Prepared in cooperation with the Bradford County Conservation District

Comparison of Regression Relations of Bankfull Discharge 

and Channel Geometry for the Glaciated and Nonglaciated 

Settings of Pennsylvania and Southern New York

Scientific Investigations Report 2018–5066

U.S. Department of the Interior

U.S. Geological Survey
Cover. Glaciated geomorphology along the West Branch Lackawaxen near Aldenville, Pa. (U.S. Geological Survey streamflow gage 

01428750). Photograph by Paul L. O’Hara, Pleasant Mount, Pa.
Comparison of Regression Relations 

of Bankfull Discharge and Channel 

Geometry for the Glaciated and 

Nonglaciated Settings of Pennsylvania 

and Southern New York

By John W. Clune, Jeffrey J. Chaplin, and Kirk E. White

Prepared in cooperation with the Bradford County Conservation District

Scientific Investigations Report 2018–5066

U.S. Department of the Interior

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

RYAN K. ZINKE, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2018

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

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

Suggested citation:

Clune, J.W., Chaplin, J.J., and White, K.E., 2018, Comparison of regression relations of bankfull discharge and 

channel geometry for the glaciated and nonglaciated settings of Pennsylvania and southern New York: U.S. Geological 

Survey Scientific Investigations Report 2018–5066, 20 p., https://doi.org/10.3133/sir20185066.

ISSN 2328-0328 (online)
iii

Acknowledgments

This project was funded by the National Fish and Wildlife Foundation under a cooperative agreement with the Bradford County Conservation District (BCCD). The authors would like to thank 

Michael Lovegreen, Ian Lathrop, Catherine Yeakel, and Joseph Quatrini of BCCD for making this 

study possible. Sincere appreciation is extended to U.S. Geological Survey colleagues for the 

geomorphic assessments conducted by Scott Sorber and Kyle Ohnstad; report review by Tammy 

Zimmerman, Barry Baldigo, Peter Cinotto, and Christiane Mulvihill; and StreamStats analysis 

performed by Kernell Ries, Peter McCarthy, Katharine Kolb, Peter Steeves, Todd Koenig, Ryan 

Thompson, and Scott Hoffman.
iv

Contents

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

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

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

Purpose and Scope ..............................................................................................................................3

Description of Study Area ...................................................................................................................3

Methods...........................................................................................................................................................3

Regression Relations of Bankfull Discharge and Channel Geometry...................................................5

Limitations.......................................................................................................................................................9

Summary and Conclusions.........................................................................................................................10

References Cited..........................................................................................................................................11

Appendix 1.....................................................................................................................................................15

West Branch Lackawaxen River near Aldenville, PA...................................................................16

Tuscarora Creek above South Addison, NY ...................................................................................17

Towanda Creek near Franklindale, PA ............................................................................................18

Sugar Creek at West Burlington, PA................................................................................................19

Brodhead Creek near Analomink, PA..............................................................................................20
v

Figures

1. Photograph showing streambank erosion in the glaciated setting of Bradford 

County, Pennsylvania...................................................................................................................2

2. Map showing location of the noncarbonate and carbonate bedrock settings, 

maximum extent of Wisconsinan glaciation, and selected glaciated and 

unglaciated streamflow-gaging stations for regional curves development 

and comparison in Pennsylvania and southern New York ....................................................4

3. Graphs showing distribution of sites, drainage area, recurrence interval, bankfull 

discharge, cross-sectional area, mean depth and width for the glaciated and 

unglaciated settings of Pennsylvania and southern New York ............................................6

4. Graphs showing drainage area in relation to A, bankfull discharge, B, crosssectional area, C, width, and D, mean depth for the glaciated setting 

of Pennsylvania and southern New York..................................................................................7

5. Graphs showing drainage area in relation to A, bankfull discharge, B, crosssectional area, C, width, and D, mean depth for the noncarbonate glaciated 

and unglaciated settings of Pennsylvania and southern New York.....................................8

6. Graphs showing drainage area in relation to A, bankfull discharge, B, crosssectional area, C, width, and D, mean depth for the noncarbonate and carbonate 

settings for streams in Pennsylvania and selected areas of Maryland..............................9

7. Diagram showing geomorphic reference points of bankfull, active-channel, 

and depositional bar...................................................................................................................10

Tables

1. Channel characteristics of the 2016 geomorphic assessments for select 

streamflow-gaging stations in the glaciated setting of Pennsylvania and 

southern New York .......................................................................................................................5

2. Results of analysis of covariance (ANCOVA) test for differences in slope 

and intercept among glaciated and unglaciated noncarbonate settings 

of Pennsylvania and New York...................................................................................................8
vi

Conversion Factors

International System of Units to U.S. customary units

Multiply By To obtain

Length

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square meter (m2) 10.76 square foot (ft2) 

Volume

cubic meter (m3) 264.2 gallon (gal) 

cubic meter (m3) 35.31 cubic foot (ft3)

Flow rate

meter per second (m/s) 3.281 foot per second (ft/s) 

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

Datum

Vertical coordinate information is reference 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.
Comparison of Regression Relations of Bankfull Discharge 

and Channel Geometry for the Glaciated and Nonglaciated 

Settings of Pennsylvania and Southern New York

By John W. Clune, Jeffery J. Chaplin, and Kirk E. White

Abstract

Streambank erosion in areas of past glacial deposition has 

been shown to be a dominant source of sediment to streams. 

