Techniques for Estimating the Magnitude

and Frequency of Floods in Rural Basins

of South Carolina, 1999

Water-Resources Investigations Report 02-4140

Prepared in cooperation with the

South Carolina Department of Transportation

U.S. Department of the Interior

U.S. Geological Survey

Techniques for Estimating the Magnitude and

Frequency of Floods in Rural Basins of

South Carolina, 1999

By Toby D. Feaster and Gary D. Tasker

U.S. Geological Survey

Water-Resources Investigations Report 02-4140

Columbia, South Carolina

2002
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

Use of trade, product, or firm names in this publication is for descriptive purposes only 

and does not imply endorsement by the U.S. Geological Survey

For additional information 

write to: 

District Chief 

U.S. Geological Survey

Suite 129

720 Gracern Road

Columbia, SC 29210-7651

Additional information about water resources in South Carolina is available on the 

World Wide Web at http://sc.water.usgs.gov

Copies of this report can be 

purchased from:

U.S. Geological Survey

Branch of Information Services

Box 25286

Denver, CO 80225-0286

888-ASK-USGS
Contents III

CONTENTS

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

Introduction................................................................................................................................................................................ 2

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

Previous Investigations .................................................................................................................................................... 2

Description of Study Area................................................................................................................................................ 2

Acknowledgments............................................................................................................................................................ 4

Peak-Flow Data.......................................................................................................................................................................... 4

Quality Assurance/Quality Control.................................................................................................................................. 5

Estimation of Flood Magnitude and Frequency at Gaging Stations ........................................................................................ 11

Flood Frequency ............................................................................................................................................................ 11

Skew Coefficient............................................................................................................................................................ 12

Synthesized Peak Flow .................................................................................................................................................. 15

Estimation of Flood Magnitude and Frequency at Ungaged Sites .......................................................................................... 16

Ordinary Least-Squares Analysis................................................................................................................................... 16

Generalized Least-Squares Analysis.............................................................................................................................. 18

Accuracy of the Method................................................................................................................................................. 21

Region-of-Influence Method.......................................................................................................................................... 22

Comparison of Methods................................................................................................................................................. 24

Limitations ..................................................................................................................................................................... 24

Computer Software ........................................................................................................................................................ 24

Application of Methods ........................................................................................................................................................... 25

Flood Frequency at Gaged Sites for Streams Draining One Physiographic Province................................................... 25

Flood Frequency Near Gaged Sites on the Same Stream Draining One Physiographic Province ................................ 26

Flood Frequency at Ungaged Sites on Streams Draining More Than One Physiographic Province............................. 26

Flood Frequency at Gaged Sites on Streams Draining More Than One Physiographic Province........................................... 27

Broad River .................................................................................................................................................................... 27

Little Pee Dee River....................................................................................................................................................... 29

Lynches River ................................................................................................................................................................ 29

Edisto River.................................................................................................................................................................... 29

Salkehatchie River ......................................................................................................................................................... 29

Flood Frequency at Gaged Sites on Regulated Streams .......................................................................................................... 30

Pee Dee River................................................................................................................................................................. 30

Catawba River................................................................................................................................................................ 30

Wateree River................................................................................................................................................................. 30

Saluda River................................................................................................................................................................... 31

Congaree River .............................................................................................................................................................. 31

Santee River ................................................................................................................................................................... 31

Savannah River .............................................................................................................................................................. 31

Pacolet River .................................................................................................................................................................. 32

Summary .................................................................................................................................................................................. 32

Selected References ................................................................................................................................................................. 33

Appendix A: Water-year peak-flow and stage data at gaging stations in South Carolina through 1999................CD in pocket

Appendix B: Station, regional, and weighted flood estimates for selected recurrence intervals for rural streamflow 

stations in South Carolina used in the regionalization study..............................................................................CD in pocket

Appendix C: Generalized least-squares model description and assumptions.........................................................CD in pocket

Appendix D: Water-year peak-flow and stage data at gaging stations in South Carolina on regulated streams and on 

streams draining more than one physiographic province through 1999.............................................................CD in pocket
IV Contents

FIGURES

1. Maps showing physiographic provinces and locations of streamflow gaging stations on rural streams in South 

Carolina and parts of North Carolina and Georgia ................................................................................................................3

2–5. Graphs showing:

2. Distribution of systematic peak-flow record lengths for rural streamflow stations used in the 

regionlization study.........................................................................................................................................................10

3. Examples of distributions with zero skew, positive skew, and negative skew ...............................................................12

4. Relation between drainage area and 100-year recurrence-interval flow for stations on streams draining the 

Piedmont physiographic province in South Carolina, North Carolina, and Georgia......................................................19

5. Relation between drainage area and 100-year recurrence-interval flow for stations on streams draining 

the upper Coastal Plain physiographic province in South Carolina and North Carolina ..............................................20

6. Map showing locations of streamflow gaging stations on regulated streams and gaging stations on streams draining 

more than one physiographic province in South Carolina ..................................................................................................27

7. Graph showing relation between drainage area and 100-year recurrence-interval flows for period of record 

and water years 1939-83 for Station 02153500, Broad River near Gaffney, S.C., Station 02156500, Broad 

River near Carlisle, S.C., and Station 02161500, Broad River at Richtex, S.C. .................................................................28

TABLES

1. Streamflow stations in South Carolina used to develop regional regression equations......................................................6

2. Streamflow stations in North Carolina and Georgia used to develop regional regression equations for South Carolina...7

3. Distribution of stations used in the regionalization analysis by State and physiographic province..................................10

4. Ordinary least-squares regression statistics for the generalized skew coefficients...........................................................13

5. Weighted generalized skew coefficients and associated statistics for rural South Carolina gaging stations ....................14

6. Sensitivity of South Carolina generalized skew coefficients (not weighted) to high and low values...............................15

7. Station and weighted flood-frequency data for the synthesized peak flows used in the regionalization analysis............16

8. South Carolina rural flood-frequency equations ...............................................................................................................21

9. Accuracy statistics for the regional regression equations, presented by physiographic province and 

recurrence interval.............................................................................................................................................................23

10. Ratio of PRESS (ROI) statistic to PRESS (RRE) statistic for each physiographic province ...........................................24

CONVERSION FACTORS, VERTICAL DATUM, AND ABBREVIATIONS

In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929)—

A geodetic datum derived from a general adjustment of the first-order level nets of both the United

States and Canada, formerly called Sea Level Datum of 1929. Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD83).

ACRONYMS

Multiply By To obtain

foot (ft) 0.3048 meter

mile (mi) 1.609 kilometer

acre 4,047 square meter

square mile (mi2

) 2.590 square kilometer

acre-foot (acre-ft) 1.233 x 103 cubic meter

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

GLM = Generalized linear model ROI = Region of influence

GLS = Generalized least squares RRE = Regional regression equations

OLS = Ordinary least squares R2 = Coefficient of determination

PRESS = Prediction error sum of squares SCDOT = South Carolina Department of Transportation

QAQC = Quality assurance / quality control USGS = U.S. Geological Survey
Abstract 1

ABSTRACT 

Data from 167 streamflow-gaging stations in or

near South Carolina with 10 or more years of record

through September 30, 1999, were used to develop two

methods for estimating the magnitude and frequency of

floods in South Carolina for rural ungaged basins that

are not significantly affected by regulation. Floodfrequency estimates for 54 gaged sites in South Carolina

were computed by fitting the water-year peak flows for

each site to a log-Pearson Type III distribution. As part

of the computation of flood-frequency estimates for

gaged sites, new values for generalized skew coefficients were developed. Flood-frequency analyses also

were made for gaging stations that drain basins from

more than one physiographic province. The U.S. Geological Survey, in cooperation with the South Carolina

Department of Transportation, updated these data from

previous flood-frequency reports to aid officials who

are active in floodplain management as well as those

who design bridges, culverts, and levees, or other structures near streams where flooding is likely to occur.

Regional regression analysis, using generalized

least squares regression, was used to develop a set of

predictive equations that can be used to estimate the

2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence-interval flows for rural ungaged basins in the

Blue Ridge, Piedmont, upper Coastal Plain, and lower

Coastal Plain physiographic provinces of South

Carolina. The predictive equations are all functions

of drainage area. Average errors of prediction for these

regression equations ranged from -16 to 19 percent for

the 2-year recurrence-interval flow in the upper Coastal

Plain to -34 to 52 percent for the 500-year recurrenceinterval flow in the lower Coastal Plain. 

A region-of-influence method also was developed that interactively estimates recurrence- interval

flows for rural ungaged basins in the Blue Ridge of

South Carolina. The region-of-influence method uses

regression techniques to develop a unique relation

between flow and basin characteristics for an individual watershed. This, then, can be used to estimate flows

at ungaged sites. Because the computations required

for this method are somewhat complex, a computer

application was developed that performs the computations and compares the predictive errors for this

method. The computer application includes the option

of using the region-of-influence method, or the generalized least squares regression equations from this

report to compute estimated flows and errors of prediction specific to each ungaged site. From a comparison

of predictive errors using the region-of-influence method

with those computed using the regional regression

method, the region-of-influence method performed

systematically better only in the Blue Ridge and is,

therefore, not recommended for use in the other physiographic provinces.

Techniques for Estimating the Magnitude and Frequency 

of Floods in Rural Basins of South Carolina, 1999

By Toby D. Feaster and Gary D. Tasker
2 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

Peak-flow data for the South Carolina stations

used in the regionalization study are provided in appendix A, which contains gaging station information, logPearson Type III statistics, information on stage-flow

relations, and water-year peak stages and flows. For

informational purposes, water-year peak-flow data for

stations on regulated streams in South Carolina also are

provided in appendix D. Other information pertaining

to the regulated streams is provided in the text of the

report. 

INTRODUCTION

One of the most important factors in the design 

of bridges, highway embankments, culverts, levees, 

and other structures near streams is the magnitude and 

frequency of floods that are likely to occur during the 

life of the structure. Federal, State, regional, and local 

officials also need these data for effective floodplain 

management and to delineate areas susceptible to 

flooding. 

In an effort to continue to improve the floodfrequency estimates for South Carolina, the U.S. Geological Survey (USGS), in cooperation with the South 

Carolina Department of Transportation (SCDOT), 

updated previous flood-frequency reports by incorporating additional data collected through the 1999 water 

year. A water year, which is the 12-month period from 

October 1 to September 30, is designated by the calendar year in which it ends. Thus, the 12-month period 

ending September 30, 1999, is called the “1999 water 

year.” Throughout this report, “peak flow” refers to 

the maximum peak for the water year. 

Purpose and Scope

Two methods for predicting the magnitude and 

frequency of floods in South Carolina at ungaged, rural 

basins that are not significantly affected by regulation 

are presented with the estimated error of each method. 

The two methods are the regional regression method 

and the region-of-influence method (Tasker and Slade, 

1994; Hodge and Tasker, 1995; Pope and Tasker, 

1999). Flood-frequency estimates at streamflowgaging stations, and methods for estimating the magnitude and frequency of floods at or near these streamflow-gaging stations also are provided. Peak-flow data 

were analyzed for 167 streamflow-gaging stations (54 

in South Carolina, 65 in North Carolina, and 48 in 

Georgia) for streams that drain rural basins without 

significant regulation and have at least 10 years of peakflow data through the 1999 water year (fig. 1; data for 

South Carolina stations shown in appendices A and B).

Previous Investigations

The earliest investigation of flood frequency of 

streams in South Carolina was made by Speer and 

Gamble (1964), who presented methods for estimating 

the magnitude of floods for selected recurrence intervals for streams in the South Atlantic slope basin. This 

area extends from the James River in Virginia to the 

Savannah River along the South Carolina-Georgia 

State line (Guimaraes and Bohman, 1991). Whetstone 

(1982) used multiple regression analyses to define the 

relation between flows and basin characteristics at 

recurrence intervals of 2, 5, 10, 25, 50, and 100 years, 

for unregulated, rural streams in South Carolina with 

drainage areas greater than 1.0 mi2. Frequencies of peak 

flows were regionalized by Guimaraes and Bohman 

(1991) using generalized least squares regression methods to define the relation of magnitude and frequency 

of flows to various basin characteristics on ungaged, 

rural streams that were not significantly affected by 

regulation. Bohman (1992) described methods for 

determining flood-frequency relations for urban 

streams in South Carolina. This report updates and 

supersedes the previous flood-frequency report for 

rural streams in South Carolina by Guimaraes and 

Bohman (1991). 

Description of Study Area

The study area includes the entire State of 

South Carolina, which is located on the South Atlantic 

slope adjacent to the Atlantic Ocean. The State has an 

area of 31,055 mi2, and generally is divided into three 

major physiographic provinces: Blue Ridge, Piedmont, 

and Coastal Plain (Cooke, 1936). The Coastal Plain is 

further divided into the upper Coastal Plain and the 

lower Coastal Plain. The physiographic provinces and 

locations of data-collection sites in South Carolina and 

in adjacent areas in North Carolina and Georgia are 

shown on figure 1.

The Blue Ridge physiographic province in South 

Carolina is a mountainous region of steep terrain with 

some stream gradients greater than 250 ft per mile 

(Bloxham, 1979). Land-surface elevation ranges from 
Introduction 3Figure 1. Physiographic provinces and locations of streamflow gaging stations on rural streams in South Carolina and parts of North Carolina and Georgia.
4 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

1,000 to more than 3,500 ft above sea level. Surface 

fractures in crystalline rock provide channels for runoff. Overlying the crystalline bedrock is a layer of 

weathered bedrock or saprolite. Although some rainfall 

infiltrates the saprolite layer, the steep-sided slopes and 

semipermeable soils in this region cause much of the 

rainfall to run off rapidly into stream channels (South 

Carolina Water Resources Commission, 1983).

