sand and 

gravel aquifer to estimate the annual 7-day low flow with a 10-

year recurrence interval (7Q10), and summer mean monthly 

and median monthly flows in Maine. 

 Methods for estimating low-flow statistics at partialrecord stations on the basis of correlations between daily mean 

discharges at the partial-record streamflow-gaging stations and 

concurrent daily mean discharges at nearby continuous-record 

streamflow-gaging stations are presented by Riggs (1972). 

Riggs also outlined a technique of regionalizing low-flow characteristics of rivers by multiple regression on basin characteristics, such as drainage area and surficial geology. Numerous 

investigators have applied this technique of regionalization to 

develop low-flow regression models, using basin characteristics 

as independent variables to predict low-flow statistics on 

ungaged streams in New England (Johnson, 1970; Cervionne 

and others, 1993; Risley, 1994; Wandle and Randall, 1994; 

Ries, 1994a, 1994b, 1997). Ries (1997) developed equations 

specifically for estimating August median streamflow in Massachusetts. These investigators all found low-flow statistics to 

be highly correlated to drainage area, and in most cases, the 

relation was specific to a geographic region of the State. Other 

variables that commonly were correlated with low-flow statistics were a measure of the basin relief or slope (Risley, 1994; 

Ries, 1994a, 1994b, 1997) and a measure of the surficial geology (Cervione and others, 1993; Wandle and Randall, 1994; 

Ries, 1994a, 1994b, 1997). 

 Description of Study Area

 Hancock and Washington Counties are in the coastal part 

of eastern Maine (fig. 1), encompass 1,522 mi2

 and 2,528 mi2, 

respectively, and had populations of 51,791 and 33,941 in 2000
Introduction 3

44 o

o

o 45

71

46 o

67 o

70 o

69 o 68 o

47 o

0

0

40

50

80 MILES

100 KILOMETERS

EXPLANATION

Streamflow-gaging station

and identifier

Location of study area

County boundary

International boundary

State boundary

National Weather Service site

Major rivers and streams

Location of city

01038000

01038000

01023000

01022500

01022000

01021500 River Narraguagus

Denny’s River

Sheepscot River

Pleasant

River

W. Branc

v

h

i

Union R

er

Machias River

Washington

County

Lincoln

County

Hancock

County

Canada

Canada

Atlantic Ocean

New Hampshire

Augusta

Augusta

Portland

Bangor

Base from U.S. Geological Survey

digital files, scale 1:2,000,000,

projection UTM, zone 19

Figure 1. Location of study area and continuous-record streamflow-gaging stations used as index stations, eastern coastal Maine. 
4 August Median Streamflow on Ungaged Streams in Eastern Coastal Maine

Maine Register, 2004). This sparsely populated region is characterized by low-relief rolling topography, and is made up primarily of forest and blueberry barrens. The surficial geologic 

materials in the basins are predominantly glacial till, and fine 

and coarse-grained glaciomarine deposits with some ice-contact glaciofluvial deposits, eskers, and bedrock (Thompson and 

Borns, 1985).

 Cold winters and cool summers typify the climate of eastern coastal Maine. The normal annual temperature based on the 

30-year period from 1971 to 2000 in Bangor is 44.7o F, with 

mean monthly temperatures ranging from 18o F in January to 

69o F in July. The mean annual precipitation is 40 in. in Bangor 

(National Weather Service, http://www.erh.noaa.gov/er/car/climate.htm). High flows typically occur in early spring and late 

fall, and low flows generally occur in the summer and early fall. 

During the summer months, streamflow comes from ground 

water discharged from aquifers (base flow), and rainfall from 

summer storms. 

Data Collection and Analysis

 A continuous-record streamflow-gaging station (continuous-record station) is a station at which data are collected with 

sufficient frequency to define daily mean values and variations 

within a day (Stewart and others, 2003). A partial-record 

streamflow-gaging station (partial-record station) is a station at 

which discrete measurements are obtained over a period of time 

without continuous data being recorded or computed (Stewart 

and others, 2003). For the purposes of this report, continuousrecord stations are divided into continuous-record stations with 

less than 10 years of record (short-term continuous-record stations), and continuous-record stations with equal to or more 

than 10 years of record (long-term continuous-record stations). 

Index stations are long-term continuous-record stations with 

daily streamflow measurements that correlate well with baseflow measurements at a partial-record station or short-term continuous-record station. 

 Ideally, equations to estimate August median streamflow 

on small, ungaged streams in eastern coastal Maine would be 

developed from long-term continuous-record data from small 

streams in the same region. Because only three stations on small 

streams in eastern coastal Maine have long-term continuous 

records with August median streamflows greater than zero, 

short-term continuous-record stations and partial-record stations also were used to develop the equations. Low-flow statistics at long-term continuous-record stations were calculated 

directly from the data. Records from index stations were used 

to estimate August median streamflow at partial-record stations 

and short-term continuous-record stations. All but one of the 

index stations used in this study are in the eastern part of Maine 

near the coast in Hancock and Washington Counties. The 

remaining index station is in Lincoln County (fig. 1). 

