79-52 

Prepared in cooperation with the 

Susquehanna River Bas in Commission 
50272-101 

REPORT DOCUMENTATION 11. REPORT NO. 

PAGE 

3. Recipient's Accession No. 

4. Title and Subtitle 

FLOW ROUTING IN THE SUSQUEHANNA RIVER BASIN: PART II -

LOW-FLOW FREQUENCY CHARACTERISTICS OF THE SUSQUEHANNA RIVER 

BETWEEN WAVERLY. NEW YORK AND SUNBURY, PENNSYLVANIA 

5. Report Date 

June 1979 

6. 

7. Author(s) 

Donald L. Bingham 9 . Performing Organization Name and Address 

U.S. Geological Survey, Water Resources Division 

Post Office Box 1107 

Harrisburg, Pennsylvania 17108 

12. Sponsoring Organization Name and Address 

U.S. Geological Survey, Water Resources Division 

Post Office Box 1107 

Harrisburg, Pennsylvania 17108 

15. Supplementary Notes 

8. Performing Organization Rept. No. 

USGS/WRI-79-52 

10. Project/Task/Work Unit No. 

11. Contract(C) or Grant(G) No. 

(C) 

(G) 

13. Type of Report & Period Covered 

Final 

14. 

Prepared in cooperation with the Susquehanna River Basin Commission 

1t5. Abstract (Limit: 200 words> Six flow-routing models were developed, calibrated, and verified for 

the Susquehanna River between Waverly, New York, and Sunbury, Pennsylvania. The models 

give the Susquehanna River Basin Commission tools to estimate effects of water-resource 

developments upstream from Waverly upon four gaged sites and two ungaged si tes within 

the study reach. The models were used to simulate a 32-year record of daily flows at 

ungaged sites A and B. Low-flow frequency curves for simulated flows at sites A and B 

were used to estimate 7-day low-flows at the 10-year recurrence interval of 540 and 

770 ft3/s, respectively. 

The model errors, differences between model results and observed streamflow at 

gaged sites, are considered to be within reasonable limits and overall quality of 

simulated streamflow and low-flow frequency curves is considered good. 

17. Document Analysis a. Descriptors 

*Low flow, *flow charact eristics, *flood routing, *model studies, *Pennsylvania, 

*River Basin Commissions, *streamflow 

b. Identifiers/Open-Ended Terms 

Resource Management 

c. COSATI Field/Group 

18. Availability Statement 

No restriction on distribution 

(See ANSI-Z39.18) 

19. Security Class (This Report) 21. No. of Pages 

UNCLASSIFIED 31 ~------------------------ --------- ---------

20. Security Class (This Page) 

UNCLASSIFIED 

See Instructions on Reverse 

22. Price 

OPTIONAL FORM 272 (4-77) 

(Formerly NTIS-35) 

Department of Commerce 
FLOW ROUTING IN THE SUSQUEHANNA RIVER BASIN: 

PART II - LOW-FLOW FREQUENCY CHARACTERISTICS OF THE 

SUSQUEHANNA RIVER BETWEEN WAVERLY, NEW YORK AND SUNBURY, PENNSYLVANIA 

By Donald L. Bingham 

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations 79-52 

Prepared in cooperation with the 

Susquehanna River Basin Commission 

June 1979 
UNITED STATES DEPARTMENT OF THE INTERIOR 

CECIL D. ANDRUS, Secretary 

GEOLOGICAL SURVEY 

H. William Menard, Director 

For additional information write to: 

U.S. Geological Survey 

Fourth Floor, Federal Building 

P.O. Box 1107 

Harrisburg, Pennsylvania 17108 
CONTENTS 

Page 

Metric conversion table ------------------------------------------- iv 

Abstract ---------------------------------------------------------- 1 

Introduction ------------------------------------------------------ 2 

Description of study reaches -------------------------------------- 2 

Data used for digital modeling ------------------------------------ 2 

Description of flow-routing models -------------------------------- 5 

Model calibration ------------------------------------------------- 7 

Verification of models -------------------------------------------- 12 

Application of models --------------------------------------------- 21 

Summary ----------------------------------------------------------- 31 

References -------------------------------------------------------- 31 

Figure 1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

ILLUSTRATIONS 

Map of study area -------------------------------------- Schematic diagram ·of the multiple linearization 

flow-routing model ----------------------------------- Schematic diagram of the Susquehanna River showing 

the relations used in flow-routing models ------------

Hydrograph comparison of observed and simulated daily 

flows at station 01554000, April-July 1968------------

Hydrograph comparison of observed and simulated daily 

flows at station 01554000, June-September 1971--------

Seven-day low-flow frequency curves computed from 

observed and simulated daily flows for station 

01531500 --------------------------------------------- Seven~day low-flow frequency curves computed from 

observed and simulated daily flows for station 

01536500 --------------------------------------------- Seven-day low-flow frequency . curves computed from 

observed and simulated daily flows for station 

01540500 --------------------------------------------- Seven-day low-flow frequency curves computed from 

observed and simulated daily flows for station 

01554000 --------------------------------------------- Seven-day low-flow frequency curve computed from 

simulated daily flows at Site A ---------------------- Seven-day low-flow frequency curve computed from 

