Comparison of the 2 -, 25 -, and 100 - year recurrence interval floods computed from observed data with the 1995 urban flood - frequency estimating equations for Georgia

GA
T700 !V\ l
\~9'1
F5

COMPARISON OFTHE 2-, 25-, AND 100-YEAR RECURRENCE INTERVAL FLOODS COMPUTED FROM
OBSERVED DATA WITH THE 1995 URBAN FLOODFREQUENCY ESTIMATING EQUATIONS FOR GEORGIA

u.s. GEOLOGICAL SURVEY

Prepared in cooperation with the
GEORGIA DEPARTMENT OF TRANSPORTATION and
FEDERAL HIGHWAY ADMINISTRATION

Water-Resources Investigations Report 97-4118

COMPARISON OFTHE 2-,25-, AND 100-YEAR RECURRENCE INTERVAL FLOODS COMPUTED FROM OBSERVED DATA WITH THE 1995 URBAN FLOODFREQUENCY ESTIMATING EQUATIONS FOR GEORGIA
By Ernest J. Inman
U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 97-4118
Prepared in cooperation with the GEORGIA DEPARTMENT OF TRANSPORTATION and FEDERAL HIGHWAY ADMINISTRATION
Atlanta, Georgia 1997

U.S. DEPARTMENT OF THE INTERIOR BRUCE BABBITT, Secretary
U.s. GEOLOGICAL SURVEY Gordon P. Eaton, Director
Any use of trade, product, or firm names is for descriptive purposes only, and does not imply endorsement by the U.S. Government

For additional information,write to:
District Chief U.S. Geological Survey Peachtree Business Center 3039 Amwiler Road, Suite 130 Atlanta, GA 30360-2824

Copies of this report can be purchased from:
U.S. Geological Survey Branch of Information Services Denver Federal Center Box 25286 Denver, CO 80225-0286

CONTENTS
Abstract 1 Introduction 2
Background 2 Purpose and scope 2 Flood-frequency analyses 6 Statistical methods used for flood-frequency comparisons 6 Comparison of flood-frequency data 6 Results of comparisons 13 Summary 14 References cited 14

ILLUSTRATIONS

Figure 1. Figures 2-4.
2.
3.
4.

Map showing the four flood-frequency regions in Georgia and cities where gaging stations were used in this study and in the previous statewide urban flood-frequency study by Inman (1995) 3
Graphs showing:
Comparison of 2-year recurrence interval floods from observed data and estimates from regional regression equations for the 26 urban stations used in this study, and the regression equation of the best-fit line of these discharges, with the line of equality 8
Comparison of 25-year recurrence interval floods from observed data and estimates from regional regression equations for the 26 urban stations used in this study, and the regression equation of the best-fit line of these discharges, with the line of equality 8
Comparison of 100-year recurrence interval floods from observed data and estimates from regional regression equations for the 26 urban stations used in this study, and the regression equation of the best-fit line of these discharges, with the line of equality 9

TABLES

Table 1. 2. 3. 4.
5.
6.

Regional flood-frequency equations for urban streams in Georgia 4 Gaging stations used in the statewide urban comparison study, by city 4 Flood-frequency data for the urban stations used in this study 7 Flood-frequency data for the 2-,25-, and 100-year floods from urban stations with observed
data, from the statewide flood-frequency estimating equations, and from the most recent (latest) 20 years of simulated data from the urban stations 10 Peak discharges and water years of the two highest flood events, from observed and simulated records for urban stations used in this study 12 Results of comparison testing of flood-frequency data based on student's t-test at 0.05 level of significance and statistical analysis of regression results for the final 26 urban stations used in this study 13

iii

COMPARISON OF THE 2-, 25-, AND 100-YEAR
RECURRENCE INTERVAL FLOODS COMPUTED
FROM OBSERVED DATA WITH THE 1995 URBAN FLOOD-FREQUENCY ESTIMATING
EQUATIONS FOR GEORGIA
By Ernest J. Inman