 Station Selection and Streamflow Measurements

 Twenty-six partial-record stations and one short-term continuous-record station were established for this project. In addition, nine existing short-term continuous-record stations and 

four existing long-term continuous-record stations were tested 

for possible inclusion in the regression analysis. Of these 40 

potential stations, nine were eliminated for the following reasons: two partial-record stations were eliminated because they 

each had two outlets, making their drainage areas difficult to 

define; one partial-record station, one short-term continuousrecord station and one long-term continuous-record station 

were eliminated because they had August median streamflows 

estimated at 0.0 ft3/s (cubic feet per second); two short-term 

continuous-record stations were eliminated because they did 

not correlate well with any of the index stations tested; and two 

short-term continuous-record stations were eliminated because 

most of their measurements were rated as poor (Stewart and 

others, 2003). The 31 remaining stations were used in the 

regression analysis to develop an equation to estimate August 

median flow on ungaged streams (fig. 2, table 1). All stations 

used in the regression analysis are in Hancock and Washington 

Counties, have relatively small drainage areas (from 0.04 mi2

to 73 mi2), are unregulated, and as a group are considered representative of eastern coastal Maine. 

In addition to the stations described above, 10 long-term 

continuous-record stations were tested for use as index stations. 

Ideally, index stations would be close to partial-record stations 

geographically and have drainage areas in the same range as the 

drainage areas of the partial-record stations (less than 100 mi2). 

Because few long-term continuous-record stations in the region 

meet these criteria, stations with drainage basins larger than 100 

mi2 also were tested for use as index stations. The 10 stations 

tested include the 4 long-term continuous-record stations tested 

for use in the regression analysis (only 3 of which were used in 

the final regression analysis), and 6 long-term continuousrecord stations that were not tested for use in the regression 

analysis because their drainage areas are greater than 100 mi2

. 

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

basis of their correlations with at least one partial-record station 

or one short-term continuous-record station (table 2). Three of 

the index stations are in Washington County, one is in Hancock 

County, and one is in Lincoln County (fig. 1). Although two of 

the stations (USGS streamflow-gaging stations 01022000 and 

01023000) are no longer active continuous-record gaging-stations, base-flow measurements were made at these stations on 

the same day that the measurements were made at the partialrecord stations in order to correlate flows at the partial-record 

stations with flows at the index stations. Selected index stations 

have been gaged by the USGS from 18 to 64 years. All streamflow data can be found in the series of USGS annual water-data 

reports and predecessor Water-Supply Papers (Stewart and others, 2003).

Standard USGS methods as described by Rantz and others 

(1982) were used to make all streamflow measurements at the 

partial-record stations. Measurements were made by wading
Data Collection and Analysis 5

01021190

01021225

01021435

01021452

01021470

01021472

01021475

01021478

01021480

01021485

01021488

01021910

01021960

01022220

01022260 01022264

01022270

01022286

01022290

01022295

01022400

01022750

01022835

01022835

01025450

01022860

01022950

01023210

01023400

01023430

01024200

01025445

01025450

Study

Area

Explanation

Continuous-record station

and number

Partial-record station and

number

County boundary

Major roads

Location of City or Town

Base from U.S. Geological Survey

digital files, scale 1:100,000,

projection UTM, zone 19

0

0

10

10

20 MILES

20 KILOMETERS

SCALE

HANCOCK

COUNTY

WASHINGTON

COUNTY

Route 1

Route 1

Route 9

Ellsworth

Machias

67O

68 06’26” o

44 29’35” o

67 26’19” o

44 56’17” o

Atlantic Ocean

Limit of study

Ellsworth

Figure 2. Location of partial-record and continuous-record streamflow-gaging stations used in regression analyses in eastern coastal 

Maine. 
Table 1. Partial-record and continuous-record stations and selected basin characteristics used in regression analyses, eastern coastal Maine. [USGS, U.S. Geological Survey; mi2, square miles; o ‘ “, degrees, minutes and seconds]. USGS station number (Fig. 2) Latitude o ‘ “ Longitude o ‘ “ Station name and location Number of base- flow measure- ments* Index station number Drain

age ar

(mi2

Partial-record stations 01021190 44 54 14 67 17 15 Venture Brook near Dennysville, Maine 10 01022000 3.13 

