U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5063

Low Flow of Streams in the Susquehanna River 

Basin of New York
Cover. Cuthrie Run, 3 miles north of Big Flats, Chemung County, New York, within an upland valley that drains 

5.3 square miles. Photograph by Matthew B. Jennings, U.S. Geological Survey, June 29, 2007, when streamflow 

in this region was moderately low (exceeded about 80 percent of the time).
Low Flow of Streams in the Susquehanna 

River Basin of New York

By Allan D. Randall

Scientific Investigations Report 2010–5063

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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Suggested citation:

Randall, A.D., 2010, Low flow of streams in the Susquehanna River basin of New York: U.S. Geological Survey 

Scientific Investigations Report 2010–5063, 57 p., at http://pubs.usgs.gov/sir/2010/5063.
iii

Contents

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

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

Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams........3

Amount of Water Available for Runoff .............................................................................................3

Annual Precipitation and Runoff ...............................................................................................3

Seasonal Precipitation and Runoff ...........................................................................................5

Extent and Properties of Surficial Sand and Gravel .......................................................................8

Modeling Properties of Surficial Sand and Gravel that Affect Groundwater

Discharge to Streams .................................................................................................10

Analytical Model ..............................................................................................................10

Numerical Model ..............................................................................................................11

Model Configuration and Operation .....................................................................14

Model Evaluation .....................................................................................................15

Evapotranspiration from Wetlands ..................................................................................................18

Underflow beneath Sites of Streamflow Measurement ..............................................................19

Less Important Factors that Affect Low Flows ..............................................................................22

Watershed Area.........................................................................................................................22

Extent and Properties of Till .....................................................................................................22

Extent and Properties of Bedrock Units.................................................................................22

Watershed Relief and Slope ....................................................................................................23

Degree of Stream Regulation and Watershed Urbanization..............................................24

Regression Analysis....................................................................................................................................24

Data Set ...............................................................................................................................................24

Low-Flow Statistics ...................................................................................................................24

Watershed Properties...............................................................................................................28

Format of Regression Equations .....................................................................................................32

Standard-Value Equations to Estimate 7-Day, 10-Year Low Flows ...................................33

Effect of Sand-and-Gravel Area and Wetland Area ...................................................33

Effect of Amount of Water Available .............................................................................33

Other Variables and Data Manipulations Tested.........................................................35

Per-Square-Mile Equations to Estimate 7-Day, 10-Year Low Flows..................................38

Comparison of Per-Square-Mile Equations with Standard-Value Equations.........38

Evaluation of the Data Set and Equations ....................................................................38

Effect of Underflow ..........................................................................................................42

Logarithmic Equations to Estimate 7-Day, 10-Year Low Flows ..........................................42

A Critique of the Rationale for Logarithmic Transformation......................................42

Comparison of Logarithmic Equations with Standard-Value Equations..................43

Equations to Estimate 7-Day, 2-Year Low Flow and 90-Percent Flow Duration ..............44

Suggested Methods for Estimating Low-Flow Characteristics at Ungaged Sites............................46

Watersheds Larger Than 30 Square Miles.....................................................................................47

Watersheds Smaller Than 30 Square Miles...................................................................................47

Summary........................................................................................................................................................48

Acknowledgments.......................................................................................................................................49

References Cited .........................................................................................................................................49
iv

Figures

1. Map showing location of the Susquehanna River basin and physiographic regions

in New York and adjacent States...............................................................................................2

2. Diagram showing principal environmental factors that control the low flow of

streams in the glaciated northeastern United States.............................................................4

3. Maps showing spatial variation in A, mean annual precipitation and B, mean

annual runoff in the Susquehanna River basin of New York, 1951–80.................................6

4. Map showing ratios of mean August–October runoff to mean annual runoff for the

period April 1937 to March 1963 in the Susquehanna River basin and adjacent areas ...9

5. Diagram showing idealized aquifer represented by analytical equations of

Rorabaugh (1963)........................................................................................................................11

6. Graphs showing effect of A, valley width and B, aquifer transmissivity on

groundwater discharge to a stream during a period of low flow, as calculated from

equations of Rorabaugh (1963).................................................................................................12

7. Diagram showing dimensions and properties of a two-dimensional

groundwater-flow model that represents an idealized vertical section across an

upland hillside and the adjacent valley...................................................................................13

8. Graph showing simulated groundwater discharge, to a stream and as

evapotranspiration, from an idealized upland hillside and valley fill after 4 months

without recharge, as a function of hydraulic conductivity of the valley fill......................16

9. Graph showing simulated groundwater discharge to a stream from an idealized

valley fill after 4 months without recharge, as a function of valley half-width ................18

10. Map showing locations of streamflow-measurement stations in the Susquehanna

River basin of New York.............................................................................................................20

11. Graph showing correlation of 7Q10 calculated from streamflow measurements 

with 7Q10 estimated using equation 3.....................................................................................34

12. Graph showing distribution of residuals from equation 5....................................................36

13. Graphs showing correlation of low-flow indices calculated from streamflow

measurements A, 7Q10 and, B, 90% FD, with selected watershed properties ................37

14. Graph showing correlation of 7Q10 per square mile calculated from streamflow

measurements with 7Q10 per square mile estimated using equation 9............................39

15. Graph showing correlation of 7Q10 per square mile calculated from streamflow

measurements with 7Q10 per square mile estimated using equation 11..........................40

16. Graph showing distribution of residuals from equation 11..................................................41

17. Graph showing correlation of 7Q10 calculated from streamflow measurements 

with 7Q10 converted to cubic feet per second from values estimated using 

equation 11...................................................................................................................................41

18. Graph showing distribution of data values for independent variables in equation 

12: A, sand and gravel exclusive of wetlands, and B, mean annual runoff .....................45

19. Graph showing correlation of 7Q10 calculated from streamflow measurements 

with 7Q10 converted to units of cubic feet per second from logarithmic values 

estimated using equation 12 .....................................................................................................46
v

Tables

1. Ratios of August–October runoff to annual runoff in the Susquehanna River basin

and adjacent areas.......................................................................................................................8

2. Model parameters that varied with time during simulations of groundwater

discharge to the stream in a hypothetical valley typical of the Susquehanna River

basin of New York.......................................................................................................................14

3. Streamflow-measurement stations in the Susquehanna River basin of New York,

and selected indices of low flow. ............................................................................................25

4. Watershed properties compiled for regression analysis of low flow in the

Susquehanna River basin of New York...................................................................................29

5. Regression equations tested for estimating low flow of streams in the

Susquehanna River basin of New York...................................................................................53
vi

Conversion Factors and Datums

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square foot (ft2) 929.0 square centimeter (cm2)

square foot (ft) 0.09290 square meter (m2)

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

cubic foot (ft3) 28.32 cubic decimeter (dm3) 

cubic foot (ft3) 0.02832 cubic meter (m3) 

Flow rate

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

foot per day (ft/d) 0.3048 meter per day (m/d)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

cubic foot per second per square 

mile [(ft3/s)/mi2]

 0.01093 cubic meter per second per square 

kilometer [(m3/s)/km2]

Hydraulic conductivity

foot per day (ft/d) 0.3048 meter per day (m/d)

Transmissivity*

foot squared per day (ft2/d) 0.09290 meter squared per day (m2/d) 

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

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

*Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times 

foot of aquifer thickness [(ft3/d)/ft2]ft. In this report, the mathematically reduced form, foot 

squared per day (ft2/d), is used for convenience.
Low Flow of Streams in the Susquehanna River Basin of 

New York

by Allan D. Randall

Abstract

The principal source of streamflow during periods 

of low flow in the Susquehanna River basin of New York 

is the discharge of groundwater from sand-and-gravel 

deposits. Spatial variation in low flow is mostly a function 

of differences in three watershed properties: the amount 

of water that is introduced to the watershed and available 

for runoff, the extent of surficial sand and gravel relative to 

till-mantled bedrock, and the extent of wetlands. These three 

properties were consistently significant in regression equations 

that were developed to estimate several indices of low flow 

expressed in cubic feet per second or in cubic feet per second 

per square mile. The equations explain 90 to 99 percent of 

the spatial variation in low flow. A few equations indicate 

that underflow that bypasses streamflow-measurement sites 

through permeable sand and gravel can significantly decrease 

low flows. Analytical and numerical groundwater-flow 

models indicate that spatial extent, hydraulic conductivity and 

thickness, storage capacity, and topography of stratified sandand-gravel deposits affect low-flow yields from those deposits. 

Model-simulated discharge of groundwater to streams at low 

flow reaches a maximum where hydraulic-conductivity values 

are about 15 feet per day (in valleys 0.5 mile wide) to 60 feet 

per day (in valleys 1 mile wide). These hydraulic-conductivity 

values are much larger than those that are considered typical 

of till and bedrock, but smaller than values reported for 

productive sand-and-gravel aquifers in some valley reaches 

in New York. Differences in the properties of till and bedrock 

and in land-surface slope or relief within the Susquehanna 

River basin of New York apparently have little effect on 

low flow. 

Three regression equations were selected for practical 

application in estimating 7-day mean low flows in cubic feet 

per second with 10-year and 2-year recurrence intervals, 

and 90-percent flow duration, at ungaged sites draining 

more than 30 square miles; standard errors were 0.88, 1.40, 

and 1.95 cubic feet per second, respectively. Equations that 

express low flows in cubic feet per second per square mile 

were selected for estimating these three indices at ungaged 

sites draining less than 30 square miles; standard errors were 

0.012, 0.018, and 0.022 cubic feet per second per square 

mile, respectively.

Introduction

The Susquehanna River basin encompasses south-central 

New York, central Pennsylvania, and a small part of northern 

Maryland (fig. 1). The part of the basin in New York is mostly 

an upland area of till-covered bedrock hills. The hills are 

separated by many narrow valleys that are floored with thin 

deposits of sand and gravel laid down by modern streams, 

and by a few broad valleys that contain thick deposits of sand 

and gravel, silt, and clay laid down by glacial meltwater. 

The exchange of water between the sand-and-gravel deposits 

and the streams that flow across them is a vital aspect of the 

hydrology of this region, as it is throughout the glaciated 

northeastern United States (Randall, 2001). Most streamflow 

during periods of low flow consists of water discharged from 

sand-and-gravel deposits, and infiltration from streams is the 

largest potential source of recharge to the thick sand-andgravel deposits that constitute the most productive aquifers in 

the region.

Accurate estimates of minimum streamflow for periods 

of several days, weeks, or months are required to evaluate the 

suitability of streams for fish habitat, recreation, water supply, 

wastewater dilution, and recharge to aquifers or well fields. 

Commonly used indices of the magnitude and frequency 

of low flow have been computed for more than 150 sites 

along streams in the Susquehanna River basin of New York, 

by analyzing multiple streamflow measurements at those 

sites (Hunt, 1967; Ku and others, 1975; Eissler, 1979), but 

information is often needed at sites where a suitable array 

of measurements has not been made and cannot be made 

within cost or time constraints. The primary objective of 

this investigation was to identify and explain concepts that 

describe the hydrologic processes and properties that control 

groundwater discharge to streams during periods of low flow, 

and to test those concepts by means of multiple-regression 

analysis. A secondary objective was to develop several 

regression equations that could be used to estimate indices 

of low flow at ungaged sites in this region. Accordingly, 

this report first presents a conceptual appraisal of watershed 

properties and processes that are considered likely to affect 

streamflow during periods of low flow, as interpreted from the 

literature and from quantitative groundwater-flow modeling 

done as part of this investigation. The report then describes 
2 Low Flow of Streams in the Susquehanna River Basin of New York

CATSKILL 

MOUNTAINS

APPALACHIAN PLATEAU

ONTARIO LOWLAND

80° 78° 76°

44°

42°

40°

0 40 80 KILOMETERS

Base from U.S. Geological Survey National Atlas, digital line graph data files, 2005 0 40 80 MILES

Source scale 1:2,000,000 decimal degrees projected to Universal Transverse Mercator 1983 (UTM 83)

Susquehanna River basin boundary, river mainstem, and tributaries coverages from Susquehanna 

River Basin Commission (140d) 12-01-2003 

NEW YORK

PENNSYLVANIA

MARYLAND

VIRGINIA

WEST

VIRGINIA

DELAWARE

NEW

JERSEY

LAKE ONTARIO

LAKE ERIE

Chesapeake Bay

Delaware Bay

D.C.

River

West Branch

River

Juniata

R iver

Susquehanna

Susquehanna

River

Chem ung

River

River Susquehanna

Susquehanna

#

YORK

ELMIRA

RENOVO

CORNING

NORWICH ONEONTA

ALTOONA

TOWANDA

CORTLAND

SCRANTON

LANCASTER

LEWISTOWN

BINGHAMTON

HARRISBURG

CLEARFIELD

W WILKES-BARRE ILLIAMSPORT

HAVRE DE

GRACE

SUNBURY

CANADA EXPLANATION

Study area

Basin boundary

State boundary

Physiographic

boundary

Location of 

major city

Figure 1. Location of the Susquehanna River basin and physiographic regions in New York and adjacent States.
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 3

the testing of these concepts through regression analysis, and 

presents a set of 18 equations that demonstrate the significance 

of particular watershed properties and computational 

procedures in estimating low-flow magnitude and frequency. 

Finally, six equations deemed conceptually and statistically 

sound are selected for practical application in estimating low 

flows in the Susquehanna River basin of New York.

This study refines a low-flow regionalization analysis by 

Ku and others (1975). The study was undertaken as part of the 

Northeast Glacial Aquifers Regional Aquifer-System Analysis 

project (NEGA-RASA), one of 28 projects designed by the 

U.S. Geological Survey to evaluate extensive aquifer systems 

that collectively cover much of the United States (Sun, 1986). 

Although the study was initially completed in 1989, revisions 

were postponed for several years to accommodate other 

priorities. Other studies of the interchange of water between 

aquifers and streams were undertaken as part of NEGARASA, including evaluations of watershed properties as 

controls on low streamflow in central New England (Wandle 

and Randall, 1994) and Connecticut (R.L. Melvin, U.S. 

Geological Survey, written commun., 1983) and studies 

of hydraulic properties and infiltration rates of streambeds 

(Lyford, 1986; Lapham, 1989; Dysart and Rheaume, 1999; 

Williams, 1991; Williams and Morrissey, 1996; Yager, 1986). 

Watershed Properties and Processes 

that Control Spatial Variation in Low 

Flow of Streams

Previous studies of the interaction of groundwater and 

surface water (cited farther on) have, collectively, led to a 

provisional conclusion that the magnitude of unregulated 

streamflow in the glaciated northeastern United States during 

summer periods of low flow is controlled chiefly by four 

factors: (1) the amount of water that is available to become 

streamflow—that is, precipitation minus evapotranspiration; 

(2) the spatial extent and hydraulic properties of surficial sand 

and gravel, much of which (unlike other earth materials) can 

store a large proportion of the water available and gradually 

release that water to streams; (3) the extent of wetlands 

(especially wetlands bordered by sand and gravel), where 

evapotranspiration is greater than elsewhere during summer 

periods of low flow; and (4) the magnitude of underflow 

through riparian sand and gravel, whereby water is transmitted 

downvalley without being measured as streamflow. These four 

principal controls on low flow of streams are illustrated in 

figure 2 and discussed below, followed by a brief discussion of 

other factors that have less effect on low flow: watershed area, 

the extent and properties of till and of bedrock, watershed 

relief and slope, and streamflow regulation and watershed 

urbanization. The intent of the following sections is to identify 

and explain the watershed properties and processes that 

control groundwater discharge to streams during periods of 

low flow, rather than to simply select a few easily measured 

watershed properties that collectively are closely correlated 

with low flow.

Amount of Water Available for Runoff 

Water input to any watershed is entirely from 

precipitation, which varies in space (from one watershed to 

another) and in time (from one season or year to another). A 

substantial fraction of that input is lost to evapotranspiration, 

which also varies in space and time; the remainder becomes 

available for immediate storm runoff to streams or for 

groundwater recharge, which is eventually discharged 

to streams.

Annual Precipitation and Runoff

Low streamflow consists predominantly of groundwater 

discharge, which is necessarily a function of prior groundwater 

recharge. Because most recharge in the glaciated Northeast 

occurs from late fall through early spring each year, as 

evidenced by an unsteady net rise in water levels during this 

period (Kontis and others, 2004, and references therein), 

annual low flows could be expected to correlate with the 

magnitude of recharge over the preceding year. Mean annual 

runoff from any watershed equals the average annual input 

to the watershed of water available for recharge or storm 

runoff (Lyford and Cohen, 1988), and closely approximates 

actual recharge in areas of surficial sand and gravel because 

precipitation can readily infiltrate nearly everywhere in these 

permeable soils. 

Annual runoff and annual precipitation are strongly 

correlated with each other throughout the glaciated 

Northeast, and both generally increase with altitude (Knox 

and Nordensen, 1955; Randall, 1996). Runoff is expected 

to increase more rapidly than precipitation with altitude, 

because evapotranspiration should decrease with altitude as 

temperature decreases (Kontis and others, 2004, p. 11–13). 

An increase in evapotranspiration with altitude was calculated 

(as precipitation minus surface runoff) by DeAngelis and 

others (1984) and by Dingman (1981), but this inrease could 

be attributed to an increase in forest cover with altitude, to 

greater deep groundwater circulation, or to underestimation of 

precipitation. Several studies have reported that the low flow 

of streams in the glaciated Northeast is in part a function of 

one or another of these three indices of water availability. For 

example, altitude was incorporated in low-flow-estimation 

equations for New Hampshire and Vermont by Dingman 

(1978) and by Wandle and Randall (1994), for Connecticut 

by Thomas and Cervione (1970), and for southeastern New 

York by Barnes (1986). Graphs first presented by Thomas 

(1966) for estimating the duration of low and high flows in 

Connecticut incorporated the ratio of mean annual runoff at 

any site of interest to the statewide average. Other studies 

have presented evidence for correlation between low flow 
4 Low Flow of Streams in the Susquehanna River Basin of New York

Figure 2. Principal environmental factors that control the low flow of streams in the glaciated 

northeastern United States.

1 Water input from precipitation

2 Area of sand or gravel (length x width)

3 Evapotranspiration from wetlands (lakes, swamps)

4 Groundwater flow downvalley (underflow)

G Groundwater flow to stream through sand and gravel

LF Low flow of stream

EXPLANATION

Sand and gravel

Till 

Bedrock

Water table

1

2

3

4 LF 4

G G

3
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 5

and mean annual runoff (Ku and others, 1975; Johnson, 

1970) or low flow and precipitation (Darmer, 1970; Male and 

Ogawa, 1982).

Maps of mean annual precipitation and mean annual 

runoff in the Susquehanna River basin in New York were 

presented by Ku and others (1975) for 1931–60 and were 

included within larger maps by Randall (1996) for 1951–80. 

In each of these reports, the two maps were drawn using 

a procedure (Randall, 1996) that forced the precipitation 

contours to parallel the runoff contours and assured that each 

set of contours was constrained both by precipitation data 

from measurement stations and by runoff data from streamgaging stations. The 1951–80 maps (excerpts reproduced here 

as figure 3) were used to estimate mean annual precipitation 

and runoff for watersheds examined as part of this study. 

According to these maps, mean annual runoff is about 

19 inches less than mean annual precipitation throughout 

the Susquehanna River basin of New York. Long-term 

mean precipitation is strongly correlated with altitude in 

western and central New York, as indicated by regression 

analysis (Ku and others, 1975, p. 10), but the correlation 

may have been controlled by large differences in altitude and 

precipitation between major physiographic regions in and 

near the Susquehanna River basin—the Appalachian Plateau, 

the much higher Catskill Mountains to the east, and the much 

lower Ontario lowland to the north (fig. 1). The narrow floors 

of major valleys in the Appalachian Plateau are commonly 

800 to 1,000 feet lower in altitude than the extensive 

surrounding upland, but whether precipitation varies as a 

function of this localized relief could not be ascertained from 

the data available.

Seasonal Precipitation and Runoff

The possibility that the effect of precipitation in late 

summer on low flow might exceed the effect of annual 

precipitation or runoff—because summer storms interrupt 

base-flow recessions, augment runoff, and cause localized 

recharge—is not supported by Ku and others (1975) nor by the 

present study. Ku and others (1975, p. 35) computed a variable 

that they called frost-free precipitation (total precipitation 

during the growing season) for 73 watersheds They reported 

that low flow correlated more closely with mean annual 

runoff than with either mean annual precipitation or frost-free 

precipitation. In the present study, records of daily flow from 

several large watersheds were examined to ascertain which 

month contained the lowest average flow for 7 consecutive 

days in each year from 1938 through 1963; 95 percent of 

these values fell in August, September, or October. Therefore, 

precipitation during these 3 months at 41 precipitation stations 

used by Ku and others (1975) was averaged for 1931–60 

and for 1941–70. (For 27 of these stations, 30-year monthly 

normals were available from National Weather Service 

publications or could be computed by estimating a few 

missing monthly values through correlation with other nearby 

stations. Monthly means for 12 to 27 years of record were 

used for the remaining 14 stations.) The ratios of 3-month 

precipitation for 1931–60 and 1941–70 to mean annual 

precipitation for 1931–60 were then computed for each of 

the 41 precipitation stations. All ratios fell within a narrow 

range (0.24–0.28 for 1931–60, 0.23–0.27 for 1941–70) and 

did not show any apparent spatial trend across the region. 

Accordingly, mean annual precipitation was judged to be as 

suitable as mean August–October precipitation as an index 

of the amount of water available for runoff to be used in 

regression analyses. Maps of annual and seasonal precipitation 

(Dethier, 1966) support this judgment, in that distribution 

patterns for annual precipitation across the Susquehanna River 

basin in New York are similar to those for summer and those 

for the entire growing season.

Seasonal runoff was also evaluated during the present 

study as an index of water availability. The ratio of mean 

August–October runoff to mean annual runoff for 1938–63 

was computed for each of eight watersheds or combinations of 

watersheds that range in size from 700 to 1,700 square miles 

(table 1) and were reasonably equidimensional (fig. 4). The 

runoff ratios varied more widely than the ratios of seasonal to 

annual precipitation. Furthermore, these runoff ratios tend to 

increase to the south and east (fig. 4)–that is, the percentage of 

annual runoff that occurs in August through October is slightly 

greater in Broome, Otsego, and Delaware Counties than in 

Cortland, Madison, and Steuben Counties. The reason for this 

pattern is not known, but spatial differences in the following 

three factors could be responsible: 

1. Precipitation minus evapotranspiration. Ratios of 

August–October precipitation to annual precipitation 

for 1931–60 were also computed, at 41 measurement 

stations; they ranged only from 0.24 to 0.28 and exhibited 

no tendency to increase in any direction. This result 

indicates that orographic effects or storm-track patterns 

are probably not a cause of the southeastward increase 

in runoff. Although annual and seasonal precipitation are 

less west of Tioga County than that farther east (fig. 3A), 

annual evapotranspiration is uniformly about 19 inches 

across the region (Randall, 1996) and occurs chiefly 

during the growing season, from April through October 

(Olmsted and Hely, 1962). Therefore, the amount of 

water available for runoff is necessarily less west of Tioga 

County than to the east, especially during the growing 

season. This contrast could account for the low ratios of 

August–October runoff to annual runoff west of Tioga 

County (fig. 4). 

