August Median Streamflow on Ungaged Streams in 

Eastern Aroostook County, Maine

U.S. DEPARTMENT OF THE INTERIOR

U.S. GEOLOGICAL SURVEY

In cooperation with the 

AROOSTOOK WATER AND SOIL MANAGEMENT BOARD

Water Resources Investigations Report 03-4225
August Median Streamflow on Ungaged Streams in 

Eastern Aroostook County, Maine

By Pamela J. Lombard, Gary D. Tasker, and Martha G. Nielsen

Augusta, Maine

2003

In cooperation with the 

AROOSTOOK WATER AND SOIL MANAGEMENT BOARD

Water- Resources Investigations Report 03-4225
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

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

from:

U.S. Geological Survey

Information Services

Building 810

Box 25286, Federal Center

Denver, CO 80225-0286

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

District Chief

U.S. Geological Survey

Maine District

196 Whitten Road

Augusta, Maine 04330

http://me.water.usgs.gov
Contents iii

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

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

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

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

Location of Study Area ............................................................................................................................................... 3

Acknowledgments....................................................................................................................................................... 3

Data Collection and Analysis................................................................................................................................................ 3

Station Selection and Streamflow Measurements....................................................................................................... 3

Basin Characteristics................................................................................................................................................... 6

Estimating August Median Streamflow at Partial-Record Streamflow-Gaging Stations ..................................................... 11

Computing August Median Streamflow at Index Stations ......................................................................................... 11

Estimating August Median Streamflow at Partial-Record Stations............................................................................ 11

Estimating August Median Streamflow on Ungaged Streams.............................................................................................. 12

Statistical Methods ..................................................................................................................................................... 13

Ordinary Least-Squares Regression..................................................................................................................... 13

Generalized Least-Squares Regression................................................................................................................ 13

Regional Regression of Expected August Median Discharge Using Generalized Least-Squares Regression ........... 14

Estimating August Median Streamflow of Continuous-Record and Partial-Record StreamflowGaging Stations.................................................................................................................................................... 14

Estimating August Median Streamflow on Ungaged Streams ............................................................................ 14

Equations for Estimating August Median Streamflow on Ungaged Streams ....................................................................... 15

Two-Variable Model................................................................................................................................................... 15

One-Variable Model.................................................................................................................................................... 17

Weighted Estimates of August Median Streamflow at Partial- and Continuous-Record Streamflow-Gaging Stations ...... 17

Summary and Conclusions.................................................................................................................................................... 17

References Cited ................................................................................................................................................................... 19

LIST OF FIGURES

1. Map showing location of study area, eastern Aroostook County, Maine .................................................................. 4

2. Map showing location of continuous-record streamflow-gaging stations used as index stations, Maine 

and New Brunswick, Canada................................................................................................................................ 5

3. Map showing location of partial-record streamflow-gaging stations in Aroostook and neighboring 

counties, Maine..................................................................................................................................................... 7

4. Graph showing example relation of base-flow measurements at partial-record station, Big Brook near

Littleton, Maine, and concurrent daily mean flow measurements at index station, Meduxnekeag

River near Belleville, New Brunswick, Canada 1994-2002................................................................................. 12

5. Graph showing two-dimensional range of explanatory variables used in regression equations for predicting

August median streamflows on ungaged streams in the eastern part of Aroostook County, Maine.................... 16

LIST OF TABLES

1. Long-term continuous-record streamflow-gaging stations in Maine and New Brunswick, Canada tested

for use as index stations ........................................................................................................................................ 8

2. Low-flow partial-record streamflow-gaging stations in Aroostook and neighboring counties, Maine ..................... 9

3. Selected basin characteristics for streamflow-gaging stations used to develop regression equations ....................... 10

4. Weighted August median streamflows at partial-record and continuous-record streamflow-gaging stations........... 18

CONTENTS
iv August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

CONVERSION FACTORS, VERTICAL DATUM, AND COORDINATE SYSTEM

To convert temperature in degrees Fahrenheit (°F) to degrees Celsius (°C) use the following equation:

°C = 5/9 * (°F - 32)

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83), in degrees, minutes and seconds.

Vertical coordinate information is referenced to the North American Vertical Datum of 1929 (NGVD 29).

Multiply By To obtain

inch (in.) 25.4 millimeter

foot (ft) 0.3048 meter

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

cubic foot per second per square 

mile (ft3

/s)/mi2 0.01094

cubic meter per second per 

square kilometer
Abstract 1

August Median Streamflow on Ungaged Streams in Eastern 

Aroostook County, Maine

by Pamela J. Lombard, Gary D. Tasker, and Martha G. Nielsen

ABSTRACT

Methods for estimating August median streamflow were developed for ungaged, unregulated streams 

in the eastern part of Aroostook County, Maine, with 

drainage areas from 0.38 to 43 square miles and mean 

basin elevations from 437 to 1,024 feet. Few long-term, 

continuous-record streamflow-gaging stations with 

small drainage areas were available from which to 

develop the equations; therefore, 24 partial-record 

gaging stations were established in this investigation. A 

mathematical technique for estimating a standard lowflow statistic, August median streamflow, at partialrecord stations was applied by relating base-flow 

measurements at these stations to concurrent daily 

flows at nearby long-term, continuous-record streamflow-gaging stations (index stations). Generalized 

least-squares regression analysis (GLS) was used to 

relate estimates of August median streamflow at 

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 varying periods of record at the 

gaging stations and the cross correlation of concurrent 

streamflows among gaging stations. Twenty-three 

partial-record stations and one continuous-record 

station were used for the final regression equations.

The basin characteristics of drainage area and 

mean basin elevation are used in the calculated regression equation for ungaged streams to estimate August 

median flow. The equation has an average standard 

error of prediction from -38 to 62 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 -40 to 67 percent. Model error 

is larger than sampling error for both equations, indicating that additional basin characteristics could be 

important to improved estimates of low-flow statistics. 

Weighted estimates of August median streamflow, which can be used when making estimates at 

partial-record or continuous-record gaging stations, 

range from 0.03 to 11.7 cubic feet per second or from 

0.1 to 0.4 cubic feet per second per square mile. Estimates of August median streamflow on ungaged 

streams in the eastern part of Aroostook County, within 

the range of acceptable explanatory variables, range 

from 0.03 to 30 cubic feet per second or 0.1 to 0.7 cubic 

feet per second per square mile. Estimates of August 

median streamflow per square mile of drainage area 

generally increase as mean elevation and drainage area 

increase.

INTRODUCTION

The need for information describing 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, agricultural irrigation, maintenance and restoration of aquatic habitat, and watershed conservation. 

Currently (2003), few streamflow-gaging stations are 

present on small streams in Aroostook County, Maine 

that could be used to estimate low-flow statistics in the 

county. New England-wide equations used to estimate 

August median streamflows on ungaged streams with 

large drainage areas may not apply to small streams in 

the county. Management and effective utilization of 

water resources could improve with low-flow estimation techniques developed specifically for small 

streams in Aroostook County.

