U.S. Department of the Interior

U.S. Geological Survey

Prediction of Velocities for a Range

of Streamflow Conditions in Pennsylvania

by Lloyd A. Reed and Marla H. Stuckey

Water-Resources Investigations Report 01-4214

In cooperation with the

PENNSYLVANIA DEPARTMENT OF ENVIRONMENTAL PROTECTION

New Cumberland, Pennsylvania

2002
ii

U.S. Department of the Interior

GALE A. NORTON, Secretary

U.S. Geological Survey

Charles G. Groat, Director

For additional information Copies of this report may be

write to: purchased from:

District Chief U.S. Geological Survey

U.S. Geological Survey Branch of Information Services

215 Limekiln Road Box 25286

New Cumberland, Pennsylvania 17070-2424 Denver Federal Center

Email: dc_pa@usgs.gov Denver, Colorado 80225-0286

Internet address: http://pa.water.usgs.gov Telephone: 1-888-ASK-USGS
iii

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

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

Purpose and scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Previous investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Prediction of stream velocities with the Jobson equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Comparison of stream velocities computed using the Jobson equation with velocities

determined from other sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Time-of-travel studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Susquehanna River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Delaware River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Lehigh River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Slope-area measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Flood-insurance studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Prediction of velocities for a range of streamflow conditions in Pennsylvania . . . . . . . . . . . . . . . . . . . 9

Development of a new equation for predicting stream velocities . . . . . . . . . . . . . . . . . . . . . . . . 9

Considerations and limitations of available velocity data for streams in

Pennsylvania . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

References cited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

ILLUSTRATIONS

Figure 1. Map showing location of time-of-travel studies conducted in parts of the

Susquehanna, Delaware, and Lehigh River Basins, Pennsylvania . . . . . . . . . . . 3

2-6. Graphs showing comparison of velocities from:

2. Time-of-travel studies and those predicted by the Jobson equation

for reaches of the Susquehanna River from Binghamton, N.Y., to

Clarks Ferry, Pa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3. Time-of-travel studies and those predicted by the Jobson equation

for reaches of the Delaware River from Hancock, N.Y., to

Delaware Water Gap, Pa.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4. Time-of-travel studies and those predicted by the Jobson equation

for reaches of the Lehigh River from Francis E. Walter Lake to

Easton, Pa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5. Slope-area measurements and those predicted by the Jobson equation

for sites in the vicinity of stream-gaging stations in Pennsylvania . . . . . . 7

6. Flood-insurance studies and those predicted by the Jobson equation

for stream reaches near stream-gaging stations in Pennsylvania . . . . . . . 8

CONTENTS

Page
iv

Figures 7-8. Graphs showing:

7. Relation between log (Q/DA0.73) and stream velocities from

time-of travel studies, slope-area measurements, and

flood-insurance studies in Pennsylvania . . . . . . . . . . . . . . . . . . . . . . . . . . 10

8. Comparison of stream velocities predicted by the new regression equation

and those from time-of-travel studies, slope-area measurements, and

flood-insurance studies in Pennsylvania . . . . . . . . . . . . . . . . . . . . . . . . . . 10

TABLE

Table 1. Statistical data for velocities from time-of-travel studies, slope-area

measurements, and flood-insurance studies in Pennsylvania . . . . . . . . . . . . . . 11

CONVERSION FACTORS AND ABBREVIATIONS

Multiply By To obtain

Length

mile (mi) 1.609 kilometer

Area

square foot (ft2) 0.09290 square meter

square mile (mi2) 2.590 square kilometer

Flow

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

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

Other abbreviations:

m/s meter per second

ILLUSTRATIONS—Continued

Page
1

PREDICTION OF VELOCITIES FOR A RANGE

OF STREAMFLOW CONDITIONS IN PENNSYLVANIA

by Lloyd A. Reed and Marla H. Stuckey

ABSTRACT

A regression equation that is used nationwide to predict traveltime in streams during

periods of low and moderate flow was developed by H.E. Jobson in 1996. Because none of the

data used in the development of the equation were from streams in Pennsylvania, velocities for

low and moderate flows predicted by the equation were compared to velocities measured during

time-of-travel studies on the Susquehanna, Delaware, and Lehigh Rivers. Although these

comparisons showed good agreement, a similar comparison using velocities for higher flows

indicated an overestimate by this regression equation. Because of the need for a method of

computing traveltimes for periods of high flows, a new regression equation was developed using

data from three sources: (1) time-of-travel studies conducted at low and moderate flow, (2) slopearea measurements of flood flows, and (3) velocities of the 100-year floodway as reported in

various flood-insurance studies.