2. Surficial sand and gravel. Eleven watersheds larger than 

145 square miles east of Tioga County were reported by 

Ku and others (1975, appendix B) to average 17 percent 

sand and gravel, substantially greater than the 11-percent 

average for seven watersheds of similar size west of 

Tioga County. Therefore, the greater seasonal runoff 

east of Tioga County might be attributed to greater 

discharge from relatively extensive surficial sand and 

gravel. The reported sand-and-gravel percentages for 
6 Low Flow of Streams in the Susquehanna River Basin of New York

River

Susquehanna

River

Chem ung

C O R T LAND

HE R K IME R

T IO G A

ONE IDA

STEUBEN

DE LAWARE

OTSEGO

ALLEGANY

BROOME

CHENANGO

ONTARIO

MADISON

ONONDAGA

YATE S SCHOHARIE LIVINGSTON

TOMPKINS

CHEMUNG

SCHUY LE R CATTARAUGUS

NEW YORK

PENNSYLVANIA

ELMIRA

CO RNING

NO RWICH O NEO NT A

CO RT LAND

BINGHAMT O N

75° 76° 77° 78° 79°

43°

42°

Map composited from U.S. Geological Survey sources 0 50 MILES

0 50 KILOMETERS

25

25

A

EXPLANATION

Line of equal mean precipitation, 1951–80; contour interval 2 inchesSusquehanna River basin boundaryLocation of city

Figure 3. Spatial variation in A, mean annual precipitation and B, mean annual runoff in the Susquehanna River basin of New York, 1951–80. (From Randall, 1996.) (These two maps were drawn interactively, with both precipitation and runoff data used to control both maps. Distribution of data values is shown in figure 3B. Precipitation at each measurement site was partitioned into runoff and evapotranspiration. Watershed outlines, rather than centroids, were used to define locations of runoff data values.) 
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 7 Figure 3. Spatial variation in A, mean annual precipitation and B, mean annual runoff in the Susquehanna River basin of New York, 1951–80. (From Randall, 1996). (These two maps were drawn interactively, with both precipitation and runoff data used to control both maps. Distribution of data values is shown in figure 3B. Precipitation at each measurement site was partitioned into runoff and evapotranspiration. Watershed outlines, rather than centroids, were used to define locations of runoff data values.)—Continued

River

Susquehanna

River

Chem ung

C O R T LAND

HE R K IME R

T IO G A

ONE IDA

STEUBEN

DE LAWARE

OTSEGO

ALLEGANY

BROOME

CHENANGO

ONTARIO

MADISON

ONONDAGA

YATE S SCHOHARIE LIVINGSTON

TOMPKINS

CHEMUNG

SCHUY LE R

NEW YORK

PENNSYLVANIA

ELMIR

A

CO

R

NIN

G

N

O

R

WICH

O

NEO

NTA

CO

RTLA

N

D

BIN

G

H

A

MTO

N

Map composited from U.S. Geological Survey sources 0 50 MILES

0 50 KILOMETERS

25

25

B

75° 76° 77° 78° 79°

43°

42°

Line of equal mean annual runoff, 1951–80; interval 2 inches. (Runoff in inches x 0.074 = runoffin cubic feet per second per square mile.)Susquehanna River basin boundaryLocation of centroid ofgaged watershedLocation of precipitationmeasurement stationLocation of city

EXPLANATION
8 Low Flow of Streams in the Susquehanna River Basin of New York

Table 1. Ratios of August–October runoff to annual runoff in the Susquehanna River basin and adjacent areas.

[ft3/s, cubic feet per second; watershed locations are shown in figure 4]

U.S. 

Geological 

Survey 

station 

numbers

U.S. Geological Survey station names 

and combinations of stations

Drainage 

area, 

in square 

miles

Mean runoff for April 1937–March 1963 Watershed 

number in 

figure 4 August–

October 

(ft3/s)

Annual 

(ft3/s) Ratio

014265 

014135

West Branch Delaware River plus East Branch 

Delaware River at Margaretville

756 520 1,328 0.392 8

015005 

015025

Susquehanna River at Unadilla plus Unadilla River 

at Rockdale

1,502 806 2,425 .332 7

015125 Chenango River at Chenango Forks 1,492 717 2,408 .298 6

015150 Susquehanna River near Waverly, less three 

upstream stations (5005, 5025, 5125)

1,786 899 2,667 .337 5

015205 Tioga River at Lindley 770 224 815 .275 2

015265 

015295

Tioga River near Erwins plus Cohocton River near 

Campbell less upstream station (5205)

1,072 283 1,041 .272 3

015310 Chemung River at Chemung less two upstream 

stations (5265, 5295)

688 229 727 .315 4

042275 Genesee River at Jones Bridge, near Mt. Morris 1,417 443 1,621 .273 1

watersheds larger than 200 square miles are in part 

estimates, however, and the easternmost and highest 

ratio of seasonal runoff to annual runoff is in the adjacent 

Delaware River basin (table 1, fig. 4), where sand-andgravel deposits on valley floors are relatively narrow 

and constitute a smaller percentage of watershed area 

than is typical of the Susquehanna River basin (Coates, 

1971, table 1). Therefore, further study would be required 

to define the extent to which differences among large 

watersheds in percent area sand and gravel affect ratios of 

seasonal to annual runoff. 

3. Bedrock geology. Grain size and fracture development 

in bedrock, and hence grain size of till, tend to increase 

to the south and east within the Appalachian Plateau of 

New York. These changes probably result in a modest 

southeastward increase in hydraulic conductivity in the 

uplands, which might be enough to augment groundwater 

discharge to streams in summer.

The foregoing discussion has shown that mean annual 

runoff is superior to mean annual or seasonal precipitation 

as an index of the amount of water available for purposes 

of estimating low flow, because low flow is derived from 

the part of precipitation that becomes runoff (rather than 

evapotranspiration). Mean annual runoff also is superior to 

seasonal runoff, because seasonal runoff is in part a function 

of surficial geology, whereas regional flow-duration graphs 

(Thomas, 1966; Kontis and others, 2004, fig. 10) indicate that 

mean flows are negligibly affected by percent area sand and 

gravel. The superiority of mean annual runoff as an index 

of water availability is consistent with the concept that low 

streamflow is derived from groundwater stored during the 

winter and spring, chiefly in sand and gravel, and released 

slowly during the following summer. The ratio of August–

October runoff to annual runoff varies systematically across 

the region, however, and may warrant consideration as a 

secondary control on low flow, but only if it can be computed 

as a function of precipitation minus evapotranspiration 

rather than from recorded streamflow, which is affected by 

surficial geology.

Extent and Properties of Surficial Sand 

and Gravel

Many studies of streamflow in glaciated regions of the 

northeastern and north-central United States have concluded 

that low flow is strongly correlated with the spatial extent 

of surficial sand and gravel (expressed as the area of glacial 

and alluvial sediments that are primarily sand and gravel and 

that immediately underlie land surface, or as the fraction of 

watershed area occupied by such sediments). The present 

investigation augments a previous study (Ku and others, 1975) 

by adding new data and developing a numerical model to 

simulate several properties of surficial sand and gravel that 

affect low flow.
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 9 Figure 4. Ratios of mean August–October runoff to mean annual runoff for the period April 1937 to March 1963 in the Susquehanna River basin and adjacent areas. Watersheds 2–7 lie within, or drain into, the New York part of the Susquehana River basin. ALLEGANY STUBEN WYOMING ONTARIO

ORLEANS

TENESEELL

LIVINGSTON

SCHUYLER

CHEMUNG

TIOGA

BROOME

CHENANGO

CORTLAND

MADISON

ONEIDA

LEWIS

OSWEGO

SULLIVAN

SCHOHARIE

MONTGOMERY

FULTON

HERKIMER

DELAWARE

OTSEGO YATES

TOMKINS

ONEDAGA

WAYNE

CAYUGA

SENECA

MONROE

HAMILTON

GREENE

ULSTER

ORANGE

NEW YORK

PENNSYLVANIA

75° 76° 77° 78°

43°42°

Base from U.S. Geological Survey National Atlas digital line graph data files, Source scale 1:2,000,000Universal Transverse Mercator Projection, NAD 83 Zone 18N

.28

.275

.275

.27

.315

.275

.30

.34

.33

.39

.40

.38

.36

.34

.32

.30

.28

EXPLANATION

Watershed number (table 1) and ratio of mean August-October runoff to mean annual runoff from watershed

.28 Line of equal ratio of mean August-October 

runoff to mean annual runoffWatershed boundary and location of streamgaging stationLocation of city or village

.275 1

1

2

4

3

6

5

7

8

UTICA

ONEONTA

BINGHAMTON ELMIRA

BATH

DANSVILLE

0 30 60 KILOMETERS

0 30 60 MILES
10 Low Flow of Streams in the Susquehanna River Basin of New York

Insights from previous studies. Morse (1946) and 

Schneider (1957) ascribed the relatively constant flow from 

certain watersheds in Ohio, and particularly the large yield per 

square mile at 90-percent flow duration, to the predominance 

of coarse-grained stratified drift (sand and gravel deposited 

by glacial meltwater) in those watersheds. Thomas (1966) 

presented a family of flow-duration curves that express flow 

per square mile of unregulated streams in Connecticut as a 

function of the percentage of watershed area underlain by 

coarse-grained stratified drift. These curves were applied in 

a series of water-resources reports covering that State (for 

example, Mazzaferro and others, 1979) to estimate flows at 

ungaged sites. Thomas and Cervione (1970) incorporated the 

extent of coarse-grained stratified drift in regression equations, 

where it proved to be an exceptionally powerful predictor of 

low flow of unregulated streams in Connecticut (Riggs, 1973, 

p. 12). Coates (1971), Flint (1968), Ku and others (1975), 

and Pagano (1987) presented regression analyses that showed 

the percentage of watershed area occupied by coarse-grained 

stratified-drift valley fill to be a powerful predictor of low flow 

per square mile in the Susquehanna River basin of New York. 

Barnes (1986) reached similar conclusions for southeastern 

New York. Wandle and Randall (1994) found that the area of 

sand and gravel and the area of till plus fine-grained sediments 

are each significant in explaining variations in low flow in 

New England.

Tasker (1972) and Male and Ogawa (1982) found low 

flow of streams in Massachusetts to be positively correlated 

with a “ground-water factor” computed from the spatial extent 

of stratified glacial drift subdivided and weighted according 

to potential well yield; this factor was considered roughly 

proportional to average transmissivity of stratified drift in each 

watershed. Neither study addressed whether correlation of 

low flow with the ground-water factor was stronger or weaker 

than correlation with area of sand and gravel or with other 

indices of coarse-grained stratified drift. Allen and Cowan 

(1985) found low flow in northern Illinois to be a function 

of watershed area and a streamflow-recession index that is 

in turn a function of percentage of watershed area underlain 

by sand and gravel. Gebert (1979) reported that low flow in 

northern Wisconsin can be estimated from watershed area, 

transmissivity (a weighted average of standard values for five 

surficial geologic units), and an estimate of 90-percent flow 

duration; Gebert’s maps indicate that not only transmissivity 

but also the 90-percent flow-duration term are functions of 

the extent of surficial sand-and-gravel outwash relative to the 

extent of end moraine and lake clay.

The studies cited above and others have demonstrated 

that variation among watersheds in the extent of sand and 

gravel correlates strongly with, and presumably causes, 

variation in the low flow of streams. Several questions 

remain, however. What attributes of surficial sand and gravel 

are responsible for the large effect of these deposits on low 

streamflow? Could equations for estimating low flow be 

improved by subdividing stratified drift into categories that 

reflect those attributes–or can imperfect prediction of low 

flow by regression equations be ascribed mostly to errors 

in calculating low-flow indices or in mapping the extent 

of sand and gravel, or to failure to consider other relevant 

watershed properties?

Emphases of the present study. Several approaches were 

used in this investigation to address the foregoing questions: 

(1) verify the interpretations of surficial geology by Ku and 

others (1975) in selected watersheds, as described in the 

next paragraph, (2) use analytical and numerical models to 

discern how certain properties of surficial sand and gravel 

affect groundwater discharge to streams, as described in 

the following section on modeling, (3) refine the selection 

of watersheds and the computation of low-flow indices, 

as described in the section “Data set,” and (4) test several 

watershed properties along with the extent of surficial sand 

and gravel in regression analysis; if the additional watershed 

properties improve estimates of low flow, the significance of 

the extent of sand and gravel is also affirmed.

Verification of surficial geology. Four watersheds whose 

low flows had been poorly estimated by the regression 

equations developed by Ku and others (1975, p. 38) were 

revisited during the present study to search for errors in the 

interpretation of surficial geology or other anomalies that 

might account for the outlier status of these watersheds in 

the regression analysis. An investigation of the watershed of 

Fivemile Creek at Kanona (station 01528000), whose low flow 

had been overestimated by a factor of 8, was described by 

Randall (1986b). Remapping of the surficial geology revealed 

that till and fine-grained lake sediments were much more 

abundant on the valley floor, and surficial sand and gravel 

were correspondingly less abundant, than had been realized 

previously. After localities where till or lake sediments cap 

the valley fill were removed from the area mapped as sand 

and gravel (even though gravel aquifers may be present at 

depth), the overestimation of low flow decreased to a factor of 

3 (Randall, 1986b, p. 253–254). Remapping in the watersheds 

of Cohocton River at Cohocton (01527000), Castle Creek 

at Wallace (01527450), and a small part of the watershed 

of Charlotte Creek (01498500) resulted in little net change 

in area of sand and gravel, and hence little improvement in 

estimation of low flow.

Modeling Properties of Surficial Sand and Gravel 

that Affect Groundwater Discharge to Streams 

Modeling groundwater discharge to a stream from a 

surficial sand-and-gravel aquifer in an idealized valley showed 

how variations in aquifer properties affect low streamflow. A 

simple analytical model is described first; discussion of a more 

realistic numerical model follows.

Analytical Model 

Rorabaugh (1960, 1963) developed equations to 

calculate groundwater discharge to streams as a function of 

transmissivity, storage coefficient, time, aquifer width from 
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 11

stream to valley wall, and prior recharge. These equations 

apply to an idealized aquifer bounded on one side by a 

discharge boundary and on the opposite side by a no-flow 

boundary (fig. 5) and are used to calculate aquifer response to 

two conditions: (1) cessation of recharge that had taken place 

at a constant rate (Rorabaugh, 1963, equation 7), and (2) an 

instantaneous water-table rise, or an instantaneous streamstage decline (Rorabaugh, 1963, equation 3 or 4).

VALLEY HALF-WIDTH

LAND SURFACE

SAND AND GRAVEL

BEDROCK

NO-FLOW BOUNDARY

DISCHARGE BOUNDARY 

STREAM

DECLINING WATER TABLE

Figure 5. Idealized aquifer represented by analytical 

equations of Rorabaugh (1963). 

Rorabaugh’s simple analytical model corresponds 

reasonably well to surficial sand-and-gravel aquifers in the 

glaciated Northeast, many of which are bordered by a stream 

in mid-valley (a discharge or recharge boundary, according 

to classical analytical conceptualizations) and by much less 

permeable till and bedrock along the valley side (a no-flow 

boundary). A typical year can be approximately represented 

as a long period of fairly constant recharge (October or 

November through April or May) followed by a period of 

no recharge (May or June through August, September, or 

October). Stream stage normally declines during the summer. 

For several large streams in the Susquehanna River basin, the 

median decline was 1.5 feet from May through August 1964, a 

dry summer with only occasional small pulses of storm runoff. 

Although the summer decline in stage is a result of declining 

groundwater discharge upstream, it can be treated as a cause 

of decline in water level in an aquifer bordering the stream 

at any given location downstream. Also, although the decline 

in stage is a gradual process, it can be simulated as several 

instantaneous steps. 

For this report, Rorabaugh’s equations were applied to 

an idealized set of aquifers and a plausible year, described 

as follows:

• constant recharge rate = 14.3 inches in 265 days = 

0.0045 feet per day,

• length of subsequent period of no recharge = 100 days,

• stream-stage decline = 1 foot on the 40th day of 

no recharge,

• stream-stage decline = 0.5 foot on the 70th day of 

no recharge,

• specific yield = 0.2, and

• transmissivity was held constant at 5,000 feet squared 

per day while valley half-width was varied from 500 to 

3,000 feet; then

• valley half-width was held constant at 2,000 feet while 

transmissivity was varied from 5 to 100,000 feet 

squared per day. 

The equations were applied to calculate discharge per 

mile of valley length to a stream located midway between 

the valley sides, at the end of 100 days with negligible 

precipitation and no recharge. Results are summarized in 

figure 6. Low-flow discharge is approximately a linear 

function of valley half-width, for half-widths of 700 to 

2,500 feet (fig. 6A). It is a nonlinear function of the logarithm 

of transmissivity, and peaks at a transmissivity of about 

2,000 feet squared per day (fig. 6B). The general form of the 

relation in figure 6B is intuitively correct: as transmissivity 

approaches zero, little water can flow through the aquifer to 

the stream; as transmissivity approaches infinity, the aquifer 

resembles a lake in that water input from each storm drains 

immediately down to stream grade after a storm and therefore 

is not available to sustain low flow.

Numerical Model

The analytical model by Rorabaugh does not fully 

describe the hydrology of valley-fill sand-and-gravel aquifers 

in that it does not allow for evapotranspiration, lateral flow 

from the adjacent upland, nor vertical flow near streams that 

only partially penetrate the aquifers. Therefore, a numerical 

groundwater-flow model was developed to incorporate 

these factors. The design, properties, and application of this 

model are explained on the following pages, followed by an 

analysis of the influence of several valley-fill properties on 

groundwater discharge to streams as revealed by results of 

model simulations. A summary of model design and principal 

results, including two figures, was published in Kontis and 

others (2004, p. C23–25).

The modular three-dimensional finite-difference digital 

code described by Mc

Donald and Harbaugh (1988) was 

adapted to represent a two-dimensional vertical section 

across half of a hypothetical valley in which the valley floor 

is underlain by sand and gravel and is bordered by an upland 

hillside of till-mantled bedrock (fig. 7). Initially, the valley 

floor was assumed to be only 100 feet wide (50 feet from 

valley wall to stream). The part of the model that represented 

an upland hillside was calibrated by assigning hydraulic 

properties that were deemed reasonable for upland till and 

bedrock and that generated a plausible head distribution within 
12 Low Flow of Streams in the Susquehanna River Basin of New York

B

A

DISCHARGE TO STREAM, IN CUBIC FEET PER SECOND PER MILE 

OF VALLEY, FROM ONE SIDE

0.10

0.05

0.00

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

DISTANCE FROM STREAM TO VALLEY WALL

(VALLEY HALF-WIDTH), IN FEET

500 1,000 1,500 2,000 2,500 3,000

TRANSMISSIVITY, IN FEET SQUARED PER DAY 50

1

5

10

500

1,000

100

5,000

10,000

50,000

100,000

DISCHARGE TO STREAM, IN CUBIC FEET PER SECOND PER MILE 

OF VALLEY, FROM ONE SIDE

0.00

0.10

0.05

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Figure 6. Effect of A, valley 

width and B, aquifer transmissivity 

on groundwater discharge to a 

stream during a period of low flow, 

as calculated from equations of 

Rorabaugh (1963). 
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 13

Figure 7. Dimensions and properties of a two-dimensional groundwater-flow model that represents an idealized vertical 

section across an upland hillside and the adjacent valley. (From Kontis and others, 2004.)

1,050

1,090

1,100

1,140

1,094

1,095

1,100

Altitude, in feet

above datum

Altitude, in feet above datum

NO-FLOW BOUNDARY

Groundwater 

divide

EXPLANATION

Vertical leakance between model layers,

in feet per day per foot (x 10-3 omitted)

Discharge to stream

Evapotranspiration

Seepage

Hydraulic conductivity

Transmissivity

Storage coefficient 

Recharge

1.7

Stratified sand and gravel

(layer 1 and layer 2)

K and S vary

Bedrock (layer 3);

T = 17.3 feet squared per day;

S = 0.0001

90 feet

1.7

.86

1.7

8.6

Streambed

(highly permeable)

Stream stage

Weathered till (layer 1);

5 feet thick;

K = 1.7 feet per day;

S = 0.05 Till (layer 2); 20 feet thick; K = 0.017 feet per day; S = 0.0001 confined, 0.03 unconfined 

NO-FLOW BOUNDARY

UPLAND HILLSIDE

2,200 feet

VALLEY

width varies

S

T

K
14 Low Flow of Streams in the Susquehanna River Basin of New York

the upland and a discharge to the stream that was typical of the 

low flow of upland streams bordered by only narrow bands of 

alluvial gravel. Then, the width, hydraulic conductivity, and 

specific yield of the valley fill were varied, and the effects on 

simulated discharge to the stream were recorded.

Model Configuration and Operation

Properties and dimensions of the model are indicated in 

figure 7. Three layers were modeled in both upland and valley. 

The upland part of the model includes a relatively permeable 

top layer 5 feet thick that represents the surficial weathered 

zone that is typical of till in the Susquehanna River basin. 

Soils reports, such as Giddings and others (1971), describe 

many upland soils in the Appalachian Plateau of New York 

as 18 to 40 inches of friable, variably well-drained, relatively 

permeable channery silt loam above dense fragipan or 

bedrock. Ku and others (1975, p. 56) report that openings at 

shallow depth in upland soils are a principal avenue of runoff 

for several days after storms. The unweathered till underlying 

this top layer in the upland was assigned a thickness of 20 

feet and a hydraulic conductivity equal to 1 percent of that in 

the top layer. The upper two model layers beneath the valley 

floor represent stratified drift and (or) alluvium, and were 

assigned identical hydraulic properties. The third or lowest 

layer represents bedrock and is uniform across the model. The 

streambed in the center of the valley, which is superimposed 

on the top layer at the far right of the model (fig. 7), was 

assigned a vertical hydraulic conductance large enough that 

the water level in the top layer directly below the stream 

would always equal the specified stream stage, because the 

intent of this exercise was to simulate effects of variations in 

properties of the sand-and-gravel aquifer as a whole, rather 

than variations in hydraulic conductivity or thickness of 

the streambed.

All simulations represented 1 year. For the first 6 months 

(November through April) evapotranspiration was specified 

as zero, river stage was constant, and water was made 

available for recharge at a constant rate through a computer 

code developed by A. L. Kontis (U.S. Geological Survey, 

written commun., 1984) and subsequently incorporated in a 

computer program described in detail by Kontis (2001). This 

code functioned much like the code that has been used to 

represent streams, in that each cell in the uppermost model 

layer was covered by an imaginary streambed that was 

assigned a conductance and thickness such that a vertical flux 

of 0.0104 feet of water per day (about 22 inches in 6 months) 

would be transmitted to the uppermost model layer as long as 

head in that layer remained well below land surface. The flux 

decreased as head rose to within 1 foot of land surface and 

ceased wherever head reached land surface and groundwater 

discharge occurred (simulating the natural development of 

seepage faces). In these simulations, seepage faces always 

developed on the lower part of the upland hillside, and 

occasionally developed in the adjacent part of the valley fill. 

Simulation of the next 6 months (May through October) 

was designed to represent a dry summer that would result 

in low streamflow. Recharge was eliminated, although 

seepage discharge could still occur where heads were above 

land surface. River stage was lowered a total of 2.0 feet1

 in 

two steps (table 2), to approximate typical seasonal stream 

behavior. Evapotranspiration was specified at maximum 

rates that varied seasonally (table 2). The model subtracted 

evapotranspiration from cells in the top layer at rates that 

decreased linearly from the specified maximum where the 

water table was at land surface to zero where the water table 

was deeper than 5 feet. The specified maximum rate for 

each time period simulated was calculated by multiplying 

1

 Reported incorrectly as 1.7 feet in Kontis and others (2004).

Table 2. Model parameters that varied with time during simulations of groundwater discharge to the stream in a hypothetical valley 

typical of the Susquehanna River basin of New York.

