Cover photograph: Styx River near Elsanor, Baldwin County, Alabama (taken by Will S. Mooty, USGS).
Magnitude and Frequency of Floods on 

Small Rural Streams in Alabama

By T.S. Hedgecock

U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the Alabama Department of Transportation

Scientific Investigations Report 2004–5135
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2004

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Suggested citation:

Hedgecock, T.S., 2004, Magnitude and frequency of floods on small rural streams in Alabama: U.S. Geological Survey 

Scientific Investigations Report 2004–5135, 10 p.
 iii

Contents

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

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

Purpose and Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Description of the Study Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Flood Data Used in the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

Flood Magnitude and Frequency at Streamflow Gaging Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

Flood-Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

Use of Flood-Frequency Relations at Gaged Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Use of Flood-Frequency Relations at Ungaged Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Flood-Frequency Relations for Streams in Adjacent States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

Figures

1. Map showing locations of physiographic provinces in Alabama. . . . . . . . . . . . . . . . . . . . . 2

2. Map showing locations of streamflow gaging stations used in the study . . . . . . . . . . . . . 3

Tables

1. Peak flow for selected recurrence intervals at selected streamflow gaging 

stations in Alabama, Tennessee, Mississippi, Georgia, and Florida . . . . . . . . . . . . . . . . . . 4

2. Accuracy of flood-frequency relations for small rural streams in Alabama. . . . . . . . . . . . 8

3. Flood-frequency relations for small rural streams in Alabama. . . . . . . . . . . . . . . . . . . . . . . 9

4. Comparison of average standard errors of prediction for the four regional 

regression equations published by Atkins (1996) and average standard errors 

from statewide regression equations for small rural streams in Alabama . . . . . . . . . . . . . 9
iv 

Conversion Factors, Datum, and Acronyms and 

Abbreviations 

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83). 

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 1929).

Acronyms and Abbreviations

A drainage area

ALDOT Alabama Department of Transportation

F forest cover

GLS generalized least squares

L main channel length

OLS ordinary least squares

S main channel slope

SEp standard error of prediction

T lag-time factor

USGS U.S. Geological Survey

W/L width to length ratio

Multiply By To obtain

Length

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2)

Flow

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)
Magnitude and Frequency of Floods on Small Rural 

Streams in Alabama

By T.S. Hedgecock

Abstract

Equations for estimating the magnitude and frequency of 

floods for small rural streams in Alabama are presented for 

recurrence intervals ranging from 2 to 500 years. Floodfrequency characteristics are documented for 43 streamflow 

gaging stations included in the analysis. Each station used has a 

drainage area less than 15 square miles and at least 10 years of 

record prior to 2003. None of these stations were affected by 

regulation or urbanization. Regression relations were developed 

using generalized least-square techniques to estimate flood 

magnitude and frequency on ungaged streams as a function of 

the drainage area of a basin.

Introduction

The magnitude and frequency of floods are important 

factors in the design of bridges, culverts, highway 

embankments, dams, and other hydraulic structures near 

streams. Flood magnitude and frequency information also is 

used in flood-plain management and development, and in 

establishing flood insurance rates.

The Alabama Department of Transportation (ALDOT) 

requires accurate flood-frequency information to efficiently 

design drainage structures for highways in Alabama. To better 

meet this need, the U.S. Geological Survey (USGS), in 

cooperation with ALDOT, updated previous flood-frequency 

estimates on small rural streams by incorporating additional 

peak flow data collected through the 2003 water year1 from 

streamflow gaging stations in Alabama, Mississippi, Georgia, 

Florida, and Tennessee. 

A flood-frequency analysis was conducted on small 

streams exclusively, to see whether the resulting equations 

would yield smaller standard errors of prediction than previous 

analyses. The previous flood-frequency study conducted by 

Atkins (1996) incorporated a database in which 85 percent of 

the stations used were larger streams (greater than 15 square 

miles [mi2

]). The intent of the current study was to remove any 

bias caused by a database dominated by larger streams. 

Purpose and Scope

The purpose of this report is to update previous floodfrequency reports for Alabama by providing an alternative 

method of estimating the magnitude and frequency of floods for 

small rural streams, and to provide frequency estimates of water 

year peak flow data at streamflow gaging stations using peaks 

collected through September 2003. This report includes 

regression equations for estimating the magnitude of floods for 

streams having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, 

and 500 years for ungaged rural streams. These equations are 

applicable for streams having drainage areas less than 15 mi2

.