simulated daily flows at Site B ----------------------

iii 

Page 

3 

6 

8 

10 

11 

16 

17 

18 

19 

22 

23 
ILLUSTRATIONS.--Continued 

Page 

Figure 12. Flow-duration curves of observed and simulated daily 

flows for station 01531500 -----------------~--------- 25 

13. Flow-duration curves of observed and simulated daily 

flows for station 01536500 --------------------------- 26 

14. Flow-duration curves of observed and simulated ·daily 

flows for station 01540500 --------------------------- 27 

15. Flow-duration curves of observed and simulated daily 

flows for station 01554000 --------------------------- 28 

16. Duration curve of simulated daily flows at Site A ------ 29 

17. Duration .curve of simulated daily flows at Site B ------ 30 

TABLES 

Page 

Table 1. Data available for use in routing study for the 

Susquehanna River reaches ------------------------------ 4 

2. Model parameters used in final flow-routing 

models ------------------------------------------------- 9 

3 . . Examples of errors encountered during model calibration--- 13 

4. Errors, in percent, _ between simulated and observed 

flows for the period October 5, 1941 to September 30, 

1973 --------------------------------------------------- 15 

5. Summary of average absolute errors between observed 

and simulated annual minimum flows --------------------- 20 

6. Comparison of computed 7-day low-flows at the 10-year 

recurrence interval ------------------------------------ 24 

METRIC CONVERSION TABLE 

The following factors may be used to convert the Inch-pound units 

published herein to the International System of Units (SI). 

Multiply Inch-pound·units 

feet per second (ft/s) 

square feet per second (f~2/s) 

cubic feet per second (ft3/s) 

~ 

.3048 

.09290 

.02832 

iv 

To obtain SI units 

meters per second (m/s) 

square meters per 

second (m2/s) 

cubic meters per 

second (m3/s) 
FLOW ROUTING IN THE SUSQUEHANNA RIVER BASIN: 

PART II - LOW-FLOW FREQUENCY CHARACTERISTICS OF THE 

SUSQUEHANNA RIVER BETWEEN WAVERLY, NEW YORK AND SUNBURY, PENNSYLVANIA 

By Donald L. Bingham 

ABSTRACT 

Six flow-routing models were developed, calibrated, and verified for 

the Susquehanna River between Waverly, New York, and Sunbury, Pennsylvania. 

The models give the Susquehanna River Basin Commission tools to estimate 

effects of water-resource developments upstream from Waverly upon four gaged 

sites and two ungaged sites within the study reach~ The models were used to 

simulate a 32-year record of daily flows at ungaged sites A and B. Low-flow 

frequency curves for simulated flows at sites A and B were used to estimate 

7-day low-flows at the 10-year recurrence interval of 540 and 770 ft3/s, 

respectively. 

The model errors, differences between model results and observed streamflow at gaged sites, are considered to be within reasonable limits and overall 

quality of simulated streamflow and. low-flow frequency curves is considered 

good. 

1 
INTRODUCTION 

In 1975 the U.S. Geological Survey and the Susquehanna River Basin 

Commission (SRBC) initiated a series of cooperative projects designed to 

provide SRBC wi~h tools for effective water-resources management. The 

tools were to be a series of flow-routing models for all the major streams 

within the Susquehanna River basin which would give SRBC the capability 

to translate effects of proposed water-resource developments anywhere in 

the basin to points downstream. Models completed by Armbruster (1977) 

provide SRBC with coverage of the Juniata River and Susquehanna River 

below Sunbury, Pennsylvania. 

The primary objective of this study, second in the series, is the 

, development, calibration, and verification of flow-routing models for the 

Susquehanna River from Waverly, New York, to Sunbury, Pennsylvania. These 

models will permit SRBC to estimate the effects of water-resource developments 

upstream from Waverly at six locations on the Susquehanna River. They were 

also used to simulate streamflow for existing conditions at two ungaged sites. 

DESCRIPTION OF STUDY REACHES 

The Susquehanna River from Waverly, New York, to Sunbury, Pennsylvania 

will be referred to in this report as the Susquehanna River. In this 

portion of the river, gaging stations are located on the mainstem at Waverly, 

Towanda, Wilkes-Barre, Danville, and Sunbury. These stations define four 

reaches: 1) Waverly to Towanda, length 18.0 mi; 2) Towanda to Wilkes-Barre, 

length 82.7 mi; 3) Wilkes-Barre to Danville, length 52.1 mi; and 4) Danville 

to Sunbury, length 15.0 mi (fig. 1). The reaches from Towanda to WilkesBarre and from Wilkes-Barre to Danville were each split into two reaches by 

selecting two ungaged sites referred to hereafter as sites A and B. The two 

ungaged sites were selected because they were near the center of the reach 

or near a tributary or some other feature which would provide an intermediate 

point for water-resources management decisions. 

Site A, located immediately upstream from Tunkhannock Creek, divided 

reach 2 into reaches 2a (length 52.8 mi) and 2b (length 29.9 mi). Site B 

located immediately upstream from Wapwallopen Creek, divided reach 3 into 

reaches 3a (length 21.8 mi) and 3b (length 30.3 mi). 

DATA USED FOR DIGITAL MODELING 

Streamflow records for 14 stations for water years 1942-73 were used 

in the modeling. The stations, their period of record, and drainage areas 

are listed in Table 1. 