The new regression equation can be used for predicting velocities associated with flows up

to the 100-year flood for Pennsylvania streams. It has standard errors of estimate of 0.18 feet per

second, 0.37 feet per second; and 0.31 feet per second, for time-of-travel studies in the

Susquehanna, Delaware, and Lehigh Rivers, respectively. The standard error of estimate is

1.71 feet per second for velocities determined from the slope-area measurements and 1.22 feet

per second for velocities determined from the flood-insurance studies.

INTRODUCTION

Under Federal guidelines, Pennsylvania is required to complete surface-water assessments for all public-water systems for potential spill contamination. The U.S. Geological Survey

(USGS) in cooperation with the Pennsylvania Department of Environmental Protection (PaDEP)

delineated the boundaries for the 5- and 25-hour traveltimes of public surface-water-supply

intakes on Pennsylvania streams. The traveltimes of 5 and 25 hours were predetermined by the

State to be zones of critical concern and high concern, respectively. These delineated boundaries

are based on stream velocities during periods of high flow and will aid state and municipal

officials in the event of contamination of a water supply upstream from the intake.1 As part of

this surface-water assessment, a method of determining mean stream velocity over

a range of streamflow conditions was required.

Regression equations were developed by Jobson (1996) to predict traveltime and dispersion

in streams and rivers in the United States. Jobson’s time-of travel of peak concentration

equation was based on data from about 90 different streams and more than 980 subreaches

nationwide during periods of low to moderate flow. Data from Pennsylvania streams were not

used in the development of these equations.

1 The 5- and 25-hour traveltime delineations were developed using an unpublished version of the equation

presented in this report prior to the inclusion of the Lehigh River time-of-travel study.
2

Purpose and Scope

This report presents an evaluation of the applicability of the Jobson velocity equation

(Jobson, 1996) for predicting velocities of streams during a range of low to high flow conditions

commonly experienced in Pennsylvania. Data were used from three time-of-travel studies

(Kauffman and others, 1976; White and Kratzer, 1994; Kauffman, 1982), 57 slope-area

measurements of high flow made by the USGS from about 1965 through 1999, and over 50 floodinsurance studies published between 1978 and 1999. A new regression equation is presented for

predicting velocities of the flow in Pennsylvania streams during a range of low to high flow

conditions.

Previous Investigations

A time-of-travel study was conducted on the Susquehanna River during periods of low flow

during 1965-67 by Kauffman and others (1976) (fig. 1). Time-of-travel studies also were

conducted on the upper Delaware River during periods of low and median flow in 1991 (White

and Kratzer, 1994) and on the Lehigh River during periods of low and median flow during

1970-77 (Kauffman, 1982) (fig. 1). Velocity data from slope-area measurements in stream reaches

near stream-gaging stations have been collected after periods of high water by USGS from about

1965-99. Velocity data were provided in flood-insurance studies (Federal Emergency

Management Agency, 1978-99) conducted for stream reaches near stream-gaging stations in

Pennsylvania. Jobson (1996, 1997) developed equations to predict traveltime of low and

moderate flows in streams in the United States. None of the above data sources were used in the

development of Jobson’s equations.

Prediction of Stream Velocities with the Jobson Equation

Regression equations were developed by Jobson (1996) to predict traveltime and dispersion

of a soluble, conservative constituent in streams and rivers nationwide for low to moderate flow.

Data from approximately 90 different rivers and streams were used to develop the equations and

a total of 986 data points were used. The equations were based on drainage area, the reach slope,

the mean annual discharge, and the discharge at the time of the measurement (Jobson, 1996).

The velocities used in the development of the equation for velocity of peak concentration ranged

from 0.01 m/s (0.03 ft/s) to 1.51 m/s (4.95 ft/s) with more than 90 percent of the velocities less

than 2.0 ft/s (Jobson, 1996).