Simulation period Duration of period 

(days)

Cumulative

 time 

simulated

(days)

Maximum areal 

recharge rate, 

where water table 

is less than

 1 foot below 

land surface 

(feet per day)

Stream stage 

(feet)

Maximum

 evapotranspiration, 

where water table is 

at land surface

 (feet per second)

November–April 180 180 1.04 × 10-2 1,097.0 0

May 30 210 0.0 1,097.0 .10 × 10-6

June 30 240 0.0 1,096.0 .14 × 10-6

July 30 270 0.0 1,096.0 .16 × 10-6

August 30 300 0.0 1,095.0 .14 × 10-6

September–October 65 365 0.0 1,095.0 .065 × 10-6
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 15

an annual lake evaporation or potential evapotranspiration 

rate for south-central New York of 24 inches (averaged 

from Thornthwaite and Mather, 1955; Hely and Nordenson, 

1961; and Todd, 1970) by an estimate of the percentage of 

annual evapotranspiration occurring in that time period near 

Binghamton, New York (Randall, 1986a). That estimate 

treated evapotranspiration as proportional to the product of 

mean air temperature and hours of daylight (Olmsted and 

Hely, 1962).

A simulation was considered stable if water levels in the 

valley fill at the end of the simulated year were within 1 foot 

of those assumed at the start of the simulation, or if the water 

table ceased rising at some time during the 180-day period of 

recharge (which happened at high hydraulic conductivities). 

The rate of discharge to the stream at the end of August (that 

is, after 180 days with recharge followed by 120 days without 

recharge) was then recorded as the result of the simulation. If a 

simulation was not considered stable, a second simulation was 

run in which the starting heads in the valley fill were the same 

as those at the end of the initial simulation. Starting heads in 

cells representing the upland hillside were the same as starting 

heads used in the initial simulation, however, because (1) the 

model code did not allow for rewetting cells that had gone dry 

during the initial simulation, and (2) till in the uplands of the 

Appalachian Plateau becomes saturated nearly to land surface 

every spring. 

Model Evaluation

Results of 38 simulations were used to plot the curves 

in figure 8, which depict groundwater discharge under lowflow conditions, at the end of 120 days without recharge. 

Two curves are plotted for each valley half-width simulated. 

The lower curve represents groundwater discharge to the 

stream: the upper curve represents total groundwater 

discharge (discharge to the stream plus evapotranspiration of 

groundwater). At the higher hydraulic conductivities, the two 

curves for each valley half-width are parallel and separated 

by about 0.04 × 10-4 cubic foot per second; the difference 

represents evapotranspiration of groundwater from the 

upland part of the model. This set of simulations indicated 

that groundwater discharge to the stream is controlled by 

four properties of the valley fill—hydraulic conductivity, 

specific yield, topography (which affects groundwater 

evapotranspiration), and width (or area) of valley-fill sand 

and gravel. Each of these properties is discussed in turn in the 

following paragraphs.

1. Hydraulic conductivity. The lowest hydraulicconductivity value assigned to the valley fill (1.1 feet 

per day, fig. 8) is comparable to the value assigned to the 

uppermost till layer in the upland (1.7 feet per day, fig. 7). 

As the hydraulic conductivity of the valley fill was 

increased incrementally, discharge to the stream at the 

end of the recession increased at first, then decreased. 

At large hydraulic-conductivity values (typical of clean 

gravel) or at narrow valley widths, discharge to the 

stream approached 0.37 × 10-4 cubic foot per second, 

which was the simulated rate of discharge from the 

upland. Thus, under either condition the valley fill served 

only as a conduit from upland to stream at times of low 

flow. Groundwater discharge to the stream at the end 

of the simulated period of low flow was greatest where 

hydraulic conductivity of the valley fill ranged from about 

15 feet per day, equivalent to that of fine sand (in valleys 

with a half-width of about 0.25 mile) to about 60 feet per 

day, equivalent to that of medium sand (in valleys with a 

half-width of about 0.5 mile) (fig. 8). Saturated thickness 

could vary from 45 feet, with the water table at stream 

stage, to 90 feet, with the water table at land surface 

(fig. 7, table 2). Much larger average values of hydraulic 

conductivity have been reported for some valley-fill 

aquifers in New York (Randall, 1977; Reynolds, 1987; 

Bergeron, 1987); figure 8 suggests that such productive 

aquifers may contribute less water to streams during 

periods of low flow than fine-sand aquifers that drain 

more slowly. Such an inverse correlation between 

hydraulic conductivity of surficial sand and magnitude 

of low flows has been observed in the Coastal Plain of 

Delaware, where surficial fine to coarse sand (comparable 

to the valley component of figure 7) underlies entire 

watersheds (Johnston, 1971).

2. Specific yield. Specific yield of the valley fill was 0.2 in 

all simulations depicted in figure 8. In another simulation 

(not shown in figure 8), specific yield was decreased 

to 0.035 (a value similar to that assigned to weathered 

upland till); valley half-width was 2,400 feet, and 

hydraulic conductivity of the valley fill was 112 feet per 

day. The decrease in specific yield caused water-table 

altitude and discharge to the stream to increase early in 

the summer, but, as shown in the following table, also 

caused discharge to the stream to decrease during the 

period of low flow in late summer. 

Mode 

of 

discharge

Groundwater discharge, in cubic feet per 

second, after 120 days without recharge

Specific yield 

= 0.2

 Specific yield 

= 0.035

To stream 1.641 × 10-4 0.557 × 10-4

Evapotranspiration 0.060 × 10-4 0.050 × 10-4 

Total 1.701 × 10-4 0.607 × 10-4

The model code used for this analysis treated specific 

yield as constant with time, and drainage as occurring 

immediately in response to a decline in head, although 

some delay in complete drainage of granular sediments is 

commonly observed (Rasmussen and Andreasen, 1959, 

p. 83; Kruseman and deRidder, 1990, p. 99). Delayed 

drainage could be expected to decrease groundwater 

runoff early in any period without recharge, and increase 

it later, relative to results of these simulations.
16 Low Flow of Streams in the Susquehanna River Basin of New York

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

100,000 10,000 1,000 100 10 1

SIMULATED GROUNDWATER DISCHARGE PER FOOT OF VALLEY LENGTH FROM ONE HALF OF VALLEY, IN CUBIC FEET PER SECOND x 10-4

SIMULATED HYDRAULIC CONDUCTIVITY OF VALLEY FILL, IN FEET PER DAY

Discharge to stream

Discharge to stream

Total discharge

Half-width of valley = 600 feet

Total discharge

Half-width of valley = 1,200 feet

Half-width of valley = 1,800 feet

Half-width of valley = 2,400 feet

Discharge to stream Total discharge

Discharge to stream

Total discharge

Total discharge Half-width of valley = 75 feet

Discharge to stream

MEDIAN GRAIN SIZE OF ALLUVIAL SEDIMENT OF EQUIVALENT HYDRAULIC CONDUCTIVITY

GRAVEL SAND SILT

VERY COARSE COARSE MEDIUM FINE VERY FINE

(Source: Bedinger, 1961)

Figure 8. Simulated groundwater discharge, to a stream and as evapotranspiration, from an idealized upland hillside 

and valley fill after 4 months without recharge, as a function of hydraulic conductivity of the valley fill. Successive curves 

illustrate the effect of half-width of valley, which is the distance from the base of the upland hillside to a stream flowing 

along the valley axis. Total discharge for each half-width is groundwater discharge to the stream plus groundwater 

evapotranspiration. (From Kontis and others, 2004.)
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 17

3. Topography and groundwater evapotranspiration. Stream 

stage was 43 to 45 feet below most of the valley floor in 

the model (fig. 7, table 2), and in many simulations the 

water table remained far below the valley floor throughout 

the year. Under these conditions, simulated groundwater 

evapotranspiration was small. As hydraulic conductivity 

was decreased, however, the water-table gradient toward 

the stream increased and the water table rose closer to 

land surface seasonally, resulting in progressively greater 

groundwater evapotranspiration for longer periods and a 

corresponding decrease in discharge to the stream. This 

trend is expressed in figure 8 by an increase in separation 

of the two curves for each simulated valley half-width as 

hydraulic conductivity decreases. If land surface on the 

valley floor were higher than specified in figure 7, the 

water table would seldom approach land surface even in 

fine sand; if land surface were lower than specified, the 

loss of groundwater through evapotranspiration would 

decrease low flows even where the valley fill consisted 

of coarse, permeable sand. Trial simulations were run 

with a valley half-width of 2,400 feet and a hydraulic 

conductivity of 112 feet per day, first with the topography 

in figure 7, then with land surface lowered to 1 foot 

above the simulated water-table profile at the start of the 

120-day period of no recharge. Results were as follows:

Mode of 

groundwater 

discharge

Groundwater discharge, 

in cubic feet per second, after 

120 days without recharge

Land surface 

as depicted 

in figure 7

Land surface 1 foot 

above maximum 

water table

To stream 1.641 × 10-4 1.231 × 10-4 

Evapotranspiration 0.061 × 10-4 0.217 × 10-4 

Total 1.702 × 10-4 1.448 × 10-4

The topography of many valley reaches in the 

Susquehanna River basin of New York is similar to that 

depicted in figure 7 in that terraces or irregular collapsed 

landforms of permeable sand or gravel are many feet 

higher than the stream and cover a substantial part of 

the valley floor. Some valley reaches, however, contain 

low-lying areas where the water table is close enough to 

land surface that evapotranspiration limits discharge to 

streams during dry periods. In contrast, the water table 

throughout the uplands rises nearly to land surface every 

spring, allowing substantial evapotranspiration, localized 

groundwater discharge, and much runoff from rejected 

recharge—processes that together leave little water 

available for discharge to streams in late summer.

4. Width, or area, of valley-fill sand and gravel. 

Figure 8 indicates that in coarse-sandy valley fills, the 

maximum rate of groundwater discharge to the stream 

increases in proportion to the increase in valley width 

(and therefore in proportion to the increase in area of 

valley fill, inasmuch as the model represents a unit length 

of valley). At low hydraulic conductivity, however, this 

relation of discharge to width is masked by the effects 

of topography and groundwater evapotranspiration, as 

explained earlier. Figure 9 depicts the relation of valley 

half-width to groundwater discharge derived from the 

valley fill (that is, simulated discharge to the stream at 

the end of the 120-day recession minus the 0.37 × 10-4 

cubic foot per second derived from the upland part 

of the model). That relation is nearly linear, except 

where the water table is close enough to land surface 

to allow appreciable groundwater evapotranspiration. 

Evapotranspiration of groundwater becomes appreciable 

where valley half-width exceeds about 1,800 feet in 

medium to fine sand with a hydraulic conductivity of 

30 feet per day, or about 700 feet in fine to very fine sand 

with a hydraulic conductivity of 10 feet per day.

Although the numerical-model simulations indicate 

that groundwater discharge from valley-fill sand and gravel 

to streams is generally proportional to the area of sand and 

gravel, total low-flow yield per square mile from a long, 

moderately narrow valley-fill aquifer may exceed that from a 

wide aquifer of equal area because the long, narrow valley fill 

is likely to receive, store, and subsequently discharge more 

runoff from adjacent uplands (Morrissey and others, 1988). 

Accordingly, a regression equation of the form:

Low flow = a(area of sand and gravel) + b(valley-wall 

perimeter of sand and gravel)

where 

a and b are regression coefficients,

might estimate low flow more accurately than if area of sand 

and gravel were the only independent variable. However, 

nearly every watershed in the glaciated Northeast contains 

many stream reaches that are bordered only by till and receive 

small amounts of groundwater discharge from the till during 

periods of low flow. Therefore, an equation of the form

Low flow = a(area of sand and gravel) + b(area of till) 

could be expected to account approximately for the small 

low-flow yields from till areas whether discharged directly to 

streams or transmitted through sand and gravel. Equations of 

this form, in which regression coefficient a is much larger than 

b, were developed for streams in New England by Cervione 

and others (1982) and Wandle and Randall (1994).
18 Low Flow of Streams in the Susquehanna River Basin of New York

0

0.1

0.2

0.3

0.4

1.0

1.1

1.2

1.3

0.6

0.5

0.7

0.8

0.9

1.4

0 600 1,200 1,800 2,400

SIMULATED GROUNDWATER DISCHARGE TO THE STREAM DERIVED FROM VALLEY FILL, 

PER FOOT OF VALLEY LENGTH FROM ONE SIDE, IN CUBIC FEET PER SECOND x 10-4

VALLEY HALF-WIDTH, IN FEET

1,000

600

300

200

100

30

10

Hydraulic conductivity of valley fill, in feet per day

600

300

200

100

30

10

1,000

recharge, as a function of valley half-width. Upward flattening of some curves reflects evapotranspiration from 

a shallow water table.

Figure 9. Simulated groundwater discharge to a stream from an idealized valley fill after 4 months without 

Evapotranspiration from Wetlands

Although low flow in the Susquehanna River basin of 

New York is strongly correlated with the spatial extent of sand 

and gravel, that correlation consistently overestimates low 

flow from watersheds that contain extensive lakes or swamps 

(Ku and others, 1975, fig. 16). The area occupied by lakes and 

swamps was found to have a significant negative correlation 

with low flow in Connecticut (R.L. Melvin, U.S. Geological 

Survey, written commun., 1983), in Massachusetts (Male 

and Ogawa, 1982), and in central New England (Wandle 

and Randall, 1994). Barnes (1986) deleted areas of sand and 

gravel overlain by lakes or swamps in southeastern New York 

before correlating the remaining areas of sand and gravel with 

low flow. Johnson (1970) demonstrated that the percentage 

of upland area underlain by poorly drained soils in northern 

Vermont is negatively correlated with low flow.

An inverse correlation between the extent of wetlands 

(such as lakes, ponds, or swamps) and low flow in the 

Susquehanna River basin could be expected for two reasons: 

(1) Precipitation cannot infiltrate where the water table is 

at land surface, so most precipitation on wetlands becomes 

surface runoff rather than groundwater recharge and discharge. 

(2) Most swamps and lakes border or are part of the stream 

network. During the growing season, these wetlands are sites 

of intense evapotranspiration that captures and returns to the 
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 19

atmosphere groundwater that was recharged nearby and would 

have been discharged to streams in the absence of wetlands.

The area of riparian wetlands also commonly correlates 

inversely with high flow (for example, Zembrzuski and Dunn, 

1979), presumably because wetlands provide temporary 

storage for floodwaters, thereby damping flood peaks and 

delaying runoff. This process may be operative to some extent 

during ordinary storms as well as major floods. Therefore, 

wetland area may correlate positively with increased 

streamflow over a wide range of moderate flow conditions, 

when the stored water is gradually released.

For this study, the extent of lakes and swamps shown on 

U.S. Geological Survey 7.5-minute topographic quadrangle 

maps was taken to be representative of wetland area. At least 

three alternative conceptualizations of wetland area, discussed 

below, may ultimately prove more useful as indices of 

evapotranspiration:

1. Include all poorly and very poorly drained soils as part of 

wetland area. Modern soils maps, prepared by the Natural 

Resources Conservation Service and cooperating agencies 

for large areas of the glaciated Northeast including the 

Susquehanna River basin, classify each soil-mapping 

unit with respect to drainage. Poorly drained soils are 

saturated to land surface periodically during the growing 

season; very poorly drained soils have free water on 

land surface during most of the growing season. Pagano 

(1987) measured areas of these two drainage classes in 

several watersheds in the Susquehanna River basin, and 

reported that in each watershed the area of poorly and 

very poorly drained soils was much larger than the area 

of swamps and lakes shown on topographic maps. Pagano 

(1987, p. 95) found that correlation of stratified valleyfill deposits with low flow was improved by deleting any 

areas of poorly or very poorly drained soils from the area 

of valley-fill deposits. He also reported a few equations in 

which area of upland soils with poor drainage correlated 

positively with low flow (probably because these soils 

were quite extensive and served as surrogates for 

drainage area).

2. Include alluvium as part of wetland area. Wandle and 

Randall (1994) distinguished alluvium (flood plains and 

alluvial fans) from sand and gravel deposited by glacial 

meltwater in 49 watersheds in central New England, and 

found that the inverse correlation of wetlands with low 

flow was improved by including alluvium with wetlands. 

An inverse correlation of alluvium with low flow might 

reflect the high hydraulic conductivity of coarse alluvium 

as well as abundant evapotranspiration from flood plains. 

3. Use National Wetlands Inventory delineation of wetlands. 

National Wetlands Inventory maps, prepared by the 

U.S. Fish and Wildlife Service at a scale of 1:24,000, 

cover large areas of the Northeast. These maps delineate 

permanent (saturated) and temporary (seasonal) wetlands 

of several types (Cowardin and others, 1979) on the 

basis of detailed photointerpretation, field studies, and 

interagency review. The maps have achieved accuracies 

above 95 percent (Swartwout, 1982) and, in central New 

England, depict a different and generally larger extent of 

wetlands than those shown on U.S. Geological Survey 

topographic maps (S.W. Wandle, U.S. Geological Survey, 

written commun., 1988).

Underflow beneath Sites of 

Streamflow Measurement

Total runoff from a watershed consists of the flow of the 

stream that drains the watershed, plus any groundwater that 

leaves the watershed below land surface. In the uplands of 

the Susquehanna River basin, groundwater divides coincide 

with topographic divides, so no groundwater leaves a 

watershed beneath its upland perimeter. In valleys, however, 

the water-table gradient has two near-horizontal components, 

one oriented toward the main stream, the other oriented 

downvalley parallel to that stream and approximately equal 

to the stream gradient. Groundwater flow in response to this 

downvalley gradient is termed underflow. 

Underflow can range widely from site to site along 

streams in the Susquehanna River basin. Ku and others 

(1975) measured streamflow and reported low-flow statistics 

at 40 upland sites where tributary streams are incised in 

till or bedrock, both of which are so poorly permeable that 

underflow is virtually nil. Most reaches of upland streams 

are either incised in till or bordered by flood plains that are 

only a few hundred feet wide and are underlain by alluvial 

gravel, sand, and silt probably less than 10 feet thick, through 

which underflow is likely to be small. The larger valleys, 

however, commonly contain several tens of feet of permeable 

sand and gravel that could transmit appreciable underflow. 

Rates of underflow in reaches of three broad valleys that 

are underlain by coarse, permeable stratified drift near the 

modern Susquehanna River basin divide were estimated by 

Randall and others (1988, p. 25, p. 68, p. 79). Underflow in 

one valley was estimated by two methods to average about 

4 cubic feet per second over 11 months, and underflow in two 

other valleys was estimated less precisely from streamflow 

measurements to be nearly 3 cubic feet per second and several 

cubic feet per second, respectively. Ku and others (1975, 

p. 14, p. 33) noted that wherever a tributary leaves its own 

valley to cross sand and gravel within a larger valley, water 

seeps out of the tributary channel into the sand and gravel, 

and is transmitted as underflow within the larger valley. The 

seepage losses typically exceed 1 cubic foot per second per 

1,000 feet of channel (Randall, 1978). Dry channel reaches 

have been observed during periods of extreme low flow along 

a few major streams, including Tuscarora Creek (near station 

01526000, fig. 10), where drainage area is 114 square miles 

(U.S. Geological Survey, 1970) and East Branch Owego 

Creek (near Newark Valley, fig. 10), where drainage area 

is about 90 square miles. Watershed runoff under extreme 
20 Low Flow of Streams in the Susquehanna River Basin of New York

STEUBEN

TIOGA

CORT

CHEMUNG

Fremont

Howard

River

Mud C reek

Meads Creek

Cohocton Rive r

Canisteo River

Fivemile 

Creek Tus c arora Cree k

T oi g a River

Cayuta Cre ek

East Br anch Ow egoCree k

Susquehann a

Riv e r

CORNING

BATH

NEWARK

VALLEY

ELMIRA 

CORT

01530500

01530450

01530240

01528000

01527600

01527450

01527000

01526980

01526495

01526000

01525800

01525750

01524500

01523500

01522500

01522300

01521610

01521500

01520990 01520990

01520520

01515850

01515580

01514839

01514820

01514663

01514298

01514000

01513862

01513829

0150

01508000 

01522000

01513840

01524550

78° 77°30' 77° 76°30' 

43°

42°30'

42° 

Base from U.S. Geological Survey National Atlas digital line graph data files, Source scale 1:2,000,000

Universal Transverse Mercator Projection, NAD 83 Zone 18N

Thematic material from U.S. Geological Survey and Susquehanna River Basin Commission sources

ME

NH

VT

MA

CT RI

NY

NJ

PA

80° 75° 70°

AREA SHOWN BELOW

45°

40°

Figure 10. Locations of streamflow-measurement stations in the Susquehanna River basin of New York.
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 21

OTSEGO

TIOGA

BROOME

CHENANGO

MADISON

CORTLAND

T oi ughnioga River

Genegantslet Creek

Chenango Rive r

Susqu ehanna

River

Unadilla River

Butternut Creek

Ouleout Creek

Charlotte Creek

Schenevus Creek

Ot ego Creek

Wharto n Cre ek

Oaks Creek

East Br anch Ow egoCree k

Susquehann a

Riv e r

Otscelic River

NEWARK

VALLEY

BINGHAMTON

CORTLAND

ONEONTA

NORWICH

01515850

01514839

514820

01514663

01514298

01514000

01513862

01513829

01513280 01512797

01512780

01510000

01509300

01508803

01508500

01508000 01507975

01507500

01507470

01507100

01505500

01502899

01502670

01502550

01502500

01502000

01501900

01501500

01501190

01501000

01500983

01500000

01499470

01499300

01499195

01499050 01499000

01498500

01497985

01497910

01497530

01496920

01496780

01496500

01513840

01513190

0 10

0 10 20 KILOMETERS

30' 76° 75°30' 75° 74°30'

20 MILES

EXPLANATION

U.S. Geological Survey streamflow measurement 

station and number

Susquehanna River basin boundary

County boundary

Location of city or village

01526980
22 Low Flow of Streams in the Susquehanna River Basin of New York

low-flow conditions at these two locations was probably in 

the range of 1 to 4 cubic feet per second, and occurred entirely 

as underflow. 

If underflow is as great as a few cubic feet per second in 

some valley reaches, but virtually zero in others, this variation 

needs to be accounted for in estimating low flow, especially 

along small streams.

Less Important Factors that Affect Low Flows

Five additional watershed properties or conditions 

that may affect low streamflow are watershed area, extent 

and properties of till, extent and properties of bedrock, 

watershed relief and slope, and degree of stream regulation 

and urbanization. Evidence briefly summarized on the 

following pages suggests that these properties were of less 

importance than water availability, surficial sand and gravel, 

evapotranspiration, and underflow in the Susquehanna River 

basin of New York during the period of streamflow record 

studied (1941–71).

Watershed Area

Streamflow could logically be expected to increase in 

proportion to watershed area, all other factors being equal. 

All other factors are seldom equal, however, and a principal 

reason for developing equations for estimating low flow is 

to improve on the imprecise method of extrapolating low 

flows on a per-square-mile basis. According to studies in 

Connecticut and central New England, regression equations 

that incorporated area of sand and gravel and area of till 

as explanatory variables, or only area of sand and gravel, 

estimated low flow much more accurately than equations that 

relied simply on watershed area (Cervione and ohers, 1982; 

Wandle and Randall, 1994, p. 19). Trial equations tested as 

part of the present study confirmed this result. Therefore, 

drainage area alone is not used as an explanatory variable in 

the regression analyses presented in this report. Some of these 

equations account for the effect of area by dividing some or 

all watershed properties by drainage area. Other equations 

incorporate sand-and-gravel area and till area, which together 

equal drainage area but are more powerful individually as 

controls on groundwater discharge to streams.

Extent and Properties of Till

Variations in till thickness, grain size, and permeability 

of the weathered soil zone had little effect on low flow from 

14 watersheds in the Susquehanna River basin of New York 

and northernmost Pennsylvania (Pagano, 1987). Nine of these 

watersheds are included in the data set for this report. The 

spatial extent of surficial stratified drift and alluvium in these 

watersheds was strongly correlated with low flow. Pagano 

(1987) classified most of the till in these watersheds into 

three categories according to properties reported in modern 

soils surveys:

1. till, less than 3 feet to bedrock;

2a. till, less than 20 percent silt and clay, permeability greater 

than 0.2 inches per hour; and

3. till, more than 20 percent silt and clay, permeability less 

than 0.2 inches per hour.