The New England Aquatic Base-Flow (ABF) 

policy was developed by the U.S. Fish and Wildlife 

Service (USFWS) (1981) to better manage low streamflows for aquatic organisms while still allowing for 

water withdrawals for human consumption. The ABF 
2 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

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 on 48 streamflow-gaging stations in 

New England (US Fish and Wildlife Service, 1981). In 

the absence of adequate streamflow data from unregulated streams necessary to develop the August median 

statistic, the policy recommends that an ABF of 0.5 

(ft3

/s)/mi2 of drainage area can be used to approximate 

August median flow. 

The definition of August median streamflow has 

varied in previous investigations, and 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 streamflow-gaging 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 estimated the August 

median 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. 

County and statewide policies and regulations 

are being developed with limited information on 

streams in Maine. The Aroostook Water and Soil 

Management Board developed a policy in 1996 for 

water use during low-flow periods in Aroostook 

County to ensure that farmers had adequate resources 

to maintain yields and quality of agricultural crops 

while protecting the environment from excessive drawdown of lakes, rivers and streams. This policy, How to 

Deal with Low-flow periods and Irrigating Farmer’s 

and Environmental Concerns in Aroostook County [sic] 

(Aroostook Water and Soil Management Board, 1996), 

states that site-specific ABF withdrawal limits will be 

implemented where drawdown is creating damage to 

fish and wildlife. It also states that State and Federal 

agencies will help to establish these low-flow withdrawal limits. Additionally, the State of Maine recently 

adopted legislation to ensure water withdrawal 

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. Better equations to 

estimate low-flow statistics, including August median 

streamflows, are a critical first step in establishing 

these standards. To develop regression equations that 

could be used to better estimate the August median 

streamflow on ungaged, unregulated streams in Aroostook County, Maine, the U.S. Geological Survey 

(USGS) began a cooperative study with the Aroostook 

County Water and Soil Management Board in 1998.

Purpose and Scope

This report presents equations to estimate 

August median streamflow in streams in the populated, 

eastern part of Aroostook County, as well as an estimate of the accuracy of these equations. The report 

describes (1) how instantaneous streamflow measurements at partial-record gaging stations were correlated 

to daily mean streamflows at continuous-record index 

stations to estimate August median streamflows at the 

partial-record stations (2) how regression equations to 

predict August median streamflow on small, ungaged 

streams were developed, and (3) how weighted estimates of August median streamflow at partial-record 

stations were calculated in the study area. 

Previous Studies 

Methods for estimating low-flow statistics at 

partial-record stations on the basis of correlations 

between daily mean discharges at the partial-record 

stations and concurrent daily mean discharges at 

nearby continuous-record index stations are presented 

by Riggs (1972). Riggs also outlines a technique of 

regionalizing low-flow characteristics of rivers by 

multiple regression on basin characteristics, such as 

drainage area and surficial geology. Numerous investigators in New England 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 

(Johnson, 1970; Parker, 1977; 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-
Data Collection and Analysis 3

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). 

Location of Study Area

The majority of the streamflow-gaging stations 

used in this study are in the eastern part of Aroostook 

County, Maine (fig. 1). Aroostook County encompasses 6,453 mi2

 in northern Maine and borders 

Canada on its western, northern and eastern borders. 

Aroostook County had a population of 73,938 in 2000 

(Maine Register, 2000). Nearly all the population lives 

in the eastern part of the county. The northwestern part 

of the county largely is unpopulated, forested, and 

consists predominantly of private land managed for 

forest products. 

Cold winters and cool summers typify the 

climate of northern Maine. The average annual temperature is 36 o F with the mean monthly temperatures 

ranging from 19o

F in January to 62o F in July. The 

mean annual precipitation is 35 in. (U.S. Department of 

Commerce, 1997). Water from snowmelt can be a 

major source of streamflow during April and May. 

During the summer months, streamflow comes from 

ground water discharged from aquifers (base flow), and 

rainfall from summer storms. 

A large part of the county is in the St. John River 

Basin, which includes the upper part of the St. John, the 

Allagash, the Fish, the Aroostook, and the Meduxnekeag Rivers. A small section of the southern part of 

the county lies in the Penobscot River Basin and drains 

into the Mattawamkeag River, and the St. Croix River. 

Currently, there are nine active surface-water gaging 

stations in Aroostook County, all in the St. John River 

Basin. One station has a drainage area less than 50 mi2

. 

Seven continuous-record streamflow-gaging 

stations used as index stations in the study are in Aroostook and Washington Counties, Maine and New Brunswick, Canada (fig. 2). Canadian stations were chosen 

on the basis of their proximity to the Maine border. The 

partial-record stations used in the final analysis are 

shown on figure 3. Twenty-two stations are in Aroostook County and 1 station is just over the border of 

southwestern Aroostook County, in Penobscot County.

Acknowledgments

Many USGS employees provided appreciable 

assistance in all aspects of this project. Sarah Canon, 

Laura Flight, Jason Cyr, Tim Sargent, Andy Cloutier, 

Jim Caldwell, and Gregory Stewart collected low-flow 

measurements; Gloria Morrill assisted with GIS work; 

and Glenn Hodgkins and Joseph Nielsen provided 

statistical and technical guidance.

DATA COLLECTION AND ANALYSIS

Ideally, equations to estimate August median 

streamflow on small, ungaged streams in Aroostook 

County would be developed from long-term continuous-record data from small streams in this same 

region; however, there only is one gaging station with 

greater than 15 years of record on a small stream in 

Aroostook County and thus it was necessary to use 

partial-record stations to develop these equations. All 

partial-record stations included in these analyses had a 

minimum of 10 base-flow measurements. Although it 

is possible to extend the record of a partial-record 

station with less than 10 measurements graphically, it is 

preferable to have at least 10 measurements (Riggs, 

1972). Base-flow measurements and a correlation with 

a gaging station with a long period of record were used 

to extend the record and estimate an August median 

flow at partial-record stations. 

Station Selection and Streamflow Measurements

Twenty-four partial-record stations were established specifically for this project. Standard USGS 

methods as described by Rantz and others (1982) were 

used to make streamflow measurements at these 

stations, including wading current-meter measurements, portable Parshall flume measurements, and 

volumetric measurements. All measurements were 

published in the USGS series of annual water-data 

reports from 1994 to 2002, the most recent of which is 

referenced (Stewart and others, 2001). Two partialrecord stations were discontinued after 2 years of data 

collection because more than half of the base-flow 

measurements at each one of these stations were zero. 

Streamflow at the remaining 22 partial-record stations 

was measured 10 to 19 times from 1994 to 2002. Two 

additional partial-record stations were eliminated 

during the analysis because measurements at these 

stations did not correlate well with daily flow measurements at any of the index stations.
4 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

Study Area

Aroostook County

Penobscot

County Washington

County

MAINE

NEW

BRUNSWICK

0

0

40

50

80 MILES

100 KILOMETERS

EXPLANATION

Major rivers and streams

County boundary

State boundary

International boundary

70o

71o

43o

44o

45o

46o

47o

48o

69o

68o

67o

St. Joh iv

n R er

St. John River

Alla

h

g

r

as

Rive

Penobscot

e

Riv

r Mattawamkeag

Fish River

Aroo

o

sto

k River

St. Croix Rive

River

r Meduxnek g ea Ri ver

Base from U.S. Geological Survey

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

projection UTM, zone 19.