Acknowledgments

The assistance of Kathryn Green and Kristin Justice, 

USGS engineering students, was instrumental in the success 

and completion of this study. Also, special thanks is given to 

Brian Atkins, USGS, for his assistance with the statistical 

analyses used in this study

Previous Studies

Magnitude and frequency of floods in Alabama have been 

described by Pierce (1954), Speer and Gamble (1964), Gamble 

(1965), Barnes and Golden (1966), Hains (1973), Olin (1984), 

and Atkins (1996). Magnitude and frequency of floods have 

been described by Olin and Bingham (1977) for small rural 

streams, and by Olin and Bingham (1982) for urban streams.

Description of the Study Area

The study area includes all of Alabama, which has an area 

of about 51,600 mi2

, and is located in five physiographic 

1Water year refers to the 12-month period from October 1 through September 30 and is designated by the calendar year in which the period ends.
2 Magnitude and Frequency of Floods on Small Rural Streams in Alabama

Figure 1. Locations of physiographic provinces in Alabama (modified 

from Miller, 1990).

provinces—Coastal Plain, Piedmont, Valley and Ridge, 

Appalachian Plateaus, and Interior Low Plateaus (fig. 1). The 

area north of the Fall Line, which delineates the contact of the 

Coastal Plain with the other provinces, has a diverse topography 

with land-surface elevations ranging from 200 to 2,400 feet (ft) 

above NGVD 1929. In the Coastal Plain, elevations range from 

sea level at the coast to 1,000 ft above NGVD 1929 in the 

northwestern part of the State. The land surface generally slopes 

to the south and west.

Average annual precipitation ranges from about 50 inches 

(in.) in central and west-central Alabama to about 65 in. near the 

Gulf of Mexico and averages about 55 in. statewide. Rainfall in 

Alabama generally is associated with the movement of warm 

and cold fronts across the State during November through April 

and with isolated summer thunderstorms occurring from May 

through October. Occasionally, tropical storms or hurricanes 

entering the State along the Gulf Coast produce unusually 

heavy amounts of rainfall (U.S. Geological Survey, 1986).

Average annual runoff varies from approximately 18 to 

30 in. Runoff typically is greatest from February through 

April with flooding commonly occurring during March and 

April. Runoff usually decreases as rainfall decreases from 

September through November (U.S. Geological Survey, 

1986).

Flood Data Used in the Analysis

This study is based on peak flow data collected through 

water year 2003 at 43 rural streamflow gaging stations 

(fig. 2), each having a drainage area less than 15 mi2. All of 

the stations used have 10 or more years of record. Of these 

43 stations, 27 were located within Alabama and 16 were 

located near the Alabama State boundary in adjacent States 

of Florida, Georgia, Mississippi, and Tennessee. Eleven of 

these 43 stations have drainage areas less than 1 mi2

, nine 

have drainage areas ranging from 1 to 3 mi2

, six have 

drainage areas ranging from 3 to 6 mi2, eight have drainage 

areas ranging from 6 to 10 mi2

, and nine have drainage areas 

ranging from 10 to 15 mi2

. The peak flow records used in the 

study were not affected to any great degree by regulation, 

channelization, or urbanization.

Flood Magnitude and Frequency at 

Streamflow Gaging Stations

A flood-frequency relation is the relation of peak 

flow to the probability of exceedance or recurrence 

interval. Probability of exceedance refers to the chance 

that a given peak flow will be exceeded in any one 

year. For example, the probability that a 25-year flood 

will be exceeded in any given year is 0.04 (or 4-percent 

chance). Recurrence interval is the reciprocal of the 

probability of exceedance and is the average number 

of years between exceedances for a long period of record. A 25-

year flood may be expected to be exceeded on the average of 

once in 25 years, or four times in 100 years. This does not mean 

that floods occur at uniformly spaced intervals of time; rather, a 

flood of this magnitude can be exceeded more than once in the 

same year or can occur in consecutive years.

