Estimating Monthly, Annual, and Low 7-Day, 10-Year 

Streamflows for Ungaged Rivers in Maine

Scientific Investigations Report 2004-5026

In cooperation with the

Maine Department of Transportation

Maine Department of Environmental Protection and

Maine Atlantic Salmon Commission

U.S. Department of the Interior

U.S. Geological Survey
Estimating Monthly, Annual, and Low 7-Day, 10-Year 

Streamflows for Ungaged Rivers in Maine

By Robert W. Dudley

U.S. Department of the Interior

U.S. Geological Survey

In Cooperation with the

Maine Department of Transportation

Maine Department of Environmental Protection and

Maine Atlantic Salmon Commission

Scientific Investigations Report 2004-5026
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Augusta, Maine: 2004

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reproduce any copyrighted materials contained within this report.

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

Box 25286, Denver Federal Center

Denver, CO 80225
 iii

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

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

Purpose and Scope.........................................................................................................................................................1

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

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

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

Monthly and Annual Streamflow...........................................................................................................................4

Low 7-day, 10-year Streamflow.............................................................................................................................4

Basin and Climatic Characteristics ................................................................................................................................4

Regression Analyses .................................................................................................................................................................4

Ordinary Least Squares Regression ...............................................................................................................................4

Final Explanatory Variables............................................................................................................................................8

Drainage Area ........................................................................................................................................................8

Fraction of Drainage Basin Underlain by Sand and Gravel Aquifers.....................................................................8

Distance from the Coast to the Drainage Basin Centroid ...................................................................................10

Mean Annual Precipitation ..................................................................................................................................10

Mean Winter Precipitation ..................................................................................................................................10

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

Regression Equations for Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for

Ungaged Rivers in Maine..................................................................................................................................................12

Accuracy and Limitations of the Equations..................................................................................................................12

Summary..................................................................................................................................................................................20

References Cited .....................................................................................................................................................................21

Figures

1. Map showing locations of U.S. Geological Survey streamflow-gaging stations used to derive 

regression equations for estimating monthly, annual, and low 7-day, 10-year streamflows 

for ungaged rivers in Maine ...................................................................................................................................3

2. Map showing locations of significant sand and gravel aquifers in Maine ................................................................11

3. Map showing locations of the Gulf of Maine Line (GOM Line) and study basin centroids .......................................13

4. Graph showing the two-dimensional range of explanatory variables for regression equations 

estimating mean and median July, August, September, and October streamflows, and low 

7-day, 10-year streamflows for unregulated, rural rivers in Maine .....................................................................18

5. Graph showing the two-dimensional range of explanatory variables for regression equations 

estimating mean and median December, January, February, March, and May streamflows 

for unregulated, rural rivers in Maine ..................................................................................................................18

6. Graph showing the two-dimensional range of explanatory variables for regression equations 

estimating mean and median April streamflows for unregulated, rural rivers in Maine ....................................19

7. Graph showing the two-dimensional range of explanatory variables for regression equations 

estimating mean and median annual streamflows for unregulated, rural rivers in Maine.................................19

CONTENTS
iv 

Tables

1. Computed mean monthly and mean annual streamflows for selected U.S. Geological Survey 

streamflow-gaging stations in Maine ..................................................................................................................5

2. Computed median monthly and median annual streamflows for selected U.S. Geological Survey

streamflow-gaging stations in Maine ..................................................................................................................6

3. Computed 7-day low streamflows with 10-year recurrence interval (7Q10) for selected U.S. Geological

Survey streamflow-gaging stations in Maine ...................................................................................................... 7

4. Basin and climatic characteristics for selected U.S. Geological Survey streamflow-gaging stations in Maine....... 9

5. Point coordinates that define the Gulf of Maine Line ...............................................................................................12

6. Regression equations and their accuracy for estimating mean annual, median annual, and low 7-day,

10-year (7Q10) streamflows for ungaged, unregulated streams in rural drainage basins in Maine...................15

7. Regression equations and their accuracy for estimating mean monthly streamflows for ungaged,

unregulated streams in rural drainage basins in Maine ......................................................................................16

8. Regression equations and their accuracy for estimating median monthly streamflows for ungaged,

unregulated streams in rural drainage basins in Maine ......................................................................................17

Conversion Factors

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

°C = 5/9 * (°F - 32)

Multiply By To obtain

gallon per minute (gal/min) 3.785 liter per minute

inch (in.) 25.4 millimeter

foot (ft) 0.3048 meter

mile (mi) 1.609 kilometer

square mile (mi2) 2.589 square kilometer

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

cubic foot per second (ft3/s) 0.02832 cubic meter per second
Estimating Monthly, Annual, and Low 7-Day, 10-Year 

Streamflows for Ungaged Rivers in Maine

By Robert W. Dudley

Abstract

Regression equations to estimate monthly, 

annual, and low 7-day, 10-year (7Q10) streamflows 

were derived for rivers in Maine. The derived regression equations for estimating mean monthly, mean 

annual, median monthly, median annual, and low 7Q10 

streamflows for ungaged rivers in Maine presented in 

this report supersede those derived in previous studies. 

Twenty-six U.S. Geological Survey streamflowgaging stations on unregulated, rural rivers in Maine 

with 10 years or more of recorded streamflow were 

used to develop the regression equations. Ordinary 

least squares (OLS) regression techniques were used to 

select the explanatory variables (basin and climatic 

characteristics) that would appear in the final regression equations. OLS regression of all possible subsets 

was done with 62 explanatory variables for each of 27 

response variables. Five explanatory variables were 

chosen for the final regression equations: drainage 

basin area, areal fraction of the drainage basin underlain by sand and gravel aquifers, distance from the 

coast to the drainage basin centroid, mean drainage 

basin annual precipitation, and mean drainage basin 

winter precipitation (the sum of mean monthly precipitation for December, January, and February). Generalized least-squares regression techniques were used to 

derive the final coefficients and measures of uncertainty for the regression equations.

The forms of many of the derived regression 

equations indicate some physical, mechanistic 

processes. Drainage basin area is the most statistically 

important explanatory variable and appears in all 

derived regression equations. Monthly streamflows are 

related inversely to the distance from the coast to the 

drainage basin centroid during December, January, 

February, and March; that is, the closer a river basin is 

to the coast, the higher monthly streamflows are per 

unit drainage basin area during the winter. The relation 

reverses in May when higher streamflows are attributed to basins farther from the coast. These relations 

are consistent with colder, inland drainage basins 

storing more water in snowpack during the winter and 

releasing it in the spring. The monthly streamflows 

(and low 7Q10) during July, August, September, and 

October are related positively to areal fraction of the 

drainage basin underlain by sand and gravel aquifers. 

In general, sand and gravel aquifers underlying Maine 

river basins have excellent water-yielding characteristics and can provide water to streams during low-flow 

conditions in the summer and early fall.

Introduction

The ability to estimate monthly, annual, and low 

streamflow statistics for rivers is needed by Federal, 

State, regional, and local water- and natural-resources 

professionals to effectively manage resources and plan 

projects. Streamflow data sufficient to estimate these 

statistics are available for only a small percentage of 

rivers in Maine. Earlier studies by Parker (1977), 

“Methods for Determining Selected Flow Characteristics for Streams in Maine,” and by Hayes and Morrill 

(1970), “A Proposed Streamflow Data Program for 

Maine,” presented regression equations that could be 

used to estimate some streamflow statistics. In 2002, 

the U.S. Geological Survey (USGS) began a cooperative investigation with the Maine Department of Transportation (MDOT), the Maine Department of 

Environmental Protection (MDEP), and the Maine 

Atlantic Salmon Commission (ASC) to update 

methods that can be used to estimate streamflow statistics for ungaged rivers in Maine. 

Purpose and Scope

This report presents updated regression equations that were derived to estimate mean monthly, 
2 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

mean annual, median monthly, median annual, and low 

7-day, 10-year (7Q10) streamflows for unregulated, rural 

rivers in Maine. The regression equations were developed 

using streamflow data from 26 USGS streamflow-gaging 

stations on unregulated, rural rivers with 10 or more years 

of recorded streamflow; streamflow statistics for these 26 

stations also are included in the report.

The regression equations can be used at sites on 

rivers where streamflow data are not available, assuming 

no diversions, regulation, or appreciable urbanization are 

present upstream from the site in the drainage basin. 

Because of improved accuracy and updated information, 

the regression equations presented here to estimate mean 

monthly, mean annual, and low 7Q10 streamflows supersede earlier equations derived by Parker (1977) and 

Hayes and Morrill (1970).