The equation recommended by Jobson (1996) for predicting traveltime of the peak

concentration of a conservative constituent, modified for English units, is

V(p)=0.0656 0.051 (Da′)0.821 × (Qa′)-0.465 × Q/Da, (1)

where

V(p) is mean stream velocity of peak concentration of a slug of a dissolved

constituent, in feet per second.

The factor 0.0656 has units of feet per second; and

Da′ = (Da1.25 × g0.5)/Qa, (2)

where

Da is drainage area, in square feet;

g is acceleration of gravity, in feet per second squared; and

Qa is mean annual streamflow, in cubic feet per second; and

Qa′ = Q/Qa, (3)

where

Q is streamflow at the time of interest, in cubic feet per second; and

Qa is mean annual streamflow, in cubic feet per second.
3

Figure 1. Location of time-of-travel studies conducted in parts of the Susquehanna, Delaware, and Lehigh River Basins,Pennsylvania.
4

As an example, the velocity of the maximum concentration of a dye cloud for a time-oftravel study on the Susquehanna River between Shickshinny and Danville was 1.16 ft/s. The

drainage area of the river at Shickshinny is about 10,600 mi2 (2.955 × 1011 ft2), and the mean

annual streamflow for the period of record at Shickshinny, on the basis of data from the streamgaging station at Danville, is about 14,360 ft3/s. At the time of the study, the streamflow was

3,610 ft3/s.

 Substituting into equation (1);

V(p) = 0.0656 ft/s (0.051) {[(2.955×1011 ft2)

1.25] × ((32.2 ft/s2)0.5)/(14,360 ft3/s)}0.821

× {[(3,610 ft3/s)/(14,360 ft3/s)]-0.465} × ((3,610 ft3/s)/(2.955×1011 ft2)

V(p) = 0.0656 ft/s (0.051) (9.4978×108)(1.90036)(1.2216×10-8 ft/s)

V(p) = 0.0656 ft/s 1.124 ft/s

V(p) = 1.19 ft/s

Note the velocity calculated by use of Jobson’s equation, 1.19 ft/s, is within 3 percent of the

measured velocity of 1.16 ft/s.

COMPARISON OF STREAM VELOCITIES COMPUTED USING THE JOBSON EQUATION

WITH VELOCITIES DETERMINED FROM OTHER SOURCES

To evaluate the applicability of Jobson’s equation for predicting velocities for a range of low

to high flows in streams in Pennsylvania, velocities computed by use of the Jobson equation were

compared to velocities determined during time-of-travel studies, and to velocities determined

from indirect methods used in slope-area measurements, and to velocities determined in floodinsurance studies.

Time-of-Travel Studies

Time-of-travel studies are conducted by adding a traceable constituent to a river and

determining the time required for the tracer to arrive at and pass selected downstream points in

a study reach. This information is crucial in the event of a contaminant spill. The velocities

determined from time-of-travel studies are dependent on the discharge and the hydraulic

characteristics of a river. Collecting time-of-travel data at two (or more) different discharges can

define a relation through the study reach that integrates the combination of discharge and

hydraulics. For example, velocity usually increases and traveltime decreases as the discharge

increases. If a selected reach of a river has a deep pool, the velocity may be slower and the

traveltime may be longer than those determined from a reach with uniform depths. Time-oftravel studies in Pennsylvania have been limited to the Susquehanna, Delaware, and Lehigh

Rivers. These studies are discussed below and the study areas are shown on figure 1.

Susquehanna River

Time-of-travel studies were conducted on the Susquehanna River at low or moderately low

flow at six times during 1965-67 (Kauffman and others, 1976). Flows during the studies ranged

from 67- to 98-percent exceedence probability, which is the percentage of time flows are equalled

or exceeded based on the gaged period of record. The river between Binghamton, N.Y., and

Clarks Ferry, Pa. (fig. 1), was divided into 17 reaches. Velocities obtained for the reaches by the

time-of-travel studies are compared to velocities predicted by the Jobson equation for

corresponding flows in figure 2. Velocities from the time-of-travel studies ranged from 0.22 ft/s to

1.86 ft/s. Although the Jobson equation tended to overestimate at low velocities, the velocities

predicted by the Jobson equation generally are in good agreement with those measured during
5

the time-of-travel studies (fig. 2). The mean and standard deviation of the measured velocities

were 1.05 and 0.40 ft/s, respectively, and the mean and standard deviation of the velocities

predicted by the Jobson equation were 1.08 and 0.27 ft/s, respectively. The standard error of the

differences in velocities predicted by the Jobson equation and the time-of-travel studies on the

Susquehanna River was 0.24 ft/s.