The flood-frequency relation for a stream where 

streamflow gaging-station data of 10 or more years of record are 

available can be defined by fitting a theoretical frequency 

distribution to the logarithms of water year peak flows (largest 

instantaneous flow for each water year). The Interagency 

Advisory Committee on Water Data (1982) has described and 

recommended a consistent technique for determining flood 

magnitudes and frequencies by fitting a Pearson Type III 

distribution to the logarithms of water year peak flows. This 
Flood-Frequency Analysis 3

technique is commonly referred to as the log-Pearson Type III 

frequency analysis and is generally accepted by most Federal 

and State agencies. Water year peak flows for each streamflow 

gaging station used in this study were fitted to the log-Pearson 

Type III distribution (Interagency Advisory Committee on 

Water Data, 1982). Flood magnitudes for recurrence intervals of 

2, 5, 10, 25, 50, 100, 200, and 500 years were computed for each 

station using the following equation:

, (1)

where

Qp is the flood magnitude at a selected exceedance probability, p;

Mx is the mean of the logarithms of the water year peak 

flows;

Kp is a Pearson Type III factor for a coefficient 

of skewness (G) computed from the logarithms of the water year peak flows and a 

selected probability, p; and

Sx is the standard deviation of the logarithms of 

the water year peak flows.

The flood magnitudes for the above-mentioned 

recurrence intervals for each of the streamflow 

gaging stations are listed in table 1. Station frequency 

estimates are listed for each of the 43 streamflow 

gaging stations even though two of the stations were 

not used in the final regression analyses. Floodfrequency estimates from adjacent states were used 

strictly to supplement the database; these estimates 

for sites in other states should not be used for design 

purposes. Persons needing official flood-frequency 

data in other states should contact the USGS office in 

that state. 

Flood-Frequency Analysis

The flood magnitudes obtained from station 

frequency curves were related to basin and climatic 

characteristics, using generalized least squares 

(GLS) multiple-regression analysis. The equations 

resulting from these analyses can be used to estimate 

flood magnitudes for ungaged basins using the 

respective basin characteristics. The basin 

characteristics that were tested for significance in the 

GLS regression analysis were:

• contributing drainage area (A), in square 

miles, which is the contributing drainage area 

upstream from the streamflow gaging station;

• main channel slope (S), in feet per mile, which is 

the average slope between points that are 10 and 85 percent of the distance from the streamflow gaging station 

to the basin divide;

• main channel length (L), in miles, which is the length 

of the main channel between the streamflow gaging 

station and the basin divide;

• lag-time factor (T), which is a basin lag-time factor, 

defined by the ratio L/S1/2 with L and S defined above;

• forest cover (F), in percent, which is the area of forest 

cover expressed as a percentage of the total contributing drainage area; and

• width to length ratio (W/L), which is the ratio of the 

average basin width to basin length. The average basin 

width is the average of the basin widths at points that 

are 33 and 67 percent of the distance from the streamflow gaging station to the basin divide.

Qp log Mx KpS = + x

Figure 2. Locations of streamflow gaging stations used in the study.
Table 1. Peak flow for selected recurrence intervals at selected streamflow gaging stations in Alabama, Tennessee, Mississippi, Georgia, and Flori[mi2, square miles; ft/mi, feet per mile; Q, peak flow, in cubic feet per second, for indicated recurrence interval in years; top line for each entry is the log-Pearson Type III dischaweighted-average or best-estimate discharge; *, station not used in regional analysis] Station number Station name Drainage area (mi2) Period of record used (years) Slope (ft/mi) Q2 Q5 Q10 Q25 Q50 Q1

02342200 Phelps Creek near Opelika, Ala. 6.67 16 (1959–74) 31.0 812 808 1,490 1,450 2,020 1,940 2,760 2,650 3,350 3,240 3,9

3,8

02343700 Stevenson Creek near Headland, Ala. 14.0 15 (1960–70) 30.8 1,060 1,090 1,830 1,930 2,450 2,670 3,370 3,780 4,150 4,700 5,0

5,6

02363005 Pea River Tributary near Roeton, Ala. 0.76 13 (1990–2002) 78.4 136 138 256 260 355 360 504 508 631 633 7

7

02363055 Moores Branch near Victoria, Ala. 2.17 10 (1973–82) 65.8 276 285 384 441 457 593 552 817 625 988 6

1,1

02365310 Grants Branch Tributary near Fadette, Ala. 1.44 10 (1972–81) 39.6 367 344 650 567 878 725 1,210 969 1,490 1,190 1,8

1,4

02371200 Indian Creek near Troy, Ala. 8.87 30 (1959–86) (1990, 1994) 27.1 569 588 1,180 1,240 1,780 1,870 2,840 2,910 3,880 3,870 5,2

5,0

02400033 Nances Creek near White 

Plains, Ala.

4.62 11

(1971–81)

138 693

675

1,0001,000

1,2101,280

1,4701,700

1,6702,030

1,82,3

02407900* Paint Creek near Marble 

Valley, Ala.