The updated regression equations were derived 

using new regression techniques that test every possible 

combination of explanatory variables and account for 

correlation of flows between sites and the relative accuracy of computed flows from different sites. The derivation of the updated regression equations made use of an 

additional 25 years of streamflow-gaging data for Maine 

and new, up-to-date information from Geographic Information System (GIS) data layers and associated spatial 

analysis tools describing basin and climate characteristics 

such as geology, land use, and precipitation.

Description of the Study Area

The state of Maine (fig. 1) has a land area of 30,862 

mi2 and population of 1.27 million people in 2000 (U.S. 

Census Bureau, 2002). Topographic relief is predominantly moderate to low throughout the State except for 

high-relief areas (the Appalachian Mountains) in westcentral Maine (Randall, 2001). Elevations range from 0 ft 

at the coast to 5,266 ft (National Geodetic Vertical Datum 

(NGVD) of 1929) in the Appalachian Mountains.

To derive the regression equations for estimating 

streamflows, 26 unregulated, rural river basins 

throughout Maine (fig. 1) were analyzed. Mean basin 

elevations for the 26 sites range from 200 ft to 1,860 ft, 

with a mean of 710 ft (NGVD 1929) . The East Machias 

River Basin, in a broad, coastal lowland region in eastern 

Maine, has the lowest mean elevation, and the Swift 

River Basin, in the high-relief parts of west-central 

Maine, has the highest mean elevation.

According to the National Land Cover Data 

(NLCD) GIS coverages (Vogelmann and others, 1998a; 

1998b) for the basins used in this study, forest is the 

predominant land-use classification. The percentage of 

forested area in the 26 study basins ranges from 65 to 98 

percent with a mean of 82 percent. The greatest change in 

land use in Maine during the 20th century has been the 

replacement of agriculture and pasture lands by forest. 

The overall forest cover in the State is estimated to have 

been at its lowest around 1900 at approximately 70 

percent. Forest cover increased to about 90 percent by 

1995 (Irland, 1998). None of the basins studied are 

considered urbanized nor do any of them have substantial 

channelization or other drainage improvements.

Maine generally has a temperate climate with mild 

summers and cold winters. From 1971 to 2000, the mean 

annual temperature for Maine was about 42 o

F, with a 

range from 36 oF in Allagash in northern Maine to 47 o

F 

in Sanford in southern Maine. For the same time period, 

statewide mean monthly temperatures ranged from 15 o

F 

in January to 67 o

F in July (National Oceanic and Atmospheric Administration, 2002). 

Precipitation in Maine is fairly evenly distributed 

throughout the year. The mean annual precipitation from 

1971 to 2000 for Maine was 43 in., ranging from 35 in. in 

Presque Isle, northern Maine, to 57 in. in Acadia National 

Park, coastal Maine. For the same time period, statewide 

mean monthly precipitation was 3.6 in., with a standard 

deviation of 0.6 in. (National Oceanic and Atmospheric 

Administration, 2002).

Data Used for this Study

Streamflow

Streamflow data from 26 streamflow-gaging 

stations in Maine (fig. 1) were used to develop the regression equations for estimating monthly, annual, and low 

7Q10 streamflows presented in this report. The following 

criteria were used to select the streamflow-gaging 

stations: (1) continuous streamflow records represent 

natural streamflow, (2) the length of streamflow record 

for each site is 10 years or more, and (3) the drainage 

basins of the stations are entirely within the State of 

Maine. Natural streamflow is defined as flow from a 

predominately rural basin unaffected by diversions and 

(or) regulation by dams or reservoirs.

Streamflow data were retrieved from the National 

Water Information System (NWIS) (U.S. Geological 

Survey, 1998) for all available USGS streamflow-gaging 

stations that met the criteria of the study. Periods of 

record of streamflow data for the 26 selected stations
Data Used for this Study 3

01011000

01013500

01016500

01018000

01021500

01022000

01022260

01022500

01023000

01024200

01031500

01033500

01030500

01035000

01038000

01046000

01047000

01048000

01049373

01049550

01054300 01055000

01055500 01057000

01057000

01059800

01060000

47o

67o

68o 69o

70o

71o

46o

45o

44o

43o

0

0 30 60 KILOMETERS

10 20 30 40 MILES

SCALE

EXPLANATION

U.S. Geological Survey streamflowgaging station with identifier

County boundary

National Weather Service

climate station location

State boundary

International boundary

Drainage basin

Base from USGS digital files

scale 1:2,000,000, projection UTM,

zone 19

Atlantic Ocean

CANADA

CANADA

NEW HAMPSHIRE

Acadia National Park

Sanford

Sanford

Presque Isle

Allagash

Figure 1. U.S. Geological Survey streamflow-gaging stations used to derive regression equations for estimating monthly, annual, and low

7-day, 10-year streamflows for ungaged rivers in Maine.
4 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

range from 14 to 99 years in length, with a mean of 52 

years. The earliest and latest dates for streamflow data 

used in this study are October 1, 1902, and September 30, 

2001, respectively.

Monthly and Annual Streamflow

For each month, the mean monthly streamflow was 

computed as the mean of all monthly means over the 

entire period of record for each streamflow-gaging 

station. The mean monthly values used in the computation are updated and published annually by the USGS in 

the water-resources data report series and stored in 

NWIS. Mean monthly mean streamflows were retrieved 

directly from the NWIS database for this study. Mean 

annual streamflows were computed as the mean of all 

annual means (calendar year basis) over the period of 

record for each streamflow-gaging station as retrieved 

from NWIS (table 1).

The computation of median monthly streamflows 

was a two-step process. First, the monthly median 

streamflow for each month was computed on the basis of 

daily mean streamflow data from NWIS. Second, the 

median monthly streamflow was computed as the median 

of all monthly medians over the entire period of record 

for each streamflow-gaging station. Median annual 

streamflows were computed in a similar manner. First, 

the annual median streamflow for each calendar year was 

computed on the basis of daily mean streamflow data 

from NWIS. Second, the median annual streamflow was 

computed as the median of all annual medians over the 

entire period of record for each streamflow-gaging 

station (table 2).

Low 7-day, 10-year Streamflow

Many regulatory agencies use the low 7Q10 

streamflow statistic to regulate wastewater discharge to 

streams. The low 7Q10 streamflow for a stream is the 

lowest average streamflow for a period of 7 consecutive 

days that recurs, on long-term average, once every 10 

years. The computation of low 7Q10 streamflows for 

each streamflow-gaging station was a two-step process. 

First, the lowest streamflow, averaged over a consecutive 

7-day window, was computed for each climatic year 

(from April 1 to March 31) for each site. The climatic 

year typically is used when analyzing low streamflows in 

Maine because the annual low-flow period usually occurs 

in the summer and early fall and the highest annual 

streamflows usually occur in the spring. Once the yearly 

low 7-day streamflows were computed, a log-Pearson 

Type III distribution was fitted to the flows, from which 

the low 7-day streamflow with an annual non-exceedance 

probability of 0.10 (10-year recurrence interval) was 

determined for each streamflow-gaging station (table 3). 

At least 10 years of streamflow record are needed to 

determine the low 7Q10 streamflow statistic with reasonable confidence (Ries and Friesz, 2000).

Basin and Climatic Characteristics

For the regression analysis in Parker (1977), nine 

different explanatory basin and climatic characteristics 

were step-wise regressed against response variables of 

mean monthly, mean annual, and low 7Q10 streamflows. 

Results from the regression analysis reduced the nine 

explanatory variables to three final characteristics: 

drainage area, mean annual precipitation, and maximum 

24-hour precipitation intensity with a 2-year recurrence 

interval (also referred to as the 2-year, 24-hour rainfall).

For this study, 62 basin and climatic characteristics 

were derived and tested as potential explanatory variables 

in the regression analysis, with an emphasis on GISderived characteristics. The explanatory variables 

included the following characteristics and variations 

thereof: basin drainage area; mean monthly, seasonal, 

and annual precipitation; basin elevation, shape, and 

slope; latitude and longitude; NLCD land-cover classifications; areas of wetlands, lakes and ponds; March 1 

snowpack; area of sand and gravel aquifers; and distance 

from the coast. Where appropriate, basinwide averages 

and basin centroid values were computed for each characteristic, providing two variables for a single characteristic. For example, elevation was averaged over the entire 

basin and derived at the basin centroid, as well.