Water resource managers are faced with the challenge of 

developing long and short term (emergency) stream restoration efforts that rely on the most suitable channel geometry for 

project design. A geomorphic dataset of new (2016, n=5) and 

previous (1999–2006, n=96) estimates of bankfull discharge 

and channel dimensions at U.S. Geological Survey streamflow-gaging stations was compiled to present and contrast the 

glaciated and unglaciated noncarbonate settings of southern 

New York and Pennsylvania that included selected areas of 

Maryland. Empirical models were developed by using simple 

linear regressions that relate bankfull discharge and channel 

geometry to drainage area (regional curves). Significant relations (p<0.05) were able to explain variability with coefficient 

of determination (R2) values of 0.89 for bankfull discharge, 

0.94 for cross-sectional area, 0.87 for bankfull width, and 

0.83 for bankfull depth. These regression relations for the 

glaciated noncarbonate settings of northern Pennsylvania and 

southern New York were able to provide a slightly better fit 

than regional curve models developed previously for the entire 

noncarbonate region of Pennsylvania. Although, the analysis 

of covariance (ANCOVA) results for comparison between 

regression equations for the glaciated and unglaciated settings 

showed that except for the significant intercept of bankfull 

discharge versus drainage area (F=8.26, p-value<0.005), the 

regression equations are not significantly different between the 

glaciated and unglaciated setting of Pennsylvania and southern 

New York. Therefore, data stratification by glaciation does 

not improve regional curves relations developed previously 

for the noncarbonate (glaciated and unglaciated) and carbonate settings of Pennsylvania and Maryland. Further analysis 

that incorporates data stratification or multivariate approaches 

based on mean annual runoff, precipitation, slope, stream 

classification, or other relevant parameters may optimize the 

accuracy and utility of statewide models. The new estimates 

of bankfull discharge and channel dimensions at streamflowgaging sites and updated drainage areas from StreamStats 

were incorporated into previously developed regional curves 

to produce an updated set of regression relations of bankfull 

discharge and channel geometry for the noncarbonate and 

carbonate settings of Pennsylvania and Maryland. 

Introduction

The seventh leading cause of impairment to assessed 

streams and rivers in the Nation is sediment (U.S. Environmental Protection Agency, 2009). Historically, the major 

legacy sediment inputs to streams have resulted from deforestation, loss of beaver wetland habitat, and water-powered 

mill dams (Miller, 1986; Naiman and others, 1988; MüllerSchwarze and Sun, 2003; Walter and Merritts, 2008; Bain and 

others, 2012; James, 2013), but currently in the Chesapeake 

Bay watershed for example, the greatest amount of sediment 

is generated from urban and agricultural settings (Gellis and 

other, 2009; Brakebill and others, 2010). Although upland erosion can be a major contributor to soil loss (Clune and others, 

2010), streambank erosion has also been shown to be a significant source of suspended sediment in streams (Gellis and others, 2004; Gellis and others, 2015). In particular, streambank 

erosion in areas of past glacial deposition has been shown to 

be a dominant source of sediment to streams (fig. 1) (Gordon, 1979; Ashmore, 1993; Sekely and others, 2002; Nagle 

and others, 2007). Sediment, and particles that adhere to its 

surfaces (for example, particles containing phosphorus), can 

cause downstream damage to aquatic biota, water treatment 

facilities, reservoir capacity, and estuaries (Dearmont and others, 1998; Henley and others, 2000; Langland, 2015). Restoring unstable stream morphology in the continental United 

States costs more than $1 billion per year (Bernhardt, 2005).

Management strategies to minimize and reduce streambank erosion in order to maintain stable and biologically 

productive (unimpaired) watersheds include watershed 
2 Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York

Figure 1. Streambank erosion in the glaciated setting of Bradford County, Pennsylvania. Photograph taken by Joseph Quatrini, 

Bradford County Conservation District. 

planning, storm water controls, riparian buffers, and streambank stabilization (Federal Interagency Stream Restoration 

Working Group, 1998). Streambank stabilization techniques 

include traditional armoring and natural stream design (Rosgen, 1997; Bernard and others, 2007). Designs for stream 

restoration efforts often rely on established relations between 

stream channel dimensions and the surrounding drainage area 

(Rosgen, 1996). Stream channel dimensions are shaped by a 

dominant, reoccurring streamflow that transports and deposits 

most of the sediment during the point when a stream becomes 

full and begins to overtop its banks (Leopold and others, 

1964; Leopold, 1992). This bankfull discharge often occurs 

at a relative frequency of every 1–2 years to form the channel 

morphology (Wolman and Miller, 1960; Dunne and Leopold, 1978). Bankfull discharge and channel dimensions for a 

given stream can be estimated by using established regression 

equations that relate bankfull discharge and channel geometry 

to drainage area, and serve as ancillary information to aid the 

design of stream restoration projects (Rosgen, 1996). 