2 
w 

77° 

42°-------• r.-

41° 

0 10 20 

chemurig 

01531000 

30 MILES 

I I I I I I I 

0 10 20 30 KILOMETERS 

Lewisburg 

01553500 

Waverly 76° 

01515000 NEW YORK 

--- PENNSYLVANIA - --

~ ~ 

~ 

Figure 1.--Map of study area. 
Table 1.--Data available for use in routing study for the 

Susquehanna River reaches 

Station number Station name 

01515000 

01531000 

01531500 

. 01532000 

01534000 

01536000 

01536500 

01537000 

01537500 

01538000 

01539000 

01540500 

01553500 

01554000 

Susquehanna River near Waverly, N.Y. 

Chemung River at Chemung, N.Y. 

Susquehanna River at Towanda, Pa. 

Towanda Creek near Monroeton, Pa. 

Tunkhannock Creek near Tunkhannock, Pa. 

Lackawanna River at Old Forge, Pa. 

Susquehanna River at Wilkes-Barre, Pa. 

Toby Creek at Luzerne, Pa. 

Solomon Creek at Wilkes-Barre, Pa. 

Wapwallopen Creek near Wapwallopen, Pa. 

Fishing Creek near Bloomsburg, Pa. 

Susquehanna River at Danville, Pa. 

West Branch Susquehanna River at 

Lewisburg, Pa. 

Susquehanna River at Sunbury, Pa. 

4 

Water years 

, of 

record 

1938-73 

1904-73 

1914-73 

1915-73 

1915-73 

1939-73 

1900-73 

1942-73 

1941-73 

1920-73 

1939-73 

1900-73 

1940-73 

1938-73 

Drainage 

area (mi2) 

4,773 

2,506 

7,797 

215 

383 

332 

9,960 

32.4 

15.7 . 

43.8 

274 

11,200 

6,847 

18,300 
DESCRIPTION OF FLOW-ROUTING MODELS 

To determine the low-flow characteristics at the two ungaged 

sites, a flow-routing model was developed and calibrated for each of the 

six reaches. A period of 32 water years of concurrent, observed data 

were used to provide as much data as possible to verify and evaluate the 

models. 

Each model was a unit-response, flow-routing model that used the 

diffusion analogy (Keefer, 1974) and multiple linearization (Keefer and 

McQuivey, 1974). A one-day routing interval was used throughout the 

reaches. The two model parameters--wave celerity and wave dispersion--

have been described by Armbruster (1977). Celerity describes the speed 

of the simulated water wave traveling downstream and wave dispersion 

defines the amount of damping or attenuation of the wave. 

The diffusion analogy is the mechanism used to derive the routingresponse functions. Multiple linearization is a means to allow for both 

variable travel time and attenuation of flows while using linear flowropting models. Multiple linearization is useful for this study because 

a wide range of discharges are encountered. As shown in figure 2, the 

inflow hydrograph is separated into a number of segments or selected 

discharge ranges. Flows are routed downstream, one segment at a time, 

and then summed -to obtain an outflow hydrograph. 

Flow-routing models were first developed for reaches 1, 2, 3, and 

4. Each required a separate model to properly account for both gaged and 

ungaged inflow into the reach. Flow from ungaged areas was estimated by 

multiplying the flow at an index station by a suitable ratio. Initial 

estimates of this ratio were derived by dividing the drainage area of a 

group of tributaries, gaged and ungaged, by the drainage area of the 

index station. Trial and error adjustments to the ratio were made to 

balance flows within each reach. Model parameters also were determined 

for each model. 

Subsequently, the flow-routing model for reach 2 was divided into 

two models for reaches 2a and 2b and the model for reach 3 was divided 

into two models for reaches 3a and 3b. New model parameters were determined 

for each of these four models. 

Groundwater discharge, not treated as a separate item in the model 

input, was implicitly included as total streamflow was used in the 

calibrations. No errors were noted that could be attributed to this 

method. 

5 
TIME-----? 

lA. 