Delaware River

Time-of-travel studies were conducted on the Delaware River from Hancock, N.Y., to

Delaware Water Gap, Pa. (fig. 1), in May and August of 1991 (White and Kratzer, 1994). The May

study was conducted when river flows ranged from 25- to 30-percent exceedence probability, and

the August study was conducted when river flows ranged from 85- to 95-percent exceedence

probability. The flows from the May study were higher than flows measured during the

Susquehanna River studies. The river was divided into 15 reaches. Velocities determined during

the time-of-travel studies for 14 of the reaches are compared to velocities predicted by the Jobson

equation (fig. 3). The Jobson equation was not used to predict velocities for the reach near

Narrowsburg known as the Narrowsburg pool and eddy because depths in the Narrowsburg pool

exceed 110 ft and traveltime in the pool, which is about 0.5 mi long, is not representative of the

rest of the river. Velocities measured during the May study ranged from 1.76 to about 2.71 ft/s,

and velocities measured during the August study ranged from 0.64 to about 1.18 ft/s. The mean

and standard deviation of the measured velocities were 1.59 and 0.71 ft/s, respectively, and the

mean and standard deviation of the velocities predicted by the Jobson equation were 1.47 and

0.62 ft/s, respectively. The standard error of the differences in velocities predicted by the Jobson

equation from the time-of-travel studies on the Delaware River was 0.31 ft/s.

Figure 2. Comparison of velocities from time-of travel studies (Kauffman and others, 1976) and those

predicted by the Jobson equation (Jobson, 1996) for reaches of the Susquehanna River from

Binghamton, N.Y., to Clarks Ferry, Pa.
6

Lehigh River

Time-of-travel studies were conducted on the Lehigh River from the outlet of Francis E.

Walter Lake to Easton (fig. 1) four times during 1970 to 1977 (Kauffman, 1982). The streamflows

on the Lehigh River were at 42-percent exceedence probability during the 1970 study, 80 percent

during the 1973 study, 67 percent during the 1974 study, and 92 percent during the 1977 study.

Velocities determined from the time-of-travel studies on the Lehigh River are compared in

figure 4 to velocities predicted by Jobson’s equation. Velocities from the time-of-travel studies

ranged from 0.37 ft/s to 1.88 ft/s. The mean and standard deviation of the measured velocities

were 0.89 and 0.48 ft/s, respectively, and the mean and standard deviation of velocities predicted

by the Jobson’s equation are 0.93 and 0.37 ft/s, respectively. The standard error of the difference

in velocities predicted by Jobson’s equation to the measured velocities on the Lehigh River was

0.30 ft/s.

Slope-Area Measurements

Slope-area measurements made in the vicinity of stream-gaging stations in the Delaware

and Susquehanna River Basins were reviewed and the mean velocity, streamflow, drainage area,

and number of cross-sections were tabulated. A comparison between velocities computed from

the slope-area measurements and velocities computed by use of the Jobson equation for the

57 slope-area measurements is shown in figure 5. Many of the slope-area measurements had

mean velocities that exceeded the maximum velocity used in the development of the Jobson

equation but were included in the comparison to evaluate Jobson’s equation at higher flows.

Velocities from the slope-area measurements ranged from 2.43 to 14.4 ft/s. Velocities predicted by

the Jobson equation averaged about 40 percent higher than those determined by the slope-area

measurements. The mean and standard deviation of the velocities determined by the slope-area

measurements were 6.67 and 2.26 ft/s, respectively. The mean and standard deviation of the

velocities computed by use of the Jobson equation were 9.70 and 4.05 ft/s, respectively. The

standard error of the velocities computed by use of the Jobson equation relative to mean

velocities from the slope-area measurements was 4.10 ft/s.

Figure 3. Comparison of velocities from time-of-travel studies and those predicted by the Jobson equation

(Jobson, 1996) for reaches of the Delaware River from Hancock, N.Y., to Delaware Water Gap, Pa.
7

Figure 4. Comparison of velocities from time-of-travel studies and those predicted by the Jobson

equation (Jobson, 1996) for reaches of the Lehigh River from Francis E. Walter Lake to Easton, Pa.