Early studies used regression equations to develop sediment discharge relations for a range of drainage areas (Leopold and Maddock, 1953). More specific relations have been 

developed to create regional curves that aid states with stream 

classification and assessment, as well as design of restoration 

projects (Somerville, 2010; U.S. Department of Agriculture, 

2017). In New York, regional curves were developed based 

on eight hydrologic regions for which only region 3 differed 

significantly (p-value<0.05) from the other regions (Lumia, 

1991; Mulvihill and others, 2005, 2007, 2009; Westergard 

and others, 2005; Mulvihill and Baldigo, 2007). Despite more 

accurate regional curves based on other covariable models (for 

example, mean annual runoff), data stratification by hydroregions that were derived with determinate, unbiased, and reproducible procedures has shown the most advantage to resource 

managers by providing better overall coefficients of determination (R2

) and standard errors of estimate (SEE) (Mulvihill and 

Baldigo, 2012). Regional curves for Pennsylvania were first 

published for the Piedmont Physiographic Province (White, 

2001; Cinotto, 2003) region and later combined with the all 

physiographic provinces within the state to produce significant regression relations for the carbonate and noncarbonate 

settings (Chaplin, 2005). National approaches to optimize 

regional curves continue to use a combination of data stratification methods (Keaton and others, 2005) and have found that 

considering precipitation and runoff as explanatory variables 

can improve bankfull relations (Wilkerson and others, 2014). 
Methods 3

The research described in this report builds upon the previous national and regional curve development approaches by 

assessing whether regression relations of bankfull discharge 

and channel geometry stratified by glaciation further minimizes variability for Pennsylvania and southern New York. 

The results of this study will serve the needs of water resource 

managers in Pennsylvania that are faced with the challenge of 

developing long and short term (emergency) stream restoration 

efforts and need to utilize natural stream design techniques that 

rely on the most suitable channel geometry (Bradford County 

Conservation District, 2013). This study was conducted by 

the U.S. Geological Survey (USGS) in cooperation with the 

Bradford County Conservation District as part of an effort to 

provide an evaluation of the most reliable model estimates 

and predictions of bankfull discharge and channel geometry 

to aid classification, monitoring, and restoration efforts of 

streams in the glaciated areas of Pennsylvania and southern 

New York. This research is part of a larger effort to incorporate 

regional curves for Pennsylvania into the USGS StreamStats 

web application, which provides online streamflow and basin 

characteristics for ungaged sites and can be used by stream 

rehabilitation personnel to provide publicly accessible and 

reproducible estimates of stream channel dimensions (Ries III 

and others, 2004, 2008).

Purpose and Scope

The purpose of this report is to (1) present regional 

relations of bankfull discharge and channel dimensions with 

drainage area for the glaciated settings of Pennsylvania and 

southern New York, and (2) compare these relations with the 

unglaciated setting of Pennsylvania. These objectives were 

met by analyzing geomorphic data previously collected along 

stream reaches from 96 streamflow-gaging stations between 

1999 and 2006 in Pennsylvania and New York, and from five 

additional sites in Pennsylvania during the summer of 2016. A 

synthesized geomorphic dataset of the new and previous estimates of bankfull discharge, width, depth, and cross-sectional 

area was used to present and contrast the glaciated and unglaciated settings of Pennsylvania and southern New York.

Description of Study Area

The study area is located in the northeast region of the 

United States, within the states of Pennsylvania and New 

York. The area is underlain by consolidated carbonate and 

noncarbonate bedrock. Unconsolidated sediment (till, drift, 

and so forth) was deposited during the advance and retreat 

of four major periods of past glaciation (Shultz, 1999). The 

youngest glaciation (Wisconsinan) provides the most observable characteristics of the depositional and erosional features 

of the previous periods (fig. 2; Shultz, 1999).

The topography is relatively mountainous with elevations from 626 to 2,437 feet above NAVD 88 (U.S. Geological 

Survey, 2013a). Stream channel slopes can range from high 

gradient headwaters to lowland valleys. The local climate and 

hydrology provide a wet season of increased precipitation and 

runoff from March through May with low streamflow periods 

during June through September (Shultz, 1999). Intermediate 

storms provide peak discharge events from localized thunderstorms and regional hurricanes during the summer and fall 

months. Stream morphology ranges from steep incised valleys 

with limited overbank flow to lower valley areas with wider 

floodplains and more frequent overbank flow. Transportation 

corridors often follow stream channels and restrict natural 

meandering and floodplain areas.

Methods

Site selection and data collection for five new sites was 

performed during the summer of 2016 and incorporated into 

older datasets for regional curves of Pennsylvania and New 

York in order to compare noncarbonate glaciated and unglaciated settings. The site selection, data collection, and data 

analysis are described in the following section. 

The selection of five new streamflow-gaging stations 

for use in channel-geometry regional-curve development was 

based on the following filtering criteria adapted from Chaplin 

(2005):

1. Glaciation—The watershed of the streamflow-gaging 

station must be located within the extent of the Wisconsinan glaciation.

2. Land use—The watershed of the streamflow-gaging station must not be subject to mining that alters surface and 

(or) underground hydrology, and land cover classified as 

urban development can be no greater than 20 percent.

3. Period of record—The station has to have a period of 

record of at least 7 years.

4. Streamflow regulation—No greater than 20 percent of 

the streamflow to the gaging station is subject to regulation by reservoirs, dams, and so forth.

5. Accessibility—The stream must be wadeable (drainage 

area<215 square miles [mi2]) in order to perform the 

field geomorphic survey.