ABSTRACT
Flood-frequency relations were computed for 28 urban stations, for 2-, 25-, and 100-year recurrence intervalfloods and the computations were compared to corresponding recurrence interval floods computed from the estimating equations from a 1995 investigation. Two stations were excluded from further comparisons or analyses because neither station had a significant flood during the period of observed record.
The comparisons, based on the student's t-test statistics at the 0.05 level of significance, indicate that the mean residuals of the 25- and 100-year floods were negatively biased by 26.2 percent and 31.6 percent, respectively, at the 26

stations. However, the mean residuals ofthe 2-year floods were 2.5 percent lower than the mean of the 2-year floods computed from the equations, and were not significantly biased. The reason for this negative bias is that the period of observed record at the 26 stations was a relatively dry period. At 25 of the 26 stations, the two highest simulated peaks used to develop the estimating equations occurred many years before the observed record began. However, no attempt was made to adjust the estimating equations because higher peaks could occur after the period of observed record and an adjustment to the equations would cause an underestimation of design floods.

INTRODUCTION
A knowledge of flood characteristics of streams is essential for designing roadway drainage structures, establishing flood-insurance rates, and for other uses by urban planners and engineers. Because urbanization can produce significant changes in the flood-frequency characteristics of streams, natural (rural) basin floodfrequency relations are not applicable to urban streams.
Recognizing the need for additional data for comparison or verification of the statewide urban estimating equations presented by Inman (1995), the U.S. Geological Survey (USGS), in cooperation with the Georgia Department of Transportation and the Federal Highway Administration, began a project in 1987 to monitor urban floods in Georgia. The study was expanded to cover the South Georgia areas of Albany, Moultrie, Thomasville, and Valdosta in 1994.
Background
Recognizing the need for reliable urban peak-flood data and improved equations for estimating floods in Georgia, the USGS collected data at 65 rainfall-runoff stations-beginning in 1973 in Metropolitan Atlanta (Inman, 1983); continuing in 1978 in Athens, Augusta, Columbus, Rome, and Savannah (Inman, 1988); and continuing in 1986 in Albany, Moultrie, Thomasville, and Valdosta, Ga. (Inman, 1995) (fig. 1). These data were used to calibrate a USGS rainfall-runoff model (RRM), as described by J.M. Bergmann, EJ. Inman, and A.M. Lumb (U.S. Geological Survey, written commun.,1990).
After the RRM was successfully calibrated for each drainage basin, long-term rainfall and daily panevaporation data from nearby National Weather Service stations were used to synthesize about 60 to 90 years of annual peak flows, depending on the length of the long-term rainfall. These synthesized peaks were used to develop flood-frequency relations for each basin. The final step in analyzing these data was to develop regression equations that can be used to estimate the magnitude and frequency of floods at ungaged urban sites in Georgia. Detailed descriptions of the RRM calibration, the long-term simulation, and the regression analyses were given by Inman (1995). The estimating equations for the four flood-frequency regions in Georgia for the 2- through 500-year floods, also given in Inman (1995), are shown in table 1.

Six to eight years of observed annual peak flows are insufficient for developing reliable flood-frequency estimates. Collection of additional flood data at about 40 percent of the stations used in the statewide report (Inman, 1995) would provide a data base of sufficient length for verification or comparison with the floodfrequency data computed using the statewide estimating equations.
Purpose and Scope
This report describes the results of the expanded study to compare the results of the statewide floodfrequency estimating equations presented by Inman (1995) with the flood-frequency data computed from observed data. To accomplish the project objectives, 28 urban stations were selected from previous urban flood-frequency investigations to collect additional data through September 1996, which provides a data base of sufficient length to compare flood frequencies.
At least two urban stations were selected in each of the 10 cities from the previous study (Inman, 1995) (fig. 1, table 2). Stability of the stage-discharge relations at each site was the primary selection criterion; together with range in size of drainage areas, and percent impervious areas.
The U.S. Geological Survey is responsible for the information contained in this report. The report does not necessarily reflect the official view or policy of the Georgia Department of Transportation or the Federal Highway Administration, nor does the report constitute a standard, specification, or regulation.

2

EXPLANATION

City

Athens;: Number of urban gages



~ in previous study

<,
Number of urban gages

in this study

o

20

40

60 MILES

I

I I

o 20 40 60 KILOMETERS

Base from U.S. Geological Survey digital files
Figure 1. Four flood-frequency regions in Georgia and cities where gaging stations were used in this study and in the previous statewide urban flood-frequency study by Inman (1995).