Figure 5. Comparison of velocities from slope-area measurements and those predicted by the Jobson

equation (Jobson, 1996) for sites in the vicinity of stream-gaging stations in Pennsylvania.
8

Current-meter measurements, contracted-opening measurements, and flow-over-dam

measurements were not used in the evaluation. Velocities obtained from current-meter

measurements of streamflow were not used because many of these measurements have been

made by wading at or near riffles where the flow is confined and velocities are higher than the

mean velocity in a reach of the stream or river. Current-meter measurements of streamflow can

also be made by suspending a meter from a bridge. Because many bridges were built at a natural

narrow point or the bridge itself provides some constriction to flow, velocities from these

measurements also are higher than the mean velocity of a nearby reach of the stream or river

and therefore were not used. Because velocities obtained from contracted-opening and flow-overdam measurements do not represent mean velocities in long stream reaches, they were not used.

Flood-Insurance Studies

The floodway data tables published in many flood-insurance studies (Federal Emergency

Management Agency, 1978-99) list stream velocities at each of the cross sections used in the

computation of floodways for a 100-year flood. Mean velocities published in the floodway data

tables represent the mean velocity for that part of the channel and flood plain that is conveying

most of the flood water. Cross sections with over-bank areas of relatively low velocity water that

can be blocked by fill material and not produce significant increases in stage during the

100-year flood generally are not used in the calculation of the mean velocities reported in the

floodway data tables. Velocities from flood-insurance studies ranged from 0.84 to 12.4 ft/s. The

velocities computed by use of the Jobson equation averaged about 40 to 50 percent greater than

those published in the floodway data tables for reaches above and below stream-gaging stations

(fig. 6). The data shown on figure 6 include every stream in Pennsylvania with a stream-gaging

station for which one or more floodway data tables were available. A total of 191 stream reaches

were evaluated. The mean and standard deviation of the velocities from the floodway data tables

were 6.59 and 2.17 ft/s, respectively, very close to the mean and standard deviation of the

Figure 6. Comparision of velocities from flood-insurance studies (Federal Emergency Management

Agency, 1978-99) and those predicted by the Jobson equation (Jobson, 1996) for stream reaches

near stream-gaging stations in Pennsylvania.
9

velocities from the data set from slope-area measurements. The mean and standard deviation of

the velocities computed by use of the Jobson equation were 10.6 and 2.50 ft/s, respectively. The

standard error of the velocities computed by use of the Jobson equation relative to velocities from

the floodway data tables was 2.77 ft/s.

PREDICTION OF VELOCITIES FOR A RANGE OF

STREAMFLOW CONDITIONS IN PENNSYLVANIA

The evaluation of Jobson’s equations for use in high-flow conditions showed that the

equations tended to overestimate velocities during high flows. This meant the equation could not

be used to accurately predict velocities above the maximum velocity of 4.95 ft/s that was used in

the development of the equation. Therefore, a new equation was developed to predict velocities in

Pennsylvania streams using data from the time-of-travel studies on the Susquehanna, Delaware,

and Lehigh Rivers, from the slope-area measurements, and from the floodway data tables in the

flood-insurance studies.

Development of a New Equation for Predicting Stream Velocities

The two most important variables for predicting stream velocities in Pennsylvania are

streamflow and drainage area. Many other variables could be included in an equation to predict

velocity including stream slope, channel roughness, cross-sectional area at bank full stage,

channel storage at low flow, and over-bank storage at high flow. For Pennsylvania streams,

recurrence-interval discharges are related closely to drainage area raised to varying coefficients

(Flippo, 1982).

Stuckey and Reed (2000) developed regression equations for predicting flows with

recurrence intervals of 10, 25, 50, 100, and 500 years. These equations include the term drainage

area raised to a coefficient that ranges from 0.678 to 0.777 depending on the recurrence interval

and the region of the State. The median of these coefficients is 0.73, excluding that for the

500-year flood due to the extremity of the flood event. The 0.73 coefficient was used to develop a

relation for predicting stream velocities for specific streamflow, based on discharge divided by

drainage area as shown below.