None of these three till categories proved significant in 

regression equations designed to estimate low flow. Pagano 

(1987) also identified two other categories of till, present 

in only a few watersheds, that had a significant inverse 

correlation with low flow:

2b. till, similar to 2a, but with thicker soil profiles and located 

only on valley sides or floors; and

4. till overlying or interbedded with outwash sand and 

gravel, located chiefly in valleys.

Abundant evapotranspiration from poorly drained till soils 

might result in an inverse correlation of those soils with 

low flow, but till categories 2b and 4 are not poorly drained. 

Because these two till categories are present largely in 

watersheds with valley floors 600 to 2,000 feet wide that 

are underlain by substantial thicknesses of stratified drift, 

they might have functioned in Pagano’s regression analyses 

as surrogates for a decrease in low streamflow caused by 

underflow through stratified drift.

Extent and Properties of Bedrock Units

The sedimentary bedrock of Devonian age that underlies 

the Susquehanna River basin of New York was classified 

into several facies by Rickard (1975). Arranged in order of 

decreasing grain size and percentage of detrital fragments, 

they are:

Catskill: shales, mudstones, siltstones, medium to coarse 

sandstones, pebble conglomerates;

Cattaraugus: shales, siltstones, sandstones;

Chemung and Hamilton: shales, mudstones, siltstones, fine to 

medium sandstones;

Portage: shales, mudstones, siltstones, rare fine sandstones;

Portage and Marcellus: shales, thin argillaceous limestones; 

and

New Scotland: argillaceous calcisiltites and calcilutites, 

calcareous shales.

Although these facies interfinger to a considerable extent 

within the Appalachian Plateau of New York, the coarsest 

facies are generally found to the southeast with successively 

finer facies to the north and west, as shown on charts by 

Rickard (1975) and on the Geological Map of New York 

(Fisher and others, 1970).

Two indices of bedrock lithology were computed by 

Coates (1971) for each of 13 watersheds in the Delaware River 

basin and 12 watersheds in the Susquehanna River basin, on 

the basis of measurements at outcrops. A “sandstone index” 

was defined as the percentage of total stratigraphic thickness 

made up of sandstones; a “massiveness index” was defined 

as the percentage of stratigraphic thickness made up of beds 
Watershed Properties and Processes that Control Spatial Variation in Low Flow of Streams 23

in which the thickness between bedding planes was greater 

than 1 foot. Both indices were much higher in Delaware 

River basin watersheds than in most Susquehanna River 

basin watersheds. Within the Susquehanna River basin, these 

indices were highest along the Pennsylvania border and in the 

extreme eastern part of the basin, in agreement with the facies 

distribution presented by Rickard (1975).

These trends in bedrock lithology might be expected to 

affect groundwater discharge to streams, causing low flows to 

increase to the south and east across the Susquehanna River 

basin, for two reasons: (l) the open fractures through which 

groundwater flows tend to be larger and more persistent in 

massive sandstone layers than in shales, and (2) the grain 

size and lithologic composition of glacial till reflects those 

properties in the underlying bedrock. (For example, a notable 

decrease in carbonate content of till southward from the 

carbonate outcrops along the northern edge of the Appalachian 

Plateau was reported by Holmes (1952), Denny and Lyford 

(1963), and Moss and Ritter (1962).) Accordingly, one might 

expect till to become somewhat sandier and more permeable 

to the southeast, reflecting the increased percentage of 

sandstone in the bedrock. However, available evidence does 

not support the hypothesis that these trends cause low flow 

to increase southeastward. Coates (1971, table 6) showed 

that low flow correlated well with his sandstone index and 

massiveness index in 13 Delaware River basin watersheds, but 

not in 12 Susquehanna River basin watersheds. Furthermore, 

although spatial extent of valley-fill sand and gravel was 

strongly correlated with low flow in his Susquehanna River 

basin watersheds, no improvement in correlation resulted 

from adding the two bedrock indices as additional variables. 

In the present study, the spatial distribution of positive and 

negative residuals from several regression equations was 

compared with facies distribution in bedrock. If the inferred 

northwestward decrease in grain size of bedrock and till 

were a significant limitation on groundwater discharge to 

streams, one would expect equations that ignored these 

factors to underestimate low flow from southern and eastern 

watersheds and overestimate low flow from northern and 

western watersheds. No consistent southeastward increase in 

underestimation was obvious, however, nor were low flows 

in the few watersheds underlain by the Catskill (nonmarine) 

facies consistently underestimated. The distribution of 

positive and negative residuals generally seemed random, 

and some equations underestimated low flows in the western 

watersheds. The ratio of seasonal (August through October) 

runoff to annual runoff increases from northwest to southeast 

(fig. 4), but this ratio is not strongly correlated with either 

the sandstone index or the massiveness index computed by 

Coates (1971) for 12 Susquehanna River basin watersheds 

(correlation coefficient (R) less than 0.58; Spearman rank 

correlation less than 0.56). Furthermore, as explained in 

the section “Seasonal Precipitation and Runoff,” the trend 

in figure 4 might result from seasonal differences across 

the region in precipitation minus evapotranspiration, or 

variation in the percentage of surficial sand and gravel among 

large watersheds. 

Watershed Relief and Slope

Topographic relief, average land-surface slope, and 

(or) stream-channel gradient have commonly been included 

among the watershed properties tested as explanatory 

variables in regression analyses designed to estimate low 

or high streamflow. These geomorphic indices have been 

included because they could be measured conveniently on 

topographic maps and because steep slopes were perceived by 

the investigators to favor greater storm runoff and (or) more 

rapid depletion of groundwater storage than gentle slopes 

(Paulsen and others, 1940, p. 440; Schumm, 1956; Zecharias 

and Brutsaert, 1988a, b). Although the low flows of several 

small upland tributaries in the Susquehanna River basin were 

found to decrease with increasing average land-surface slope 

(Pagano, 1987, p. 46), the low flows of larger streams consist 

chiefly of groundwater discharged from valley-fill sand and 

gravel, and are likely to increase with increasing watershed 

relief or slope because increased relief is associated with 

increased infiltration of upland runoff into the valley fill 

(Morrissey and others, 1988). Watershed slope and (or) relief 

indices have not proved consistently significant in regression 

equations designed to estimate low flow. For example, Sopper 

and Lull (1970) found main-channel gradient to be significant 

in estimating the duration of the longest period that includes 

5 percent of annual streamflow in only two of four regions 

in the glaciated Northeast; moreover, its apparent influence 

was positive in one of these regions but negative in the other. 

This result implies that an increase in main-channel gradient 

(and hence in streamflow velocity, underflow, and alluvial 

grain size) does not inherently lengthen or shorten episodes 

of low streamflow; where main-channel gradient proved 

significant in their analyses, it may have functioned as a 

surrogate for untested watershed properties. Darmer (1970) 

included main-channel gradient in equations to estimate 

7-day 10-year low flows over much of New York, but found 

relief to be more significant than main-channel gradient in 

the eastern Susquehanna and Delaware River basins; neither 

variable proved significant in estimating 7-day 2-year low 

flows anywhere in New York. On the other hand, Ku and 

others (1975) found valley gradient (similar to main-channel 

gradient) in the Susquehanna River basin to be significant 

in estimating 7-day 2-year low flows, but not 7-day 10-year 

low flows. Main-channel slope proved not to be significant 

in estimating 7-day 10-year and 7-day 2-year low flows in 

eastern New York (Barnes, 1986), Massachusetts (Male and 

Ogawa, 1982), and Wisconsin (Gebert, 1979). Comer and 

Zimmerman (1969) showed that a small till-covered basin 

with steep slopes in northern Vermont had more low flow per 

unit area than a larger adjacent basin with distinctly gentler 

slopes, but attributed the contrast to the greater extent of 

shallow poorly drained soils in the larger basin. Seasonal 

average runoff from eight till-covered upland watersheds 
24 Low Flow of Streams in the Susquehanna River Basin of New York

in northern Vermont in the summer and in the fall of an 

unusually dry year was not strongly correlated with the 

percentage of watershed area having a slope of 25 percent or 

more (R=0.67 or less) (DeAngelis and others, 1984). Coates 

(1971), in a detailed geomorphic analysis of watersheds in 

the Susquehanna River basin of New York, computed four 

slope or relief properties: maximum watershed relief, stream 

relief (the average vertical distance between drainage divides 

and streams), average topographic slope in upland areas, and 

tributary stream gradients. Individually and as a group, these 

properties were not strongly correlated with 90-percent flow 

duration nor with base-flow recession rates (R= 0.60 or less). 

Given the inconsistent and inconclusive results of numerous 

studies cited above, measurements of watershed slope, relief, 

and gradient were not included in the data set for regression 

analysis in this study.

Degree of Stream Regulation and 

Watershed Urbanization

Several of the larger streams in the Susquehanna 

River basin are affected by regulation, including interbasin 

transfers of water for purposes of power generation or canal 

operation, intermittent release of water stored in hydropower 

reservoirs, and seasonal release of water stored in lakes and 

reservoirs for recreational purposes. Most of these activities 

are mentioned in the notes accompanying published records of 

daily streamflow at gaging stations (U.S. Geological Survey, 

1951–2005); information on regulation is also available 

from the Susquehanna River Basin Commission. Most of the 

streams analyzed for this report were unregulated. The effects 

of regulation on low flows of four streams were eliminated 

by adjustments based on reservoir-stage records or by 

deleting part of the watershed area, and for two other streams 

regulation was judged to be insignificant, as explained in 

footnotes to table 3.

Urbanization can have varied and complex effects on 

low flow. Buildings, pavement, roadside ditches on upland 

hillsides, and storm sewers can increase the volume and rate of 

storm runoff and thereby decrease the infiltration that sustains 

low flows. Groundwater development can lower the water 

table enough to locally eliminate groundwater discharge to 

streams. Conversely, some urban processes can augment low 

flows: buildings and pavement decrease evapotranspiration, 

leaky sewers and water mains can raise the water table 

locally, and discharge to streams from wastewater-treatment 

facilities continues during periods of low flow. Accordingly, 

and inasmuch as urbanization did not affect more than a 

small percentage of the land surface in any of the watersheds 

analyzed for this report during the period of data collection, 

the findings of this study are considered representative of 

nonurbanized conditions.

Regression Analysis

Multiple regression analysis provides a means of testing 

and quantifying the significance of environmental factors that 

are hypothesized to affect the low flow of streams. Statistical 

tests measure the accuracy with which the equations estimate 

low flows and the relations among environmental variables 

and data values in those equations.

Data Set 

 The regression analyses described in this report are based 

on data from 70 watersheds, including statistical indices of 

low streamflow and several watershed properties hypothesized 

to affect low streamflow.

Low-Flow Statistics

Three commonly used statistical indices of low flow were 

computed for each watershed:

7-day 10-year low flow (7Q10): The annual lowest 

streamflow, averaged over 7 consecutive days, that has a 

1 in 10 chance of not being exceeded in a given year.

7-day 2-year low flow (7Q2): The annual lowest streamflow, 

averaged over 7 consecutive days, that has a 1 in 2 chance 

of not being exceeded in a given year.

90-percent flow duration (90%FD): The flow that was 

equaled or exceeded 90 percent of the time during the 

period of analysis.

The array of watersheds that make up the data set and the 

computation of low-flow statistics for each watershed were 

refined during four successive studies, including this one. The 

contribution of each study is summarized below.

Hunt (1967) adjusted records of streamflow through 1964 

at all gaging stations in the Susquehanna River basin of New 

York to represent flow during 1931–60, and established many 

partial-record stations on small streams at which streamflow 

was measured occasionally during periods of low flow. He 

presented flow statistics for all stations, but made no attempt 

to regionalize low flow.

Ku and others (1975) noted that many older partialrecord stations were located where tributaries begin to flow 

across sand and gravel in major valleys. Underflow in these 

localities is substantial and increases rapidly downstream (Ku 

and others, 1975, p. 14; Randall, 1978); hence, flow statistics 

for these stations represent only part of the yield from the 

watershed. Ku and others flagged these stations as unsuitable 

for extrapolating flow statistics to other sites on a per-squaremile basis, and excluded them from their subsequent regional 

analysis. They established many new stations on small streams 

at sites where underflow was expected to be minimal, and 

estimated flow statistics for each partial-record station through 

graphical correlation (Riggs, 1972) with one or two long-term 
Regression Analysis 25

Table 3. Streamflow-measurement stations in the Susquehanna River basin of New York, and selected indices of low flow.

[Br, branch; Rd, road; SH, State Highway; FD, Flow Duration; flow values are in cubic feet per second; station locations are shown in figure 10; columnheading terms in brackets are variables used in regression equations shown in table 5 (at end of report)]

U.S.

Geological 

Survey 

station 

number

Station name

Type 

of 

record1

Watershed 

area

(square 

miles)

[DAREA]

Lowest annual 

7-day mean flow, 

April 1941–March 1971, 

with recurrence

 interval of

90-percent

flow duration, 

October 1941–

September 1971

10 years 

[7Q10]

2 years

[7Q2] [90 % FD]

01496500 Oaks Creek at Index G12 102 3.3 10.1 13.9

01496780 Cherry Valley Creek tributary at Roseboom P 1.60 0.015 0.04 0.08

01496920 Shellrock Creek near Middlefield P 5.45 0.03 0.13 0.21

01497500 Susquehanna River at Colliersville G13

01497530 Oak Creek near East Worcester P 5.55 0.04 0.14 0.24

01497910 Center Brook at West Harpersfield P 12.9 0.40 0.70 1.1

01497985 Kortright Creek at East Meredith P 25.6 0.70 1.25 1.9

01498500 Charlotte Creek at West Davenport G1 164.5 8.9 14.7 22.1

01499000 Otego Creek near Oneonta G2 108 7.0 12.4 17.4

01499024 West Branch Otsdawa Creek near Otego P 4

01499050 Flax Island Creek near Otego G4 4.22 0.01 0.05 0.14

01499195 Brier Creek near Otego P 6.96 0.03 0.11 0.26

01499300 West Branch Handsome Brook near Franklin P 8.27 0.10 0.24 0.38

01499470 East Branch Handsome Brook near Franklin G4 9.12 0.26 0.55 0.90

01500000 Ouleout Creek at East Sidney G1 5 103 3.5 8.5 12.6

01500983 Center Brook near New Berlin P 10.9 0.085 0.21 0.42

01501000 Unadilla River near New Berlin G1 199 15.3 24.5 32.6

01501190 Wharton Creek at Pittsfield P 84.4 7.0 11.0 14.0

01501500 Sage Brook near South New Berlin G2 0.70 0.001 0.015 0.033

01501900 Butternut Creek near Garratsville P 6 16.0 1.1 1.8 2.5

01502000 Butternut Creek at Morris G1 59.7 4.2 7.2 9.6

01502500 Unadilla River at Rockdale G1 520 41.1 70.8 92.7

01502550 Guilford Creek at East Guilford P 17.8 0.15 0.40 0.65

01502670 Big Brook above Bennetsville P 25.4 0.32 0.68 1.2

01502899 Little Snake Creek above SH7 at Conklin P 30.6 0.25 0.45 0.70

01505500 Canasawacta Creek near South Plymouth G2 57.9 0.80 2.4 5.3

01506050 Bear Brook at Walker Corners P 4

01507100 Five Streams near Smithville Flats P 10.1 0.01 0.12 0.52

01507470 Red Brook at Smithville Flats G4 7.06 0.017 0.06 0.13

01507500 Genegantslet Creek at Smithville Flats G2 82.3 2.3 5.0 7.7

01507975 Muller Gulf Creek near Cuyler G4 6 2.67 0.001 0.02 0.11

01508000 Shackham Brook near Truxton G2 2.95 0.04 0.11 0.17

01508500 Albright Creek at East Homer G2 6.80 0.07 0.30 0.57

01508803 West Branch Tioughnioga River at Homer G3 7 71.5 9.3 15.5 20.5

01508803 West Br Tioughnioga River plus adjacent area 8 73.7 10.1 16.8 22.0
26 Low Flow of Streams in the Susquehanna River Basin of New York

Table 3. Streamflow-measurement stations in the Susquehanna River basin of New York, and selected indices of low flow.

[Br, branch; Rd, road; SH, State Highway; FD, Flow Duration; flow values are in cubic feet per second; station locations are shown in figure 10; columnheading terms in brackets are variables used in regression equations shown in table 5 (at end of report)]

U.S.

Geological 

Survey 

station 

number

Station name

Type 

of 

record1

Watershed 

area

(square 

miles)

[DAREA]

Lowest annual 

7-day mean flow, 

April 1941–March 1971, 

with recurrence

 interval of

90-percent

flow duration, 

October 1941–

September 1971

10 years 

[7Q10]

2 years

[7Q2] [90 % FD]

01509300 Hunts Creek at Marathon P 10.8 0.15 0.40 0.6

01510000 Otselic River at Cincinnatus G2 147 8.4 15.5 21.7

01511550 Halfway Brook near Triangle P 4

01512780 Thomas Creek at Chenango Forks P 6 8.69 1.5 2.0 2.4

01512797 Castle Creek at Glen Castle P 27.7 0.12 0.35 0.60

01513190 Little Choconut Creek at Stella P 12.2 0.12 0.23 0.31

01513280 Finch Hollow Creek at Oakdale P 3.96 0.04 0.07 0.095

01513829 Little Nanticoke Creek at Day Hollow Rd Owego P 19.7 0.22 0.34 0.43

01513840 Pumpelly Creek at Owego G4 8.59 0.03 0.06 0.08

01513862 East Br Owego Creek tributary at Harford Mills P 5.77 0.05 0.10 0.16

01514000 Owego Creek near Owego G1 185 9.9 14.6 17.2

01514298 Sulphur Springs Creek near Spencer P 8.64 0.06 0.12 0.16

01514663 Willseyville Creek at Willseyville P 8.49 0.75 1.15 1.3

01514820 Thorn Hollow Creek near Owego P 4.13 0.025 0.055 0.065

01514839 Hunts Creek near Owego P 6.78 0.027 0.055 0.075

01515580 Carter Creek near Cayuta P 4.76 0.02 0.045 0.07

01515850 Langford Creek near Van Etten P 6 5.26 0.004 0.02 0.03

01520520 North Branch Glendenning Creek at Presho P 9.27 0.05 0.14 0.18

01520990 Canisteo River at Bishopville P 21.6 0.13 0.29 0.44

01521500 Canisteo River at Arkport G1 30.6 0.60 1.1 1.5

01521610 Big Creek near North Hornell P 16.8 0.25 0.60 0.90

01522000 Canisteo River at Hornell G4 4

01522300 Canacadea Creek near Almond P 17.1 0.75 1.4 1.8

01522500 Karr Valley Creek at Almond G2 27.4 0.11 0.55 0.95

01523500 Canacadea Creek near Hornell G2 9 57.9 4.6 6.9 7.5

01524500 Canisteo River minus several tributaries 10 70.1 10.6 14.2 15.6

01524500 Canisteo River below Canacadea Creek Hornell G29,11 145 11.6 16.5 19.0

01524550 Cunningham Creek near Canisteo P 5.34 0.015 0.055 0.095

01525750 Tuscarora Creek tributary near Woodhull G4 9.50 0.004 0.05 0.08

01525800 South Branch Tuscarora Creek near Woodhull P 7.40 0.002 0.015 0.03

01526000 Tuscarora Creek near South Addison G2 114 0.001 0.6 1

01526495 Mulholland Creek near Erwins G4 5.06 0.01 0.04 0.055

01526980 Kirlkwood Creek near Atlanta G4 4.64 0.08 0.17 0.26

01527000 Cohocton River at Cohocton G3 52.2 3.15 5.5 7.2

01527450 Castle Creek near Wallace P 9.23 2.3 3 3.4
Regression Analysis 27

Table 3. Streamflow-measurement stations in the Susquehanna River basin of New York, and selected indices of low flow.

[Br, branch; Rd, road; SH, State Highway; FD, Flow Duration; flow values are in cubic feet per second; station locations are shown in figure 10; columnheading terms in brackets are variables used in regression equations shown in table 5 (at end of report)]

U.S.

Geological 

Survey 

station 

number

Station name

Type 

of 

record1

Watershed 

area

(square 

miles)

[DAREA]

Lowest annual 

7-day mean flow, 

April 1941–March 1971, 

with recurrence

 interval of

90-percent

flow duration, 

October 1941–

September 1971

10 years 

[7Q10]

2 years

[7Q2] [90 % FD]

01527600 Goff Creek near Howard P 17.9 1.4 2.3 2.8

01528000 Fivemile Creek near Kanona G1 66.8 0.7 1.6 2.2

01530240 Gillette Creek near South Corning P 3.77 0.01 0.03 0.04

01530450 Latta Brook at Horseheads P 5.29 0.02 0.045 0.06

01530500 Newtown Creek at Elmira G1 77.5 7.6 12.8 13.5

1

 Symbols defined as follows:

G1 Gaging station, continuous record 1941–71 or longer.

G2 Gaging station, record nearly complete 1941–71, 7-day low flows for missing years estimated by correlation prior to frequency analysis.

G3 Gaging station, less than 22 years of record 1941–71, low-flow indices estimated by correlation of 7-day low flows.

G4 Gaging station, about 2 years of record 1941–71, low-flow indices estimated by correlation of daily flows.

P Partial-record station, measurements chiefly 1966–68, low-flow indices estimated by correlation of individual measurements with daily flows at 

index stations. 

2

 Low dam constructed at outlet of Canadarago Lake June 1964; thereafter, lake level was raised slightly each spring and lowered at end of summer. Records 

of lake stage 1968–71 and daily flow records indicated that this regulation had little or no effect on annual 7-day low flows of Oaks Creek. 

3

 Deleted from data set. Regulation during periods of low flow, presumably by powerplant 0.25 mile upstream, typically resulted in several days of low, 

steady flow interrupted by single days of several times higher flow unrelated to rainfall. Daily flows between 30 and 50 ft3/s are rare in some years.

4

 This watershed was deleted from the data set compiled by Ku and others (1975, appendix B) because low-flow indices were poorly defined.

5

 Flow unregulated through 1949; thereafter, East Sidney Reservoir has regulated high flows but is reported not to significantly affect low flows.

6

 Correlation of this partial-record station with long-term index stations was rated as fair to poor because of large scatter of data. Accordingly, this station was 

deleted from the data set for several regression analyses, as described in text section “Per-square-mile equations to estimate 7-day 10-year low flow.” 

7

 Continuous streamflow record 1967–68, 1973–85; 7-day low flows for these years as well as daily flows during base-flow periods were correlated with corresponding flows at three nearby stations.

8

 West Branch Tioughnioga River at Homer, station 01508803, plus a small area near Tully draining by way of numerous springs to Onondaga Creek 

(St. Lawrence River basin).

9

 Low flows unregulated through March 1965. Daily flows April 1965–March 1971 adjusted as necessary for changes in contents of Almond Reservoir, based 

on reservoir stage recorded daily at midnight (1965–86) or daily mean reservoir stage (1969–71) published by U.S. Geological Survey (1951–2005) and on 

capacity curve furnished by U.S. Army Corps of Engineers. Stages that were published only to the nearest 0.1 ft (1965–69) were adjusted as much as ± 0.04 ft 

during periods of changing stage to smooth the rates of change. In all but one of the 6 years of adjusted flows, the 7 consecutive days of lowest flow apparently 

occurred when adjustments were 0 to 40 percent of the recorded flow of Canacadea Creek, and on nearly the same days as the 7-day low flow of Canisteo River 

at Arkport (station 01521500).

10 Canisteo River below Canacadea Creek at Hornell, station 01524500, minus stations 01521500, 01521610, and 01522500, and minus 13 square miles 

above Hornell municipal reservoirs on Carrington Creek.