67 o

0

0

40

50

80 MILES

100 KILOMETERS

MAINE

New

Brunswick,

Canada

New

Hampshire

Vermont

Massachusetts

Connecticut

Rhode

Island

Quebec, Canada

Atlantic Ocean

Study

Area

Figure 1. Location of study area, eastern Aroostook County, Maine.
Data Collection and Analysis 5

01010000

01010000 Continuous-record streamflow-gaging station and number

Location of study area

01022500

01016500

01017900

01AJ003

01AF007

01AJ004

MAINE

NEW

BRUNSWICK

0

0

40

50

80 MILES

100 KILOMETERS

EXPLANATION

70o

71o

43o

44o

45o

46o

47o

48o

69o

68o

67o

Base from U.S. Geological Survey

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

projection UTM, zone 19.

Figure 2. Location of continuous-record streamflow-gaging stations used as index stations, Maine and New Brunswick, Canada.
6 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

Streamflow data were used from three additional 

streamflow-gaging stations, USGS number 01012520, 

Bald Mountain Brook near Bald Mountain (1980-84); 

USGS number 01012525, Bishop Mountain Brook 

near Bishop Mountain (1981-84) (Fontaine, 1989); and 

USGS number 01017550, Williams Brook at Phair 

(Stewart and others, 2001). Although Bald Mountain 

Brook and Bishop Mountain Brook were operated as 

continuous-record gaging stations during the period of 

their operation, 3 to 4 years is not sufficient to calculate 

the August median streamflow, and thus, these stations 

were treated as partial-record stations. Williams Brook 

at Phair has been in operation as a continuous-record 

gaging station since 1999, but also does not have a 

sufficient period of record from which to calculate an 

August median streamflow. The locations of the 23 

partial-record stations used in the regression analysis 

are shown in figure 3.

Measurements taken at the partial-record 

stations were correlated with daily flows at long-term 

gaging stations to extend the record at the partialrecord stations. Partial-record stations were tested for 

correlation with unregulated long-term continuousrecord stations in Maine and Canada. Nine continuousrecord stations in northern, central, and eastern Maine, 

as well as seven stations in New Brunswick, Canada, 

were tested. Station identification numbers, station 

names, station locations, periods of record, and 

drainage areas for all stations that were tested are listed 

in table 1. Although three of the stations have been 

discontinued, these rivers have all been gaged by the 

USGS or the Water Survey of Canada for 18 to 50 

years. The data can be found in the USGS annual 

water-data reports and predecessor Water-Supply 

Papers for the stations in Maine and the Water Survey 

of Canada’s Surface Water Data Books for stations in 

New Brunswick. The most recent data reports are 

Stewart and others (2001) and Inland Waters Directorate (2001) for Maine and New Brunswick, respectively.

Stations with the best correlation with partialrecord stations were chosen 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 50 mi2), but few continuous-record stations 

in the region meet these criteria. Three of the index 

stations are in Aroostook County, Maine, one is in 

Washington County, Maine and three are in New Brunswick, Canada. The locations of all index stations used 

in this study are shown in figure 2. 

Station identification numbers, station names, 

station locations, and number of measurements for the 

23 partial-record stations are listed in table 2. All 

stations but one are in Aroostook County, have relatively small drainage areas (from 0.38 mi2

 to 50 mi2), 

are unregulated, and as a group are considered representative of the populated, eastern part of Aroostook 

County. 

Streamflows at the partial-record stations were 

measured during independent base-flow events, separated by storms. A range of flows throughout the 

summer months was sought, and rapidly changing 

flows or flows that could be attributed directly to rain 

runoff were avoided. Measurements for a given lowflow event were made within a 30-hour period at all 

stations, including the two discontinued index stations 

(USGS streamflow-gaging station numbers 01016500 

and 01017900) that were treated as partial-record 

stations during this period. 

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 

included drainage area, average and maximum basin 

slope, mean elevation, elevation range, relative basin 

relief (median elevation minus minimum elevation), 

main-channel length, total stream length, main-channel 

slope, stream density, percent wetland and pond area, 

and annual and average summer precipitation and 

temperature 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 quadrangles. Basin 

characteristics including drainage area were calculated 

for each basin after the basin boundary was digitized 

using GIS. Mean and maximum basin slope, elevation 

range, relative basin relief, and mean elevation all were 

computed using a 30-meter-resolution USGS digital 

elevation model (DEM) obtained from the Maine 

Office of GIS. Slope was determined using a 9-pixel 

moving average of the DEM for each pixel. Mean 

basin slope was computed as the mean of all pixel 

slopes in the basin. Mean elevation was determined 
Data Collection and Analysis 7

1

1A

11

I-95

01017295

01017300

01012520

01012525

01012790

01012800

01013550

01014700

01015005

01015008

01015007

01017010

01017050

01017115

01017450

01017550

01017555

01017600

01018050

01018060

01018070

01030050

01018100

0

0

10

10

20 MILES

20 KILOMETERS

SCALE

68o

68 35’46” o

47o

46o

County boundary

International boundary

Major Roads

EXPLANATION

Base from U.S. Geological Survey

digital files, scale 1:100,000,

projection UTM, zone 19 Limit of study

Limit of study

Fort Kent

Houlton

Presque

Isle

Caribou

01017450 Low-flow partial-record streamflow-gaging station and number

Figure 3. Location of partial-record streamflow-gaging stations in Aroostook and neighboring counties, Maine.
8 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine Table 1. Long-term continuous-record streamflow-gaging stations in Maine and New Brunswick, Canada tested for use a

[USGS, U.S. Geological Survey; Latitude and Longitude in degrees, minutes and seconds] *The water year is the 12-month period October 1 through September 30.** 01017900 is the only index station that is also used in the regression equation for estimating August median flow at ungaged stations because index station with a drainage area less than 50 square miles.

USGS or Canadian station number

Latitude

o ‘ “

Longitude

o ‘ “ Station name

Period of record 

(water years*)

Drai

(squ

Continuous-record stations used as index stations (shown on fig.2)

01010000 46 42 00 69 42 59 St. John River at Ninemile Bridge, Maine 1950-2002 01016500 46 37 42 68 26 07 Machias River near Ashland, Maine 1951-1983 01017900** 46 08 42 68 03 42 Marley Brook near Ludlow, Maine 1964-1982 01022500 44 36 29 67 56 10 Narraguagus River at Cherryfield, Maine 1948-2002 01AF007 47 14 46 67 55 16 Grande Riviere at Violette Bridge, New Brunswick 1977-2002 01AJ003 46 12 58 67 43 42 Meduxnekeag River near Belleville, New Brunswick 1967-2002 01AJ004 46 26 14 67 44 41 Big Presque Isle Stream at Tracy Mills, New Brunswick 1967-2002 

Continuous-record stations tested, but not used

01010070 46 53 38 69 45 08 Big Black River near Depot, Maine 1983-2002 01015800 46 31 21 68 22 23 Aroostook River near Masardis, Maine 1957-2002 01018000 46 06 17 67 52 00 Meduxnekeag River near Houlton, Maine 1941-1982 01031500 45 10 31 69 18 55 Piscataquis River at Dover Foxcroft, Maine 1902-2002 01022295 44 51 34 68 06 23 West Branch Bear Brook near Beddington, Maine 1988-2002 01AK001 45 56 42 67 19 20 Shogomoc Stream near Trans Canadian Highway, New 

Brunswick

1948-2002 

01AK007 46 02 57 67 14 25 Nackawic Stream near Temperence Vale, New Brunswick 1967-2002 01AH002 47 10 24 67 12 36 Tobique River at Riley Brook, New Brunswick 1954-2002 01AJ010 46 20 27 67 27 58 Becaguimec at Coldstream, New Brunswick 1973-2002 
Data Collection and Analysis 9

.*Three and two years of daily summer flows from June-September were used for the correlations at 01012520 and 01012525, respectively.** Station 01017550 has been run as a continuous-record station from 1999 to the present. It was treated as a partial-record station for this report period of record to calculate an August median flow.