Rolling hills, elongated ridges, and moderately 

deep to shallow valleys characterize the Piedmont 

physiographic province of South Carolina. Piedmont 

land-surface elevations range from about 1,000 ft 

above sea level at the Blue Ridge foothills to about 

400 ft above sea level at the Fall Line, which is the 

name given to the boundary between the Piedmont and 

Coastal Plain physiographic provinces. In general, this 

boundary is characterized by a series of rapids or falls 

where the streams tumble off the more resistant rocks 

of the Piedmont into the deeper valleys worn in the 

softer sediments of the Coastal Plain (Cooke, 1936). 

The Piedmont is underlain by fractured crystalline rock 

consisting of intrusive granite, gneiss, schist, and metamorphosed volcanic rock. Most overlying soil is moderately to poorly permeable silty clay loams. Alluvial 

deposits of clay, silt, and sand are found along the valley floors (Bloxham, 1981).

Gradual slopes and rounded summits characterize the upper Coastal Plain physiographic province in 

South Carolina, although there are several areas of 

intensely irregular terrain. Some hilltop elevations 

exceed 700 ft above sea level near the Fall Line, but 

land-surface elevations commonly are less than 200 ft 

above sea level at the boundary of the lower Coastal 

Plain. Extensive swamps and very wide floodplains are 

common to the four large, through-flowing rivers 

(fig. 1) (Bloxham, 1976).

In the lower Coastal Plain physiographic province, the land surface slopes from elevations of about 

200 ft above sea level near the boundary of the upper 

Coastal Plain to sea level at the coast. Topographic 

relief in this area is much less than that in other areas of 

the State, and small stream drainage patterns are characteristically more erratic in the seaward direction. 

Large parts of the lower Coastal Plain river systems are 

swamplands. The highly permeable soils in this region 

are similar to those of the upper Coastal Plain, which 

readily absorb rainfall and retard runoff to stream channels, causing streamflow to rise and fall gradually 

(Bloxham, 1981).

Acknowledgments

The authors gratefully acknowledge the assistance and support of William H. Hulbert formerly with 

the SCDOT. Mr. Hulbert worked cooperatively with 

the USGS on this and numerous other projects in South 

Carolina. The peak-flow data used in the analyses 

described in this report were collected throughout 

South Carolina and adjoining States at streamflow 

gages operated in cooperation with a variety of Federal, 

State, and local agencies. The authors also acknowledge the dedicated work of the USGS field office staff 

in collecting, processing, and storing the peak-flow 

data necessary for the completion of this report.

PEAK-FLOW DATA

The empirical basis for estimating specific 

recurrence-interval flows is the water-year peak flows 

collected at streamflow-gaging stations. The first 

streamflow data collected in the study area was for the 

Savannah River at Augusta, Ga. The U.S. Weather 

Bureau, now the National Weather Service, began collecting data at this site in 1884. By 1930, streamflow 

data were collected at a network of sites by the USGS, 

in cooperation with the South Carolina State Highway 

Department, now the SCDOT (Guimaraes and 

Bohman, 1991). By 1999, the USGS systematic datacollection program in South Carolina included 118 

streamflow gaging stations and 53 crest-stage partialrecord sites. These data are collected in cooperation 

with many Federal, State, and local agencies in South 

Carolina (Cooney and others, 1999). With World Wide 

Web Internet access, peak-flow data can be obtained at 

http://water.usgs.gov/sc/nwis/sw. 

At continuous-record stations, the water-surface 

elevation, or stage, of the stream is recorded at fixed 

intervals, typically ranging from 5 to 60 minutes. At 

crest-stage partial-record stations, only the crest, or 

highest, stages that occur between site visits, usually 

6 to 8 weeks, are recorded. Measurements of flow are 

determined throughout the range of recorded stages 

and a relation between stage and flow is developed for 

the gaged site. Using this stage-flow relation, or rating, 

flows for recorded stages are estimated. Because 

stream channels are dynamic, periodic streamflow 

measurements are made to verify that the hydraulic 

conditions at the site remain stable. If the measurements indicate conditions have changed, additional 
Peak-Flow Data 5

data are collected and used to make adjustments to the 

stage-streamflow relation. At some crest-stage sites, 

indirect-flow computation methods are used to develop 

a theoretical rating. This method has been used extensively to compute flows from small drainage areas 

(Bodhaine, 1968).

Data from 167 gaging stations on streams in 

South Carolina (54 stations) and adjacent areas of 

North Carolina (65 stations) and Georgia (48 stations) 

were used in the development of regionalized floodfrequency relations presented in this report (fig. 1, 

tables 1 and 2). The distribution of gaging stations used 

to develop these regression equations are presented by 

State and physiographic province in table 3. The distribution of systematic peak-flow record lengths used in 

the regional analyses is shown in figure 2. Appendix A 

of this report contains the following data for each of the 

South Carolina stations: station description, drainage 

area, type of data recorder, extreme gage heights and 

flows for the period of record, description of the stageflow relation, and water-year peak stages and flows for 

the period of record. Flood-frequency data derived 

from the peak flows for South Carolina stations also 

are included in appendix A. Similar information can be 

obtained for the Georgia and North Carolina stations in 

reports by Stamey and Hess (1993) and Pope and others (2001), respectively. Those flood-frequency data, 

however, may be slightly different from the data used 

in this study because of additional data that may have 

been collected since those studies were completed and 

because different regionalized skew coefficients were 

used. Station, regional, and weighted flows for selected 

recurrence intervals for the South Carolina stations used 

in the regional regression are presented in appendix B.

Five stations for which streamflow data are 

available were not included in the regionalization analysis for various reasons (fig. 1). Stations 02197300, 

02197310, and 02197315 (map index numbers 57, 58, 

and 59, respectively, fig. 1) in the Upper Three Runs 

basin of the upper Coastal Plain physiographic province were not included in the regionalization analysis 

because of the effects of large sand deposits in the 

upper end of the basin on rainfall runoff. Substantial 

amounts of rainfall runoff are stored in the sand deposits, diminishing the magnitude of peak flows for the 

Upper Three Runs basin compared to other basins in 

the upper Coastal Plain province. Therefore, the 

regionalized flood-frequency equations developed for 

the upper Coastal Plain province do not apply to this 

basin or to other basins physiographically similar to the 

Upper Three Runs basin (Guimaraes and Bohman, 

1991). In addition, Lanier (1996), noted that Station 

02197315 is affected by backwater from the Savannah 

River and, therefore, the data are not suitable for a 

flood-frequency analysis.

Catfish Canal near Conway, S.C. (map index 

number 55, station number 02131150) and Great 

Swamp near Ridgeland, S.C. (map index number 56, 

station number 02176875) were not included in the 

regional analysis because the flows are affected by 

channelization.

Quality Assurance/Quality Control

For this study, a comprehensive review was 

made of the peak-flow data. A minimum of 10 years of 

record was required for a station to be included in the 

analysis. The data at each station also were reviewed 

for homogeneity (time trends), which implies relatively 

constant watershed conditions during the period of 

record. The Kendall’s tau statistic was chosen to assess 

the homogeneity of the record at each station. If it was 

determined that a station’s record was not homogeneous, the station was excluded from the analysis. 

Additionally, the drainage basin for each station had to 

be substantially unaffected by regulation or urbanization. The peak-flow data for the stations that met these 

minimum criteria were then reviewed for quality assurance and quality control (QA/QC). Several computer 

programs were developed using commercial statistical 

software to automate the QA/QC reviews (C.L. Sanders, Jr., U.S. Geological Survey, written communs., 

December 1999). 

The QA/QC computer program for reviewing 

continuous-record stations performs the following 

checks:

1. Computes a Kendall’s tau to check for trends in 

the data over time;

2. Plots the peak streamflow by water year;

3. Plots peak stage against peak streamflow, which 

are then overlaid on the most recent rating to check for 

significant or abrupt changes;

4. Plots peak streamflow with the daily-value 

hydrographs by water year to compare the date of the 

peak with the date of the water-year maximum daily 

flow;
6 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

Table 1. Streamflow stations in South Carolina used to develop regional 

regression equations

Map

index

number

(fig. 1)

Station 

number Station name and location

Drainage area 

(in square 

miles)

Blue Ridge

24 02162350 Middle Saluda River near Cleveland 21.0

41 02184500 Whitewater River near Jocasse 47.3

42 02185000 Keowee River near Jocasse 148

43 02185200 Little River near Walhalla 72.0

44 02185500 Seneca River near Newry 455

Piedmont

3 02131309 Fork Creek near Jefferson 24.3

4 02131472 Hanging Rock Creek near Kershaw 23.7

10 02147500 Rocky Creek at Great Falls 194

12 02154500 North Pacolet River at Fingerville 116

13 02157000 North Tyger near Fairmont 44.4

14 02157500 Middle Tyger River at Lyman 68.3

15 02158000 North Tyger River near Moore 162

16 02158500 South Tyger River near Reidville 106

17 02159000 South Tyger River near Woodruff 174

18 02159500 Tyger River near Woodruff 351

19 02160000 Fairforest Creek near Union 183

20 02160105 Tyger River near Delta 759

21 02160500 Enoree River near Enoree 307

22 02160700 Enoree River at Whitmire 444

23 02162010 Cedar Creek near Blythewood 48.9

25 02162500 Saluda River near Greenville 295

26 02163000 Saluda River near Pelzer 405

27 02163500 Saluda River near Ware Shoals 581

28 02165000 Reedy River near Ware Shoals 236

29 02165200 South Rabon Creek near Gray Court 29.5

30 02166970 Ninety Six Creek near Ninety Six 17.4

45 02186000 Twelve Mile Creek near Liberty 106

46 02187900 Broadway Creek near Anderson 26.4

47 02192500 Little River near Mt. Carmel 217

54 02195660 Log Creek near Edgefield 1.26

48 02196000 Stevens Creek near Modoc 545

49 02196250 Horn Creek near Colliers 13.9

Upper Coastal Plain

2 02130900 Black Creek near McBee 108

6 02132500 Little Pee Dee River near Dillon 524

7 02135300 Scape Ore Swamp near Bishopville 96.0

11 02148300 Colonel Creek near Leesburg 40.2

31 02169550 Congaree Creek near Cayce 122

32 02169630 Big Beaver Creek near St. Matthews 10.1

34 02172500 South Fork Edisto near Montmorenci 198

35 02173000 South Fork Edisto near Denmark 720

36 02173500 North Fork Edisto at Orangeburg 683

37 02174000 Edisto River near Branchville 1,720
Peak-Flow Data 7

Lower Coastal Plain

1 02110500 Waccamaw River near Longs 1,110

51 02110700 Crabtree Swamp near Conway 14.0

5 02132100 Two Mile Branch near Lake City 18.4

52 02135050 Reedy Creek near Rains 10.4

8 02135500 Black River near Gable 401

9 02136000 Black River at Kingstree 1,252

33 02169960 Lake Marion Tributary near Vance 2.12

38 02174250 Cow Castle Creek near Bowman 23.4

53 02174300 Buck Branch at Bowman 11.9

39 02176000 Combahee River near Yemassee 1,100

40 02176500 Coosawhatchie River near Hampton 203

50 02197410 Miller Creek Tributary near Baldoc 7.82

Table 2. Streamflow stations in North Carolina and Georgia used to develop regional 

regression equations for South Carolina

Map 

index

number

(fig. 1)

Station 

number Station name and location

Drainage area 

(in square 

miles)

Blue Ridge

60 02177000 Chattooga River near Clayton, Ga. 207

61 02178400 Tallulah River near Clayton, Ga. 56.5

104 02331000 Chattahoochee River near Leaf, Ga. 150

105 02331500 Soque River near Demorest, Ga. 156

106 02331600 Chattahoochee River near Corneila, Ga. 315

107 03545000 Hiwasse River at Presley, Ga. 45.5

153 03439000 French Broad River at Rosman, N.C. 67.9

154 03439500 French Broad River at Calvert, N.C. 103

155 03440000 Catheys Creek near Brevard, N.C. 11.7

156 03441000 Davidson River near Brevard, N.C. 40.4

157 03441440 Little River above High Falls near Cedar Mt., N.C. 26.8

158 03441500 Little River near Penrose, N.C. 41.4

159 03442000 Crab Creek near Penrose, N.C. 10.9

160 03443000 French Broad River at Blantyre, N.C. 296

161 03444500 South Fork Mills River at The Pink Beds, N.C. 9.99

162 03446000 Mills River near Mills River, N.C. 66.7

163 03446410 Laurel Branch near Edneyville, N.C. 0.57

164 03446500 Clear Creek near Hendersonville, N.C. 42.2

165 03447000 Mud Creek at Naples, N.C. 109

166 03447500 Cane Creek at Fletcher, N.C. 63.1

167 03448000 French Broad River at Bent Creek N.C. 676

168 03448500 Hominy Creek at Candler, N.C. 79.8

169 03449000 North Fork Swannanoa River near Black Mountain, N.C. 23.8

170 03450000 Beetree Creek near Swannanoa, N.C. 5.46

Table 1. Streamflow stations in South Carolina used to develop regional 

regression equations (Continued)

Map

index

number

(fig. 1)