Q/DA0.73

A measure of the recurrence interval of each of the flows in the three data sets was

determined. A scatter plot is shown in figure 7 of the streamflow of interest divided by drainage

area raised to the 0.73 coefficient plotted against the measured velocities from the time-of-travel

studies in the Susquehanna, Delaware, and Lehigh Rivers, the velocities computed from slopearea measurements, and the velocities reported in floodway data tables in the flood-insurance

studies. The regression equation describing the relation shown in figure 7 is given below.

 V = 0.6067 e[0.8834 (log(Q/DA0.73))], (4)

where

V is velocity, in feet per second;

e is log to base e;

log is log to base 10;

Q is streamflow, in cubic feet per second; and

DA is drainage area, in square miles.

This new regression equation has standard errors of estimate of 0.18 ft/s, 0.37 ft/s, and 0.31 ft/s for

reaches with time-of-travel studies on the Susquehanna, Delaware, and Lehigh Rivers, respectively.

The standard error of estimate is 1.71 ft/s for the slope-area measurements, and 1.22 ft/s for data

from the floodway data tables. The equation has a coefficient of determination (R2) equal to 0.83.
10

Standard errors for the regression equation shown in figure 7 and statistical data for velocities from

time-of-travel studies, slope-area measurements, and flood-insurance studies are summarized in

table 1. A comparison between velocities predicted by the regression equation and the measured

velocities from the time-of-travel studies and the computed velocities from the slope-area

measurements and flood-insurance studies is shown in figure 8.

Figure 7. Relation between log (Q/DA0.73) and stream velocities from time-of-travel studies, slopearea measurements, and flood-insurance studies in Pennsylvania.

Figure 8. Comparison of stream velocities predicted by the new regression equation and those from

time-of-travel studies, slope-area measurements, and flood-insurance studies in Pennsylvania.
11

The Jobson equation is relatively accurate for Pennsylvania streams if the factor

log (Q/DA 0.73) is about 2 or less, as shown in figure 7. If the factor log (Q/DA 0.73) is over 2,

velocities predicted by the Jobson equation can be notably higher than those from slope-area

measurements or floodway data tables and the regression equation shown on figure 7 should be

used to compute velocities.

Table 1. Statistical data for velocities from time-of-travel studies, slope-area

measurements, and flood-insurance studies in Pennsylvania

[ft/s, feet per second; Q = discharge in cubic feet per second; DA = drainage area in

square miles]

Mean

Standard

deviation

(ft/s)

Standard

error of

difference

in

velocities

(ft/s)

Range of the

term

Q/DA0.73

Susquehanna River time-of-travel 0.97 - 7.51

Measured velocity 1.05 0.40

Jobson equation 1.08 .27 0.24

Regression equation 1.99 .18 .27

Delaware River time-of-travel 2.06 - 16.0

Measured velocity 1.59 .71

Jobson equation 1.47 .62 .31

Regression equation 1.34 .37 .40

Lehigh River time-of-travel .87 - 9.29

Measured velocity .89 .48

Jobson equation .93 .37 .30

Regression equation 1.06 .31 .28

Slope-area measurements 88.3 - 1,567

Measured velocity 6.67 2.26

Jobson equation 9.70 4.05 4.10

Regression equation 6.17 1.71 2.52

Federal Emergency Management Floodway data tables 65.6 - 1,340

Measured velocity 6.59 2.17

Jobson equation 10.6 2.50 2.77

Regression equation 6.38 1.22 2.29
12

Considerations and Limitations of Available Velocity Data

for Streams in Pennsylvania

Time-of-travel data are not available for periods of high flow, and the relation between

velocities from slope-area measurements and actual velocities in long stream reaches during

periods of high flow is not known. The relation between traveltime obtained from data published

in the floodway data tables of flood-insurance studies and actual stream velocities also is not

known. Floodway velocities are not measured data; rather, they are determined based on a

maximum 1-ft rise in the 100-year water-surface elevation while encroaching the 100-year flood

plain boundary. These velocities may not always duplicate real streamflow conditions. Velocities

computed from the slope-area measurements and those published in the floodway data tables of

the flood-insurance studies have similar means (6.67 and 6.59 ft/s, respectively) and a similar

standard deviation (2.26 and 2.17 ft/s, respectively). Although the two sets of velocities are

similar, it should be noted that both numbers are computed from the same open-channel

equations. Further analysis of equations to predict stream velocities at high flows would be

needed if time-of-travel studies are conducted at high flows.