USGS station 

number

Latitude

o ‘ “

Longitude

o ‘ “ Station name

Index 

station

01012520 46 44 23 68 45 21 Bald Mountain Brook near Bald Mountain, Maine 01016500 01012525 46 44 43 68 45 11 Bishop Mountain Brook near Bishop Mountain, Maine 01016500 01012790 47 13 32 68 20 24 North Fork McLean Brook near St. Agatha, Maine 01022500 01012800 47 14 39 68 22 04 Unnamed tributary to East Fork Dickey Brook near St. Agatha, Maine 01AF007 01013550 47 14 26 68 32 32 Unnamed tributary to Pearly Brook near Michigan Settlement, Maine 01022500 01014700 47 21 09 68 17 50 Factory Brook near Madawaska, Maine 01AF007 01015005 47 07 12 67 57 46 Unnamed tributary to Hammond Brook near Cyr Plantation, Maine 01016500 01015007 47 06 18 67 53 12 Unnamed tributary to St. John River near Hamlin, Maine 01AF007 01015008 47 04 56 67 49 34 Martin Brook near Hamlin, Maine 01016500 01017010 46 45 19 68 06 30 Unnamed tributary to Aroostook River at Crouseville, Maine 01010000 01017050 46 41 29 68 10 44 Libby Brook near Mapleton, Maine 01016500 01017115 46 50 55 68 02 35 Caribou Stream at Caribou, Maine 01AJ003 01017295 46 52 25 67 54 07 Nichols Brook near Limestone, Maine 01016500 01017300 46 51 29 67 56 17 Nichols Brook near Caribou, Maine 01016500 01017450 46 45 53 67 54 26 Ginn Brook near Fort Fairfield, Maine 01AJ004 01017550** 46 37 37 67 57 12 Williams Brook at Phair, Maine 01AJ003 01017555 46 33 14 67 50 27 Hilt Brook near Mars Hill, Maine 01AJ004 01017600 46 30 25 67 47 39 Unnamed tributray to Young Brook near Mars Hill, Maine 01022500 01018050 46 12 01 67 49 08 Big Brook near Littleton, Maine 01AJ003 01018060 46 15 12 67 50 23 Unnamed tributary to Meduxnekeag River near Littleton Station, Maine 01AJ004 01018070 46 13 54 67 47 10 Unnamed tributary to meduxnekeag River near Littleton, Maine 01AF007 01018100 46 19 02 67 48 03 Unnamed tributary to Dead Stream near Monticello, Maine 01AJ003 01030050 46 00 05 68 26 58 Webb Brook near Patten, Maine 01017900 

Table 2. Low-flow partial-record streamflow-gaging stations in Aroostook and neighboring counties, Maine.[USGS, U.S. Geological Survey; Latitude and Longitude in degrees, minutes and seconds]
10 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

similarly as the the mean elevation of all pixels in the 

basin. Main-channel length and total stream length 

were computed using digital line graphs of the 7.5-

minute USGS quadrangles in each area. Main-channel 

length was the length of the main channel of each 

stream, projected to the basin divide. Total stream 

length was the summed lengths of all stream segments 

appearing on the 7.5-minute quadrangles. Mainchannel slope was determined by intersecting the total 

stream length with the slope grid, buffered by 10 

meters, producing a line of slope pixels. The mean of 

the pixels in this line was used as the mean-channel 

slope. Stream density was defined as the total stream 

length of a basin divided by its drainage area. Pond 

areas also were calculated using the digital line graphs 

of the 7.5-minute USGS topographic quadrangles, 

served by the Maine Office of GIS at 

http://apollo.ogis.state.me.us/. Wetland areas were 

calculated using digital National Wetland Inventory 

maps produced by the U.S. Fish and Wildlife Service 

(USFWS) at a scale of 1:24,000. Temperature and 

precipitation data were obtained from the Oregon State 

University Spatial Climate Analysis Service. These 

gridded datasets were produced using the ParameterElevation Regressions on Independent Slopes Model 

(PRISM) (Daly and Neilson, 1992; Daly and others, 

1997). Precipitation and temperature data were determined for the centroid of each basin. Selected basin 

characteristics for each station that were used in the 

final regression equations are presented in table 3.

* Station 01017550 has been run as a continuous-record station from 1999 to the present. It was treated as a partial-record 

station for this report because it did not have a sufficient period of record to calculate an August median streamflow. 

USGS 

station 

number Station name

Mean elevation 

(feet)

Drainage 

area 

(square 

miles)

Partial-record stations

01012520 Bald Mountain Brook near Bald Mountain, Maine 1,024 1.73

01012525 Bishop Mountain Brook near Bishop Mountain, Maine 978 1.04

01012790 North Fork McLean Brook near St. Agatha, Maine 796 0.56

01012800 Unnamed tributary to East Fork Dickey Brook nr St. Agatha, Maine 919 0.38

01013550 Unnamed tributary to Pearly Brook near Michigan Settlement,Maine 974 0.39

01014700 Factory Brook near Madawaska, Maine 922 5.96

01015005 Unnamed tributary to Hammond Brook near Cyr Plantation, Maine 848 0.55

01015007 Unnamed tributary to St. John River near Hamlin, Maine 639 0.66

01015008 Martin Brook near Hamlin, Maine 731 12.06

01017010 Unnamed tributary to Aroostook River at Crouseville, Maine 530 0.44

01017050 Libby Brook near Mapleton, Maine 719 2.63

01017115 Caribou Stream at Caribou, Maine 656 43.06

01017295 Nichols Brook near Limestone, Maine 627 1.69

01017300 Nichols Brook near Caribou, Maine 556 2.03

01017450 Ginn Brook near Fort Fairfield, Maine 676 6.13

01017550* Williams Brook at Phair, Maine 654 3.82

01017555 Hilt Brook near Mars Hill, Maine 798 2.48

01017600 Unnamed tributray to Young Brook near Mars Hill, Maine 849 0.45

01018050 Big Brook near Littleton, Maine 496 14.26

01018060 Unnamed tributary to Meduxnekeag River nr Littleton Station, Maine 518 1.26

01018070 Unnamed tributary to meduxnekeag River near Littleton, Maine 437 5.07

01018100 Unnamed tributary to Dead Stream near Monticello, Maine 463 2.09

01030050 Webb Brook near Patten, Maine 736 1.04

Continuous-record station

01017900 Marley Brook near Ludlow, Maine 795 1.5

Table 3. Selected basin characteristics for streamflow-gaging stations used to develop regression equations

[USGS, U.S. Geological Survey]
Estimating August Median Streamflow at Partial-Record Streamflow-Gaging Stations 11

ESTIMATING AUGUST MEDIAN STREAMFLOW 

AT PARTIAL-RECORD STREAMFLOW-GAGING 

STATIONS 

August median streamflow at partial-record 

gaging stations was estimated using base-flow 

measurements at the partial-record stations and the 

correlation between those base-flow measurements and 

concurrent mean daily streamflow values at continuous-record streamflow-gaging stations with a 

minimum of 15 years of record (index stations). This 

method is presented by Riggs (1972) and follows the 

USGS guidelines for regional low-flow analyses where 

appropriate (U.S. Geological Survey, 2003). 