1F---------------

0: 

~~~ 

<t -------------- J: 

~ I /""'\. 

0 

TIME---7 

Model with multiple 

response functions. 

Mt)LTIPLE LINEARIZATION FLOW ROUTING 

MODEL 

I High flow I db db rib 

rrnm 

I Low flow 

lilii II II II fhT1Jr-rTJ I"T"T'1111~11 ........... 111~111 -. 

Recombine 

routed 

outflow 

TIME~ 

outflow 

J 

Figure 2.--Schematic diagram of the multiple linearization flow-routing 

model. (From Keefer and McQuivey, 1974.) 

6 
MODEL CALIBRATION 

Each of the six flow-routing models was calibrated by adjusting the 

preliminary values for the wave dispersion coefficient, the wave celerity, 

and amount of flow from ungaged areas. The calibration process, as discussed by Shearman and Swisshelm (1973) and Armbruster (1977), consisted 

of the following trial and error procedure. 

1. Several segments of at least one year's duration of concurrent 

streamflow record were selected. Each segment contained at 

least one significant rise and recession. The segments exhibited a wide range of flows; however, due to the objectives of 

the study, flows in the low-to-medium flow range were emphasized. 

2. Preliminary values for dispersion coefficients and celerities 

were estimated using the methods published by Keefer and McQuivey 

(1974). 

3. To account for flow from ungaged areas, a preliminary set of 

ratios was calculated. 

4. 

5. 

Simulated outflows from a reach were produced by the models, 

using observed inflows to the reach, preliminary model parameters, 

and preliminary ratios as input to the models. 

The simulated outflows for each reach were then evaluated by: 

a. A visual comparison of hydrograph plots .of observed and 

simulated outflows. 

b . . An analysis of average absolute deviations between observed 

and simulated daily flows. 

c. A comparison of volume differences between the observed and 

simulated hydrographs for the calibration period. 

6. Steps 4 and 5 were repeated until adjustments of the ratios 

and model parameters provided minimum errors. 

Figure 3 is a schematic diagram of the study area that shows the 

final ratios used in the calibration of the models. Table 2 lists the 

final model parameters used for each reach. 

Figures 4 and 5 present comparisons of observed and simulated 

hydrographs for parts of two water years for the Susquehanna·River at 

Sunbury (01554000) station. Data for the simulated hydrograph were 

obtained by routing observed data from Waverly through all six models. 

Both figures show good agreement between observed and simulated data, which 

indicates good calibration of ~he model. 

7 
EXPLANATION 

01536500 Gaging station and 

number 

Doily flow at station 

01536500 

01553500 

01540500 

01554000 

05315 = (02(05150 )+ 1.!6(05310~ v 

routed 

Osite A= ~.00(05315) + 2.41 (05320~ v 

routed 

05365 =~.OO(Osite A)+ 2.03(0534cl + 1.96 (05360) 

v 

routed 

Qsite B ~I.OO(Q536s)t5.76 C0537o) +5.92(05375), 

v 

routed 

05405 =I.OO(Osite~ +2.38(05380) +2.77(05390) 

' v I 

routed 

05540 = \ I.OI v 540~ __ .....,., + 1·03(05535 ) 

routed 

01536000 

01536500 · 

I 37500 

Figure 3. -,-s-c:n.ematic diagram of the Susquehanna River showing 

· the relations used in flow-routing models. 

8 
(q, 

Reach 1 

g_ c K 

400 2.5 2,000 

800 3.2 4,000 

\.0 

2,000 3.7 6,000 

4,000 4.2 9,000 

10,000 5.3 15,000 

20,000 6.2 27,000 

50,000 8.7 61,000 

80,000 10.5 90,000 

110,000 11.9 121,000 

Table 2.--Model parameters used in final flow-routing models 

flow in cubic feet per second; C, celerity i n feet per second; 

and !' dispersion coefficient in square feet per second) 

Reach 2a Reach 2b Reach 3a Reach 3b 

c K c K c K c K 

1.5 500 1.5 500 1.7 2,000 1.7 1,500 

2.0 1,000 2.0 1,000 2.6 4,000 2.1 3,000 

3.6 2,000 3.6 2,000 3.0 7,000 2.5 5,000 

3.8 6,000 3.8 6,000 3.1 12,000 2.8 8,000 

4.7 15,000 4.7 15,000 3.9 22,000 3.6 17,000 

5.6 32,000 5.6 32,000 4.7 40,000 4.4 28,000 

7.7 75,000 7.7 75,000 6.4 80,000 5.9 60,000 

9.4 120,000 9.4 120,000 7.5 130,000 6.3 90,000 

10.7 160,000 10.7 160,000 8.5 180,000 6.6 124,000 

Reach 4 

c K 

1.2 1,300 

1.4 2, 500 

1.5 4, 500 

1.8. 5, 000 

2.4 12,000 

3.0 22' 000 

4.2 50,000 

4.9 78,000 

5.4 107,000 
~ 0 

(.) 

~ 100 

a:: 

w 

a.. 

rw 

~ 

(.) 

CD 

::::> 

(.) 

LL. 

0 

en 

0 ~ z 0 <t 

en 

::::> 

0 

I 

rz 

w 10 

(!) 

a:: 

<t 

I 

(.) 

en 

0 

• 

Observed daily flows 

Simulated daily flows 

APRIL MAY 

Susquehanna River at Sunbury 

JUNE JULY 

Figure 4.--Comparison of observed and simulated daily flows at station 01554000, 

