Prepared in cooperation with the Pennsylvania Department of Environmental Protection

Estimation of Base Flow on Ungaged, Periodically Measured 

Streams in Small Watersheds in Western Pennsylvania

Scientific Investigations Report 2018–5150

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2018–5150

U.S. Department of the Interior

U.S. Geological Survey
Cover: Photo of U.S. Geological Survey station 03114094, representative of the streams that were monitored for this project, Herod Run near New 

Freeport Pa., April 16, 2015, photograph by Stephanie Roussel, U.S. Geological Survey.
Estimation of Base Flow on Ungaged, 

Periodically Measured Streams in Small 

Watersheds in Western Pennsylvania

By Elizabeth Hittle and Dennis W. Risser

Prepared in cooperation with the 

Pennsylvania Department of Environmental Protection

Scientific Investigations Report 2018–5150

U.S. Department of the Interior

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

DAVID BERNHARDT, Acting Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2019

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

resources, natural hazards, and the environment—visit https://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit https://store.usgs.gov.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

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

Suggested citation:

Hittle, E., and Risser, D.W., 2019, Estimation of base flow on ungaged, periodically measured streams in small watersheds in western Pennsylvania: U.S. Geological Survey Scientific Investigations Report 2018–5150, 42 p., https://doi.

org/10.3133/sir20185150.

ISSN 2328-0328 (online)
Acknowledgments

The authors wish to acknowledge Michele Hamlin at the Pennsylvania Department of Environmental Protection for her help with data requests and general information throughout the project 

and the U.S. Geological Survey (USGS) personnel in the Pennsylvania Water Science Center, 

Pittsburgh office, for their hard work and dedication to this project. The authors thank William 

Farmer, Greg Koltun, Marla Stuckey, and Linda Zarr, of the USGS, for their careful reviews and 

helpful suggestions.

iii

Contents

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

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

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

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

Streamgage Network....................................................................................................................................3

Development of a Method for the Estimation of Base Flow on Ungaged, Periodically

Measured Streams...........................................................................................................................3

Index-Gage Method..............................................................................................................................3

MOVE.1 Regression Technique .................................................................................................3

Regression Diagnostics..............................................................................................................7

Nash-Sutcliffe Efficiency Coefficient ..............................................................................7

Pearson’s Correlation Coefficient ....................................................................................7

Prediction Interval ..............................................................................................................8

MOVE.1 Regression Comparison ..............................................................................................8

Analysis of Streamflow Estimation .............................................................................................................8

Data Selection.......................................................................................................................................8

Runoff-Influenced Streamflow ..................................................................................................9

Zero Streamflow Values ...........................................................................................................10

Instantaneous and Daily Mean Streamflow..........................................................................10

Frequency of Streamflow Measurements......................................................................................11

Zero Streamflow Recorded at the Estimation Site ..............................................................14

Zero Streamflow Not Recorded at Estimation Site ..............................................................16

Current PADEP Schedule .........................................................................................................17

Streamflow-Measurement Summary.....................................................................................18

Index-Gage Method Results .............................................................................................................19

MOVE.1 Regression Discussion .......................................................................................................19

Representative Index Streamgages ................................................................................................23

Base-Flow Characteristics of the Newly Established Streamgages .........................................28

Base-Flow Duration Curves .....................................................................................................28

Median Recession Index..........................................................................................................29

Evaluation of Streamflow Not Used for Regression Development.............................................33

Accuracy and Limitations...........................................................................................................................35

Application of Techniques to Estimate Natural Streamflow at an Ungaged Site .............................37

Summary and Conclusions.........................................................................................................................37

References Cited..........................................................................................................................................39

Appendix 1. Results of MOVE.1 regression diagnostics for streamflow at U.S. Geological 

Survey streamgage 03111235 (DogTrib) streamflow estimated by using U.S. Geological 

Survey streamgages 03111200 (Dunkle) and 03111890 (MWheeling) with and without 

runoff-influenced streamflow.......................................................................................................41

v
vi

Figures

1. Map showing location of existing and newly established streamgages in the

study area in western Pennsylvania .........................................................................................4

2. Graph showing streamflow at U.S. Geological Survey streamgages 03114094,

Herod Run near New Freeport, and 03111675, Job Creek at Delphene,

Pennsylvania, during a precipitation event .............................................................................9

3. Graphs showing for U.S. Geological Survey (USGS) streamgage 03111235,

Unnamed Trib to Dog Run at Dunsfort, Pennsylvania, A, log prediction interval

width and B, Nash-Sutcliffe Efficiency values, as estimated using USGS

streamgage 03111200, Dunkle Run near Claysville, Pennsylvania, and

C, log prediction interval and D, Nash-Sutcliffe Efficiency values as estimated

using USGS streamgage 03111890, Middle Wheeling Creek near Claysville,

western Pennsylvania, for six MOVE.1 regressions with and without runoffinfluenced streamflow...............................................................................................................11

4. Schematic diagram showing example calendar of measurement schedules during a

hypothetical month.....................................................................................................................14

5. Graph showing observed streamflow in relation to estimated streamflow at

U.S. Geological Survey streamgage 03111200, Dunkle Run near Claysville,

western Pennsylvania, for streamflow-measurement schedules PO1, PO2, and

PO8 with the 95-percent prediction intervals ........................................................................17

6. Graph showing prediction interval widths for the Zero streamflow example

for U.S. Geological Survey streamgage 03111235, Unnamed trib to Dog Run at

Dunsfort, estimated using streamflow at USGS streamgage 03107698, Traverse

Creek near Kendall; Outliers example for USGS streamgage 0311200, Dunkle

Run near Claysville, estimated using streamflow at USGS streamgage

03107698, Traverse Creek near Kendall; and No outliers example for USGS

streamgage 03107698, Traverse Creek near Kendall, estimated using

streamflow at USGS streamgage 03108010 Fishpot Run near Shippingport,

western Pennsylvania................................................................................................................18

7. Graphs showing distance from the estimation site to the index streamgage in

relation to the log prediction interval width for each of the 12

newly established streamgages, in western Pennsylvania ...............................................25

8. Graphs showing ratio of the estimation site watershed area to the index

streamgage watershed area for the 12 newly established streamgages in

western Pennsylvania in relation to the log prediction interval width..............................26
vii

9. Graphs showing log prediction interval widths calculated from the MOVE.1

regressions for selected index streamgages in A, Greene County, B, Washington

County, and C, Beaver/Fayette/Butler Counties, western Pennsylvania ..........................27

10. Graph showing example of hydrograph separation using the PART method and

the daily streamflow record for U.S. Geological Survey estimation site

03111675, Job Creek at Delphene, western Pennsylvania, during 2015 ............................29

11. Graph showing base-flow duration curves for 12 small watersheds in western

Pennsylvania plotted for the period of concurrent record from June 18, 2015,

through March 31, 2017 .............................................................................................................30

12. Graphs showing median Recession Index (K) for recession periods in A,

November 2015, B, April 2016, and C, February 2017 at U.S. Geological Survey

streamgage 03111235, Unnamed trib to Dog Run at Dunsfort and U.S.

Geological Survey streamgage 03111890, Middle Wheeling Creek near

Claysville in western Pennsylvania .........................................................................................32

13. Graph showing estimated streamflow in relation to observed streamflow at U.S.

Geological Survey streamgage 03072890, Fonner Run near Deer Lick, western

Pennsylvania, with the 95-percent prediction intervals.......................................................34

14. Graph showing estimated streamflow in relation to observed streamflow at

U.S. Geological Survey streamgage 03111235 Unnamed trib to Dog Run at

Dunsfort, western Pennsylvania, with the 95-percent prediction intervals .....................36
viii

Tables

1. Description of streamgages used in analysis, by county, in western Pennsylvania ........5

2. Description of newly established streamgages with the physiographic section

and percentages of each underlying geologic formation, by county, in western

Pennsylvania .................................................................................................................................6

3. Descriptions of streamflow-measurement schedules, including whether

runoff-influenced streamflow was used in the schedule, an explanation of the

schedule, whether it is possible to implement the schedule for data collection,

and examples explaining the schedules.................................................................................12

4. Results of MOVE.1 regression diagnostic factors, using a 95-percent

confidence interval, for 14 measurement schedules for three streamgage pairs

in western Pennsylvania. The PO1, PO2, and PO8 schedules are highlighted

because they best represent the scenario where the estimation site recorded

days of zero streamflow ............................................................................................................15

5. Summary of MOVE.1 regression coefficient of correlation, Nash-Sutcliffe

Efficiency value, and log prediction interval width for streamgage pairs in

western Pennsylvania................................................................................................................20

6. Estimation sites, by county in western Pennsylvania, with the lowest and

highest non-runoff influenced observed streamflow, May 1, 2015–March 31,

2017, and logarithmic transformed streamflow and streamflow range difference.........23

7. Distance between the watershed area centroids for pairs of U.S. Geological

Survey streamgages in western Pennsylvania .....................................................................24

8. Median recession index (K) in days per log (base 10) cycle of streamflow for

newly established streamgages in western Pennsylvania, by county..............................31
ix

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

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) 

Streamflow rate

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

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)

Datum

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).

Abbreviations

GZF Gage height of Zero Streamflow

HISAZ Highest Index Streamflow At Zero 

K Median Recession Index

MOVE.1 Maintenance of Variance Extension, Type 1

MRC Master Recession Curve

NSE Nash-Sutcliffe Efficiency 

PADEP Pennsylvania Department of Environmental Protection

r Pearson’s correlation coefficient

USGS U.S. Geological Survey

Estimation of Base Flow on Ungaged, Periodically 

Measured Streams in Small Watersheds in Western 

Pennsylvania

By Elizabeth Hittle and Dennis W. Risser

Abstract

A 2.5-year data collection program was undertaken by the 

U.S. Geological Survey, in cooperation with the Pennsylvania 

Department of Environmental Protection (PADEP), to quantify 

and estimate base flow in small watersheds in western Pennsylvania where only periodic streamflow measurements had 

been obtained. Twelve streamgages with watershed areas of 

less than 10 square miles were established in western Pennsylvania for this study, with most established within Greene and 

Washington Counties (an area where a type of underground 

coal mining known as longwall mining occurs). Data from 

five previously established streamgages with watershed areas 

ranging from 48.9 to 281 square miles were also used in the 

analyses for this study. The index-gage method was used to 

relate streamflow at one streamgage referred to as the “index 

streamgage” to streamflow at another site of interest (usually 

an ungaged site, but for this study another streamgage) using a 

regression technique.

Streamflow regressions were developed for all newly 

established streamgages by using the Maintenance of Variance Extension, Type 1 (MOVE.1) method. Not all streamflow 

data from the newly established streamgages were used for 

MOVE.1 regression development; only data that have little to 

no influence from runoff were considered. Runoff-influenced 

streamflow for this study was defined as streamflow on a day 

that precipitation occurs plus streamflow on the following 

2 days. One streamflow value per day selected from a specified schedule that captures numerous non-runoff periods was 

used to develop a MOVE.1 regression.

Prediction limits were calculated from the regression 

to provide the upper and lower bounds for the regressionproduced streamflow estimates. Using these data, base flow 

at a site can be estimated with the index-gage method. The 

log10-tranformed prediction interval width and other regression 

diagnostics were used as indicators of regression quality 

when comparing streamgage relations to determine the best 

index streamgage among the streamgages established for this 

study. It was determined that index streamgages within about 

10 miles of the site of interest provided the best estimated base 

flow and could, in the future, be used by mine operators and

the PADEP to quantify base flow and to evaluate the effects of 

mining on streamflow.

Introduction

In areas where human activity can affect streamflow 

overall and base flow specifically, there is a need for water 

resource managers to assess hydrologic conditions and 

estimate base flow in a watershed of a stream as if it were 

not appreciably affected by human activities, such as mining, 

water regulation, municipal/industrial water supply, or other 

water withdrawals or inputs. It is acknowledged that there 

are other activities in the stream watersheds, such as farming, 

oil and gas production, and water supply for private wells, 

but these factors were not considered for this study. Base 

flow is the sustained flow of a stream in the absence of direct 

runoff (U.S. Geological Survey, 2017). If periodic streamflow measurements at an ungaged site are made to establish 

base-flow conditions in advance of land-use change or land 

disturbance and a similar watershed, that is unchanged or 

undisturbed, with an established streamgage that continuously 

monitors streamflow is present in the area, it is possible to 

develop a relation and estimate base flow at the periodically 

measured site.

Longwall mining is an example of a human activity with 

the potential to affect streamflow in southwestern Pennsylvania. The Kentucky Coal Education organization describes 

longwall mining as follows: “longwall mining is a highly productive underground coal mining technique. Longwall miners 

extract ‘panels’, which are rectangular blocks of coal. Massive 

shearers cut coal from a wall face, which falls onto a conveyor belt for removal. As a longwall miner advances along a 

panel, the roof behind the miner’s path is allowed to collapse.” 

(http://www.coaleducation.org/technology/Underground/

Longwall_Mining.htm, accessed December 15, 2017). As the 

roof collapses, a void is created causing the void walls to compress and the overlying rock to tilt and collapse into the void. 

The effects of this collapse can be seen at the surface because 

the land directly above and some distance beyond the void 

collapses vertically; the collapse is called land subsidence. 
2 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

(http://www.iesc.environment.gov.au/publications/subsidencelongwall-coal-mining, http://pittgeosociety.dot5hosting.com/

subsidence.pdf, accessed June 15, 2018). In 2008, the size 

of the longwall panels in southwestern Pennsylvania ranged 

between 1,200 and 1,500 feet (ft) in width and were often 

more than 10,000 ft in length (Tonsor and others, 2014). Subsidence caused by longwall mining of coal beneath streams 

can cause streamflow to be temporarily or permanently 

disrupted. This disruption can be a change to the streamflow in 

the guise of streamflow reduction, a difficult scenario to quantify, or complete loss of streamflow in the stream. Although 

cessation of flow in small headwater streams can be a natural 

occurrence during seasonally dry periods in a given year, 

mining induced subsidence may enhance the effect by temporarily or permanently affecting the groundwater hydrogeology 

by creating fractures, changing hydraulic conductivity, and 

increasing the capacity of the subsurface to store water. Studies have been done in Greene County documenting changes 

in hydraulic conductivity (Karacan and Goodman, 2009) and 

groundwater hydrogeology (Walker, 1988; Li and others, 

2015) due to longwall mining.

For mining plans that may cause subsidence of intermittent or perennial streams or valley floors immediately adjacent 

to streams, the Pennsylvania Department of Environmental 

Protection (PADEP) requires coal-mine operators to make 

periodic streamflow measurements. Measurements of instantaneous streamflow must be made at locations representative 

of the undermined area in these streams monthly for 2 years 

prior to mining, on a weekly basis for 6 months immediately 

prior to mining, and every day for 2 weeks prior to undermining the area of interest (Pennsylvania Department of Environmental Protection, 2005). Daily streamflow measurements 

must continue until the longwall face advances beyond the 

area of concern. Additionally, if a streamflow loss occurs, 

which is defined by PADEP as the absence of water in an 

intermittent or perennial stream channel, daily streamflow 

measurements must continue until streamflow fully recovers 

to a normal range of conditions, is fully restored, or it is found 

that the loss of streamflow in the stream is not the result of 

underground mining operations. A normal range of conditions 

for streamflow is defined as “the variation of a monitored 

parameter (especially flow) that exists in the absence of 

drought or human influences....” (Pennsylvania Department 

of Environmental Protection, 2005). All streamflow measurement results are provided to PADEP to characterize the 

normal range of streamflow in the stream and determine 

whether a mining induced streamflow loss has occurred. If 

mining induced streamflow loss has occurred, the operator 

must implement remediation efforts until streamflow has 

been restored (Pennsylvania Department of Environmental 

Protection, 2005). Owing to the high density of streams in 

southwestern Pennsylvania, the streams that potentially can be 

affected by longwall mining often have watershed areas less 

than 1 square mile (mi2).

As described in the previous paragraph, streamflow 

is monitored for approximately 2.5 years before mining 

commences to determine the normal range of streamflow; base 

flow is not necessarily targeted. However, if the time frame 

that is monitored is particularly wet or dry, these conditions 

may not relate well to future conditions. Techniques used 

to describe ranges of flow, such as the 7-day 10-year low 

streamflow frequency statistic, require at least 10 years of 

continuous daily streamflow record (Ries and Eng, 2010) in 

order to capture a wide range of environmental conditions. 

A technique that uses another streamgage to help estimate 

streamflow statistics at an ungaged site is the watershed-area 

ratio method. This technique assumes that the streamflow at an 

ungaged site is the same per unit area as at a nearby site, and 

streamflow statistics such as those mentioned earlier in this 

paragraph are adjusted accordingly. Sloto and others (2017) 

show that the watershed-area ratio method is generally most 

accurate when the watershed-area ratio for an ungaged site 

of interest is 0.33–3 times the watershed area of the index 

streamgage. However, existing streamgages that can be used 

as index streamgages are often in watersheds with watershed 

areas many times larger than the site of interest.