3

Table 1. Regional flood-frequency equations for urban stream in Georgia [UQT' peak discharge for an urban drainage basin, in cubic feet per second; A, drainage area, in square miles; TIA, area that is impervious to infiltration of rainfall, in percent; , plus-minus; table from Inman (1995)]

2 167A0.73TIA0.31 34 107A0.73TIA0.31 40 145A0.70 TIA0.31 35 54.6A0.69 TIA0.3 I 34 110A0.66TIA0.3 I 34

5 301A0.71TIA0.26 31 183A0.71TIA0.26 36 258A0.69TIA0.26 31 99.7A0.69 TIA0.26 31 237A0.66TIA0.26 31

10 405A0.7oTIA0.21 31 249A0.7oTIA0.21 35 351A0.7oTIA0.21 31 IMAO.71TIAO.21 32 350A0.68 TIA0.21 30

25 527AO.70TIA0.20 29

33 452A0.7oTIA0.20 29 226Ao.71TIAo.20 30 478A0.69 TIA0.20 29

50 643A0.69TIA0.18 28 379AO.69 TIAO.18 33 548A0.70TIA0.18 29

30 596Ao.70 TIAO.18 28

100 762A0.69TIA0.17 28 440A0.69 TIA0.17 33 644A0.70TIA0.17 29 355AO.72TIAo.17 30 717A0.70 TIA0.1 7 28

200 892A0.68TIA0.16 28 505A0.68 TIA0.16 34

28 428AO.72TIA0.16 30 843A0.70 TIA0.16 28

500 1063A0.68TIA0.14 28 589AO.68TIAO. 14 34 888A0.70TIA0.14 28 531Ao.72TIAO. 14 30

28

Table 2. Gaging stations used in the statewide urban comparison study, by city

Station numberl/

Station name

02352605 Flint River tributary 1, at Albany 02352964 Percosin Creek tributary, at Albany

02217505 Brooklyn Creek, at Athens 02217905 Tanyard Creek, at Athens

02203835 Shoal Creek, near Atlanta 02203845 Shoal Creek tributary, near Atlanta 02203884 Conley Creek, near Forest Park

Location

Albany Athens Atlanta

Lat 3132'52", long 8409'28", Dougherty County, at culvert on Emily Avenue, at Albany
Lat 3135'47", long 8414'03", Dougherty County, at culvert on Dean's Road, at Albany
Lat 3356'32", long 8324'07", Clarke County, at culvert on Dudley Drive, at Athens
Lat 3357'05", long 8322'42", Clarke County, at culvert on Baxter Street, at Athens
Lat 3344'48", long 8416'50", DeKalb County, at culvert on Line Street, near Atlanta
Lat 3343'05", long 8415'45", DeKalb County, at culvert on Glendale Drive near Atlanta
Lat 3338'08", long 8420'38", Clayton County, at culvert on Rock Cut Road, near Forest Park

4

Table 2. Gaging stations used in the statewide urban comparison study, by city-Continued

Station number ll

Station name

Location

02336090 North Fork Peachtree Creek tributary, near Chamblee 02336102 North Fork Peachtree Creek tributary, near Atlanta 02336238 South Fork Peachtree Creek tributary, near Atlanta 02336700 South Utoy Creek tributary, at East Point

Lat 3350'53", long 8417'51", DeKalb County, at culvert on Meadowcliff Drive, near Chamblee
Lat 3351'20", long 8419'19", DeKalb County, at culvert on Drew Valley Road, near Atlanta
Lat 3347'11", long 8420'29", DeKalb County, at culvert on East Rock Springs Road, near Atlanta
Lat 3341'25", long 8428'05", Fulton County, at culvert on Headland Drive, at East Point

Augusta

02196725 Oates Creek, at Augusta 02196760 Rocky Creek tributary, at Augusta

Lat 3327'19", long 8202'23", Richmond County, at culvert on White Road, at Augusta
Lat 3327'01", long 8202'51", Richmond County, at culvert on U.S. Highways 78 and 278, at Augusta

Columbus

02341544 Mill Branch, at Columbus 02341546 Bull Creek tributary, at Columbus 02341548 Lindsey Creek tributary, at Columbus