April - July, 1968. 
50 

0 

z 

0 

(.) 

w 

CJ) 

0::: 

w 

a.. 

tw 

w 

lL. 

(.) 10 

CD 

::> 

(.) 

~ lL. 

~ 0 

CJ) 

0 

z 

<( 

· CJ) 

::> 

0 

I 

tz 

-

. 

w 

(.!) r 0::: 

<( • 

I 

(.) 

CJ) 

0 

I I I 

Susquehanna River at Sunbury 

Observed daily flows 

Simulated daily flows 

I I I I I I I 

JUNE JULY AUGUST SEPTEMBER 

Figure 5.--Comparison of observed and simulated daily flows at station 01554000, 

June - September, 1971. 
The errors discussed in step 5 were computed using the following 

relations: 

Daily flow error (in percent) X 100 

N 

where Q0QS and Qsim are the observed and simulated flows respectively 

for the 1th day and N is the number of days in the calibration period; 

and 

v -v . · obs s1m x 100 

vobs 

Volume error (in percent) = 

where VQb and Vsim are the volumes of observed and simulated flows 

respect1v~ly for the calibration period. Several sets of typical 

calibration errors for each reach are given in table 3. Errors for 

reaches 2 and 3 are given for both undivided and divided conditions. 

Daily flow errors ranged from 3.2 percent in reach 4 to 9.3 percent 

in undivided reach 2. Flow-volume errors ranged from -3.0 percent 

in reaches 1, 2a + 2b, and undivided reach 2, to 2.3 percent in 

reaches 3a + 3b undivided reach 3. 

VERIFICATION OF MODELS 

To verify the models, daily streamflows for 32 water years were 

simulated at all six sites. The data were simulated in the following 

manner: 

Reach 1 -Susqueha11na River (Waverly to Towanda).--Observed daily 

streamflows at Waverly were added to daily streamflows for the 

Chemung River at Chemung, N.Y., and routed 18.0 mi to Towanda. 

Reach 2a- Susguehanna River (Towanda to Site A).--Simulated flows at 

Towanda were added to observed flows from Towanda Creek and 

routed 52.8 mi to site A (immediately upstream from Tunkhannock 

Creek). Reach 2 was divided at this point to provide low-flow 

frequency data at an ungaged site. 

12 
Table 3.--Examples of errors encountered 

Reach 

number 

1 Oct. 5, 

Oct. 5, 

Oct. 5, 

Oct. 5, 

2a + 2b 1/ Oct. 5, 

Oct. 5, 

Oct. 5, 

Oct. 5, 

2 ~/ Oct. 5, 

Oct. 5, 

Oct. 5, 

Oct. 5, 

3a + 3b !/ Oct. 5, 

Oct. 5, 

Oct. 5, 

Oct. 5, 

3 ~/ Oct. 5, 

Oct. 5, 

Oct. 5, 

Oct. 5, 

4 Oct. 5, 

Oct. 5, 

Oct. 5, 

Oct. 5, 

1/ Divided reach II Undivided reach 

Calibration 

period 

1964, to Sept. 29, 1965 

1967, to Sept. 28, 1968 

1970, to Sept. 29, 1971 

1971, to Sept. 28, 1972 

1964, to Sept. 29, 1965 

1967, to Sept. 28, 1968 

1970, to Sept. 29, 1971 

1971, to Sept. 28, 1972 

1964, to Sept. 29, 1965 

1967, to Sept. 28, 1968 

1970, to Sept. 29, 1971 

1971, to Sept. 28, 1972 

1964, to Sept. 29, 1965 

1967, to Sept. 28, 1968 

1970, to Sept. 29, 1971 

1971, to Sept. 28, 1972 

1964, to Sept. 29, 1965 

1967, to Sept. 28, 1968 

1970, to Sept. 29, 1971 

1971, to Sept. 28, 1972 

1964, to Sept. ·29, 1965 

1967, to Sept. 28, 1968 

1970, to Sept. 29, 1971 

1971, to Sept. 28, 1972 

13 

during model calibration 

Errors (Eercent) 

Daily flows Flow volume 

6.2 0.3 

7.2 -3.0 

5.1 1.3 

5.4 0.6 

9.1 0.1 

6.2 -1.3 

7.1 -3.0 

6.9 -2.6 

9.3 0.1 

6.7 -1.3 

6.9 -3.0 

6.7 -2.6 

5.7 0.8 

5.3 2.3 

5.3 0.1 

6.1 0.6 

5.5 0.8 

4.9 2.3 

5.0 0.1 

5.8 0.6 

3.7 -0.4 

3.2 -0.2 

4.4 0.5 

3.4 -0.2 
Reach 2b- Susquehanna River (Site A to Wilkes-Barre).--The simulated 

daily streamflows at site A were added to observed flows from 

Tunkhannock Creek and routed 29.9 mi to Wilkes-Barre. Observed 

flows from the Lackawanna River were then added to the routed 

flows to simulate the flows at Wilkes-Barre. 

Reach 3a- Susquehanna River (Wilkes-Barre to Site B).--The simulated 

flows at Wilkes-Barre were added to observed flows from Toby and 

Solomon Creeks and then routed 21.8 mi to site B (immediately upstream from Wapwallopen Creek). Reach 3 was divided at thi~ point 

to provide low~flow frequency data at a second ungaged site. 

Reach 3b- Susq~ehanna River (Site B to Danville).--Simulated flows 

from site B were added to observed flows from Wapwallopen Creek 

and routed 30.3 mi to Danville, where observed flows from Fishing 

Creek were added to provide simulated flows at Danville. 

Reach 4 -Susquehanna River (Danville to Sunbury).--Simulated flows 

at Danville were routed 15.0 mi to Sunbury where observed flows 

from the West Branch at Lewisburg were added to provide simulated 

flows at Sunbury. 

The adequacy of each model may be judged by comparing simulated and 

