U.S. Department of the Interior

U.S. Geological Survey

Fact Sheet 2009–3085

September 2009

Prepared in cooperation with the South Carolina Department of Transportation

Methods for Estimating Magnitude and Frequency of Floods in 

Rural Basins in the Southeastern United States: South Carolina

Introduction

For more than 50 years, the U.S. Geological Survey (USGS) has been developing regional regression equations that can 

be used to estimate flood magnitude and 

frequency at ungaged sites. Flood magnitude relates to the volume of flow that 

occurs over some period of time and usually is presented in cubic feet per second. 

Flood frequency relates to the probability 

of occurrence of a flood; that is, on average, 

what is the likelihood that a flood with 

a specified magnitude will occur in any 

given year (1 percent chance, 10 percent 

chance, 50 percent chance, and so on). Such 

flood estimates are needed for the efficient 

design of bridges, highway embankments, 

levees, and other structures near streams. 

In addition, these estimates are needed for 

the effective planning and management of 

land and water resources, to protect lives 

and property in flood-prone areas, and to 

determine flood-insurance rates. 

Issue

Historically, flood-frequency studies 

have been done on a statewide basis using 

hydrologic regions that represent areas of 

relatively homogeneous flood characteristics determined for the particular State of 

interest. Flood-frequency estimates made 

at gaged sites and regional flood-frequency 

equations developed from the gagedsite estimates contain varying degrees of 

uncertainty based on numerous factors, 

such as length of record, number of stations available for regionalization, range of 

basin characteristics, and so on. To provide 

simple methods of estimating flood-peak 

flows, the USGS has developed and published regression equations for every State, 

the Commonwealth of Puerto Rico, and a 

number of metropolitan areas in the United 

States. These investigations typically are 

not coordinated between neighboring States 

and are, therefore, based on various periods 

of record and sometimes result in hydrologic regions that are not contiguous at the 

State boundaries. Thus, if flood-frequency 

estimates are needed for a basin that crosses 

State boundaries, engineers and waterresource managers may have to work with 

several equations based on an assortment of 

basin characteristics with results that have 

varying degrees of uncertainty. 

To address this issue in the Southeast, 

the USGS Water Science Centers in South 

Carolina, Georgia, and North Carolina, 

worked cooperatively with the South 

Carolina Department of Transportation, 

the Georgia Department of Transportation, 

the North Carolina Department of Transportation, and the North Carolina Floodplain 

Mapping Program, to develop floodfrequency techniques that are applicable 

across State boundaries in these 

three States. 

Regression Analysis

Flood-frequency estimates for 828 

gaged stations in South Carolina, 

Georgia, North Carolina, and surrounding 

States were computed following methods 

described in Bulletin 17B of the Hydrology 

Subcommittee of the Interagency Advisory 

Committee on Water Data (1982). Based on 

assessments of geographical patterns in the 

residuals of the regression estimates, five 

hydrologic regions were established using 

U.S. Environmental Protection Agency 

ecoregions (2007) (fig. 1): Ridge and 

Valley–Piedmont (Region 1), Blue Ridge 

(Region 2), Sand Hills (Region 3), Coastal 

Plain (Region 4), and Southwest Georgia 

Figure 1. Hydrologic regions in the study area and the location of streamflow gaging stations 

used in the regional regression analysis.