11 City of Hornell diverts an average of 3.5 cubic feet per second for municipal supply from Carrington Creek, a tributary upstream from station; sewage enters 

Canisteo River downstream from station. Runoff from the 13 square miles above Hornell reservoirs is presumed to be zero during periods of low flow, so this 

part of the watershed is excluded from drainage area and other data tabulated in this report.
28 Low Flow of Streams in the Susquehanna River Basin of New York

gaging stations that were nearby and (or) geologically similar 

to the partial-record station. They selected a data set of 73 

stations for regression analysis, from which they developed 

equations to estimate 7Q2, 7Q10, and 90%FD for 1931–60. 

Eissler (1979) estimated 7Q2 and 7Q10 for measurement 

sites throughout New York. He discerned that data for three 

of the partial-record stations used by Ku and others (1975) 

were insufficient for reliable analysis. Eissler’s results for 

other stations differed somewhat from those reported by Ku 

and others, because Eissler (1) analyzed periods of record 

through 1975, and did not adjust records to a single common 

time period; (2) used a computer program to calculate and 

plot least-squares linear regressions relating measured flows 

at each partial-record station to concurrent flows at three or 

more long-term gaging stations, and averaged the resulting 

estimates of low-flow characteristics; and (3) plotted the data 

from a few partial-record stations incorrectly because pertinent 

information was not readily available.

Statistical indices of streamflow for differing periods 

of years commonly differ substantially because of trends or 

random variations in climate. Therefore, the usual practice 

when comparing streamflow records for different time 

periods is to adjust all records to a common reference period, 

typically 30 years in length (Searcy, 1959; Cervione and 

others, 1982). As part of the present study, low-flow indices 

for 70 watersheds in the Susquehanna River basin were 

recomputed to represent a reference period extending from 

October 1941 through September 1971 for flow duration, and 

from April 1941 through March 1971 for low-flow frequency. 

Results are presented in table 3. A 30-year period ending in 

1971 was selected because (1) it corresponds more closely 

than any other 30-year period to the actual period of record 

of most gaging stations in the Susquehanna River basin of 

New York, and (2) it corresponds to the period used in similar 

regionalizations of low-flow indices in Connecticut (Cervione 

and others, 1982) and in central New England (Wandle and 

Randall, 1994). Unregulated streams in the northeastern 

United States have experienced a small (not statistically 

significant) increase in annual runoff during the 20th century, 

but no significant trend in magnitude or timing of summer or 

fall low flows (Hodgkins and others, 2005; Hayhoe and others, 

2007, p. 392). Changes in magnitude of annual 7-day low 

flows of 51 unregulated streams in the Northeast during the 

21st century, as projected by an array of climate models, range 

from a decrease of more than 10 percent to little or no change 

(Hayhoe and others, 2007, p. 398). 

The data set includes 10 gaging stations with 30 years 

of continuous record through 1971, 11 stations lacking only 

a few years of record from this period, and 2 stations with 

long records obtained mostly after 1971. Flow duration for 

these 23 stations was determined by using computer programs 

developed by the U.S. Geological Survey (1985); incomplete 

records were adjusted as described by Searcy (1959). Lowflow frequency for incomplete records was adjusted by first 

correlating 7-day annual minimum flows at each short-term 

station with 7-day annual minimum flows for the same years 

at nearby gaging stations, then selecting the index station that 

provided the largest product-moment correlation coefficient 

exceeding 0.8 (Matalas and Jacobs, 1964). The data for each 

pair of stations selected were plotted on logarithmic scales and 

lines of relation fitted by eye. If only a few years were missing 

from the base period, these graphs were used to predict 7-day 

low flows for the missing years, and the reconstructed array 

of data for the 30-year period was then analyzed by computer 

programs that used the log-Pearson method. If many years 

were missing, 7Q2 and 7Q10 for the 30-year period were 

estimated directly from the graphs. Records for a few stations 

were adjusted individually to correct for local circumstances, 

as explained in footnotes to table 3. 

The data set also includes 8 gaging stations operated 

for only a few years and 37 partial-record stations. For 

these 45 stations, graphs were available from earlier studies 

(Eissler, 1979; Ku and others, 1975) that related instantaneous, 

daily, and (or) monthly flows at each short-term station to 

corresponding flows at several long-term index stations, 

including some just outside the Susquehanna River basin. 

These graphs were re-examined, and data points were 

corrected or added for several stations. Trend lines were fitted 

by eye (Riggs, 1972) with emphasis on the data points that 

represent relatively low flow, and were used to transfer indices 

of low flow from the index stations. For a few of these shortterm stations, one graph showed much better fit than others 

and was used exclusively, but for most stations the results 

from two to four graphical correlations were averaged.

 Low-flow indices and drainage area for each watershed 

used in regression analyses described in this report are 

presented in table 3. Locations of the measurement stations 

are shown in figure 10. Table 3 also lists (without data) five 

watersheds that were analyzed by Ku and others (1975) but 

deleted from the data set during the present study.

Watershed Properties

The data set includes 13 watershed dimensions or 

properties measured as part of the study by Ku and others 

(1975) or the present study. All measured values are listed 

in table 4 (except drainage area, which is listed in table 3). 

Each term is explained below. Each name is followed by an 

abbreviation or acronym (in parentheses) that is used in table 

4 and also in the regression equations presented in table 5 (at 

end of report). All determinations of area were made on U.S. 

Geological Survey 7.5-minute topographic maps, measured at 

least twice by planimeter or electronic digitizer. 

Drainage area (DAREA). The drainage area upstream 

from each streamflow-measurement site is measured routinely 

by the U.S. Geological Survey; these areas have been 

published in annual data reports (U.S. Geological Survey, 

1951–2005) and interpretive studies (for example, Eissler, 

1979). Watersheds with drainage areas greater than 200 square 

miles were generally excluded from the data set for this 

report because measurement of some watershed properties 

would have been quite time-consuming, and because the 
Regression Analysis 29

Table 4. Watershed properties compiled for regression analysis of low flow in the Susquehanna River basin of New York.[Column-heading terms in capital letters are acronyms for these properties used in regression equations]

Watershed

or station 

number 

(from 

table 3) 

Area of 

surficial 

sand and 

gravel 

(square miles)

Mean 

annual 

precipitation 

(inches)

Mean 

annual 

runoff

(cubic feet 

per second)

Ratio of 

August–

October 

runoff to 

mean annual 

runoff

Area of wetlands 

(square miles) 

bordered mostly by

Dimensions of sand and 

gravel aquifer (feet) at 

measurement station

Stream gradient 

at measurement 

station 

(dimensionless)

Underflow 

factor 

(width 

× thickness 

× slope) 

(feet squared)

Forested 

area 

(square miles)

Till Sand and gravel Width Thickness

STATION SGAREA MAP MAQ RUNRATIO LKSWTL LKSWSD WIDTH THICK SLOPE UNDER1 FOREST

01496500 19.5 42.17 174.1 0.323 1.55 6.6 3,500 10 0.0032 112 129.2101496780 0.02 40.2 2.5 0.330 0 0 20 1 0.0571 1.142 10.6401496920 0.19 39.9 8.4 0.330 0.05 0 100 5 0.04 20 12.2701497530 0.3 39.5 8.4 0.335 0.1 0.04 50 1 0.0143 0.715 12.9301497910 0.95 42.4 22.2 0.360 0.04 0 1,000 5 0.0073 36.5 110.9301497985 1.35 41.5 42.4 0.355 0.31 0 100 1 0.0143 1.43 17.6401498500 17.7 40.21 257.0 0.345 2.06 0.09 3,500 80 0.0014 392 171.2601499000 16.5 40.62 172.0 0.330 0.73 0.68 2,500 20 0.001 50 135.8301499050 0.15 39.3 6.3 0.335 0 0 50 2 0.02 2 0.9 01499195 0.26 39.5 10.5 0.335 0 0 20 1 0.02 0.4 1.701499300 0.2 44.1 15.3 0.360 0.01 0 200 8 0.0118 18.88 2.701499470 0.32 43.6 16.5 0.355 0.05 0 250 8 0.009 18 201500000 6.9 42.21 176.1 0.350 0.19 0.06 200 12 0.0063 15.12 4001500983 0.49 40 16.9 0.315 0.03 0 50 2 0.01 1 2.3801501000 39.2 40.75 318.9 0.310 1.09 1.48 2,400 25 0.0009 54 16501501190 14.2 42.3 144.9 0.315 0.5 0.35 3,800 100 0.002 760 21.101501500 0.001 40.75 1.1 0.323 0 0 10 1 0.067 0.67 0.701501900 1.25 43.2 28.5 0.323 0.2 0.06 1,200 12 0.008 115.2 401502000 8 42.44 103.1 0.325 0.48 0.16 3,,000 70 0.0038 798 2501502500 91.5 41.31 854.7 0.320 4.07 2.86 4,500 10 0.0007 31.5 17301502550 0.56 40.2 27.8 0.330 0.21 0.06 50 2 0.05 5 3.101502670 0.98 43.1 45.1 0.350 0.13 0 500 8 0.0111 44.4 6.301502899 0.75 40.5 48.5 0.360 0.35 0 500 8 0.0077 30.8 4.501505500 3.2 42.85 101.7 0.305 0.33 0.13 500 15 0.005 37.5 2901507100 0.4 41.5 16.7 0.310 0.18 0.06 1,100 14 0.02 308 4.58
30 Low Flow of Streams in the Susquehanna River Basin of New York Table 4. Watershed properties compiled for regression analysis of low flow in the Susquehanna River basin of New York. [Column-heading terms in capital letters are acronyms for these properties used in regression equations] Watershed or station number (from table 3) Area of surficial sand and gravel (square miles) Mean annual precipitation (inches) Mean annual runoff (cubic feet per second) Ratio of August– October runoff to mean annual runoff Area of wetlands (square miles) bordered mostly by Dimensions of sand and gravel aquifer (feet) at measurement station Stream gradient at measurement station (dimensionless) Underflow factor (width × thickness × slope) (feet squared) Forested area (square miles) Till Sand and gravel Width Thickness STATION SGAREA MAP MAQ RUNRATIO LKSWTL LKSWSD WIDTH THICK SLOPE UNDER1 FOREST 01507470 0.46 41 11.4 0.315 0.41 0.11 250 5 0.025 31.25 4.1 01507500 4.7 41.93 138.4 0.315 1.57 0.77 2,000 25 0.0049 245 48 01507975 0.03 44.1 4.9 0.280 0 0 100 5 0.0222 11.1 2.5 01508000 0.06 43.15 5.3 0.275 0 0 10 1 0.0154 0.154 2.7 01508500 0.2 43.03 12.0 0.280 0 0 500 10 0.0174 87 1.4 01508803 22.2 41.2 116.9 0.278 0.02 2.58 5,000 40 0.0011 220 126.15 01508803 23.9 41.1 120.0 0.278 0.02 2.59 5,000 40 0.0011 220 126.97 01509300 0.67 43 19.1 0.310 0 0 250 8 0.0133 26.6 2 01510000 21.3 43.17 261.8 0.295 0.45 0.49 3,600 70 0.0026 655.2 64 01512780 2 36 10.9 0.340 0.01 0.27 4,000 55 0.0008 176 13.32 01512797 1 37 36.7 0.330 0.21 0.01 10 1 0.0063 0.063 12.5

01513190 0.33 36 15.3 0.340 0.05 0 10 1 0.01 0.1 5.801513280 0.1 36.2 5.0 0.340 0.01 0 50 2 0.02 2 1.0101513829 0.7 36.8 25.8 0.340 0.12 0 50 3 0.0086 1.29 7.701513840 0.4 38.5 12.3 0.340 0.02 0 100 2 0.0214 4.28 301513862 0.15 41.3 9.5 0.315 0.01 0 100 2 0.02 4 1.501514000 23.8 39.7 282.1 0.330 0.2 0.3 3,200 20 0.0027 172.8 9501514298 0.33 35.4 10.4 0.327 0.01 0 350 8 0.01 28 2.201514663 2.8 35.4 10.3 0.323 0 0.32 1,900 20 0.0015 57 18.4501514820 0.05 36.8 5.4 0.340 0.04 0 10 1 0.0235 0.235 11.5801514839 0.11 37.9 9.4 0.345 0 0 10 1 0.0154 0.154 13.1201515580 0.07 32.9 4.9 0.310 0 0 200 7 0.0166 23.24 14.4801515850 0.12 35.9 6.5 0.328 0 0 200 3 0.0375 22.5 12.1301520520 0.1 32 8.9 0.280 0.03 0 10 1 0.02 0.2 13.2401520990 0.83 35.2 25.8 0.275 0.07 0 800 10 0.0083 66.4 113.61
Regression Analysis 31

Table 4. Watershed properties compiled for regression analysis of low flow in the Susquehanna River basin of New York.[Column-heading terms in capital letters are acronyms for these properties used in regression equations]

Watershed

or station 

number 

(from 

table 3) 

Area of 

surficial 

sand and 

gravel 

(square miles)

Mean 

annual 

precipitation 

(inches)

Mean 

annual 

runoff

(cubic feet 

per second)

Ratio of 

August–

October 

runoff to 

mean annual 

runoff

Area of wetlands 

(square miles) 

bordered mostly by

Dimensions of sand and 

gravel aquifer (feet) at 

measurement station

Stream gradient 

at measurement 

station 

(dimensionless)

Underflow 

factor 

(width 

× thickness 

× slope) 

(feet squared)

Forested 

area 

(square miles)

Till Sand and gravel Width Thickness

STATION SGAREA MAP MAQ RUNRATIO LKSWTL LKSWSD WIDTH THICK SLOPE UNDER1 FOREST

01521500 2.9 35.29 36.7 0.272 0.07 0.01 450 10 0.009 40.5 116.8601521610 0.88 33.4 17.8 0.270 0.02 0 10 1 0.0118 0.118 14.8401522300 3.2 36.3 21.8 0.273 0.06 0.01 1,700 45 0.0111 849.15 17.2701522500 2.4 35.16 32.6 0.272 0.06 0 400 20 0.0077 61.6 116.4901523500 9.5 34.3 65.3 0.272 0.12 0.21 700 12 0.0057 47.88 129.9501524500 24.3 32.2 68.2 0.272 0.08 0.71 3,300 25 0.0011 90.75 127.301524500 30.5 32.5 144.1 0.272 0.23 0.72 3,300 25 0.0011 90.75 165.4801524550 0.12 32.7 5.4 0.268 0 0 10 1 0.0125 0.125 11.6501525750 0.47 31.3 8.6 0.272 0.07 0 100 2 0.0133 2.66 12.0101525800 0.33 31.7 6.9 0.275 0 0 150 2 0.0125 3.75 11.9401526000 7.1 31.17 102.2 0.272 0.21 0 1,500 10 0.0054 81 129.1701526495 0.07 32.1 4.9 0.285 0.01 0 100 5 0.0333 16.65 13.9801526980 0.14 35.1 5.5 0.269 0 0 300 8 0.0143 34.32 11.8601527000 14.8 33.81 57.0 0.271 0 1.79 4,800 80 0.0026 998.4 116.4301527450 2.92 34.2 10.3 0.268 0.02 0.17 50 2 0.025 2.5 12.9201527600 4.84 33.6 19.3 0.268 0.1 0.18 100 2 0.0111 2.22 14.5801528000 6.7 35 78.7 0.268 0.57 0.15 2,600 20 0.0044 228.8 118.7501530240 0.01 32 3.6 0.300 0.01 0 50 1 0.05 2.5 12.3801530450 0.08 34.3 6.0 0.322 0 0 150 2 0.0166 4.98 12.401530500 16.8 34.35 87.6 0.322 0.02 0.14 9,000 16 0.0009 129.6 122

1 Forested area measured manually using an electronic digitizer; for other watersheds, area estimated by point-counter methods.
32 Low Flow of Streams in the Susquehanna River Basin of New York

regression equations developed in this study are likely to be 

applied to small watersheds or parts of large watersheds, so 

it seemed prudent to rely chiefly on data from watersheds of 

comparable size.

Area of surficial sand and gravel (SGAREA). The 

extent of surficial sand and gravel was inferred largely from 

topographic maps and county soils maps; the maps were 

augmented in some localities by well records (Randall, 1972) 

and examination of earth materials exposed in excavations 

and roadcuts. SGAREA includes deposits of glacial meltwater 

and deposits of postglacial streams in alluvial fans and flood 

plains. Small areas along the valley sides in some watersheds 

could not be classified with confidence as sand and gravel or 

as till; therefore, maximum and minimum plausible areas of 

sand and gravel were delineated and an intermediate value 

was selected for use in this study. The areas of sand and gravel 

reported in table 4 include any wetlands within the boundaries 

of the sand and gravel. 

Area of till (TLAREA). Till area was computed by 

subtracting the measured area of sand and gravel from the 

drainage area. Two watersheds, Fivemile Creek (01528000) 

and Newtown Creek (01530500, fig. 10), contain small 

areas of surficial silt and (or) clay that were deposited in 

late-deglacial lakes but not later capped by outwash and 

(or) alluvium; these areas were included with till in the 

regression analysis.

Mean Annual Precipitation (MAP). A value for each 

watershed was estimated by overlaying an outline of the 

watershed on contours of mean annual precipitation for 

1951–80 (fig. 3A). 

Mean Annual Runoff (MAQ). Values for long-term gaging 

stations were calculated from daily-flow records that had been 

adjusted to 1951–80, as explained by Randall (1996). Values 

for short-term gaging stations and partial-record stations 

were estimated by overlaying an outline of the watershed on 

contours of mean annual runoff for 1951-80 (fig. 3B).

Ratio of mean August–October runoff to mean annual 

runoff (RUNRATIO). A value for each watershed was 

estimated by interpolation of watershed location among the 

contours in figure 4, which denote the ratio of mean runoff 

from August through October to mean annual runoff, and are 

based on 1938–63 data from a few large watersheds.

Area of wetlands underlain by sand and gravel 

(LKSWSD) and by till (LKSWTL). Area of lakes and area 

of swamps shown on U.S. Geological Survey 7.5-minute 

topographic maps were measured separately, then aggregated 

as wetland areas for regression analysis. Wetlands mostly 

bordered by till were compiled separately from wetlands 

mostly bordered by sand and gravel. Where a large lake 

or swamp occupies the entire valley floor and is bordered 

upstream and downstream by stratified sand and gravel, but 

bordered on the sides mostly by till or bedrock, the entire area 

of that lake or swamp was included in the area of wetlands 

underlain by sand and gravel (LKSWSD), as well as in the 

area of surficial sand and gravel (SGAREA).

Width of sand and gravel at measurement station 

(WIDTH). The width of surficial sand and gravel was 

measured along a line perpendicular to the valley axis through 

the streamflow- measurement station.

Thickness of sand and gravel (THICK). The average 

saturated thickness of sand and gravel along the line used 

to measure width was estimated from well and test-boring 

records (where available) and interpretation of topographic 

maps. A minimum value of 1 foot was assigned where the 

stream is incised in bedrock or till; the maximum value 

allowed was 100 feet.

Stream gradient (SLOPE). The average stream gradient 

near the streamflow-measurement station was calculated from 

the topographic map by dividing the contour interval by the 

distance between successive contours where they intersect 

the stream, measured parallel to the valley axis. The stream 

gradient is presumed to be nearly identical to the downvalley 

component of the water-table gradient.

Underflow factor (UNDER1). This term was computed 

as the product of width of sand and gravel, thickness of sand 

and gravel, and stream gradient, and therefore encompasses all 

factors other than hydraulic conductivity that would control 

the rate of underflow downvalley through sand and gravel, 

according to Darcy’s Law.

Forested area (FOREST). Areas with green overprint on 

U.S. Geological Survey 7.5-minute topographic maps were 

considered to be forested. The total area of green overprint 

in each of 38 watersheds was measured manually using 

an electronic digitizer as part of this study. The remaining 

32 watersheds were assigned values previously compiled by 

Darmer (1970) or R.D. MacNish (U.S. Geological Survey, 

written commun., 1968), who counted whether forested or 

nonforested land lay beneath nodes of a grid placed over a 

map of the watershed. Results obtained from the two methods 

did not match closely, but agreed within 25 percent in 20 of 

24 watersheds where both methods were used. How well the 

topographic maps represent forested area during the period of 

study is uncertain, inasmuch as many farm fields or pastures 

in the Susquehanna River basin were abandoned and allowed 

to revert gradually to brush and trees between 1941 and 1971. 

Because most of the topographic maps used were produced 

in the 1950s and 1960s, however, they may represent nearly 

average conditions for 1941–71.

Format of Regression Equations 

Three equation formats were used during this study:

1. Low-flow indices in cubic feet per second as a function 

of watershed properties expressed in common units of 

measurement: for example, area in square miles, mean 

flow in cubic feet per second. With this format, large 

watersheds are more influential than small watersheds 

because the regression process selects an equation that 

minimizes estimation error measured in cubic feet 
Regression Analysis 33

per second. These equations are referred to herein as 

“standard-value equations.”

2. Low-flow indices in cubic feet per second per square mile 

as a function of measured values of watershed properties 

divided by watershed area (referred to as “per-square-mile 

equations”). With this format, all watersheds in the data 

set have equal weight regardless of size.

3. Logarithms of low-flow indices as a function of the 

logarithms of measured watershed properties (referred to 

as “logarithmic equations”). Logarithmic transformations 

have commonly been applied to data sets to generate 

an array of values that are normally distributed and 

also consistent with other assumptions on which most 

statistical tests of estimation accuracy are based.

Many equations were tested, 18 of which are presented 

in table 5 (at end of report), along with statistical measures of 

their predictive accuracy and integrity. Each is described on 

the following pages. The rationale for presenting these several 

equations is not to offer alternative options for estimation of 

low streamflow, but rather to demonstrate how incorporating 

particular explanatory variables or data manipulations affect 

predictive accuracy and integrity. Eight standard-value 

equations for estimation of 7Q10 are described first, then 

three per-square-mile equations and a logarithmic equation for 

estimation of 7Q10, and finally six equations for estimation of 

7Q2 or 90%FD.

Standard-Value Equations to Estimate 7-Day, 

10-Year Low Flows 

This section first demonstrates how the predictive 

accuracy of standard-value regression equations is improved 

by successively incorporating sand-and-gravel area, wetland 

area, and water availability, and then considers the effects of 

several alternative variables and data manipulations.

The first five equations demonstrate how predictive 

accuracy and statistical integrity are progressively improved 

by incorporating sand and gravel area, wetland area, and mean 

annual runoff (a measure of the amount of water available) as 

explanatory variables. Equations 6 to 8 illustrate the effects of 

three data manipulations that offer some promise for further 

improvement, although only equation 8 is of practical use 

at present.

Effect of Sand-and-Gravel Area and Wetland Area

Equation 1 (table 5, at end of report) indicates that 

area of sand and gravel is positively correlated with 7Q10 

low flow, and that it explains most of the variation in low 

flow. As explained earlier, the area of sand and gravel 

in each watershed, as compiled in table 4, includes any 

wetlands that are bordered and underlain by sand and gravel. 

Equation 2 removes these wetland areas from the total area 

underlain by sand and gravel, resulting in significantly 

better estimation of 7Q10 low flow. Equation 3 separates 

the two mechanisms whereby wetlands diminish 7Q10 low 

flow. The first independent variable in equation 3, SGAREA 

minus LKSWSD, accounts for the failure of precipitation 

on wetlands to contribute to the amount of recharge that 

is stored in sand and gravel, because the water table is 

virtually at land surface in wetlands. The second independent 

variable in equation 3, LKSWSD, accounts for the intense 

evapotranspiration in wetlands that directs to the atmosphere 

some groundwater that was recharged nearby–water that 

would have become streamflow if the wetlands were absent. 