Lat 3228'19", long 8453'58", Muscogee County, at culvert on Chalbena Road, at Columbus
Lat 3228'38", long 8455'36", Muscogee County, at culvert on Woodland Drive, at Columbus
Lat 3231'33", long 8456'21", Muscogee County, at culvert on Canberra Avenue, at Columbus

Moultrie

02318565 Okapilco Creek tributary, at Moultrie 02327203 Tributary to Ochlockonee River tributary, at Moultrie

Lat 3110'12", long 8346'40", Colquitt County, at culvert on Southeast 10th Street, at Moultrie
Lat 3109'54", long 8347'35", Colquitt County, at culvert on Southwest 4th Street, at Moultrie

Rome

02395990 Etowah River tributary, near Rome 02396510 Silver Creek tributary no. 2 at Lindale Road, near Rome 02396550 Silver Creek tributary no. 3, at Rome

Lat 3416'02", long 8508'18", Floyd County, at culvert on Atteiram Road, near Rome
Lat 3412'56", long 8510'09", Floyd County, at culvert on Lindale Road, near Rome
Lat 3413'26", long 8509'14", Floyd County, at culvert on U.S. Highway 27, 0.4 mile north of U.S. Highway 411 interchange, at Rome

Savannah

02203543 Wilshire Canal, near Savannah 02203544 Wilshire Canal tributary, near Savannah

Lat 3159'21", long 8108'15", Chatham County, at culvert on Tibet Avenue, near Savannah
Lat 3158'25", long 8108'20", Chatham County, at culvert on Windsor Road, near Savannah

Thomasville

02327467 Oquina Creek, at Thomasville 02327471 Bruces Branch, at Thomasville

Lat 3050'12", long 8359'38", Thomas County, at culvert on Wolf Street, at Thomasville
Lat 3050'39", long 8358'36", Thomas County, at culvert on North Hansell Street, at Thomasville

Valdosta

02317564 Dukes Bay Canal, at Valdosta 02317566 Dukes Bay Canal at Industrial Boulevard, at Valdosta 023177554 Onemile Branch, at Wainwright Drive at Valdosta

Lat 3049'13", long 8316'20", Lowndes County, at culvert on South Patterson Street at intersection with State Route 94, at Valdosta
Lat 3048'34", long 8315'43", Lowndes County, at culvert on Industrial Boulevard, at Valdosta
Lat 3050'34", long 8318'04", Lowndes County, at culvert on Wainwright Drive, at Valdosta

lIu.S. Geological Survey downstream order number.

5

FLOOD-FREQUENCY ANALYSES
A log-Pearson Type III frequency distribution was fitted to the logarithms of the annual peak discharges at each of the 28 urban stations in accordance with "Guidelines for Determining Flood Flow Frequency," Bulletin l7B (Interagency Advisory Committee on Water Data, 1982) recommendations. These recommendations include the proper handling of low and high outliers. Skew coefficients were computed directly from the observed data. No attempt was made to adjust the skew coefficients of the frequency curves based on regionalized skews because the data did not meet the criteria specified in the Interagency Advisory Committee on Water Data (1982). The generalized skew-coefficient map in Interagency Advisory Committee on Water Data (1982), was used in the adjustment computations only for rural watersheds and is not applicable to urban flood peaks.
Frequency curves for the observed annual flood peaks of the 28 urban stations represent an "as is" storage condition that may be present at upstream roadway embankments with culverts of limited capacity, or minor floodplain storage. The annual peaks for the frequency curves in the earlier study were simulated with the RRM using the same storage conditions of the observed peaks. Therefore, any difference in flood frequency is due to temporal climatological differences. At least 10 years of record were available at the 28 urban stations as recommended in the Interagency Advisory Committee on Water Data (1982). Eighteen of the urban stations had 18 or more years of record and one station in Atlanta had 33 years. Flood-frequency data from the log-Pearson Type III frequency analysis for selected recurrence intervals at the 28 urban stations are shown in table 3.
Statistical Methods Used for Flood-Frequency Comparisons
The statistical analyses and computations for the flood-frequency comparisons were conducted using procedures defined by the SAS Institute, Inc. (1989). All peak-discharge data were transformed to logarithmic units before conducting the statistical analysis and computations. The logarithmic residual, x, of the estimated discharges minus the observed discharges for each series of differences for the 2-, 25-, and 100-year floods were analyzed using the student's ttest at the 0.05 level of significance, to determine if the
mean, X, was significantly different from zero. A mean
residual (x) significantly different from zero indicates possible bias in the flood-frequency estimating