A list of streamflow-gaging stations and attribute data 

for the glaciated setting of New York and Pennsylvania was 

retrieved from the USGS Automated Data Processing System 

(ADAPS; U.S. Geological Survey, 2013b). A spatial analysis 

was performed to estimate the percentage of mining, urban 

development, and streamflow regulation within the watershed 

A subset of eligible sites was produced based on the filtering 

criteria described above and reconnaissance was performed 

for each site to assess the extent of any stream channelization 

or armoring that would provide restrictions to overbank flow 

into the floodplain and obscure bankfull indicators. This final 
4 Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York

0

0

40 80

20 40 60 80 MILES

KILOMETERS

44°

42°

40°

80° 78° 76° 74° 72°

ATLANTIC OCEAN

LAKE ERIE

LAKE

HURON

LAKE ONTARIO

NEW YORK

PENNSYLVANIA

EXPLANATION

Geology

Noncarbonate bedrock

Carbonate bedrock

Wisconsinan glaciation

Glaciated

Unglaciated

New site

Streamflow gaging stations

Base from U.S. Bureau of the Census digital data, 2000 and Statistics Canada, 2006

1:100,000 Albers Equal-Area Conic projection: Standard Parallels 40° N and 42° N,

Central Meridian -78° W, Latitude of Origin 39°

Figure 2. Location of the noncarbonate and carbonate bedrock settings, maximum extent of Wisconsinan glaciation, and 

selected glaciated and unglaciated streamflow-gaging stations for regional curves development and comparison in Pennsylvania 

and southern New York. Generalized carbonate rock dataset used for Pennsylvania StreamStats application (https://pa.water.usgs.

gov/infodata/gis/carbonate_metadata.htm).

selection process produced five new sites for incorporation 

into the regional-curve analysis (table 1). 

At each site, bankfull indicators were identified and a 

reach section established (Leopold and others, 1964; Harrelson 

and others, 1994). A longitudinal profile of each reach and two 

cross sections along riffles were surveyed by using standard 

USGS survey methods to capture the topographic features of 

bankfull, thalweg, and other changes of slopes (U.S. Geological Survey, 1966; Harrelson and others, 1994). Transect pebble 

counts were performed at each cross section to determine the 

particle size distribution (Wolman, 1954; Harrelson and others, 

1994). Additional information collected at each site included a 

field sketch, photographs, and field notes. 

The longitudinal profile, cross-sectional surveys, and 

pebble count data were used to calculate and plot the bankfull 

discharge and stream channel dimensions. The bankfull discharge, cross-sectional area, width, mean depth, value of the 

particle diameter at 50 percent in the cumulative distribution 

(D50), and geomorphic parameters were determined for each 

cross section. The stream classification was assigned based on 

Rosgen (1994). The reach channel geometry was averaged for 

each of the three parameters of cross-sectional area, depth, and 

width from the two cross sections. The bankfull and water surface at the gage was extrapolated from the longitudinal profile 

plot to obtain the gage height corresponding to the bankfull 

feature (Chaplin, 2005, p. 11).
Regression Relations of Bankfull Discharge and Channel Geometry 5

The new bankfull discharge and channel geometry data 

were combined with previously published regional curve 

datasets for noncarbonate sites in Pennsylvania and hydrologic 

regions 4, 4A, 5, and 6 of southern New York (White, 2001; 

Cinotto, 2003; Miller and Davis, 2003; Chaplin, 2005; Westergard and others, 2005; Mulvihill and others, 2005, 2009). Data 

from hydrologic region 3 in New York was excluded since 

this region was previously shown to differ significantly from 

the other regions (Mulvihill and Baldigo, 2007, 2012). There 

were six sites in New York in which the drainage area was 

greater than the 215 mi2 limit used in Pennsylvania. The full 

range of the parameter values available was included (drainage 

areas from 0.7 to 332 mi2) in the final dataset for the glaciated 

settings of Pennsylvania and southern New York in order to 

better capture variability and provide the best model fit. 

A simple linear regression was used to relate drainage area to bankfull depth, width, cross-sectional area, and 

discharge. A log transformation of the best fit line produced 

a power function in which bankfull discharge and channel 

dimensions are a function of drainage area. To test if stratifying the data by glaciation improved previous regional curve 

relations, an analysis of covariance (ANCOVA) was performed to compare any differences between models (Helsel 

and Hirsch, 2002; Fox and Weisberg, 2011; R Core Team, 

2017). Significant differences (p-value<0.05) in slope and 

intercept between regression lines would indicate that separate 

curves would yield better estimates of channel dimensions 

(Chaplin, 2005).

Regression Relations of Bankfull 

Discharge and Channel Geometry

The bankfull discharge and channel geometry for five 

newly surveyed sites are shown in table 1 (See appendix 1 for 

the locations, photographs, and data associated with cross-sectional surveys for the five stream reaches.). These data were 

combined with previous regional-curve channel-geometry 

data developed for the glaciated settings of Pennsylvania and 

southern New York (fig. 3). The median recurrence interval for 

bankfull discharge for the glaciated setting was 1.4 years and 

within the typical range of 1 to 2 years for similar geomorphic 

studies conducted nationally (Dunne and Leopold, 1978; Lawlor, 2004) and within Pennsylvania and New York (Chaplin, 

2005; Mulvihill and others, 2009). 

Regional curves for the glaciated setting were based on 

an empirical model using a simple linear regression of drainage area versus bankfull discharge, cross-sectional area, width, 

and depth; these significant relations (p-value<0.05) explained 

the variability with coefficients of determination (R2) of 0.89, 

0.94, 0.87, and 0.83, respectively (fig. 4). The log-log transformed power function for each relation is shown in figure 4 

and several observations fall outside the 95 percent confidence 

interval. The confidence interval provides the level of certainty 

for which the range of values sampled encompasses the true 

population. The overall spread in data for the glaciated setting 

of Pennsylvania and southern New York is comparable to the 

Table 1. Channel characteristics of the 2016 geomorphic assessments for select streamflow-gaging stations in the glaciated setting of 

Pennsylvania and southern New York.