The regression coefficient for LKSWSD in equation 3 is 

smaller than the coefficient for SGAREA-LKSWSD, which 

implies that evapotranspiration has a smaller negative effect 

on 7Q10 low flow than the lack of recharge. Figure 11 depicts 

the accuracy of 7Q10 estimates from equation 3.

Equation 4 incorporates the same watershed variables as 

equation 3, but is applied to a slightly smaller data set created 

by deleting five partial-record stations whose low-flow indices 

may have been imprecisely calculated. (The purpose of this 

deletion is explained farther on, in the section on per-squaremile equations.) Most statistical test results for equations 3 

and 4 are nearly identical.

One watershed has much larger low flow than the rest, 

as indicated in figure 11. That watershed, Unadilla River 

at Rockdale (01502500, fig. 10), has a drainage area of 

520 square miles, whereas all other watersheds drain less than 

200 square miles. The one large watershed was included in the 

data set because watershed properties for 343 of its 520 square 

miles had already been compiled to describe three smaller 

watersheds; therefore, the remaining 177 square miles were 

less than the 200-square-mile cutoff limit for data compilation. 

Unadilla River at Rockdale has the largest influence of 

any individual watershed on several of the standard-value 

equations, as indicated by the DFFITS statistic (table 5, 

column K), but it falls nearly on the trend of other watersheds 

in figure 11 (and similar graphs for other equations) and 

therefore is not unduly influential.

Effect of Amount of Water Available

Equation 5 is the best of many standard-value equations 

tested that incorporates mean annual runoff (MAQ) as an 

index of annual water input to a watershed. Mean annual 

runoff had a positive sign, as expected, when incorporated 

without modification in preliminary trial equations. Its 

significance was weak, however (the pr>t statistic in column 

H of table 5 (at end of report) was 0.05 or more) unless the 

equation also included till area, a term that was strongly 

collinear with mean annual runoff and that had a negative sign, 

which was illogical in that the contribution of groundwater to 

streams at 7Q10 low flow from upland till is small, but cannot 

be negative. (One such preliminary equation was presented 

by Randall and Johnson (1988, table 1).) Collinearity can be 

eliminated from some regression equations by subtracting 

a constant from a collinear independent variable, thereby 
34 Low Flow of Streams in the Susquehanna River Basin of New York

Line where estimated 7Q10

would equal calculated 7Q10

0

3.0

0 3.5

-0.5

0.5

1.0

1.5

2.0

2.5

3.5

0.5 1.0 1.5 2.0 2.5 3.0 0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45

7Q10 ESTIMATED FROM EQUATION 3,

IN CUBIC FEET PER SECOND

7Q10 CALCULATED FROM STREAMFLOW MEASUREMENTS,

IN CUBIC FEET PER SECOND

-5

Figure 11. Correlation of 7Q10 calculated from streamflow measurements with 7Q10 estimated using equation 3. 

Inset graph expands scale at lower left corner of main graph. All data and analyses pertain to the Susquehanna River 

basin in New York. 7Q10, annual lowest streamflow averaged over 7 consecutive days that has a 1 in 10 chance of not 

being exceeded in a given year. See table 5 (at end of report) for equation 3; terms therein are defined in the “Data 

Set” section of the report.

resetting the datum from which that variable is measured 

(D. Helsel, U.S. Geological Survey, written commun., 1988). 

To test this approach, the mean annual runoff in cubic feet 

per second from each watershed was divided by drainage 

area in square miles, to obtain values that ranged from 

0.90 to 1.85 cubic feet per second per square mile. Next, 

several arrays of 70 reset mean annual runoff values were 

generated by subtracting successively larger constants from 

the per-square-mile runoff value for each watershed, then 

multiplying the results by drainage area to convert back to 

units of cubic feet per second. Each data array thus generated 

was tested as an independent variable in a regression equation, 

along with area of sand and gravel, area of wetlands in sand 

and gravel, and till area. The collinear till-area term was 

eliminated (regression coefficient of zero) and the statistical 

indices reported in table 5 were optimized when the amount 

subtracted was 1.85 cubic feet per second per square mile, 

just large enough to convert the reset mean annual runoff 

term to values of zero or less for all watersheds. Therefore, 

this optimized term represents the spatial variation in mean 

annual water input per unit area, multiplied by drainage area to 

convert the term to units of cubic feet per second and with the 

datum shifted to place zero at one end of the array of values. 

Equation 5 (table 5) incorporates this term, and estimates 

7Q10 substantially better than equations 1 through 4. The 

regression coefficient for sand-and-gravel area in equation 5 

apparently represents groundwater discharge to streams per 

square mile of sand and gravel in localities where mean annual 

runoff is 1.85 cubic feet per second per square mile, and the 

mean annual runoff term in equation 5 serves to adjust the 

estimate of 7Q10 for each watershed downward to the extent 

that mean annual runoff from that watershed is less than 

1.85 cubic feet per second per square mile.

Equation 6 (table 5) is similar to equation 5, but the 

mean annual runoff term incorporates the ratio of mean 

August-through-October runoff to mean annual runoff in 

large watersheds (fig. 4). In effect, this modification converts 

the term to an estimate of seasonal August-through-October 

runoff. The datum was reset by the same mechanism used 

in equation 5, although the constant subtracted from the 

estimated values of watershed runoff is only 0.6 cubic foot 

per second per square mile because the magnitude of Augustthrough-October runoff is about one-third that of mean annual 

runoff. Nearly all statistical indices for equation 6 are slightly 

better than those for equation 5 (table 5). However, the same 

modification resulted in only insignificantly small statistical 

improvements in equations (described farther on) that estimate 

low flow per square mile–which probably means that only 

in some of the larger watersheds in the data set was low 

flow more closely correlated with estimated seasonal runoff 

than with annual runoff. Furthermore, as pointed out earlier, 

the reason for the spatial variation in the ratio of seasonal 
Regression Analysis 35

runoff to annual runoff depicted in figure 4 is uncertain, 

and the contours in figure 4 are not tightly controlled by the 

sparse data values, all from large watersheds. Accordingly, 

the use of figure 4 and equation 6 to estimate low flow is 

probably not warranted. Nevertheless, the statistical indices 

for equations 5 and 6 suggest that some measure of average 

seasonal amount of water available (computed as precipitation 

minus evapotranspiration rather than by interpolation among 

measured runoff values) might ultimately prove useful as an 

index of water input in regression analysis to estimate 7Q10.

Other Variables and Data Manipulations Tested

Equation 7 (table 5, at end of report) is the best of several 

equations formulated to test the hypothesis that low-flow yield 

from sand and gravel, and evapotranspiration from wetlands, 

may each be proportional to the product of the area of that 

watershed property multiplied by mean annual runoff per 

unit area. Several fractional-power transformations of mean 

annual runoff were tested, because such transformations can 

improve the fit of regression equations by making relations 

more linear and residual variations constant (Montgomery and 

Peck, 1982, p. 25). The 0.4 power transformation in equation 7 

implies that only a fraction of any increase in water input to a 

watershed translates to increased low-flow yield from sand and 

gravel and increased evapotranspiration loss from wetlands. 

The statistical tests of estimation accuracy of equation 7 are 

superior to those of equations 1 through 4 (table 5), again 

confirming that water input (as represented by mean annual 

runoff) significantly influences low flow, but these tests are 

inferior to those of equations 5 and 6.

Four additional watershed properties were tested during 

the development of standard-value equations 2 through 7, but 

were found to be insufficiently significant:

1. Till area. The low flow of streams in New England is best 

estimated by regression equations that include till area 

as well as sand-and-gravel area as explanatory variables 

(Cervione and others, 1982; Wandle and Randall, 

1994), even though these two variables are not mutually 

independent (their sum is equal to drainage area). The 

equations express low flow as the sum of a large yield 

per unit area of sand and gravel plus a much smaller 

yield per unit area of till, which is entirely consistent 

with conventional concepts of groundwater discharge 

to streams. None of the equations presented in table 5 

for estimating 7Q10 in cubic feet per second could be 

improved by including till area, however. This result 

seems to imply that groundwater discharge to streams 

from till-covered uplands in the Susquehanna River basin 

is negligible at 7Q10 low flow. Indeed, the low flows of 

upland tributaries in the Susquehanna River basin might 

be expected to be smaller than those of similar streams in 

New England, because the shale bedrock and silty clay 

tills derived from shale in the uplands of the Susquehanna 

River basin are likely to be less permeable than the 

metamorphic bedrock and coarser tills that predominate in 

the uplands of New England. Tributaries draining several 

square miles of upland in the Susquehanna River basin 

never completely cease flowing, however; small flows are 

present even during severe droughts where the channels 

are incised in till or bedrock (Randall, 1978, 1981). Most 

of the measurement sites on upland tributaries included 

in this data set are at such locations (Ku and others, 

1975, p. 37). Furthermore, detailed observations of the 

extent of the stream network in late summer in three 

small watersheds (Kirkwood, Mulholland, and Pumpelly 

Creeks, table 3) revealed several small springs that issued 

from bedrock or from sand lenses in till (unpublished data 

in project files at the U.S. Geological Survey, New York 

Water Science Center, Troy, N.Y.) Therefore, the low 

flows of these streams cannot be ascribed solely to the 

narrow bands of alluvial gravel, sand, and silt that border 

their channels. All upland streams in the Susquehanna 

River basin lose water where they flow across the 

stratified drift in major valleys (Ku and others, 1975, 

p. 14), and most go dry almost every summer within the 

major valleys. Therefore, 7Q10 low flows of the larger 

streams probably do not include the concurrent discharge 

from most of their upland tributaries, but instead consist 

almost entirely of groundwater discharged from sand and 

gravel in the major valleys (part of which was derived 

from earlier seepage losses from upland tributaries). 

These observations may explain the absence of till area 

as a significant explanatory variable in standard-value 

regression equations for estimating 7Q10. 

2. Wetlands in till. The area of wetlands in till proved 

significant in a few trial equations, but this variable, and 

the total area of wetlands in the watershed, generally 

were less significant than the area of wetlands in sand and 

gravel in regression equations. This result is consistent 

with the observation that many wetlands in till-mantled 

uplands are in headwater localities where streamflow 

often ceases in dry weather; hence, evapotranspiration 

from these wetlands cannot further decrease low flow.

3. Mean annual precipitation. This term proved to be less 

significant than mean annual runoff in regression analysis.

4. Forested area. Several studies (Weeks and Stangland, 

1971; Lewis, 1958; Trousdell and Hoover, 1955) have 

shown that evapotranspiration is greater from forested 

area than from comparably located grassland or cropland. 

No significant differences were detected in other studies, 

however (Hibbert, 1969; Schneider and Ayer, 1961). The 

FOREST term, compiled from U.S. Geological Survey 

topographic maps as described in the section “Watershed 

Properties,” did not significantly improve any equation in 

which it was tested.

Trimming the Data Set. Evaluation of the statistical 

integrity of equations 1 through 7, explained below, led to 

a decision to apply the best of these equations to a smaller 

data set that provided a more nearly normal distribution of 
36 Low Flow of Streams in the Susquehanna River Basin of New York

residuals. (Residuals are the differences between the observed 

values of the dependent variable and the values estimated 

by the regression equation.) One of the assumptions on 

which least-squares linear regression analysis is based is that 

residuals are normally distributed (Iman and Conover, 1983, 

p. 368). Residuals from equations 1 through 7 are not normally 

distributed, as indicated by the coefficient of correlation of 

residuals with normal scores (table 5, column L, at end of 

report; normal scores are defined in table 5 explanation). 

A correlation coefficient of 0.983 or greater is consistent 

with a normal distribution for a data set of 70 stations, at 

a significance (alpha) level of 0.05 (Looney and Gulledge, 

1985). The departure of residuals from a normal distribution 

is illustrated in figure 12 by the departure of data points 

from a straight line. If residuals are not normally distributed, 

the parametric statistical tests used to gauge the estimation 

accuracy of regression equations are not precisely valid 

(Ryan and others, 1985, p. 177). Therefore, the coefficient 

of determination and the standard error reported in table 

5 for equations 1 through 7 should be considered only 

approximately correct. 

A method of testing the slope of a regression (such as 

the relation between observed low-flow indices and lowflow indices estimated by regression equations) is explained 

by Iman and Conover (1983, p. 381). This nonparametric 

method, which is valid whether or not residuals are normally 

distributed, is based on correlation between the ranks of 

estimated low-flow indices and the ranks of the residuals. If 

the absolute value of the Spearman rank correlation coefficient 

is less than 0.235 (for 70 stations) or 0.244 (for 65 stations), 

the slope of the regression line is accepted as correct. 

Equations 5 through 7 easily meet this criterion, as indicated 

in the last column of table 5, as do several other equations 

described farther on.

Another assumption of least-squares linear regression is 

that the variance of the residuals is constant over the range of 

estimated values (Iman and Conover, 1983, p. 368). Casual 

examination of graphs in which low flows calculated from 

streamflow measurements are plotted against individual 

watershed properties (fig. 13) or against low flows estimated 

with a particular equation (fig. 11) suggests that this criterion 

may be met, in that departures of data points from the equality 

line or regression line seem to be of similar magnitude along 

most of the line. This is certainly true of the large watersheds, 

but the data set also includes many smaller watersheds, nearly 

all with flow measured at partial-record stations, that have 

small low flows and correspondingly small residuals. Because 

these many small watersheds with small residuals are clustered 

at one end of the array of low flows, the data set fails to meet 

a test for constant variance of residuals (Gary Tasker, U.S. 

Geological Survey, written commun., 1981), in which the 

values of the independent variables in a regression equation 

are correlated with the absolute values of residuals from the 

regression. For equations 1 through 7, the Spearman rank 

correlation coefficients for such correlations ranged from 0.45 

to 0.75, and the null hypothesis of no correlation was rejected 

at all significance levels.

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

NORMAL SCORE

RESIDUAL FROM EQUATION 5, IN CUBIC FEET PER SECOND

Figure 12. Distribution of residuals from equation 5. All points would fall on a straight line if their 

distribution were exactly normal. See table 5 (at end of report) for equation 5 and for explanation 

of normal scores.
Regression Analysis 37

Regression line

0

2

4

6

8

10

12

14

0 2 4

SGAREA-LKSWSD, IN SQUARE MILES

7Q10 CALCULATED FROM STREAMFLOW MEASUREMENTS,

IN CUBIC FEET PER SECOND

R = 0.991

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

1 3 5

A

Regression line

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

SGAREA, IN SQUARE MILES

90%FD CALCULATED FROM STREAMFLOW MEASUREMENTS,

IN CUBIC FEET PER SECOND

R = 0.980

1

0 10

-1

3

5

7

9

11

13

15

2 4 6 8 12 14

B

Figure 13. Correlation of low-flow indices calculated from streamflow measurements A, 7Q10 and, B, 90% FD, with 

selected watershed properties. Inset graph expands scale at lower left corner of main graph. All data and analyses 

pertain to the Susquehanna River basin in New York. 7Q10, annual lowest streamflow averaged over 7 consecutive 

days that has a 1 in 10 chance of not being exceeded in a given year; 90% FD, the flow that was equaled or exceeded 

90 percent of the time during the period of analysis; SGAREA, area of surficial sand and gravel, including any overlying 

lakes or swamps; LKSWSD, area of lakes and swamps underlain by sand and gravel; R, Pearson product-moment 

correlation coefficient
38 Low Flow of Streams in the Susquehanna River Basin of New York

The departure of standard-value equations from normal 

distribution and from constant variance of residuals was 

decreased greatly by deletion of 38 small watersheds from 

the data set. The remaining 32 watersheds include all longterm continuous-record gaging stations and all partial-record 

stations that represent watersheds larger than 30 square miles 

or watersheds in which more than 18 percent of the area is 

underlain by sand and gravel. Analysis of this smaller data 

set yielded equation 8 (table 5), which is similar to equation 5 

in that all variables and regression coefficients are the same–

probably because the large watersheds that predominate in 

the 32-station data set on which equation 8 is based include 

all 14 stations that are moderately influential in equation 5, as 

indicated by DFFITS values greater than 0.3. Mean watershed 

size is larger for equation 8 than for equation 5; therefore, 

standard error is also larger in cubic feet per second, but 

is smaller as a percentage of mean 7Q10. The distribution 

of residuals from equation 8 is normal, as evidenced by 

the correlation of residuals with normal scores (table 5, 

column L), which exceeds the minimum limit of 0.966 for 

normal distribution at the 5-percent significance level in a data 

set of 32 stations (Looney and Gulledge, 1985). The variance 

of residuals easily passes the test described in the previous 

paragraph at a 5-percent significance level. Therefore, 

equation 8 is conceptually and statistically acceptable, at least 

with respect to watersheds larger than about 30 square miles, 

which make up 72 percent of the data set. 

Per-Square-Mile Equations to Estimate 7-Day, 

10-Year Low Flows

The large watersheds were more influential than the more 

numerous small watersheds in the development of standardvalue equations 1 through 8 in table 5 (at end of report), 

but the chief practical application of regression equations 

is to estimate low flow from small ungaged watersheds, 

or small increments within larger watersheds between 

measurement sites and sites where an estimate of low flow 

is desired. Therefore, several equations were tested in which 

all variables were divided by watershed area to give equal 

weight to all watersheds, regardless of size. Three per-squaremile equations for estimating 7Q10 are presented in table 5 

(equations 9, 10, and 11). 

Comparison of Per-Square-Mile Equations with 

Standard-Value Equations

Some of the statistical indices of estimation accuracy 

(table 5, at end of report) computed by the regression program 

for the per-square-mile equations are not directly comparable 

to indices computed for the standard-value equations 

because the variables are scaled in different units. To permit 

quantitative comparison, each per-square-mile equation was 

converted to standard values, as follows: (1) each predicted 

value of low flow in cubic feet per second per square mile was 

multiplied by watershed area; then (2) the resulting estimated 

low flows in cubic feet per second were correlated with 

observed low flows in cubic feet per second. The statistical 

indices of estimation accuracy for this correlation are reported 

in parentheses in table 5.

 The statistical indices of estimation accuracy reported for 

equation 9 after conversion to standard values are similar to 

those reported for equation 2, in which standard values of the 

same variables were used directly in the regression. Therefore, 

per-square-mile equations seem to be at least comparable to 

standard-value equations in estimation accuracy, despite the 

different values of some statistical indices that result from 

different numerical expression of watershed properties.

Evaluation of the Data Set and Equations

Graphs in which 7Q10 low flow per square mile 

calculated from streamflow records is plotted against 7Q10 

estimated using equation 9 showed appreciable scatter 

(fig. 14). Two stations plot far from the trend of other data in 

figure 14 because the estimated low flows for these stations 

are much smaller than the calculated low flows. Both stations, 

Thomas Creek at Chenango Bridge and Castle Creek at 

Wallace, are partial-record stations on streams draining 

relatively small watersheds (about 9 square miles in area) that 

contain an unusually large proportion of sand and gravel. As 

might be expected, the DFFITS influence statistic shows these 

two watersheds to have greater influence on equation 9 than 

any other watersheds in the data set. Recalculation of 7Q10 

low flow for these two watersheds and remapping the surficial 

geology of Castle Creek watershed did not result in significant 

changes in the input data. A hypothesis that low flow per 

square mile of sand and gravel might be greater in small 

watersheds than in large ones was tested by mathematical 

manipulations of the input data, and rejected. A re-evaluation 

of the data set, explained in the following paragraphs, led to 

a decision to delete Thomas Creek, Castle Creek, and three 

other small watersheds. 

The graphical correlations used in previous studies 

to calculate low-flow indices at partial-record stations in 

the Susquehanna River basin were reviewed at the start of 

this study. Four stations, Butternut Creek near Garratsville 

(station 01501900), Muller Gulf Creek near Cuyler (station 

01507975), Thomas Creek at Chenango Bridge (station 

01512780), and Langford Creek at Van Etten (station 

01515850), were rated as having large scatter of data and 

rather poorly defined correlations, but were retained in the 

data set to ensure inclusion of a wide variety of watersheds. 

Imprecise calculation of low-flow indices for these stations 

may, however, explain why regression equations could not 

closely reproduce the indices for Thomas Creek, nor for 

Butternut Creek, which also departs from the general trend 

as illustrated in figure 14. Thomas Creek drains a broad 

valley that is filled with stratified drift, much like many broad 

valleys in the Susquehanna River basin except that it is not 

traversed by a major river, a condition present in only a few 

scattered localities (Randall and others, 1988, fig. 2; Reynolds 
Regression Analysis 39

and Brown, 1984; Randall, 1977). Consequently, the ratio of 

valley-floor width at the measurement site to watershed area 

is larger for Thomas Creek than for any other watershed in 

the data set, and one might expect underflow to constitute 

an unusually large fraction of the yield from Thomas Creek 

watershed. If this were the case, regression equations that 

ignore underflow would overestimate low streamflow 

for this watershed, and yet equation 9 does the opposite 

(fig. 14). Furthermore, this watershed had a large influence 

on regression equations that included a variable intended 

to represent underflow, causing other variables to have a 

sign opposite from what was expected and was achieved 

after deletion of this watershed from the data set. Either the 

7Q10 low flow calculated from correlation of streamflow 

measurements at Thomas Creek is too large, or underflow here 

is unusually small for unknown reasons.

The graphical correlation of measured flows at Castle 

Creek at Wallace (partial-record station 01527450) with 

concurrent flows at two nearby gaging stations exhibited 

less scatter than the correlations cited in the previous 

paragraph. Nevertheless, six flow measurements in Castle 

Creek spaced over 22 days in 1967 ranged from 4.29 to 

4.03 cubic feet per second, while daily flows on the same days 

at the nearby gaging stations ranged from 14 to 8.6 and from 

13 to 7.4 cubic feet per second. The much smaller fluctuation 

in the flow of Castle Creek implies a significant difference in 

rates or timing of recession that could lead to miscorrelation 

of the frequency of low flows. The watershed of Castle 

Creek (01527450, fig. 10) lies within a distinctive small 

upland terrane between the Cohocton and Canisteo Rivers 

in Steuben County, in which abundant stratified drift was 

deposited when a tongue of ice blocked the Cohocton valley 

at Bath (Randall, 1986b). The stratified drift was deposited as 

deltas in lakes graded to saddles on modern divides, but has 

been deeply incised by postglacial streams, which in some 

places have cut entirely through the stratified drift to till or 

bedrock. The incised stratified drift is mostly unsaturated, 

but springs and seeps near its base contribute to streamflow. 

Castle Creek and nearby Goff Creek are the only watersheds 

in the data set in which this type of terrane is prominent; in 

most upland watersheds, sand and gravel is limited to the 

alluvium on narrow valley floors. In New England, sand and 

gravel perched above stream grade on upland hillsides or 

capping fine-grained sediment in valleys apparently generates 

moderately greater low flows per square mile than coarsegrained stratified drift or alluvium on the floors of major 

valleys (Wandle and Randall, 1994, p. 24). Thus, the unusually 

large 7Q10 low flow per square mile calculated for Castle 

Creek might be an accurate representation of an uncommon 

upland terrane, or the result of an erroneous correlation of 

streams in which recession rates and timing differ.

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28

7Q10 ESTIMATED FROM EQUATION 9,

IN CUBIC FEET PER SECOND PER SQUARE MILE 

7Q10 CALCULATED FROM STREAMFLOW MEASUREMENTS,

IN CUBIC FEET PER SECOND PER SQUARE MILE

Long-term continuous-record streamgage

Partial-record station or short-term streamgage

Butternut Creek

at Garratsville

Thomas Creek

at Chenango Bridge

Castle Creek

at Wallace

estimated using equation 9. All data and analyses pertain to the Susquehanna River basin in New York. 7Q10, annual 

lowest streamflow averaged over 7 consecutive days that has a 1 in 10 chance of not being exceeded in a given year. 

See table 5 (at end of report) for equation 9; terms therein are defined in the “Data set” section of the report.