equations, or a bias of the observed discharge due to the time of the sampling period. The SAS univariate procedure was used for all mean-bias testing and to determine if all distributions were normal according to the Shapiro-Wilk statistic (SAS Institute, Inc.,1989).
In order to determine if a bias exists and if the bias varies with the magnitude of discharge, logarithms of observed discharges are regressed against logarithms of discharges estimated from regional regression equations. Then, if the slopes of the regression lines are significantly different from an equal yield line, a bias may exist. In particular, if the slopes are significantly different from 1.0, the bias is a function of magnitude of flow. The student's t-test at the 0.05 significance level is used to determine if the slopes of the regressions is different from 1.0 and if the intercepts are different from zero. Iman and Conover's (1983) methodology of using the student's t-test determines if the slopes or intercepts are biased. Plots of these comparisons are shown in figures 2, 3, and 4.
Data from the 26 urban stations were analyzed as one group, rather than dividing the stations into regions, because some regions had only five or six stations. Groups having five or six stations are too small to make reliable statistical analyses of basins.
Comparison of Flood-Frequency Data
Flood-frequency data are used to determine if significant differences exist between the flood frequency of observed discharges from the 28 selected urban stations and the discharges computed from the estimating equations for the four urban flood-frequency regions (Inman, 1995). Flood-frequency data for the 2-, 25-, and 100-year floods from the 28 urban stations with observed data, from the estimating equations, and from the most recent (latest) 20 years of simulated data at each of the 28 urban stations are shown in table 4. Stations 02196725 in Augusta and 02318565 in Moultrie were deleted from further comparisons, because neither station had as much as a 2-year flood during the period of observed record.

6

Table 3. Flood-frequency data for the urban stations used in this study

Station number

Floodfrequency
region

02352605

3

02352964

3

02217505

2

02217905

2

02203835

2

02203845

2

02203884

2

02336090

02336102

02336238

02336700

02196725

3

02196760

3

02341544

2

02341546

2

02341548

2

02318565

4

02327203

4

02395990 02396510 02396550

02203543

3

02203544

3

02327467

4

02327471

4

02317564

3

02317566

3

023177554

4

Drainage area
(in square miles)

Period of record

0.16

1987-96

0.05

1987-96

1.44

1979-96

0.42

1979-96

3.43

1973-96

0.84

1973-96

1.88

1974-96

0.32

1973-96

2.19

1973-96

0.90

1974-96

0.79

1964-96

1.44

1979-88

1.56

1979-96

1.58

1977-96

0.26

1977-96

1.42

1977-96

0.27

1986-96

0.38

1986-96

0.37

1979-96

0.04

1979-96

0.19

1979-96

0.95

1979-96

0.18

1979-96

1.07

1986-96

0.21

1986-95

1.27

1986-96

3.81

1986-96

2.66

1987-96

Stream statistical data

Mean (log)

Standard deviation
(log)

Albany

1.622

0.296

0.691

.282

Athens

2.722

.131

2.617

.163

Atlanta

2.876

.164

2.613

.176

2.826

.168

2.062

.301

2.855

.118

2.777

.112

2.481

.117

Augusta

2.155

.139

2.554

.194

Columbus

2.763

.162

1.870

.196

2.618

.166

Moultrie

1.697

.151

2.147

.153

Rome

1.975

.265

1.278

.232

2.153

.100

Savannah

2.416

.130

1.911

.108

Thomasville

2.335

.131

1.974

.134

Valdosta

2.368

.143

2.539

.156

2.860

.074

Skew of logarithms
-0.528 1.035
0.605 0.272
0.453 -0.427 -0.073 0.206 -0.281 0.512 0.122
-0.585 0.530
-0.077 0.941 0.025
1.221 0.425
-0.867 0.008 -0.288
0.586 -0.409
0.320 1.836
-0.992 0.463 -0.262

Recurrence interval flood (in cubic feet per second)