observed flows for the entire simulation period, October 1, 1941, to 

September 30, 1973 (see table 4). Errors in daily flows ranged from 5.1 

percent to 8.5 percent. Flow-volume errors were between 0.0 percent in 

reaches 2a + 2b and 0.9 percent in reaches 3a + 3b. (The 0.0 value was a 

result of rounding to the nearest tenth of a percent). 

Low-flow characteristics are of primary interest. Comparisons of lowflow frequency curves for simulated versus observed data provide a valuable 

means for evaluating adequacy of the models. Low-flow analyses are generally 

based on the climatic year (April 1 to March 31), thus low-flow frequency 

comparisons are based on 31 years of data, since only 31 climatic years of 

data can be obtained from 32 water years. 

Seven-day low-flow frequency curves computed from the simulated and 

observed data, at each of the four gaged sites are presented in figures 6-9. 

Visual comparison of the curves indicates very good agreement between 

observed and simulated data. Furthermore, figure 7 also indicates that the 

frequency curve of simulated flows at Wilkes-Barre using one model for reach 

2 compares favorably with simulated flows using ~odels for reaches 2a and 2b. 

Similarly, figure 8 also indicates good agreement between the simulated flows 

using one model for reach 3 and the simulated flows using models for reaches 

3a and 3b. Thus, the models of the divided reaches, which are necessary for 

simulation of streamflows at sites A and B, are implicitly verified. Table 

5 presents the average absolute errors between observed and simulated annual 

minimum flows at the gaged sites for one-, three-, and seven-day periods. 

14 
Table 4.--Errors, in percent, between simulated and observed flows 

for the period October 5, 1941, to September 30, 1973 

Reach Daily Flow 

number flows volume 

1 5.1 0.3 

2a + 2b 7.7 0.~1 

3a + 3b 8.5 0.9 

4 5.7 0.4 

~/ Rounded to tenths 

15 
,.. 

w 

(.!) 

a: 

<t 

I: 

0 

U'>o 

oz 

0 LLio 

(!)LLI 

<t(f) 

a: 

wa: 

>w f-1 <:( a.. 

0\ ~ tJ 

ow 

t.._LL 

~0 

::>CD 

~:::> 

-0 

zz 

~­

_J 

<t 

:::> 

z 

~ 

3000~~--------~--~----~--~--------~--~--~--~~ 

2000 

1000 

900 

800 

700 

600 

500 

400 

0 Observed flows at Towanda 

8 Simulated flows at Towanda 

Susquehanna River at Towarrla 

(1943-73) 

300 ~----------~--~----._ __ _. ____________ ~ __ ._ __ ~~ 

1.005 1.01 1.1 1.2 1.5 2 5 10 20 50 100 

RECURRENCE INTERVAL, IN YEARS 

Figure 6.--Seven~day low-flow frequency curves computed from observed 

and simulated daily flows for station 01531500. 
,.. 

w 

(.!) 

0:::: 

<I 

::r: 

Oo CJ)z 

oo 

wo <.!>w 

<I(/) 

0::::0:::: 

ww 

>0.. 

<I 

t- ~~w -.....low 

,lJ.. 

t--o 

~-=>CD 

~5 

Zz 

~-

_J 

<I 

:J 

z 

z 

<I 

5000 

4000 Susquehanna River at Wilkes ... Barre 

~ ( 1943-73) 

8 3000 

8 

2000 8 

8 

I @ 

1000 

900~ 800 0 Observed flows at W i I kes- Barre ~ 700 8 Simulated flows at Wilkes-Barre reaches 2a 4-2 b ~ 600 r::J Simulated flows at Wilkes -Bar_re reach 2 0 

D 

500 

~ --~--------~--~----~--~--------~--~--~--~~ 1.0051 .01 1.1 1.2 1.5 2 5 10 20 50 100 

RECURRENCE INTERVAL, IN YEARS 

Figure 7.--Seven-day low-flow frequency curves computed from 

observed and simulated daily flows for station 01536500. 
w 

(.!) 

a:: 

<( 

I 

~0 

0~ 

wo <.!>w 

<((f) 

a:: a:: 

~~ 

>-tJ ~ CS LLI 00 I U.. 

1'--0 

~-:Jm 

~a 

Zz 

~ 

_j 

<( 

::::) 

z 

z 

<( 

6000 

1000 

900 

800 

700 

~ ~ ill 

Susquehanna River at Danville 

( 1943-73) 

~ 

g 

9 

0 Observed flows at Danvi lie 

A Simulated flows at Danville reaches 3a+3b 

[J Simulated flows at Danville reach 3 

g 

\. 

c 

c 

1.005 1.01 1.1 1.2 1.5 2 5 10 20 50 100 

RECURRENCE INTERVAL, IN YEARS 

Figure 8.--Seven-day low-flow frequency curves computed from observed 

and simulated daily flows for station 01540500. 
........ 

\.0 

w 

(.!) 

0::: 

<( 

I 

() 

({) 

oo 

z 

wo 

(.!)0 

<IW 

a::({) 

Wo:: 

>w <I a_ 

~)- oW 

,w 

I'-LL 

~() 

::>CD 

~::::> _() 

Zz 

~­

_J 

<I 

::::> 

z 

z 

<I 

7000 

6000 

4000 

Susquehanna River at Sunbury 

( 1943-73) 

0 Observed flows at Sunbury 

.8 Simulated flows at Sunbury 

1000 ~~--------~--~----~--_.--------~--~--~--~~ 

1.005 LOI 1.1 1.2 1.5 2 5 10 20 so roo 

RECURRENCE INTERVAL, IN YEARS 

Figure 9.--Seven-day low-flow frequency curves computed from observed 

and simulated daily flows for station 01554000. 
Table 5.--Summary of average absolute errors between observed and 