[mi2, square miles; ft, feet; ft3/s, cubic feet per second; POR, period(s) of record; ft2, square feet; yrs, years; PA, Pennsylvania; NY, New York; NA, not available; cross section stream type from Rosgen (1994)]

Station 

number Station name POR

Drainage 

area

(mi2)

Bankfull 

discharge

(ft3/s)

Bankfull 

cross 

sectional 

area

(ft2)

Bankfull 

width

(ft)

Bankfull 

mean 

depth

(ft)

Recurrence 

interval

(yrs)

Reach 

slope

Mean 

D50

Crosssection 

stream 

type

01428750

West Branch 

Lackawaxen River 

near Aldenville, PA

1986–present 40.6 1,810 256.18 76 3.38 1.5 0.005 63 C4, C3

01440400 Brodhead Creek near 

Analomink, PA 1957–present 65.9 2,325 390.25 115 3.51 1.4 0.004 85 C3, F4

01531325 Sugar Creek at West 

Burlington, PA 2010–present 93.6 2,638 504.74 149 3.42 NA 0.002 45 C4, C4

01525981

Tuscarora Creek 

above South 

Addison, NY

2000–present 102.0 3,975 568.03 123 4.73 1.4 0.005 75 C3, C4

01531908 Towanda Creek near 

Franklindale, PA 2010–present 112.0 3,311 585.61 129 4.54 NA 0.002 109 C3, C4
6 Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York

39.6 percent

unglaciated sites

(n=40)

60.4 percent

glaciated sites

(n=61)

Distribution of sites

350

300

250

200

150

100

50

0

Bankfull width,

in feet

Bankfull mean depth,

in feet

Glaciated Unglaciated Glaciated Unglaciated

7

6

5

4

3

2

1

0

2,000

1,500

1,000

500

Bankfull cross-sectional area,

0

in square feet

10,000

8,000

6,000

4,000

2,000

0

Bankfull discharge, 

in cubic feet per second

3.5

3

2.5

2

1.5

1

0.5

Recurrence interval,

in years

350

300

250

200

150

100

50

0

-50

Drainage area,

in square miles

EXPLANATION

Maximum

75th percentile

25th percentile

Median

Mimimum

Outlier

Figure 3. Distribution of sites, drainage area, recurrence interval, bankfull discharge, cross-sectional 

area, mean depth and width for the glaciated and unglaciated settings of Pennsylvania and southern 

New York. (n, number of samples)
Regression Relations of Bankfull Discharge and Channel Geometry 7

10

20

30

40

60

50

70

80

90 100

200

300

40

20

60

80

100

200

400

600

800

1,000

10,000

2,000

4,000

6,000

8,000

A

C

10

40

4

100

20

200

400

1,000

2,000

1

0.9

0.8

0.7

0.6

2

3

4

5

6

7

B

D

0.4 1 4 10 40 100 400

0.4 1 4 10 40 100 400

Drainage area (DA), in square miles

Drainage area (DA), in square miles

0.4 1 4 10 40 100 400

Drainage area (DA), in square miles

0.4 1 4 10 40 100 400

Drainage area (DA), in square miles

Bankfull mean depth (bf depth),

in feet

Bankfull width (bf width),

in feet

Bankfull cross-sectional area (bf area),

in square feet

Bankfull discharge (bf Q),

in cubic feet per second

bf width = 14.82DA0.455

R 2 = 0.87

bf Q = 52.62DA0.861

R 2 = 0.89

bf area = 12.70DA0.791

R 2 = 0.94

bf depth = 0.46DA0.335

R 2 = 0.83

EXPLANATION

95-percent confidence interval

Glaciated setting

Figure 4. Drainage area in relation to A, bankfull discharge, B, cross-sectional area, C, width, and D, mean depth for the glaciated 

setting of Pennsylvania and southern New York.

natural variability seen in other studies (Doll and others, 2002; 

Sweet and Geratz, 2003; McCandless, 2003; Lawlor, 2004; 

Keaton and others, 2005; McCandless and others, 2015). 

These glaciated relations explain variability slightly better 

than regional curves developed for the entire noncarbonate 

region of Pennsylvania (Chaplin, 2005), but further statistical 

analysis was performed to determine whether or not a data 

stratification based on glaciation would produce better relations than a combination of all data across settings.

The data for both the glaciated and unglaciated settings 

included 61 (60.4 percent) and 40 (39.6 percent) sites, respectively (fig. 3). The median and interquartile range of the recurrence interval and mean depth are similar among settings. The 

median values for the drainage area, bankfull discharge, crosssectional area, and width are lower for the glaciated setting, 

but the data had a larger range within the group. A comparison 

of drainage areas in relation to bankfull discharge and channel 

dimensions for the glaciated and unglaciated setting are shown 

in figure 5. The results of the ANCOVA for comparison among 

regression equations for the glaciated and unglaciated settings 

are shown in table 2. Except for the significantly different 

intercept of the regional curve relating bankfull discharge to 

drainage area (table 2, F=8.26, p-value<0.005), the equations 

are not significantly different among the glaciated and unglaciated settings. Therefore, data stratification by glaciation does 

not further optimize regional curves developed for the noncarbonate (glaciated and unglaciated) and carbonate settings of 

Pennsylvania and Maryland (Chaplin, 2005). Further analysis 

that incorporates data stratification or multivariate approaches 

based on mean annual runoff, precipitation, slope, stream 

classification, and other relevant parameters may optimize the 

accuracy and utility of statewide models. 