Figure 14. Correlation of 7Q10 per square mile calculated from streamflow measurements with 7Q10 per square mile 
40 Low Flow of Streams in the Susquehanna River Basin of New York

Accordingly, Castle Creek at Wallace and the four partialrecord stations for which low-flow correlations were poorly 

defined were deleted from the data set used for per-squaremile regression analysis. Equations 10 and 11 in table 5 (at 

end of report) are based on this smaller data set of 65 stations.

Three per-square-mile equations are presented in 

table 5. Equations 9 and 10 show that much of the variation 

in 7Q10 per square mile can be explained by variation in the 

percentage of watershed area underlain by surficial sand or 

gravel exclusive of wetlands; the regression coefficients differ 

because equation 9 is based on the full data set of 70 stations 

whereas equation 10 is based on the data set of 65 stations. 

The deletion of five small watersheds significantly improved 

the standard error expressed in cubic feet per second per 

square mile or in percent of mean cubic feet per second per 

square mile, and improved the statistical indices of influence 

and normality presented in columns J through M of table 5. 

After equation 10 is converted to cubic feet per second, 

however, the standard error is appreciably larger than those for 

equations 1 through 9 (columns D through F, table 5).

Equation 11 is the most sophisticated of the persquare-mile regression equations. All terms in equation 11 

are significant at the 0.01 level and have the expected sign; 

all statistical measures of estimation accuracy (table 5) are 

improved relative to equation 10. The relation appears to be 

Figure 15. Correlation of 7Q10 per square mile calculated from streamflow measurements 

with 7Q10 per square mile estimated using equation 11. All data and analyses pertain to the 

Susquehanna River basin in New York. 7Q10, annual lowest streamflow averaged over 7 

consecutive days that has a 1 in 10 chance of not being exceeded in a given year. See table 5 (at 

end of report) for equation 11; terms therein are defined in the “Data set” section of the report.

homoscedastic; that is, the spread of data appears relatively 

uniform throughout the range of values, as shown in figure 15. 

Residuals are normally distributed, as indicated by their 

correlation with normal scores (table 5, column L) and by the 

nearly straight array of data values in figure 16. The Variance 

Inflation Factor (table 5, column I) indicates the variables to 

be mutually independent, and the DFFITS statistic (table 5, 

column K) revealed influence to be widely distributed, with 

values for seven stations ranging from 0.78 to 0.91 but none 

higher, the lowest maximum of any 7Q10 equation in table 5. 

Low flows estimated with equation 11 and converted to cubic 

feet per second show no systematic departure from equality 

with observed values (fig. 17).

Equation 11 substantially underestimates the low flow of 

one of the watersheds deleted from the data set, Castle Creek 

at Wallace. Calculated 7Q10 for this station is 0.249 cubic 

foot per second per square mile (2.3 cubic feet per second), 

whereas equation 11 estimates a 7Q10 of 0.117 cubic foot 

per second per square mile (1.1 cubic feet per second). As 

explained earlier, this station lies within and may be typical 

of a small area in Steuben County where upland valleys are 

filled with stratified drift. Therefore, application of equation 

11 to upland watersheds in the towns of Howard and Fremont 

(fig. 10) that contain substantial areas of stratified drift may 

result in underestimation of low flow.

Line where estimated 7Q10

would equal calculated 7Q10

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

7Q10 ESTIMATED FROM EQUATION 11,

IN CUBIC FEET PER SECOND PER SQUARE MILE 

7Q10 CALCULATED FROM STREAMFLOW MEASUREMENTS,

IN CUBIC FEET PER SECOND PER SQUARE MILE
Regression Analysis 41

Figure 17. Correlation of 7Q10 calculated from streamflow measurements with 7Q10 converted to cubic feet per 

second from values estimated using equation 11. All data and analyses pertain to the Susquehanna River basin 

in New York. (7Q10, annual lowest flow averaged over 7 consecutive days that has a 1 in 10 chance of not being 

exceeded in any one year. See table 5 (at end of report) for equation 11 and conversion to cubic feet per second.

Figure 16. Distribution of residuals from equation 11. See table 5 (at end of report) for equation 

11 and for explanation of normal scores.

-3

-2

-1

0

1

2

3

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

NORMAL SCORE

RESIDUAL FROM EQUATION 11,

IN CUBIC FEET PER SECOND PER SQUARE MILE

Line where estimated 7Q10

would equal calculated 7Q10

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45

7Q10 ESTMATED FROM EQUATION 11,

AFTER CONVERSION TO CUBIC FEET PER SECOND 

7Q10 CALCULATED FROM STREAMFLOW MEASUREMENTS,

IN CUBIC FEET PER SECOND
42 Low Flow of Streams in the Susquehanna River Basin of New York

Effect of Underflow 

Equation 11 is the only equation in table 5 (at end of 

report) that includes an explanatory variable intended to 

represent underflow, although this variable (UNDER1) also 

proved significant at the 0.05 or 0.1 level in a few other 

per-square-mile equations tested during this investigation. 

Comparison of equation 10 with equation 11 (table 5) shows 

that mean annual runoff and underflow together produce only 

a modest improvement in the statistical tests of estimation 

accuracy and normality. Nevertheless, the fact that the 

UNDER1 term proved significant in equation 11 supports the 

hypothesis that underflow can be one of the principal causes 

of low-flow variation. The regression coefficient obtained for 

this term is also consistent with this hypothesis. UNDER1 

incorporates all the components of Darcy’s Law that are 

required for computation of underflow except hydraulic 

conductivity, and is scaled in units of feet squared [length 

(feet) × width (feet) of surficial sand and gravel × downvalley 

gradient (feet per foot)]. Therefore, the regression coefficient 

of the UNDER1/DAREA variable in equation 1l, 0.00059, 

must be scaled in units of hydraulic conductivity, feet per 

second, such that multiplication by UNDER1 (feet squared) 

and division by DAREA (miles squared) yields a number 

scaled in cubic feet per second per square mile, which is 

the unit in which the dependent variable in equation 11 is 

scaled. A hydraulic conductivity of 0.00059 foot per second 

(51 feet per day), which would be typical of medium-grained 

alluvial sand (fig. 8), is a plausible value for average hydraulic 

conductivity of surficial sand and gravel.

 The failure of underflow indices to prove significant 

in other equations may result from any or all of the 

following reasons:

1. The saturated thickness of surficial sand and gravel 

and (or) the downvalley water-table gradient at some 

measurement sites may be inaccurately estimated.

2. Differences from place to place in hydraulic conductivity 

of surficial sand and gravel may cause large variations 

in underflow, but were ignored in this study because no 

reliable means of estimating hydraulic conductivity at 

each measurement station was devised.

3. Underflow may be so small relative to 7Q10 at nearly all 

sites that it rarely diminishes low streamflow significantly.

Logarithmic Equations to Estimate 7-Day, 

10-Year Low Flows 

 Streamflow and watershed properties have been 

transformed into logarithms prior to regression analysis in 

many studies directed to estimation of 7Q10 or other indices 

of low or high streamflow. Logarithmic transformations 

were judged to be unsuitable and unnecessary in the 

present study, as explained in the next section. To verify 

this judgment, several logarithmic regression equations 

were developed; the best of these is included in table 5 (at 

end of report), and an evaluation of that equation confirms 

that it has serious limitations relative to standard-value and 

per-square-mile equations.

A Critique of the Rationale for Logarithmic Transformation

Logarithmic transformations were deemed unsuitable and 

unnecessary in this study for three reasons: (1) logarithmic 

formulations are inconsistent with the conceptual physical 

relations of some watershed properties; (2) logarithmic 

transformations require artificial adjustments to data 

values that degrade the integrity of the data set; and (3) the 

distribution of values in this data set were statistically 

adequate without transformation. These reasons are explained 

in the following paragraphs.

Conceptual physical relations. As explained earlier, low 

flow of streams in the glaciated Northeast is conceived to 

be the sum of large groundwater discharge per square mile 

from sand and gravel and much smaller discharge per square 

mile from till, augmented or decreased by spatial variation in 

annual or seasonal water input, and decreased by groundwater 

evapotranspiration from wetlands and by underflow. 

These relations could be plausibly expressed in equations 

conceptually formulated in several ways. The simplest concept 

is expressed by the following equation: 

7Q10 = a(area sand and gravel) + b(area till) + 

c(water input) – d(area wetlands) – e(underflow) (A)

where 

a, b, c, d, and e are regression coefficients.

Standard-value equations 1 through 6 (table 5, at end 

of report) and per-square-mile equations 9 through 11 are 

all variations on the general form of equation A. (The “area 

till” term in equation A did not prove significant in any of 

the equations in table 5 that estimate 7Q10, but appears in 

such equations for Connecticut (Cervione and others, 1982) 

and central New England (Wandle and Randall, 1994). An 

alternative formulation, also conceptually plausible and 

exemplified by equation 7 (table 5), is

7Q10 = a(area sand and gravel)(water input) + 

b(area till) (water input) –d(area wetlands)

(water input) –e(underflow) (B)

A conceptually plausible logarithmic formulation is

log(7Q10) = a log(area sand and gravel) + 

b log(water input) (C)

which is equivalent to

7Q10 = (area sand and gravel)

a (water input)b (D)
Regression Analysis 43

Equation D resembles equation B in that sand-andgravel area multiplied by water input is used to estimate low 

flow. The other watershed properties considered in equations 

A and B (till, wetlands, and underflow) cannot be plausibly 

incorporated as independent variables in a logarithmic 

equation, however. That is,

log(7Q10) = a log(area sand and gravel) + 

b log(water input) + c log(area till) + 

d log(wetland area) + e log(underflow) (E)

is equivalent to

7Q10 = (area sand and gravel)

a

 (water input)

b (till area)c

(wetland area)

d (underflow)e

 . (F)

Equation F is conceptually implausible because low flow 

should not be proportional to the product of sand-and-gravel 

area, till area, wetland area, and underflow.

Data Integrity. The data set for this investigation contains 

some zero values of watershed properties and a few values of 

low-flow indices that are virtually zero (0.001 cubic foot per 

second). Because zero cannot be expressed as a logarithm, 

and extremely small values are unduly influential, common 

practice is to substitute some small number for each zero 

value, or to add some small number to all values in the 

data set. During this investigation, 1.0 was added to each 

value of each independent and dependent variable tested 

(including variables derived as a sum or difference of 

individual watershed properties) before conversion to natural 

logarithms. Later, as a test, 0.1 was added instead of 1.0, and 

the magnitude of regression coefficients and the significance 

of watershed properties changed, as explained farther on. The 

sensitivity of logarithmic equations to such necessary but 

arbitrary adjustments was deemed undesirable.

Data Distribution. Riggs (1985, p. 84–85) gives two 

reasons for considering logarithmic transformations of 

variables prior to regression analysis: to achieve equal 

variation about the regression line over its entire length, and to 

linearize curved data distributions.

1. Equal variation about the regression line over its entire 

length. Plots of dependent against independent variables 

in some data sets show close grouping of points near 

the origin but increasingly wide scatter as data values 

increase, a condition known as heteroscedasticity (Iman 

and Conover, 1983, p. 369). Logarithmic transformations 

tend to compress large values and expand small values, 

thereby producing a more nearly equal distribution of 

variances along the regression line. However, plots of 

low-flow indices in this data set against individual or 

combined watershed properties (for example, figures 11, 

13, 15, and 17) depict a range of scatter that is similar 

all along the regression line. A quantitative test for 

heteroscedasticity was applied to the seven equations 

for which residuals are normally distributed (table 

5, column L). For each equation, the variance of the 

residuals from the larger half of the low flows (in cubic 

feet per second or in cubic feet per second per square 

mile) exceeded the variance of the residuals from the 

smaller half, thus confirming that some heteroscedasticity 

exists, but F-tests (Iman and Conover, 1983, p. 274–276) 

indicated that the variances were statistically equivalent at 

the 0.05 significance level for four of the seven equations.

2. Curved data distributions. Plots of the low-flow indices 

in this data set against watershed properties (fig. 13) show 

very little curvature, as do plots of these indices against 

estimated low flows (figs. 11, 15). 

Accordingly, application of logarithmic transformations 

to this data set was judged to have little theoretical 

justification. Male and Ogawa (1982, p. 29–30) also concluded 

from analysis of streams in Massachusetts that “short-duration 

low flows may be better described by a linear model than by a 

log-linear model.”

Comparison of Logarithmic Equations with 

Standard-Value Equations

The statistical measures of estimation accuracy for 

logarithmic equations are not directly comparable to those for 

standard-value equations because they are scaled in different 

units. To permit comparison, the following detransformation 

procedure was undertaken: 

1. The logarithm of 7Q10 estimated for each station was 

converted to cubic feet per second.

2. Each value of estimated 7Q10 in cubic feet per 

second was multiplied by e0.5(mean square error) to correct for 

detransformation bias, as recommended by Choquette 

(1988) and Miller (1984).

3. The constant 1.0 that had been added to each value 

of 7Q10 in preparation for logarithmic regression 

was subtracted.

4. Standard error in cubic feet per second was computed 

from the following equation, then divided by the mean 

value of 7Q10 for the data set to obtain standard error in 

percent of the mean; results are given (in parentheses) in 

table 5 (at end of report) for logarithmic equation 12.

where

SE = Standard Error,

n = number of stations in the data set,

v = number of independent variables in the 

regression equation,

a = observed value of 7Q10 at a station, and

p = detransformed estimated value of 7Q10 at 

that station. 

Equation 12, the only logarithmic equation in table 5, 

had the highest statistical measures of estimation accuracy of 

any logarithmic equation tested. Its two independent variables 

are normally distributed at an alpha level of 0.01 or higher 

SE a p n v n= − [{ ( ) }/ ( ) − − ] 2 .

1

0 5 Σ 1
44 Low Flow of Streams in the Susquehanna River Basin of New York

(fig. 18), highly significant (pr>t=< 0.0001, table 5), and 

independent (VIF = 1.1, table 5). No station had a DFFITS 

influence statistic greater than 1.0 (table 5), and residuals 

are normally distributed at the 0.01 alpha level (table 5, 

column L). Like the standard-value and per-square-mile 

equations described earlier, equation 12 is consistent with the 

concept that low flow is positively correlated with surficial 

sand-and-gravel area and with amount of water available. 

Nevertheless, equation 12 has several serious limitations:

1. Wetland area was subtracted from the total area underlain 

by sand and gravel in formulating equation 12, as in 

equations 2 through 11. However, the estimation accuracy 

of equations 3 through 8 and 11 was enhanced by also 

including wetland area underlain by sand and gravel as a 

separate independent variable, whose negative regression 

coefficient was inferred to calibrate the loss of water 

through evapotranspiration. This refinement could not be 

logically incorporated in a logarithmic equation.

2. An index of underflow also could not be logically 

incorporated as an independent variable in a logarithmic 

equation. Its effect could be accounted for in logarithmic 

equations if underflow could be independently computed 

at each station by Darcy’s Law, then added to 7Q10 low 

flow. This approach would not easily accommodate the 

iterative testing and weighting inherent in regression 

analysis, however, and was not considered feasible in this 

study because information on hydraulic conductivity at 

measurement stations was lacking.

3. The statistical measures of estimation accuracy for 

equation 12 after conversion to cubic feet per second 

are larger (less accurate) than those for other equations 

in table 5. Equation 12 systematically underestimates 

7Q10 low flow in cubic feet per second at most stations, 

especially the larger values (fig. 19). 

4. The addition of constant values to each variable, as 

required for logarithmic analysis, strongly influenced 

the results of the regression. An alternative test in which 

0.1 rather than 1.0 was added to all data values yielded 

a logarithmic regression equation with much worse 

statistical indices of estimation accuracy and normality, 

although the conversion of that equation to cubic feet 

per second yielded low-flow estimates that were slightly 

closer to observed low flows. Most important, the 

low flows estimated with this alternative test differed 

substantially from those estimated with equation 12, 

solely because of the difference in magnitude of the 

arbitrary constant added to measured values to facilitate 

computation. Addition of constants to individual 

watershed properties such as SGAREA and LKSWSD 

rather than to combined terms such as (SGAREA–

LKSWSD) or (SGAREA – LKSWSD)/DAREA also 

changed the results substantially. A computational 

technique that requires arbitrary data distortions that 

significantly alter the results was deemed unreliable.

Equations to Estimate 7-Day, 2-Year Low Flow 

and 90-Percent Flow Duration

Watershed properties were also tested in regression 

analyses to estimate 7Q2 and 90%FD, which respectively 

average 1.7 and 2.2 times 7Q10 (table 3). In general, the 

watershed properties that proved most influential were the 

same properties that proved influential in the 7Q10 analysis. 

At these larger low flows, till area also had a significant 

positive effect, although the regression coefficients indicate 

that groundwater discharge to streams per square mile of 

till-mantled uplands was only a small percentage of the 

discharge per square mile of sand and gravel (equations 

13–16, table 5, at end of report). Substitution of the term till 

area minus area of wetlands in till for till area had almost no 

effect on regression coefficients nor on any of the statistical 

indices for these equations in table 5. Area of wetlands in sand 

and gravel, which had proved significant as an independent 

variable in estimating 7Q10, was not significant in any 7Q2 or 

90%FD equation, which implies that the loss of water through 

evapotranspiration from wetlands is too small to significantly 

diminish flows that are about twice as large as 7Q10.

Standard-value equations developed from the full data 

set of 70 stations to estimate 7Q2 and 90%FD resemble 

their 7Q10 counterparts in that residuals are not normally 

distributed, as indicated by the correlation with normal 

scores for equations 13 and 15 (table 5, column L). 

Furthermore, the one watershed in the data set that is larger 

than 200 square miles has a greater influence on regression 

equations for 7Q2 and 90%FD than on the 7Q10 equations. 

Values of the influence statistic DFFITS for this watershed 

from equations 13 and 15 ranged from 6.1 to 4.3. These 

statistical weaknesses were rectified by deleting 38 small 

watersheds (as in equation 8) and the one unusually large 

watershed; 31 stations remained. These deletions did not 

change the relative significance of watershed properties 

(compare equations 13 and 14, or 15 and 16, in table 5) 

and changed estimated values of low flow from individual 

watersheds only moderately (the median difference in 

estimated 7Q2 between equations 13 and 14 was only 

0.34 cubic foot per second, or 6 percent). Equations 14 and 

16 have normally distributed residuals and fairly low variance 

inflation. Therefore, these equations are suitable for estimating 

7Q2 and 90%FD in moderately large unregulated watersheds. 

Per-square-mile equations 17 and 18 are appropriate 

for estimating 7Q2 and 90%FD in watersheds or segments 

of watersheds smaller than about 30 square miles. These 

equations are based on data sets dominated by small 

watersheds; they also have smaller standard errors in cubic 

feet per second than equations 14 and 16, and better statistical 

indices of normality, influence, significance of variables, 

and collinearity (variance inflation). Like equations 10 and 

11, however, equations 17 and 18 may underestimate low 

flows from a small area in Steuben County, between Bath 

and Hornell, where upland watersheds contain abundant 

stratified drift. Equations 17 and 18 incorporate the product 
Regression Analysis 45

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-3 -2.5 -2 -1.5 -1 -0.5

NORMAL SCORE

Ln[(SGAREA-LKSWSD+1.0) / (DAREA+1.0)]

R = 0.994

A

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7

NORMAL SCORE

Ln [MAQ + 1.0]

R = 0.979

B

gravel exclusive of wetlands, and B, mean annual runoff. See table 5 at end of report for equation 

12, and for explanation of normal scores. (Ln, natural logarithm; SGAREA, area of surficial sand 

and gravel, including any overlying lakes or swamps; LKSWSD, area of lakes and swamps 

underlain by sand and gravel; DAREA, drainage area; MAQ, mean annual runoff; R = Pearson 

product-moment correlation coefficient)

Figure 18. Distribution of data values for independent variables in equation 12: A, sand and 
46 Low Flow of Streams in the Susquehanna River Basin of New York

Line where estimated 7Q10

would equal calculated 7Q10

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40 45

7Q10 ESTIMATED FROM EQUATION 12

AFTER DETRANSFORMATION 

7Q10 CALCULATED FROM STREAMFLOW MEASUREMENTS,

IN CUBIC FEET PER SECOND

Figure 19. Correlation of 7Q10 calculated from streamflow measurements with 7Q10 converted to units of cubic feet per 

second from logarithmic values estimated using equation 12. All data and analyses pertain to the Susquehanna River basin 

in New York. (7Q10, annual lowest streamflow averaged over 7 consecutive days that has a 1 in 10 chance of not being 

exceeded in a given year. See table 5 (at end of report) for equation 12 and detransformation to cubic feet per second.)

of sand-and-gravel area (exclusive of wetlands) multiplied by 

mean annual runoff per square mile, which proved better than 

sand-and-gravel area alone in estimating 7Q2 or 90%FD per 

square mile.

Suggested Methods for Estimating 

Low-Flow Characteristics at 

Ungaged Sites

The most accurate and reliable way to define the low 

flow of a stream at a particular site is to measure the full range 

of flow by constructing and operating a streamflow-gaging 

station at that site. The accuracy of the calculated low-flow 

characteristics will increase with the length of the record. Less 

exact estimates of low-flow characteristics can be obtained 

by making 10 or more streamflow measurements at the site of 

interest that represent different periods of streamflow recession 

and that include a range of low flows, then correlating 

those measurements with concurrent flows at one or more 

continuous-record streamflow-gaging stations. For best results, 

the gaging station(s) should be on a nearby unregulated 

stream that drains a watershed similar in size and geology to 

the watershed of interest. Procedures for estimating low-flow 

characteristics at a site by correlating an array of individual 

streamflow measurements made at that site with daily 

mean flows at nearby continuous-record gaging stations are 

explained by Cervione and others (1982), Hardison and Moss 

(1972), Matalas and Jacobs (1964), Riggs (1972), Searcy 

(1959), and Stedinger and Thomas (1985). Use of correlation 

procedures in this study was facilitated by the availability 

of records from the many gaging stations that were operated 

on unregulated streams in and near the Susquehanna River 

basin prior to 1972; fewer gaging stations have been operated 

during subsequent years (through 2010), which may limit the 

reliability of such correlation procedures in some localities.

Streamflow measurements had been made at more than 

150 sites in the Susquehanna River basin of New York as of 

1975. Site locations and low-flow characteristics computed for 

these sites are given by Eissler (1979) and by Ku and others 

(1975). Additional sites are established from time to time by 

the U.S. Geological Survey. Daily mean streamflows at gaging 

stations and individual flow measurements at other sites have 

been published in annual water-data reports (U.S. Geological 

Survey, 1951–2005); information can also be obtained from 

a U.S. Geological Survey Website (http://ny.water.usgs.gov). 

Low-flow characteristics computed for a site generally can 

be extrapolated to a site of interest nearby along the same 

stream in proportion to drainage area, but if either the site of 

interest or the previously established site happens to be where 

a tributary enters or crosses the valley of a larger stream, persquare-mile extrapolation is not advisable because low flows 

may vary greatly over short distances in this geologic setting 

(Ku and others, 1975; Randall, 1978). 
Suggested Methods for Estimating Low-Flow Characteristics at Ungaged Sites 47

The regional regression equations developed in this 

study can be used to estimate low flows at sites where no 

measurements have been made nearby and there is no prospect 

of obtaining measurements over a suitable range of low 

flow. These equations can be applied to entire unregulated 

watersheds. If a site of interest is on a stream where lowflow indices have been computed for a station some distance 

upstream or downstream, however, application of the regional 

equations to the intervening area would allow any unique 

natural condition or regulation that might affect low flow 

from the remainder of the watershed to be preserved in the 

final estimate. 