12.7 13

(1960–72)

31.3 1,410

1,390

3,2502,890

5,1404,050

8,4805,840

11,800

7,560

16,0

9,6

02409540 Proctor Creek near Rockford, 

Ala.

1.01 10

(1972–81)

80.0 545

457

788592

956671

1,180

828

1,350

982

1,51,1

02410000 Patterson Creek near Central, 

Ala.

4.91 37

(1952–88)

71.4 627

626

1,0801,080

1,4601,460

2,0502,040

2,5802,560

3,13,1

02413400 Wedowee Creek above 

Wedowee, Ala.

6.87 14

(1960–72)

(1979)

43.6 904

890

1,2101,250

1,4201,570

1,6802,060

1,8802,450

2,02,8
02414800 Harbuck Creek near 

Hackneyville, Ala.

7.97 21

(1951–70)

(1979)

68.6 1,240

1,200

2,1802,030

2,9902,670

4,2403,650

5,3604,550

6,65,6

02416481 Norrell Branch near 

Dadeville, Ala.

0.50 14

(1999–2003)

123 66.0

70.0

151162

235248

397387

518492

66

02421105 Pintlalla Creek Tributary 

near Sellars, Ala.

0.45 13

(1991–2003)

56.2 152

145

236220

304281

406376

496462

55

02421300 Ivy Creek at Mulberry, Ala. 10.7 13

(1961–73)

(1990)

25.9 470

526

1,1801,340

1,9102,150

3,2103,380

4,5104,460

6,15,7

02424010 Sandy Creek near 

Centerville, Ala.

0.59 17

(1970–80)(1991–96)

139 180

174

298280

395361

541488

667600

87

02427300 Prairie Creek near Oak Hill, 

Ala.

10.3 15

(1960–74)

20.5 1,030

1,030

1,3901,490

1,6501,920

1,9902,570

2,2603,080

2,53,5

02428300 Tallatchee Creek near 

Vredenburgh, Ala.

13.2 16

(1959–74)

16.0 1,530

1,500

2,9302,730

4,2803,750

6,6105,360

8,9106,900

11,8

8,7

02437800 Barn Creek near Hackleburg, 

Ala.

13.1 15

(1959–73)

23.7 1,300

1,300

2,3902,330

3,3403,190

4,8504,490

6,2305,660

7,87,0

02437900* Woods Creek near Hamilton, 

Ala.

14.3 12

(1960–70)

(1972)

31.2 789

853

1,1401,400

1,4001,980

1,7802,850

2,0903,500

2,44,1

02443730 Kincaide Creek Tributary 

near Ethelsville, Ala.

0.24 13

(1991–2003)

88.2 68

68

117117

155156

210215

254263

33

02449400 Jones Creek near Epes, Ala. 11.8 16

(1959–74)

15.9 2,210

2,060

2,9702,710

3,5003,200

4,2104,030

4,7704,760

5,35,5

Table 1. Peak flow for selected recurrence intervals at selected streamflow gaging stations in Alabama, Tennessee, Mississippi, Georgia, and Flori[mi2, square miles; ft/mi, feet per mile; Q, peak flow, in cubic feet per second, for indicated recurrence interval in years; top line for each entry is the log-Pearson Type III discha

weighted-average or best-estimate discharge; *, station not used in regional analysis]

Station 

number Station name

Drainage 

area

(mi2)

 Period of 

record used

(years)

Slope 

(ft/mi) Q2 Q5 Q10 Q25 Q50 Q1
02450200 Dorsey Creek near Arkadelphia, Ala. 13.0 16 (1959–74) 29.9 1,560 1,520 2,240 2,220 2,700 2,780 3,280 3,620 3,730 4,310 4,1

5,0

02462600 Blue Creek near Oakman, Ala. 5.32 22 (1960–73) (1977–84) 61.8 1,580 1,470 2,910 2,440 3,940 2,990 5,380 3,810 6,540 4,600 7,7

5,5

02464146 Turkey Creek near Tuscaloosa, Ala. 6.16 20 (1981–84) (1987–2002) 69.0 626 635 1,190 1,200 1,710 1,710 2,590 2,500 3,430 3,220 4,4

4,0

02465205 Jay Creek near Coker, Ala. 3.65 13 (1964–74) (1997–98) 52.6 369 383 833 836 1,250 1,210 1,900 1,740 2,470 2,200 3,1