Computing August Median Streamflow at Index 

Stations

August median streamflow values at the index 

station and the daily mean streamflows that coincided 

with base-flow measurements at the partial-record 

stations were needed to estimate August median 

streamflows at the partial-record stations. Initially, 

annual August medians were calculated at each index 

station. A Mann Kendall trend test (Helsel and Hirsch, 

1992) indicated that there was no trend over time in this 

annual series of August medians at any of the index 

stations. The expected August median streamflow was 

estimated at the index station 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 was preferable because it 

allowed for the calculation of the variance around the 

median. 

Daily mean streamflows at the continuousrecord stations that corresponded to concurrent baseflow measurements at partial-record stations were used 

to establish a relation between the two stations. Daily 

mean streamflow collection was discontinued at 

Marley Brook near Ludlow in 1982 and the Machias 

River in Ashland in 1983. These stations still were 

used as index stations because they had sufficient 

periods of record to calculate August medians and were 

treated as partial-record stations from 1997 to 2002 to 

obtain daily mean streamflows that corresponded with 

base-flow measurements at the partial-record stations.

Estimating August Median Streamflow at PartialRecord 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-day consecutive low flow 

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

this technique to calculate the monthly median at a 

partial-record station, as opposed to the d-day T-year 

low flow, is appropriate if the logarithms of the 

monthly medians at the index station are approximately 

normally distributed. Estimates are made on the basis 

of the relation between base-flow measurements at the 

partial-record station and concurrent daily streamflows 

at a continuous-record gaging station. This relation is 

defined using 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 partialrecord station. The Stedinger-Thomas technique was 

used to calculate the August median and the variance of 

the August median at each partial-record station. This 

technique fits a least-squares regression to the data 

after the user determines if the base-flow measurements have an adequate linear relation with the concurrent daily streamflows at the index station. 

To estimate an August median and standard deviation of the August median at the partial-record 

stations, the logarithm of the measured streamflows at 

a partial-record station has to have a linear relation 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 4. All the 

low-flow partial-record stations used in the analysis 

had a correlation coefficient of greater than 0.65 with 

an index station. If measurements at a partial-record 

station correlated well with measurements from more 

than one index station, the index station with the higher 

correlation coefficient was used. If the correlation 

coefficient was similar for two index stations, the index 

station was chosen on the basis of the graphical relation 

between the two stations. Base-flow measurements at 

the partial-record station and 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 medians at the index station were used to 
12 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

compute the base-10 logarithms of the median and its 

variance at the partial-record station.

All measurements at partial-record stations were 

included in the Stedinger-Thomas technique except in 

the following cases. Two partial-record stations had 

one streamflow measurement of zero each. The stations 

were used, but the zero streamflow measurements were 

not used because of the impossibility of taking the 

logarithm of zero and because the estimated August 

median was above the region of the graph that would 

have included these zero streamflow estimates. At 

some additional partial-record stations, measurements 

were taken for which no concurrent daily mean streamflow estimate was available at the most appropriate 

index station, number 01016500, Machias River near 

Ashland, Maine. This station was operated from 1951 

to 1983 as a continuous-record station, resulting in 32 

years from which to calculate the historic August 

median streamflow, and from 1997 to 2002 as a partialrecord station to obtain corresponding streamflows 

with which to establish a correlation and extend the 

record of partial-record stations. Measurements from 

1994 to 1996 were not available at this station; 

however, it still was the most appropriate index station 

in various cases based on measurements taken from 

1997 to 2002. Estimates of the August medians at the 

partial-record stations are given in the section titled 

Weighted Estimates of August Median Streamflow at 

Partial-record and Continuous Record Streamflow 

Gaging Stations in this report. 

ESTIMATING AUGUST MEDIAN STREAMFLOW 

ON UNGAGED STREAMS

Ordinary and general multiple-linear regression 

analyses were used to develop equations to estimate 

August median streamflow on ungaged streams. 

August median streamflow at 23 partial-record stations 

and 1 continuous-record station were related statistically to physical and climatic characteristics of the 

drainage basins of these stations. Station number 

10 100 1,000

MEDUXNEKEAG RIVER NEAR BELLEVILLE, NEW BRUNSWICK, CANADA. DISCHARGE IN CUBIC FEET PER SECOND

1

10

2

3

4

5

6

7

8

9

20

BIG BROOK NEAR LITTLETON, MAINE. DISCHARGE, IN CUBIC FEET PER SECOND

CORRELATION COEFFICIENT (R)= 0.89

Figure 4. Example relation of base-flow measurements at partial-record station, Big Brook near Littleton, Maine, and concurrent daily 

mean flow measurements at index station, Meduxnekeag River near Belleville, New Brunswick, 1994-2002.
Estimating August Median Streamflow on Ungaged Streams 13

01017900, Marley Brook near Ludlow (Fig.2), was the 

only index station that also was used in the analysis to 

generate equations for ungaged streams because it is 

the only long-term continuous-record station with a 

drainage area less than 50 mi2

. The independent variables or basin characteristics that best explain the variability in the dependent variable, August median 

streamflow, were used to develop regression equations. 

These equations can be used to estimate August median 

streamflow on a river if basin characteristics can be 

calculated, but no streamflow data are available. 

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 leastsquares (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 least-squares (WLS) 

for regionalizing streamflow statistics where the 

streamflow records at the gaged 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 especially can be problematic 

when working with partial-record stations where two or 

more partial-record stations are extended with the same 

index station. Another benefit of GLS over OLS and 

WLS is that the prediction error of the resulting equations can be separated into model error and sampling 

error. 

Ordinary Least-Squares Regression

Ordinary least-squares 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. 

Transformation was not necessary for the remaining 

explanatory variables. The equations with the strongest relations between the explanatory variables and 

the response variables were chosen on the basis of the 

p-values of the T-statistic, the adjusted R2, and 

Mallow’s Cp statistic. 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 and predicted plots were 

examined. Top one- and 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 three models that best satisfied the abovementioned criteria had the following combinations of 

explanatory variables: (1) the logarithm of the drainage 

area, (2) the logarithm of the drainage area and mean 

elevation, and (3) the logarithm of the drainage area 

and average summer precipitation. 