01021225 44 53 07 67 19 02 Cathance Stream at Marion, Maine 10 01022000 27 01021435 44 55 41 67 52 09 Crooked River near Beddington, Maine 10 01022500 17.5 01021472 44 49 12 67 41 04 Holmes Brook near Northfield, Maine 10 01038000 5.43 01021475 44 59 24 67 49 24 Dead Stream near Wesley, Maine 10 01038000 0.9901021478 44 55 22 67 45 50 Honeymoon Brook near Wesley, Maine 10 01022500 0.401021485 44 50 35 67 39 47 Old Stream near Northfield, Maine 10 01022500 73.2 01021488 44 53 52 67 40 09 New Stream near Wesley, Maine 11 01021500 10.3 01021910 45 00 32 67 36 58 Harmon Brook near Crawford, Maine 10 01021500 3.24 01021960 44 56 33 67 30 32 Northern Stream near Cooper, Maine 10 01022000 24 01022220 44 46 08 67 55 23 Pleasant River near Crebo Flat, Maine 10 01022500 25.5 01022264 44 41 53 67 44 16 Little River near Columbia Falls, Maine 10 01022500 5.25 01022270 44 38 04 67 49 46 Harrington River near Harrington, Maine 10 01022500 6.53 01022286 44 53 06 68 08 24 Humpback Brook near Beddington, Maine 10 01022500 3.2 01022290 44 50 34 68 04 10 Narraguagus River near Beddington, Maine 10 01022500 67.8 01022400 44 46 17 68 05 20 Pork Brook near Lower Beddington, Maine 10 01022500 2.1 01022750 44 35 48 68 10 46 Card Mill Stream near Franklin, Maine 10 01022000 15.2 01022950 44 58 14 68 13 59 Alligator Stream near Great Pond, Maine 10 01022000 7.83 01023210 44 52 16 68 11 23 Unnamed Trib. to Lower Lead Mtn Pond near Beddington, Maine 10 01022500 1.79 01023400 44 51 42 68 17 43 Middle Branch Union River near Aurora, Maine 8 01022500 28.1 01023430 44 49 18 68 14 59 Leighton Brook near Aurora, Maine 10 01023000 2.14 01025445 44 37 37 68 37 42 Unnamed tributary to Winkumpaug Brook near Ellsworth, Maine 10 01021500 0.2501025450 44 37 37 68 37 42 Winkumpaug Brook near Ellsworth, Maine 12 01021500 1.98 
* All base-flow measurements made between 2000 and 2003.** The water year is the 12-month period from October 1 through September 30.*** August median flow can be calculated at stations with 10 or more years of continuous record, thus, these stations do not need an index station for record extension.Table 2. Long-term continuous-record streamflow-gaging stations in Maine used as index stations.[USGS, U.S. Geological Survey; o ‘ “, degrees, minutes and seconds; ft3/s, cubic feet per second; mi2, square miles].*The water year is the 12-month period October 1 through September 30.

USGS station 

number

(Fig. 2)

Latitude

o ‘ “

Longitude

o ‘ “ Station name and location

Period of continuous record (water years**)

Index 

station

number

Drain

age are

(mi2)

Continuous-record stations

01021452 44 52 16 67 56 27 Mopang Stream near Beddington, Maine 2001-03 01021500 18.8 01021470 44 48 03 67 43 31 Libby Brook near Northfield, Maine 2002-03 01038000 7.79 01021480 44 56 09 67 44 08 Old Stream near Wesley, Maine 1998-03 01022500 29.1 01022260 44 41 52 67 47 16 Pleasant River near Epping, Maine 1980-91, 2000-03 NA*** 60.6 01022295 44 51 34 68 06 23 West Bear Brook near Beddington, Maine 1988-03 NA*** .04 01022835 44 20 41 68 13 02 Cadillac Brook near Bar Harbor, Maine 1999-2003 01038000 .1201022860 44 19 54 68 16 48 Hadlock Brook near Northeast Harbor, Maine 1999-2003 01038000 .1801024200 44 43 17 68 24 40 Garland Brook near Mariaville, Maine 1964-82 NA*** 9.79 

USGS station number

(Fig. 1)

Latitude

o ‘ “

Longitude

o ‘ “ Station name

Period of continuous record 

(water years*)

Drainage area

(mi2)

Au

s

Continuous-record stations used as index stations

01021500 44 43 23 67 31 15 Machias River at Whitneyville, Maine 1905-1921, 1929-1976, 2001-2003 458 01022000 44 46 05 67 24 30 East Machias River near East Machias, Maine 1927-1958 251 01022500 44 36 29 67 56 10 Narraguagus River at Cherryfield, Maine 1948-2003 227 01023000 44 50 25 68 22 22 West Branch Union River at Amherst, Maine 1910-1919, 1929-1979 148 01038000 44 13 23 69 35 38 Sheepscot River at North Whitefield, Maine 1938-2003 145 

Table 1. Partial-record and continuous-record stations, and selected basin characteristics used in regression analyses, eastern coastal Maine--C[USGS, U.S. Geological Survey; mi2, square miles; o ‘ “, degrees, minutes and seconds].
8 August Median Streamflow on Ungaged Streams in Eastern Coastal Maine

current-meter methods, portable Parshall flume methods, and 

volumetric methods. Streamflows at the partial-record stations 

were measured during independent base flows that were separated by storms. A range of flows throughout the summer 

months was sought, and flows that changed rapidly or flows that 

could be attributed directly to rain runoff were avoided. Measurements of low flow were made within a 30-hour period at all 

stations for each independent base flow event. All flow records 

are published in the series of USGS annual water-data reports 

(Stewart and others, 2003).