This study, conducted by the U.S. Geological Survey 

(USGS) in cooperation with the PADEP, examined the indexgage method for estimating base flow at ungaged, periodically 

measured sites in the bituminous coal region of southwestern 

Pennsylvania. To augment periodic streamflow measurements, 

an estimate of base flow in a small watershed can be made 

using an index streamgage for comparison. Index streamgages 

should account for short-term fluctuations in precipitation that 

are different from long-term trends that would be captured by 

streamflow statistics mentioned such as the 7-day 10-year low 

streamflow frequency statistic. For the purposes of this report, 

the term “periodically measured” refers to a stream that does 

not have an autonomous sensor that is measuring stage at a 

continuous interval, such as 15 or 60 minutes (ungaged site). A 

small watershed is herein defined as a watershed with a watershed area of less than 10 mi2

. Estimating the base flow of a 

stream not appreciably affected by human activities will assist 

mine operators and water-resource managers in determining 

whether or when a stream that has been affected by longwall 

mining returns to its natural streamflow conditions as defined 

by PADEP. For this application, the measurement period of the 

stream before mining occurs is approximately 2.5 years.

Purpose and Scope

The purpose of this report is to describe the results of a 

study that examined the use of index streamgages to estimate 

base flow at streams in small, ungaged watersheds where periodic streamflow measurements are made. This report describes 

the streamgage network established for this study, methods 

used to determine relations between streamgages, frequency 

of periodic streamflow measurements at the streamgages, 

and base-flow characteristics that can be used to determine 

how well the base flow at an index streamgage relates to 

streamflow at an estimation site in bituminous coal region of 

southwestern Pennsylvania and adjacent states. Analysis of the 
Development of a Method for the Estimation of Base Flow on Ungaged, Periodically Measured Streams 3

streamflow relations is used to determine a schedule for making the streamflow measurements needed to estimate base flow 

not appreciably affected by human activities and to evaluate 

the defined streamgage relations over a large area.

Description of Study Area

The study area is located in western Pennsylvania 

and encompasses low-streamflow region 4, as described 

by Stuckey (2006; fig. 1). Low-streamflow regions within 

Pennsylvania share similar geologic characteristics, base-flow 

characteristics, and precipitation patterns. The study area 

lies within three physiographic sections of the Appalachian 

Plateaus Physiographic Province and is underlain by twelve 

geologic formations ranging in age from Permian to Mississippian (fig. 1). The predominant land cover/uses in the region 

are urban and forested.

Streamgage Network

There were seven streamgages in the study area before 

the study began. One of the streamgages (03049800) is within 

an urban area and was excluded from this study owing to 

potential anthropogenic effects on streamflow. Streamflow at 

another streamgage (03106300) in the northernmost part of 

the study area is completely regulated by a dam and therefore 

was excluded from this study. Watersheds of the remaining 

five streamgages range in area from 48.9 to 281 mi2 (table 1; 

fig. 1). To analyze streamflow in small watersheds with areas 

less than 10 mi2, it was necessary to establish additional 

streamgages within the study area.

Potential watersheds for the establishment of streamgages 

were located using the website “eMapPA” developed by 

PADEP (http://www.depgis.state.pa.us/emappa/, accessed 

May 1, 2014). This website was used to identify water-use 

activities in the area that could affect streamflow, including 

water discharges, groundwater withdrawals, and surface-water 

withdrawals. Additionally, maps of past, current, and permitted longwall mining available on “eMapPA” were consulted. If 

an activity that could appreciably affect streamflow, including 

permitted longwall mining, was found to occur in a watershed, 

that area was not considered for a new streamgage. Other 

considerations for streamgage establishment included ability 

to obtain good streamflow record and ease of access. Locations that were relatively close to roads and bridges were given 

preference.

Twelve streamgages were established within the study 

area between August 2014 and May 2015; most were established in Greene and Washington Counties (fig. 1). Basin 

characteristics were determined using the USGS program 

StreamStats (http://streamstats.usgs.gov). Watershed areas of 

the newly established streamgages ranged from 0.28 mi2 to 

10.0 mi2 (table 1). The percentage of urban land cover (2011) 

in these watershed areas was less than 12 percent, except for 

one streamgage (22 percent), and percentage of area covered 

by forest varied greatly among the watersheds (40–94 percent). The geologic unit formations that are closest to the land 

surface and the percentage of those formations at the surface 

in each watershed are listed in table 2.

Six of the newly established streamgages were continuous-record streamgages, where streamflow was measured at all 

stages to support a rating that would be applicable at all flows 

(table 1). The other six new streamgages were established as 

partial-record streamgages, where streamflow was measured 

only at low and medium stages.

Development of a Method for the 

Estimation of Base Flow on Ungaged, 

Periodically Measured Streams

The index-gage method is used to estimate streamflow 

at one site (ungaged) on the basis of streamflow from another 

hydrologically similar streamgage site referred to as the “index 

streamgage.” The method and regression technique used to 

estimate base flow on an ungaged, periodically measured 

stream, based on the index-gage method, is described in the 

next section.

Index-Gage Method

The index-gage method relates instantaneous or daily 

mean values of streamflow at an index streamgage to instantaneous streamflow values at a site of interest using regression 

modeling. For this study, the index-gage method was used to 

estimate streamflow at the site of interest (referred to herein 

as the “estimation site”) for a period when observed streamflow occurred at the index streamgage and estimation site; 

then the observed and estimated streamflow values could be 

compared. Data from the index streamgage and the estimation 

site were analyzed in MOVE.1. Streamflow values (1 value 

per day or 1 value every 2 or 3 days) from the estimation site 

were selected to simulate periodically measured streamflow. 

Each set of MOVE.1 regressions was evaluated as a function 

of the Nash-Sutcliffe Efficiency, Pearson’s correlation coefficient (r), and the log prediction interval width. The results of 

all index-gage method analyses are available in a companion 

data release (Hittle, 2019a). The data release contains an Excel 

workbook for every data regression developed for this study; 

each workbook includes the MOVE.1 regression development 

data, regression analysis, regression diagnostics, and streamflow evaluation (if data were available).

MOVE.1 Regression Technique

The relation between streamflow at two streamgages in 

this study is described by a Maintenance of Variance Extension, Type 1 (MOVE.1) regression (Hirsch, 1982; Helsel and 
4 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

Base from U.S.Geological Survey digital data, 1972,

Albers Equal-Area Conic Projection

Geology from Miles and Whitfield, 2001

WEST 

VIRGINIA

OHIO

MARYLAND

LAWRENCE

BEAVER

CRAWFORD

VENANGO

BUTLER

MERCER

ALLEGHENY

WESTMORELAND

WASHINGTON

GREENE

FAYETTE

SOMERSET

ARMSTRONG

03081800 

(Bear)

03074500

(Redstone)

03072890

(Fonner)

03105927

(Crab)

03108010 

(Fishpot)

03108000 

(Raccoon)

03107698

(Traverse)

03111200 (Dunkle)

03111235 (DogTrib)

03111215 (Bonar)

03111890 

(MWheeling)

03111675 (Job)

03114094 

(Herod)

03111705 

(SF Dunkard)

03072000 (Shannopin)

03110830

(Kings)

03112000

(Wheeling)

-80°30' -80°0' -79°30'

41°30'

40°30'

40°

41°

-79°

0 15 30 MILES

0 15 30 KILOMETERS

Greene Formation

Washington Formation

Waynesburg Formation

Monongahela Group, Casselman 

Formation and Glenshaw Formations

Allegheny and Pottsville Formations

Mauch Chunk Formation

Burgoon Sandstone

Shenango through Venango Formations, 

undivided

Rockwell through Foreknobs Formations, 

undivided

Existing USGS Gage Basins

New Project Gage Basins

Geology

EXPLANATION

PENNSYLVANIA

Location of study area (low-streamflow 

region 4) highlighted in blue

Figure 1. Location of existing and newly established streamgages in the study area in western Pennsylvania.
Development of a Method for the Estimation of Base Flow on Ungaged, Periodically Measured Streams 5

Table 1. Description of streamgages used in analysis, by county, in western Pennsylvania.

[USGS, U.S. Geological Survey; PA, Pennsylvania; WV, West Virginia; NLCD, National Land Cover Database; *, streamflow computed at all stages]

USGS 

station 

identifier

Station name

Station 

short 

name

Watershed 

area 

(square miles)

Pennsylvania county

Developed 

(urban) land, 

from NLCD (2011) 

(percent)

Forested 

area, from 

NLCD (2011) 

(percent)

03111675 * Job Creek at Delphene, PA Job 6.57 Greene 5.5 87

03111705 * South Fork Dunkard Fork at 

Aleppo, PA SF Dunkard 7.68 Greene 6.5 73

03114094 Herod Run near New Freeport, 

PA Herod 1.79 Greene 5.2 80

03072890 Fonner Run near Deer Lick, PA Fonner 0.99 Greene 3.1 90

03072000 * Dunkard Creek at Shannopin, 

PA1 Shannopin 229 Greene 6.5 78

03112000 * Wheeling Creek at Elm 

Grove, WV1 Wheeling 281 Greene/Washington 6.1 73

03111890 Middle Wheeling Creek near 

Claysville, PA MWheeling 1.24 Washington 5.4 46

03111215 Bonar Creek near Claysville, PA Bonar 1.62 Washington 12.4 51

03111235 Unnamed trib to Dog Run at 

Dunsfort, PA DogTrib 0.28 Washington 1.5 79

03111200 * Dunkle Run near Claysville, 

PA Dunkle 7.70 Washington 5.6 40

03110830 * Kings Creek at Weirton, WV1 Kings 48.9 Beaver/Washington 11.2 86

03107698 * Traverse Creek near Kendall, 

PA Traverse 3.82 Beaver 6.7 66

03108010 Fishpot Run near Shippingport, 

PA Fishpot 2.11 Beaver 22.0 61

03108000 * Raccoon Creek at Moffatts 

Mill, PA1 Raccoon 178 Allegheny/Beaver/Washington 12.6 64

03105927 * Crab Run near 

Connoquenessing, PA Crab 10.0 Butler 10.5 53

03081800 * Bear Run at Kauffman, PA Bear 5.77 Fayette 4.1 94

03074500 * Redstone Creek at 

Waltersburg, PA1 Redstone 73.7 Fayette 24.9 55

1

Pre-existing streamgage, not established for this study.
6 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania Table 2. Description of newly established streamgages with the physiographic section and percentages of each underlying geologic formation, by county, in western Pennsylvania. [USGS, U.S. Geological Survey; PA, Pennsylvania] USGS station identifier Station name Pennsyl- vania county Station short name Physio- graphic section Geologic unit closest to land surface from map of Miles and Whitfield (2001), as percent of watershed area Greene Forma- tion of Permian age Wash- ington Forma- tion of Permian age Waynesburg Formation of Permian and Penn- sylvanian ages Monon- gahela Group of Pennsyl- vanian age Casselman Formation of Pennsyl- vanian age Glenshaw Formation of Pennsyl- vanian age Allegheny Formation of Pennsyl- vanian age Pottsville Formation of Pennsyl- vanian age Mauch Chunk Formation of Missis- sippian age Burgoon Sandstone of Missis- sippian age 03111675 Job Creek at Delphene, PA Greene Job Waynesburg Hills 100.0 03111705 South Fork Dunkard Fork at Aleppo, PA Greene SF Dunkard Waynesburg Hills 100.0 03114094 Herod Run near New Freeport, PA Greene Herod Waynesburg Hills 100.0 03072890 Fonner Run near Deer Lick, PA Greene Fonner Waynesburg Hills 100.0 03111890 Middle Wheeling Creek near Claysville, PA Washington MWheeling Waynesburg Hills 88.5 11.6 03111215 Bonar Creek near Claysville, PA Washington Bonar Waynesburg Hills 75.7 24.3 03111235 Unnamed trib to Dog Run at Dunsfort, PA Washington DogTrib Waynesburg Hills 55.8 38.9 5.3 03111200 Dunkle Run near Claysville, PA Washington Dunkle Waynesburg Hills 16.5 62.4 17.8 3.3 03107698 Traverse Creek near Kendall, PA Beaver Traverse Pittsburgh Low Plateau 85.6 14.4 03108010 Fishpot Run near Shippingport, PA Beaver Fishpot Pittsburgh Low Plateau 0.8 89.3 9.8 03105927 Crab Run near Connoquenessing, PA Butler Crab Pittsburgh Low Plateau 86.6 13.4

03081800 Bear Run at Kauffman, PA Fayette Bear Allegheny Mountain 37.6 17.4 8.0 37.0
Development of a Method for the Estimation of Base Flow on Ungaged, Periodically Measured Streams 7

Hirsch, 2002). This regression technique is commonly used for 

extending the length or filling missing periods of the streamflow record at a continuous-record streamgage. MOVE.1, 

which is referred to as the line of organic correlation, is preferred over more common linear regression techniques, such 

as ordinary least squares, because it preserves the inherent 

variance of streamflow data at the site to be estimated and 

results in an estimate of flow that is less biased than estimates 

from other methods. MOVE.1 is recommended when eight 

or more base-flow measurements are available for a partialrecord streamgage and requires concurrent streamflow from 

a hydrologically similar index streamgage. The MOVE.1 

method follows the equation

ˆ ˆ = ( ) y

x

y

S

y xx S+ − (1)

where

yˆ is the estimated streamflow (transformed to 

log units) at the estimation site,

y is the average of the observed streamflows 

(log units) at the estimation site,

Sy is the standard deviations of the log 

transformed observed streamflows at the 

estimation site,

Sx is the standard deviations of the log 

transformed observed streamflows at the 

index streamgage,

xˆ is streamflow (log units) at the index 

streamgage for which yˆ is estimated, and

x is the average of concurrent streamflows 

(log units).

MOVE.1 regressions were performed using the R statistical program (version 3.4.3) with the SMWRStats package 

(R Core Team, 2017; Lorenz, 2015) on log10-transformed data 

(referred to hereafter as “log transformed”). The following 

code within R was used.

library (smwrStats)

outputfile <- move.1 (estimation site

data ~ index streamgage data, data = datafile, distribution = “commonlog”)

Because log transformations are required, measurements of

zero streamflow cannot be used (Curan and others, 2012). 

MOVE.1 regression output can be applied to the 

log-transformed index streamgage streamflow to estimate 

the streamflow at the estimation site.

Regression Diagnostics

To quantify MOVE.1 regression performance and aid in 

evaluation of the regression, three different regression diagnostics are presented, the Nash-Sutcliffe Efficiency, Pearson’s 

correlation coefficient (r), and the prediction interval.

Nash-Sutcliffe Efficiency Coefficient

The Nash–Sutcliffe Efficiency (NSE) coefficient is used 

to assess the predictive power of hydrological models (Nash 

and Sutcliffe, 1970; McCuen and others, 2006; Jain and 

Sudheer, 2008). It is defined as

( )

( )

2

1

2

1

ˆ

1

T tt

t=

T t

t=

y y

E =

y y

−

−

Σ

−

Σ

(2)

where

E is Nash-Sutcliffe model efficiency,

yˆ is estimated value at time t,

y is observed value at the estimation site at 

time t, and

y is average of the observed values at the 

estimation site.

Krause and others (2005) describe the NSE as a value 

that can range from −∞ to 1. An NSE value of 1.0 indicates a 

perfect fit between the estimated and observed values. An NSE 

value of zero indicates the goodness-of-fit is as good as using 

the mean of the observed values for the period, and a negative 

NSE value indicates that the mean of the observed values for 

the period provides a better fit than the individual estimated 

result. Differences between the observed and estimated values 

are calculated as squared values, and as a result, the model 

performance during extreme high or low streamflow is overestimated or underestimated, respectively. For this study, the 

NSE was calculated on the log transformed values to reduce 

the sensitivity to extreme values (Krause and others, 2005).

Pearson’s Correlation Coefficient

Pearson’s correlation coefficient (r) measures the linear 

association between two variables (Helsel and Hirsch, 2002). 

It is defined as

1

1 * 1

n

i i

i x y

xx yy r = n = S S− −

−

   

          ∑ (3)

where

r is Pearson’s correlation coefficient,

n is number of values,

xi is observed value at index streamgage for 

value i,

x is average of the observed values at index 

streamgage,

Sx is standard deviation of the observed values 

at index streamgage,

yi is observed value at the estimation site for 

value i,

y is average of the observed values at the 

estimation site, and

Sy is standard deviation of the observed values 

at estimation site.
8 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

The r value can range from 0 to 1; if two variables are 

perfectly correlated with a positive slope, then r = 1. The r 

value is sensitive to outliers and nonlinearity and thus is most 

useful when comparing log transformed streamflow.