Station 

number Station name and location

Drainage area 

(in square 

miles)
8 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

171 03451000 Swannanoa River at Biltmore, N.C. 130

172 03451500 French Broad River at Asheville, N.C. 945

Piedmont

108 02102908 Flat Creek near Inverness, N.C. 7.63

118 02124060 North Prong Clarke Creek near Huntersville, N.C. 3.61

119 02124130 Mallard Creek near Charlotte, N.C. 20.7

120 02125000 Big Bear Creek near Richfield, N.C. 55.6

121 02125410 Chinkapin Creek near Monroe N.C. 8.50

122 02126000 Rocky River near Norwood, N.C. 1,372

123 02127000 Brown Creek near Polkton, N.C. 110

124 02127390 Palmetto Branch at Ansonville, N.C. 0.90

125 02128000 Little River near Star, N.C. 106

126 02128260 Cheek Creek near Pekin, N.C. 15.4

127 02129440 South Fork Jones Creek near Morven, N.C. 16.7

135 02142480 Hagan Creek near Catawba, N.C. 7.80

136 02142900 Long Creek near Paw Creek, N.C. 16.4

137 02143000 Henry Fork near Henry River, N.C. 83.2

138 02143040 Jacob Fork at Ramsey, N.C. 25.7

139 02143310 Lithia Inn Branch near Lincolnton, N.C. 1.00

140 02143500 Indian Creek near Laboratory, N.C. 69.2

141 02144000 Long Creek near Bessemer City, N.C. 31.8

142 02145000 South Fork Catawba River at Lowell, N.C. 628

143 02146890 East Fork Twelve Mile Creek near Waxhaw N.C. 41.8

144 02146900 Twelve Mile Creek near Waxhaw, N.C. 76.5

145 02149000 Cove Creek near Lake Lure, N.C. 79.0

146 02150420 Camp Creek near Rutherfordton, N.C. 13.0

147 02151000 Second Broad River at Cliffside, N.C. 220

148 02151500 Broad River near Boiling Springs, N.C. 875

149 02152100 First Broad River near Casar, N.C. 60.5

150 02152420 Big Knob Creek near Fallston, N.C. 16.4

151 02152500 First Broad River near Lawndale, N.C. 200

152 02152610 Sugar Branch near Boiling Springs N.C. 1.42

62 02188500 Beaverdam Creek at Dewy Rose, Ga. 35.8

63 02189020 Indian Creek near Carnesville, Ga. 7.63

64 02189030 Stephens Creek tributary at Carnesville, Ga. 0.39

65 02189600 Bear Creek near Mize, Ga. 3.62

66 02190100 Toms Creek near Eastanollee, Ga. 3.79

67 02190200 Toms Creek tributary near Avalon, Ga. 1.20

68 02190800 Double Branch at Bowersville, Ga. 0.50

69 02191200 Hudson River at Homer, Ga. 60.9

70 02191270 Scull Shoal Creek near Danielsville, Ga. 8.75

71 02191280 Mill Shoal Creek near Royston, Ga. 0.32

72 02191300 Broad River above Carlton, Ga. 760

73 02191600 Double Branch near Danielsville, Ga. 4.77

74 02191750 Fork Creek at Carlton, Ga. 13.8

75 02191890 Brooks Creek near Lexington, Ga. 12.3

76 02191910 Trouble Creek at Lexington, Ga. 2.70

77 02191930 Buffalo Creek near Lexington, Ga. 5.60

Table 2. Streamflow stations in North Carolina and Georgia used to develop regional 

regression equations for South Carolina (Continued)

Map 

index

number

(fig. 1)

Station 

number Station name and location

Drainage area 

(in square 

miles)
Peak-Flow Data 9

78 02191960 Macks Creek near Lexington, Ga. 3.45

79 02191970 Little Macks Creek near Lexington, Ga. 1.73

80 02192000 Broad River near Bell, Ga. 1,430

81 02192300 Hog Fork Fishing Creek tributary near Tignall, Ga. 0.10

82 02192400 Anderson Mill Creek near Danburg, Ga. 5.49

83 02192420 Anderson Mill Creek tributary near Danburg, Ga. 0.92

84 02193300 Stephens Creek near Crawfordville, Ga. 6.30

85 02193400 Harden Creek near Sharon, Ga. 3.98

86 02193500 Little River near Washington, Ga. 291

87 02193600 Rocky Creek near Washington, Ga. 1.14

88 02197520 Brier Creek near Thomson, Ga. 55.0

89 02197550 Little Brier Creek near Thomson, Ga. 24.0

Upper Coastal Plain

109 02102910 Dunhams Creek tributary near Carthage, N.C. 2.20

110 02103000 Little River at Manchester, N.C. 348

111 02103390 South Prong Anderson Creek near Lillington, N.C. 7.57

112 02103500 Little River at Linden, N.C. 459

113 02104500 Rockfish Creek near Hope Mills, N.C. 292

128 02132230 Bridge Creek tributary at Johns N.C. 6.20

129 02133500 Drowning Creek near Hoffman, N.C. 183

130 02133590 Beaverdam Creek near Aberdeen, N.C. 4.66

131 02133624 Lumber River near Maxton, N.C. 365

132 02133960 Raft Swamp near Red Springs, N.C. 39.8

133 02134380 Tenmile Swamp near Lumberton N.C. 16.1

134 02134500 Lumber River at Boardman, N.C. 1,228

Lower Coastal Plain

114 02108960 Buckhead Branch near Bolton, N.C. 15.3

115 02109500 Waccamaw River at Freeland, N.C. 680

116 02109640 Wet Ash Swamp near Ash, N.C. 16.0

117 02110020 Mill Branch near Tabor City, N.C. 3.80

90 02197600 Brushy Creek near Wrens, Ga. 28.0

91 02200900 Big Creek near Louisville, Ga. 95.8

92 02200930 Spring Creek near Louisville, Ga. 14.2

93 02201350 Buckhead Creek near Waynesboro, Ga. 64.0

94 02201800 Richardson Creek near Millen, Ga. 43.0

95 02201830 Sculls Creek near Millen, Ga. 4.38

96 02202600 Black Creek near Blitchton, Ga. 232

97 02202800 Canoochee Creek near Swainsboro, Ga. 46.0

98 02202820 Reedy Creek near Twin City, Ga. 9.36

99 02202850 Reedy Branch near Metter, Ga. 3.41

100 02202900 Fifteenmile Creek near Metter, Ga. 147

101 02202910 Tenmile Creek tributary at Pulaski, Ga. 1.14

102 02203000 Canoochee River near Claxton, Ga. 555

103 02203280 Canoochee River near Daisy, Ga. 833

Table 2. Streamflow stations in North Carolina and Georgia used to develop regional 

regression equations for South Carolina (Continued)

Map 

index

number

(fig. 1)

Station 

number Station name and location

Drainage area 

(in square 

miles)
10 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

0

10

20

30

40

50

60

70

10-20 21-30 31-40 41-50 51-60 More

than 60

YEARS OF SYSTEMATIC PEAK-FLOW RECORD

NUMBER OF GAGING STATIONS

5. Computes the peak gage height using the peak 

streamflow and the current rating, then compares the 

computed value with the peak gage height listed in the 

peak-flow file;

6. Computes the peak streamflow from the peak 

gage height and the current rating, then compares the 

computed value with the peak streamflow listed in the 

peak-flow file;

7. Relates the peak streamflow with the water-year 

maximum daily-value streamflow by regression;

8. Plots the peak streamflow regression line from 

the relation previously described (7) with the upper 

95 percent confidence limit for daily-value streamflow, 

and the 1:1 line. If the peak-flow plots above the 95 

percent confidence limit of the regression or below the 

1:1 line, an error in the data may have occurred;

9. Flags September 30 and October 1 peak streamflow to verify that the maximum value did not occur at 

midnight at the beginning or end of the water year, on 

the recession from or rise toward a higher peak in the 

adjoining water year.

10. Checks for changes in flow patterns that might 

be a result of regulation or changes in regulation by 

plotting the cumulated ratio of 90 to 50 percentile 

daily-value streamflow by water year, cumulated weekday water-year 50 percentile streamflow, cumulated 

water-year mean weekday streamflow, cumulated 

Table 3. Distribution of stations used in the regionalization analysis by 

State and physiographic province

Physiographic 

province

South 

Carolina

North 

Carolina Georgia Total

Blue Ridge 5 20 6 31

Piedmont 27 29 28 84

Upper Coastal Plain 10 12 0 22

Lower Coastal Plain 12 4 14 30

Totals 54 65 48 167

Figure 2. Distribution of systematic peak-flow record 

lengths for rural streamflow stations used in the 

regionalization study.

Wateree River dam being overtopped by high flows on 

July 25, 1997 (photo by Toby Feaster).
Estimation of Flood Magnitude and Frequency at Gaging Stations 11

water-year mean weekend streamflow, cumulated ratio 

of 10 to 50 percentile streamflow by climatic year (April 1 

to March 31), and cumulated weekday climatic-year 50 

percentile streamflow; and

11. Presents data used in plots and regressions 

in tables.

The QA/QC computer program for reviewing 

crest-stage, partial record sites performs the following 

checks:

1. Computes a Kendall’s tau to check for trends 

in the data over time;

2. Plots the peak streamflow by water year;

3. Determines an index station (if one exists) by 

correlating concurrent water-year peak streamflow at the 

crest-stage station with water-year peak streamflow at 

all other stations statewide. The criterion for an index 

station to be chosen was that the index station peaks 

must be within +8 days of the crest-stage station peaks, 

must have more concurrent peaks than half the number 

of peaks at the crest-stage station, and must have a coefficient of determination (R2) greater than 0.60;

4. Relates concurrent peak flows at the index 

station and the station being reviewed and plots the 

95 percent confidence limits of the regression. If the 

peak-flow plots above the 95 percent confidence limit 

of the regression or below the 1:1 line, an error in the 

data may have occurred;

5. Flags September 30 and October 1 peak streamflow to verify that the maximum value did not occur at 

midnight at the beginning or end of the water year, on 

the recession from or rise toward a higher peak in the 

adjoining water year;

6. Plots the peak gage height against the peak 

streamflow and current rating (if available) to check for 

anomalies;

7. Plots water-year hydrographs of peak streamflow at the crest-stage station and daily-value streamflow at the index station to check the estimated date of 

the crest-stage peak;

8. Presents data used in plotting and regressions 

in tables.

According to Rantz and others (1982), “. . . only 

as a last resort should the rating be extrapolated beyond 

a discharge value equal to twice the greatest measured 

discharge.” Therefore, an additional check was made at 

the stations with established ratings by using the flowmeasurement files. The peak flows were plotted 

against water year along with the maximum (at this 

point in time) measured flow and the value equal to 

two times that maximum measured flow. This plot was 

used to review peaks that may have been estimated 

from an excessive stage-flow rating extension but not 

updated when the rating was later defined by higher 

flow measurements. 

ESTIMATION OF FLOOD MAGNITUDE 

AND FREQUENCY AT GAGING 

STATIONS 

A frequency analysis of water-year peak-flow 

data at a gaging station on a stream provides an estimate 

of the flood magnitude and frequency at that specific 

site. The estimates are typically presented as a set of 

exceedance probabilities or, alternatively, recurrence 

intervals along with the associated flows. Exceedance 

probability is defined as the probability of exceeding a 

specified flow in a 1-year period and is expressed as 

decimal fractions less than 1.0 or as percentages less 

than 100. A flow with an exceedance probability of 0.01 

has a 1 percent chance of being exceeded in any given 

year. Recurrence interval is defined as the number of 

years, on average, during which the specified flow is 

expected to be exceeded one time. A flow with a 100-

year recurrence interval is one that, on average, will be 

exceeded once every 100 years. Recurrence interval and 

exceedance probability are the mathematical inverses of 

one another; therefore, a flow with an exceedance probability of 0.01 has a recurrence interval of 1/0.01 or 100 

years. It is important to understand, however, that recurrence intervals, regardless of length, always refer to the 

average number of occurrences over a period of time. 

For example, a 100-year flood is one that might occur 

one time in a 100-year period, rather than exactly once 

every 100 years. Therefore, a flood with a 100-year 

recurrence interval can occur more frequently than once 

every 100 years and could even occur more than once in 

a given year. When interpreting the flood-frequency 

probabilities and recurrence intervals, it is helpful to 

remember that the analysis is based on water-year 

peaks; therefore, the results are relative to probability 

of exceedance in any given year.

Flood Frequency

Flood-frequency estimates at gaged sites can 

be computed by fitting the water-year peak flows to a 

known statistical distribution. For this study, floodfrequency estimates were computed by fitting the 
12 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999 PROBABILITY

(b)

WATER-YEAR PEAK FLOW

Median Mean

Positive Skew

WATER-YEAR PEAK FLOW

(c)

PROBABILITY

Mean Median

Negative Skew

(a)

PROBABILITY

WATER-YEAR PEAK FLOW

Mean = median

Zero Skew

logarithms (base 10) of the water-year peak flows to a 

log-Pearson Type III distribution, following the guidelines and computational methods described in Bulletin 

17B of the Hydrology Subcommittee of the Interagency Advisory Committee on Water Data (1982). 

The equation for fitting the log-Pearson Type III distribution to an observed series of water-year peak flows is 

as follows: 

, (1)

where

Values for K for a wide range of recurrence intervals 

and regionalized skew coefficients are published in 

appendix 3 of Bulletin 17B (Hydrology Subcommittee 

of the Interagency Advisory Committee on Water Data, 

1982).

A series of water-year peak flows at a station 

may include low or high outliers, which are data points 

that depart significantly from the range of the remaining data. The station record also may include information about peak flows that occurred outside of the 

period of regularly collected, or systematic, record. 

These peak flows are known as historic peaks and are 

often the peak flows known to have occurred during an 

extended period of time, longer than the period of collected record. Bulletin 17B (Hydrology Subcommittee 

of the Interagency Advisory Committee on Water Data, 

1982) provides guidelines for detecting and interpreting low and high outliers and historic data points and 

provides computational methods for making appropriate corrections to the distribution to account for their 

presence. In some cases, low or high outliers may be 

excluded from the record, so that the number of systematic peaks may not be equal to the number of years 

in the period of record.

QT is the T-year recurrence-interval flow, in 

cubic feet per second (ft3/s);

X is the mean of the log-transformed water-year 

peak flows;

K is a factor dependent on recurrence interval 

and the skew coefficient of the log-transformed water-year peak flows; and

S is the standard deviation of the log-transformed water-year peak flows.

QT log = X KS +

Skew Coefficient

A skew coefficient measures the symmetry of 

the distribution of a set of peak flows about the median 

of the distribution. A peak-flow distribution with the 

mean equal to the median is said to have zero skew 

(fig. 3a). A positively skewed distribution has a mean 

that exceeds the median typically as a result of one or 

more extremely high peak flows (fig. 3b). A negatively 

skewed distribution has a mean that is less than the 

median, typically because of one or more extremely 

low peak flows (fig. 3c) (Pope and others, 2001).