 Basin Characteristics 

 Topographic, climatic, and geologic basin characteristics, 

which potentially could be linked to the low-flow statistic 

August median streamflow, were delineated and calculated 

using a geographic information system (GIS). Calculated basin 

characteristics include drainage area, minimum, maximum and 

mean elevation, elevation range, mean basin slope, percent of 

basin underlain by a sand and gravel aquifer, percent wetlands, 

percent ponds, percent total storage, and annual precipitation at 

the basin centroids. The base-10 logarithmic transformation of 

each basin characteristic also was calculated.

 Basin delineation was done by hand using contours on 

1:24,000-scale USGS quadrangle maps. Basin characteristics 

including drainage area were calculated for each basin after the 

basin boundary was digitized using GIS. Minimum, maximum, 

and mean elevation, elevation range, and mean basin slope were 

computed from a 30-meter-resolution USGS digital elevation 

model (DEM). Slope for each pixel was determined using a 9-

pixel moving average of the DEM. Mean basin slope was computed as the mean of all pixel slopes in the basin. Pond areas 

were calculated from the digital line graphs of 1:24,000-scale 

7.5 minute USGS topographic quadrangle maps. Fraction of 

basin underlain by a sand and gravel aquifer were calculated 

from drainage maps compiled by Maine Geological Survey. 

Wetland, pond, and total storage areas were calculated from 

digital National Wetland Inventory maps produced by USFWS 

at a scale of 1:24,000. Mean annual precipitation for each basin 

was computed using Parameter-elevation Regressions on Independent Slopes Model (PRISM) output grids (Daly and Neilson, 1992; Daly and others, 1997). The NRCS PRISM Internet 

site below serves non-proprietary versions of annual and 

monthly PRISM precipitation data (http://

www.ftw.nrcs.usda.gov/prism/prismdata_state.html).

August Median Streamflows at StreamflowGaging Stations 

 August median streamflows were estimated at all partialrecord and continuous-record stations including index stations. 

August median streamflows for the partial-record stations and 

short-term continuous-record stations were estimated by correlating the low streamflow measurements made at the stations to 

daily mean streamflows on the same days at index stations. 

This method is described by Riggs (1972) and follows the 

USGS guidelines for regional low-flow analyses where appropriate (U.S. Geological Survey, 2003). Weighted estimates of 

the August median streamflows at all stations used in the regression analyses are presented near the end of this report. 

 Computation of August Median Streamflow at LongTerm Continuous-Record Stations including Index 

Stations

 August median streamflows were calculated at all longterm continuous-record stations including index stations. Initially, the series of annual August medians was calculated at 

each long-term continuous-record station. The Mann Kendall 

trend test (Helsel and Hirsch, 1992) indicated that there was no 

trend with time in the annual series of August medians at any of 

the long-term continuous-record stations. The expected August 

median streamflow was estimated by computing the median of 

the observed annual August medians. This method of computing the August median streamflow closely approximates the 

method of taking the August daily mean streamflow that is 

exceeded 50 percent of the time during the period of all August 

daily streamflows for the period of record, but is preferable 

because it allows for the calculation of the variance around the 

median. This estimate of variance is essential for the generalized least-squares regression analyses, providing an estimate of 

error for the final regression equations.

 Collection of daily mean streamflow data was discontinued at the East Machias River near East Machias, Maine (USGS 

station 01022000) in 1958 and the West Branch of the Union 

River at Amherst (USGS station 01023000) in 1979. These stations were still used as index stations because they had sufficient periods of record to calculate August median streamflows; 

base-flow measurements were collected from 2000 to 2003 to 

correspond with base-flow measurements at the partial-record 

stations. Machias River at Whitneyville (USGS station 

01021500) was discontinued in 1976, but restarted in 2001. 

Base-flow measurements were collected in 2000 at this station 

to correspond with base-flow measurements at the partialrecord stations.

Estimation of August Median Streamflows at PartialRecord Stations and Short-Term Continuous-Record 

Stations

 August median streamflows for the partial-record stations 

and short-term continuous-record stations were estimated by 

relating the low streamflow measurements made at the stations 

to daily mean streamflows on the same days at index stations. 