The Jobson equation works reasonably well for Pennsylvania streams if the factor

log (Q/DA0.73) is 2.0 or less; however, it tends to overpredict velocities if the factor log (Q/DA0.73)

is greater than 2.0. The new regression equation can be used throughout the range of flow

conditions up to the 100-year flood event. The velocities used to develop the equation ranged

from 0.22 to 14.4 ft/s. Streams used in the analysis and development of the equation had

drainage areas from 2.4 to 26,000 mi2 and discharges from 58 to 740,000 ft3/s.
13

SUMMARY

The USGS, in cooperation with PaDEP, delineated the boundaries for the 5- and 25-hour

traveltimes of public surface-water-supply intakes on Pennsylvania streams. To determine these

traveltimes, a method of calculating mean stream velocity over a range of streamflow conditions

was required. Equations to predict traveltime in streams in the United States were presented by

Jobson (1996, 1997). Most of the data used to develop the equations were collected during periods

of low and moderate flow and none of the data were from Pennsylvania streams. Three data sets

were used to evaluate the Jobson equation for Pennsylvania streams over a range of low to high

flows: time-of-travel studies on the Susquehanna, Delaware, and Lehigh Rivers, slope-area

measurements of flood flows, and velocities of the 100-year floodway as reported in floodinsurance studies.

A comparison of velocities computed from the traveltime regression equation by Jobson to

velocities measured during the time-of-travel studies showed good agreement for low and

moderately low flow. Comparison of velocities computed with the Jobson regression equation to

velocities from slope-area measurements of high flows and to velocities of the 100-year floodway

from various flood-insurance studies (Flood Emergency Management Agency, 1978-99) indicated

that velocities were over-estimated by the regression equation. Although the low and moderateflow comparisons showed good agreement, an equation was needed for computing velocities

during the range of low to high flows commonly experienced in Pennsylvania streams.

A new regression equation was developed to predict velocities from 0.22 to 14.4 ft/s for

streams in Pennsylvania. This new regression equation was developed using data from three

sources: 1) time-of-travel studies conducted at low and moderate flow, 2) slope-area

measurements of flood flows, and 3) velocities of the 100-year floodway as reported in floodinsurance studies. The regression equation had standard errors from 0.18 to 0.37 for the time-oftravel studies, 1.71 for the slope-area measurements, and 1.22 for the flood-insurance studies.

REFERENCES CITED

Federal Emergency Management Agency, 1978-99, Flood insurance studies (About 50 townships and

boroughs in Pennsylvania): Washington, D.C. [variously paged] (http://www.fema.gov/maps/).

Flippo, H.N., Jr., 1982, Evaluation of the streamflow-data program in Pennsylvania:

U.S. Geological Survey Water-Resources Investigations Report 82-21, 56 p.

Jobson, H.E., 1996, Prediction of traveltime and longitudinal dispersion in rivers and streams:

U.S. Geological Survey Water-Resources Investigations Report 96-4013, 69 p.

_____1997, Predicting travel time and dispersion in rivers and streams: Journal of Hydraulic

Engineering, November 1997, p. 971-978.

Kauffman, C.D., Jr., 1982, Time-of-travel and dispersion studies, Lehigh River, Francis E. Walter

Lake to Easton, Pennsylvania: U.S. Geological Survey Open-File Report 82-861, 32 p.

Kauffman, C.D., Jr., Armbruster, J.T., and Voytik, Andrew, 1976, Time-of-travel studies Susquehanna

River, Binghamton, New York to Clarks Ferry, Pennsylvania: U.S. Geological Survey Open-File

Report 76-247, 24 p.

Stuckey, M.H., and Reed, L.A., 2000, Techniques for estimating magnitude and frequency of peak

flows for Pennsylvania streams: U.S. Geological Survey Water-Resources Investigations

Report 00-4189, 43 p.

White, K.E., and Kratzer, T.W., 1994, Determination of traveltime in the Delaware River, Hancock,

New York, to the Delaware Water Gap by use of a conservative dye tracer:

U.S. Geological Survey Water-Resources Investigations Report 93-4203, 54 p.