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 mean basin elevation, 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 adjusted for the records of varying lengths, 

and the cross correlation of concurrent streamflows 

among partial-record stations, especially those 

extended 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 partialrecord stations. A more detailed statistical analysis and 

rational for the use of GLS follows.
14 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

Regional Regression of Expected August Median 

Streamflow Using Generalized Least-Squares 

Regression

A regional regression model was used to estimate expected August median streamflow at a stream 

site based on physical, climatological, and land-use 

characteristics of the drainage basin. Assume a linear 

model is of the form

ψ=Xβ + ε, (1)

where ψ is a (N x 1) column vector of logarithms of 

expected August median discharge values, X is a (N x 

p) matrix of known basin characteristics augmented by 

a column of 1’s, β is a (p x 1) column vector of 

unknown regression coefficients to be estimated, and ε

is a (N x 1) column vector of errors with E[ε]=0 and 

E[εε’]=Iγ2

. The scalar value γ2 is called the model error 

variance and N is the number of gaging stations and 

partial-record stations in the region.

Estimating August Median Streamflow of ContinuousRecord and Partial-Record Streamflow Gaging Stations

The first operational problem with the regression 

model in equation 1 is that the logarithm of expected 

August median discharge, ψ, is to be estimated from 

streamflow records and base-flow measurements made 

at partial-record stations. 

At gaged, continuous-record station i with ni

years of record, the expected August median discharge, 

, is estimated by computing the median of the 

observed annual August medians. For the regional 

regression in equation 1, the dependent variable is the 

base-10 log of the August median. Assuming the logarithms of annual August medians approximate a 

normal distribution, the standard error of the log of the 

median of annual August medians can be estimated as

Si=c[(Sx)i/ni

0.5] (Stuart and Ord, 1987), (2)

where (Sx)i is the standard deviation of the logarithms 

of the annual August medians at station i with ni

 years 

or record and c is a constant equal to 1.2533.

The analysis for partial-record stations is based 

on an assumed linear model between the logarithms of 

annual August medians, yi,t, at partial-record station i 

in year t and the annual August medians, xi,t, at a 

nearby continuous station:

yi,t = αi + δixi,t + ei,t , (3)

where ei,t are independent, identical normally distributed errors with mean zero and variance σ2

e. Because 

no observations of August medians are available for the 

partial-record station, α, δ, and σe in equation 3 are 

estimated by an ordinary least-squares regression of 

independent base-flow measurements at the partialrecord station, , on concurrent daily flows, , at the 

index station. An estimate of the expected August 

median at the partial-record station is obtained from

log( ) = ai + bi Mx (4)

where ai and bi are estimates of αi and δi from a 

regression of on and Mx is the sample median of 

annual August medians for the index station. The 

variance of log( ) is estimated by 

(Stedinger and Thomas, 1985), (5)

in which Li is the number of base-flow measurements 

at the partial-record station, mx is the mean of the 

logarithms of the concurrent daily flows at the index 

station, sx is the standard deviation of concurrent daily 

flows at the index station, c is a constant equal to 

1.2533, and (se)i

 is the standard error of estimate of the 

regression of on .

Estimating August Median Streamflow on Ungaged Streams

For the regional equation (1), yi=log( ) is the estimate 

of ψi at the partial-record or continuous-record stations 

and has a random error component such that 

ψi = yi− ηi, (6)

where ηi is a random error with E[ηi]=0 and Var[ηi]=

Si

2. Substituting equation 6 into equation 1, in matrix 

notation, the regional regression model is

y = Xβ + ε + η, (7)

with E[ε+η]=0 and E[(ε+η)(ε+η)’]=Λ. The covariance 

matrix of errors, Λ, is given by

Qi

y ̃

i x ̃i

Qi

y ̃

i x ̃i

Qi

Si

2 Var Qi = ( ) log( ) =

se ( )i

2 1

Li

---- Mx mx ( ) – 2

s2

x Li ( ) – 1

+ -------------------------- bi

2 c Sx ( )j ( )2

nj

+ ---------------------------

y ̃

i x ̃i

Qi
Equations for Estimating August Median Streamflow on Ungaged Streams; 15

Λ=γ2I + Σ, (8)

where the (N x N) matrix Σ has elements of

Σij= (9)

where i and j index rows and columns of the matrix, 

ρ(yi

,yj) is the correlation between estimates of logarithms of expected August medians at stations i and j, 

and Cij is defined as in Tasker and Driver (1988) as 

(10)

A regression model with this error structure was 

considered by Stedinger and Tasker (1985; 1986a; 

1986b) to develop a generalized-least-squares (GLS) 

method for regional hydrologic regression. The method 

provides for possibly more accurate estimates of 

regression coefficients when compared to ordinary 

least-squares methods when stations have different 

sampling variances, an unbiased model-error estimator, 

and a better description of the relation between hydrologic data and information for hydrologic network 

analysis and design (Tasker and Stedinger, 1989; Moss 

and Tasker, 1991).

The GLS method for regional regression of 

annual recharge generally proceeds as follows. The Σ

matrix is estimated by entering the Si

’s from the N atstation regressions and using the relation between 

cross-correlation coefficients between mean annual 

values and annual values (Moss, 1973) as

ρ(yi,yj)= (11)

where mij is the concurrent record length between 

index stations for partial-record stations i and j, ni is the 

record length at station i, and ρij is the correlation 

between concurrent annual August median values at 

the pair of stations. The values of ρij used to compute 

ρ(yi

,yj) in equation 11 are estimated by an average 

value based on pairs of long-term continuous-record 

stations. It is necessary to use the averaged values to 

avoid problems with inverting the Λ matrix (Tasker and 

Stedinger, 1989). Once the Σ matrix is filled out from 

the sample data, the EGLS regression estimators of the 

model parameters, β, are determined by solving 

{X’Λ-1X}β = X’Λ-1y, (12)

with model-error variance γ2 determined so that

(y-Xβ)’Λ-1(y-Xβ) = N - p. (13)

The predicted log of the August median at ungaged 

station k with basin characteristics 

xk =(1, xk,1, xk,2,..., xk,p) is =xkb (14)

 The standard error of prediction is

(15)

EQUATIONS FOR ESTIMATING AUGUST MEDIAN 

STREAMFLOW ON UNGAGED STREAMS 

Two-Variable Model

The final equation using mean elevation (E) in 

feet and drainage area (A) in square miles to predict 

August median streamflow at ungaged stations on 

ungaged streams ( ) is 

 = 0.061 (A)1.28 100.00059(E) . (16)

Drainage area and mean elevation are both 

significant (p-values equal to 0.0001 and 0.0489, 

respectively). The average standard error of prediction 

(ASEP) is from -38 to 62 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 peak flow at a station will be within the range 

of the standard error of prediction. 

Equation 16 is appropriate for predicting August 

median streamflows at unregulated drainage basins on 

ungaged streams in the eastern part of Aroostook 

County within the two-dimensional range of variables 

shown by the shaded area in figure 5. If the equations 

are used with explanatory variables outside the twodimensional range shown in figure 5, or if the explanaSi

2 for i=j

ρ yi yj ( ) , Cij  for i j, ≠





Cij

bibj Sx ( )i Sx ( )j

ninj

= --------------------------------

mijρij

ninj

-------------

yk

ˆ

S yˆ

k () γˆ 2 xkX'Λ

ˆ –1

X–1x' = + k

Qi

Qi
16 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

tory variables are calculated with methods other than 

those outlined above, the resulting estimates of August 

median streamflow will be of unknown accuracy.