The four new estimates of bankfull discharge and channel dimensions at streamflow- gaging sites in Pennsylvania (table 2, excluding USGS 01525981 in New York) and 

updated drainage areas from StreamStats (Clune and others, 

2018) were incorporated into previous regional curves developed by Chaplin (2005) to produce a set of updated regression 
8 Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York

10

20

30

40

60

50

70

80

90 100

200

300

400

40

20

60

80

100

200

400

600

800

1,000

10,000

2,000

4,000

6,000

8,000

A

C

10

40

4

100

20

200

400

1,000

2,000

1

0.9

0.8

0.7

0.6

2

3

4

5

6

7

B

D

0.4 1 4 10 40 100 400

0.4 1 4 10 40 100 400

Drainage area (DA), in square miles

Drainage area (DA), in square miles

0.4 1 4 10 40 100 400

Drainage area (DA), in square miles

0.4 1 4 10 40 100 400

Drainage area (DA), in square miles

Bankfull mean depth (bf depth),

in feet

Bankfull width (bf width),

in feet

Bankfull cross-sectional area (bf area),

in square feet

Bankfull discharge (bf Q),

in cubic feet per second

Glaciated setting

Unglaciated setting

EXPLANATION

Figure 5. Drainage area in relation to A, bankfull discharge, B, cross-sectional area, C, width, and D, mean depth for the noncarbonate 

glaciated (yellow) and unglaciated (green) settings of Pennsylvania and southern New York. 

Table 2. Results of analysis of covariance (ANCOVA) test 

for differences in slope and intercept among glaciated and 

unglaciated noncarbonate settings of Pennsylvania and 

New York.

[<, less than]

Covariate

Slope Intercept

F[1,97] p-value F[1,98] p-value

Bankfull discharge 0.16 0.69 8.26 <0.005

Bankfull cross sectional area 0.02 0.89 0.62 0.43

Bankfull width 0.13 0.72 0.46 0.50

Bankfull mean depth 1.51 0.22 0.16 0.69

relations of bankfull discharge and channel geometry for the 

noncarbonate and carbonate settings of Pennsylvania and 

Maryland (fig. 6). The use of previous drainage areas from 

the National Water Information System (NWIS) was avoided 

because watershed delineations were often subject to the 

accuracy of the topographic and positional features from 

USGS 1:24,000 topographic map series (U.S. Geological 

Survey, 2012). Additionally, the previous carbonate regional 

curves were found to be disproportionately influenced by the 

smallest watershed (Sucker Run near Coatesville, PA, USGS 

01480610) and the updated StreamStats analysis has shown 

that this site is better represented by the noncarbonate setting (the watershed underlain by 30 percent or less carbonate 

rock). The revised regional curves for the carbonate setting 

have larger confidence intervals compared to those for the 

noncarbonate setting. Possible explanations for this difference include the small number of carbonate watersheds in the 

dataset (n=10), the lack of any explanatory variables for karst 
Limitations 9

10

20

30

40

60

50

70

80

90

100

200

300

60

80

100

200

400

600

800

1,000

2,000

4,000

6,000

A

C

10

40

4

100

20

200

400

1,000

2,000

1

0.9

0.8

0.7

0.6

2

3

4

5

6

7

B

D

1 2 4 10 20 40 100 200 400 1 2 4 10 20 40 100 200 400

1 2 4 10 20 40 100 200 400 1 2 4 10 20 40 100 200 400

Drainage area (DA), in square miles

Drainage area (DA), in square miles Drainage area (DA), in square miles

Drainage area (DA), in square miles

Bankfull mean depth (bf depth),

in feet

Bankfull width (bf width),

in feet

Bankfull cross-sectional area (bf area),

in square feet

Bankfull discharge (bf Q),

in cubic feet per second

bf Q = 47.02DA0.854

R 2 = 0.92

bf Q = 4.81DA1.135

R 2 = 0.87

bf area = 12.36DA0.794

R 2 = 0.93

bf area = 2.35DA1.027

R 2 = 0.89

bf depth = 0.91DA0.321

R 2 = 0.73

bf depth = 0.49DA0.418

R 2 = 0.74

bf width = 14.29DA0.459

R 2 = 0.84

bf width = 5.03DA0.601

R 2 = 0.73

EXPLANATION

95-percent confidence interval

Noncarbonate setting

Carbonate setting

Figure 6. Drainage area in relation to A, bankfull discharge, B, cross-sectional area, C, width, and D, mean depth for the noncarbonate 

(black) and carbonate (blue) settings for streams in Pennsylvania and selected areas of Maryland.

features in the drainage-area model, and the availability of few 

watersheds of less than 40 mi2. Additional bankfull discharge 

and channel geometry data, particularly from small watersheds 

in the carbonate setting, would improve regional curve relations for Pennsylvania.