Prediction Interval

Prediction intervals were computed for the MOVE.1 

regressions. A prediction interval has a stated probability that 

a new data point with a specified magnitude will fall within 

it (Helsel and Hirsch, 2002). Both parametric and non-parametric methods are available for the calculation of prediction 

interval limits; however, the parametric method requires that 

the MOVE.1 regression residuals are normally distributed. A 

test for normalcy was accomplished on each MOVE.1 regression, and about one-third of the regressions examined had 

residuals (observed value minus estimated value) that were 

not normally distributed on the basis of skewness or kurtosis. 

For consistency among the numerous MOVE.1 regressions, 

the non-parametric prediction interval method was used. The 

equation to calculate the non-parametric prediction upper 

and lower interval limits is as follows (equations 4 and 5, 

respectively):

( ) ˆ + L y e (4)

( ) ˆ + U y e (5)

where

yˆ is estimated value of y given xo

,

e(L) is the 1-α/2 quantile of the residuals, or the 

Lth ranked residual where L = (n+1) * α/2. 

(n = count, α = probability exceedance), 

and

e(U) is the α/2 quantile of the residuals, or the Uth 

ranked residual where U = (n+1) *1-α/2. 

(n = count, α = probability exceedance).

The 95-percent prediction interval was used in this study, 

meaning that there is a 95-percent probability that future estimated streamflow values will be contained within the upper 

and lower limits of the prediction interval, based on the regression calibration dataset. Prediction intervals were calculated 

for each estimation site using many index streamgages. A 

perfect relation between two sites would result in zero residual 

values for all data, and the resulting prediction interval would 

be zero. The smaller the prediction interval, the smaller the 

regression residual values are at a given confidence interval.

MOVE.1 Regression Comparison

The log prediction interval width is used as a qualitative 

measure of the MOVE.1 regression performance along with 

NSE and Pearson’s correlation coefficient r values. Since 

non-parametric intervals are used, the prediction interval 

width is not symmetrical around the regression line; therefore, 

the prediction interval is presented in log space. Utilizing the 

prediction interval width in log space gives equal weight to the 

upper and lower prediction interval limits and thus is useful 

when making comparisons between MOVE.1 regressions. 

As described in the “Index-Gage Method Results” section, it 

was seen that in general when comparing various MOVE.1 

regressions developed for one estimation site that has numerous index streamgages, the smallest log prediction interval 

width corresponded to the highest or second highest NSE and 

r values. This lends confidence that the log prediction interval width can be used as an additional variable for regression 

comparison.

Analysis of Streamflow Estimation

For the analysis of streamflow estimation, data were 

obtained and analyzed in a consistent manner for the 12 newly 

established and 5 existing streamgages in the study area. All 

data that were obtained at the streamgage were not used for 

analysis. Considerations were used in data selection such as 

whether the data were influenced by runoff and whether zero 

streamflow was observed. In practice, streamflow will be 

measured only periodically at an estimation site. However, the 

streamgages that were used in this analysis compute continuous streamflow from the stage, producing values of streamflow 

at 5-minute increments of time. To simulate the measurement 

constraints in practice, data were selected from the continuous 

record using specific criteria and by following various measurement schedules. Once the data were selected, MOVE.1 

regressions were performed. Zero streamflow values were not 

used in the MOVE.1 regression but are important for evaluation purposes.

To improve the MOVE.1 regressions from streamgages 

with various watershed sizes, analysis includes only streamflow that was not affected appreciably by runoff and that could 

be considered base flow. Runoff-influenced streamflow for 

this study is defined operationally as streamflow on the day 

of precipitation plus streamflow on the following 2 days. The 

frequency of periodic streamflow measurements to best obtain 

the most relevant information without measuring continuously was determined and is described later in the “Frequency 

of Streamflow Measurements” section. Prediction intervals, 

NSE coefficients, and r values were computed. Evaluation of 

streamflow not used for MOVE.1 regression development was 

performed if streamflow data before May 1, 2015, were available for both streamgages. Results of the MOVE.1 regressions 

for all 12 newly established streamgages and selected regressions for previously established streamgages are discussed in 

the next sections.

Data Selection

The index-gage method for estimating streamflow 

requires that data be available for overlapping periods 
Analysis of Streamflow Estimation 9

of record at two sites (the estimation site and the index 

streamgage). The following discussion focuses on the way 

periodic streamflow measurements made at various times can 

affect the relations developed with the index-gage method. The 

assumption is that the estimation site will not have continuous stage or streamflow data, but measurements will be made 

on a specified schedule. The index streamgage, however, will 

have stage measured, discrete streamflow computed every 5 or 

15 minutes, and daily mean streamflow values computed. To 

simulate periodic streamflow measurements at an ungaged site 

of interest, discrete computed streamflow values from the estimation site were selected at prescribed time intervals (such as 

9:00 a.m. every Monday). These discrete values were matched 

with same day (and time if discrete values were used) streamflows at the index streamgage, and analyses were run.

The following considerations will be discussed with 

respect to the index-gage method: (1) runoff-influenced 

streamflow, (2) zero streamflow at the estimation site and (or) 

index streamgage, (3) instantaneous or daily mean streamflow 

values to be used at the index streamgage, and (4) data-collection frequency for streamflow at the estimation site.

Runoff-Influenced Streamflow

The lack of continuous streamflow at the estimation site 

limits one’s ability to understand the shape of a streamflow 

hydrograph during and after a rainfall event. It is recognized 

that the shape of the hydrograph is dependent on various basin 

characteristics, such as land use, geology, and topography, 

and there are studies that use these characteristics to assist in 

streamflow estimation (Stuckey, 2006). For the purposes of 

this study, streamflow alone is examined for use in MOVE.1 

regressions, though basin characteristics can be used to 

explain regression variability. It is anticipated that the index 

streamgage and estimation site may be some distance away 

from each other and that rainfall amount and intensities may 

vary between streamgages. Even if the two streamgages are 

in close proximity to each other, the index streamgage and 

estimation site may have different watershed-area sizes or 

other basin characteristics that affect how the stream responds 

to a precipitation event, as determined by a local rain gage 

and (or) radar data. Streamflows at streamgages 03114094 

(Herod) and 03111675 (Job) are shown in figure 2 as an 

4.00

1.86

4.00

4.36

0.1

1

10

11/27/2015 11/29/2015 12/1/2015

Streamflow, in cubic feet per second

Date

Single observed streamflow value at

U.S. Geological Survey streamgage 03114094 (Herod)

Single observed streamflow value at

U.S. Geological Survey streamgage 03111675 (Job)

EXPLANATION

Continuous streamflow at U.S. Geological Survey streamgage 03114094 (Herod)

Continuous streamflow at U.S. Geological Survey streamgage 03111675 (Job)

Figure 2. Streamflow at U.S. Geological Survey streamgages 03114094, Herod Run near New Freeport, and 03111675, Job Creek at 

Delphene, Pennsylvania, during a precipitation event.
10 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

example of this. The two streamgages are adjacent to one 

another and have watershed areas of about 1.8 mi2 (03114094 

Herod) and about 6.6 mi2 (03111675 Job). Streamflows of 

4 ft3/s on the rising and falling limbs of the hydrograph for 

streamgage 03111675 (Job) are shown in figure 2 with black 

circles; for comparison, the streamflows at the same time for 

streamgage 03114094 (Herod) are shown with black triangles 

at 4.36 ft3/s and 1.86 ft3/s, respectively. In this example, if the 

streamflows at streamgage 03114094 (Herod) were estimated 

using data from streamgage 03111675 (Job), the index-gage 

method would not capture the differences in the response to 

the precipitation event that occurred on November 29, 2015, 

between the two streamgages.

To examine the potential effects of precipitation and 

runoff events more closely, relations were developed using 

MOVE.1 between estimation site 03111235 (DogTrib) 

and index streamgages 03111200 (Dunkle) and 03111890 

(MWheeling) using (1) all concurrent streamflow data and 

(2) data with streamflow removed on the day precipitation 

occurred and the 2 days following the precipitation event. 

Six different MOVE.1 regressions were developed for each 

situation, one regression with all streamflow and five regressions with 100 random concurrent data points for a total of 

12 regressions. Prediction intervals at the 95-percent confidence interval, NSE values, and the r value were computed 

for all MOVE.1 regressions. The NSE values were calculated 

using the same dataset for all 12 MOVE.1 regressions. This 

analysis was done at the two different streamgage pairs. 

Statistical summaries of the log prediction interval width 

and NSE values for the two streamgage pairs are shown in 

figure 3; (regression statistics are available in appendix 1.) 

For both sets of streamgage pairs, the NSE values for the two 

datasets (runoff and non-runoff influenced data) were similar, 

but the log prediction interval width was generally greater 

when the runoff-influenced periods were included, indicating 

greater uncertainty.

To minimize the effect of precipitation runoff in the 

watershed, runoff-influenced streamflow was not considered 

in further data analysis unless otherwise specified. Data on at 

least 3 days per precipitation event anywhere in a watershed, 

as determined by a local rain gage and (or) radar data, were 

removed from the streamflow record for each streamgage, 

including the day (or days) precipitation occurred and the 

2 days following the precipitation event.

Zero Streamflow Values

During streamgage inspections, the gage height of zero 

streamflow (GZF) was determined by measuring the lowest 

point on the streamflow control such as rock riffle. When 

there was no streamflow over the control, as evidenced by the 

gage height being lower than the GZF, zero streamflow was 

calculated. The occurrence of zero flow does not necessarily mean that the stream was completely dry; pools of water 

may have been present in the stream channel. In addition, it 

is possible that there may have been a small amount of water 

leaking through the control; however, it was assumed to be 

negligible. The relatively short 18-month streamflow record 

indicates that it is not unusual for small streams in southwestern Pennsylvania not appreciably affected by human activities to have zero flow conditions during summer and autumn 

months.

Zero streamflows were not used in the MOVE.1 regression analysis. The MOVE.1 regression analysis utilizes log 

streamflow, thus a streamflow of zero is undefined and cannot 

be used. Setting zero streamflow to a very small number was 

attempted, but it was found that arbitrary numbers affected the 

MOVE.1 regression analysis. Even though zero streamflow 

cannot be estimated directly, the MOVE.1 regression equation 

can be rearranged to estimate the streamflow at the index 

streamgage at which the flow at the estimation site would be 

very close to zero. Data collected during the MOVE.1 regression development period can guide zero flow determination as 

well. When zero streamflows were reported at the estimation 

site, two values were noted: (1) the highest corresponding 

streamflow at the index streamgage (“highest index streamflow 

at zero,” or HISAZ for purposes of this report) and (2) the 

highest value at the estimation site when the index streamgage 

streamflow was less than or equal to the HISAZ value. These 

two values are used for evaluation of streamflow after the 

MOVE.1 regression development period, as described in the 

“Evaluation of Streamflow Not Used for Regression Development” section that begins on page 33.

Instantaneous and Daily Mean Streamflow

Future application of the index-gage method will require 

periodic streamflow measurements typically made over a short 

period of time (approximately 1 hour or less) at an estimation 

site; however, the index streamgage may have instantaneous 

and daily mean streamflow time series. An analysis was done 

to determine the implications of using daily mean streamflow values computed at the index streamgage as opposed to 

5- or 15-minute instantaneous values (with runoff-influenced 

streamflow removed). Daily mean streamflows are available 

for USGS streamgages on the National Water Information 

System NWISWeb (https://waterdata.usgs.gov/nwis) and may 

be easier to work with than instantaneous values where the 

time stamp of the value needs to be taken into consideration.

There does not appear to be a clear basis for using daily 

mean streamflow rather than instantaneous streamflow for the 

data comparison. Instantaneous streamflow values were used 

for this analysis when comparing data for 11 of the 12 newly 

established streamgages. The analysis using previously 

established index streamgages was completed using daily 

mean streamflow data that are publicly available. Additionally, 

daily mean streamflow values were used for one of the newly 

established streamgages (03072890, Fonner) when the instantaneous values were temperature affected and the daily mean 

value was considered a better value (Hittle, 2019b).
Analysis of Streamflow Estimation 11

2.500

2.000

1.500

1.000

0.500

0.000

Log prediction Interval width, 

in number of log cycles

03111890 (MWheeling)

1.000

0.900

0.800

0.700

0.600

0.500

Nash-Sutcliffe efficiency

03111890 (MWheeling)

0.400

0.300

0.200

0.100

0.000

1.000

0.900

0.800

0.700

0.600

0.500

Nash-Sutcliffe efficiency

03111200 (Dunkle)

0.400

0.300

0.200

0.100

0.000

EXPLANATION

Streamflow

Runoff influenced

Non-runoff influenced

A B

C D

2.500

2.000

1.500

1.000

0.500

0.000

Log prediction Interval width, 

in number of log cycles

03111200 (Dunkle)

Figure 3. For U.S. Geological Survey (USGS) streamgage 03111235, Unnamed Trib to Dog Run at Dunsfort, Pennsylvania, A, log 

prediction interval width and B, Nash-Sutcliffe Efficiency values, as estimated using USGS streamgage 03111200, Dunkle Run near 

Claysville, Pennsylvania, and C, log prediction interval and D, Nash-Sutcliffe Efficiency values as estimated using USGS streamgage 

03111890, Middle Wheeling Creek near Claysville, western Pennsylvania, for six MOVE.1 regressions with and without runoff-influenced 

streamflow.

Frequency of Streamflow Measurements

The current PADEP streamflow-measurement schedule 

starts about 2.5 years in advance of any longwall mining 

activity underneath a stream. Streamflow is measured prior 

to mining once a month for 2 years, weekly for 6 months, 

and daily for 2 weeks (Pennsylvania Department of Environmental Protection, 2005), regardless of the timing of antecedent precipitation. This schedule results in approximately 

60 measurements made over 2.5 years at the site of interest. 

The purpose of examining streamflow-measurement schedules 

was to determine how to get the maximum amount of information from a prescribed measurement schedule while attempting 

to keep a similar number of measurements as the current 

PADEP schedule. The various streamflow-measurement 

schedules evaluated are listed in table 3. An example calendar 

of selected measurement schedules is shown in figure 4. These 

streamflow-measurement schedules were applied at three 

streamgage pairs. MOVE.1 regression diagnostic factors and 

results are discussed in the following paragraphs and presented 

in table 4 and figure 5.

Three streamgage pairs were analyzed to illustrate 

three different scenarios that could be seen in practice. (1) 

A MOVE.1 regression to estimate streamflow at streamgage 

03111235 (DogTrib) using streamflow data from streamgage 

03107698 (Traverse) represents the scenario where the 
12 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania Table 3. Descriptions of streamflow-measurement schedules, including whether runoff-influenced streamflow was used in the schedule, an explanation of the schedule, whether it is possible to implement the schedule for data collection, and examples explaining the schedules. Streamflow-measurement schedule identifier Runoff-influenced streamflow included? Streamflow-measurement schedule explanation Is this schedule possible to implement for data collection? Example ALL_PO No Streamflow measurement made every 5 minutes This scenario represents a continuous- record streamgage, not a periodically measured streamgage If a day is not influenced by precipitation, every 5-minute data point in the day is used, so there would be 288 points for 1 day PO1 No One streamflow measurement per day every day when the streamflow is not affected by precipitation (the day of precipitation and 2 days following is considered affected by precipitation) Yes See figure 4, PO1 schedule in orange text PO2 No One streamflow measurement per day on days 1,3,5,7,10,13,16 and every 3 days after when the streamflow is not affected by precipitation (the day of precipitation and 2 days following is considered affected by precipitation) Yes See figure 4, PO2 schedule in dark blue text PO3 No One streamflow measurement every month for 2 years, one streamflow measurement a week for 6 months, one streamflow measurement a day for 2 weeks Yes Using only streamflow not influenced by precipitation, the DEP schedule was followed. This schedule has fewer measurements than expected because many days in the final 2 weeks may have been precipitation influenced PO4 No One streamflow measurement once a week on the same day. If no stream- flow measurement is able to be obtained due to precipitation, the first non-runoff influenced day is measured, then immediately back to regular 

schedule

Yes See figure 4, PO4 schedule in light blue 

text
Analysis of Streamflow Estimation 13

Table 3. Descriptions of streamflow-measurement schedules, including whether runoff-influenced streamflow was used in the schedule, an explanation of the schedule, whether it is possible to implement the schedule for data collection, and examples explaining the schedules.—Continued

Streamflow-measurement 

schedule identifier

Runoff-influenced 

streamflow included?