2,7

02479980 Crooked Creek near Fairview, Ala. 8.08 12 (1991–2002) 19.5 710 733 1,270 1,340 1,740 1,870 2,450 2,670 3,070 3,340 3,7

4,0

03574700 Big Huckleberry Creek near Belvidere, Tenn. 2.18 20 (1955–74) 18.2 386 381 691 668 938 891 1,300 1,220 1,610 1,510 1,9

1,8

03579800 Miller Creek near Cowan, Tenn. 4.30 24 (1955–78) 88.9 1,590 1,470 2,390 2,040 2,950 2,360 3,670 2,870 4,220 3,350 4,7

3,8

03587200 Bluewater Creek Tributary 

near Leoma, Tenn.

0.49 29

(1955–83)

62.1 148

145

212210

256258

314331

359389

44

02429980 Pollard Mill Branch at 

Paden, Miss.

2.01 34

(1967–2001)

35.2 190

195

359379

503547

727803

924

1,020

1,11,2

02437550 Nicholas Creek Tributary 

near Quincy, Miss.

0.54 34

(1966–2001)

95.0 168

165

266258

340328

446432

533521

66

02448620 Flat Scooba Creek Tributary 

near Scooba, Miss. 

0.44 35

(1967–2001)

48.0 128

126

186185

232235

296308

349369

44

Table 1. Peak flow for selected recurrence intervals at selected streamflow gaging stations in Alabama, Tennessee, Mississippi, Georgia, and Flori[mi2, square miles; ft/mi, feet per mile; Q, peak flow, in cubic feet per second, for indicated recurrence interval in years; top line for each entry is the log-Pearson Type III discha

weighted-average or best-estimate discharge; *, station not used in regional analysis]

Station 

number Station name

Drainage 

area

(mi2)

 Period of 

record used

(years)

Slope 

(ft/mi) Q2 Q5 Q10 Q25 Q50 Q1
02469672 Little Okatubba Creek near 

Quitman, Miss.

4.35 19

(1966–84)

43.0 787

762

1,1401,100

1,3801,360

1,6901,750

1,9202,060

2,12,3

02478600 Granny Branch at Piave, 

Miss.

0.69 18

(1967–84)

55.6 230

219

326308

387371

461468

515547

56

02327860 Popple Branch near 

Whigham, Ga.

1.71 25

(1977–2001)

37.6 170

176

302 327

413 468

584684

734862 

9

1,0

02350685 Choctahatchee Creek 

Tributary near Plains, Ga.

0.32 24

(1977–2001)

38.1 23.0

25.0

72.081.0

136150

273273

431393

65

02388200 Storey Mill Creek near 

Summerville, Ga.

6.02 23

(1966–87)

(1990)

112 777

772

1,2201,220

1,5501,580

2,0202,130

2,3902,570

2,73,0

02397750 Duck Creek above Lafayette, 

Ga.

6.34 12

(1965–74)

(1977, 1990)

71.7 777

772

1,0901,140

1,3201,480

1,6402,010

1,9102,440

2,12,8

02411735 McClendon Creek Tributary 

near Dallas, Ga.

0.88 25

(1977–2001)

59.4 238

232

357347

449438

582578

693698

88

02358998 Holliman Branch near Altha, 

Fla.

2.04 18

(1969–86)

50.5 297

299

539543

743747

1,0501,050

1,3201,320

1,61,6

02366859 Pate Branch near Freeport, 

Fla.

1.87 19

(1969–86)

(1989)

31.0 172

181

280319

367454

494655

602814

79

02370750 Hurricane Branch near 

Milton, Fla.

2.95 23

(1961–82)

(1989)

54.5 119

132

440482

900924

1,9801,740

3,3202,590

5,33,7

Table 1. Peak flow for selected recurrence intervals at selected streamflow gaging stations in Alabama, Tennessee, Mississippi, Georgia, and Flori[mi2, square miles; ft/mi, feet per mile; Q, peak flow, in cubic feet per second, for indicated recurrence interval in years; top line for each entry is the log-Pearson Type III discha

weighted-average or best-estimate discharge; *, station not used in regional analysis]

Station 

number Station name

Drainage 

area

(mi2)

 Period of 

record used

(years)

Slope 

(ft/mi) Q2 Q5 Q10 Q25 Q50 Q1
8 Magnitude and Frequency of Floods on Small Rural Streams in Alabama

The climatic characteristics that were considered and 

compiled for each station included mean annual precipitation 

(P) and the 24-hour 2-year rainfall intensity (I24,2). These basin 

characteristics were computed and checked for each station in 

the first year of this study.