2-year 25-year

100-year

44

121

4

19

512

948

407

826

731 1,540

422

782

672 1,310

113

406

726 1,120

586

983

301

491

147

234

345

844

582 1,100

69

186

414

813

46

103

137

273

103

224

19

48

144

208

253

465

83

121

213

379

86

185

246

366

336

685

730

963

156 36
1,210 1,070
2,050 925
1,610 640
1,280 1,200
581
262 1,200
1,350 286
1,020
149 354
263 66
232
593 134
468 278
395 901 1,040

7

10,000 ~-----'-----.------r---.---r---.--,---,--,------.---r--,.----,--~r-r-T-'

Cl
ooZw
(f)
a:
~ 1,000

I-

W

W

LL

o

iIi

:o:J
Z

100

o-auc.:i oI
(f)
Ci 10
Cw>a:l
w
(f)
!oD
1'--

10

2-YEAR RECURRENCE INTERVAL FLOOD
o Region 1
Rome, Georgia
o Region 2
!::::. Region 3
<>Region 4

PRED. Q2-P redicted 2-year flood from regression equation
EQUA. Q2-2 -year flood from regional equations

o

----'_ _---'-_----'-_-'---'----'---'----'---'---

--'----_ _-'--_.L..---'-_'--.L..-J....-.!-----'

100

1,000

ESTIMATED REGIONAL REGRESSION-EQUATION DISCHARGE, IN CUBIC FEET PER SECOND

Figure 2. Comparison of 2-year recurrence interval floods from observed data and estimates from regional regression equations for the 26 urban stations used in this study, and the regression equation of the best-fit line of these discharges, with the line of equality.

Cl
oowZ
(f)
a:
w
n,
tu 1,000
w
LL
o
iIi
o::J
Z

25-YEAR RECURRENCE INTERVAL FLOOD

o

Region 1



Rome, Georgia

o

Region 2

!::::. Region 3

<>

Region 4

u.i
(!)
a:
<l: 100
oI
(f)
Ci

Cl

>aW:

w

(f)

!oD

/'

1 0 "'-_ _--'---_-'-----'-----'--'-............--L.<

PRED. Q2s-Predicted 25-year flood from regression equation

/'
/'
/'

EQUA. Q2s-25-year flood from

/'

regional equations

o
<>

-'--_"'---'----'-----'---'---'-..L..'-_ _----''----------'_-'----'--'-'-'-'--'

10

100

1,000

10,000

ESTIMATED REGIONAL REGRESSION-EQUATION DISCHARGE, IN CUBIC FEET PER SECOND

Figure 3. Comparison of 25-year recurrence interval floods from observed data and estimates from regional regression equations for the 26 urban stations used in this study, and the regression equation of the best-fit line of these discharges, with the line of equality.

8

10,000 '_-------r-----,--.---.---r-r-.---r---,----,---,----,---,---.-,-TT-,------.-----,-----,----.-,----,--n71

0 Z
o0
W
(/)
a:
w
n,
Iw- 1,000
W L.L.
o
iii
o=>
~
L.Li
a<.9: 100 Io
(/)
is
0
>ua:i
w
(/)
CD
0
10
10

100-YEAR RECURRENCE INTERVAL FLOOD

o

Region 1

III

Rome, Georgia

o

Region 2

b.

Region 3

<> Region 4

,/
100

,/

PRED. 0100-P redicted 1OO-year flood from regression equation

,/ ,/

EOUA. 100-1 OO-year flood from regional equations

,o/

1,000

10,000

ESTIMATED REGIONAL REGRESSION-EQUATION DISCHARGE, IN CUBIC FEET PER SECOND

Figure 4. Comparison of 100-year recurrence interval floods from observed data and estimates from regional regression equations for the 26 urban stations used in this study, and the regression equation of the best-fit line of these discharges, with the line of equality.