Regression Analyses

Regression analysis commonly is used to develop 

equations for estimating streamflow statistics for 

ungaged streams. In this analysis, a streamflow statistic 

of interest (the response variable) for a group of streamflow-gaging stations in a region is statistically related to 

the physical and (or) climatic characteristics (the explanatory variables) of the drainage basin for the streamflowgaging stations (Ries and Friesz, 2000). 

Ordinary Least Squares Regression

Ordinary least squares (OLS) regression techniques (Helsel and Hirsch, 1992) of all possible subsets of
U.S. Geological Survey streamflow-gaging stations in Maine Drainage 

area 

(mi2)

Mean monthly streamflow (ft3/s) M

an

str

fl

(ft

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

01011000 Allagash River near Allagash 1,229 727 601 789 4,760 6,470 2,230 1,380 1,080 1,060 1,260 1,580 1,190 1,9501013500 Fish River near Fort Kent 873 626 499 581 3,130 5,110 1,780 947 673 572 757 1,180 1,060 1,4301016500 Machias River near Ashland 329 191 191 255 1,600 2,000 517 295 288 275 376 498 381 5701018000 Meduxnekeag River near Houlton 175 152 156 264 1,080 619 216 108 88.1 112 178 331 284 2901021500 Machias River at Whitneyville 458 802 699 1,190 2,400 1,720 859 463 310 340 541 913 1,000 9301022000 East Machias River near East Machias 251 564 444 630 1,270 859 423 220 137 141 253 506 660 5001022260 Pleasant River near Epping 60.6 101 153 190 307 184 115 66 63.6 60.5 82.1 151 168 1401022500 Narraguagus River at Cherryfield 227 514 476 727 1,200 673 338 191 130 163 265 572 640 4901023000 West Branch Union River at Amherst 148 243 211 352 814 459 209 111 58.6 72.2 141 278 316 2701024200 Garland Brook near Mariaville 9.79 17.4 19.8 37.2 61.4 29.0 14.7 8.00 4.92 6.77 14.8 24.7 29.4 201030500 Mattawamkeag River near Mattawamkeag 1,418 1,420 1,280 2,220 8,470 5,500 1,980 1,030 720 811 1,400 2,710 2,600 2,5201031500 Piscataquis River near Dover-Foxcroft 298 312 276 612 2,080 1,260 472 242 170 185 394 679 546 6001033500 Pleasant River near Milo 323 381 340 618 2,000 1,670 643 344 258 276 479 848 692 7001035000 Passadumkeag River at Lowell 297 357 333 469 1,260 1,070 606 344 208 211 278 454 488 5001038000 Sheepscot River at North Whitefield 145 234 235 447 742 341 166 75.2 47.1 51.5 87.9 244 323 2501046000 Austin Stream at Bingham 90.0 79.4 63.8 139 578 435 127 69.5 53.1 62.5 112 225 153 1701047000 Carrabassett River near North Anson 353 378 330 846 2,340 1,560 618 330 219 242 496 770 604 7201048000 Sandy River near Mercer 516 558 504 1,260 3,420 1,910 786 400 244 278 555 969 839 9701049373 Mill Stream at Winthrop 32.7 42.7 44.6 91.4 168 97.1 53.6 22.6 16.7 11.4 19.3 34.8 56.5 501049550 Togus Stream at Togus 23.7 39.2 34.6 79.4 120 50.1 30.1 8.77 8.43 7.18 16.2 44.9 57.4 401054300 Ellis River at South Andover 130 133 151 243 759 565 201 114 75.4 69.4 159 246 234 2401055000 Swift River near Roxbury 96.9 112 93.8 205 623 487 177 86.0 60.0 73.7 144 212 154 2001055500 Nezinscot River at Turner Center 169 218 227 490 969 447 223 119 81.8 81.6 165 311 298 3001057000 Little Androscoggin River near South Paris 73.5 89.2 83.4 210 465 214 110 51.9 37.3 41.5 78.0 138 128 1301059800 Collyer Brook near Gray 13.8 22.6 25.5 44.1 55.3 31.9 23.6 18.0 16.0 17.1 20.9 25.9 28.4 201060000 Royal River at Yarmouth 141 230 237 556 746 318 185 92.4 74.9 86.9 145 308 305 27

Table 1. Computed mean monthly and mean annual streamflows for selected U.S. Geological Survey streamflow-gaging stations in Maine

[ft3/s, cubic feet per second; mi2, square miles]
U.S. Geological Survey streamflow-gaging stations in Maine Drain- age area (mi2) Median monthly streamflow (ft3/s) 

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

01011000 Allagash River near Allagash 1,229 580 450 440 3,050 5,730 1,740 1,040 700 721 765 1,200 910 01013500 Fish River near Fort Kent 873 528 402 405 2,070 5,060 1,500 731 418 340 429 922 812 01016500 Machias River near Ashland 329 148 101 102 667 1,700 391 175 149 159 152 398 278 01018000 Meduxnekeag River near Houlton 175 116 86.0 135 878 412 138 57.0 36.0 47.5 72.0 246 188 01021500 Machias River at Whitneyville 458 508 498 765 2,170 1,700 606 327 235 224 305 634 677 01022000 East Machias River near East Machias 251 545 345 540 1,200 745 374 183 81.5 83.2 149 358 558 01022260 Pleasant River near Epping 60.6 76.0 108 138 296 138 78.5 52.0 44.5 40.0 66.0 118 97 01022500 Narraguagus River at Cherryfield 227 328 324 461 974 480 243 132 84.0 84.5 174 395 405 01023000 West Branch Union River at Amherst 148 152 142 228 727 404 151 62.5 31.0 33.0 71.0 200 223 01024200 Garland Brook near Mariaville 9.79 9.65 9.78 18.0 46.2 19.0 9.05 3.25 2.45 3.50 7.60 14.5 15.0 01030500 Mattawamkeag River near Mattawamkeag 1,418 1,015 805 1,210 7,480 4,260 1,360 642 384 356 762 2,240 1,690 01031500 Piscataquis River near Dover-Foxcroft 298 205 174 300 1,790 938 288 126 86.0 80.0 168 413 328 01033500 Pleasant River near Milo 323 270 255 310 1,700 1,340 493 238 167 159 240 534 450 01035000 Passadumkeag River at Lowell 297 305 269 313 1,200 1,000 528 290 168 140 192 344 354 01038000 Sheepscot River at North Whitefield 145 142 158 326 596 304 116 54.5 30.5 24.8 35.5 133 236 01046000 Austin Stream at Bingham 90.0 52.0 44.2 62.0 438 343 79.5 37.0 23.5 22.2 46.0 131 90.5 01047000 Carrabassett River near North Anson 353 235 214 362 1,800 1,140 388 193 122 116 220 446 336 01048000 Sandy River near Mercer 516 372 349 618 3,050 1,400 522 255 134 135 211 526 498 01049373 Mill Stream at Winthrop 32.7 33.0 39.0 53.0 144 91.0 29.5 21.0 16.0 10.0 6.20 9.65 44.0 01049550 Togus Stream at Togus 23.7 28.5 27.8 59.5 90.8 38.5 15.8 6.45 5.50 4.65 4.90 34.5 47.5 01054300 Ellis River at South Andover 130 81.0 82.5 128 616 437 159 58.5 38.0 32.8 82.0 144 125 01055000 Swift River near Roxbury 96.9 58.0 53.0 81.0 479 363 101 45.0 26.0 31.0 57.0 124 94.0 01055500 Nezinscot River at Turner Center 169 124 134 280 784 343 151 70.0 49.0 38.0 72.5 201 188 01057000 Little Androscoggin River near South Paris 73.5 54.5 54.5 104 382 152 61.0 28.0 15.0 15.0 34.5 78.8 76.0 01059800 Collyer Brook near Gray 13.8 17.0 16.8 22.5 47.5 28.5 19.5 16.0 14.0 13.5 15.0 20.0 18.5 01060000 Royal River at Yarmouth 141 115 134 331 494 213 106 63.0 51.0 44.0 59.0 154 180 

Table 2. Computed median monthly and median annual streamflows for selected U.S. Geological Survey streamflow-gaging stations in Maine[ft3/s, cubic feet per second; mi2, square miles]
Regression Analyses 7

62 explanatory variables for each of 27 response variables were used to select the explanatory variables that 

would appear in the final regression equations. Explanatory variables were chosen on the basis of their 

capacity to explain the variability in the response variable. Explanatory variables with inadequate individual 

statistical significance (p-values from the T-statistics of 

greater than 0.10) in their capacity to explain the variability in the response variable were eliminated. 