Multiple regression analyses were performed relating the 

station frequency curves to basin characteristics using ordinary 

least squares (OLS) regression techniques. Results of the 

analysis showed that contributing drainage area, main channel 

slope, and forest cover were considered to be the explanatory 

variables of greatest relevance to peak flows predicted at the 

streamflow gaging stations. Each of these basin characteristics 

were used in GLS regression analyses.

A plot of the 50-year peak flow and drainage area for all 

43 streamflow gaging stations showed that there was no distinct 

correlation between geographic location and the magnitudes of 

peak flows at streamflow gaging stations. Neither stations north 

or south of the Fall Line plotted consistently on one side of a 

best-fit line through the data points. 

Additional analyses were performed using qualitative 

variables (indicating region) along with cross products of all the 

variables to determine whether the resulting equations might be 

improved. Using OLS regression techniques, this exploratory 

analysis indicated that there was some geographical bias for the 

smaller recurrence interval floods (2-year to 25-year) for the 

non-Coastal Plain region of the State (north of Fall Line). This 

analysis indicated that there should be two sets of regression 

equations; one for north of the Fall Line for the 2-year to 25-year 

recurrence intervals, and one equation for south of the Fall Line 

for the 2-year to 25-year recurrence intervals. The equations for 

each recurrence interval have the same slope but different 

intercepts. For each recurrence interval between 50 and 500 

years, however, only one equation was needed to estimate floodfrequency values for both regions. When a qualitative variable 

for a region was incorporated into GLS regression analyses, the 

resulting equations yielded estimated peak flows that were 

within 5 percent of the previously developed statewide 

equations and standard errors that were slightly higher. 

Consequently, the analyses indicated that using one regression 

equation for each recurrence interval was not biased and, as 

such, is applicable statewide.

GLS regression analysis was applied to the study area with 

contributing drainage area, channel slope, and percent forest 

cover designated as the explanatory variables used in the 

analysis. Stedinger and Tasker (1985, 1986) have shown that 

GLS regression analysis can provide more accurate estimates of 

regression coefficients and better estimates of the regression 

model error than OLS regression analysis. OLS regression 

analysis does not account for the errors associated with 

estimates of flood magnitude, varying with the length of 

observed record, nor does it account for the cross correlation of 

concurrent peak flow data between sites. GLS regression 

analysis accounts for these errors by using a weighted matrix so 

that sites are weighted proportionally according to standard 

errors and the cross correlation of the peak flow estimates. GLS 

regressions were performed using multiple combinations of the 

three explanatory variables. These combinations included the 

following four scenarios: drainage area; drainage area and 

slope; drainage area and percent forest; and drainage area, slope, 

and percent forest. The scenario that produced the equations 

with the lowest standard error included drainage area as the only 

explanatory variable.

The accuracy of a flood-frequency relation can be 

expressed in two ways: as the average standard error of 

prediction (SEp) or as equivalent years of record. The SEp is a 

measure of how well the regression relation will estimate flood 

magnitudes when applied to ungaged basins. The SEp can also 

be expressed as equivalent years of record (Hardison, 1971). 

The equivalent years of record represents the number of years of 

peak flow record necessary to provide a flood estimate with 

accuracy equal to that of the regional regression flood estimate. 

For example, the 100-year flood estimate from the regression 

relation could be estimated with the same degree of accuracy as 

that which could be obtained from 14 years of actual peak flow 

record (table 2). After conducting initial regression analyses, a 

second set of analyses was performed using 41 of the 43 initial 

streamflow gaging stations. Based on the plot of the 50-year 

flow and drainage area for all of the streamflow gaging stations, 

Table 2. Accuracy of flood-frequency relations for small 

rural streams in Alabama.

Recurrence 

interval 

(years)

Standard error of 

prediction 

(percent)

Equivalent years 

of record

2 53 2

5 35 5

10 30 9

25 29 13

50 31 14

100 35 14

200 40 13

500 47 12

two of the stations (Paint Creek near Marble Valley, Alabama, 

02407900, and Woods Creek near Hamilton, Alabama, 

02437900) were determined to have flood frequencies that were 

not closely related to the flood frequencies of the other stations. 