Estimates of August median streamflow on 

ungaged streams can range from 0.03 to 30 ft3

/s within 

the appropriate range of explanatory variables. If estimates are divided by the drainage area, they can range 

from 0.1 to 0.7 (ft3/s)/mi2 and these values generally 

increase as mean elevation and the drainage area 

increase. 

The generalized least-squares 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 incomplete 

model, one that does 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 

because of 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 

0.0361 (base-10 logs) and the average sampling-error 

variance is 0.0074 (base-10 logs). The model error is 

about five times greater than the sampling error. This 

result indicates that future research should focus more 

on improving the model by developing new basin characteristics rather than on additional data collection at 

present partial-record stations, or creation of new 

partial-record stations to reduce the error in the regression equation. 

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. Although the sand and gravel aquifers in 

Maine have been mapped (Maine Geological Survey, 

2003), the surficial geology in eastern Aroostook 

County is not particularly variable. Only one of the 

partial-record station drainage basins overlaps with a 

sand and gravel aquifer as shown by the current 

mapping. Either the mapping is not detailed enough to 

be accurate for small drainage basins or there is little 

variability in this eastern section of Aroostook County. 

Until additional, more detailed geologic mapping is 

available, the variability of the surficial geology cannot 

be accounted for. In addition, the sampling error may 

result from the lack of small index stations in the region 

of interest. Better correlations of index stations and 

partial-record stations could lower the sampling error.

Figure 5. Two-dimensional range of explanatory variables used in regression equations for predicting August median streamflows on 

ungaged streams in the eastern part of Aroostook County, Maine. [Shaded area shows range.]
Equations for Estimating August Median Streamflow on Ungaged Streams; 17

One-Variable Model

A simplified technique using only drainage area 

(A) in mi2

, to estimate August median streamflow on 

ungaged streams ( ) is presented below. This technique is quicker and easier to apply than other techniques, but should only be used when estimates of less 

accuracy are acceptable. 

 = 0.17 (A)1.217 (17)

Drainage area is highly significant (p-value < 

0.0001). The average standard error of estimation is 

from -40 to 67 percent. This error is made up of an 

average model-error variance of 0.0435 (base-10 logs) 

and an average sampling-error variance of 0.0061 

(base-10 logs). Estimates of August median streamflow range from 0.06 to 15 ft3

/s within the appropriate 

range of drainage areas. If these estimates are divided 

by the drainage area, they range from 0.1 to 0.4 

(ft3

/s)/mi2 and these values increase as drainage area 

increases.

WEIGHTED ESTIMATES OF AUGUST MEDIAN 

STREAMFLOW AT PARTIAL- AND CONTINUOUSRECORD STREAMFLOW-GAGING STATIONS 

It is appropriate to use weighted estimates of 

August median streamflow at partial-record and 

continuous-record streamflow-gaging stations. 

Weighted estimates average measurements taken at the 

station with an estimate for the August median at the 

station using the equation for ungaged stations. The 

weights for this average are based on the variance of the 

base-10 logs of the respective estimates. The variance 

of the regression prediction, is given by

VR=S2( ) , (18)

where S( ) is given in equation 15. The variance of 

the estimate based on at-station streamflow data is VO=

Si

2 , where Si is given by equations 2 or 5, depending 

on the type of gaging station. The weighted estimate of 

the log of August median is

Yw = w +(1-w) log , (19)

where 

w=VO/(VO+VR). (20)

Assuming independence of the two estimators, the

variance of Yw would be 

Var(Yw)=(VOVR)/(VO+VR). (21)

Weighted estimates of August median streamflow at the partial-record stations used in this report are 

presented in table 4. The weighted estimates of August 

median streamflow at the partial-record stations range 

from 0.03 to 11.67 ft3/s or from 0.1 to 0.4 (ft3/s)/mi2. 

SUMMARY AND CONCLUSIONS

This report, prepared by the U.S. Geological 

Survey in cooperation with the Aroostook County 

Water and Soil Management Board, presents equations 

to estimate August median streamflow on any unregulated stream in the eastern part of Aroostook County, 

Maine, with a drainage area from 0.38 to 43 mi2 and a 

mean basin elevation from 437 to 1024 ft. August 

median streamflows were estimated at 1 continuousrecord station and 23 partial-record stations to develop 

equations for estimating August median streamflow on 

ungaged streams. Each estimate of August median 

streamflow at a partial-record station was based on the 

stations’s relation with one of seven continuous-record 

stations in Maine and New Brunswick Canada. 

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 mean basin elevation. A high standard error of 

prediction of from -38 to 62 percent probably can be 

explained by the small number of index stations with 

small drainage areas in the region, and by the lack of 

variability in the current surficial geology mapping, 

which often explains a great deal of variability in lowflow statistics. 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 

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

accounted for records of different lengths as well as 

Qi

Qi

yˆ

k

yˆ

k

yˆ

k

yˆ

k Qi
18 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

cross correlation between the stations in both the oneand two-variable models. 

Weighted estimates of August median streamflow should be used at the partial-record stations and 

the one continous-record station, as they combine 

regional regression equation estimates with specific 

estimates based on base-flow measurements for each 

station. The weighted estimates of August median 

streamflow at the partial-record stations range from 

0.03 ft3

/s to 11.67 ft3/s. The weighted estimates of 

August median streamflow per square mile of drainage 

area at the partial-record stations range from 0.1 to 0.4 

(ft3/s)/mi2

. Estimates of August median streamflow 

on ungaged streams range from 0.03 to 30 ft3

/s or from 

0.1 to 0.7 (ft3

/s)/mi 2 when the equation is applied 

within the range of acceptable explanatory variables. 

Estimates generally increase as mean elevation 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. It is also a result of the smaller 

drainage basins used in this analysis. Previous investigations often had few or no stations less than 10 mi2 in 

drainage area. This investigation has shown that 

August median streamflows per square mile of 

drainage area increase as the basin size increases.

* Station 01017550 has been run as a continuous-record station from 1999 to the present. It was treated as a partial-record 

station for this report because it did not have a sufficient period of record to calculate an August median flow.

USGS 

station 

number Station name

Weighted August 

median flow (cubic 

feet per second)

Partial-record stations

01012520 Bald Mountain Brook near Bald Mountain, Maine 0.44

01012525 Bishop Mountain Brook near Bishop Mountain, Maine .26

01012790 North Fork McLean Brook near St. Agatha, Maine .10

01012800 Unnamed tributary to East Fork Dickey Brook near St. Agatha, Maine .06

01013550 Unnamed tributary to Pearly Brook near Michigan Settlement,Maine .09

01014700 Factory Brook near Madawaska, Maine 1.33

01015005 Unnamed tributary to Hammond Brook near Cyr Plantation, Maine .15

01015007 Unnamed tributary to St. John River near Hamlin, Maine .06

01015008 Martin Brook near Hamlin, Maine 4.77

01017010 Unnamed tributary to Aroostook River at Crouseville, Maine .03

01017050 Libby Brook near Mapleton, Maine .31

01017115 Caribou Stream at Caribou, Maine 11.67

01017295 Nichols Brook near Limestone, Maine .40

01017300 Nichols Brook near Caribou, Maine 1.33

01017450 Ginn Brook near Fort Fairfield, Maine 1.65

01017550* Williams Brook at Phair, Maine 1.06

01017555 Hilt Brook near Mars Hill, Maine .78

01017600 Unnamed tributray to Young Brook near Mars Hill, Maine .03

01018050 Big Brook near Littleton, Maine 5.02

01018060 Unnamed tributary to Meduxnekeag River near Littleton Station, Maine .12

01018070 Unnamed tributary to Meduxnekeag River near Littleton, Maine .56

01018100 Unnamed tributary to Dead Stream near Monticello, Maine .20

01030050 Webb Brook near Patten, Maine .21

Continuous-record station

01017900 Marley Brook near Ludlow, Maine .20

Table 4. Weighted August median streamflows at partial-record and continuous-record streamflow-gaging stations.