In addition to statistical significance, the ease of 

computation of each explanatory variable was weighed 

against its ability to describe variability in the response 

variable. If a particular variable was easy to compute 

(such as distance from the coast), it was chosen over 

another variable that had slightly greater explanatory 

power but was more difficult to compute. Emphasis 

also was placed on developing a coherent set of equations. If a particular explanatory variable appeared 

frequently in many regression equations (especially on 

a seasonal basis such as fraction of the drainage basin 

underlain by sand and gravel aquifers, or distance from 

the coast), it was likely to indicate a physical process, 

thereby increasing confidence in the use of the variable. Such an explanatory variable was favored for use 

in other regression equations even if it did not introduce the maximum increase in explanatory power. 

Residual plots were used to check for linearity, 

homoscedasicity (constant variance), normality, and

U.S. Geological Survey streamflow-gaging stations in Maine Drainage 

Area (mi2

)

7Q10 streamflow (ft3 Number Name /s) Period of record (calendar years)

01011000 Allagash River near Allagash 1,229 146 1910-11, 1931-2001

01013500 Fish River near Fort Kent 873 83.1 1903-08, 1911, 1929-2001

01016500 Machias River near Ashland 329 19.1 1951-83

01018000 Meduxnekeag River near Houlton 175 5.46 1940-82

01021500 Machias River at Whitneyville 458 60.2 1905-21, 1929-77, 2001

01022000 East Machias River near East Machias 251 15.0 1926-58

01022260 Pleasant River near Epping 60.6 22.2 1980-91, 2000-01

01022500 Narraguagus River at Cherryfield 227 30.3 1948-2001

01023000 West Branch Union River at Amherst 148 6.16 1909-19, 1929-79

01024200 Garland Brook near Mariaville 9.79 0.447 1964-82

01030500 Mattawamkeag River near Mattawamkeag 1,418 65.8 1934-2001

01031500 Piscataquis River near Dover-Foxcroft 298 17.7 1902-2001

01033500 Pleasant River near Milo 323 48.4 1920-79

01035000 Passadumkeag River at Lowell 297 46.6 1915-79

01038000 Sheepscot River at North Whitefield 145 9.01 1938-2001

01046000 Austin Stream at Bingham 90.0 4.35 1931-69

01047000 Carrabassett River near North Anson 353 46.0 1902-07, 1925-2001

01048000 Sandy River near Mercer 516 46.0 1928-79, 1987-2001

01049373 Mill Stream at Winthrop 32.7 2.23 1977-92

01049550 Togus Stream at Togus 23.7 1.48 1981-95

01054300 Ellis River at South Andover 130 14.3 1963-82, 2000-01

01055000 Swift River near Roxbury 96.9 6.93 1929-2001

01055500 Nezinscot River at Turner Center 169 13.8 1941-96, 2001

01057000 Little Androscoggin River near South Paris 73.5 2.48 1913-24, 1931-2001

01059800 Collyer Brook near Gray 13.8 7.95 1964-82, 1998-2000

01060000 Royal River at Yarmouth 141 24.0 1949-2001

Table 3. Computed low 7-day streamflows with 10-year recurrence interval (7Q10) for selected U.S. Geological Survey streamflow-gaging 

stations in Maine

[ mi2

, square miles; ft3/s, cubic feet per second;]
8 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

 the presence of outliers. Residuals were plotted against 

predicted values, and partial residuals were plotted. 

These residual plots indicated whether explanatory variables showed bias over their ranges and whether variables 

needed to be transformed to ensure a linear relation 

between explanatory and response variables—a requirement for satisfactory OLS regression. Multicollinearity 

among the explanatory variables was measured using the 

Variance Inflation Factor. No problems with multicollinearity were noted. 

Influence of the individual stations on the regression equations was measured using the Cook’s D statistic. 

The Cook’s D statistic indicated that drainage basins 

smaller than approximately 10 mi2

 exerted high influence 

on the derivation of regression equations across almost all 

response variables (monthly and annual). For this reason, 

4 study basins were culled from an original set of 30, 

reducing the final number of study basins to 26. 

Final Explanatory Variables

Using OLS regression analysis, the 62 basin and 

climatic characteristics were winnowed to 5 final explanatory variables: drainage area, fraction of the drainage 

basin underlain by sand and gravel aquifers, distance 

from the coast to the drainage basin centroid, mean 

annual precipitation, and mean winter precipitation (table 

4). Detailed descriptions of the final 5 explanatory variables are provided below:

Drainage Area

Published values for drainage areas (in square 

miles) for the 26 streamflow-gaging stations were 

retrieved from NWIS. Drainage areas used for this study 

were computed by measuring the planar area enclosed by 

the drainage-basin boundary on 1:24,000-scale USGS 

topographic maps using either an analog or digital 

planimeter. The drainage-basin boundary is defined as 

the topographic divide from which direct surface runoff 

from precipitation normally drains or falls by gravity into 

the body of water upstream of the point of interest 

(Stewart and others, 2003). References to drainage area in 

this report refer to contributing drainage area. Contributing drainage area is defined as the surface area of the 

river basin that contributes to surface-water runoff. 

Contributing drainage area is an important distinction to 

make because some drainage basins may have parts of 

their drainage area that do not contribute directly to 

surface-water runoff. The 26 drainage basins range in 

size from 9.79 mi2 (Garland Brook, USGS streamflowgaging station number 01024200) to 1,418 mi2

(Mattawamkeag River, 01030500), with a mean of 303 

mi2

 (table 4).

Fraction of Drainage Basin Underlain by Sand and 

Gravel Aquifers

The surficial geology of Maine has been largely 

shaped by the last period of glaciation about 24,000 years 

ago through the erosion and widespread, highly variable 

redeposition of soil and bedrock (Randall, 2001). The 

redeposited soil and bedrock, called glacial drift, consist 

of a wide variety of materials that vary in composition 

depending on how they were deposited by the glaciers. 

Most of the State is covered by a layer of till—a 

nonsorted mixture of material ranging from clay to boulders—overlying bedrock (Randall, 2001). In general, till 

has poor water-bearing characteristics. Interspersed 

among the till, especially in major river valleys, are 

glacial stratified deposits that include gravel, sand, silt, 

and clay. Sand and gravel stratified-drift deposits and 

fractured bedrock serve as the water-bearing geologic 

features (aquifers) in Maine. 

Since 1992, the Maine Department of Conservation, Maine Geological Survey (MGS) systematically has 

been delineating and digitizing at a 1:24,000 scale all 

sand-and-gravel glacial deposits in the State that are 

determined to be a “significant” aquifer (a significant 

aquifer is an aquifer having the potential to yield 10 

gal/min or more to a properly constructed well). The 

aquifer boundaries are delineated on the basis of field 

observations of surficial materials, geophysical studies, 

wells, test borings, water-company exploration data, 

construction project information, and municipal well 

inventories. In some areas, a thin layer (usually less than 

10 ft) of water-bearing, coarse-grained material may be 

readily identifiable on the surface, overlying poor waterbearing materials such as till or bedrock. In these cases, if 

it is determined that a well open to that surficial material 

could not sustain a yield of at least 10 gal/min, the area is 

not mapped as an aquifer. The converse may be true as 

well where poor water-bearing materials may overlie 

coarse-grained sediments causing the underlying deposit 

not to be recognized as a potentially significant aquifer. 

To determine the capacity of an aquifer to yield water, the 

MGS conducts geophysical studies, installs wells, and 

does test borings. This work provides information on the 

depth to water table and bedrock surface, and water yields 

(Marc Loiselle, Maine Geological Survey, oral commun., 

2003).
Regression Analyses 9

The Maine office of GIS (MEGIS) maintains a 

digital coverage of the mapped significant sand and 

gravel aquifers in Maine (http://apollo.ogis.state.me.us/). 

The coverage includes mapped aquifers for the entire 

State except for the sparsely populated, heavily forested, 

northwestern region of the State that has not yet been 

completed (fig. 2). The coverage includes an attribute 

table that stores aquifer-classification information for 

each polygon. The classification value is stored in the 

attribute label, ATYPE. A value of ATYPE = 1 denotes 

a high-yield aquifer with an estimated yield greater than 

50 gal/min, whereas a value of ATYPE = 2 denotes an 

aquifer with an estimated yield of 10 to 50 gal/min.