Stedinger and Thomas (1985) developed a technique to estimate the mean and standard deviation of an annual event such 

as the d-day T-year low flow, which is the annual, minimum d-
August Median Streamflows at Streamflow-Gaging Stations 9

day consecutive low flow that will be exceeded, on average, 

every T years. Using this technique to calculate the August 

median at a partial-record station, as opposed to the d-day Tyear low flow, is appropriate if the logarithms of the monthly 

medians at the index station are approximately normally distributed (G.D. Tasker, U.S. Geological Survey, oral commun., 

2003). Estimates are made on the basis of the relation between 

base-flow measurements at the partial-record station and concurrent daily streamflows at an index station. This relation is 

defined by use of least-squares-regression analysis of the logarithms of the flows. The regression analysis and the low-flow 

statistic at the index station are used to estimate the desired flow 

characteristics at the partial-record station. The Stedinger-Thomas technique was used to calculate the August median streamflow and the variance of the August median streamflow at partial-record stations and short-term continuous-record stations. 

This technique fits a least-squares regression to the data after 

the user determines whether the base-flow measurements have 

an adequate linear relation with the concurrent daily streamflows at the index station. 

 In order to estimate an August median and standard deviation of the August median at partial-record and short-term continuous-record stations, the logarithm of the measured streamflows must have a linear correlation with the logarithm of the 

concurrent daily mean streamflows at an index station. An 

example of the correlation between concurrent measurements at 

a partial-record station and an index station is shown in

figure 3. All the partial-record stations and short-term continuous-record stations used in the analysis had a correlation coefficient of 0.70 or greater with an index station. If measurements 

at a partial-record station correlated well (coefficient greater 

than 0.70) with measurements from more than one index station, then the index station with the higher correlation coefficient was used. If the correlation coefficient was similar for two 

index stations, then the index station was chosen on the basis of 

a visual observation of the graphical relation between the two 

stations. Base-flow measurements at the partial-record station, 

the corresponding daily mean streamflows at an index station, 

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

median and standard deviation of the base-10 logarithms of the 

August median streamflows at the index station were used to 

compute the base-10 logarithms of the median streamflow and 

its variance at the partial-record station.

 The Stedinger-Thomas technique was used to estimate the 

August median streamflow at all partial-record stations and 

short-term continuous-record stations except when the station 

had one or more measurements of zero streamflow. Two partial-record stations (USGS stations 01022400 and 01025445) 

and two short-term continuous-record stations (USGS stations 

01022835 and 01022860) had at least one measurement of zero 

streamflow. Ordinary least-squares regression is based on the 

assumption that the residuals from the regression equation are 

approximately normally distributed. A logarithmic transformation of streamflow is generally required to achieve approximate

10 100 1000

NARRAGUAGUS RIVER AT CHERRYFIELD, MAINE. DISCHARGE IN CUBIC FEET PER SECOND

1

10

100

PLEASANT RIVER NEAR CREBO FLAT, MAINE.

STREAMFLOW, IN CUBIC FEET PER SECOND

CORRELATION COEFFICIENT (R) = 0.98

Figure 3. Relation of base-flow measurements at partial-record station, Pleasant River near Crebo Flat, Maine, and concurrent daily 

mean flow measurements at index station, Narraguagus River at Cherryfield, Maine, 2000-2003.
10 August Median Streamflow on Ungaged Streams in Eastern Coastal Maine

normality; however, the occurrence of zero flows makes the 

logarithmic transformation difficult to apply. Therefore, 

streamflow values below a small threshold (0.01 ft3

/s) were 

treated as censored values (less than 0.01 ft3

/s) and Tobit regression (Judge and others, 1985) was used to estimate the regression coefficients. A similar approach was used Perry and others 

(2002) in Kansas to estimate median streamflows in the presence of zero values. In these cases, the Tobit regression was 

computed including the zero observations, but the standard 

error of the residuals was computed using only the residuals 

from the non-zero observations (A.V.Vechia, U.S. Geological 

Survey, oral commun., 2004).

 Estimation of August Median Streamflow 

on Ungaged Streams

 Multiple-linear regression analyses were used to develop 

equations to estimate August median streamflow on ungaged 

streams. August median streamflow at the 31 partial- and continuous-record stations were related statistically to physical and 

climatic characteristics of the drainage basins of these stations. 

The independent variables drainage area and percent of basin 

underlain by a sand and gravel aquifer best explain the variability in the dependent variable, August median streamflow, and 

are included in the final regression equation. This equation can 

be used to estimate August median streamflow on a river in the 

absence of streamflow data if these basin characteristics can be 

calculated. 

 Statistical Methods

 Initially, variations in the median August streamflow were 

related to variations in the drainage-basin characteristics 

through ordinary least-squares regression analysis (OLS) 

(Helsel and Hirsch, 1992). A regression of all possible subsets 

in OLS was used to reduce the number of drainage-basin characteristics and determine the best combination of independent 

variables to use in the final equation. Generalized least-squares 

(GLS) regression techniques were used to develop the final 

equations and estimates of accuracy presented in this report. 