Streamflow-measurement 

schedule explanation

Is this schedule possible to 

implement for data collection? Example

PO5 (1–2) No

Every month for 2 years, the first (PO5-1) 

or second (PO5-2) non-runoff influenced days are measured as described in PO2. For 6 months, all days as described in PO2 are measured. 

Yes See figure 4, PO5 schedule in green text

PO6 No

Every month, the first non-runoff influenced days are measured as described 

in PO2; however, if only one measurement is made (due to precipitation), the next set of non-runoff influenced days are measured until at least day 1, and day 3 are measured

Yes See figure 4, PO6 schedule in purple text

PO7 No

Every month, only the first non-runoff 

influenced days are measured as described in PO2 that results in measuring at least day 1 and day 3 

No - It would not be possible to predict 3 

days ahead if rain would fall, and if a measurement was made, one would use it, mimicing PO6

See figure 4, PO7 schedule in grey text

PO8 No

Every month, streamflow measurements 

are made on the PO2 schedule so the longest period of non-runoff influenced streamflow is measured but the same numbered day is not measured twice. This could result in measurements being made after several precipitation events in one month

Yes See figure 4, PO8 schedule in red text

DEP (1–4) Yes

One streamflow measurement every 

month for 2 years, one streamflow measurement a week for 6 months, one streamflow measurement a day for 2 weeks

Yes

The same day each week was chosen. 

This is accomplished 4 times, starting on a different day of the week each time
14 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

P P R R 1 2

P R R 1 2 3 4

5 6 7 8 P P R

R 1 2 P R R 1

2 3 4 5 6 7 8

9 10 P R R 1 2

Sunday Thursday

PO1 PO2 PO8

PO5-2 PO6 PO7

Monday

PO1 PO2 PO8

PO5-2 PO6 PO7

PO1

PO4

PO1 PO2 PO8

PO5-1 PO6 PO1

Tuesday Wednesday Friday Saturday

PO1 PO2 PO1

PO1

PO1 PO2 PO8

PO1 PO1 PO2 PO8 PO4 PO5-1 PO6 PO1

PO1

PO1 PO2

PO4

PO1 PO1 PO2 PO1

PO1 PO2

PO4 PO1 PO1 PO2 PO1

PO1 PO2

PO4 PO5-2 PO6

PO7 PO1

PO1 PO2 PO8

PO5-2 PO6 PO7

Figure 4. Example calendar of measurement schedules during a hypothetical month. The text within the calendar indicates whether 

a streamflow measurement should be made on that day according to selected measurement schedules. Measurement schedules are 

color coded to enhance readability. (PO1, measurement schedule; 1–10, number of days for which streamflow is no longer influenced by 

runoff; R, streamflow influenced by runoff; P, precipitation observed; = (double line), delineates 1 month)

estimation site (DogTrib) experiences zero streamflow. (2) 

A MOVE.1 regression to estimate streamflow at streamgage 

03111200 (Dunkle, where zero streamflow was not recorded) 

using streamflow data from streamgage 03107698 (Traverse) 

represents a scenario that has several outliers, likely owing 

to localized conditions or uncertain shift application. (3) A 

MOVE.1 regression to estimate streamflow at streamgage 

03107698 (Traverse, where zero streamflow was not recorded) 

using streamflow at streamgage 03108010 (Fishpot) represents 

a scenario that does not appear to have outliers.

The ALL_PO streamflow-measurement schedule mimics 

a continuous-record streamgage with 5-minute data collected 

but with no runoff-influenced streamflow included in the 

analysis. The MOVE.1 regression results from this schedule 

serve as a standard to which all other measurement schedules 

can be compared with regard to regression prediction intervals 

and zero streamflow. As can be seen in table 4, there are log 

prediction interval widths for some schedules that are smaller

than the ALL_PO value. A small log prediction interval width 

indicates better agreement between the streamgages based on 

the calibration data collected and results in a better MOVE.1 

regression than is produced when the entire dataset is sampled.

Zero Streamflow Recorded at the Estimation Site 

On the basis of the analysis of measurement frequency, 

only measurement schedules that do not include runoffinfluenced streamflow are discussed here. The prediction 

of zero streamflow at an estimation site requires a streamflow-measurement frequency that is likely to include zero 

streamflow during the MOVE.1 regression development 

period. To do this, a measurement scenario that measures 

the longest non-runoff influenced period needs to be used. 

Three of the streamflow-measurement schedules (PO5, PO6, 

and PO7) did not include any zero streamflow values for the 

estimation site; therefore, they were excluded from further 
Analysis of Streamflow Estimation 15

Table 4. Results of MOVE.1 regression diagnostic factors, using a 95-percent confidence interval, for 14 measurement schedules for 

three streamgage pairs in western Pennsylvania. The PO1, PO2, and PO8 schedules are highlighted because they best represent the 

scenario where the estimation site recorded days of zero streamflow.

[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; *, zero streamflow, not observed at the estimation site during the model development period; n/a, 

datapoints selected for this measurement schedule did not include zero streamflow at the estimation site even though zero streamflow was observed during the 

model development period; brown highlighted schedules are those that best represent the scenario where the estimation site recorded days of zero streamflow; 

log, logarithm base 10]

Streamflowmeasurement 

schedule

Number of 

streamflow 

measurements

Number of 

measurements 

used in 

analysis

Coefficient of 

correlation 

r

Nash-Sutcliffe 

Efficiency 

value 

(computed on a 

mutual dataset)

Width 

of log 

prediction 

interval 

(number of 

log cycles)

Back-transformed 

Prediction Interval Limits at 

1.00 ft3/s

Highest 

index 

streamflow 

at estimated 

streamflow 

of zero (ft3/s)

Lower 

prediction 

interval limit

Upper 

prediction 

interval limit

USGS streamgage 03111235, Unnamed trib to Dog Run at Dunsfort, streamflow estimated by using USGS streamgage 03107698, Traverse Creek near Kendall

ALL_P0 53,937 49,575 0.901 0.819 1.213 0.310 5.068 0.57

PO1 193 181 0.905 0.814 1.354 0.256 5.789 0.47

PO2 114 108 0.908 0.815 1.322 0.292 6.127 0.38

PO3 37 36 0.895 0.815 1.327 0.273 5.805 0.23

PO4 71 68 0.904 0.818 1.353 0.273 6.150 0.38

PO5-1 51 51 0.896 0.822 1.206 0.292 4.694 n/a

PO5-2 46 45 0.907 0.821 1.093 0.287 3.559 0.23

PO6 73 73 0.906 0.818 1.230 0.278 4.722 n/a

PO7 51 51 0.913 0.816 1.135 0.324 4.421 n/a

PO8 58 55 0.906 0.816 1.283 0.271 5.204 0.38

DEP-11 61 61 0.895 0.814 1.450 0.144 4.060 n/a

DEP-21 61 60 0.838 0.806 1.699 0.190 9.487 0.18

DEP-31 61 58 0.863 0.812 1.334 0.221 4.779 2.35

DEP-41 60 59 0.873 0.822 1.221 0.293 4.883 0.23

USGS streamgage 03111200, Dunkle Run near Claysville, streamflow estimated by using USGS streamgage 03107698, Traverse Creek near Kendall

ALL_P0 67,976 67,976 0.898 0.793 0.783 0.426 2.585 *

PO1 246 246 0.886 0.778 0.854 0.396 2.833 *

PO2 144 144 0.882 0.786 0.876 0.393 2.952 *

PO3 46 46 0.944 0.759 0.830 0.386 2.605 *

PO4 72 72 0.885 0.776 1.056 0.323 3.673 *

PO5-1 63 63 0.901 0.803 1.094 0.245 3.037 *

PO5-2 62 62 0.933 0.787 0.836 0.423 2.905 *

PO6 90 90 0.852 0.804 0.909 0.310 2.513 *

PO7 69 69 0.886 0.801 0.809 0.353 2.272 *

PO8 76 76 0.870 0.801 1.152 0.247 3.500 *

DEP-11 61 61 0.929 0.748 0.868 0.354 2.618 *

DEP-21 59 59 0.928 0.800 0.796 0.463 2.894 *

DEP-31 61 61 0.932 0.756 0.960 0.405 3.692 *

DEP-41 64 64 0.901 0.736 1.255 0.286 5.151 *

USGS streamgage 03107698, Traverse Creek near Kendall, streamflow estimated by using USGS streamgage 03108010, Fishpot Run near Shippingport

ALL_P0 72,244 72,244 0.933 0.872 0.777 0.431 2.650 *

PO1 259 259 0.930 0.873 0.778 0.422 2.523 *

PO2 150 150 0.927 0.873 0.807 0.402 2.579 *

PO3 45 45 0.927 0.863 0.745 0.436 2.423 *

PO4 85 85 0.923 0.874 0.768 0.411 2.411 *
16 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

Table 4. Results of MOVE.1 regression diagnostic factors, using a 95-percent confidence interval, for 14 measurement schedules for 

three streamgage pairs in western Pennsylvania. The PO1, PO2, and PO8 schedules are highlighted because they best represent the 

scenario where the estimation site recorded days of zero streamflow.—Continued

[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; *, zero streamflow, not observed at the estimation site during the model development period; n/a, 

datapoints selected for this measurement schedule did not include zero streamflow at the estimation site even though zero streamflow was observed during the 

model development period; brown highlighted schedules are those that best represent the scenario where the estimation site recorded days of zero streamflow; 

log, logarithm base 10]

Streamflowmeasurement 

schedule

Number of 

streamflow 

measurements

Number of 

measurements 

used in 

analysis

Coefficient of 

correlation 

r

Nash-Sutcliffe 

Efficiency 

value 

(computed on a 

mutual dataset)

Width 

of log 

prediction 

interval 

(number of 

log cycles)

Back-transformed 

Prediction Interval Limits at 

1.00 ft3/s

Highest 

index 

streamflow 

at estimated 

streamflow 

of zero (ft3/s)

Lower 

prediction 

interval limit

Upper 

prediction 

interval limit

PO5-1 79 79 0.926 0.867 0.818 0.417 2.745 *

PO5-2 84 84 0.941 0.866 0.801 0.441 2.787 *

PO6 86 86 0.917 0.873 0.798 0.384 2.415 *

PO7 68 68 0.92 0.870 0.856 0.375 2.691 *

PO8 78 78 0.925 0.871 0.878 0.372 2.804 *

DEP-11 62 62 0.956 0.871 0.702 0.396 1.998 *

DEP-21 64 64 0.915 0.864 1.018 0.418 4.353 *

DEP-31 64 64 0.931 0.874 0.834 0.400 2.727 *

DEP-41 62 62 0.956 0.872 0.697 0.472 2.347 *

1

Schedules include runoff-influenced streamflow.

measurement-schedule analyses. Streamflow-measurement 

schedules PO3 and PO4 also were excluded from further measurement-schedule analysis because of the high probability 

of missing zero streamflow days. The other streamflow-measurement schedules (PO1, PO2, PO8) included days with zero 

streamflow values, although the HISAZ values as compared to 

the ALL-PO schedule were less.

The MOVE.1 regression developed with data from the 

PO8 streamflow-measurement schedule produced log prediction interval widths similar to those from the MOVE.1 

regression developed with data from the ALL_PO schedule 

when estimating streamflow at site 03111235 (DogTrib) using 

streamflow at streamgage 03107698 (Traverse). The HISAZ 

value and the log prediction interval width from the MOVE.1 

regression developed with data from the PO8 schedule 

(0.38 ft3/s and 1.283 log cycles, respectively) were comparable 

to those from the regression developed with data from the 

ALL_PO schedule (0.57 ft3/s and 1.213 log cycles, respectively), and the number of required streamflow measurements 

was similar to that for the DEP schedules.

Zero Streamflow Not Recorded at Estimation Site

On the basis of the analysis of the streamgage pairs in the 

previous section where streamflow at the estimation site went 

to zero, the PO1, PO2, and PO8 streamflow-measurement 

schedules are the focus of additional analysis. Estimated 

streamflows in relation to observed streamflows at streamgage 

03111200 (Dunkle) and the 95-percent prediction intervals 

for the MOVE.1 regressions developed with data from the 

PO1, PO2, and PO8 streamflow-measurement schedules are 

shown in figure 5. For any estimation site, a crucial factor in 

determining the optimum streamflow-measurement schedule is 

ensuring data are collected during as many non-runoff periods 

as possible and for the longest period possible. However, it 

does not appear that measurements are needed every day during the entire non-runoff influenced period. This is evidenced 

by the similarity between the log prediction interval width of 

the MOVE.1 regression developed with data from the PO2 

schedule (0.876 log cycles) and that of the PO1 schedule 

(0.854 log cycles) for 03107698 (Traverse) as estimated using 

03111200 (Dunkle) (table 4). However, the log prediction 

interval width for the MOVE.1 regression developed with 

data from the PO8 schedule (1.152 log cycles) is larger than 

those developed with data from the PO1 and PO2 schedules. 

The same outliers were observed in the MOVE.1 regressions 

using data from the PO2 and PO8 schedules (fig 5); however, 

the larger log prediction interval width can be explained by 

the fact that there are more streamflow measurements in the 

regression calibration dataset (144 streamflow measurements) 

for the PO2 streamflow-measurement schedule compared to 

the PO8 schedule (76 streamflow measurements). Thus, the 

MOVE.1 regression residual chosen for the log prediction 

interval width was different for the two datasets.

Measurement schedule data for streamflow estimated 

at streamgage 03107698 (Traverse) using streamflow at 

streamgage 03108010 (Fishpot) show trends in the log 

prediction interval widths similar to those for streamgage 

03111200 (Dunkle). The log prediction interval widths are 

similar for the MOVE.1 regressions developed with data from
Analysis of Streamflow Estimation 17

0.1

1

10

0.1 1 10

Observed streamflow, in cubic feet per second

Estimated streamflow, in cubic feet per second

PO1 95-percent prediction interval

PO2 95-percent prediction interval

PO8 95-percent prediction interval

EXPLANATION

PO1

PO2

PO8

Outliers observed using data selected 

by the streamflow measurement

Figure 5. Observed streamflow in relation to estimated streamflow at U.S. Geological Survey (USGS) streamgage 03111200, Dunkle 

Run near Claysville (Dunkle), western Pennsylvania, for streamflow-measurement schedules PO1, PO2, and PO8 with the 95-percent 

prediction intervals. Streamflow at USGS 03111200 (Dunkle) was estimated using streamflow at USGS 03107698, Traverse Creek near 

Kendall.

the PO2 schedule (0.807 log cycles) and the PO1 schedule 

(0.777 log cycles) but lower than the log prediction interval 

width for the MOVE.1 regressions developed with data from 

the PO8 data (0.878 log cycles).

Current PADEP Schedule

To examine what is currently required, MOVE.1 regressions were produced with data selected for the current PADEP 

schedule labeled DEP. MOVE.1 regressions produced with 

data from the DEP schedule were examined with four different regressions starting on any day of the week (DEP-1, 

DEP-2, DEP-3, and DEP-4). These four scenarios (DEP-1 to 

DEP-4) emphasize data at the end of the analysis period, in 

which more than one-half of the measurements are collected 

in the last 6 months, and a one-quarter of them are collected 

in the last 2 weeks. Despite the inclusion of runoff-influenced 

streamflow, the DEP schedule sometimes resulted in smaller 

log prediction interval widths than the ALL_PO schedule. This 

was seen in the MOVE.1 regression to estimate streamflow at 

03107698 (Traverse) using streamflow at 03108010 (Fishpot) 

using the DEP-1 and DEP-4 scenarios, which produced 

smaller log prediction interval widths. When zero streamflow 

at the estimation site is considered, the DEP-1 scenario missed 
18 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

instances where zero streamflow occurred, which is considered a critical piece of information for future streamflow 

examination.

Streamflow-Measurement Summary

A graphical summary of the log prediction interval width 

produced by MOVE.1 regressions with data from streamflow-measurement schedules All_PO, DEP, PO1, PO2, and 

PO8 is shown in figure 6. The symbol for the DEP schedule 

shows the maximum and minimum prediction interval widths 

because this schedule was examined using four different 

MOVE.1 regressions for the four scenarios run (DEP-1 to 

No outliers 

(Traverse estimated from Fishpot)

Outliers 

(Dunkle estimated from Traverse)

Zero streamflow 

(DogTrib estimated from Traverse)

1.8

1.6

1.4

1.2

1

0.8

0.6

Log prediction interval width, in number of log cycles, 95-percent confidencel level

ALL_PO

DEP

PO1

EXPLANATION

PO2

PO8

Figure 6. Prediction interval widths for the Zero streamflow example for U.S. Geological Survey (USGS) streamgage 03111235, 

Unnamed trib to Dog Run at Dunsfort (DogTrib), estimated using streamflow at USGS streamgage 03107698, Traverse Creek near Kendall

(Traverse); Outliers example for USGS streamgage 0311200, Dunkle Run near Claysville (Dunkle), estimated using streamflow at USGS 

streamgage 03107698, Traverse Creek near Kendall; and No outliers example for USGS streamgage 03107698, Traverse Creek near 

Kendall, estimated using streamflow at USGS streamgage 03108010 Fishpot Run near Shippingport (Fishpot), western Pennsylvania. The 

DEP streamflow-measurement schedule is shown with the highest and lowest log prediction interval widths because this schedule was 

analyzed four times using different data. The ALL_PO, PO1, PO2, and PO8 streamflow-measurement schedules were each analyzed only 

once.