The skew coefficient computed for a series 

of water-year peak flows at a single station can be 

weighted with a generalized, or regional, skew coefficient to obtain a better estimate of the station skew 

Figure 3. Examples of distributions with (a) zero skew, (b) 

positive skew, and (c) negative skew.
Estimation of Flood Magnitude and Frequency at Gaging Stations 13

coefficient. A generalized skew coefficient can be 

obtained by combining skew estimates from nearby, 

similar sites. A nationwide skew study was conducted 

for the investigation documented in Bulletin 17B. 

Skew coefficients for long-term gaging stations 

throughout the Nation were computed and used to 

produce a map of isolines of generalized skew.

Bulletin 17B describes three methods for developing generalized skews using skew coefficients computed from long-term (25 or more years of record) 

gaging stations: (1) plot computed skew coefficients on 

a map and construct skew isolines, (2) use regression 

techniques to develop a skew prediction equation that 

would relate station skew coefficients to some set of 

basin characteristics, or (3) use the arithmetic mean of 

computed skew coefficients from long-term sites in the 

area. For this study, all three methods were attempted.

To develop the skew isoline map, skew coefficients from long-term gaging stations were plotted at 

the centroid of the watershed for each station. The map 

was then reviewed to determine if any geographic or 

topographic trends were visually apparent. No clearly 

definable patterns were found. Additionally, commercial contouring software was used to draw the skew 

isolines. Again, no definite geographic or topographic 

trends were revealed and the attempt to develop the 

skew isoline map was abandoned. It was noted, 

however, that skews in the Piedmont Province were 

predominately negative (24 of 35 stations). For the 

Blue Ridge, upper Coastal Plain, and lower Coastal 

Plain, the ratio of stations with negative skews to the 

total number of stations for that physiographic province were 10 of 20, 9 of 23, and 5 of 14, respectively. 

Ordinary least squares regression was used to 

determine if a relation between the station skew and 

selected basin characteristics could be obtained. The 

regressions were performed on the complete data set 

and on the four physiographic provinces determined 

during the previous flood-frequency study (table 4).

Multiple regression analysis, using ordinary 

least squares regression, was used to determine the 

relation between the station skew coefficients and 

selected basin characteristics. Table 4 list the explanatory 

variables that were found to be statistically significant for 

each region and for the State as a whole. Although the 

variables shown were determined to be statistically significant, the R2 values only ranged from 0.11 to 0.53, 

which indicates the fraction of the variance explained 

by the regression (Helshel and Hirsch, 1992). Consequently, it was concluded the relation between the station skews and the basin characteristics was weak and 

determining the generalized skew coefficients based on 

the regression analysis was not justified.

The third method for computing the generalized 

skew coefficients was to use the arithmetic mean of 

computed skew coefficients from long-term sites in the 

area. Before this was done, all stations with 25 or more 

years of record were evaluated to verify that all stations 

with significant regulation or that drained more than 

one physiographic province were removed from the 

data set. In addition, data at stations having low and 

high outliers in the frequency study as computed during the log-Pearson Type III analysis were not included 

in the skew computations. Descriptive statistics were 

computed for the different regions and the whole data 

set. Results from the statistics suggested that the skews 

were normally distributed. The SAS procedure Generalized Linear Model (GLM) was used to compare the 

Table 4. Ordinary least-squares regression statistics for the generalized skew coefficients

[R2, coefficient of determination; --, no data}

Region Number

of sites Explanatory variables R2 Standard error

Mean square 

error

All stations 102 Longitude, precipitation 

times elevation

0.15 0.490 0.241

Blue Ridge 21 Latitude times latitude 0.38 0.380 0.145

Piedmont 47 Latitude 0.11 0.439 0.193

Upper Coastal Plain 16 No variables found -- -- --

Lower Coastal Plain 18 Elevation, percent forest 0.53 0.253 0.064
14 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

station skews (SAS Institute, Inc., 1989). The results 

indicated that the skews in the Piedmont region had a 

larger difference from the other regions than would 

be expected by chance at a significance level of 0.05. 

No significant difference was observed among the 

three remaining regions. Consequently, the Blue Ridge, 

upper Coastal Plain and lower Coastal Plain skews 

were combined and a weighted skew was computed. 

The skews were weighted based on record length. 

Additionally, a weighted skew also was computed 

for the Piedmont (table 5). 

Table 5. Weighted generalized skew coefficients and 

associated statistics for rural South Carolina gaging 

stations

To review the sensitivity of the mean skew to 

maximum and minimum skews, the mean skews were 

recomputed after excluding the maximum and minimum skews from each physiographic province and 

after excluding the two highest and two lowest skews. 

The results, which are provided in table 6, indicated 

that the weighted skews were not significantly affected 

by high and (or) low outliers.

 The skew coefficients shown in table 5 were 

weighted based on years of record at the station. The 

skew coefficients shown in table 6 were not weighted. 

Although, it seems reasonable and appropriate to 

weight the skew coefficients by years of record, a comparison of the two tables suggest that, for the South 

Carolina generalized mean skew coefficients, the data 

were not significantly changed by weighting. The 

weighted skews from table 5, however, were used to 

compute the log-Pearson Type III frequency distributions for the regional regression analysis.

Blue Ridge, 

upper Coastal Plain, 

and 

lower Coastal Plain

Piedmont

Number of stations 54 35

Mean 0.082 -0.190

Maximum 0.811 0.524

Median 0.087 -0.177

Minimum -0.547 -0.728

Mean square error 0.105 0.090

Root mean square error 0.324 0.299

Bulletin 17B (Hydrology Subcommittee of the 

Interagency Advisory Committee on Water Data, 1982) 

states that a mean square error of generalized skew of 

0.302 should be used when the generalized skews are 

read from Plate I. As noted in table 5, the mean square 

errors of the generalized skews for South Carolina are 

much lower. The generalized skew map provided in 

Bulletin 17B was generated by averaging groups of 15 

or more stations in areas covering four or more onedegree quadrangles of latitude and longitude. Consequently, the regions used for the current study in South 

Carolina do not compare geographically with the contours on the generalized skew map in Bulletin 17B and, 

therefore, a comparison of the means from the two 

studies does not necessarily provide substantial information. However, based on the results from the GLM 

test and on the improved mean square error when compared to the Bulletin 17B mean square error, the 

weighted skews listed in the table 5 were used to compute the log-Pearson Type III distributions. 

 Following Bulletin 17B guidelines, the assumption is made that the regionalized skew coefficient is an 

unbiased and independent estimate of the station skew. 

The mean square error of the weighted estimate, therefore, is minimized by weighting the station and regionalized skew in inverse proportion to their individual 

mean square errors. The following weighting equation 

was adopted from Tasker (1978), and is used in computing the weighted skew coefficients:

, (2)

where 

The function MSEG can be approximated with 

sufficient accuracy by the following equation (Hydrology 

Subcommittee of the Interagency Advisory Committee 

on Water Data, 1982):

Gw is the weighted skew coefficient;

G is the station skew coefficient;

G is the regionalized skew coefficient;

MSEG is the mean square error of regionalized 

skew coefficient; and

MSEG is the mean square error of station skew 

coefficient.

Gw

MSEG( ) G MSEG + ( ) G

MSEG MSEG + = ----------------------------------------------------------
Estimation of Flood Magnitude and Frequency at Gaging Stations 15

, (3)

where

where MSEG is previously defined, |G| is the absolute 

value of the station skew coefficient (used as an estimate of population skew coefficient), and N is the 

record length, in years.

The USGS computer program PEAKFQ 

(W.O. Thomas, Jr., A.M. Lumb, K.M. Flynn, and 

W.H. Kirby, written commun., January 1998), was 

used to compute the relation between flood magnitude 

and probability of occurrence. PEAKFQ includes the 

features described in Bulletin 17B, but requires the user 

to exercise judgment when providing data on historic 

peaks, specifying screening levels for outliers, and interpreting the appropriateness of the resultant frequency 

curve to the observed data set. The weighted and station 

skew coefficients for the South Carolina stations used in 

the flood-frequency analyses are listed in appendix A. 

A = -0.33 + 0.08 |G| if |G| < 0.90

-0.52 + 0.30 |G| if |G| > 0.90; and

B = 0.94 - 0.26 |G| if |G| < 1.50

0.55 if |G| > 1.50;

MSEG 10A B log – ( ) 10( ) N ⁄ 10

≅ Synthesized Peak Flow

Long-term flow records are not always available at a site; however, if concurrent rainfall and flow 

data are available, a rainfall-runoff model may be used 

to extend the records. Frequency data for four stations 

used in this report were from a study by Whetstone 

(1982) in which the USGS Rainfall-Runoff Model 

(Dawdy and others, 1972) was used to synthesize a 

series of water-year peak flows. The model utilizes 

10 parameters to simulate the hydrologic processes of 

antecedent soil moisture, infiltration, and surface-runoff routing. Daily rainfall and evaporation data, and 

unit-value flow and rainfall data from several storm 

events collected over a period of 3 to 5 years were used 

to calibrate the model for each of the four basins. Longterm precipitation and evaporation data (more than 

50 years of record) were used to synthesize a series 

of water-year peaks for use in subsequent frequency 

analyses (Guimaraes and Bohman, 1991). Synthesized 

flows for these stations are not listed in this report; 

however, flood-frequency data derived from the synthesized flows are listed in table 7 along with the 

weighted flows computed for each site using the appropriate regression equations for each physiographic 

province and individual station flood-frequency data.

Table 6. Sensitivity of South Carolina generalized skew coefficients (not weighted) to high and low values

Piedmont

Piedmont, 

with the 

maximum 

and minimum 

skews

removed

Piedmont, 

with the two 

highest and 

two lowest 

skews

removed

Blue Ridge, 

upper Coastal

Plain, and lower 

Coastal Plain 

combined

Blue Ridge, 

upper Coastal 

Plain, and lower 

Coastal Plain 

combined, with 

the maximum and 

minimum skews 

removed

Blue Ridge, 

upper Coastal 

Plain, and lower 

Coastal Plain 

combined, with 

the two highest and 

two lowest skews 

removed

Number of stations 35 33 31 54 48 42

Mean -0.168 -0.172 -0.174 0.095 0.096 0.091

Maximum 0.524 0.418 0.334 0.811 0.771 0.588

Median -0.152 -0.152 -0.152 0.089 0.089 0.089

Minimum -0.728 -0.717 -0.665 -0.547 -0.377 -0.296

Mean square error 0.103 0.086 0.070 0.104 0.074 0.054

Root mean square error 0.321 0.292 0.265 0.323 0.271 0.232
16 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

ESTIMATION OF FLOOD MAGNITUDE 

AND FREQUENCY AT UNGAGED SITES 

For this study, two regional analyses were used 

to develop methods for estimating flows for ungaged 

rural basins in South Carolina. Traditional regional 

regression analysis using generalized least squares 

regression was used to define a set of predictive equations. These equations relate peak flows for the 2-, 5-, 

10-, 25-, 50-, 100-, 200-, and 500-year recurrenceinterval flows to selected basin characteristics for 

ungaged, rural basins that are not significantly affected 

by regulation in each of four physiographic provinces 

of South Carolina (fig. 1). A second analysis was made 

using the region-of-influence method, which resulted 

in the development of a computer application to derive, 

for any given ungaged rural site in the Blue Ridge 

physiographic province, a unique predictive relation 

between the 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-

year recurrence intervals and selected basin characteristics. Just as in the traditional regional regression, generalized least squares regression is used to develop this 

predictive relation. In the region-of-influence analysis, 

however, regression techniques are applied to only a 

selected subset of gaged sites, rather than the entire 

database of gaged sites. 

Ordinary Least Squares Analysis

Ordinary least squares (OLS) regression techniques were used to select the explanatory variables 

that would define the final regression equations. In 

OLS regression, linear relations between the explanatory and response variables are necessary; consequently, variables must often be transformed. For 

example, the relation between drainage area and peak 

flow is typically not linear; however, the relation 

between the logarithms of drainage areas and the logarithms of peak flows often is linear. Homoscedasicity 

(a constant variance in the response variable over the 

range of the explanatory variables) about the regression 

line and normality of residuals also are requirements 

for OLS regression. Transformation of the flow data 

and other variables to logarithms enhances the 

homoscedasicity of the data about the regression line. 

Linearity, homoscedasicity, and normality of residuals 

were examined in residual plots. 

Initially, eight explanatory variables for the 

gaged, unregulated streams in rural drainage basins in 

South Carolina and additional gaging stations in North 

Carolina and Georgia were included in this study. 

These eight explanatory variables were: drainage area, 

the area, in square miles, of a basin; main-channel 

length, the length of the main channel, in miles, from 

Table 7. Station and weighted flood-frequency data for the synthesized peak flows used in the regionalization analysis

Map 

index 

number

(fig. 1)

Station name and 

number

Drainage

area 

(square 

miles)

Physiographic 

province

Type of 

data

Flows in cubic feet per second by

recurrence interval (years)

2 5 10 25 50 100 200 500

51 Crabtree Swamp near 

Conway, S.C. 

(02110700)

14.0 Lower Coastal 

Plain

Station1

Weighted2

206

214

388

411

544

579

784

835

994

1,060

1,230

1,310

1,500

1,590

1,910

2,020

52 Reedy Creek near 

Rains, S.C. (02135050)

10.4 Lower Coastal 

Plain

Station1

Weighted2

242

242

478

472

680

667

991

967

1,260

1,230

1,570

1,530

1,920

1,860

2,440

2,370

53 Buck Branch at Bowman, S.C. (02174300)11.9 Lower Coastal 

Plain

Station1

Weighted2

210

215

438

446

639

646

955

956

1,240

1,230

1,550

1,540

1,920

1,890

2,460

2,430

54 Log Creek near Edgefield, S.C. (02195660)1.26 Piedmont Station1

Weighted2

42.0

43.7

93.0

97.8

140

149

215

230

282

304

360

386

450

479

586

618

1The station data are computed by fitting the logarithms of water-year peak flows to a log-Pearson Type III distribution.