Stedinger and Tasker (1985) showed that GLS regression techniques are more appropriate than OLS or weighted leastsquares (WLS) for regionalizing streamflow statistics where the 

streamflow records at the index stations are of varying lengths 

and concurrent streamflows at different stations are cross-correlated. Although WLS can adjust for records of varying lengths, 

it does not adjust for the cross-correlation of concurrent streamflows at sites. The cross-correlation can be especially problematic when working with partial-record stations where two or 

more partial-record stations are correlated with the same index 

station. Another benefit of GLS over OLS and WLS is that the 

prediction error of the resulting equations in GLS can be separated into model error and sampling error. 

 Ordinary Least-Squares Regression

 OLS equations were developed in a regression of all possible subsets. To establish linearity, logarithmic transformations of the response variable (August median streamflow) and 

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

explanatory variables and the response variables were chosen 

on the basis of three values: the p-values of the T-statistic, the 

adjusted R2, and Mallow’s Cp statistic (Helsel and Hirsch, 

1992). The p-values of the T-statistic indicate the significance 

of the individual explanatory variables, the adjusted R2

 value 

indicates the amount of variance in the response variable 

explained by the explanatory variable(s), and Mallow’s Cp statistic is a compromise between maximizing the explained variance by including all relevant variables and minimizing the 

standard error by keeping the number of variables as small as 

possible (Helsel and Hirsch, 1992). Partial residual plots and 

residuals against predicted plots were examined. The best oneand two-variable models were tested for regression assumptions 

including linearity, homoscedasticity (constant variance in the 

response variable over the range of explanatory variables), and 

normality. 

 The best one- and two- variable models that satisfied the 

above-mentioned criteria had the following combinations of 

explanatory variables: the logarithm of the drainage area; the 

logarithm of the drainage area and the fraction of basin underlain by a sand and gravel aquifer. 

 Generalized Least-Squares Regression

 Final one-, and two-variable models and their coefficients 

and estimates of error were selected with GLS. A model that 

estimated August median streamflow using the explanatory 

variables drainage area and fraction of basin underlain by a sand 

and gravel aquifer minimized the standard error and maximized 

the explained variance. A second model only using drainage 

area was selected for cases where reduced accuracy was acceptable. The GLS regression was adjusted for records of different 

lengths and the cross correlation of concurrent streamflows 

among partial-record stations, especially those correlated with 

the same index stations. Residuals were mapped for each partial-record station, and no spatial patterns were found. A computer program was developed for performing GLS regression in 

situations where the majority of stations being used to develop 

an equation for August median streamflow are partial-record 

stations. A more detailed statistical analysis and rationale for 

the use of GLS can be found in Lombard and others (2003).
Equations for Estimating August Median Streamflow on Ungaged Streams 11

 Equations for Estimating August Median 

Streamflow on Ungaged Streams 

 Two-Variable Model

 The final equation using fraction of basin underlain by a 

sand and gravel aquifer (Aq) and drainage area (DA) in square 

miles to predict August median streamflow at ungaged stations 

on ungaged streams (Qi) is

 Qi = 0.148 (DA)1.18466 100.409(Aq) . (1)

 Drainage area and fraction of basin underlain by a sand 

and gravel aquifer are both significant (p-values equal to 0.0001 

and 0.0104, respectively). The average standard error of prediction (ASEP) is from -27 to 38 percent. The ASEP is a measure of how well the regression equation estimates the response 

variable when it is applied to ungaged drainage basins that were 

not used to develop the equation. There is a 68-percent probability that the true value of a median flow at a station will be 

within the range of the standard error of prediction. 

 The equation listed above is appropriate for predicting 

August median streamflows at unregulated drainage basins on 

ungaged streams in the coastal part of Hancock and Washington 

Counties within the two-dimensional range of variables shown 

by the shaded area in figure 4. If the equations are used with 

explanatory variables outside the two-dimensional range shown 

in figure 4, or if the explanatory variables are calculated with 

methods other than those outlined earlier, then the resulting estimates of August median streamflow will be of unknown accuracy.

Estimates of August median streamflow on ungaged 

streams range from 0.003 to 45 ft3/s within the appropriate 

range of explanatory variables. If estimates are divided by the 

drainage area, these estimates range from 0.1 to 0.6 (ft3/s)/mi2, 

and these values generally increase as fraction of basin underlain by a sand and gravel aquifer and drainage area increase. 

 The GLS analysis results in an error that can be divided 

into sampling-error variance and model-error variance. The 

model-error variance is a measure of error resulting from an

0.01 0.1 1 10 100

DRAINAGE AREA, IN SQUARE MILES

0

0.2

0.4

0.6

0.8

FRACTION OF BASIN UNDERLAIN BY

A SAND AND GRAVEL AQUIFER

Figure 4. Two-dimensional range of explanatory variables used in regression equation for predicting August median streamflows on 

ungaged streams in eastern coastal Maine [shaded area shows range].
12 August Median Streamflow on Ungaged Streams in Eastern Coastal Maine

incomplete model, one that does not include all the variables 

that would be necessary to completely explain the variability in 

the entire population of the dependent variable. Sampling-error 

variance is a measure of the error resulting from only being able 

to sample a subset of the complete population (both in time and 

in space). The average model-error variance in the above model 

is 0.0149 (base-10 logs), and the average sampling-error variance is 0.0044 (base-10 logs). The model error is more than 

three times as great as the sampling error. This result indicates 

that future research on ungaged streams in Maine should focus 

on improving the model by developing new basin characteristics rather than by collecting additional data at present partialrecord stations or by establishing new partial-record stations to 

reduce the error in the regression equation. 