Limitations

Regional curves are best used as an initial estimate of 

bankfull parameters and not a substitute for field identification of bankfull and other techniques used for stream restoration design (White, 2001). Increasing the number of sites 

and the range of drainage areas would strengthen regional 

curve relations, but the analysis is limited by the availability 

of streamflow-gaging stations with an adequate period of 

record. The filter criteria used in this study creates limitations, as it excluded watersheds with greater than 20 percent 

land use alteration (coal mining, urban development) and flow 

regulation (dams, and so forth) (Schueler, 1994). Urbanization of even less than 20 percent has been shown to increase 

discharge amounts and frequency that can change the relation 

of channel dimensions with the surrounding drainage area. 

Site specific factors such as beaver dam activity and water 

withdrawals may also affect flow regulation. 

The new (2016) streamflow-gaging stations selected for 

this study are assumed to not have been significantly altered 

by flood events. Surveyed stream reaches are often located 

near bridges that constrict stormflow and produce artificial 

scouring and filling of the stream’s bedload, which can introduce increased variability of estimates. Cross-sectional channel dimensions can vary along stream reaches and the mean 

values of bankfull area, width, and depth should be used as a 

guide and not a substitute for site specific field assessment and 

verification. The regression relations for bankfull discharge 

and channel dimensions are only applicable to the range of 

drainage areas used for this study. Extrapolated regions for 

smaller drainage areas (less than 18 mi2) are presented in the 
10 Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York

regression relations for the carbonate setting of Pennsylvania 

based on a linear assumption of relation and is limited by the 

confidence intervals shown in figure 6.

Low geomorphic topographic reference points such as the 

active channel or depositional bars were observed consistently 

at the five newly (2016) surveyed sites in the glaciated settings 

of Pennsylvania and southern New York, and at numerous 

sites during previous assessments (fig. 7). These features are 

shaped at a frequency less than the bankfull discharge recurrence interval and have been used to develop relations among 

streamflow and channel geometry (Hedman and Osterkamp, 

1982). Glacial outwash streams transport a large amount 

of sediment and the depositional point bars can be distinct 

features, but are generally topographically lower than bankfull 

features (D.L. Rosgen, Wildland Hydrology, written commun., 

2017). Discretion should be used by stream restoration practitioners especially in glacial outwash streams, because these 

low depositional features can often be mistaken for bankfull. 

Simple linear regression of drainage area versus bankfull 

discharge and channel dimensions does not include all the 

possible explanatory parameters (precipitation, runoff, and 

so forth) that may help reduce variability of the models. The 

glaciated setting in particular is highly variable based on the 

amount of outwash materials. The ANCOVA statistical analysis provides further understanding of the geomorphology in a 

glaciated setting, but does not replace the statewide regional 

curves previously published for Pennsylvania and the hydroregions of New York (Chaplin, 2005; Mulvihill and others, 

2009) or the updated statewide regional curves for Pennsylvania presented in figure 6.

Summary and Conclusions

Streambank erosion in areas of past glacial deposition has 

been shown to be a dominant source of sediment to streams. 

A geomorphic dataset of the new (2016, n=5) and previous (1999–2006, n=96) estimates of bankfull discharge and 

channel dimensions at USGS streamflow- gaging stations was 

compiled to present and contrast the noncarbonate glaciated 

and unglaciated settings of Pennsylvania and southern New 

York. Empirical models were developed using simple linear 

regressions that relate bankfull discharge and channel geometry to drainage area (regional curves). Significant relations 

(p-value<0.005) were able to explain variability with coefficients of determination (R2

) of 0.89 for bankfull discharge, 

0.94 for cross-sectional area, 0.87 for bankfull width, and 0.83 

for bankfull depth. These regression relations were able to provide a slightly better fit than regional curve models developed 

for the entire noncarbonate region of Pennsylvania. 

The results of the ANCOVA analysis comparing regression equations for the glaciated and unglaciated setting 

indicate that except for the significant intercept of bankfull 

discharge versus drainage area (F=8.26, p<0.05), the equations 

are not significantly different among the settings. Therefore, 

data stratification by glaciation does not improve regional 

curves relations developed previously for the noncarbonate 

(glaciated and unglaciated) and carbonate settings of Pennsylvania and Maryland. Further analysis that incorporates data 

stratification or multivariate approaches based on mean annual 

runoff, precipitation, slope, stream classification, or other 

relevant parameters may optimize the accuracy and utility of 

Bankfull

Active channel

Depositional bar

Modified from Hedman and Osterkamp, 1982

Figure 7. Geomorphic reference points of bankfull, active-channel, and depositional bar.
References Cited 11

statewide models. The new estimates of bankfull discharge 

and channel dimensions at streamflow-gaging sites and revised 

drainage areas from StreamStats were incorporated into previously developed regional curves to produce updated regression relations of bankfull discharge and channel geometry 

for the noncarbonate and carbonate settings of Pennsylvania 

and Maryland.

As streamflow-gaging stations with an adequate period 

of record become available overtime, this would increase the 

number of sites and the range of drainage areas that would 

further strengthen regional curve relations. This report provides an evaluation of the most reliable model estimates and 

predictions of bankfull discharge and channel geometry to aid 

classification, monitoring and restoration efforts of streams 

in the glaciated settings of Pennsylvania. Regional curves are 

best used as an initial estimate of bankfull parameters and not 

as a substitute for field identification of bankfull and other 

techniques used for stream restoration design.

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Appendix 1.