2The weighted data are computed by weighting the station data with flows computed using the regional flood-frequency relations. The weighted data 

should be used rather than the station data.
Estimation of Flood Magnitude and Frequency at Ungaged Sites 17

the gaging station to the basin divide; main-channel 

slope, the slope of the main channel, in feet per mile, 

between points that are 10 percent and 85 percent of 

the main-channel length from the gaging station; elevation, the mean basin elevation in feet above sea level; 

forest cover, forested area, in percent of contributing 

drainage area; storage, area of lakes, ponds, and 

swamps, in percent of contributing drainage area; precipitation, the water-year mean precipitation, in inches, 

at the centroid of the basin; and runoff, the water-year 

mean runoff, in inches, at the centroid of the basin. In 

addition, cross products, such as drainage area times 

length, computed using the eight explanatory variables 

also were included in the exploratory OLS regression 

analysis. The use of cross products allows the regression lines to converge or diverge, thereby decreasing or 

increasing the effect of one variable with the effect of 

another variable. For example, the effect of main-channel 

slope on flood frequency may decrease with increasing 

drainage area.

In the initial OLS regressions, the regionalization scheme used by Guimaraes and Bohman (1991), 

which divided the State into the Blue Ridge, Piedmont, 

upper Coastal Plain, and lower Coastal Plain, was 

found to be valid based on statistical significance of 

explanatory variables, comparisons of R2, and standard 

errors of the OLS regression equations for the regions 

and the State as a whole. In addition, plots of the logarithms of drainage area and logarithms of the 100-year 

recurrence-interval flows were used to graphically 

compare the regions and to help determine the validity 

of the boundaries of those regions. Regression residuals (for the 100-year peak flows) also were plotted at 

the centroid of their respective drainage basins and 

inspected for geographical patterns of bias. No distinct 

patterns were apparent in the mapped residuals for the 

four regions.

The hydrologic model used in the regression 

analysis is of the form:

QT = aAbBcCd..., (4)

where

QT is the flood magnitude having T-year 

recurrence interval;

A, B, C are explanatory variables (basin characteristics); and 

a, b, c, d are regression coefficients.

(c)

(b)

(a)

Bridge over the Enoree River at S.C. Highway 418 collapsed 

on August 27, 1995, due to severe flooding caused by 

Tropical Depression Jerry:

(a) August 27, 1995; photo by Michael Hall

(b) August 28, 1995; photo by Toby Feaster

(c) September 1, 1995; photo by Toby Feaster
18 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

If the dependent and explanatory variables are logarithmically transformed, the hydrologic model has the following linear form:

Log QT = log a + b (log A) + c (log B) 

+ d (log C) + ..., (5)

where the variables are previously defined. The logarithmic relation is the form that was used in this study.

Basins in the Piedmont province of South Carolina tend to be more elongated than basins in Georgia 

and North Carolina, and the recurrence-interval flows 

for the Piedmont stations in South Carolina tend to be 

lower than those in Georgia and North Carolina. This 

difference in the recurrence-interval flows could be 

attributed to the difference in basin shapes because an 

elongated basin would tend to have a lower peak with a 

more spread-out hydrograph than a similarly sized 

basin that was wider and shorter. Consequently, a 

“qualitative variable” for State was included in the 

regression model to account for these differences. This 

qualitative variable also was found to be significant in 

the upper Coastal Plain. Guimaraes and Bohman 

(1991) also used a qualitative variable to differentiate 

between flows in the Piedmont of South Carolina and 

flows in the Piedmont of Georgia and North Carolina.

An example of the linear form of the hydrologic 

model including qualitative variables is:

log QT = log a + b (log A) + c (log B) 

+ d (log C) + ... + eV, (6)

where V is a qualitative variable that is set to 0 if the 

variable is geographically in State “x” or 1 if geographically in State “y”. If the qualitative variable is determined to be significant by the regression analysis, the 

regression lines for the two States have the same slope, 

but different intercepts. The qualitative variable can be 

used to detect significant differences between States 

and to utilize data from both States where data are 

sparse. 

Within each physiographic province, the 100-

year recurrence-interval flow was regressed against the 

explanatory variables and a qualitative variable that 

denotes location by State. As previously mentioned, the 

qualitative variable was determined to be statistically 

significant by the regression analysis in the Piedmont 

and upper Coastal Plain (figs. 4 and 5) and indicated no 

statistically significant difference between the States 

for the Blue Ridge and lower Coastal Plain. For the 

Piedmont, the regressions indicated that Georgia and 

North Carolina data were not significantly different 

from each other, but were both significantly different 

from South Carolina (fig. 4). Note that on figure 4, the 

South Carolina data plots generally below the data 

points from Georgia and North Carolina. Although it is 

possible to use only South Carolina data in the regressions, the relation using the data from all three States 

with the qualitative variable was considered to be more 

definitive because of sparseness of the South Carolina 

data. Inclusion of the qualitative variable allows the 

data from each State to influence the slope of the overall relation, and at the same time permits a unique intercept value for the South Carolina relation. 

As can be seen on figure 5, no Georgia stations 

were included in the South Carolina upper Coastal 

Plain regression analysis. The North Carolina Sandhills 

physiographic province is hydrologically similar to the 

South Carolina upper Coastal Plain. Georgia also has a 

Sandhill region that is narrowly banded near the South 

Carolina-Georgia border. However, there were no 

Georgia stations near the South Carolina border that 

were found to be hydrologically similar to the South 

Carolina upper Coastal Plain. 

In addition to the qualitative variable described 

above, the explanatory variable determined to be the 

most significant in the OLS analyses for all regions 

was drainage area. In the Blue Ridge, other significant 

variables were chosen by the OLS regression model 

but did not reduce the standard error enough to warrant 

inclusion or were significant in only a few of the QT

flows and then became statistically insignificant in the 

higher recurrence intervals (50 years and above). The 

explanatory variables determined in the OLS regression analyses were used in the generalized least squares 

regression procedures.

Generalized Least Squares Analysis

Generalized least squares (GLS) regression, as 

described by Stedinger and Tasker (1985), was used to 

compute the final coefficients and the measures of 

accuracy for the regression equations, using the USGS 

computer program GLSNET (G.D. Tasker, K.M. Flynn, 

A.M. Lumb, and W. O. Thomas, Jr., written commun., 

1995). Stedinger and Tasker (1985) found that GLS 

regression equations are more accurate and provide a 
Estimation of Flood Magnitude and Frequency at Ungaged Sites 19

100,000

10,000

1,000

100

0 1 10 100 1,000 10,000

DRAINAGE AREA, IN SQUARE MILES

LOW, IN CUBIC FEET PER SECOND 100-YEAR RECURRENCE-INTERVAL F EXPLANATION Georgia 100-year flood flows North Carolina 100-year flood flows South Carolina 100-year flood flows Regression equation using North Carolina and Georgia stations Regression equation using South Carolina stations

Figure 4. Relation between drainage area and 100-year recurrence-interval flow for stations on streams draining the Piedmont physiographic province in South Carolina, North Carolina, and Georgia.
20 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999 100,000 10,000 1,000 100 1 10 100 1,000 10,000 DRAINAGE AREA, IN SQUARE MILES

LOW, IN CUBIC FEET PER SECOND 100-YEAR RECURRENCE-INTERVAL F EXPLANATION North Carolina 100-year flood flows South Carolina 100-year flood flows Regression equation using North Carolina stations Regression equation using South Carolina stations

Figure 5. Relation between drainage area and 100-year recurrence-interval flow for stations on streams draining the upper Coastal Plain physiographic province in South Carolina and North Carolina.
Estimation of Flood Magnitude and Frequency at Ungaged Sites 21

better estimate of the accuracy of the equations than 

OLS regression equations when streamflow records at 

gaging stations are of different and widely varying 

lengths and when concurrent flows at different stations 

are correlated. Generalized least squares regression 

techniques give less weight to streamflow-gaging stations that have shorter periods of record than other stations. Less weight also is given to those stations where 

concurrent peak flows are correlated with other stations 

(Hodgkins, 1999). Table 8 shows the peak-flow regression equations for recurrence intervals of 2, 5, 10, 25, 

50, 100, 200, and 500 years that resulted from the GLS 

regression analysis for South Carolina.

Accuracy of the Method

As shown in table 8, the regional regression 

analyses for South Carolina resulted in the development of a set of equations that allow the user to estimate the 2-, 5-, 10-, 25-, 50-, 100-, 200-, or 500-year 

recurrence-interval flood at an ungaged, unregulated 

stream in a rural drainage basin. When applying these 

equations, users should not interpret these empirical 

results as exact. These regression equations are statistical models that should be interpreted and applied 

within the limits of the data and with the understanding 

that the results are best-fit estimates with an associated 

scatter or variance.

One measure of how well the regression equations estimate the peak flows at an ungaged site is the 

standard error of prediction (Sp). The Sp is the square 

root of the mean square error of prediction, MSEp. The 

MSEp is the sum of two components--the mean square 

error resulting from the model, γ2, and the sampling 

mean square error, MSEs,i,

 which results from estimating 

the model parameters from samples of the population. 

The mean square model error, γ2, is a characteristic of 

the model, is constant for all sites, and cannot be 

reduced by additional data collection. The mean square 

sample error, MSEs,i, for a given site, however, depends 

on the values of the explanatory variables, in this case 

drainage area (DA), used to develop the flow estimate 

at that site. Consequently, the sampling error can be 

reduced by additional data collection at existing stations, or by installing new stations in the same physiographic province, or some combination of both. The 

standard error of prediction for a site, i, is computed as: 

, (7)

(variables previously defined) and varies from site to 

site. Assuming the explanatory variables for the gaged 

sites in the regression are a representative sample of all 

sites in the region, the average accuracy of prediction 

for the regression model can be determined by computing the average standard error of prediction:

Sp i , γ

2 MSEs i , ( ) +

1

2

--

=

Table 8. South Carolina rural flood-frequency equations 

[DA, drainage area, in square miles. Result will be in cubic feet per second]

Rural flood 

recurrence 

interval 

(years)

Physiographic province

Blue Ridge Piedmont Upper Coastal 

Plain

Lower Coastal 

Plain

2 116 (DA) 0.757 111 (DA) 0.678 21.2 (DA) 0.754 51.7 (DA) 0.663

5 204 (DA) 0.734 197 (DA) 0.656 32.4 (DA) 0.752 96.6 (DA) 0.653

10 281 (DA) 0.720 262 (DA) 0.647 40.6 (DA) 0.753 136 (DA) 0.646

25 395 (DA) 0.705 353 (DA) 0.637 51.5 (DA) 0.754 197 (DA) 0.639

50 491 (DA) 0.695 426 (DA) 0.631 60.1 (DA) 0.755 251 (DA) 0.634

100 595 (DA) 0.688 503 (DA) 0.626 69.1 (DA) 0.757 312 (DA) 0.631

200 707 (DA) 0.681 584 (DA) 0.621 78.7 (DA) 0.759 381 (DA) 0.628

500 868 (DA) 0.675 698 (DA) 0.615 92.1 (DA) 0.761 486 (DA) 0.624
22 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

, (8)

where n is the number of observations and all other 

variables are previously defined.

The standard error of the model (SE(model)) can 

be converted from log (base 10) units to percentage 

error by using the transformation formulas, 

+ (9)

and

– , (10)

where the variables were previously defined.

Similarly, the average standard error of prediction (Sp) can be transformed to positive or negative percentage error by substituting Sp

2 for γ2 in equations 6 

and 7, respectively. Computation of Sp,i for a given 

ungaged site, i, involves fairly complex matrix algebra; 

therefore, a computer program that computes the standard error of prediction for any study site has been 

developed. Appendix C provides details of the GLS 

regression method and calculation of prediction errors 

and intervals. 

Another overall measure of how well regression 

equations can be used to estimate flood peaks when 

applied to ungaged basins is the PRESS (“PRediction 

Error Sum of Squares”) (Helsel and Hirsch, 1992) statistic. The PRESS statistic is a validation-type statistic. 

To compute the PRESS statistic, one gaging station is 

removed from the stations used to develop the regression equation, then the value of the one removed is predicted. The difference between the predicted value 

from the regression equation and the observed peak 

flow at that station is computed. The gaging station that 

is removed is then changed and the above process 

repeated until every station has been left out once. The 

prediction errors are then squared and summed (Helsel 

and Hirsch, 1992). PRESS/n is analogous to the average variance of prediction, and the square root of 

PRESS/n is analogous to the average standard error of 

prediction. Values of the square root of PRESS/n close 

to the values of the average standard error of prediction 

provide some measure of validation of the regression 

equations (Hodgkins, 1999).

Sp γ

2 1

n

-- MSEs i ,

i = 1

n

+ ∑

         

1

2

--

=

PercentSE( ) model 100 10γ = [ ] – 1

PercentSE( ) model 100 10–γ = [ ] – 1

A third measure of the overall accuracy of the 

regression equations is the average equivalent years of 

record. This measure represents the average number of 

years of peak-flow data needed to provide an estimate 

by using log-Pearson Type III techniques that would be 

equal in accuracy to an estimate made by using 

regional methods (table 9). The average equivalent 

years of record is a function of the accuracy of the 

regression equations, the recurrence interval, and the 

average variance and skew of the water-year peak 

flows at gaging stations (Hardison, 1971).