DEP-4). In general, figure 6 shows that the MOVE.1 regressions produced with data from the PO1 and PO2 schedules 

resulted in log prediction interval widths at the 95-percent 

confidence level that are similar to each other and larger 

than the widths from regressions produced with data from 

the ALL_PO schedule. The MOVE.1 regression prediction 

interval width using data from the PO8 schedule was larger 

than that from the ALL_PO data regression but fell either 

above or below the prediction interval widths for the regressions produced with data from the PO1 and PO2 schedules. 

For MOVE.1 regressions produced with data from the PO1, 

PO2, and PO8 schedules, the NSE values were within 0.02, 

indicating the data selected by these schedules produced 
Analysis of Streamflow Estimation 19

similar regressions. Data from the DEP schedule were examined using four different regressions starting on any day of 

the week. The differences in the log prediction interval widths 

indicate that the data selected by these scenarios for the current PADEP schedule included various outliers, depending on 

the day the measurement schedule was started. Interestingly, 

these scenarios measured runoff-influenced data; however, 

two of the DEP MOVE.1 regression prediction interval widths 

(DEP-1 scenario and the DEP-4 scenario for estimation site 

03108010 [Fishpot] estimated by index streamgage 03107698 

[Traverse]) were lower than the ALL_PO data regression prediction interval width, indicating it is not only the runoff influence that affected the prediction interval width; otherwise, all 

interval widths would be larger. The distribution of the measurement selection (concentrating most of the measurements 

within 6 months versus spacing the measurements evenly 

throughout the regression development period) also seems to 

play a part in the prediction interval width.

For this study, the PO2 schedule was used to select data 

for MOVE.1 regression development to capture all non-runoff 

influenced streamflow periods during the regression development period. This schedule was used to eliminate a potential 

source of error when comparing multiple index streamgages 

for use with an estimation site and to assure that the lowest 

streamflow was sampled. In the PO8 schedule, the lowest 

streamflows may not be measured if the longest non-runoff 

influenced period occurs at the beginning of the month and 

the lowest streamflow occurs later. This is one of the cautions of using the PO8 schedule for data selection; the range 

and number of outliers can change depending on whether the 

PO8 schedule started at the beginning of a month or in the 

middle of a month.

Index-Gage Method Results

Once the streamflow-measurement schedule for analysis 

was determined, regressions using MOVE.1 were developed 

for all streamgage pairs to determine which index streamgage 

best estimated streamflow at the estimation site. The log 

prediction interval width, NSE, and correlation coefficient (r) 

were used to select the best index streamgage. The width of 

the log prediction interval provided an indication of the uncertainty associated with the MOVE.1 regression; the smaller the 

log prediction interval width, the better the streamgage regression. This was generally confirmed with the NSE and r values 

computed with each MOVE.1 regression. An analysis was 

done to determine whether watershed size or distance might 

affect the selection of the best index streamgage. Non-runoff 

influenced data from May 2015 to March 2017 were used for 

all streamgages. A summary of all data is presented in the 

remainder of this section. The MOVE.1 regression diagnostics 

for all streamgage pairs are shown in table 5. The log prediction interval width is listed for each streamgage pair; the number in red is the lowest value for a particular streamgage. For 

any one estimation site, the highest NSE value corresponds 

to the first or second lowest log prediction interval width. 

However, the lowest log prediction interval width was not 

the same for every newly established gage; it ranged from 

0.609 log cycles at 03107698 (Traverse) to 1.451 log cycles at 

03114094 (Herod). Further, NSE and log prediction interval 

widths do not correspond between estimation sites. For 

instance, an NSE value of 0.841 corresponds to a log prediction interval width of 1.410 log cycles at station 03111675 

(Job) when the index streamgage is 03111705 (SF Dunkard). 

When the same index streamgage (SF Dunkard) was used to 

estimate streamflow at 03111200 (Dunkle), the NSE value 

was 0.602, and the log prediction interval width was 1.129 log 

cycles. The MOVE.1 regressions developed using SF Dunkard 

as the index streamgage produced lower values for NSE and 

log prediction interval width for estimation site 03111200 

(Dunkle) than for estimation site 03111675 (Job), indicating 

that even though the regression fit at Dunkle was not as good, 

a smaller log prediction interval width was produced. Differences in lowest log prediction interval width appear to correspond to the range in log-transformed streamflows observed at 

the estimation site during the regression development period. 

The lowest and highest non-runoff influenced streamflow 

values that were observed at each estimation site from May 1, 

2015, to March 31, 2017, are shown in table 6. The log range 

in streamflow at estimation site 03111200 (Dunkle) is less than 

that at estimation site 03111675 (Job). Of the newly established sites, those in Greene County have the largest range in 

log streamflow, whereas those in Washington County have 

middle ranges in log streamflow.

MOVE.1 Regression Discussion

Development of MOVE.1 regressions using all the newly 

established sites as estimation sites revealed that there was not 

one index streamgage that was ideal for use with all estimation sites in the study area. Two aspects of the estimation site/

index streamgage relations can be easily discerned— distance 

between streamgages (table 7) and the watershed-area ratio of 

the streamgages. These aspects are examined in relation to the 

index-gage method performance.

Distance from the index streamgage in relation to the log 

prediction interval width for 12 newly established streamgages 

is shown in figure 7. For purposes of this illustration, any log 

prediction interval width greater than 1.7 is shown as a value 

of 1.7. For 10 of 12 newly established sites, using the closest 

streamgage as the index streamgage produced MOVE.1 

regressions with the first or second smallest log prediction 

interval width except for 03072890 (Fonner) and 03105927 

(Crab).

Streamflow statistics can be transferred from a gaged 

site to an ungaged site on the same stream within a certain 

watershed-area ratio. A previous study by Sloto and others 

(2017) showed that for most transferred statistics, the watershed-area ratio 0.33–3.0 performs as well as, if not better than, 

the more traditional ratios of 0.5–1.5 or 2.0. For this study, 

the streamgages were evaluated on how well they estimate 

base flow at a periodically measured site based on prediction 
20 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania Table 5. Summary of MOVE.1 regression coefficient of correlation, Nash-Sutcliffe Efficiency value, and log prediction interval width for streamgage pairs in western Pennsylvania. [PI, prediction interval; r, correlation coefficient; NSE, Nash-Sutcliffe Efficiency value; red italicized font indicates the smallest log predicition interval width, the largest correlation coefficient, or the largest NSE value; x, the estimation site and index streamgage are the same streamgage; -, the index streamgage was not used to estimate streamflow at the estimation site] Index streamgage Estimation site 03072890 03081800 03105927 03107698 PI width (number of log cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

03072890 x x x 1.295 0.874 0.874 1.670 0.821 0.644 1.099 0.827 0.65303081800 1.642 0.888 0.776 x x x 1.463 0.864 0.727 0.921 0.896 0.79203105927 1.949 0.821 0.643 1.119 0.864 0.727 x x x 0.738 0.937 0.87303107698 1.770 0.827 0.653 1.026 0.896 0.792 1.055 0.937 0.873 x x x03108010 2.220 0.717 0.434 1.348 0.823 0.646 1.655 0.871 0.742 0.774 0.935 0.871

03111200 2.033 0.840 0.681 1.393 0.822 0.644 1.636 0.847 0.694 0.859 0.896 0.79203111215 1.382 0.860 0.719 1.193 0.880 0.760 1.521 0.888 0.776 1.005 0.888 0.77503111235 1.577 0.863 0.725 1.155 0.882 0.763 1.724 0.856 0.713 0.972 0.908 0.81603111675 2.150 0.716 0.432 1.506 0.830 0.660 1.648 0.834 0.668 1.358 0.831 0.66103111705 2.227 0.710 0.419 1.188 0.842 0.685 1.460 0.878 0.755 1.060 0.849 0.69803111890 1.625 0.884 0.767 0.823 0.935 0.869 1.223 0.906 0.813 0.785 0.925 0.850

03114094 2.202 0.667 0.334 1.181 0.821 0.642 1.236 0.825 0.649 1.070 0.837 0.674

103072000 1.752 0.821 0.641 - - - - - - - - -103074500 - - - 0.906 0.926 0.853 - - - - - -103108000 - - - - - - - - - 0.661 0.955 0.909

103110830 - - - - - - - - - 0.609 0.972 0.945103112000 1.230 0.898 0.796 - - - - - - 0.909 0.898 0.797
Analysis of Streamflow Estimation 21

Table 5. Summary of MOVE.1 regression coefficient of correlation, Nash-Sutcliffe Efficiency value, and log prediction interval width for streamgage pairs in western Pennsylvania.—Continued[PI, prediction interval; r, correlation coefficient; NSE, Nash-Sutcliffe Efficiency value; red italicized font indicates the smallest log predicition interval width, the largest correlation coefficient, or the largest NSE value; x, the estimation site and index streamgage are the same streamgage; -, the index streamgage was not used to estimate streamflow at the estimation site]

Index 

streamgage

Estimation site

03108010 03111200 03111215 03111235

PI width 

(number of 

log cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

03072890 1.340 0.717 0.434 1.098 0.834 0.668 1.231 0.861 0.721 1.317 0.861 0.72203081800 1.105 0.823 0.646 1.139 0.822 0.644 1.506 0.880 0.760 1.369 0.882 0.76303105927 1.126 0.871 0.742 1.078 0.851 0.702 1.467 0.888 0.776 1.602 0.856 0.71203107698 0.726 0.935 0.871 0.800 0.895 0.790 1.370 0.887 0.775 1.319 0.908 0.81603108010 x x x 1.048 0.847 0.694 1.670 0.796 0.591 1.485 0.822 0.645

03111200 1.064 0.847 0.694 x x x 1.479 0.886 0.772 0.990 0.929 0.85703111215 1.127 0.796 0.591 1.019 0.885 0.771 x x x 1.247 0.886 0.77303111235 1.054 0.822 0.645 0.649 0.930 0.859 1.329 0.886 0.773 x x x03111675 1.465 0.744 0.488 1.336 0.793 0.587 1.447 0.866 0.731 1.422 0.845 0.69003111705 1.151 0.788 0.576 1.129 0.801 0.602 1.447 0.874 0.748 1.278 0.827 0.65403111890 1.016 0.846 0.692 1.027 0.865 0.730 1.047 0.931 0.861 1.221 0.886 0.772

03114094 0.999 0.820 0.641 0.940 0.771 0.541 1.353 0.763 0.527 1.466 0.770 0.541

103072000 - - - - - - - - - - - -103074500 - - - - - - - - - - - -103108000 0.713 0.912 0.824 0.873 0.915 0.830 - - - 1.345 0.866 0.732

103110830 - - - - - - - - - 1.271 0.881 0.761103112000 1.190 0.840 0.682 0.852 0.912 0.823 1.074 0.937 0.873 1.261 0.912 0.822
22 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania Table 5. Summary of MOVE.1 regression coefficient of correlation, Nash-Sutcliffe Efficiency value, and log prediction interval width for streamgage pairs in western Pennsylvania.—Continued [PI, prediction interval; r, correlation coefficient; NSE, Nash-Sutcliffe Efficiency value; red italicized font indicates the smallest log predicition interval width, the largest correlation coefficient, or the largest NSE value; x, the estimation site and index streamgage are the same streamgage; -, the index streamgage was not used to estimate streamflow at the estimation site] Index streamgage Estimation site 03111675 03111705 03111890 03114094 PI width (number of log cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

PI width 

(number of log 

cycles)

r NSE

03072890 2.460 0.702 0.405 2.871 0.710 0.419 1.171 0.880 0.759 2.278 0.667 0.33403081800 2.397 0.832 0.663 2.321 0.842 0.685 1.105 0.926 0.851 1.703 0.864 0.72903105927 2.132 0.834 0.668 2.244 0.881 0.761 1.014 0.906 0.813 1.675 0.826 0.65203107698 2.357 0.831 0.661 2.296 0.849 0.698 0.962 0.924 0.848 1.784 0.837 0.67403108010 2.760 0.744 0.488 2.748 0.788 0.576 1.340 0.846 0.692 1.607 0.841 0.681

03111200 2.401 0.793 0.587 2.555 0.801 0.602 1.295 0.866 0.732 1.786 0.771 0.54103111215 1.903 0.865 0.729 2.299 0.874 0.748 0.926 0.931 0.861 1.906 0.763 0.52703111235 2.066 0.845 0.690 2.165 0.828 0.656 1.100 0.886 0.772 1.830 0.769 0.53803111675 x x x 1.674 0.921 0.841 1.585 0.839 0.677 1.529 0.877 0.75403111705 1.410 0.921 0.841 x x x 1.289 0.849 0.699 1.451 0.927 0.85403111890 2.339 0.845 0.690 2.430 0.849 0.699 x x x 1.714 0.821 0.642

03114094 1.411 0.878 0.755 1.536 0.927 0.854 1.152 0.821 0.642 x x x

103072000 1.424 0.914 0.829 1.962 0.885 0.771 1.101 0.919 0.840 1.603 0.841 0.682103074500 - - - - - - - - - - - -103108000 - - - - - - - - - - - -

103110830 - - - - - - - - - - - -103112000 1.443 0.905 0.809 2.161 0.888 0.776 0.965 0.939 0.879 1.656 0.800 0.599

1Pre-existing streamgage, not established for this study.
Analysis of Streamflow Estimation 23

Table 6. Estimation sites, by county in western Pennsylvania, with the lowest and highest non-runoff influenced observed streamflow, 

May 1, 2015–March 31, 2017, and logarithmic transformed streamflow and streamflow range difference.

[*, indicates during the model development period, zero streamflow was observed; **; indicates only non-runoff influenced streamflow is considered; ft3/s, cubic 

foot per second]

Streamgage County

Lowest observed 

**streamflow

(ft3/s)

Highest observed 

**streamflow

(ft3/s)

Log base 10 

transformed 

lowest observed 

**streamflow

Log base 10 

transformed 

highest observed 

**streamflow

Difference between 

log base 10 transformed 

highest and lowest 

observed **streamflow

03108010 Beaver 0.07 8.56 −1.1549 0.9325 2.0874

03107698 Beaver 0.13 19.90 −0.8861 1.2989 2.1849

03081800 Fayette 0.22 34.84 −0.6576 1.5421 2.1997

03111200 Washington 0.23 38.90 −0.6383 1.5899 2.2282

03111890 Washington 0.01 4.96 −2.0000 0.6955 2.6955

03111215 Washington *0.01 8.65 −2.0000 0.9370 2.9370

03111235 Washington *0.001 1.197 −3.0000 0.0781 3.0781

03111675 Greene *0.01 24.94 −2.0000 1.3969 3.3969

03072890 Greene *0.001 3.174 −3.0000 0.5016 3.5016

03111705 Greene *0.01 33.45 −2.0000 1.5244 3.5244

03114094 Greene *0.01 42.70 −2.0000 1.6304 3.6304

03105927 Butler 0.02 71.97 −1.6990 1.8572 3.5561

interval width, regardless of location or watershed-area ratio. 

Figure 8 shows the watershed-area ratio of the estimation 

gage to the index gage versus log prediction interval width. 

The shaded area between the red lines represents where the 

index streamgage watershed area is 0.33 to 3 times the size of 

the estimation site. The streamgages outside the shaded area 

performed as well as those within it, and there does not appear 

to be any pattern between watershed-area ratio and log prediction interval widths (figure 8). An example is the streamflow 

relation between streamgage 03111235 (DogTrib) as estimated 

by streamgage 03112000 (Wheeling), with a watershed-area 

ratio of 0.001 and a log prediction interval width of 1.261 log 

cycles which makes it the fourth smallest log prediction interval width of the 14 index sites that were analyzed (table 5; 

Hittle, 2019c).

The distance between the streamgage pairs appears to be 

a major contributing factor to how well the index streamgage 

can estimate streamflow at the estimation site. The closest streamgage to estimation sites 03072890 (Fonner) and 

03105927 (Crab) is more than 10 miles away, and using the 

index streamgage closest to the estimation streamage did 

not produce MOVE.1 regressions having the first or second 

smallest log prediction interval widths. To further explore 

the distance issue, only index streamgages that were greater 

than 10 miles from the estimation site were examined. In 

this case, the closest streamgage produced MOVE.1 regressions with the first or second smallest prediction intervals for 

only 5 of 11 estimation sites; for 1 estimation site (03111705, 

SF Dunkard), all log prediction interval widths were greater 

than 1.7 log cycles. This indicates that it is ideal to have an 

index streamgage within about 10 miles of the site of interest 

but by no means indicates that acceptable prediction interval 

widths cannot be produced using streamgages further away.