The significant sand and gravel aquifer GIS 

coverage was used to derive the fraction of the drainage 

basin underlain by significant sand and gravel aquifers in 

each study basin. The fraction of drainage basin underlain by sand and gravel aquifer is computed as the sum of 

polygon areas of the mapped sand and gravel aquifers in 

the basin (coded as ATYPE=1 or 2), divided by the total 

basin drainage area. The explanatory power of ATYPE=

1, ATYPE=2, and the combination of both types in the 

regression analysis was tested. Among these three variables tested, the sum of both aquifer types had the 

greatest explanatory power. Fractions of drainage basin 

underlain by sand and gravel aquifers among basins used 

in this study range from 0.000 (Allagash River, 

01011000, and Togus Stream, 01049550) to 0.455 

(Collyer Brook, 01059800), with a mean of 0.076 

(table 4). 

Fraction of 

drainage basin 

underlain by 

sand and 

gravel aquifers

Distance from 

the coast to the 

drainage basin 

centroid (mi)

U.S. Geological Survey streamflow-gaging stations in Maine Drainage 

area 

(mi2

)

Mean annual 

precipitation 

(in.)

Mean winter 

precipitation 

(in.) Number Name

01011000 Allagash River near Allagash 1,229 0.000 189 37.8 7.72

01013500 Fish River near Fort Kent 873 0.003 193 39.3 7.71

01016500 Machias River near Ashland 329 0.001 175 40.0 7.78

01018000 Meduxnekeag River near Houlton 175 0.030 121 39.8 8.59

01021500 Machias River at Whitneyville 458 0.162 51.4 46.4 12.0

01022000 East Machias River near East Machias 251 0.032 46.1 46.6 12.1

01022260 Pleasant River near Epping 60.6 0.346 42.7 47.9 12.6

01022500 Narraguagus River at Cherryfield 227 0.151 47.0 46.4 12.1

01023000 West Branch Union River at Amherst 148 0.047 65.4 43.5 10.6

01024200 Garland Brook near Mariaville 9.79 0.103 54.1 43.8 11.0

01030500 Mattawamkeag River near Mattawamkeag 1,418 0.020 111 42.2 9.33

01031500 Piscataquis River near Dover-Foxcroft 298 0.018 111 44.1 9.78

01033500 Pleasant River near Milo 323 0.052 116 46.4 10.4

01035000 Passadumkeag River at Lowell 297 0.030 76.7 44.0 10.5

01038000 Sheepscot River at North Whitefield 145 0.043 55.6 44.2 10.4

01046000 Austin Stream at Bingham 90.0 0.025 112 47.6 9.91

01047000 Carrabassett River near North Anson 353 0.089 111 46.4 10.1

01048000 Sandy River near Mercer 516 0.049 98.4 46.9 10.7

01049373 Mill Stream at Winthrop 32.7 0.005 70.1 44.0 10.1

01049550 Togus Stream at Togus 23.7 0.000 57.6 42.7 10.0

01054300 Ellis River at South Andover 130 0.057 107 44.1 10.1

01055000 Swift River near Roxbury 96.9 0.012 109 46.2 10.2

01055500 Nezinscot River at Turner Center 169 0.086 77.7 45.4 10.6

01057000 Little Androscoggin River near South Paris 73.5 0.029 84.1 45.1 10.2

01059800 Collyer Brook near Gray 13.8 0.455 52.7 46.0 11.5

01060000 Royal River at Yarmouth 141 0.127 50.7 46.0 11.5

Table 4. Basin and climatic characteristics for selected U.S. Geological Survey streamflow-gaging stations in Maine

[mi2, square miles; mi, miles; in., inches]
10 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

The Allagash River (01011000) drainage basin is 

located just outside the significant sand-and-gravel 

mapped region, and the Fish River (01013500) and 

Machias River (01016500, near Ashland) each have a 

small part of their drainage basins outside the mapped 

region (fig. 1, fig. 2). On the basis of available published 

and unpublished geologic and topographic information 

for the unmapped region, it was estimated that the Allagash River Basin has no significant sand and gravel aquifers (table 4) (Marc Loiselle, Maine Geological Survey, 

oral commun., 2003). Similarly, the Fish and Machias 

River Basins were estimated not to have any additional 

significant sand and gravel aquifers other than the small 

amounts already mapped (fig. 2, table 4) (Marc Loiselle, 

Maine Geological Survey, oral commun., 2003).

Distance from the Coast to the Drainage Basin 

Centroid

The distance from the coast to the drainage basin 

centroid is derived as the shortest distance (in miles) from 

an arbitrary line in the Gulf of Maine (referred to as the 

GOM Line; fig. 3) to the basin centroid. The GOM Line 

approximately parallels the Maine coast (table 5, fig. 3). 

The shortest line of measure between a basin centroid 

point and the GOM Line is a perpendicular intersector of 

the GOM Line. For this study, all distance measurements 

were made in a GIS using North American Datum (horizontal) 1983, Universal Transverse Mercator Zone 19 

coordinate system. Distances from the GOM Line to the 

centroid of river basins used in this study range from 42.7 

mi (Pleasant River near Epping, 01022260) to 193 mi 

(Fish River, 01013500), with a mean of 91.7 mi (table 4).

Mean Annual Precipitation

Mean annual precipitation for each drainage basin 

was computed using output grids from the Parameterelevation Regressions on Independent Slopes Model 

(PRISM). PRISM precipitation output grids were chosen 

for use in this study because the PRISM products are 

GIS-compatible. The PRISM GIS grids provide a convenient data set for computing spatial values of precipitation such as basinwide averages. 

PRISM precipitation output grids are derived using 

a hybrid statistical-geographic modeling approach (Daly 

and Neilson, 1992; Daly and others, 1994; 1997). PRISM 

uses observed precipitation data, a digital elevation 

model (DEM), and other spatial data sets specific to the 

region being simulated (such as snowpack) to derive 

spatial estimates of annual and monthly precipitation. As 

evidenced by Randall’s (1996) map of mean annual 

precipitation in the northeastern United States, landsurface elevation is a dominant factor in the distribution 

of precipitation. For this reason, PRISM uses a general 

elevation regression function that serves as the main 

predictive equation in the precipitation model (Natural 

Resources Conservation Service, 1998).

The PRISM modeling effort is a part of the Spatial 

Climate Mapping Project managed and funded by the 

Natural Resources Conservation Service’s (NRCS) 

National Water and Climate Center (NWCC) in cooperation with Oregon State University. The NRCS maintains 

the PRISM Internet site containing non-proprietary 

versions of the annual and monthly PRISM precipitation 

data for all 50 States in the U.S. These data can be 

accessed at 

http://www.ftw.nrcs.usda.gov/prism/prismdata_state.html.

For this study, a non-proprietary PRISM GIS map 

of mean annual precipitation for the State of Maine 

(derived on the basis of precipitation data collected from 

1961 to 1990) was downloaded from the NRCS PRISM 

Internet site. The NRCS PRISM map was loaded into a 

GIS application and interpolated to 1-km grids. Basinwide averages of mean annual precipitation (in inches) 

were computed for each study basin by averaging the 

values of all 1-km grids within the bounds of the drainage 

basin on an area basis. Mean annual precipitation for river 

basins used in this study range from 37.8 in. (Allagash 

River, 01011000) to 47.9 in. (Pleasant River near Epping, 

01022260), with a mean of 44.3 in. (table 4).

Mean Winter Precipitation

Mean winter precipitation was computed similarly 

to the mean annual precipitation using non-proprietary 

PRISM GIS grids. The mean winter precipitation was 

computed for each study basin as the sum of the basinwide averages of mean December, January, and February 

precipitation (in inches). The monthly PRISM grids were 

handled in the same way as the annual grids: downloaded 

from the NRCS PRISM internet site, converted to 1-km 

grids, and averaged on an area basis for each study basin. 

Mean winter precipitation for river basins used in this 

study range from 7.7 in. (Allagash River, 01011000 and 

Fish River, 01013500) to 12.6 in. (Pleasant River near 

Epping, 01022260), with a mean of 10.3 in. (table 4).

Generalized Least Squares Regression

Generalized least squares (GLS) regression techniques (Stedinger and Tasker, 1985) were used to derive
Regression Analyses 11

47o

67o

68o 69o

70o

71o

46o

45o

44o

43o

0

0 30 60 KILOMETERS

10 20 30 40 MILES

SCALE

EXPLANATION

Area where sand and gravel aquifers

have not been mapped

Drainage basin

Sand and gravel aquifer with potential

to yield 10 or more gallons per minute

County boundary

State boundary

International boundary

Base from USGS digital files

scale 1:2,000,000, projection UTM,

zone 19. Geology from Maine

Geological Survey.