Region-of-Influence Method

A new technique for estimating flood frequency 

at ungaged sites is the region-of-influence (ROI) 

method (Tasker and Slade, 1994; Tasker and others, 

1996; Asquith and Slade, 1999; Pope and others, 

2001). In this method a regression equation is estimated for each ungaged site and for each recurrenceinterval peak flow. The regression equation for a site is 

computed using data from a unique region called the 

region of influence by Burn (1990a, 1990b) and suggested by Acreman and Wiltshire (1987). The subset of 

gaging stations that make up the region of influence for 

each ungaged site is made up of the N nearest neighbors. In this method, the nearness of two neighbors is 

measured, not by the physical distance between the 

sites, but by a distance defined in terms of the watershed characteristics. The distance between any two 

sites, indexed by i and j, is determined by the Euclidean 

distance metric:

, (11)

where

dij is the distance between sites i and j in the 

Cartesian product space of the watershed 

characteristics;

p is the number of watershed characteristics 

needed to calculate dij ;

 Xk represents the kth watershed characteristic;

sd(Xk) is the sample standard deviation for Xk ;

xik is the value of Xk at the ith streamflowgaging station; and

xjk is the value of Xk at the ungaged site, j. 

dij

xik xjk –

sd Xk ( ) -------------------

      2

k = 1

p

∑

   

  1 2/

=
Estimation of Flood Magnitude and Frequency at Ungaged Sites 23

For this method to work, the value of N, the number of 

streamflow-gaging stations, should be large enough to 

have enough degrees of freedom in the regression to 

estimate two or three parameters.

To adapt the ROI method to South Carolina 

sites, the parameters p and N must be determined along 

with the identity of the basin characteristics that are 

used to compute dij. Selection of the number of gaged 

sites, N, and the number and identity of the basin characteristics that will define the region of influence for 

South Carolina was done by systematically evaluating 

the PRESS (Helsel and Hirsch, 1992) statistic for N

and p and for different basin characteristics. As previously mentioned, the PRESS statistic is a validationtype estimator of error that uses all observations except 

one to develop the equation, then estimates the value of 

the one left out. It then selects another observation to 

be left out, and repeats the process for each observation. The difference between the predicted and 

observed logarithms of flood peaks are squared and 

summed to compute PRESS. After testing several combinations of N and p with different combinations of 

basin characteristics, it was concluded that the best 

combination for South Carolina sites is, N=25, p=2, 

with basin characteristics log(elevation) and log(slope) 

used to define the distance metric based on minimizing 

the PRESS. Further, it was found that if the prediction 

site was in the Blue Ridge or Piedmont Province, the 

search for similar sites was limited to the Blue Ridge 

and Piedmont sites; If the prediction site was in one of 

the Coastal Plain Provinces, the search was limited to 

Coastal Plain Provinces.

To estimate recurrence-interval flows at an 

ungaged rural site, the ROI method performs GLS 

regression using estimation data from the 25 most similar sites in terms of elevation and slope. The ROI-GLS 

regression for each site where an estimate is needed 

uses log-transformed T-year flood peaks as response 

variables and log(AREA) and two qualitative variables 

as explanatory variables. The qualitative variables 

(STATE and PIED) are zero-one variables defined as 

follows:

STATE = 1 if site is in South Carolina and STATE = 0 if not in South Carolina, and

PIED = 1 if site is in the Piedmont Province and PIED = 0 if not in Piedmont.

Table 9. Accuracy statistics for the regional regression 

equations, presented by physiographic province and 

recurrence interval

[PRESS, PRediction Error Sum of Squares; n, number of sites] 

Recurrence 

interval

(years)

Mean standard 

error of 

prediction 

(percent)

(PRESS/n)1/2

(percent)

Average 

equivalent 

years of 

record

Blue Ridge

2 -27 to 37 -28 to 39 3.1

5 -24 to 32 -27 to 36 5.6

10 -23 to 31 -27 to 36 8.6

25 -23 to 30 -27 to 38 12.8

50 -23 to 30 -28 to 40 15.6

100 -24 to 31 -30 to 42 17.8

200 -25 to 33 -31 to 45 19.2

500 -26 to 35 -33 to 49 20.1

Piedmont

2 -30 to 43 -31 to 46 2.6

5 -27 to 38 -29 to 41 4.1

10 -27 to 36 -29 to 40 5.8

25 -26 to 35 -29 to 40 8.3

50 -26 to 35 -29 to 41 10.1

100 -26 to 36 -30 to 43 11.7

200 -27 to 36 -31 to 44 13.0

500 -27 to 38 -32 to 46 14.3

Upper Coastal Plain

2 -16 to 19 -18 to 22 7.8

5 -17 to 21 -19 to 24 10.3

10 -19 to 23 -21 to 27 11.7

25 -21 to 27 -24 to 32 12.6

50 -23 to 31 -26 to 36 12.8

100 -25 to 34 -28 to 40 12.8

200 -27 to 38 -31 to 44 12.6

500 -30 to 43 -33 to 50 12.3

Lower Coastal Plain

2 -22 to 27 -25 to 34 7.8

5 -20 to 25 -24 to 32 13.3

10 -21 to 27 -26 to 35 15.8

25 -24 to 32 -29 to 41 16.9

50 -27 to 36 -32 to 47 17.0

100 -29 to 41 -35 to 53 16.7

200 -31 to 46 -37 to 59 16.4

500 -34 to 52 -40 to 68 15.8
24 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

Comparison of Methods

The predictive abilities of the Regional Regression Equations (RRE) and ROI methods were compared using the ratio of the PRESS computed from the 

ROI method to the PRESS computed from the RRE. 

A ratio of less than one indicated that the ROI method 

is a better predictor at an ungaged site than the RRE 

method. Table 10 shows that the ROI method performed systematically better only in the Blue Ridge, 

and therefore, should be used only for that Province.

Limitations

The following limitations should be recognized 

when using either the regional regression equations or 

the region-of-influence method.

1. The methods should be used only for ungaged 

sites where the basin drainage area is between 0.6 and 

945 mi2 for the Blue Ridge, 0.1 to 1,430 mi2 for the 

Piedmont, 4.7 to 1,720 mi2 for the upper Coastal Plain, 

and 1.1 to 1,250 mi2 for the lower Coastal Plain.

2. The methods should not be used for sites where 

the watershed is substantially affected by regulation 

from impoundments, channelization, levees, or other 

man-made structures.

3. The methods should not be used for sites on 

streams in urban areas unless the effects of urbanization are insignificant.

4. The methods do not apply where flooding is 

influenced by extreme tidal events.

5. The methods should be used with caution in 

areas where the streamflow characteristics have not 

been sufficiently defined by high-flow measurements 

(fig. 1). In York and Chester Counties, the regional 

equations tend to produce flow results that may be 

significantly lower than those obtained using flow 

records (Guimaraes and Bohman, 1991). C.L. Sanders, Jr. 

(U.S. Geological Survey, written commun., Nov. 1993) 

observed that this area can be defined by the extent of 

the Iredell-Mecklenburg and Wilkes-Winnsboro-Mecklenburg soil types shown on the “General Soil Map, 

South Carolina” (Smith and Hollbick, 1979). Sanders 

showed that the regressions equations developed by 

Gunter and others (1987) tend to produce more reasonable results in this area than do the equations developed 

by Guimaraes and Bohman (1991). Until the streamflow characteristics in this area are sufficiently defined 

by higher flow measurements, the North Carolina rural 

flood-frequency equations by Pope and others (2001) 

and the North Carolina urban flood-frequency equations 

by Robbins and Pope (1996) can be used to estimate 

the magnitude and frequency of floods in the York and 

Chester County area.

6. The methods should be used with caution in the 

Upper Three Runs Basin in Aiken and Barnwell Counties in the western part of the upper Coastal Plain physiographic province. The regional equations tend to 

produce flows that may be substantially higher than 

those obtained using observed flow records for the 

Upper Three Runs Basin. To obtain flows for the Upper 

Three Runs Basin, either the station recurrence-interval 

flow should be used (appendix A) or the flow at an 

ungaged site should be adjusted by drainage area, using 

an appropriate Upper Three Runs gaging station as an 

index station.

Computer Software 

A computer software program was 

developed that estimates flood frequency 

at rural ungaged sites in South Carolina. 

The computer application includes an executable program file and three supporting 

data files. All of these files must be 

located in a common directory for the 

computer program to work properly. 

Flood-frequency estimates provided by 

the computer program can be used alone 

or weighted with data from a nearby gaging station, as described in the Application 

of Methods section of this report.

Table 10. Ratio of PRESS (ROI) statistic to PRESS (RRE) statistic for 

each physiographic province

[PRESS, PRediction Error Sum of Squares] 

Recurrence 

interval

(years)

Physiographic province

Blue Ridge Piedmont Upper 

Coastal Plain

Lower 

Coastal Plain

2 0.87 1.17 1.53 0.91

5 0.79 1.13 1.17 1.08

10 0.75 1.09 1.40 1.12

25 0.73 1.04 1.36 1.14

50 0.73 1.02 1.32 1.10

100 0.74 1.00 1.30 1.08

200 0.75 0.98 1.28 1.07

500 0.77 0.97 1.25 1.05
Application of Methods 25

Each time the computer program is executed, it 

produces flood-frequency estimates using the RRE 

method and, if the site is in the Blue Ridge Province, 

the ROI method. The computer program produces onscreen summary results and generates one or two output files containing the results of flood-frequency estimates at rural ungaged sites in South Carolina. The 

first output file contains flood-magnitude predictions, 

standard error of the predictions, and 90 percent prediction intervals for each recurrence-interval flow. 

The second output file is produced if the ROI method 

is used and contains detailed diagnostic information for 

the ROI method, including a listing of the ungaged 

site’s "region of influence," as well as for each recurrence-interval flow, the unique regression equations, 

and overall prediction error statistics for the method. 

Appendix C provides details of the GLS regression 

method and calculation of prediction errors and 

intervals.

The computer program and necessary data files 

can be downloaded to a personal computer from the 

USGS website. To download the computer files using 

an internet browser, enter the following address: http://

wwwsc.er.usgs.gov/SCFFREQ/. From there, download the compressed (or zipped) file named scff.zip to a 

designated directory on your personal computer. 

Extract the following six files from scff.zip: (1) scff.for 

is the program source code; (2) scff.exe is the executable file; (3) sc.cmn is a common block file used with 

the source code; (4) sc115.txt, (5) scroi.cr, and (6) 

scroi.rl are data files for the region-of-influence 

method. Once the files have been extracted, open a 

DOS window and type scff to run the program. 

APPLICATION OF METHODS 

The methods presented in this report can be 

used to estimate the 2-, 5-, 10-, 25-, 50-, 100-, 200-, 

and 500-year recurrence-interval flows at ungaged sites 

and to improve estimates at gaged sites for unregulated, rural streams in South Carolina. To improve the 

estimated flow for a selected recurrence-interval flood 

at a gaged site, the flow at the gaged site should be 

weighted with the regional flow estimate using the 

number of years of station record and the accuracy of 

the regional flood-frequency relation, expressed in 

equivalent years of record (Hydrology Subcommittee 

of the Interagency Advisory Committee on Water Data, 

1982). The accuracy of the regional flood-frequency 

relations is the same as would be determined by gaging 

a stream for the number of equivalent years of record 

listed in table 9. Accuracy for the weighted estimate is 

the sum of the accuracy of each estimate in equivalent 

years of record, assuming the estimates are independent.

For ungaged sites, the regional peak-flow estimate for a selected recurrence interval can be improved 

if the site is located near a gaged site on the same 

stream that has at least 10 years of peak-flow record. 

Flows for ungaged sites are weighted according to the 

relative proximity, with respect to drainage area, of the 

ungaged site to the gaged site. Gaged sites having less 

than 10 years of peak-flow record should be treated as 

ungaged sites.

Flood Frequency at Gaged Sites for 

Streams Draining One Physiographic 

Province

Flood-frequency estimates at gaged sites can be 

improved by combining the estimate determined by 

regional methods with the estimate determined by fitting the log-Pearson Type III distribution to the peakflow record at the gaged site. The procedure for estimating a selected recurrence-interval flow at gaged 

sites can be computed using the following equation 

(Hydrology Subcommittee of the Interagency Advisory 

Committee on Water Data, 1982):

, (12)

where

The log-Pearson Type III flood-frequency data 

and weighted flows for the 2-, 5-, 10-, 25-, 50-, 100-, 

200-, and 500-year recurrence interval floods for the 

South Carolina streamflow sites used in this report are 

presented in appendix B. The log-Pearson Type III 

flood-frequency data also are presented in appendix A. 

QT(w) is the weighted flow for the selected T-year 

recurrence interval, in cubic feet per second;

N is the number of years of record used to compute QT(s);

QT(s) is the estimated flow at the station from the 

log-Pearson Type III analysis for the selected 

T-year recurrence interval, in cubic feet per 

second;

EY is the equivalent years of record for QT(r) 

from table 9; and

QT(r) is the regional flow at the station for the 

selected T-year recurrence interval computed 

using the applicable regional relation from 

table 8, in cubic feet per second.

LogQT w( )

N QT s( ) ( ) log EY QT r( ) + ( ) log

N EY + = -----------------------------------------------------------------------
26 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

The flood-frequency data were computed using available records through the 1999 water year and supersede 

the values presented by Guimaraes and Bohman (1991).

Flood Frequency Near Gaged Sites on 

the Same Stream Draining One 

Physiographic Province

Peak flows for a selected recurrence interval at 

an ungaged site on a stream can be estimated by determining in which physiographic province (fig. 1) the 

basin is located, computing the drainage area for the 

basin, and computing the flow using the appropriate 

regional flood-frequency relation from table 8. The 

regional estimate can be improved if the site is located 

on the same stream as a gaged site having at least 10 

years of record and the drainage area of the ungaged 

site is within 50 percent of the drainage area of the 

gaged site. The weighted flow, QT(w), at the gaged site 

can be transferred to the ungaged site using the following equation:

(13)

and then a weighted flow value can be computed by the 

equation

(14)

Qu

Au

Ag

-----

      b

QT w( ) =

Qu w( )

2 ∆A

Ag

-------------     Qr 1 2 ∆A

Ag

– -------------     Qu = +

where

Qu is the flow at the ungaged site transferred 

from the gaged site in cubic feet per second 

(ft3/s);

Au is the drainage area of the ungaged site, in 

square miles (mi2);

Ag is the drainage area of the gaged site, in 

square miles;

b is the exponent of the drainage area term of 

the regional flood-frequency relation for the 

applicable physiographic province and 

recurrence interval, from table 8;

QT(w) the weighted flow at the gaged site for the 

selected T-year recurrence interval, in cubic 

feet per second; 

Qu(w) is the weighted flow at the ungaged site for 

the selected T-year recurrence interval, in 

cubic feet per second; 

This procedure should only be used to adjust the 

RRE estimate of flow if the drainage area of the ungaged 

site on the same stream as a nearby gaged site is within 

50 percent of the drainage area of the gaged site. If it is 

not, use of the regional regression equations as described 

previously will provide the best estimate of flow.