Representative Index Streamgages

In the previous section “MOVE.1 Regression Discussion,” we looked at how factors related to the watershed 

area and location of the index streamgage are related to the 

MOVE.1 regression performance at one estimation site. The 

analysis in this section examines how one index streamgage 

relates to a number of estimation sites. The estimation sites are 

discussed in four county groups, (1) Washington County, (2) 

Beaver County, (3) Greene County and (4) Butler and Fayette Counties. As was discussed in the “Index-Gage Method 

Results” section beginning on page 19, the log prediction 

interval width cannot be used to look at the performance of 

one index streamgage for multiple estimation sites because the 

range of flow at the estimation site will influence this number. 

Therefore, the estimation sites are broken up into groups to 

determine the best index streamgage for an area as determined 

by log prediction interval width.

The log prediction interval widths from the MOVE.1 

regressions that were produced for each index streamgage are 

shown in figure 9. On the basis of the MOVE.1 regression log 

prediction interval widths, the streamflows at streamgages in 

Washington County are generally well estimated. MOVE.1 

regressions using streamgages 03112000 (Wheeling), 

03111890 (MWheeling), and 03111215 (Bonar) as index 

streamgages produced log prediction interval widths less than 

1.3 log cycles for all the Washington County streamgages. 
24 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania Table 7. Distance between the watershed area centroids for pairs of U.S. Geological Survey streamgages in western Pennsylvania. [x, the estimation site and index streamgage are the same streamgage; -, the index streamgage was not used to estimate streamflow at the estimation site] Index streamgage Distance, in miles Estimation site 03072890 03081800 03105927 03107698 03108010 03111200 03111215 03111235 03111675 03111705 03111890 03114094 03072890 x 44.1 60.9 39.8 43.5 18.6 13.0 17.4 14.3 16.2 12.4 16.8 03081800 44.1 x 72.1 69.6 70.8 54.7 55.3 59.7 51.0 54.1 55.9 52.2 03105927 60.9 72.1 x 31.1 21.7 49.1 59.0 54.1 74.6 75.8 59.0 77.1 03107698 39.8 69.6 31.1 x 7.5 22.4 31.1 26.1 50.3 50.3 32.3 52.2 03108010 43.5 70.8 21.7 7.5 x 28.0 37.3 32.9 55.3 55.9 38.5 57.8 03111200 18.6 54.7 49.1 22.4 28.0 x 9.9 5.6 28.6 28.6 10.6 29.8 03111215 13.0 55.3 59.0 31.1 37.3 9.9 x 6.5 19.3 19.3 1.6 21.7 03111235 17.4 59.7 54.1 26.1 32.9 5.6 5.6 x 24.9 24.9 6.8 26.1 03111675 14.3 51.0 74.6 50.3 55.3 28.6 19.3 24.9 x 3.1 18.0 2.5 03111705 16.2 54.1 75.8 50.3 55.9 28.6 19.3 24.9 3.1 x 18.0 2.5 03111890 12.4 55.9 59.0 32.3 38.5 10.6 1.6 6.8 18.0 18.0 x 19.9 03114094 16.8 52.2 77.1 52.2 57.8 29.8 21.7 26.1 2.5 2.5 19.9 x

103072000 19.2 - - - - - - - 11.0 13.4 27.8 11.7103074500 - 14.8 - - - - - - - - - -103108000 - - - 7.4 10.6 17.5 - 22.3 - - - -

103110830 - - - 6.0 - - - 20.1 - - - -103112000 14.4 - - 40.2 46.8 19.0 10.0 14.4 12.5 11.3 8.5 13.2

1Pre-existing streamgage, not established for this study.
Analysis of Streamflow Estimation 25

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03081800

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03105927

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03107698

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03108010

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03111200

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03111215

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03111235

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03111675

0.4000.6000.8001.0001.200

1.4001.6001.800

1 10 100

03111705

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03111890

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03114094

Prediction interval width,

in number of log cycles

Prediction interval width,

in number of log cycles

Prediction interval width,

in number of log cycles

Prediction interval width,

in number of log cycles

0.4000.6000.8001.0001.2001.4001.6001.800

1 10 100

03072890

Distance from index gage to 

estimation streamgage

Distance from index gage to 

estimation streamgage

Distance from index gage to 

estimation streamgage

Figure 7. Distance (on log scale) from the estimation site to the index streamgage in relation to the log prediction interval width for each of the 12 newly established streamgages, in western Pennsylvania.
26 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania Index gage drainage area is 0.33−3 times the esti- mation streamgage drainage area EXPLANATION

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03081800

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03105927

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03107698

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03108010

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03111200

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03111215

0.4000.6000.8001.0001.2001.4001.6001.800

0.0001 0.01 1

03111235

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03111675

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03111705

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03111890

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03114094

Prediction interval width,

in number of log cycles

Prediction interval width,

in number of log cycles

Prediction interval width,

in number of log cycles

Prediction interval width,

in number of log cycles

0.4000.6000.8001.0001.2001.4001.6001.800

0.001 0.1 10

03072890

Watershed area ratio Watershed area ratio Watershed area ratio

0.01 10.01 10.01 10.01 1 0.01 1

0.001 0.1

0.01 1

0.01 1 0.01 1

0.01 10.01 10.01 1

10

Figure 8. Ratio of the estimation site watershed area to the index streamgage watershed area for the 12 newly established streamgages in western Pennsylvania in relation to the log prediction interval width. The shaded area between the red lines represents the area where the index streamgage watershed area is 0.33 to 3 times the size of the estimation site watershed area. 
Analysis of Streamflow Estimation 27

Greene County

03072890 (Fonner)

Washington County

Butler/Fayette Counties

Beaver County

EXPLANATION

0.000

0.500

1.000

1.500

2.000

2.500

3.000

Index streamgage

0307289003081800031059270310769803108010031112000311121503111235031116750311170503111890031140940307200003074500031080000311083003112000

Prediction interval width, in 

number of log cycles

0.000

0.500

1.000

1.500

2.000

2.500

3.000

Index streamgage

0307289003081800031059270310769803108010031112000311121503111235031116750311170503111890031140940307200003074500031080000311083003112000

Prediction interval width, in 

number of log cycles

0.000

0.500

1.000

1.500

2.000

2.500

3.000

Index streamgage

0307289003081800031059270310769803108010031112000311121503111235031116750311170503111890031140940307200003074500031080000311083003112000

Prediction interval width, in 

number of log cycles

A

B

C

Figure 9. Log prediction interval widths calculated from the MOVE.1 regressions for selected index streamgages in A, Greene County, 

B, Washington County, and C, Beaver/Fayette/Butler Counties, western Pennsylvania.
28 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

This may indicate that these streamgages represent streamflow 

well for Washington County streams.

The estimation sites in Greene County (depicted in green 

in fig. 9) using streamgages 03114094 (Herod) and 03111705 

(SF Dunkard) as index streamgages produced the smallest 

log prediction interval widths when streamgage 03072890 

(Fonner; circled in black in fig. 9) is excluded as an estimation site. This may indicate that these streamgages represent 

streamflow well for Greene County streams. For Greene 

County, the previously established streamgages—03072000 

(Shannopin) and 03112000 (Wheeling)—performed 

adequately as index streamgages, but the results were not 

consistent. Consequently, for a site of interest in Greene 

County, MOVE.1 regressions need to be developed using a 

newly established streamgage and a previously established 

streamgage to determine the best index streamgage.

Although the streamgages identified previously in the 

section produced the smallest consistent log prediction interval widths, this study has shown that, in general, MOVE.1 

regressions for an estimation site can be developed using 

any streamgage in the area surrounding the estimation site. 

The NSE coefficients (table 5) computed from the MOVE.1 

regression show that when station 03072890 (Fonner) is not 

included as an index streamgage, 9 of the 12 estimation sites 

have values greater than 0.50 from all index streamgages, giving a qualitative indication that a relation between the stations 

is possible. The Greene County estimation sites, however, 

produce MOVE.1 regressions with the largest log prediction 

intervals when the index streamgage is not in Greene County. 

In addition to the streamflow range discussed in the “IndexGage Method Results” on page 19, examining the continuous 

record of the newly established estimation sites and concentrating on the base-flow characteristics of the streamgages may 

provide insight for further analysis.

Base-Flow Characteristics of the Newly 

Established Streamgages

Examining the base-flow characteristics of the 12 newly 

established streamgages can provide further insight into the 

streamgage relations and possibly help in identifying areas 

where future index streamgages should be placed or retained. 

Base flow is the sustained streamflow of the stream in the 

absence of direct runoff (U.S. Geological Survey, 2017) and 

is mostly attributed to groundwater entering the stream under 

natural conditions. Within the study area, there are differences 

in physical characteristics, such as land use, geologic formation, and climate, that could cause differences in base-flow 

characteristics of the 12 small streams. The base flow of a 

stream can be affected by underground mining activities 

that change the groundwater elevation or alter groundwater 

divides. Although loss of base flow (zero streamflow) in small 

headwater streams can be a natural occurrence during seasonally dry periods, subsidence due to mining may enhance 

the effect by inducing fracturing, increasing hydraulic 

conductivity, and increasing the capacity of the subsurface 

to store water. Greater hydraulic conductivity and subsurface 

storage may lower groundwater levels in the affected area, 

resulting in the reduction or removal of the base-flow component of streamflow and extending periods of zero streamflow 

when runoff and recharge from precipitation are minimal.

Streamflow records were analyzed to document base-flow 

characteristics of the small watersheds. The contribution of 

base flow was investigated by analysis of streamflow records 

at continuous-record streamgages (hydrograph analysis). The 

base flow of streams draining small watersheds was determined with the computerized base-flow separation method 

PART (Rutledge, 1998) by use of the USGS Groundwater 

Toolbox (Barlow and others, 2015). Although PART is not recommended for watershed areas less than 1 mi2

 and other methods of base-flow separation are available, PART was chosen 

because it has been recently applied in Pennsylvania (McCoy 

and others, 2015; Reese and Risser, 2010). Hydrographs of 

daily mean streamflow from continuous-record streamgages 

were separated into base flow and direct runoff components. 

Daily mean streamflows at the 12 newly established sites 

(table 2) were analyzed. An example of hydrograph separation 

by the PART method is shown for the streamflow record for 

estimation site 03111675 (Job) during 2015 (fig. 10).

The streamgages used for the base-flow analysis, along 

with some watershed characteristics and underlying geology, are listed in table 2. Records of daily mean streamflow 

were available from August 2014 through December 2016 

for some streamgages, but the data were not complete for all 

streamgages for that entire period. To compare conditions 

among all 12 small watersheds, the period of concurrent 

record from June 18, 2015, through December 31, 2016, was 

used, except for the derivation of master-recession curves, for 

which all available data were used. The results of the comparisons would likely differ if streamflow records of longer duration were available. Two base-flow analysis techniques were 

examined, base-flow-duration curves and the median recession 

index (K). These analyses were done with the use of the USGS 

Groundwater Toolbox (Barlow and others, 2015).

Base-Flow Duration Curves

A base-flow duration curve illustrates the percentage of 

time a given streamflow is likely to be equaled or exceeded. 

Base-flow duration curves for streamflow in the 12 small 

watersheds (normalized for watershed area) were plotted for 

the period of concurrent record from June 18, 2015, through 

March 31, 2017 (fig. 11). The base-flow duration curves show 

variation among the streamgages, although the streamgages 

could be divided into three groups, as shown in figure 11 by 

the different line colors.

One factor that might be contributing to base-flow differences seen in figure 11 is the bedrock geology, particularly 

at the Greene County sites (table 2). Watersheds of the four 

Greene County streams (depicted in red in fig. 11) are underlain entirely by bedrock of the Greene Formation. The Greene 
Analysis of Streamflow Estimation 29

0

10

20

30

40

50

60

70

80

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

Streamflow, in cubic feet per second

2015

Job Creek

Streamflow

Base flow

EXPLANATION

Figure 10. Example of hydrograph separation using the PART method and the daily streamflow record for U.S. Geological Survey 

estimation site 03111675, Job Creek at Delphene, western Pennsylvania, during 2015.

Formation of Permian age is known to be a poor aquifer that 

often does not provide even the small quantities of groundwater to wells needed for domestic use (Stoner and others, 

1987). It is probable that the Greene Formation provides 

less groundwater discharge to streams per square mile of 

watershed than other older geologic formations in the study 

area. The 03111890 (MWheeling) and 03111215 (Bonar) 

streamgages, which have higher base-flow yields (base flow 

per square mile) than the Greene County sites, are mostly 

underlain by the Greene Formation (75 percent or greater), 

which may account for the lower base-flow yields than those 

sites to the north. Streamgage 03111235 (DogTrib) goes dry 

about 5 percent of the year and could have been grouped with 

the streamgages shown in blue (fig. 11) because it followed 

their trend approximately 87 percent of the time. It is not 

unexpected that streamflow in a watershed area of this size 

could go to zero owing to underflow that is not measured by 

the streamgage. In the future, it would not be possible to establish base-flow duration curves for a periodically measured 

stream; however, these graphs depicting base-flow yields 

could lend themselves to the identification of 2 or 3 groups 

of streamgages that would relate best to each other. Index 

streamgage establishment could then be guided by placing 

streamgages in the area generally represented by the grouped 

streamgages.

Median Recession Index

The master recession curve (MRC) for a stream is a plot 

of streamflow recession over time (Q/t) during periods when 

the stream is chiefly sustained by base flow. It provides an 

average characterization of base-flow response developed by 

assembling multiple segments of continuous recession from 

the streamflow hydrograph that represents a period greater 

than any single recession in the recorded data. The rate of 

base-flow decline shown by the MRC is related to the transmissivity and subsurface storage of the aquifer beneath the 

watershed, among other factors (Rutledge, 1998).

The MRC for the 12 streams draining small watersheds 

was determined using a computer program called RECESS 

(Rutledge, 1998) as implemented in the USGS Groundwater 

Toolbox (Barlow and others, 2015). The program computes 

an equation for the MRC and the median recession index (K), 

which is the median slope of multiple streamflow-recession 

periods selected for each stream (table 8). Specifically, the 

value of K is the median time in days for the streamflow to 

decline one log cycle (after the influence of surface runoff 

or interflow has ceased) for the multiple recession segments 

analyzed. A smaller K value indicates that the base flow in 

the watershed decreases faster than that in a watershed with 

a larger K value. A smaller K value could also indicate the 

watershed may experience zero flow before another watershed 
30 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

03108010 (Fishpot)

03107698 (Traverse)

03081800 (Bear)

03111200 (Dunkle)

03105927 (Crab)

03111890 (MWheeling)

Steamgage identifier (station short name)

EXPLANATION

03111215 (Bonar)

03072890 (Fonner)

03111235 (DogTrib)

03111675 (Job)

03111705 (SFDunkard)

03114094 (Herod)

0.0001

0.001

0.01

0.1

1

60 65 70 75 80 85 90 95 100

Percent of time streamflow was equalled or exceeded

Base-flow yield, in cubic feet per second per square mile

Figure 11. Base-flow duration curves for 12 small watersheds in western Pennsylvania plotted for the period of concurrent record 

from June 18, 2015, through March 31, 2017. The three colors of lines present a visual grouping of the streamgages.
Analysis of Streamflow Estimation 31

Table 8. Median recession index (K) in days per log (base 10) cycle of streamflow for newly established streamgages in western 

Pennsylvania, by county.

[USGS, U.S. Geological Survey]

USGS 

station 

identifier

Station name Pennsylvania

county

Median recession index (K), 

in days per log (base 10) cycle of streamflow

03111675 Job Creek at Delphene Greene 11.35

03111705 South Fork Dunkard Fork at Aleppo Greene 14.82

03114094 Herod Run near New Freeport Greene 12.23

03072890 Fonner Run near Deer Lick Greene 14.63

03111890 Middle Wheeling Creek near Claysville Washington 17.08

03111215 Bonar Creek near Claysville Washington 21.64

03111235 Unnamed trib to Dog Run at Dunsfort Washington 14.34

03111200 Dunkle Run near Claysville Washington 25.5

03107698 Traverse Creek near Kendall Beaver 16.68

03108010 Fishpot Run near Shippingport Beaver 18.96

03105927 Crab Run near Connoquenessing Butler 13.69

03081800 Bear Run at Kauffman Fayette 22.35

of similar size with a larger K value. Periods of streamflow recession from the months of September through May 

were examined using the period of record available for each 

streamgage. Recession segments during June–August were not 

used to avoid periods when the recessions could be strongly 

affected by evapotranspiration.