The rating curves (stage and flow relation) for these two sites 

were poorly defined at the upper end. The larger water year peak 

flows for both stations were based on extensions of these poorly 

defined ratings. For this reason, both streamflow gaging stations 

were excluded in the final regression analysis. Removing these 

stations lowered the SEp by about 5 percent for floods having a 

10-year or greater recurrence interval. The flood-frequency 

relations developed from this final set of regression analyses are 

summarized in table 3. The SEp and the equivalent years of 

record for the regression relations are listed in table 2. A 

comparison between the SEp for the regional regression 

equations published by Atkins (1996) and the SEp for the 

equations presented in this report are provided in table 4. 
Use of Flood-Frequency Relations at Gaged Sites 9

Table 3. Flood-frequency relations for small rural streams in 

Alabama.

[A, contributing drainage area, in square miles; Q, peak flow, in cubic feet per 

second]

Recurrence interval (years) Regression equation

2 Q = 189A0.742

5 Q = 331A0.732

10 Q = 449A0.731

25 Q = 626A0.732

50 Q = 776A0.733

100 Q = 941A0.733

200 Q = 1,126A0.732

500 Q = 1,401A0.731

Use of Flood-Frequency Relations at 

Gaged Sites

Flood estimates at gaged sites for a selected recurrence 

interval can be determined best by weighting the regression and 

station flood estimates for the specified recurrence interval 

using the number of years of station record and the accuracy of 

the regression equations expressed as equivalent years of 

record. This procedure for estimating flood magnitude for a 

given recurrence interval at gaged sites can be expressed in the 

following equation (Interagency Advisory Committee on Water 

Data, 1982):

, (2)

where

Qw is the weighted flood estimate for the streamflow 

gaging station for the selected recurrence interval, in 

cubic feet per second (ft3

/s);

N is the number of years of station record used to compute 

Qg from table 1;

Qg is the flood estimate from the log-Pearson Type III 

analysis for the selected recurrence interval, in ft3

/s, at 

the streamflow gaging station;

EY is the equivalent years of record for Qr from table 2; 

and

Qr is the flood estimate from the regional flood-frequency 

equation from table 3 for the selected recurrence interval, in ft3/s.

Use of Flood-Frequency Relations 

at Ungaged Sites

Flood magnitudes at ungaged sites can be 

estimated by computing the drainage area for the site of 

interest and then using the appropriate flood-frequency 

relation from table 3. Flood estimates can be improved 

if the ungaged site is located on the same stream as a 

gaged site having 10 or more years of peak flow record 

and if the drainage area of the ungaged site is 

equivalent to 0.5 to 1.5 times the drainage area of the 

gaged site. The weighted flow, Qw, at the gaged site can 

be transferred to the ungaged site using the equation

, (3)

and a weighted flood estimate at the ungaged site can 

be computed by the equation

, (4)

where 

Qu is the flood estimate at the ungaged site after transferring the weighted peak flow from the gaged site, in 

ft3

/s;

Qw is the weighted flood estimate at the gaged site for the 

selected recurrence interval, from table 1, in ft3

/s;

Qu(w) is the weighted flood estimate at the ungaged site, in 

ft3

/s;

Qr is the flood estimate from the statewide flood-frequency 

equation for the selected recurrence interval, in ft3

/s;

b is the exponent of the drainage area term of the floodfrequency relation for the applicable recurrence interval, from table 3;

Au is the drainage area of the ungaged site, in mi2;

Ag is the drainage area of the gaged site, in mi2; and

is the absolute difference in drainage areas between the 

ungaged site and the gaged site, in mi2.

Qw log N Qg ( ) log EY Qr + ( ) log

N EY + = ---------------------------------------------------------

Qu

Au

Ag

-----

⎝ ⎠ ⎜ ⎟ ⎛ ⎞ b

= Qw

Qu w( )

2∆A

Ag

----------

⎝ ⎠ ⎜ ⎟ ⎛ ⎞ b

Qr 1

2∆A

Ag

---------- – ⎝ ⎠ ⎜ ⎟ ⎛ ⎞ = + Qu

∆A

Table 4. Comparison of average standard errors of prediction for 

the four regional regression equations published by Atkins (1996) and 

average standard errors from statewide regression equations for small 

rural streams in Alabama.