Flood Frequency at Ungaged Sites on 

Streams Draining More Than One 

Physiographic Province

For an ungaged site that drains more than one 

physiographic province, the selected recurrence-interval 

flow may be computed by solving the appropriate 

equations for each physiographic province as though 

the drainage area were located entirely in each province, 

and then weight the flow as described below. For 

example, if the drainage area is 80 mi2 with 60 percent 

of the basin located in the Piedmont and 40 percent 

located in the Blue Ridge, computation of the 100-year 

flow is as follows:

Piedmont: Q100 = 503 (80)0.626 = 7,810 ft3/s,

Weighted Piedmont Q100 = 7,810 x 0.60 = 4,690 ft3/s, 

Blue Ridge: Q100 = 595 (80)0.688 = 12,100 ft3/s,

|∆A| is the absolute value of difference in 

drainage areas of the gaging station and the 

ungaged site, in square miles; and

Qr is the regional flow for the selected recurrence interval at the ungaged site computed, 

using the applicable regional relation from 

table 8, in cubic feet per second.

Weighted Blue Ridge Q100 = 12,100 x 0.40 = 4,840 ft3/s, and 

Final weighted Q100 at site = 4,690 + 4,840 = 9,530 ft3/s.

Flooding along the Waccamaw River due to Hurricane Floyd 

at railway station on S.C. Highway 905. Photo by Andy 

Caldwell on September 29, 1999.
Flood Frequency of Gaged Sites on Streams Draining More Than One Physiographic Province 27

A tlantic O cean

82° 80°

82° 80°

34°

32°

32°

34°

0 20 40 60 80 MILES

0 20 40 60 80 KILOMETERS

N orth C arolina

G eorgia

200

S outh C arolina

Broad

River

Con gare e Ri ver

Saluda

River

Lynches Riv er

Pee Dee River

Waccamaw River

Wat eree River

Santee Ri ver

Edi sto

Ri ver

Sal kehatchie River

Sa vannah

River

Lake

Wylie

Lake

Keowee

Lake

Jocassee

Lake

Hartwell

Richard

B. Russell

Lake

J. Strom

Thurmond

Lake

Lake

Murray

Lake

Wateree

Lake

Robinson

Lake

Greenwood

Lake William

C. Bowen

Lake

Marion

Lake

Moultrie

Paco let River

R

Tugaloo

iver

Chatoog a River

Fishing

Creek

Reservoir

Parr Reservoir

Little

Pee Dee River

Cooper Rive

Ash r

ley Riv er

Co mb ahee Riv er

173

174

175

176 177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

Gaging station and station index number

Stream or lake

State boundary

Lower Coastal Plain physiographic province

Upper Coastal Plain physiographic province

Piedmont physiographic province

Blue Ridge physiographic province

EXPLANATION

FLOOD FREQUENCY AT GAGED SITES 

ON STREAMS DRAINING MORE THAN 

ONE PHYSIOGRAPHIC PROVINCE 

Flood frequencies for gaged sites along the 

mainstem of the Broad, Little Pee Dee, Lynches, Edisto, 

and Salkehatchie Rivers (fig. 6) were not determined 

using the regional flood-frequency analysis because 

these sites are located on streams draining more than one 

physiographic province. The flood-frequency relations 

at such sites are not representative of the other sites used 

to develop the regional relations. Some of the streams 

listed above are subject to minor regulation at low to 

medium flows that do not significantly affect water-year 

peak flows. The logarithm of water-year peak flows for 

these stations was fitted to a log-Pearson Type III 

distribution to determine flows for selected recurrence 

intervals and are described in unnumbered text tables 

that follow.

Broad River

The Broad River originates in the Blue Ridge 

Province of North Carolina and flows eastward and 

southward through the Piedmont to Columbia, S.C., 

where it merges with the Saluda River to form the 

Congaree River (fig. 6). Floods on the Broad River 

consist primarily of unregulated runoff, although there 

is some regulation at low to medium flows (Guimaraes 

and Bohman, 1991).

Figure 6. Locations of streamflow gaging stations on regulated streams and gaging stations on streams draining more than one 

physiographic province in South Carolina.
28 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

1,000,000

100,000

1,000 5,000 10,000

500,000

DRAINAGE AREA, IN SQUARE MILES

STATION 02153500 Broad River

near Gaffney

Station 02156500 Broad River

near Carlisle

Station 02161500 Broad River

near Richtex

Flow for water years 1939-83

Flow for period of record

100-YEAR RECURRENCE-INTERVAL

FLOW, IN CUBIC FEET PER SECOND

Flows were computed for Station 02153500, 

Broad River near Gaffney, S.C., for the period 1939-90 

(map index number 178); Station 02156500, Broad 

River near Carlisle, S.C., for the period 1926-99 (map 

index number 179); and Station 02161500, Broad 

River near Richtex, S.C., for the period 1897-1907 and 

1926-99 (map index number 181) (appendix C). The 

drainage area at Station 02161500 is 4,850 mi2 and the 

period of record is 1926-83. Stage and flow data also 

were collected from 1897-1907 and 1981-99 at Station 

02161000, Broad River at Alston, S.C. (map index 

number 180), which has a drainage area of 4,790 mi2. 

Because the difference in the size of these two stations 

is small (approximately 1 percent), the data were combined. The combined period of record (1897-1907 and 

1926-99) was used to compute the flood frequencies at 

Station 02161500.

Significant floods were recorded at Station 

02161500 during water years 1928, 1930, and 1936. 

To incorporate these historical floods into the frequency 

analysis at Station 02156500, which has an actual period 

of record for water years 1939-99, the water-year peak 

flows at Station 02156500 were regressed against the 

water-year peak flows at Station 02161500 for the concurrent peaks. The R2 for this regression was 0.85 and 

the standard error of estimate was 15 percent. Therefore, 

the 1928, 1930, and 1936 peak floods were estimated at 

Station 02156500 from this regression. The peaks were 

then included in the Station 02156500 data as historical 

peaks and a historical period of 74 years (1926-99) was 

used in the log-Pearson analysis.

A similar regression 

analysis was made for Station 

02153500 with Station 

02161500. The R2 from that 

regression was 0.56 and the standard error of estimate was 28 

percent. Based on the R2, the 

standard error of estimate, and 

the difference in the drainage 

areas between the two stations 

(1,490 mi2 and 4,850 mi2, 

respectively), the log Pearson 

analysis at Station 02153500 was 

computed using only the systematic record (1939-90).

An additional analysis 

was made using the period from 

1939-83 for which data were 

simultaneously collected at Stations 02153500, 

02156500, and 02161500. The relation between the 

drainage area and the 100-year flow at the three stations is shown in figure 7. For the analysis using the 

complete period of record, the graph indicates a relatively linear relation with a slight increase in the slope 

between Stations 02156500 and 02161500. The plot of 

the simultaneous period from 1939-83 shows a similiar 

pattern with a slope between Stations 02153500 and 

02156500 that is flatter but with a similiar increase in 

slope between Stations 02156500 and 02161500. Figure 7 also shows that the flood frequencies are sensitive 

to the larger flows (1928, 1930, and 1936). Given the 

sensitivity to the larger flows and the similar change in 

slopes between Stations 02156500 and 02161500, the 

data suggest that using the estimated floods at Station 

02156500 results in a more accurate estimate of the 

flood frequency.

The flows for selected recurrence intervals are 

tabulated below for Station 02153500, Broad River 

near Gaffney, S.C., Station 02156500, Broad River 

near Carlisle, S.C., and Station 02161500, Broad River 

at Richtex, S.C.

Map 

index 

No.

Station 

name and 

number

Drainage 

area 

(square 

miles)

Flow, in cubic feet per second, for indicated recurrence 

interval, in years

2 5 10 25 50 100 200 500

178 Broad River 

near 

Gaffney, 

S.C. 

(02153500)

1,490 31,500 47,900 59,000 73,300 84,100 94,800 106,000 120,000

179 Broad River 

near Carlisle, S.C. 

(02156500)

2,790 42,000 63,400 79,300 101,000 119,000 137,000 157,000 186,000

181 Broad River 

at Richtex, 

S.C. 

(02161500)

4,850 58,800 88,700 112,000 147,000 177,000 210,000 247,000 304,000

Figure 7. Relation between drainage area and 100-year recurrence-interval flows for 

period of record and water years 1939-83 for Station 02153500, Broad River near 

Gaffney, S.C., Station 02156500, Broad River near Carlisle, S.C., and Station 02161500, 

Broad River at Richtex, S.C.
Flood Frequency of Gaged Sites on Streams Draining More Than One Physiographic Province 29

Little Pee Dee River

The Little Pee Dee River and the Lumber River 

are unregulated streams that originate in the Sandhill 

region of North Carolina and flow southward and eastward to the lower Coastal Plain of South Carolina (fig. 6). 

Soon after entering South Carolina, the Lumber River 

merges with the Little Pee Dee River and continues to 

be known as the Little Pee Dee River below the confluence. Station 02132500, Little Pee Dee River near 

Dillon, S.C., was included in the regional analysis 

because the drainage area is predominately located in 

one physiographic province. Flows for selected recurrence intervals are tabulated below for Station 

02135000, Little Pee Dee River at Galivants Ferry, S.C. 

(map index number 177, period of record 1942-99).

Lynches River

The Lynches River originates in the Piedmont 

of North Carolina, and flows southeastward through 

the upper Coastal Plain to the lower Coastal Plain of 

South Carolina (fig. 6). Flows for selected recurrence 

intervals are tabulated below for Station 02131500, 

Lynches River near Bishopville, S.C. (map index 

number 175, period of record 1943-99), and Station 

02132000, Lynches River at Effingham, S.C. (map 

index number 176, period of record 1928-99). Bulletin 

17B, appendix 7 (Hydrology Subcommittee of the 

Interagency Advisory Committee on Water Data, 

1982), outlines a procedure for adjusting the logarithmic mean and standard deviation of a short-record site 

on the basis of a regression analysis with a nearby 

long-record site. This procedure was used to adjust the 

logarithmic mean and standard deviation at Station 

02131500. The flows for the selected recurrence intervals listed in the table below are smaller for the downstream station, Lynches River near Effingham, S.C., 

because as the Lynches River flows from the upper to 

lower Coastal Plain, the flood peaks are attenuated due 

to increased storage in the floodplain.

Map 

index 

No.

Station 

name and 

number

Drainage 

area 

(square 

miles)

Flow, in cubic feet per second, for indicated 

recurrence interval, in years

2 5 10 25 50 100 200 500

177 Little Pee Dee 

River at Galivants Ferry, 

S.C. 

(02135000)

2,790 12,400 18,000 21,700 26,300 29,600 33,000 36,300 40,600

Edisto River

The North Fork Edisto River and South Fork 

Edisto River originate in the upper Coastal Plain of 

South Carolina and flow southeastward to the lower 

Coastal Plain. The South and North Forks of the Edisto 

River merge in the lower Coastal Plain to form the 

Edisto River (fig. 6). Stations 02172500, South Fork 

Edisto near Montmorence, S.C., 02173000, South Fork 

Edisto near Denmark, S.C., and 02173500, North Fork 

Edisto at Orangeburg, S.C. were included in the 

regional analysis because their respective drainage 

areas are located in one physiographic province. In 

addition, Station 02174000, Edisto River near Branchville, S.C. was included in the regional analysis 

because the drainage area is predominately located in 

one physiographic province. Flows for selected recurrence intervals for Station 02175000, Edisto River near 

Givhans, S.C. are tabulated below (map index number 

182, period of record 1939-99).

Salkehatchie River

The Salkehatchie River originates in the upper 

Coastal Plain of South Carolina and flows southeastward 

to the lower Coastal Plain (fig. 6). Flows for selected 

recurrence intervals for Station 02175500, Salkehatchie 

River near Miley, S.C. are tabulated below (map index 

number 183, period of record 1951-99). 

Map 

index 

No.

Station name 

and number

Drainage 

area 

(square 

miles)

Flow, in cubic feet per second, for indicated 

recurrence interval, in years

2 5 10 25 50 100 200 500

175 Lynches River 

near Bishopville, 

S.C. (02131500)

675 7,710 11,900 14,900 18,700 21,600 24,500 27,500 31,500

176 Lynches River 

near Effingham, 

S.C. (02132000)

1,030 5,640 9,170 11,800 15,600 18,700 22,000 25,500 30,600

Map 

index 

No.

Station 

name and 

number

Drainage 

area 

(square 

miles)

Flow, in cubic feet per second, for indicated recurrence 

interval, in years

2 5 10 25 50 100 200 500

182 Edisto 

River near 

Givhans, 

S.C. 

(02175000)

2,730 9,770 15,000 18,400 22,800 26,000 29,200 32,400 36,600

Map 

index 

No.

Station 

name and 

number

Drainage 

area 

(square 

miles)

Flow, in cubic feet per second, for indicated 

recurrence interval, in years

2 5 10 25 50 100 200 500

183 Salkehatchie 

River near 

Miley, S.C. 