With periodic measurement only, MRCs cannot be 

obtained. However, Eng and Milly (2007) describe the 

technique of using measurements spaced apart on a recession 

curve to estimate the K value. Using two measurements of 

base flow on successive days after cessation of surface runoff 

and interflow, the recession index can be estimated as

K = ∆t/ (logQ1 – logQ2) (6)

where

K is the recession index, in days per log 

(base 10) cycle of streamflow;

Q1 is the base flow measured in the stream at 

time 1, in ft3/s;

Q2 is the base flow measured at a later time 2, in 

ft3/s; and 

∆t is the time between Q1 and Q2, in days.

This is an estimate of K based on two values; however, using the PO2 streamflow-measurement schedule, it is 

possible that numerous values on a recession curve can be 

determined. The following technique was used to determine 

an estimate of K from a recession curve. Log streamflow 

from a recession period was plotted against the day from the 

streamflow-measurement schedule (day 1, day 3, day 5, and so 

on from the PO2 schedule), and a linear trend line and associated equation were developed. The equation was then reversed 

to estimate the days when streamflow would be 10.00 ft3/s and 

100.0 ft3/s; the number of days for streamflow to drop one log 

cycle (for example, the number of days for the logarithm of 

flow to drop from 3 to 2) is the K value for that period.

With continuous streamflow record, the recession trend 

is determined by evaluating relatively large recession events 

over a period long enough to measure the recession over a 

complete log cycle to determine an overall recession trend. 

For streamgages with periodic streamflow measurements 

only, it may not be possible to measure multiple days in a row, 

depending on precipitation patterns. This implies judgment 

will be needed in selecting the recession periods for evaluation on the basis of partial record, realizing there will be great 

variability in estimates of K for one streamgage. For example, 

figure 12 shows the K value computation for streamgage 

03111235 (DogTrib) for three recession periods greater than 

3 days during non-summer months (so evapotranspiration 

would not be an issue). Estimates of K ranged from 14 to 

24 days per log cycle of streamflow. However, these snapshots of K values can be useful in predicting how well two 

streamgages relate to each other. Analyzing the same recession 

periods at 03111890 (Middle Wheeling), the K values ranged 

from 18 to 24 days per log cycle of streamflow (fig. 12 A, 

B, C). The K values in April and November are very similar 

but not those in February. One would predict that the relation 

between the streamgages should be stronger in November and 

April than in February on the basis of this recession data.
32 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

Linear (03111890, MWheeling)

Linear (03111235, DogTrib)

03111890, MWheeling

03111235, DogTrib

EXPLANATION

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 2 4 6 8

Day

February 2017

C

Log10 streamflow, in cubic

feet per second

K = 20, MWheeling

K= 14, DogTrib

y = -0.05x + 0.3476

y = -0.0723x + 0.033

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 1 2 3 4 5 6 7 8

Day

April 2016

B

Log10 streamflow, in cubic

feet per second

K = 18, MWheeling

K= 16, DogTrib

y = -0.0543x + 0.4246

y = -0.0625x -0.1375

K = 24, MWheeling

K = 24, DogTrib

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 2 4 6 8 14

Day

November 2015

A

10 12

Log10 streamflow, in cubic

feet per second

y = -0.0423x -0.9753

y = -0.0412x -0.4058

Figure 12. Median Recession Index (K) for recession periods in A, November 2015, B, April 2016, and C, February 2017 at U.S. 

Geological Survey streamgage 03111235, Unnamed trib to Dog Run at Dunsfort (DogTrib) and U.S. Geological Survey streamgage 

03111890, Middle Wheeling Creek near Claysville (MWheeling) in western Pennsylvania. The simple linear equation for DogTrib is shown 

in red, and the equation for MWheeling is shown in blue.
Analysis of Streamflow Estimation 33

Evaluation of Streamflow Not Used for 

Regression Development

An independent streamflow dataset (evaluation dataset) 

that was collected outside the regression development 

period was used to evaluate the MOVE.1 regression models. 

Observed streamflow at the estimation site was evaluated to 

determine whether the streamflow was within the log prediction interval width calculated from the observed streamflow 

at the index streamgage. If the observed streamflow at the 

estimation site is outside the calculated prediction interval, 

then there is a 95-percent chance that it is outside the range of 

values observed during the regression development period.

Evaluation of zero streamflow at the estimation site is not 

accomplished with the MOVE.1 regression, but from observed 

streamflow measurements during the regression development 

period. During evaluation, if zero streamflow occurs at the 

estimation site while the index streamflow is at or below the 

HISAZ value, it means this condition was observed during 

the regression development period. If the index streamflow 

was above the HISAZ value, this condition was not observed 

during the regression development period, and further evaluation not discussed here is necessary. Another piece of information related to zero flow that is not accomplished with the 

MOVE.1 regression is the highest streamflow at the estimation 

site when the streamflow at the index streamgage is at or 

below the HISAZ value. If streamflow at the index streamgage 

is below the HISAZ value and the observed streamflow at the 

estimation site also is below that HISAZ value, it means this 

condition has been observed during the regression development period. Even though the condition was observed during 

the regression development period, it may fall outside the 

prediction interval. If this occurs, further evaluation of the data 

point may be necessary.

For this study, the evaluation dataset was streamflow 

data from September 2014 to April 2015. As described in 

the “Frequency of Streamflow Measurement” section, the 

PO2 streamflow-measurement schedule was used to select 

streamflow values for the evaluation dataset. An example of 

streamflow estimated at streamgage 03072890 (Fonner) using 

streamflow at streamgage 03112000 (Wheeling) is shown 

in figure 13. There is a 95-percent probability that estimated 

streamflow data will be contained within the prediction 

intervals. Four observations plotted outside of the prediction 

intervals. For the data on November 28, 2014, the observed 

streamflow at streamgage 03072890 (Fonner) is 0.249 ft3/s. 

The upper 95-percent prediction limit computed for an index 

streamflow of 38.3 ft3/s is 0.140 ft3/s. The observed streamflow 

is greater than the prediction limit and, thus, is outside of the 

95-percent prediction interval. The data on November 15, 

2014, have the opposite scenario; observed streamflow is less 

than the lower prediction limit. However, one more piece of 

information is available. For this streamflow measurement, the 

observed streamflow at the estimation site is 0.001 ft3/s, and 

the observed streamflow at the index streamgage is 26.3 ft3/s, 

which is less than the HISAZ value of 30.3 ft3/s. The lower 

MOVE.1 regression prediction limit is 0.005 ft3/s (greater than 

the observed streamflow of 0.001 ft3/s at the estimation site), 

and thus the estimation streamflow is outside the prediction 

interval. However, looking at all the data from the regression 

development period where streamflow at the index streamgage 

was at or less than 30.3 ft3/s, the highest streamflow at the estimation site is 0.086 ft3

/s. Given that this estimation streamflow 

scenario occurred during the regression development period 

but falls outside the MOVE.1 regression prediction interval, 

this data point may need further evaluation. This example 

(Hittle, 2019d) and evaluation spreadsheets for all MOVE.1 

regressions for streamgage pairs with data available before 

May 2015 are fully illustrated in the companion data release 

for this report (Hittle, 2019a). If 03112000 (Wheeling) were 

continued as an index streamgage, the streamflow should be 

periodically evaluated to ensure that it has not been affected by 

a basin changing event warranting the development of a new 

MOVE.1 regression.
34 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

95-percent prediction

interval

03072890

EXPLANATION

0.001

0.01

0.1

1

10

0.001 0.010 0.100 1.000 10.000

Observed streamflow, in cubic feet per second

Estimated streamflow, in cubic feet per second

November 11, 2014 Value outside of

prediction interval; however, falls

within a range where the estimated

streamgage has recorded zero flow at

or less than this index gage

streamflow during the model

development period

November 28, 2014

Value outside of

prediction interval

Figure 13. Estimated streamflow in relation to observed streamflow at U.S. Geological Survey (USGS) streamgage 03072890, Fonner 

Run near Deer Lick (Fonner), western Pennsylvania, with the 95-percent prediction intervals. Streamflow at USGS streamgage 03072890 

(Fonner) was estimated using streamflow at USGS streamgage 03112000 Wheeling Creek at Elm Grove, West Virginia.
Accuracy and Limitations 35

Accuracy and Limitations

There are many important limitations and considerations 

for the data collected for this project and the applicability of 

this technique for the future. The first limitation is how the 

streamflow for the index streamgage and estimation site was 

obtained. Streamflow at the newly established streamgages 

was calculated using a stage-streamflow rating that was 

developed from several streamflow measurements made over 

the course of the project. Streamflow measurements also were 

used to shift the rating to account for minor changes in the 

stream control over time. There is no way to know exactly 

when the stage–discharge relation changed between field 

visits; therefore, the best hydrologic judgment was used when 

applying shifts. This is a source of uncertainty at any location 

and can be minimized in the future by making more frequent 

measurements or establishing permanent control structures, 

such as a weir, where practical. This source of uncertainty is 

present for the index streamgage and estimation site, whereas 

in the future, the uncertainty associated with application of 

shifts will be present only at the index streamgage because the 

estimation site will have only periodic measurements.

Omitting the runoff-influenced streamflow data in developing the MOVE.1 regressions limits the range of streamflow 

used in future predictions because there is no mechanism to 

predict runoff-influenced streamflow when that streamflow 

was not part of the regression development. Although the 

MOVE.1 regressions were developed with limited data owing 

to the time constraint of this project (about 2 years), observations from the evaluation dataset generally fell within the 

95-percent prediction intervals. Localized rain events that 

affect one watershed more than another will always occur 

and can result in data falling outside the prediction intervals. 

Thus, it is important to realize that the prediction interval is 

a statistic and will not capture every relation between two 

streamgages. An example of localized rain events affecting 

the relation between two streamgages is illustrated by the 

estimation of site 03111235 (DogTrib) from index streamgage 

03111215 (Bonar). An analysis of all newly established 

streamgages used as index streamgages to estimate streamflow at 03111235 (DogTrib) shows streamgage 03111215 

(Bonar) was the fifth best index streamgage, as determined 

by examining the prediction interval width, and the second 

closest at 6.5 miles (tables 5 and 7). The observed streamflow 

in relation to estimated streamflow for streamgage 03111235 

(DogTrib) is shown in figure 14. Two data points that are 

outside the 95-percent prediction interval (data points circled 

in red) occurred on July 18, 2016, and September 14, 2016. 

The position of the data points is explained by storms that 

concentrated over the watershed of streamgage 03111215 

(Bonar) during July 14–15 and September 10, 2016; however, 

the storms did not affect the 03111235 (DogTrib) watershed. 

There could be some geographic feature located to the west 

of the streamgages that funnels storms particularly over the 

03111215 (Bonar) watershed. If that is the case, it would be 

evidenced by a larger prediction interval width that would 

account for more data points that do not appear to follow the 

general trend. Any data point that is above the upper prediction interval limit indicates that the observed streamflow at a 

streamgage is higher than expected. This is the case for the 

data point enclosed in a red triangle.
36 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

95-percent prediction

interval

03111235

Storms affected streamflow at the index

streamgage, but not

the estimation site

Observed streamflow at 

the estimation site 

greater than the upper 

prediction limit

EXPLANATION

0.001

0.01

0.1

1

0.001 0.01 0.1 1

Observed streamflow, in cubic feet per second

Estimated streamflow, in cubic feet per second

Figure 14. Estimated streamflow in relation to observed streamflow at U.S. Geological Survey (USGS) streamgage 03111235 Unnamed 

trib to Dog Run at Dunsfort (DogTrib), western Pennsylvania, with the 95-percent prediction intervals. Streamflow at USGS streamgage 

03111235 (DogTrib) was estimated using streamflow at USGS streamgage 03111215 Bonar Creek near Claysville. 
Summary and Conclusions 37

Application of Techniques to Estimate 

Natural Streamflow at an Ungaged Site

The techniques described earlier in this report to estimate non-runoff influenced base flow in small watersheds in 

western Pennsylvania, based on the index-gage method, are 

illustrated in this section. At the estimation site, streamflow 

measurements are obtained following the PO2 schedule for 

about 2.5 years (a measurement is made starting 3 days after 

a precipitation event [considered day 1] and continuing on 

subsequent days 3, 5, 7, 10, 13, 16, and every third day until 

another precipitation event occurs). Rainfall in the area ideally 

is determined using a local rain gage or historical radar data. A 

MOVE.1 regression is developed that relates streamflow at the 

estimation site to streamflow at a nearby streamgage (index 

streamgage). The precipitation record is examined to assure 

that runoff-influenced streamflow at the index streamgage 

is not used. The associated 95-percent prediction intervals 

and the median recession index (K) also are produced for the 

regression development period. Lastly, streamflow measurements collected following the PO2 schedule for an additional 

amount of time (independent dataset not used in regression 

development) are evaluated.

All data used to develop the MOVE.1 regressions and the 

resulting regression output, including diagnostics, are detailed 

in a companion data release (Hittle, 2019a). For example, 

spreadsheet “Index Streamgage 03111705, Estimation Site 

03111675; Data, Regression Models, Evaluation.xlsx” 

(Hittle, 2019e) was developed by using streamgage 03111705 

(SF Dunkard) as the index streamgage and streamgage 

03111675 (Job) as the estimation site. Streamflow measurements were selected at the estimation site for the period of 

May 1, 2015 – March 31, 2017, according to the PO2 schedule. Instantaneous streamflow for that period were matched to 

streamflow observed at the index streamgage. Observed values 

from the estimation site were examined for zero streamflow. 

Because zero streamflow was measured at the estimation site, 

the HISAZ value and the highest estimated value at or less 

than the HISAZ value were recorded for use in data evaluation. All streamflow data selected during the regression development period, minus periods of zero streamflow, were used 

for MOVE.1 regression development. Using the R statistical 

program (version 3.4.3) with the SMWRStats package (R Core 

Team, 2017; Lorenz, 2015), a MOVE.1 regression analysis 

was done using log transformed streamflow data. From this 

MOVE.1 regression, streamflow at the estimation site is 

estimated and 95-percent prediction intervals are determined. 

Regression residuals were examined to determine whether 

parametric or non-parametric prediction intervals need to be 

utilized for evaluation. In this case, the test located on the 

“Model Development (nonparamet)” tab indicates the residuals were not normally distributed; therefore, the nonparametric 

prediction intervals are used on the “Evaluation” tab.

Data that were collected outside the regression development period are evaluated using the developed MOVE.1 

regression. Streamflow estimates at the estimation site, along 

with the non-parametric 95-percent prediction intervals, are 

computed using the MOVE.1 regression. A determination can 

then be made as to whether the streamflow observed at the 

estimation site falls within the prediction intervals or whether 

the observed streamflow at the index streamgage is less than 

the HISAZ value when zero streamflow was observed at the 

estimation site.

Other information that could be analyzed are the K values 

for multiple recession periods. For the regression development 

period, plots were developed of streamflow-measurement day 

in relation to log streamflow for every recession period that 

had data recorded for at least 7 days. A simple trend line was 

calculated along with a trend-line equation for each recession 

period to calculate the K (recession index) value. Sites that 

have similar K values should have streamflows during nonrunoff periods that are more strongly correlated than streamflows at sites with dissimilar K values.

Summary and Conclusions

A study was conducted by the U.S. Geological Survey, 

in cooperation with the Pennsylvania Department of Environmental Protection (PADEP), to develop a method for estimating base flow at an ungaged, periodically measured site in 

the bituminous coal region of southwestern Pennsylvania and 

adjacent states. This report describes an index-gage method 

that can be used to estimate streamflow that is predominately 

unaffected by human activities (such as mining) and not influenced by runoff at a periodically measured site (referred to as 

the “estimation site”) as a function of streamflow measured at 

a streamgage site (referred to as the “index streamgage”). The 

index-gage method employs a regression technique known 

as Maintenance of Variance, Type 1 (MOVE.1). The period 

for this study was about 2.5 years, and the number of discrete 

streamflow measurements initially examined (60) followed 

current recommendations by PADEP (DEP schedule) for 

measuring streams that will be undermined by longwall mining. The PADEP requires that streamflow be measured prior 

to mining once a month for 2 years, weekly for 6 months, and 

daily for 2 weeks (Pennsylvania Department of Environmental 

Protection, 2005).