 The statewide study in Maine for larger basins (Dudley, 

2004) and low-flow studies in other northeastern States (Cervione and others, 1993; Wandle and Randall, 1994; Ries, 1994a, 

1994b, 1997) indicate that surficial geology can be important 

in explaining the variability of low flows. More detailed mapping of the sand and gravel aquifers in Maine, as well as more 

index stations on small streams in the region of interest may 

increase the accuracy of future low-flow equations.

One-Variable Model

A simplified technique using only drainage area (DA) in 

square miles to estimate August median streamflow on ungaged 

streams (Qi) is presented in the equation below. This technique 

is quicker and easier to apply than the two-variable model, but 

should be used only when estimates of less accuracy are acceptable. 

Qi = 0.167 (DA)1.2236 (2)

Drainage area is highly significant (p-value < 0.0001). 

The average standard error of prediction is from -30 to 43 percent. This error is made up of an average model-error variance 

of 0.0197 (base-10 logs) and an average sampling-error variance of 0.0042 (base-10 logs). Estimates of August median 

streamflow range from 0.003 to 31 ft3

/s within the appropriate 

range of drainage areas. If these estimates are divided by the 

drainage area, they range from 0.1 to 0.6 (ft3

/s)/mi2, and these 

values increase as drainage area increases. The estimates of 

August median streamflow on the small streams analysed in this 

report are lower than estimates of August median streamflow in 

previous investigations that had few or no stations less than 10 

mi2

.

Weighted Estimates of August Median 

Streamflow at Partial- and Short-Term 

Continuous- Record Streamflow-Gaging 

Stations 

It is appropriate to use weighted estimates of August 

median streamflow at partial-record and short-term continuousrecord stations where available. If two independent estimates 

are weighted inversely proportional to their variance, the variance of the weighted average is less than the variance of either 

estimate (Interagency Advisory Committee on Water Data, 

1982). Weighted estimates are made up of 1) measurements collected at the station and 2) the estimate for the August median 

streamflow at the station from the equation for ungaged stations. The weights for this estimate are based on the variance 

of the base-10 logs of the respective estimates (Lombard and 

others, 2003).

Weighted estimates of August median streamflow for the 

partial-record and short-term continuous-record stations used in 

this report are presented in table 3. The weighted estimates of 

August median streamflow range from 0.003 to 31 ft3/s or from 

0.1 to 0.6 (ft3/s)/mi2. 

Summary and Conclusions

August median streamflows in eastern coastal Maine were 

studied by the U.S. Geological Survey in cooperation with the 

Maine Geological Survey, with additional support from the 

Maine Department of Environmental Protection, the Maine 

State Planning Office, the Maine Department of Agriculture, 

and the Maine Department of Transportation. This report presents equations that can be used to estimate August median 

streamflow on any unregulated stream in eastern coastal Maine 

that has a drainage area ranging in size from 0.04 to 73.2 mi2

and a fraction of basin underlain by a sand and gravel aquifer 

ranging from 0 to 71 percent. August median streamflows were 

estimated at 3 long-term continuous-record stations (with 

records greater than or equal to 10 years), 23 partial-record stations, and 5 short-term continuous-record stations (records less 

than 10 years) to develop equations for estimating August 

median streamflow on ungaged streams. Each estimate of 

August median streamflow at a partial-record station or shortterm continuous-record station was based on the stations’s relation with one of five index stations in coastal Maine. 
Summary and Conclusions 13

Table 3. Weighted August median streamflows at partial-record and short-term continuous-record streamflow-gaging stations, 

eastern coastal Maine. 