The flood-frequency data computed from the statewide regression equations are higher than the flood-frequency data computed from observed data for the 2-year flood at 15 urban stations and are equal at one urban station; higher for the 25-year flood at 20 stations and equal at one station; and higher for the 100-year flood at 22 stations (see table 4). Therefore, the peak flows computed with the statewide estimating equations generally are higher than those computed using the observed data. The two highest simulated floods used in developing the estimating equations occurred before the observed record began; thus, indicating a relatively dry period of observed record at 25 of the 26 urban stations. The dates and peak discharges of the two highest observed and simulated floods are shown in table 5. Further evidence that a relatively dry period of record occurred can be observed in table 4 by comparing the results of the log-Pearson flood-frequency analysis of the simulated annual peaks for the most recent (latest) 20 years of record for each urban station with the flood-frequency

data from the estimating equations. The magnitudes of the 2-, 25-, and 100-year floods computed from the statewide regression equations, were higher than the corresponding 2-,25-, and 100-year floods computed from the latest 20 years of record at 20 urban stations. Data in Savannah do not indicate this trend, because the highest simulated annual peaks occurred in Savannah in 1971.
Even though Georgia experienced one of the largest floods of record on the Flint and Ocmulgee Rivers in the southwestern part of Georgia in July 1994, following Tropical Storm Alberto, the very heavy rainfall accompanying this flood did not occur in any of the 10 cities in which the observed record was collected. The city of Albany had extensive flooding caused by very heavy rainfall upstream of the city. Albany had 6.75 inches of rainfall over a five-day period (U.S. Department of Commerce, National Weather Service, 1994). The 1994 annual peak flow for the two Albany urban stations occurred in August.

9

Table 4. Flood-frequency data for the 2-, 25-, and 1DO-yearfloods from urban stations with observed data, from the statewide flood-frequency estimating equations, and from the most recent (latest) 20 years of simulated data from the urban stations

Station number
02352605 02352964
02217505 02217905
02203835 02203845 02203884 02336090 02336102 02336238 02336700
02196725 02196760
02341544 02341546 02341548
02318565 02327203
02395990 02396510 02396550
02203543 02203544
02327467 02327471
02317564 02317566 023177554

Flood-frequency observed data (in cubicfeet per second)

2-year

25-year 100-year

44

121

156

4

19

36

512

948

1,210

407

826

1,070

731

1,540

2,050

423

782

925

672

1,310

1,610

113

406

640

726

1,120

1,280

586

983

1,200

301

491

581

147

234

262

345

844

1,200

582

1,100

1,350

69

186

286

414

813

1,020

46

103

149

137

273

354

103

224

263

19

48

66

144

208

232

253

465

593

83

121

134

213

379

468

86

185

278

246

366

395

336

685

901

730

963

1,040

Flood-frequency regression equation data
(in cubicfeet per second)
2-year 25-year 100-year
Albany

44

120

168

15

44

Athens

588

1,220

283

561

Atlanta

939

2,050

371

793

937

1,360

181

428

824

1,770

467

1,000

396

872

Augusta

224

619

196

580

Columbus

486

1,100

133

306

444

1,020

Moultrie

123

363

152

459

Rome

124

276

25

59

79

178

Savannah

151

429

45

128

Thomasville

295

920

125

345

Valdosta

169

498

350

1,070

601

1,850

62
1,560 707
2,650 1,020 1,750
573 2,290 1,310 1,140
873 833
1,440 402
1,330
489 622
357 78 230
609 180
1,260 455
715 1,550 2,530

Flood-frequency simulated data, usinglatest20 years
(in cubicfeetper second)

2-year

25-year 100-year

33

77

102

6

20

29

480

1,080

1,400

311

658

862

749

1,920

2,580

321

800

1,050

523

1,300

1,720

120

335

461

472

1,200

1,590

325

933

1,320

254

601

769

145

359

488

315

894

1,230

594

1,160

1,310

92

204

255

418

954

1,190

68

147

187

160

310

372

93

215

275

22

49

63

69

160

221

173

614

967

92

248

326

250

510

622

102

181

219

156

381

505

326

726

931

521

1,050

1,290

10

Table 5. Peak discharges and water years of the two highest flood events, from observed and simulated records for urban stations used in this study

Station number 02352605 02352964
02217505
02217905
02203835 02203845 02203884 02336090 02336102 02336238 02336700 02196725 02196760 02341544 02341546 02341548

Observed data
112 79 20 8
1,040 796
821 715
2,140 1,390
797 751 1,230 1,070 608 343 1,110 1,070 1,140 945 533 498
219 201 1,110 557
1,390 858 244 134 871 725

Peak discharges, in cubic feet per second

Water year"