The primary objective of the regression analysis in this 

investigation was to identify and quantify the watershed 

properties that control low streamflow, but several regression 

equations presented in table 5 (at end of report) are useful 

tools that can be applied throughout the Susquehanna River 

basin of New York to estimate three commonly used indices of 

low flow for the period 1941–70:

7Q10 (annual lowest streamflow averaged over 7 consecutive 

days that has a 1 in 10 chance of not being exceeded in a 

given year);

7Q2 (annual lowest streamflow averaged over 7 consecutive 

days that has a 1 in 2 chance of not being exceeded in a 

given year);

90%FD (flow equaled or exceeded 90 percent of the time 

during the 30-year period of analysis).

The six equations listed below are suggested for practical 

application. In these equations, areas are in square miles, 

length and width in feet, gradient in feet per foot, and 

mean annual runoff in cubic feet per second. Abbreviations 

for independent variables are defined in the section 

“Watershed properties.”

Watersheds Larger Than 30 Square Miles

7Q10 = 0.047 + 0.51 (SGAREA - LKSWSD) - 0.42 

(LKSWSD) + 0.029 [(MAQ/DAREA) – 1.85](DAREA)

[Equation 8 (table 5, at end of report); standard error 

0.58 cubic foot per second, median percent error of estimate 

22 percent]

7Q2 = 0.412 + 0.70 (SGAREA - LKSWSD) + 0.019 

(TLAREA) + 0.059 [(MAQ/DAREA)-1.85](DAREA)

[Equation 14 (table 5); standard error 1.40 cubic feet per 

second, median percent error of estimate 23 percent ]

90%FD = 0.58 + 0.83 (SGAREA - LKSWSD) + 0.052 

(TLAREA) + 0.106 [(MAQ/DAREA) – 1.85] (DAREA)

[Equation 16 (table 5); standard error 1.95 cubic feet per 

second, median percent error of estimate 23 percent]

Watersheds Smaller Than 30 Square Miles

7Q10 = DAREA { 0.0042 

+ 0.46 [(SGAREA – LKSWSD) / DAREA]

- 0.40 (LKSWSD/DAREA) 

+ 0.021 [(MAQ/DAREA) – 1.85] 

- 0.00059 (WIDTH)(THICK)(SLOPE) / DAREA}

[Equation 11 (table 5, at end of report); standard error 0.0115 

cubic foot per second per square mile, median percent error of 

estimate 36 percent ]

7Q2 = DAREA { - 0.00069 

+ 0.475 [(SGAREA – LKSWSD) (MAQ/DAREA)/DAREA]}

[Equation 17 (table 5); standard error 0.018 cubic foot per 

second per square mile, median percent error of estimate 

29 percent]

90%FD = DAREA { 0.026 

+ 0.56 [(SGAREA-LKSWSD)(MAQ / DAREA) / DAREA] 

+ 0.034 [(MAQ / DAREA) – 1.85]}

[Equation 18 (table 5), standard error 0.022 cubic foot per 

second per square mile, median percent error of estimate 

31 percent] 

The independent variables required by the foregoing 

equations can be compiled largely, but not entirely, from 

published sources. Drainage area, area of wetlands, and 

stream gradient at sites of interest can be measured from U.S. 

Geological Survey topographic maps. Mean annual runoff 

can be estimated from figure 3 of this report, or from maps in 

U.S. Geological Survey Open-File Report 96–395 (Randall, 

1996) or Professional Paper 1415–C (Kontis and others, 

2004), available at http://ny.water.usgs.gov/publications. Area 

of surficial sand and gravel, and width of sand and gravel at 

sites of interest, may be compiled from county soils maps (for 

example, Giddings and others, 1971); or from unpublished 

1:24,000-scale reconnaissance maps of surficial geology in 

the files of the New York Geological Survey at Albany, New 

York; or from a series of U.S. Geological Survey aquifer 

map reports at 1:24,000 scale that cover several reaches of 

major valleys in the Susquehanna River basin and are cited 

(with locations) at http://ny.water.usgs.gov/projects/bgag/

aquifer.maps/maps.html. A map at 1:38,400 scale of surficial 

geology in Fivemile Creek watershed was prepared during 

this investigation (Randall, 1986b). Geologic and hydrologic 

maps at 1:250,000 scale (for example, Cadwell and Dineen, 

1987; Miller, 1988) are not sufficiently detailed for this 

purpose. Distinct boundaries are commonly evident on 

topographic maps where terraces and flood plains underlain 

by surficial sand and gravel on valley floors abut steep valley 

walls underlain by till and bedrock. Therefore, delineation of 

the extent of surficial sand and gravel from examination of 

1:24,000-scale topographic maps and soils maps are likely 

to be reasonably accurate and reproducible. Thickness of 
48 Low Flow of Streams in the Susquehanna River Basin of New York

sand and gravel at sites of interest can be estimated from 

the same sources; pertinent information for sites in broad 

valleys may also be available from well or test-boring records 

(for example, Randall, 1972) or aquifer-thickness maps 

(MacNish and Randall, 1982, or more detailed studies of some 

localities). For a few small watersheds that contain little 

sand and gravel, some equations will predict negative low 

flows, which should be treated as zero flow. The equations for 

watersheds smaller than 30 square miles may underestimate 

low flows from upland watersheds in the towns of Howard and 

Fremont (between the Cohocton and Canisteo Rivers, fig. 10) 

that contain appreciable sand and gravel.

Summary

Low flow of streams in the Susquehanna River basin of 

New York increases with the amount of water available for 

runoff annually (precipitation minus evapotranspiration) and 

with the spatial extent of surficial sand and gravel within the 

watershed. Low flow is decreased by evapotranspiration from 

wetlands interspersed with the surficial sand and gravel, and 

by underflow beneath the valley floor that bypasses stream 

channels. Spatial variation in the properties of till and bedrock 

and in watershed relief or slope appears to have little effect on 

low flow within this region.

The goal of this study was to identify hydrologic 

processes or properties that control groundwater discharge 

to streams during periods of low streamflow, and to test and 

quantify their importance through multiple regression analysis. 

Such information is likely to improve our ability to understand 

and reliably model aquifers, runoff, and particularly the 

magnitude and quality of low streamflow. A data set was 

assembled that consists of low-flow characteristics at 

23 long-term continuous-record streamflow-gaging stations 

and 47 short-term or partial-record stations or combinations 

thereof, along with measurements of several dimensions 

and properties of the corresponding watersheds. Regression 

analyses based on this data set led to an array of equations 

that estimate 7-day mean low flows with 2-year and 10-year 

recurrence intervals, and flow equaled or exceeded 90 percent 

of the time, from 1941 through 1971. These equations 

estimate low-flow characteristics as a function of area of 

sand and gravel, area of wetlands overlying sand and gravel, 

area of till-mantled uplands, mean annual runoff, and, in a 

few equations, aquifer properties associated with underflow. 

At the lowest low flow evaluated (7-day low flow with 

10-year recurrence interval), groundwater discharge from 

till becomes insignificantly small, and evapotranspiration 

from wetlands consumes a larger fraction of groundwater 

discharge to streams than at larger low flows. Equations that 

estimate low flow in cubic feet per second and are based 

on a subset of 31 or 32 watersheds, mostly between 30 and 

200 square miles in size, have standard errors between 16 and 

21 percent of the mean values of low-flow characteristics. 

Equations that estimate low flow in cubic feet per second per 

square mile and are based on a subset of 65 watersheds have 

somewhat larger percent standard errors but estimate more 

accurately the low-flow characteristics in watersheds smaller 

than 30 square miles. These equations may underestimate 

low flows from the rare upland watersheds that contain 

extensive surficial sand and gravel, however. Logarithmic 

equations cannot express some inferred conceptual relations 

and are sensitive to the values of arbitrary constants added 

to avoid zero values of variables. Nevertheless, logarithmic 

equations indicate low flows to be a function of the same 

watershed properties that proved most significant in the 

absence of logarithmic transformation. Six equations deemed 

conceptually and statistically sound are suggested for practical 

application in estimating low flows at ungaged sites.

Variations in hydraulic conductivity of stratified 

valley-fill deposits are in principle a powerful but nonlinear 

influence on low flow, as confirmed by multiple simulations 

conducted with a cross-sectional model of a hypothetical 

aquifer. Groundwater discharge to streams is small where 

hydraulic conductivity of the valley fill is small (comparable 

to that of till) because the rate of groundwater flow is small 

and because the water table may be so close to land surface 

that much of the precipitation cannot infiltrate or is lost to 

evapotranspiration. Groundwater discharge is also small 

during periods of low flow where hydraulic conductivity is 

large, especially in narrow valleys, because the water table 

drains quickly down to stream grade, long before periods 

of low flow. Therefore, fine-sandy deltas, thin sand aquifers 

overlying fine-grained lacustrine sediment, and mostly 

unsaturated large stratified deposits on upland hillsides are 

likely to contribute more groundwater to streams per unit 

area during periods of low flow than thick, highly permeable 

aquifers in valleys or coarse alluvium beneath flood palins. 

This concept could not be tested by regression analysis, but 

some support is provided by one watershed in the data set 

(Castle Creek at Wallace) that is atypical in that it contains 

abundant stratified drift on upland hillsides and in upland 

valleys; low flow per unit area from this watershed was 

calculated to be considerably larger than that from many 

watersheds in which stratified sand and gravel are mostly 

below stream grade in major valleys. A parameter designed 

to represent underflow beneath streamflow-measurement 

sites incorporated the width, thickness, and downvalley 

gradient of surficial sand and gravel, but not its hydraulic 

conductivity. The reasonable accuracy of regression equations 

that incorporate this parameter suggests that, although the 

hydraulic conductivity of stratified drift commonly varies 

widely over distances of a few hundred feet, this variability 

may approach some uniform average value on a scale of entire 

valley systems or watersheds.
References Cited 49

Acknowledgments

The computation of low-flow indices for gaging stations 

in the Susquehanna River basin for 1941–71 was done chiefly 

by Charles Barnes of the U.S. Geological Survey.

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52 Low Flow of Streams in the Susquehanna River Basin of New York

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Table 5 53

Table 5. Regression equations tested for estimating low flow of streams in the Susquehanna River basin of New York.[Terms in column headings are explained following the table; acronyms for variables are defined in the “Data Set” section of the report; a dash (--) indicates value could not be computed for that equation; parentheses enclose values that were recomputed after equations were converted to cubic feet per second; ft3/s, cubic feet per second; <, less than; R2, coefficient of determination]

Equation 

number

(A)

Number 

of 

stations

(B)

Tests of accuracy of equation in 

estimating low flow

Tests of independent 

variables

Tests of influence

of data values Tests related to normality

Adjusted 

R2

(C)

Standard error Median 

percent 

error of 

estimate

(G)

Largest 

pr>t

(H)

Largest 

varianceinflation 

factor 

(VIF)

(I)

Prediction 

sum of 

squares

(PRESS)

(J)

Maximum 

absolute 

value of 

DFFITS

(K)

Correlation 

of residuals 

with normal 

scores

(L)

Nonparametric 

test 

for slope

(M)

Cubic feet 

per second

(D)

Cubic feet 

per second 

per square 

mile

(E)

Percent of 

mean of 

dependent 

variable

(F)

1 7Q10 = -0.219 + 0.43 (SGAREA)

70 0.973 0.97 -- 37.4 95 <0.0001 1.0 88 4.2 0.826 -0.248

2 7Q10 = -0.194 + 0.45 (SGAREA - LKSWSD)

70 0.982 0.80 -- 30.7 80 <0.0001 1.0 57 3.8 0.882 -0.139

3 7Q10 = -0.165 + 0.46 (SGAREA-LKSWSD) - 0.30 (LKSWSD)

70 0.983 0.765 -- 29.4 68 0.0096 1.4 57 3.5 0.892 -0.193

4 7Q10 = -0.223 + 0.46 (SGAREA-LKSWSD) - 0.30 (LKSWSD) 

65 0.984 0.76 -- 28.0 96 0.0098 1.4 52 3.4 0.880 -0.264

5 7Q10 = 0.050 + 0.51 (SGAREA-LKSWSD) - 0.42 (LKSWSD) + 0.029 [(MAQ / DAREA)-1.85] DAREA

70 0.990 0.58 -- 22.3 55 <0.0001 2.9 27 1.4 0.926 -0.006

6 7Q10 = 0.054 + 0.51 (SGAREA-LKSWSD) - 0.39 (LKSWSD) +0.083 [{(MAQ)(RUNRATIO) / DAREA} -0.6] DAREA

70 0.992 0.54 -- 20.9 51 <0.0001 2.8 25 2.7 0.940 -0.105

7 7Q10 = -0.079 + 0.39(MAQ/DAREA)0.4 (SGAREA-LKSWSD) - 0.29(MAQ / DAREA)0.4 (LKSWSD)

70 0.986 0.70 -- 27.0 65 0.0009 1.4 41 2.8 0.916 -0.073

8 7Q10 = 0.047 + 0.51 (SGAREA-LKSWSD) -0.42 (LKSWSD) + 0.029 [(MAQ / DAREA) - 1.85 ] DAREA

32 0.987 0.88 -- 15.9 23 0.0041 2.2 27 1.1 0.978 0.089

9 7Q10/DAREA = -0.0074 + 0.48 [(SGAREA-LKSWSD) / DAREA] 

70 0.768 -- 0.023 65.7 52 <0.0001 1.0 0.041 2.2 0.865 -0.254

Equation 9 converted to ft3/s: 7Q10 = DAREA (equation above)

(0.83) (30.7) (52)

10 7Q10/DAREA = -0.0048 + 0.41 [(SGAREA-LKSWSD) / DAREA)]

65 0.867 -- 0.0135 44.7 52 <0.0001 1.0 0.013 0.9 0.983 -0.019

Equation 10 converted to ft3/s: 7Q10 = DAREA (equation above) 

(1.22) (44.7) (52)
54 Low Flow of Streams in the Susquehanna River Basin of New York Table 5. Regression equations tested for estimating low flow of streams in the Susquehanna River basin of New York. [Terms in column headings are explained following the table; acronyms for variables are defined in the “Data Set” section of the report; a dash (--) indicates value could not be computed for that equation; parentheses enclose values that were recomputed after equations were converted to cubic feet per second; ft3/s, cubic feet per second; <, less than; R2, coefficient of determination] Equation number (A) Number of stations (B) Tests of accuracy of equation in estimating low flow Tests of independent variables Tests of influence of data values Tests related to normality Adjusted R2 (C) Standard error Median percent error of estimate (G) Largest pr>t (H) Largest variance- inflation factor (VIF) (I) Prediction sum of squares (PRESS) (J) Maximum absolute value of DFFITS (K) Correlation of residuals with normal scores (L) Non- parametric test for slope (M) Cubic feet per second (D) Cubic feet per second per square mile (E) Percent of mean of dependent variable (F) 11 7Q10/DAREA = 0.0042 + 0.46 [(SGAREA-LKSWSD) / DAREA] - 0.40 (LKSWSD / DAREA) + 0.021[(MAQ / DAREA) - 1.85] - 0.00059(UNDER1 / DAREA) 65 0.903 -- 0.0115 38.1 36 0.0127 1.6 0.010 0.9 0.994 -0.193 Equation ll converted to ft3/s: 7Q10 = DAREA (equation above) (0.63) (23.4) (36) 12** Ln(7Q10+1.0) = 0.173 + 0.996 Ln[{(SGAREA - LKSWSD)+1.0} / (DAREA+1.0)] + 0.722 Ln(MAQ + 1.0) 70 0.929 -- 0.249* 36.0 74 <0.0001 1.1 4.6 1.0 0.973 -0.204 Equation 12 converted to ft3/s: 7Q10 = 1.19 C (equation above) - 1.0 (1.94) (74.8) (104) 13 7Q2 = -0.028 +0.74 (SGAREA-LKSWSD) + 0.025 (TLAREA) + 0.067 [(MAQ / DAREA) − 1.85] DAREA 70 0.990 1.01 -- 22.7 42 <0.0001 8.2 109 5.1 0.903 -0.183 14 7Q2 = 0.412 + 0.70 (SGAREA-LKSWSD) + 0.019 (TLAREA) + 0.059 [(MAQ / DAREA) − 1.85] DAREA

31 0.957 1.40 -- 19.0 23 0.032 2.4 74 1.6 0.993 0.117

15 90%FD = -0.013 + 0.876 (SGAREA-LKSWSD) + 0.059 (TLAREA) + 0.114 [(MAQ / DAREA) - 1.85] DAREA

70 0.989 1.35 -- 23.3 30 <0.0001 8.2 184 3.9 0.897 -0.154

16. 90%FD = 0.58 + 0.83 (SGAREA-LKSWSD) + 0.052(TLAREA) + 0.106 [(MAQ / DAREA) - 1.85] DAREA

31 0.951 1.95 -- 20.3 23 0.0001 2.4 149 1.6 0.982 0.154

17 7Q2/DAREA= -0.00069 +0.475 [(SGAREA-LKSWSD)(MAQ / DAREA) / DAREA]

65 0.898 -- 0.018 32.7 29 <0.0001 1.0 0.022 0.8 0.987 -0.173

Equation 17 converted to ft3/s: 7Q2 = DAREA (equation above)

(1.24) (26.6) (29)

18 90%FD/DAREA= 0.026 +0.56 [(SGAREA-LKSWSD)(MAQ / DAREA) / DAREA] +0.034[(MAQ / DAREA)-1.85] 

65 0.897 -- 0.022 28.9 31 0.0007 1.0 0.033 0.8 0.993 -0.081

Equation 18 converted to ft3/s: 90%FD = DAREA (equation above)

(1.54) (25.2) (31)

 *For equation 12 only: standard error is in natural logarithm units, not in cubic feet per second per square mile.

**Ln = natural logarithm (base e). For conversion to ft3/s: 1.19 = e0.173; C = detransformation bias correction (Miller, 1984) = e(0.5 mean square error) = e0.03105 = 1.03154
Explanation of Table 5 55

Explanation of Columns in Table 5

Tests of Accuracy of Equation in Estimating Low Flow (columns C–G)

Adjusted R2 (coefficient of determination)

Adjusted R2 can range from 0 to 1 and shows the fraction of the variation in the dependent variable (low flow) that is 

explained by the regression equation. It is adjusted for the number of variables in the equation and the number of observations 

according to the following formula (terms are defined below):

Adjusted R2 = 1 – (SSE / TSS)(n−1/n−p)

Standard error

Standard error is expressed in units of the dependent variable (cubic feet per second, cubic feet per second per square mile, 

or natural logarithm of cubic feet per second), and in percent of the mean of the dependent variable. It is computed as follows:

SE = [∑ (qo − qe)

2

 / (n − p -1) ]0.5

%SE = SE / (∑ qo / n )

where:

n = number of observations (measurement sites)

p = number of independent variables in the equation

qo = observed low flow

qe = low flow estimated by regression equation

TSS = total sum of squares

SSE = sum of squares of error [∑ (qo − qe)

2

 ]

Median percent error of estimate

Percent error of estimate = 100 [(qo − qe) / qo ]

The median value is selected from the array of absolute values of percent error of estimate for stations in the data set.

For each equation that estimates low flow in cubic feet per second per square mile, or in the natural logarithm of low flow 

plus 1.0 cubic feet per second, the estimate for each station was converted to low flow in cubic feet per second. From the array 

of low-flow estimates thus generated and the corresponding array of observed low flows in cubic feet per second, standard error 

in cubic feet per second, standard error in percent of the mean of the observed values, and median percent error of estimate were 

computed as described above. The resulting values are given in parentheses in table 5.
56 Low Flow of Streams in the Susquehanna River Basin of New York

Tests of Independent Variables (columns H, I)

pr>t

This statistic was computed for each independent variable in each regression equation. It expresses the probability that 

the true coefficient for that variable might actually be zero rather than the value computed by the regression program (in which 

case the variable would not be significant and should not be included in the equation). The pr>t statistic is typically assessed as 

follows (SAS Institute, Inc., online help):

< 0.01 Strong evidence that the variable is significant,

0.01 – 0.05 Appreciable evidence that the variable is significant,

0.05 – 0.1 Weak evidence that the variable is significant.

(Technically, the regression program computes the Student’s t statistic, which is the variable coefficient divided by its 

standard error; then the program calculates the probability of obtaining by chance alone a t statistic greater in absolute value 

than what was computed, if the true coefficient were zero. This calculation assumes the data to have an approximately normal 

distribution.) In table 5, the largest (least significant) pr>t statistic for any independent variable in each equation is listed. The 

pr>t statistics for all other independent variables in each equation indicated strong significance. The pr>t statistic was also 

computed for the intercept term in each equation, and commonly indicated a lesser significance for that term.

Variance Inflation Factor

Variance Inflation Factor was computed for each independent variable. It measures the degree to which that variable 

is correlated with the other independent variables in the equation. It is computed as 1/(1-R2), where R2 is the coefficient of 

determination from a regression of that variable on all other independent variables (Marquardt, 1970). Variables that are totally 

uncorrelated with (orthogonal to) one another, which is ideal, will have a Variance Inflation Factor of 1.0. A Variance Inflation 

Factor near or exceeding 10 (which implies R2 > 0.9) indicates that variable to be closely correlated (collinear) with one or more 

other independent variables. As collinearity increases, the magnitudes of regression coefficients become less stable and less 

representative of the true influence of those watershed variables on low flow.

Tests of Influence of Data Values (columns J, K)

Prediction sum of squares (PRESS) 

A “prediction residual” can be calculated for each streamflow station as follows: first remove that station from the data set, 

then estimate low flow for that station from a regression analysis that includes only the remaining stations; the difference (error) 

between that estimate and the observed low flow constitutes the “prediction residual”, ei, for that station. The PRESS statistic 

can then be calculated as the sum of the squared prediction residuals: PRESS = ∑ n

i = 1 ei

2 

.

Low values of this statistic imply that the regression relation includes few outliers that fall far from the average regression 

line (and, therefore, generate large squared prediction residuals). The PRESS statistic is scaled in units of the dependent 

variable; therefore, comparisons between equations scaled in different units (cubic feet per second, cubic feet per second per 

square mile, or logarithmic units) are not meaningful.

Maximum DFFITS

The DFFITS statistic is computed for each station in the data set for each equation. It is a scaled measure of the change in 

the estimated value of the dependent variable for that station that results from regenerating the equation after deleting data for 

that station from the data set. The maximum absolute value thus computed is listed in table 5 for each equation; the larger the 

value, the more influence a single station has within its neighborhood in the data array.
Explanation of Table 5 57

Tests Related to Normality (columns L, M)

Correlation of residuals with normal scores

One of the assumptions on which least-squares regression analysis is based is that residuals or errors (observed minus 

estimated low flows) have a normal distribution. Normal scores for a particular set of data values are an array of the same 

number of values that have exactly a normal distribution. If the distribution of values in the data set is nearly normal, a plot 

of the data values against normal scores (each ranked in order from large to small) would approach a straight line, and the 

coefficient of correlation of the data values with the normal scores would approach 1. This column reports the coefficients of 

Pearson product-moment correlations between the residuals and normal scores computed from the ranks of the residuals, using 

PROC RANK, NORMAL=BLOM option, and PROC CORR (SAS Institute, Inc., 1990). If the correlation coefficient is greater 

than 0.983 for regressions with 70 stations, 0.981 for 65 stations, or 0.965 for 31 stations, the distribution of residuals is accepted 

as normal at the 0.05 alpha (5 percent significance) level (Looney and Gulledge, 1985).

Nonparametric test for slope

This column reports Spearman correlation coefficients (rho) between ranks of residuals and ranks of estimated values. If the 

absolute value of the coefficient is less than 0.235 (for 70 stations), 0.244 (for 65 stations), or 0.349 (for 32 stations), the slope or 

fit of the regression equation is accepted as correct at the alpha level of 0.025. This test is valid whether or not the residuals are 

normally distributed (Iman and Conover, 1983, p. 342, 381).
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Randall—Low Flow of Streams in the Susquehanna River Basin of New York—Scientific Investigations Report 2010–5063