Twelve streamgages with watershed areas less than 

10 square miles were established for this study, with most 

established within Greene and Washington Counties, Pennsylvania. Stage data were collected for the entire period of operation at all 12 streamgages. However, streamflow was computed only for medium to low streamflow at 6 streamgages 

(partial-record streamgages), whereas streamflow was computed at all stages at the other 6 streamgages (continuousrecord streamgages). Data from five previously established 

continuous-record streamgages with watershed areas ranging 

from 48.9 to 281 square miles were also used in analyses in 

this study.
38 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

Runoff-influenced streamflow data, defined in this study 

as streamflow on the day of a precipitation event and 2 days 

following the precipitation event, were not used in MOVE.1 

regression analysis. Once the runoff-influenced data were 

removed, the remaining streamflow data were analyzed to 

determine whether daily mean or instantaneous streamflow 

values would be used for the index streamgage. The analyses 

did not show a clear advantage to using instantaneous or daily 

mean streamflow data, so both daily and instantaneous data 

were used for analyses.

Ten different streamflow-measurement schedules were 

examined to determine how best to obtain information about 

the relation between streamflows at two sites when only periodic measurements were made at one site, while maintaining 

the number of measurements similar to the number PADEP 

currently (2016) requires. The PO2 schedule (a streamflow 

measurement is made starting 3 days after a precipitation 

event [considered day 1], then every other day to day 7, then 

every third day [days 3, 5, 7, 10, 13, 16, ...] until another 

precipitation event occurs) was used to select data for analysis. 

Though the number of measurements is greater than 60, this 

schedule sampled all non-runoff influenced streamflow periods 

within a month and yielded a good chance of including the 

lowest streamflow for the regression development period. 

Thus, when examining relations between all streamgages, the 

larger dataset was used (PO2 schedule) to have a good chance 

of including the lowest streamflow.

In general, when a streamflow-measurement schedule 

that targets the lowest streamflows and includes measurements 

made only during non-runoff streamflow periods is used, the 

MOVE.1 regressions developed are comparable to using one 

streamflow measurement per day with the runoff-influenced 

streamflow removed, as described by the Nash-Sutcliffe Efficiency values. The resulting log prediction interval widths varied at the 95-percent confidence interval. When similar data, 

sampled following three different measurement schedules, 

were used, the number of streamflow measurements included 

in the dataset, based on the schedule selected, caused different 

ranked residuals to be used in calculating the prediction interval limits. When the number of measurements was similar to 

the number currently (2016) in the PADEP schedule, satisfactory results were obtained with the PO8 schedule that targets 

measurements that occur every other day for 7 days then every 

third day during non-runoff periods, with the exception that a 

given day sequence number (1, 3, 5, 7, ... days after cessation 

of runoff) is sampled only once in a month. It is acknowledged 

that the lowest streamflow at the estimation site may not be 

measured if the longest non-runoff influenced period occurred 

at the beginning of the month and streamflow wasn’t measured 

again, even though the streamflow was lower. Additionally, the 

range and number of outliers could change if the PO8 schedule 

were started at the beginning or end of a month.

The distances between the estimation site and the index 

streamgage was a factor related to how well streamflow was 

estimated at the estimation site. For all of the newly established streamgages used as estimation sites, except 2, the best 

index streamgage, as indicated by the log prediction interval 

width, was 1 of the 2 streamgages closest to the estimation 

site. For the remaining two sites, the closest index streamgage 

was more than 10 miles away. For the study area, this could 

indicate that an ideal index streamgage would be within 

10 miles but does not imply that a satisfactory relation cannot 

be developed with a streamgage further away.

The ratio of the watershed area of the estimation site to 

that of the index streamgage was compared to the prediction 

interval width. No relation between the two variables could be 

determined from the graphical analysis. Size of the index-gage 

watershed does not appear to affect the MOVE.1 regression 

log prediction interval width. MOVE.1 regression prediction 

intervals for the existing streamgages are comparable to the 

prediction intervals for the newly established streamgages, 

even though the watershed area of the existing streamgage was 

many times greater.

Index streamgages with the smallest prediction intervals 

could make ideal index streamgages for future estimation 

of streamflow in small watersheds in western Pennsylvania. 

Using the Washington County streamgages 03111890 

(MWheeling), 03111215 (Bonar), and previously established 

streamgage 03112000 (Wheeling) as index streamgages 

produced MOVE.1 regressions with the smallest prediction 

interval widths for most of the streamgages in the county, 

despite their distances from the estimation sites. In Greene 

County, streamgages 03114094 (Herod) and 03111705 

(SF Dunkard) produced MOVE.1 regressions with the smallest 

log prediction interval widths of the three streamgages clustered together, which includes 03111675 (Job). Even though 

the streamgages with the smallest prediction interval widths 

appear to be the best fit as index streamgages for their areas, 

for this study it was found that streamflow for a site of interest 

can be estimated by using streamflow (non-runoff influenced) 

at an index streamgage regardless of the distance to the estimation site, recognizing that the further the sites are from each 

other, the more the variation in precipitation and geology will 

affect the relation. Using a streamflow-measurement schedule 

that captures numerous non-runoff periods (PO8 or PO2), base 

flow at a site can be estimated with the index-gage method. In 

addition, upper and lower prediction limits can be calculated 

to give an indication of uncertainty in the estimates.
References Cited 39

References Cited

Barlow, P.M., Cunningham, W.L., Zhai, Tong, and Gray, 

Mark, 2015, U.S. Geological Survey Groundwater Toolbox, 

a graphical and mapping interface for analysis of hydrologic 

data (version 1.0)—User guide for estimation of base flow, 

runoff, and groundwater recharge from streamflow data: 

U.S. Geological Survey Techniques and Methods, book 3, 

chap. B10, 27 p., accessed March 23, 2018, at http://doi.

org/10.3133/tm3B10.

Berg, T.M., and Dodge, C.M, eds., 1981, Atlas of preliminary 

geologic quadrangle maps of Pennsylvania: Pennsylvania 

Geological Survey, 4th series, map 61, scale 1:62,500.

Curran, C.A., Eng, Ken, and Konrad, C.P., 2012, Analysis of 

low flows and selected methods for estimating low-flow 

characteristics at partial-record and ungaged stream sites 

in western Washington: U.S. Geological Survey Scientific 

Investigations Report 2012–5078, 46 p., accessed May 23, 

2018, at https://pubs.usgs.gov/sir/2012/5078/.

Eng, K., and Milly, P.C.D., 2007, Relating low-flow characteristics to the base flow recession time constant at partial 

record stream gauges: Water Resources Research, W01201, 

v. 43, iss. 1, 8 p., accessed March 23, 2018, at https://doi.

org/10.1029/2006WR005293.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in 

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, chap. A3, 522 p., 

accessed August 10, 2018, at https://pubs.usgs.gov/twri/

twri4a3/.

Hirsch, R.M., 1982, A comparison of four streamflow record 

extension techniques: Water Resources Research, v. 18, 

p. 1081–1088.

Hittle, Elizabeth, 2019a, Index-gage regressions in support 

of estimating base flow on ungaged, periodically measured 

streams in small watersheds in western Pennsylvania: U.S. 

Geological Survey data release, https://doi.org/10.5066/

F7F18XX9.

Hittle, Elizabeth, 2019b, Estimation site 03072890; spreadsheets and metadata: U.S. Geological Survey data release, 

https://doi.org/10.5066/F7F18XX9.

Hittle, Elizabeth, 2019c, Index streamgage 03112000_daily, 

estimation site 03111235; data, regression models.zip, in

Hittle, Elizabeth, Estimation site 03111235; spreadsheets 

and metadata: U.S. Geological Survey data release, https://

doi.org/10.5066/F7F18XX9 (individual dataset).

Hittle, Elizabeth, 2019d, Index streamgage 03112000_daily, 

estimation site 03072890_daily; Data, regression models, evaluation.zip, in Hittle, Elizabeth, Estimation site 

03072890; spreadsheets and metadata: U.S. Geological 

Survey data release, https://doi.org/10.5066/F7F18XX9

(individual dataset).

Hittle, Elizabeth, 2019e, Index streamgage 03111705, estimation site 03111675; data, regression models, evaluation, in

Hittle, Elizabeth, Estimation site 03111675; spreadsheets 

and metadata: U.S. Geological Survey data release, https://

doi.org/10.5066/F7F18XX9 (individual dataset).

Jain, S.K., and Sudheer, K.P., 2008, Fitting of hydrologic 

models: A close look at the Nash-Sutcliffe Index: Journal of 

Hydrologic Engineering, v. 13, no. 10, p. 981–986.

Karacan, C.O., and Goodman, G., 2009, Hydraulic conductivity changes and influencing factors in longwall overburden 

determined by slug tests in gob gas ventholes: International 

Journal of Rock Mechanics and Mining Sciences, v. 46, 

iss. 7, accessed June 15, 2018, at https://doi.org/10.1016/j.

ijrmms.2009.02.005.

Krause, P., Boyle, D.P., Base, F., 2005, Comparison of different efficiency criteria for hydrological model assessment: 

Advances in Geosciences, v. 5, 89–97, SRef-ID: 1680-7359/

adgeo/2005-5-89 European Geosciences Union, accessed 

May 23, 2018, at https://www.adv-geosci.net/5/89/2005/

adgeo-5-89-2005.pdf.

Li, Y., Pend, S.S., Zhang, J., 2015, Impact of longwall mining on groundwater above the longwall panel in shallow 

coal seams: Journal of Rock Mechanics and Geotechnical 

Engineering, v. 7, accessed June 15, 2018, at http://doi.

org/10.1016/j.jrmge.2015.03.007.

Lorenz, D.L., 2015, smwrBase—An R package for managing hydrologic data, version 1.1.1: U.S. Geological Survey 

Open-File Report 2015–1202, 7 p., accessed June 1, 2018, 

at http://doi.org/10.3133/ofr20151202.

McCoy, K.J., Yager, R.M., Nelms, D.L., Ladd, D.E., Monti, 

Jack, Jr., and Kozar, M.D., 2015, Hydrologic budget and 

conditions of Permian, Pennsylvanian, and Mississippian aquifers in the Appalachian Plateaus Physiographic 

Province (ver. 1.1, October 2015): U.S. Geological Survey 

Scientific Investigations Report 2015–5106, 77 p., accessed 

March 23, 2018, at http://doi.org/10.3133/sir20155106.

McCuen, R.H., Knight, Z., and Cutter, A.G., 2006, Evaluation 

of the Nash-Sutcliffe Efficiency Index: Journal of Hydrologic Engineering, v. 11, iss. 6, November/December 2006, 

p. 597–602.
40 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

Miles, C.E., and Whitefield, T.G., comp., 2001, Bedrock 

geology of Pennsylvania: Pennsylvania Geological Survey, 

4th series, digital dataset, scale 1:250,000.

Nash, J.E., and Sutcliffe, J.V., 1970, River flow forecasting 

through conceptual models part I—A discussion of principles: Journal of Hydrology, v. 10, no. 3, p. 282–290.

Pennsylvania Department of Environmental Protection, 2005, 

Surface water protection–Underground bituminous coal 

mining operations: Pennsylvania Department of Environmental Protection, Technical Guidance Document 563-

2000-655, October 8, 2005, 43p.

 R Core Team, 2017, R: A language and environment for 

statistical computing: Vienna, Austria, R Foundation for 

Statistical Computing, accessed June 1, 2018, at https://

www.R-project.org/.

Reese, S.O., and Risser, D.W., 2010, Summary of groundwater-recharge estimates for Pennsylvania: Pennsylvania 

Geological Survey, 4th series, Water Resource Report 70, 

18 p., 6 pl., scale 1:2,000,000, accessed August 10, 2018, at 

http://wren.palwv.org/library/documents/PAGroundwaterReport-2010.pdf.

Ries, K.G., III, and Eng, K., 2010, Estimation of selected 

streamflow statistics for a network of low-flow partialrecord stations in areas affected by Base Realignment and 

Closure (BRAC) in Maryland: U.S. Geological Survey 

Scientific Investigations Report 2010–5170, 40 p.

Rutledge, A.T., 1998, Computer programs for describing the 

recession of ground-water discharge and for estimating 

mean ground-water recharge and discharge from streamflow 

records—Update: U.S. Geological Survey Water-Resources 

Investigations Report 98–4148, 43 p. [Also available at 

http://pubs.usgs.gov/wri/wri984148/].

Sloto, R.A., Stuckey, M.H., and Hoffman, S.A., 2017, Evaluation of the streamgage network for estimating streamflow statistics at ungaged sites in Pennsylvania and the 

Susquehanna River Basin in Pennsylvania and New York: 

U.S. Geological Survey Scientific Investigations Report 

2016–5149, 102 p., accessed March 23, 2018, at https://doi.

org/10.3133/sir20165149.

Stoner, J.D., Williams, D.R., Buckwalter, T.F., Felbinger, J.K., 

and Pattison, K.L., 1987, Water resources and the effects of 

coal mining, Greene County, Pennsylvania: Pennsylvania 

Geological Survey, 4th series, Water Resources Report 63, 

166 p.

Stuckey, M.H., 2006, Low-flow, base-flow, and mean-flow 

regression equations for Pennsylvania streams: U.S. Geological Survey Scientific Investigations Report 2006–5130, 

84 p.

Tonsor, S.J., Hale, A.N., Iannacchione, A., Bain, D.J., Kenner, M., Pfeil-McCullough, E., and Garmire, K., 2014, The 

effects of subsidence resulting from underground bituminous coal mining, 2008–2013: Pennsylvania Department 

of Environmental Protection and University of Pittsburgh, 

p. I1–XI10, A1-J36., accessed August 10, 2018, at https://

www.dep.pa.gov/PublicParticipation/CitizensAdvisoryCouncil/Issue-Areas/Pages/Act54.aspx.

U.S. Geological Survey, 2017, Water science glossary of 

terms, accessed July 14, 2017, at https://water.usgs.gov/edu/

dictionary.html.

Walker, J.S., 1988, Case study of the effects of longwall mining induced subsidence on shallow ground water sources in 

the Northern Appalachian Coalfield: U.S. Bureau of Mines, 

Report of Investigations 9198, accessed June 15, 2018, at 

https://stacks.cdc.gov/view/cdc/10345/cdc_10345_DS1.pdf.
Appendix 1 41

Appendix 1.

Table 1.1 Results of MOVE.1 regression diagnostics for streamflow at U.S. Geological Survey streamgage 03111235 (DogTrib) 

streamflow estimated by using U.S. Geological Survey streamgages 03111200 (Dunkle) and 03111890 (MWheeling) with and 

without runoff-influenced streamflow.
42 Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

Table 1.1 Results of MOVE.1 regression diagnostics for streamflow at U.S. Geological Survey streamgage 03111235 (DogTrib) 

streamflow estimated by using U.S. Geological Survey streamgages 03111200 (Dunkle) and 03111890 (MWheeling) with and without 

runoff-influenced streamflow.

[ft3/s, cubic feet per second]

Runoff-influenced 

streamflow included 

in regression?

Regression number

Logarithm (base 10) 

prediction 

interval range 

(number of 

log cycles)

Nash-Sutcliffe 

Efficiency value

Correlation 

coefficient 

(r)

Highest streamflow 

at index streamgage 

when the 

estimation site was 

zero (HISAZ) (ft3

/s)

U.S. Geological streamgage 03111235 (DogTrib) streamflow estimated by using U.S. Geological Survey Streamgage 03111200 (Dunkle) 

Yes ALL 0.998 0.861 0.913 2.59

Yes r1 1.048 0.862 0.879 0.56

Yes r2 0.972 0.853 0.925 0.62

Yes r3 1.042 0.860 0.924 0.83

Yes r4 1.062 0.858 0.893 0.99

Yes r5 0.950 0.860 0.928 0.35

No ALL_PO 0.802 0.859 0.884 0.99

No r6 0.752 0.860 0.901 0.83

No r7 0.904 0.861 0.905 0.49

No r8 0.880 0.857 0.908 0.68

No r9 0.821 0.843 0.922 0.42

No r10 0.897 0.862 0.923 0.44

U.S. Geological streamgage 03111235 (DogTrib) streamflow estimated by using U.S. Geological Survey Streamgage 03111890 (MWheeling)

Yes ALL 1.313 0.783 0.868 0.16

Yes r1 1.503 0.779 0.848 0.13

Yes r2 1.684 0.782 0.850 0.08

Yes r3 1.491 0.779 0.792 0.05

Yes r4 1.296 0.777 0.879 0.09

Yes r5 1.984 0.782 0.814 0.08

No ALL_PO 1.152 0.776 0.877 0.13

No r6 1.437 0.783 0.873 0.08

No r7 1.145 0.767 0.885 0.09

No r8 1.453 0.777 0.863 0.06

No r9 1.136 0.779 0.883 0.08

No r10 1.213 0.769 0.899 0.11
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:

http://pa.water.usgs.gov/

Publishing support provided by the 

West Trenton Publishing Service Center
Hittle and Risser

—Estimation of Base Flow on Ungaged, Periodically Measured Streams in Small Watersheds in Western Pennsylvania

—Scientific Investigations Report 2018–5150

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20185150