simulated annual minimum flows 

Average absolute error of annual minimum flows, in percent 

Station 1 day 3 day 7 day 

Towanda 

01531500 5.87 5.55 5.38 

Wilkes-Barre 

01536500 9.64 9.21 9.01 

Danville 

01540500 7.36 7.21 6.83 

Sunbury 

01554000 4.61 4.50 4.25 

20 
Without observed flow data, low-flow frequency curves for sites A and 

B cannot be verified. However, the curves may still be useful for estimating 

the 7-day low-flow at the 10-year recurrence interval (Q7 10). Figures 10 

and 11 present the 7-day low-flow frequency curves comput~d from streamflow 

data simulated for sites A and B. These relations yield estimates for 

Q7 , 10 as shown in table 6. Also shown in table 6 are e~timates of Q7,10 

for the four gaged sites, based on observed data for 1942-1973. Armbruster 

(1976) presents a method for estimating low-flow frequency characteristics 

that is based on multiple regression techniques. Use of his method yields 

the estimates of Q7 ,10 for sites A and Bas well as the four gaged sites 

that are also shown in table 6. Armbruster indicated that the average 

length of record for major stream $tations was 55 years. The shorter 

period (1942-1973) used in this report puts more emphasis on the drought 

of the 1960's, resulting in lower estimates for Q7 10• 

' 

Figures 12-15 present flow-duration curves of observed and simulated 

data for stations 01531500, 01536500, 01540500, and 01554000. It can be 

seen that good agreement exists between the observed and simulated flows 

for the entire flow range at all four stations. Therefore, the models are 

judged adequate at the four gaged sites over the entire range of flows. 

APPLICATION OF MODELS 

The model development, calibration, and verification procedure 

yielded a 32-year record of simulated flows at ungaged sites A and B that 

can be put to immediate application. For example, the low-flow frequency 

characteristics curves at sites A and B (fig. 10 and 11) can be used to 

estimate,at the 10-year recurrence interval, 7-day low-flow values of 540 

and 770 ft3/s, respectively. Other analyses of the simulated streamflows 

such as flow duration curves (fig. 16 and 17) can be made to estimate 

additional flow characteristics. Also, additional frequency analyses could 

be made to estimate high-flow and low-flow characteristics for time periods 

other than seven days. The reader must assess the applicability of any such 

estimates giving consideration to the fact that model results at sites A 

and B cannot be verified by observed flow data. 

In the future, modified streamflows at Waverly (for example, by an 

upstream reservoir whose effects on flow at Waverly are known) can be 

routed downstream to assess effects of the water resource development on 

streamflows at downstream locations. 

21 
N 

N 

w 

(!) 

a:: 

<t 

I 

~ -o Oz 

wO 

(!)0 

<tw 

a:: (f) 

WQ:: 

~w a.. 

~~ ow· .w 

f'...lJ... 

~0 

:::>m 

~:::> 

zo 

-z 

~-

_j 

<t 

:::> 

z 

z 

<t 

3000~~--~----~--~--~----~------~--~--~--~~ 

2000 

1000 

900 

800 

700 

600 

500 

400 

300 

A Simulated flows at Site A 

Susquehanna River at Site A 

(1943- 73) 

1.005 1.01 1.1 1.2 1.5 2 5 10 20 50 100 

. RECURRENCE INTERVAL 1 IN YEARS 

Figure 10.--Seven-day low-flow frequency curve computed from simulated 

daily flows at Site A. 
N 

w 

... w 

(.!) 

a: 

<( 

I 

0 

(f) 

00 

z 

wo 

<.!>o 

<tw 

a:: en 

wa:: 

>w 

<(a.. 

~...._ 

ow 

•w f'..u.. 

:EO 

=>m 

:E::> 

zO 

-z :E-

_J 

<( 

::> 

z 

z 

<( 

5~r-~-------.---r----.---.-------~--~--~~---

4000 

3000 

2000 

1000 

900 

800 

700 L 8. 

600 

Simulated flows at site 8 

Susquehanna R·rver at Site 8 

( 1943-73) 

500 ~~--------~--~----~------------~--~--~----~ 1.005 1.01 1.1 1.2 1.5 2 5 10 20 

RECURRENCE INTERVAL, IN YEARS 

Figure 11.--Seven-day low-flow frequency curve computed from 

simulated daily flows at Site B. 

50 100 
Station 

Towanda 

(01531500) 

Site A 

Wilkes-Barre 

(01536500) 

Site B 

Danville 

(01540500) 

Sunbury 

(01554000) 

Table 6.--Comparison of computed 7-day low-flows 

at the 10-year recurrence interval 

Q7,10 in cubic feet per second 

from 1942-73 from Armbruster 

data (1976) 

soil:/ 638 

54o!./ 730 

7 5,;:_! 832 

77c# 860 

89J:_I 945 

163cJ:-I 1609 

ll From frequency curves of simulated daily flows. 

~/ From frequency curves of observed daily flows. 

24 
·o 

z 

0 

(.) 

w 

(/) 

a:: 

w 

a.. 

~ 

LLJ 

w 

LL. 

(.) 

m 

:J 

(.) 

z 

w 

(.!) 

a:: 

<( 

I 