Photographic documentation, bankfull-channel geometry, and substrate data collected for new 

(2016) stream locations selected for development of regional curves
16 Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York West Branch Lackawaxen River near Aldenville, PA (Station number 01428750) View looking downstream at the reach of West Branch Lackawaxen River at station 133. Cross-sectional data at station 133 Bankfull cross-sectional area (square feet) 243.2 Bankfull width (feet) 70.5 Bankfull mean depth (feet) 3.5 D50 (millimeters) 52.2 D84 (millimeters) 151.2 View looking downstream at the reach of West Branch Lackawaxen River at station 860. Cross-sectional data at station 860 Bankfull cross-sectional area (square feet) 269.2 Bankfull width (feet) 81.2 Bankfull mean depth (feet) 3.3 D50 (millimeters) 74.5 D84 (millimeters) 221.7Streamflow

direction 0 200 400 600 800 1,000 1,200 1,400 1,600

Cross-sectional

station at 133

Cross-sectional

station at 860

U.S. Geological Survey

streamflow-gaging 

station 01428750

End of 

longitudinal 

survey

Stationing of longitudinal profile, in feet
Appendix 1 17

Tuscarora Creek above South Addison, NY (Station number 01525981)

View looking upstream at the reach of Tuscarora Creek at station 230.

Cross-sectional data at station 230

Bankfull cross-sectional area (square feet) 561.0Bankfull width (feet) 139.7Bankfull mean depth (feet) 4.0D50 (millimeters) 71.6D84 (millimeters) 188.4

View looking upstream at the reach of Tuscarora Creek at station 1324.

Cross-sectional data at station 1324

Bankfull cross-sectional area (square feet) 575.1Bankfull width (feet) 105.5Bankfull mean depth (feet) 5.5D50 (millimeters) 78.4D84 (millimeters) 207.3

Streamflowdirection

0 200 400 600 800 1,000 1,200 1,400 2,000 1,600 1,800

Cross-sectional

station at 230

Cross-sectional

station at 1324

U.S. Geological Survey

streamflow-gaging 

station 01525981

End of 

longitudinal 

survey

Stationing of longitudinal profile, in feet
18 Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York Towanda Creek near Franklindale, PA (Station number 01531908) View looking downstream at the reach of Towanda Creek at station 136. Cross-sectional data at station 136 Bankfull cross-sectional area (square feet) 624.1 Bankfull width (feet) 131.0 Bankfull mean depth (feet) 4.8 D50 (millimeters) 137.3 D84 (millimeters) 235.2 View looking upstream at the reach of Towanda Creek at station 463. Cross-sectional data at station 463 Bankfull cross-sectional area (square feet) 547.1 Bankfull width (feet) 127.0 Bankfull mean depth (feet) 4.3 D50 (millimeters) 80.4 D84 (millimeters) 232.0Streamflow

direction 0 200 400 600 800 1,000 1,200 1,400 1,800 1,600

Cross-sectional

station at 136

Cross-sectional

station at 463

U.S. Geological Survey

streamflow-gaging 

station 01531908

End of 

longitudinal 

survey

Stationing of longitudinal profile, in feet
Appendix 1 19

Sugar Creek at West Burlington, PA (Station number 01531325)

View looking upstream at the reach of Sugar Creek at station 21.

Cross-sectional data at station 21

Bankfull cross-sectional area (square feet) 541.7Bankfull width (feet) 168.0Bankfull mean depth (feet) 3.2D50 (millimeters) 41.9D84 (millimeters) 146.7

View looking downstream at the reach of Sugar Creek at station 527.

Cross-sectional data at station 527

Bankfull cross-sectional area (square feet) 467.8Bankfull width (feet) 129.5Bankfull mean depth (feet) 3.6D50 (millimeters) 48.0D84 (millimeters) 179.5

Streamflowdirection

0 200 400 600 800 1,000 1,200 1,400 2,200 1,600 2,000 1,800

Cross-sectional

station at 21

Cross-sectional

station at 527

U.S. Geological Survey

streamflow-gaging 

station 01531325

End of 

longitudinal 

survey

Stationing of longitudinal profile, in feet
20 Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York Brodhead Creek near Analomink, PA (Station number 01440400) View looking downstream at the reach of Brodhead Creek at station 340. Cross-sectional data at station 340 Bankfull cross-sectional area (square feet) 358.0 Bankfull width (feet) 90.0 Bankfull mean depth (feet) 4.0 D50 (millimeters) 122.9 D84 (millimeters) 315.6 View looking downstream at the reach of Brodhead Creek at station 948. Cross-sectional data at station 948 Bankfull cross-sectional area (square feet) 422.5 Bankfull width (feet) 139.0 Bankfull mean depth (feet) 3.0 D50 (millimeters) 48.0 D84 (millimeters) 123.1Streamflow

direction 0 200 400 600 800 1,000 1,200 1,400 1,600

Cross-sectional

station at 340

Cross-sectional

station at 948

U.S. Geological Survey

streamflow-gaging 

station 01440400

End of 

longitudinal 

survey

Stationing of longitudinal profile, in feet
For additional information, contact::

Director, Pennsylvania Water Science Center

U.S. Geological Survey

215 Limekiln Road

New Cumberland, PA 17070

or visit our website at: https://pa.water.usgs.gov/

Publishing support provided by the 

West Trenton Publishing Service Center
Clune and others—Regression Relations of Bankfull Discharge and Channel Geometry, Pennsylvania and Southern New York—Scientific Investigations Report 2018–5066

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20185066