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

USGS station 

number

(Figs. 1 and 2) Station name and location

Weighted August 

median flow (ft3

/s)

Weighted 

August median 

flow (ft3

/s/mi2)

Partial-record stations

01021190 Venture Brook near Dennysville, Maine 0.53 0.17

01021225 Cathance Stream at Marion, Maine 7.61 0.28

01021435 Crooked River near Beddington, Maine 6.28 0.36

01021472 Holmes Brook near Northfield, Maine 1.05 0.19

01021475 Dead Stream near Wesley, Maine 0.12 0.12

01021478 Honeymoon Brook near Wesley, Maine 0.05 0.12

01021485 Old Stream near Northfield, Maine 21.8 0.30

01021488 New Stream near Wesley, Maine 1.66 0.16

01021910 Harmon Brook near Crawford, Maine 0.65 0.20

01021960 Northern Stream near Cooper, Maine 5.12 0.21

01022220 Pleasant River near Crebo Flat, Maine 10.69 0.42

01022264 Little River near Columbia Falls, Maine 1.61 0.31

01022270 Harrington River near Harrington, Maine 1.48 0.23

01022286 Humpback Brook near Beddington, Maine 0.50 0.16

01022290 Narraguagus River near Beddington, Maine 20.7 0.31

01022400 Pork Brook near Lower Beddington, Maine 0.45 0.21

01022750 Card Mill Stream near Franklin, Maine 4.06 0.27

01022950 Alligator Stream near Great Pond, Maine 2.48 0.32

01023210 Unnamed Tributary to Lower Lead Mountain Pond near Beddington, Maine 0.30 0.17

01023400 Middle Branch Union River near Aurora, Maine 8.03 0.29

01023430 Leighton Brook near Aurora, Maine 0.36 0.17

01025445 Unnamed tributary to Winkumpaug Brook near Ellsworth, Maine 0.03 0.12

01025450 Winkumpaug Brook near Ellsworth, Maine 0.34 0.17

Continuous-record stations

01021452 Mopang Stream near Beddington, Maine 8.55 0.45

01021470 Libby Brook near Northfield, Maine 4.68 0.60

01021480 Old Stream near Wesley, Maine 8.26 0.28

01022260 Pleasant River near Epping, Maine 31.0 0.51

01022295 West Bear Brook near Beddington, Maine 0.003 0.08

01022835 Cadillac Brook near Bar Harbor, Maine 0.01 0.09

01022860 Hadlock Brook near Northeast Harbor, Maine 0.02 0.11

01024200 Garland Brook near Mariaville, Maine 2.32 0.24
14 August Median Streamflow on Ungaged Streams in Eastern Coastal Maine

Generalized least-squares regression analyses resulted in a 

two-variable regression equation to estimate August median 

streamflow on ungaged streams using two drainage-basin characteristics, drainage area and fraction of basin underlain by a 

sand and gravel aquifer. An average standard error of prediction from 27 to 38 percent reflects the high degree of variability 

often demonstrated by small drainage basins. Within this estimate of error, the model error was more than three times as 

great as the sampling error, indicating that future research 

should focus on improving the model by developing new basin 

characteristics rather than by establishing new partial-record 

stations or col-lecting additional data at established stations. A 

one-variable regression equation using only drainage area to 

estimate August median streamflow on an ungaged stream also 

was developed along with an estimate of its accuracy. The 

equation should be used only when reduced accuracy is acceptable. The generalized least-squares regression accounted for 

records of different lengths as well as cross correlation between 

the stations in both the one- and two-variable models. 

Weighted estimates of August median streamflow should 

be used at the partial-record stations and short-term continuousrecord stations, because they combine regional regression equation estimates with specific estimates based on base-flow measurements for each station. The weighted estimates of August 

median streamflow range from 0.003 to 31 ft3/s or from 0.1 to 

0.6 (ft3/s)/mi2. Estimates of August median streamflow on 

ungaged streams range from 0.003 to 45 ft3/s or from 0.1 to 0.6 

(ft3/s)/mi 2 when the equation is applied within the range of 

acceptable explanatory variables. Estimates generally increase 

as fraction of basin underlain by a sand and gravel aquifer and 

drainage area increase. 

Estimates of August median streamflow per square mile of 

drainage area at ungaged stations vary with drainage basin size, 

and for the smaller streams, are lower than estimates in previous 

investigations. Previously, 0.5 (ft3/s)/mi 2 was used on basins 

of all sizes to estimate August median streamflow. Differences 

in estimates are partially a result of the method of calculating 

the median streamflow. The median of the monthly median 

streamflow generally will be lower than the median of the mean 

monthly streamflow because mean streamflow data are skewed 

towards the higher flow events. Smaller August median values 

calculated in this report may also be a result of the smaller 

drainage basins used in this analysis. Previous investigations 

usually had few or no stations less than 10 mi2

 in drainage area. 

This investigation indicates that August median streamflow per 

square mile of drainage area increases as the basin size 

increases.

Acknowledgments

 Many USGS employees provided appreciable assistance 

in all aspects of this project. Sarah Giffen, Laura Flight, Jason 

Cyr, Tim Sargent, Andy Cloutier, Jim Caldwell, Josh Kempf, 

Patrick Miller, and Greg Stewart collected low-flow measurements; Martha Nielsen and Gloria Morrill assisted with GIS 

work; Gary Tasker, Joseph Nielsen, and Glenn Hodgkins provided statistical and technical guidance.

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Lombard, P.J. —August Median Streamflow on Ungaged Streams in Eastern Coastal Maine—USGS Scientific Investigations Report 2004-5157

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