(02175500)

341 1,510 2,230 2,760 3,480 4,060 4,670 5,320 6,240
30 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

FLOOD FREQUENCY AT GAGED SITES 

ON REGULATED STREAMS 

Many of South Carolina’s streams, especially 

the larger ones, are regulated by reservoirs. Flows from 

reservoirs are regulated to satisfy requirements for 

in-stream water-use downstream from the reservoirs, 

power generation, maintenance of lake levels for recreation, and flood control. Regulation procedures may 

change as flow requirements change. During extremely 

large floods, the relative effects of storage are diminished and operations are directed more toward preventing dam failure than toward flood control and 

protection of downstream property. Consequently, 

flood frequencies for regulated streams are dependent 

on many more factors than unregulated streams and 

are, therefore, quite complex and beyond the scope of 

this report.

For informational purposes, water-year peak-flow 

data for stations on regulated streams in South Carolina 

are provided in appendix C of this report. The locations of 

these gaging stations are shown on figure 5. Other useful 

information pertaining to regulated streams for which data 

are available is provided as published in the previous 

report by Guimaraes and Bohman (1991). 

Pee Dee River

The Pee Dee River originates in the Blue Ridge 

Province of North Carolina and flows through the Piedmont, upper Coastal Plain, and lower Coastal Plain physiographic provinces (fig. 6). Through most of North 

Carolina, the Pee Dee River is known as the Yadkin River.

Three reservoirs on the Yadkin River and two 

reservoirs on the Pee Dee River are used for hydroelectric power generation. A sixth reservoir (W. Kerr 

Scott Reservoir), located on the Yadkin River, is used 

for flood control and water supply. These reservoirs are 

located in North Carolina and are not shown on figure 6. 

Selected data on these reservoirs are listed below 

(Ruddy and Hitt, 1990).

Name of 

reservoir

Date of 

completion

Name of 

stream

Drainage area

(square miles)

Flood-storage

capacity

(acre-feet)

W. Kerr Scott 1963 Yadkin 350 112,000

High Rock Lake 1927 Yadkin 4,000 64,400

Tuckertown 1962 Yadkin 4,120 0

Badin Lake 1917 Yadkin 4,180 75,800

Lake Tillery 1928 Pee Dee 4,600 29,500

Blewett Falls Lake 1912 Pee Dee 6,830 7,000

Water-year peak-flow data are available for one 

gaging station on the Pee Dee River downstream from 

the lakes: Station 02131000, Pee Dee River at Peedee, 

S.C. (map index number 186, period of record 1939-99) 

(appendix C).

Catawba River

The Catawba River originates in the Blue Ridge 

Province of North Carolina, flows through the Piedmont province of South Carolina, and becomes the 

Wateree River below Lake Wateree (fig. 6). Ten reservoirs, six in North Carolina (not shown on fig. 6) and 

four in South Carolina (fig. 6), are located on the Catawba River and are storage facilities for hydroelectric 

power generation. Selected data on nine of these reservoirs are presented below (Ruddy and Hitt, 1990).

Water-year peak-flow data are available for 

Station 02146000, Catawba River near Rock Hill (map 

index number 187, period of record 1896-1903, 1942-99) 

and Station 02147000, Catawba River near Catawba 

(map index number 188, period of record 1968-91) 

(appendix C).

Wateree River

The Wateree River originates at the outflow of 

Lake Wateree (fig. 6). The Wateree River flows southeastward through the upper Coastal Plain where it 

merges with the Congaree River to form the Santee 

River (fig. 6). 

Water-year peak-flow data are available for 

Station 02148000, Wateree River near Camden 

(map index number 189, period of record 1930-99) 

(appendix C).

Name of 

reservoir

Date of 

completion

Drainage area

(square miles)

Flood-storage

capacity

(acre-feet)

Lake James 1919 380 67,900

Rhodhiss Lake 1925 1,090 50,200

Lake Hickory 1928 1,310 61,140

Lookout Shoals Lake 1915 1,450 6,240

Lake Norman 1963 1,790 182,000

Mountain Island 1923 1,860 23,300

Lake Wylie 1925 3,020 33,000

Fishing Creek 1916 3,810 0

Lake Wateree 1919 4,750 45,100
Flood Frequency at Gaged Sites on Regulated Streams 31

Saluda River

The Saluda River originates in the Blue Ridge 

Province and flows southeastward through the Piedmont province of South Carolina where it merges with 

the Broad River near Columbia, S.C., forming the Congaree River (fig. 6). Two reservoirs, Lake Greenwood 

and Lake Murray, are located on the Saluda River. 

Selected data for these reservoirs are presented below 

(Ruddy and Hitt, 1990).

The Saluda River above Lake Greenwood is not 

significantly affected by regulation. Flows for sites 

along the Saluda River above Lake Greenwood can be 

determined, by using methods described in previous sections of this report, by estimating flow at an ungaged 

site, or by estimating flow at or near a gaged site. The 

three gaging stations on the Saluda River upstream from 

Lake Greenwood (fig. 1) are Station 02162500, Saluda 

River near Greenville, S.C. (map index number 25, 

period of record 1942-99), Station 02163000, Saluda 

River near Pelzer, S.C. (map index number 26, period of 

record 1930-93), and Station 02163500, Saluda River 

near Ware Shoals, S.C. (map index number 27, period of 

record 1939-99). Records also are available for three stations downstream from Lake Greenwood as shown on 

figure 6. These are Station 02167000, Saluda River at 

Chappells, S.C. (map index number 192, period of 

record 1927-99), Station 02167500, Saluda River near 

Silverstreet, S.C. (map index number 193, period of 

record 1928-65), and Station 02169000, Saluda River 

near Columbia, S.C. (map index number 194, period of 

record 1926-99) (appendix C).

Congaree River

The Congaree River is formed at the confluence 

of the Broad River and Saluda River at Columbia, S.C. 

The Congaree River flows southeastward and joins the 

Wateree River to form the Santee River (fig. 6). The 

Broad River Basin makes up about two-thirds of the 

drainage area of the Congaree River. Flow of the Congaree River is highly regulated by Lake Murray, which 

is located on the Saluda River. Water-year peak-flow 

data are available for the Station 02169500, Congaree 

River at Columbia, S.C. (map index number 195, 

period of record 1939-99) (appendix C).

Name of 

reservoir

Date of 

completion

Drainage area

(square miles)

Flood-storage

capacity

(acre-feet)

Lake Greenwood 1940 1,150 147,000

Lake Murray 1930 2,420 125,000

Santee River

Formed at the confluence of the Congaree and 

Wateree Rivers, the Santee River flows directly into 

Lake Marion - the largest reservoir by surface area in 

South Carolina (Ruddy and Hitt, 1990).

From 1941 to 1986, most of the flow from Lake 

Marion was diverted to the Cooper River through a 

diversion canal to Lake Molutrie (fig. 6). A rediversion 

canal, completed in 1986, restored approximately 80 

percent of the previously diverted flow back to the Santee River. Due to the extensive hydrologic modification, which has taken place over the last 50 to 60 years, 

frequency computations were not made for stations 

along the Santee River. However, water-year peak 

flows for the three stations with 10 or more years of 

record are listed in appendix C; Station 02170000, Santee River at Ferguson, S.C. (map index number 196, 

period of record 1908-41), Station 02171500, Santee 

River near Pineville, S.C. (map index number, 197, 

period of record 1943-88), Station 02171650, Santee 

River below St. Stephens, S.C. (map index number 

198, period of record 1971-81).

Savannah River

The Tugaloo River and Seneca River, which was 

inundated by Lake Keowee and Lake Jocasse, originate 

in the Blue Ridge Province and converge to form the 

Savannah River (fig. 6). The Savannah River is the 

State boundary between Georgia and South Carolina 

and is regulated by three reservoirs along its main stem. 

The reservoirs are operated by the U.S. Army Corps of 

Engineers for flood control, power generation, and 

navigation. Data pertaining to the reservoirs are listed 

below (Sanders and others, 1990).

Sanders and others (1990) showed that the 

period after 1951 for Station 02197000, Savannah 

River at Augusta, Ga., was significantly free of 

extremely large floods, based on an unusually long 

period of flood data (1796-1985). A flood-frequency 

Name of 

reservoir

Date of 

completion

Drainage area

(square miles)

Flood-storage

capacity

(acre-feet)

Lake Marion 1941 14,680 255,000

Name of 

reservoir

Date of 

completion

Drainage area

(square miles)

Flood-storage

capacity

(acre-feet)

Lake Hartwell 1960 2,090 293,000

Richard B. Russell Lake 1984 2,900 140,000

J. Strom Thurmond Lake 1953 6,150 390,000
32 Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

relation was established for the site using peak flows 

computed by the routing of synthesized inflow hydrographs through the reservoirs to the site based on operating conditions at the time of the study. The frequency 

data from that study for Station 02197000 are tabulated 

below.

Water-year peak-flow data for five stations with 

10 or more years of record on the Savannah River are 

listed in appendix C: Station 02187500, Savannah 

River near Iva, S.C. (map index number 199, period of 

record 1950-81), Station 02189000, Savannah River 

near Calhoun Falls, S.C. (map index number 201, 

period of record 1897, 1900-80), Station 02195000, 

Savannah River near Clarks Hill, S.C. (map index 

number 202, period of record 1940-54), Station 

02197500, Savannah River at Burtons Ferry Bridge 

near Millhaven, Ga. (map index number 204, period of 

record 1940-99), and Station 02198500, Savannah 

River near Clyo, Ga. (map index number 205, period of 

record 1925-99). 

Pacolet River

The Pacolet River originates in the Blue Ridge 

Province and flows southeastward to the Piedmont 

Province where it merges with the Broad River (fig. 6). 

The South Pacolet River is regulated by Lake William 

C. Bowen, and the North Pacolet River is unregulated. 

Selected data for the reservoir are presented below 

(Ruddy and Hitt, 1990).

Water-year peak-flow data are available for 

Station 02155500, Pacolet River near Fingerville, S.C. 

(map index number 190, period of record 1931-99) 

and Station 02156000, Pacolet River near Clifton, S.C. 

(map index number 191, period of record 1940-78) 

(appendix C).

Map

index 

No.

Station name 

and number

Drainage 

area 

(square 

miles)

Flow, in cubic feet per second, for indicated 

recurrence interval, in years

2 5 10 25 50 100

203 Savannah River at 

Augusta, Ga. 

(02197000)

7,510 34,500 51,500 69,000 105,000 140,000 180,000

Name of 

reservoir

Date of 

completion

Drainage area

(square miles)

Flood-storage

capacity

(acre-feet)

William C. Bowen 1956 79.4 9,600

SUMMARY 

Flood magnitude and frequency estimates are 

important factors in the design of bridges, highway 

embankments, culverts, levees, and other structures 

near streams. This report describes methods for determining flood magnitude and frequency at rural streamflow-gaging stations and rural, ungaged sites in South 

Carolina. For this study, 167 streamflow-gaging 

stations in or near South Carolina were used in the 

regional regression analysis (54 in South Carolina, 65 

in North Carolina, and 48 in Georgia). Stations used for 

this study have 10 years or more of water-year peakflow data within a rural basin that is not significantly 

affected by regulation. The database has drainage areas 

that range from 0.1 to 1,720 square miles.

Peak flow data were analyzed for the mean, 

standard deviation, and skew using a log-Pearson 

Type III distribution. Using the station skew at sites 

with 25 years or more of data, generalized skew coefficients were developed for South Carolina. The skews 

were computed using a weighted arithmetic mean with 

the weight being based on record length. No statistically significant difference was found among the station skews in the Blue Ridge, upper Coastal Plain, and 

lower Coastal Plain. Station skews for the Piedmont, 

however, showed a statistically significant difference. 

Consequently, two generalized skew coefficients were 

computed for South Carolina and used in the final 

log-Pearson Type III analysis. The regional skew was 

weighted with the station skew and the weighted skew 

was used within the log-Pearson Type III analysis to 

determine the 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 

500-year recurrence interval flows at each streamflowgaging station.

Regional regression analysis, using generalized 

least squares regression, was used to develop a set of 

predictive equations that can be used to estimate the 

2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence-interval flows for rural ungaged basins in the 

Blue Ridge, Piedmont, upper Coastal Plain, and lower 

Coastal Plain physiographic provinces of South Carolina. The predictive equations are all functions of drainage area. Average errors of prediction for these regression equations ranged from -16 to 19 percent for the 

2-year recurrence-interval flow in the upper Coastal 

Plain to -34 to 52 percent for the 500-year recurrenceinterval flow in the lower Coastal Plain. 
Selected References 33

A region-of-influence method also was developed 

that interactively estimates the recurrence-interval flows 

for rural ungaged basins in South Carolina. The predictive 

errors from the regional regression method were compared with those from the region-of-influence method. 

From the comparison, it was concluded that the regionof-influence method only produced lower predictive 

errors in the Blue Ridge physiographic province; therefore, the region-of-influence method should be used 

only in the Blue Ridge. A computer program was developed that computes the selected recurrence-interval 

flows listed in the previous paragraph using the appropriate method as chosen by the user.

The methods described in this report are suitable 

only for use on unaltered, rural streams. These methods 

should not be used where dams, flood-detention structures, or other anthropogenic factors may significantly 

affect the peak-flow data. Furthermore, the models 

should be used within the range of the drainage areas 

used during model development for each physiographic province.

Appendix A provides the data for the 54 South 

Carolina gaging stations used in the frequency analyses. 

The appendix includes peak stages and flows, frequency 

and statistical data from the log-Pearson Type III analysis, and a station description. Appendix D provides 

peak stages and flows and a station description for regulated stations having 10 or more years of record. In 

addition, appendix D includes peak stages and flows, 

frequency and statistical data from the log-Pearson 

Type III analysis, and a station description for stations 

that drain more than one physiographic province but 

that are not significantly affected by regulation and 

have 10 or more years of record.

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Techniques for Estimating the Magnitude and Frequency of Floods in Rural Basins of South Carolina, 1999

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