[USGS, U.S. Geological Survey].
References Cited 19

REFERENCES CITED

Aroostook Water and Soil Management Board, 1996, How to 

deal with low flow periods and irrigating farmer’s and 

environmental concerns in Aroostook County: Presque 

Isle, Maine, Aroostook Water and Soil Management 

Program 8 p.

Cervione, M.A., Richardson, A.R. and Weiss, L.A., 1993, 

Low-flow characteristics of selected streams in Rhode 

Island: U.S. Geological Survey Water-Resources Investigations Report 93-4046, 16 p.

Charles Ritzi and Associates, 1987, Computation of US Fish 

and Wildlife Service aquatic base flow for regulated 

streams: Winthrop, Maine, 15 p.

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

approach to modeling the distribution of precipitation 

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

eds., Interdisciplinary approaches in hydrology and 

hydrogeology: American Institute of Hydrology, p. 

437-454. 

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

approach to mapping precipitation and temperature: 

Proceedings of the 10th AMS Conference on Applied 

Climatology, American Meteorological Society, Reno 

Nevada, Oct. 20-23, 1997, p.10-12. 

Fontaine, R.A, 1989, Hydrologic and meteorologic data for 

the Bald Mountain area Aroostook County, Maine, June 

1979 through June 1984: U.S. Geological Survey OpenFile Report 85-174, 166 p.

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

water resources: New York, Elsevier, 522 p.

Inland Waters Directorate, 2001, Surface water and sediment 

data: Ottawa, Ontario, Water Resources Branch, Water 

Survey of Canada.

Johnson, C.G., 1970, A proposed streamflow data program 

for central New England: U.S. Geological Survey 

Open-File Report, 38 p.

Kulik, B.H., 1990, A method to refine the New England 

aquatic base-flow policy: Rivers, v.1, no. 1, p. 8-22.

Maine Geological Survey, 2003, Sand and gravel aquifer 

mapping, served by the Maine office of GIS: accessed 

September 2, 2003 at URL 

http://apollo.ogis.state.me.us/.

Maine Register State Yearbook and Legislative Manual, 

Maine Register, No. 130, Tower Publishing Company, 

Standish, Maine, September, 2000.

Maine State Legislature, 2002, Sec 1. 38 MRSA c.3, sub-c.I, 

article 4-B.

Moss, M.E., 1973, Cross correlation of the logarithms of 

estimates of mean streamflows: Water Resources 

Research, v. 9, no. 6, p. 1681-1683.

Moss, M.E., and Tasker, G.D., 1991, An intercomparison of 

hydrologic network-design technologies: Journal of 

Hydrologic Sciences, v. 6, no. 3, p. 209-221.

Parker, 1977, Methods for determining selected flow characteristics for stream in Maine: U.S. Geological Survey 

Open-File Report 78-871, 31 p.

Rantz, S.E. and others, 1982, measurements and compuation 

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

2175, 284 p.

Ries, K.G., III, 1994a, Estimation of low-flow duration discharges in Massachusetts: U.S. Geological Survey 

Water Supply Paper 2418, 50 p.

_____1994b, Development and application of generalizedleast-squares regression models to estimate low-flow 

duration discharges in Massachusetts: U.S. Geological 

Survey Water-Resources Investigations Report 94-

4155, 33 p.

_____1997, August median streamflows in Massachusetts: 

U.S. Geological Survey Water-Resources Investigations Report 97-4190, 27 p.

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

Survey Techniques of Water-Resources Investigations, 

book 4, chap. B1, 18 p.

Risley, J.C., 1994, Estimating the magnitude and frequency 

of low flows of streams in Massachusetts: U.S. Geological Survey Water-Resources Investigations Report 94-

4100, 29 p.

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

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

9, p. 1421- 1432.

_____1986a, Correction to Regional hydrologic analysis 1. 

Ordinary, weighted, and generalized least-squares comparedí: Water Resources Research, v. 22, no. 5, p. 844.

_____1986b, Regional hydrologic analysis 2, Model error 

estimates, estimation of sigma, and log-Pearson Type 3 

distributions: Water Resources Research, v. 22, no. 10, 

p. 1487-1499.

Stedinger, J.R., and Thomas, W.O., 1985, Low-flow frequency estimation using base-flow measurements: 

U.S. Geological Survey Open-File Report 85-95, p. 22.

Stewart, G.J., Caldwell, J.M., and Cloutier, A.R., 2001, 

Water resources data-Maine water year 2001: U.S. 

Geological Survey Water-Data Report ME-01-1, 232 p. 

Stuart, A. and Ord, J.K, 1987, Kendallís Advanced Theory of 

Statistics, 5th ed., v. 1, Distribution Theory: Oxford 

University Press, 604 p.

Tasker, G.D., and Driver, N.E., 1988, Nationwide regression 

models for predicting urban runoff water quality at 

unmonitored sites: Water Resources Bulletin, v. 24, n. 

5, p. 1091-1101.

Tasker G.D., and Stedinger, J.R., 1989, An operational GLS 

model for hydrologic regression: Journal of Hydrology, 

v. 111, no. 1-4, p. 361-375.
20 August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

U.S. Department of Commerce, 1997, National Oceanic and 

Atmospheric Administration, National Environmental 

Satellite Data and Information Service, Climatological 

Data Annual Summary, New England: Vol. 109, no. 13, 

Asheville, North Carolina, National Climatic Data Center, 1997.

U.S. Fish and Wildlife Service, 1981, Interim regional policy 

for New England stream flow recommendations: Concord, N.H., U.S. Fish and Wildlife Service, Region 1. 

U.S. Geological Survey, 2003,Office of Surface Water Technical Memorandum No. 89.11, July 7, 1989, accessed 

September 2, 2003, at URL 

http://water.usgs.gov/admin/memo/SW/sw89.11.html.

Wandle, S.W., Jr., and Randall, A.D., 1994, Effects of surficial geology, lakes and swamps, and annual water availability on low flows of streams in central new Engalnd 

and their use in low-flow estimations: U.S. Geological 

Survey Water-Resources Investigations Report 93-

4092, 57 p.
Lombard, P.J., Tasker, G.D., and Nielsen, M.G., 2003—AUGUST MEDIAN STREAMFLOW ON UNGAGED STREAMS IN EASTERN AROOSTOOK COUNTY, 

MAINE — USGS WRIR 03-4225

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