Recurrence 

interval 

(years)

Standard error of prediction (percent)

Region 1 Region 2 Region 3 Region 4 Statewide

equations

2 35 40 37 38 53

5 34 36 35 33 35

10 35 35 34 33 30

25 37 35 33 35 29

50 39 36 33 38 31

100 41 37 33 42 35

200 43 39 34 46 40

500 46 43 35 52 47
10 Magnitude and Frequency of Floods on Small Rural Streams in Alabama

Flood-Frequency Relations for Streams 

in Adjacent States

Flood-frequency relations were developed for 16 streamflow gaging stations that are in adjacent states. These relations 

were used with those developed for the streams in Alabama to 

determine the regression equations presented earlier. Floodfrequency relations for sites outside of Alabama will differ 

from those published in their respective states because of 

differences in the periods of record used for the studies and 

the differences in the equations used for best-estimate 

weighting (table 1).

Summary

Flood flows for recurrence intervals of 2, 5, 10, 25, 50, 

100, 200, and 500 years were determined for 27 streamflow 

gaging stations on small rural streams in Alabama using the logPearson Type III frequency distribution. The data for 25 of 

these sites in Alabama and for 16 stations in parts of the 

adjacent States of Florida, Georgia, Mississippi, and Tennessee 

were used to develop flood-frequency relations, which can be 

used to estimate flood flows for recurrence intervals of 2, 5, 10, 

25, 50, 100, 200, and 500 years for ungaged, unregulated, rural 

streams in Alabama having drainage areas less than 15 square 

miles. These flood-frequency relations are applicable where 

urbanization, channelization, and backwater do not 

significantly affect the site. 

Drainage area was determined to be the most important 

variable used in predicting flood flow in multiple regression 

analyses using generalized least-squares methods. These 

regression methods were used to define the final regression 

coefficients used in the predictive equations and prediction 

errors.

References

Atkins, J.B., 1996, Magnitude and frequency of floods in 

Alabama: U.S. Geological Survey Water-Resources 

Investigations Report 95-4199, 234 p.

Barnes, H.H., Jr., and Golden, H.G., 1966, Magnitude and 

frequency of floods in the United States, Part 2-B, South 

Atlantic and Eastern Gulf of Mexico basins: U.S. Geological 

Survey Water-Supply Paper 1674, 409 p.

Gamble, C.R., 1965, Magnitude and frequency of floods in 

Alabama: Alabama Highway Department HPR Report No. 5, 

42 p.

Hains, C.F., 1973, Floods in Alabama, magnitude and 

frequency: Alabama Highway Department, 174 p.

Hardison, C.H., 1971, Prediction error of regression estimates 

of streamflow characteristics at ungaged sites: U.S. 

Geological Survey Professional Paper 750-C, p. c228–c236.

Interagency Advisory Committee on Water Data, 1982, 

Guidelines for determining flood flow frequency: Bulletin 

17B, variously paged.

Miller, J.A., 1990, Ground water atlas of the United States, 

Segment 6, Alabama, Florida, Georgia, and South Carolina: 

U.S. Geological Survey Hydrologic Investigations Atlas 

0730-G.

Olin, D.A., 1984, Magnitude and frequency of floods in 

Alabama: U.S. Geological Survey Water-Resources 

Investigations Report 84-4191, 105 p.

Olin, D.A., and Bingham, R.H., 1977, Flood frequency of small 

streams in Alabama: Alabama Highway Department, HPR 

Report 84-4191, 105 p.

Olin, D.A., and Bingham, R.H., 1982, Synthesized flood 

frequency for urban streams in Alabama: U.S. Geological 

Survey Water-Resources Investigations Report 82-683, 35 p.

Pierce, L.B., 1954, Floods in Alabama, magnitude and 

frequency: U.S. Geological Survey Circular 342, 105 p.

Speer, P.R., and Gamble, C.R., 1964, Magnitude and frequency 

of floods in the United States, Part 3-B, Cumberland and 

Tennessee River basins: U.S. Geological Survey WaterSupply Paper 1676, 340 p.

Stedinger, J.R., and Tasker, G.D., 1985, Regional hydrologic 

analysis 1. Ordinary, weighted and generalized least squares 

compared: Water Resources Research, v. 21, no. 9, p. 1421–

1432.

Stedinger, J.R., and Tasker, G.D., 1986, Correction to 

“Regional hydrologic analysis 1. Ordinary, weighted and 

generalized least squares compared”: Water Resources 

Research, v. 22, no. 5, p. 844.

U.S. Geological Survey, 1986, National water summary 

1985—Hydrologic events and surface-water resources: U.S. 

Geological Survey Water-Supply Paper 2300, 506 p.