Atlantic Ocean

CANADA

CANADA

NEW HAMPSHIRE

Figure 2. Significant sand and gravel aquifers in Maine.
12 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

the final coefficients and measures of uncertainty for the 

regression equations identified from the OLS analyses. 

Stedinger and Tasker (1985) found that GLS regression 

equations are more accurate and provide better estimates 

of uncertainty than OLS regression equations when 

streamflow records are of different and widely varying 

lengths, and when concurrent streamflow records are 

correlated. GLS regression techniques give less weight to 

stations with shorter periods of streamflow record and to 

stations where the streamflow record is more highly 

correlated with concurrent record of other stations in the 

analysis.

Regression Equations for Estimating 

Monthly, Annual, and Low 7-Day, 10-Year 

Streamflows for Ungaged Rivers in Maine

The final regression equations for estimating 

monthly, annual, and low 7Q10 streamflows for ungaged 

rivers in Maine are presented in tables 6, 7, and 8. 

Although an explanatory variable (basin characteristic) 

appears in a regression equation, it does not necessarily 

mean that the explanatory variable directly causes the 

response variable to occur, just that the explanatory variable explains the variability observed in the response 

variable. In most of the final regression equations, the 

explanatory variables intuitively describe the physical 

processes of the natural hydrologic system.

Drainage area is a highly significant explanatory 

variable (basin characteristic) for all equations. This is an 

intuitive relation—a larger drainage basin contributes to 

a larger streamflow. In general, the fraction of the 

drainage basin underlain by sand and gravel aquifers 

provides considerable explanation for the variability in 

low 7Q10 and summer-month response variables. This 

explanation makes sense in that sand and gravel aquifers 

typically are recharged during the spring and discharge 

ground water to streams during the summer low-flow 

period. The drainage basin centroid distance from the 

coast provides considerable explanation for the variability in flows during winter and spring months. During 

December, January, February, and March, mean and 

median streamflows are related inversely to the drainage 

basin distance from the coast; that is, the closer to the 

coast a basin is, the higher the mean monthly or median 

monthly streamflow. This results because heat in the 

Atlantic Ocean has a warming effect on winter air 

temperatures near the coast so that larger volumes and 

(or) greater rates of rain and snowmelt can take place 

closer to the coast during the winter. The distance-fromthe-coast relation reverses in May when sites farther 

inland have greater contributions to surface-water runoff 

from snowmelt relative to sites close to the coast.

Accuracy and Limitations of the Equations

Uncertainties for the equations are quantified by 

the average standard error of prediction (ASEP). ASEP is 

a measure of how well the regression equation will estimate the flow statistic of interest when applied to an 

ungaged, unregulated, rural basin in Maine. The probability that the true value of the flow statistic at a site is 

between the negative- and positive-percent ASEP is 

approximately 68 percent. For example, there is a 68-

percent probability that the true low 7Q10 streamflow at 

a site is between –34.5 and 52.6 percent (table 6) of the

X-coordinate Y-coordinate

Point A 71.00 west longitude 42.75 north latitude

336321.28 meters 4734992.89 meters

Point B 65.50 west longitude 45.00 north latitude

775853.75 meters 4988911.83 meters

Table 5. Point coordinates that define the Gulf of Maine Line (GOM Line; fig.3). Latitude and longitude coordinates referenced to North 

America Datum of 1983, meter coordinates referenced to Universal Transverse Mercator Zone 19 datum
Regression Equations for Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine 13

Figure 3. The Gulf of Maine Line (GOM Line) and study basin centroids.
14 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

computed low 7Q10 streamflow yielded by the regression equation.

The prediction error sum of squares (PRESS) 

statistic is a measure of validation for the regression 

equations. PRESS is computed by removing the observed 

streamflow statistic of interest of one study basin from 

the set of 26 study basins used to develop the regression 

equation, then predicting the value of the streamflow 

statistic for the omitted site; the procedure is done in turn 

for all 26 stations. The differences between the predicted 

streamflow statistics and the observed streamflow statistics for each site are squared and summed yielding the 

PRESS statistic. PRESS/n is analogous to the average 

variance of prediction, and the square root of PRESS/n is 

analogous to the ASEP (where n is the number of data 

points used in regression). Values of (PRESS/n)1⁄2 close 

to the values of the ASEP provide a measure of validation 

of the regression equation.

The average equivalent years of record (EYR) 

statistic is a measure of uncertainty of the regression 

equations. The EYR indicates the average number of 

years of streamflow-gaging data required to compute the 

same streamflow statistic of interest with an uncertainty 

equal to that of the regression equation.

When applying the regression equations, it is 

important that the explanatory variables (basin and 

climatic characteristics) be derived using the same or 

comparable methods as those documented in this report. 

Basin and climatic characteristics derived using techniques different from the techniques used for this study 

will yield results of unknown error. Similarly, using 

values for any explanatory variables outside the ranges 

used to develop these regression equations will yield 

results of unknown error (figs. 4-7).

The regression equations presented in this report 

have been derived on the basis of streamflow data and 

basin and climatic characteristics of unregulated, rural 

drainage basins without significant drainage improvements. Applying these equations to regulated or urbanized basins or basins with appreciable drainage 

improvements will yield results of unknown error.

For this study, a basin was considered to be unregulated if either there was no regulation of streamflow by 

dams, or historical and (or) present regulation was small 

enough so as to have no effect on the computation of a 

monthly mean streamflow value computed on the basis of 

the daily mean streamflow data (Slack and Landwehr, 

1992). 

The percentages of urban area in the 26 study 

drainage basins, classified by NLCD as either high-intensity residential or commercial/industrial/transportation 

development, ranged from less than 0.01 percent (Allagash River, 01011000, in northern Maine) to 5.91 percent 

(Collyer Brook, 01059800, in southern Maine) with a 

mean of 0.472 percent. If areas classified by NLCD as 

low-intensity residential development were included in 

the analysis, percentages of developed area in the study 

basins would range from less than 0.01 percent (Allagash 

River) to 10.6 percent (Collyer Brook) with a mean of 

1.03 percent. 

Development in the Collyer Brook Basin has been 

substantial during the period from 1964 to 1999; population doubled, the number of buildings (commercial and 

residential) tripled, and impervious area increased 161 

percent (Dudley and others, 2001). An evaluation of the 

effects of development on storm-runoff streamflow for 

Collyer Brook in 2001 by Dudley and others (2001) 

found no statistically detectable change in either amount 

or duration of runoff during the 1990’s compared to 

streamflow runoff during the 1960’s in this basin. The 

results suggest that the Collyer Brook Basin still may be 

considered a rural basin for the purposes of this investigation.

In a nationwide study of flood magnitude and 

frequency in urban drainage basins, Sauer and others 

(1983) determined that a watershed must have at least 15 

percent of the drainage area covered with commercial, 

industrial, and (or) residential development to be considered urban; however, that was for streamflow events 

much larger than the streamflow events examined in this 

report. Results presented by Sauer and others (1983) 

illustrate that small, frequently occurring peak-streamflow events are more sensitive to increases in impervious 

area, which commonly accompany development. This 

result suggests that the percentage of urban area for this 

investigation should be lower than 15 percent. The 

highest amount of development (low- and high-intensity 

combined) observed in this investigation was 10.6 

percent, of which about half was classified as either highintensity residential or commercial/industrial/transportation development.

Drainage improvements include storm sewers, 

channel modifications (straightening, enlarging), impervious channel linings, and curb-and-gutter streets. 

Drainage improvements commonly accompany urbanization. Sauer and others (1983) provide a Basin Development Factor (BDF) scoring system to quantify the 

prevalence of drainage improvements in urbanized
Regression Equations for Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine 15

Table 6. Regression equations and their accuracy for estimating mean annual, median annual, and low 7-day, 10-year (7Q10) streamflows 

for ungaged, unregulated streams in rural drainage basins in Maine

[ASEP, average standard error of prediction; PRESS, prediction error sum of squares; EYR, equivalent years of record; n, number of data 

points used in regression]

where,

Q - streamflow statistic of interest.

A - contributing drainage area, in square miles.

SG - fraction of the drainage basin that is underlain by significant sand and gravel aquifers, on a planar area basis, expressed as a decimal. 