A T L A N T I C O C E A N

G E O R G I A

ALABAMA

S O U T H C A R O L I N A

N O R T H

T E N N E S S E E

V I R G I N I A

F L O R I D A

 C A R O L I N A

75 76

73 74

72

938

903

884 883 880

878

875

871

866

857

849

847

843 841

839

835 834

831 827

770

753

745

741

737

722

607

606

332 334

305

241 243

237

229

198 200

175

132

124

113

112

735

9

8

7 6

5

4

3

2

1

99

98

97

96

95

94

93

92

91

90

89

88

87

86 85

84

83

82

81 80

79

78

77

75 76

73 74

72

70 71

69 68

67

66 65

64 63

62

61

60

59

58 57 56

55

54

53

52

51

50

49

48

47

46

45

44

43

42 41

39 40

38

37

36

35

34 33

32

31

30

28 29 27

26 25

24

23

22

21

20

19 18

17 16

15 13 14

12

11

10

943 942

941

940

939

938

937

936

935

934

933

932

931 930

929

928

927

926 925

924

923

922 921

920

919

918

917

916 915

914

913

912 911 910

909

908 907

906 905

904

903 902

901

900 898 899 897

896

895

894 893

892 891 890

889

888

887

886

885

884 883

882

881

880 879

878 877

876

875

874

873

872

871

870 869 868

867

866

865

864

863

862 861

860

859

858 857

856

855

854

853

852

851

850

849

846 847

845 844

843 842

841

840 839 838

837

836

835 834

833 832831

830

829 828

827

826

825 824

823 822

821

820

819

818 817 816 815

814

813

812

811

810

809 808 807

806 805

804

803

802

801

800 799

798 797

796

795

794

793

792 791

790

787

784

783

782

781

780

779

778

777

776

775

774

773

772

771

770

769 768

767

766

765 764

763

762

761

760 759

758

757

756 755

754 753

752

751

750

749

748

747

746

745744

743

742

741740

739

738

737

736734

733

732

731

730 729

728

727

726

725

724

723

722

721

720

719

718

717 716

715

714 713

712

711

710

709

708 707

706

705

704

703

702

701

700

699

698 697 696

695

694 693 692

691

690

689

688 687

686

685

684

683

682

681

679 680

678

677

676

675

674 673

672

671

670 669

668 667

666

665

664 663

662

661 660

659

658

657

656

655

654

653

652

651

649 650

648

647

646

645644 643

642 641 640

639

638

637

636

635

634

633

632

631

630

629

628

627

626

625 624

623

622

621

620

619 618

617

616 615

614

613

612

611

610

609

608

607

606

605

603

602 601

600

599

598

597

596

595

594 593

592

591

590

589

588

587 586

585

584

583

582

581

580

579

578

577

576

575

574

573 572 571

570

569

568

567 566

565

564

563

562

561

560 559

558

557

556 555

554

553

551 552

550

549

548

547

546

545

544

543

542

541 540 539

538

537

536

535

534

533 532

531

530 529

528

527 526

525

524

523 522

521 520

519 518

517

516

515

514

513

512

511

510

509

508

507

506

504

503 502

501

500

499

498 497

496

495

494

493 492 491 490

489

488

487

486 485

483 484

482 481

480

479

478 476 477

475

474

473

472

471

470

469

468 467

466 465

464

463

462

461 460

459 458

457

456

455

454 453

452

451 450

449

448

447

446

445 444

443 442

441

440

439

438 437 436 435 434

433

432

431

430

429

428

427

426

425

424

423 422

421

420

419

418

417

416

414 415 413

412

411 410

409 408 407

406

405

404

403

401 402 400 399

398

397

396 395

394

393

392

391

390

389 388

387 386

385384

383

382

381

380

379

378

377

376

375 374

372

371

370

369 368

366 367

365

364

363

362

361

360

359

357

358 356

355

353 354

352

351

350 349

348

347 346

345 344

343

342

341

340

339

338

337 336

335

334

333

332

331 330

328 329

327

326

325

324

323

321 322

320

319

318

317

316

315

314

313

312

311

310

309

308

307

306 305

304

303

302

301

300

299

298 297

296

295

294 293

292

291

290

289

288

287

286

285 284

283

282

281 280

279

278

277

276

275 274

273 272

271 270

269

268 267

266

265

264

263

262

261 260

259

258

257 256

255 254 253

251 252

250

249 248 247

246

245

244

243

242 241

240

239

237 238

236

235 234

233 232

231

230

229

228

227

226

225

224

223

222

221

220

218 219

217

216

215

214

213 212

211

210 209

208

207

206

205 204

203 202

201 200

199

198

197

196

195

194 193

192

191

190 189

188

187

186

185

184

183

182

181 180

179

178177

176

175 174

172173

171 170

169

168

167

166 165

164

163

162

161

160

159

158 157

156

155

154

153 152

151

150

149

148

146 147

145

144

143 142

141 140 139

137 138

136

135 134

133

132

131

130

129

127

126

124 125

123

122

121 120 119

118

117

116

115

114

113

112

111

110

109

107 108

106

105

104

103

102

101

100

735

604

505

373

128

848

85°0'

82°30'

80°0

77°30'

75°0' 37°30'

35°0'

32°30'

EXPLANATION

Station and number

Not used in regression analysis

0 50 100 MILES

0 50 100 KILOMETERS

470

548

Used in regression analysis

Hydrologic region

Region 1

Region 2

Region 3

Region 4

Region 5

Undefined

Base modified from U.S. Geological Survey 1:100,000-scale digital data

Figure 4.

Printed on recycled paper
where Q1% is the 1-percent chance exceedance flow, in cubic feet per second; PCT1

, PCT2, PCT3, PCT4, and PCT5 are 

the basin percentages in hydrologic regions 1, 2, 3, 4, and 5; and DA is the drainage area, in square miles.

(Region 5). South Carolina is wholly 

encompassed in Regions 1–4. 

Historically, USGS reports expressed 

the T-year floods based on the recurrence interval for the specified flood (for 

example, the “100-year flood”). However, 

this terminology is undergoing a shift away 

from the T-year recurrence and instead 

using the more technically appropriate 

“percent chance exceedance probability.” 

The percent chance exceedance probability conveys the probability, or odds, 

that a flood of a given magnitude will be 

equaled or exceeded in any given year. For 

example, a 1-percent chance exceedance 

flood (formerly known as the “100-year 

flood”) corresponds to the flood that has a 

probability of 0.01 (or 1 percent) of being 

equaled or exceeded in any given year. The 

P-percent chance exceedance is computed 

as the inverse of the recurrence interval (T) 

multiplied by 100. 

This study resulted in a set of predictive equations that can be used to 

estimate the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, 

and 0.2-percent chance exceedance flows 

(formerly the 2-, 5-, 10-, 25-, 50-, 100-, 

200-, and 500-year recurrence interval 

flows, respectively), for rural, ungaged 

sites in South Carolina, Georgia, and North 

Carolina. The predictive equations are all 

functions of drainage area and the percentage of the drainage basin within each of 

the defined hydrologic regions. For brevity, 

only the equation for the 1-percent chance 

exceedance flow is shown as an example at 

the bottom of the page.