(.) 

(/) 

0 

• • • • • • • • • 

·~ ~ 

• • • •• -

Observed flow 

Simu Ia ted flow 

• • • • • a 

• • • • • • • • •• 

0.01 0.1 1.0 . 0 30 50 70 90 . 99 99.9 99.99 

PERCENT OF TIME DISCHARGE IS EQUALLED OR EXCEEDED 

Figure 12.--Flow-duration curves of observed and simulated daily 

flows for station 01531500. 

25 
0 

z 

0 

0 

w 

Cf) 

a:: 

w 

CL 

..__ 

w 

w 

LL. 

0 

CD 

:::::> 

0 

z 

w · <.!) 

a:: 

<( 

I 

0 

Cf) 

0 

- e Observed flow 

• a A Simulated flow 

• • • • 

·~ • • • • 

•• ~ 

• 

• ... 

• •• • •• • •• • 

0.01 0.1 1.0 10 ?:IJ 50 70 90 99 93.9 99.99 

PERCENT OF TIME DISCHARGE IS EQUALLED OR EXCEEDED 

Figure 13.--Flow-duration curves of observed and simulated 

daily flows for station 01536500. 

26 
0 

z 

0 

@ 

(f) 

0:: 

w 

a... 

tw 

w 

LL. 

(.) 

co 

::> 

(.) 

z 

... w 

~ <t 

I 

(.) 

(f) 

0 

• • • • • •• • • •• 

•• • • • 

~ 

e Observed flow 

A Simulated flow 

• -

• • • • • • • • • • ••• .. 

.. 

0.01 0.1 1.0 10 30 S) 70 90 99 99.9 99.00 

PERCENT OF TIME DISCHARGE IS EQUALLED OR EXCEEDED 

Figure 14.--Flow-duration curves of observed and simulated 

daily flows for station 01540500. 

27 
0 

5 100,000 

(.) 

w 

(/) 

~ 

w 

Cl... 

tw 

w 

LL 

(.) 

CD 

::::> 

(.) 

z 

... w 

(!) 

~ 

<X: 

I 

(.) 

(/) 

0 

6 

• • • • • •• • • • • • • •• • • 

e Observed flow 

A Simu Ia ted flow 

• • 

.. 

• • • • • • • 

' I 000 '-----..\-----'----...&..----L-__._ _ _.____----L ___ .........__M~___._A_......,j 0.01 0.1 1.0 10 30 50 70 90 99 99.9 99.99 

PERCENT OF TIME DISCHARGE IS EQUALLED OR EXCEEDED 

Figure 15.--Flow-duration curves of observed and simulated 

daily flows for station 01554000. 

28 
0 

z 

8 

L&J 

fJ) 

ffi 

a.. 

~ lJJ 

u.. 

(.) 

m 

::J 

(.) 

z 

,. 

lJJ 

(.!) 

a::. 

<{ 

~ 

(.) 

fJ) 

cs 

.. 

• • IOO,CXX> 

IO,CXX> 

1000 

• 

• • • • 

• Simulated flows 

• • • • • • • • • • • • • • • • • • 

• • • 

• 

0.01 0.1 1.0 10 30 50 70 90 gg- 93.9 9999 

PERCENT OF TIME DISCHARGE IS EQUALLED OR EXCEEDED 

Figure 16.--Duration curve of simulated daily flows at Site A. 

29 
0 

z 

0 

0 

w 

C/) 

a: 

w 

Q.. 

..... 

w 

~ 

0 

m 

::::> 

0 

z 

w 

(.!) 

a: 

<( 

I 

0 

C/) 

0 

• 

• • 

100,000 • • • 

• 

10,000 

1000 

• -- Simulated flows 

• 

• 

• • • • • 

• • • 

• • • • 

• 

• • • • 

• • • • 

o.o1 0.1 . 1.0 10 . ,. 3Q -. 5o·.- 70 · 90 · 99 93.9 93.99 

PERCENT OF TIME DISCHARGE IS EQUALLED.OR EXCEEDED 

Figure 17.--Duration curve of simulated daily flows at Site B. 

30 
SUMMARY 

Flow-routing models for six reaches of the Susquehanna River between 

Waverly, New York, and Sunbury, Pennsylvania, have been developed, calibrated, 

and verified. These models can be used to translate the effects of proposed 

water-resource developments upstream from Waverly to six sites within the 

study area. The models have already been used to simulate 32 years of flow 

data, for existing conditions, at two ungaged sites. These simulated data 

were used to estimate the low-flow characteristics at the two ungaged sites. 

At the 10-year recurrence interval, the 7-day low-flow at site A is estimated 

to be 540 cubic feet per second and at site B it is estimated to be 770 cubic 

feet per second. Low-flow frequency curves of simulated and observed data at 

the four gaged sites are in good agreement. 

All flow-routing models contain some inherent errors, but these errors 

are within acceptable limits, indicating that the models are useful. 

REFERENCES 

Armbruster, Jeffrey T., 1976, Technical manual for estimating low-flow 

frequency characteristics of streams in the Susquehanna River basin: 

U.S. Geol. Survey Water-Resources Inv. 76-51, 51 p. 

-----------------------, 1977, Flow routing in the Susquehanna River 

basin: Part 1 - Effects of Raystown Lake on low-flow frequency 

characteristics of the Juniata and Lower Susquehanna Rivers, Pennsylvania: U.S. Geol. Survey Water-Resources Inv. 77-12, 35 p. 

Keefer, Thomas N., 1974, Desktop computer flow routing: Am. Soc. Civil 

Engineers Proc. Jour. Hydraulics Div., HY7, Proc. Paper 10669, 

p. 1047-1058. 

Keefer, Thomas N., and McQuivey, RaulS., 1974, Multiple linearization 

flow routing model: Am. Soc. Civil Engineers Proc. Jour. Hydraulics 

Div., HY7, Proc. Paper 10668, p. 1031-1046. 

Shearman, J. 0., and Swisshelm, R. V., Jr., 1973, Derivation of homogeneous 

streamflow records in the upper Kentucky River basin, southeastern 

Kentucky: U.S. Geol. Survey open-file rept., 34 p. 

31