For example, if 15 percent of the drainage area of a basin has significant sand and gravel aquifers, SG = 0.15. Based on the 

significant sand and gravel aquifer maps produced by the Maine Geological Survey and maintained as GIS data sets by the Maine 

Office of GIS.

pptW - mean winter precipitation, in inches, computed as the sum of the monthly precipitation for December, January, and February 

spatially averaged over the contributing basin drainage area. Based on non-proprietary PRISM precipitation data spanning the 30-

year period 1961-1990. Data maintained as GIS data sets by the Natural Resources Conservation Service (1998).

See the Regression Analyses section of this report for more details.

Regression equation ASEP

(in percent)

(PRESS/n)1/2

(in percent) Average EYR

Q7,10 = 0.023 (A)

1.17310 2.54(SG) -34.5 to 52.6 -35.0 to 53.8 2.90

Qannual mean = 1.151 (A)

 0.99110 0.023(pptW) -7.35 to 7.94 -7.97 to 8.66 9.87

Qannual median = 0.239 (A) 1.00610 0.057(pptW) -12.6 to 14.4 -13.2 to 15.2 6.92
16 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

Table 7. Regression equations and their accuracy for estimating mean monthly streamflows for ungaged, unregulated streams in rural drainage 

basins in Maine

[ASEP, average standard error of prediction; PRESS, prediction error sum of squares; EYR, equivalent years of record; n, number of data points 

used in regression]

where,

Q — streamflow statistic of interest.

A — contributing drainage area, in square miles.

SG — fraction of the drainage basin that is underlain by significant sand and gravel aquifers, on a planar area basis, expressed as a decimal. 

For example, if 15 percent of the drainage area of a basin has significant sand and gravel aquifers, then SG = 0.15. Based on the 

significant sand and gravel aquifer maps produced by the Maine Geological Survey and maintained as GIS data sets by the Maine Office 

of GIS.

pptA — mean annual precipitation, in inches, computed as the spatially averaged precipitation in the contributing basin drainage area. Based 

on non-proprietary PRISM precipitation data spanning the 30-year period 1961-1990. Data maintained as GIS data sets by the Natural 

Resources Conservation Service (1998).

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

centroid. The line in the Gulf of Maine is defined by end points 71.0W, 42.75N and 65.5W, 45.0N, referenced to North American Datum 

of 1983.

See the Regression Analyses section of this report for more details.

Regression equation ASEP

(in percent)

(PRESS/n)1⁄2

(in percent) Average EYR

Qjan mean = 36.36 (A)

 1.007 (DIST) –0.771 -10.2 to 11.4 -11.1 to 12.5 29.9

Qfeb mean = 46.79 (A)

 0.991 (DIST) –0.829 -9.79 to 10.8 -12.0 to 13.7 41.2

Qmar mean = 109.10 (A)

 0.924 (DIST) –0.807 -21.0 to 26.6 -22.4 to 28.8 7.27

Qapr mean = 1.362 (A)

 1.00610 0.013(pptA) -15.6 to 18.4 -16.7 to 20.0 4.94

Qmay mean = 0.350 (A)

 1.035 (DIST) 0.486 -15.8 to 18.8 -16.8 to 20.2 6.96

Qjun mean = 1.372 (A)

 1.030 -14.6 to 17.1 -15.2 to 17.9 13.1

Qjul mean = 0.475 (A)

1.08910 0.631(SG) -19.3 to 24.0 -21.4 to 27.2 8.38

Qaug mean = 0.353 (A)

1.07510 0.822(SG) -22.0 to 28.2 -22.9 to 29.6 8.60

Qsep mean = 0.434 (A)

1.04910 0.834(SG) -19.9 to 24.9 -23.2 to 30.2 13.9

Qoct mean = 1.084 (A)

0.98910 0.399(SG) -19.3 to 24.0 -22.5 to 29.1 17.0

Qnov mean = 2.497 (A)

 0.948 -18.6 to 22.9 -20.7 to 26.0 11.9

Qdec mean = 16.92 (A)

 0.979 (DIST) –0.476 -12.4 to 14.1 -13.6 to 15.7 28.9
Regression Equations for Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine 17

Table 8. Regression equations and their accuracy for estimating median monthly streamflows for ungaged, unregulated streams in rural 

drainage basins in Maine

[ASEP, average standard error of prediction; PRESS, prediction error sum of squares; EYR, equivalent years of record; n, number of data points 

used in regression]

where,

Q — streamflow statistic of interest.

A — contributing drainage area, in square miles.

SG — fraction of the drainage basin that is underlain by significant sand and gravel aquifers, on a planar area basis, expressed as a decimal. 

For example, if 15 percent of the drainage area of a basin has significant sand and gravel aquifers, then SG = 0.15. Based on the 

significant sand and gravel aquifer maps produced by the Maine Geological Survey and maintained as GIS data sets by the Maine Office 

of GIS.

pptA — mean annual precipitation, in inches, computed as the spatially averaged precipitation in the contributing basin drainage area. Based 

on non-proprietary PRISM precipitation data spanning the 30-year period 1961-1990. Data maintained as GIS data sets by the Natural 

Resources Conservation Service (1998).

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

centroid. The line in the Gulf of Maine is defined by end points 71.0W, 42.75N and 65.5W, 45.0N, referenced to North American Datum 

of 1983.

See the Regression Analyses section of this report for more details.

Regression equation ASEP

(in percent)

(PRESS/n)1⁄2

(in percent) Average EYR

Qjan median = 20.71 (A)

 1.036 (DIST) –0.762 -16.1 to 19.2 -17.3 to 20.9 8.87

Qfeb median = 36.54 (A)

 1.017 (DIST) –0.890 -13.4 to 15.5 -14.9 to 17.5 17.5

Qmar median = 183.7 (A)

 0.999 (DIST) –1.142 -16.9 to 20.4 -19.0 to 23.5 13.3

Qapr median = 0.227 (A)

 1.01010 0.028(pptA) -20.8 to 26.2 -22.0 to 28.3 3.75

Qmay median = 0.262 (A)

 1.070 (DIST) 0.461 -20.4 to 25.6 -21.0 to 26.6 3.92

Qjun median = 0.734 (A)

 1.076 -22.5 to 29.0 -23.6 to 30.8 4.26

Qjul median = 0.210 (A)

1.14910 1.02(SG) -26.1 to 35.4 -27.3 to 37.5 3.58

Qaug median = 0.152 (A)

1.12010 1.31(SG) -28.6 to 40.2 -29.6 to 42.1 3.86

Qsep median = 0.169 (A)

1.09310 1.25(SG) -26.8 to 36.7 -27.8 to 38.5 5.37

Qoct median = 0.307 (A)

1.07410 1.11(SG) -25.8 to 34.8 -30.0 to 43.0 8.28

Qnov median = 1.222 (A)

 1.004 -28.9 to 40.6 -30.6 to 44.1 4.39

Qdec median = 12.00 (A)

1.000 (DIST) –0.513 -13.1 to 15.0 -14.6 to 17.1 21.6
18 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

10 100 1,000

CONTRIBUTING DRAINAGE BASIN AREA, IN SQUARE MILES

0.00

0.10

0.20

0.30

0.40

0.50

AREAL FRACTION OF SIGNIFICANT SAND AND GRAVEL AQUIFERS

5 2,000

FRACTION OF THE DRAINAGE-BASIN AREA UNDERLAIN BY SIGNIFICFANT 

SAND AND GRAVEL AQUIFERS

10 100 1,000

CONTRIBUTING DRAINAGE BASIN AREA, IN SQUARE MILES

100

DRAINAGE BASIN CENTROID DISTANCE FROM THE COAST, IN MILES

5 2,000

40

200

DISTANCE FROM THE COAST TO THE DRAINAGE-BASIN CENTROID, IN MILES

Figure 4. Two-dimensional range of explanatory variables for regression equations estimating mean and median July, August, September, 

and October streamflows, and low 7-day, 10-year streamflows for unregulated, rural rivers in Maine. 

Figure 5. Two-dimensional range of explanatory variables for regression equations estimating mean and median December, January, 

February, March, and May streamflows for unregulated, rural rivers in Maine.
Regression Equations for Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine 19

10 100 1,000

CONTRIBUTING DRAINAGE BASIN AREA, IN SQUARE MILES

35

40

45

50

MEAN BASIN ANNUAL PRECIPITATION, IN INCHES

5 2,000

10 100 1,000

CONTRIBUTING DRAINAGE BASIN AREA, IN SQUARE MILES

6

8

10

12

14

MEAN BASIN WINTER PRECIPITATION, IN INCHES

5 2,000

Figure 6. Two-dimensional range of explanatory variables for regression equations estimating mean and median April streamflows for 

unregulated, rural rivers in Maine. 