Traditionally, flood-frequency equations only apply to a single hydrologic 

region. Thus, in a State like South Carolina 

that has four hydrologic regions, there 

would be four sets of regression equations 

(one for each region). As a result, stations 

that have significant drainage from more 

than one region are not included in the 

regression analysis. The use of the basin 

percentages allows for the inclusion of 

such stations and, in this particular study, 

resulted in an additional 83 stations used 

in the analysis. The use of basin percentages in the regression coefficients allows 

for a smooth transition of flood estimates 

for drainage basins that do not lie wholly 

within one hydrologic region. For example, 

the slopes for the Blue Ridge and Sand 

Hills hydrologic regions’ (Regions 2 

and 3, respectively) regression lines are 

visibly different from the slopes for the 

regression lines for the three remaining 

hydrologic regions (fig. 2A). As a result, 

the final equations include 

a “slope adjustment factor” 

for hydrologic regions 2 and 

3. The transition from a site 

located wholly in hydrologic 

region 1, represented by the 

“base” slope (for example, 

0.594 for the 1-percent 

chance exceedance flow), 

to a site located wholly 

in hydrologic region 2 is 

depicted in figure 2B. Note 

that the slope of the regression line becomes visibly 

steeper as a basin goes from 

100 percent in the Ridge 

and Valley–Piedmont region 

(Region 1) to a basin that 

is 100 percent in the Blue 

Ridge region (Region 2).

The average standard 

error of prediction for these 

equations ranged from 

34.0 to 47.7 percent. The 

standard error of prediction 

is a measure of the accuracy 

of the regression equations 

when predicting floods for 

watersheds not used in the 

regression analysis. About 

two-thirds of the regression 

estimates for ungaged sites 

will have errors less than the 

standard error of prediction 

for the regression equations.

References

Feaster, T.D., Gotvald, A.J., and Weaver, J.C., 

2009, Magnitude and frequency of rural 

floods in the southeastern United States, 

2006—Volume 3, South Carolina: U.S. 

Geological Survey Scientific Investigations 

Report 2009–5156, 226 p.

Gotvald, A.J., Feaster, T.D., and Weaver, J.C., 

2009, Magnitude and frequency of rural 

floods in the southeastern United States, 

2006—Volume 1, Georgia: U.S. Geological Survey Scientific Investigations Report 

2009–5043, 120 p.

Interagency Advisory Committee on Water 

Data, 1982, Guidelines for determining flood 

flow frequency: Bulletin 17B of the Hydrology Subcommittee, U.S. Geological Survey, 

Office of Water Data Coordination, 28 p., 

14 app., 1 pl.

U.S. Environmental Protection Agency, 2007, 

Ecoregions of the United States: accessed on 

July 24, 2008, at http://www.epa.gov/wed/

pages/ecoregions.htm.

Weaver, J.C., Feaster, T.D., and Gotvald, A.J., 

in press, Magnitude and frequency of rural 

floods in the southeastern United States, 

2006—Volume 2, North Carolina: U.S. 

Geological Survey Scientific Investigations 

Report 2009–5158.

Authors

Toby D. Feaster (tfeaster@usgs.gov)

Anthony J. Gotvald (gotvald@usgs.gov)

J. Curtis Weaver (jcweaver@usgs.gov)

For additional information: 

USGS South Carolina Water Science Center

Stephenson Center, Suite 129

720 Gracern Road

Columbia, South Carolina 29210

(803) 750–6100

http://sc.water.usgs.gov

Full report available online at: 

http://pubs.usgs.gov/sir/2009/5156/

Figure 2. Rural flood-frequency relations (A) by region for 

basins located wholly within one hydrologic region and (B) for 

a basin transition from the Piedmont to the Blue Ridge 

hydrologic region.

[0.0289( ) 0.0276( ) 0.0202( ) 0.0258( ) 0.0286( )] [0.594 0.00119( ) 0.00139( )] 1 2 3 4 5 2 3

1% 10 PCT PCT PCT PCT PCT PCT PCT Q DA + + + + + + Sample equation: =

A. 100-percent drainage from each region

100

1,000

10,000

100,000

1,000,000

1-PERCENT CHANCE EXCEEDANCE FLOW, IN CUBIC FEET PER SECOND

Region 1 (Ridge and Valley–Piedmont)

Region 2 (Blue Ridge)

Region 3 (Sand Hills)

Region 4 (Coastal)

Region 5 

B. Transition from Ridge and Valley–Piedmont to Blue Ridge

100

1,000

10,000

100,000

1,000,000

0.1 1 10 100 1,000 10,000

DRAINAGE AREA, IN SQUARE MILES

100% Region 1 (Ridge and Valley–Piedmont)

75% Region 1 and 25% Region 2

50% Region 1 and 50% Region 2

25% Region 1 and 75% Region 2

100% Region 2 (Blue Ridge)