Figure 7. Two-dimensional range of explanatory variables for regression equations estimating mean and median annual streamflows for 

unregulated, rural rivers in Maine. 
20 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

drainage basins. Collyer Brook is the most highly developed basin in this investigation (5.91 percent). A 2001 

field reconnaissance of the Collyer Brook Basin scored 

the basin with a BDF value of zero (Dudley and others, 

2001). Because all the drainage basins in this investigation were less developed than Collyer Brook, drainage 

improvements were assumed not to be prevalent in any of 

the study basins. 

The PRISM precipitation grids used for this study 

were downloaded from the USDA-NRCS Internet site in 

2002. The coverages are based on precipitation data spanning the 30-year period 1961-90. In the event that 

updated PRISM precipitation grids are created in future 

years, they should not be applied to these regression 

equations—using PRISM precipitation grids other than 

the ones used to develop the regression equations will 

yield results of unknown uncertainty. Currently (2003), 

the NRCS does not have any plans to prepare any new 

maps (Steven Nechero, National Cartography and 

Geospatial Center, Natural Resources Conservation 

Service, written commun., 2003).

The sand and gravel aquifer mapping has been 

completed for all but northwestern Maine. It is expected 

that if sand and gravel aquifers in these areas were 

mapped using the same or similar methods as those used 

to map aquifers in the rest of Maine, these equations 

would be applicable in those regions.

An underlying assumption in the development of 

these regression equations is that no systematic changes 

in streamflow or basin and climatic characteristics have 

taken place over time. Recent studies of the effects of 

climate variability on hydrology in Maine and New 

England (Dudley and Hodgkins, 2002; Hodgkins and 

others, 2002) show that this may not be the case. The 

development of the regression equations presented in this 

report has integrated historical streamflow and precipitation data that may be trending on a seasonal, annual, or 

longer basis. It also is well known that the greatest 

changes in land use in Maine during the 20th century 

were the replacement of agriculture and pasture lands by 

forest. In particular, a doubling in forest cover over the 

last century has occurred in river basins in southern counties of Maine (Irland, 1998). Quantification of the effects 

of climate and land-use changes on regression equations 

for estimating selected flow statistics was beyond the 

scope of this study; however, the observed trends suggest 

that future investigations of this kind should be done at 

regular intervals using a moving temporal window of 

contemporary data or consider methods for incorporating 

these large-scale hydrologic trends into the statistical 

models.

Summary

In 2002 the U.S. Geological Survey (USGS) began 

a cooperative investigation with the Maine Department of 

Transportation (MDOT), the Maine Department of Environmental Protection (MDEP), and the Maine Atlantic 

Salmon Commission (ASC) to update methods that can 

be used to estimate streamflow statistics for ungaged 

rivers in Maine. Regression equations were derived to 

estimate mean monthly, mean annual, median monthly, 

median annual, and low 7-day, 10-year (7Q10) streamflows for unregulated, rural rivers in Maine. The regression equations are used to estimate these characteristic 

streamflows at a site on a stream where streamflow data 

are not available, provided that no diversions, regulation, 

or appreciable urbanization in the basin is present 

upstream of the site. This report also provides mean 

monthly, mean annual, median monthly, median annual, 

and low 7Q10 streamflows tabulated for 26 USGS 

streamflow-gaging stations in Maine on unregulated, 

rural rivers with 10 years or more of recorded streamflow.

Because of their improved accuracy and use of 

updated information, the regression equations for estimating mean monthly, mean annual, and low 7Q10 

streamflows for ungaged rivers presented in this report 

supersede those by Parker (1977), “Methods for Determining Selected Flow Characteristics for Streams in 

Maine,” and by Hayes and Morrill (1970), “A Proposed 

Streamflow Data Program for Maine.” In addition to 

updated regression equations for estimating mean 

monthly, mean annual, and low 7Q10 streamflows, this 

report presents regression equations for estimating 

median monthly and median annual streamflows.

Streamflow-gaging station data were retrieved 

from the National Water Information System (NWIS) for 

all available USGS streamflow-gaging stations that met 

the criteria of the study. Available periods of record of 

streamflow data for the 26 study streamflow-gaging 

stations range from 14 to 99 years in length, with a mean 

of 52 years. The earliest and latest dates for streamflow 

data used in this study are October 1, 1902, and 

September 30, 2001, respectively.

For this study, 62 basin and climatic characteristics 

were derived and tested as potential explanatory variables 

in the regression analysis, with an emphasis on GISderived characteristics. The explanatory variables 
References cited 21

included the following characteristics and variations 

thereof: basin drainage area; mean monthly, seasonal, 

and annual precipitation; basin elevation, shape, and 

slope; latitude and longitude; National Land-Cover Data 

(NLCD) classifications; areas of wetlands, lakes and 

ponds; March 1 snowpack; area of significant sand and 

gravel aquifers; and distance from the coast.

OLS regression analysis winnowed the 62 basin 

and climatic characteristics down to 5 final explanatory 

variables: drainage area, fraction of the drainage basin 

underlain by sand and gravel aquifers, distance from the 

coast to the drainage basin centroid, mean annual precipitation, and mean winter precipitation. For the 26 basins 

studied, drainage areas range in size from 9.79 mi2

 to 

1,418 mi2

, with a mean of 303 mi2; fractions of the 

drainage basin underlain by sand and gravel aquifers 

range from 0.000 to 0.455, with a mean of 0.076; 

distances from the coast to the drainage-basin centroid 

range from 42.7 mi to 193 mi, with a mean of 91.7 mi; 

mean annual precipitation ranges from 37.8 in. to 47.9 

in., with a mean of 44.3 in.; and mean winter precipitation ranges from 7.7 in. to 12.6 in., with a mean of 10.3 

in. GLS regression techniques were used to derive the 

final coefficients and measures of uncertainty for the 

regression equations.

When applying the regression equations, it is 

important that the explanatory variables (basin and 

climatic characteristics) be derived using the same or 

comparable methods as those documented in this report. 

Basin and climatic characteristics derived using techniques different from those techniques used for this study 

will yield results of unknown error. Similarly, using 

values for any of the explanatory variables outside the 

ranges used to develop the regression equations will 

yield results of unknown error.

References cited

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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., Neilson, R.P. , and Phillips, D.L., 1994, A statisticaltopographic model for mapping climatological precipitation over mountainous terrain: Journal of Applied Meteorology, v. 33, p.140-158.

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

approach to mapping precipitation and temperature, in 

Conference on Applied Climatology, Proc., 10th, Reno, 

Nevada, Oct. 20-23, 1997, Proceedings: AMS American 

Meteorological Society, p. 10-12.

Dudley, R.W., and Hodgkins, G.A., 2002, Trends in streamflow, river ice, and snowpack for coastal river basins in 

Maine during the 20th century: U.S. Geological Survey 

Water-Resources Investigations Report 02-4245, 26 p. 

Dudley, R.W., Hodgkins, G.A., Mann, A., and Chisholm, J., 

2001, Evaluation of the effects of development on peakflow hydrographs for Collyer Brook, Maine: U.S. Geological Survey Water-Resources Investigations Report 

01-4156, 11 p.

Hayes, G.S., and Morrill, R.A., 1970, A proposed streamflow 

data program for Maine: U.S. Geological Survey OpenFile Report (unnumbered), 39 p.

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water resources: New York, Elsevier, 522 p.

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over the 20th Century: Journal of Hydrology, v. 278, p. 

242-250.

Irland, L.C., 1998, Maine’s forest area, 1600-1995—Review 

of available estimates: Maine Agricultural and Forest 

Experiment Station Miscellaneous Publication 736, February 1998, 12 p.

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normals of temperature, precipitation, and heating and 

cooling degree days, 1971-2000: Region 17, Maine, 16 p. 

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climate layers: Climate mapping with PRISM: An overview of the USDA-NRCS Spatial Climate Mapping 

Project, including an introduction to the PRISM (Parameter-Elevation Regressions on Independent Slopes 

Model) system developed by Oregon State University and 

used to produce spatial climate products, 49 p.

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Randall, A.D., 1996, Mean annual runoff, precipitation, and 

evapotranspiration in the glaciated northeastern United 

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4135, 81 p.
22 Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine

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K.V., 1983, Flood characteristics of urban watersheds in 

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Dudley, Robert W. —Estimating Monthly, Annual, and Low 7-Day, 10-Year Streamflows for Ungaged Rivers in Maine—USGS Scientific 

Investigations Report 2004-5026

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