Simulated data Water year

Albany

1994 1995

108

1909

99

1930

1995 1991
Athens2/

31

1930

27

1909

(Atlanta 0.5)

1994

1,390

1926

1992

1,380

1912

(Augusta 0.5)

1,540

1903

1,380

1950

(Atlanta 0.5)

1996

942

1908

1991

762

1926

(Augusta 0.5)

832

1903

800

1927

Atlanta

1980

3,180

1912

1983

2,680

1898

1994

1,090

1926

1983

988

1914

1978

1,890

1912'

1992

1,620

1898

1991

410

1908

1980

383

1912

1975

1,960

1912

1991

1,570

1980

1975

1,300

1908

1992

1,140

1912

1971

792

1912

1992

776

1908

Augusta

1983 1986

713

1930

419

1906

1991 1996

1,350 1,020

1930 1967

Columbus

1990 1994
1990 1977

2,770 1640
421 230

1923 1957
1923 1957

1991

2,200

1923

1981

1,160

1916

11

Table 5. Peak discharges and water years of the two highest flood events, from observed and simulated records for urban stations used in this study-Continued

Station number 02318565 02327203
02395990
02396510
02396550
02203543 02203544 02327467 02327471 02317564 02317566 023177554

Observed data
114 58 298 174
193 190
44 41
198 189
550 355 127 118
366 284 201 112
383 296 668 586 889 889

Peakdischarges, in cubicfeet per second

Water year!/

Simulated data Water year

Moultrie

1993

230

1930

1994

198

1909

1993 1995
Rome3/

563

1909

410

1930

(Atlanta 0.6)

1986 1979

344

1912

280

1926

(Chattanooga 0.4)

306

1912

262

1949

(Atlanta 0.6)

1989 1990

60

1914

58

1926

(Chattanooga 0.4)

55

1912

55

1969

(Atlanta 0.6)

1992

343

1908

1982

290

1926

(Chattanooga 0.4)

316

1912

282

1950

Savannah

1995

815

1971

1991

570

1945

1996

297

1971

1995

210

1950

Thomasville

1995

911

1909

1994

770

1930

1994

280

1909

1993

272

1948

Valdosta

1995 1994

562

1909

535

1930

1995

1,030

1926

1991

1,030

1930

1987 1991

2,660 1,920

1909 1930

l/Water year is the 12-month period beginning October 1 and ending September 30, and is designated in the calendar year in which it ends.
2/ATLANTA and AUGUSTA long-term rainfall data were used for ATHENS stations with 50 percent weights applied to their simulated flood frequencies.
3/ATLANTA and CHATTANOOGA long-term rainfall data were used for ROME stations with 60 percent and 40 percent weights, respectively, applied to their simulated flood frequencies.

12

RESULTS OF COMPARISONS
Mean residuals, computed as the logarithms of observed discharges subtracted from logarithms of discharges estimated by statewide regional regression equations, are higher for the 2-, 25-, and 100-year recurrence interval floods at the 26 urban stations used in this study. The mean residuals for the 2-year flood is 2.5 percent higher than the observed mean residuals; however, the t-test indicates that the differences are not significant at the 0.05 level of significance. The mean regional regression equation discharge for the 25-year and 100-year floods are higher than the mean observed discharge for the 25-year and 100-year floods by 26.2 percent and 31.6 percent, respectively. The t-tests indicate that both differences are significant at the 0.05 level of significance, but the percentages are within the range or close to the range of the standard error of prediction for the statewide regression equations (Inman, 1995).The slopes of the regression lines are not significantly different from 1.0, for the three recurrence intervals; therefore, the bias is not a function of discharge, and the bias computed by the mean residuals is assumed to apply over the whole range of discharges. The significance or non-significance of the intercept is not a valid indicator of bias because the y-intercept is too far removed from most of the data. Regression equations are computed from normal distributions, as demonstrated by the

Shapiro-Wilk statistic from the SAS univariate procedure (SAS Institute, Inc., 1989) (table 6). No attempt was made to adjust the estimating equations because higher peaks can occur after a period of observed record, and an adjustment may cause an underestimation of design floods.
Comparison of mean residuals of the 2-, 25-, and 100year floods computed using the latest 20 years of record and the mean residuals of the same floods estimated using the regional regression equations, show similar results as previous comparisons of the observed data with the same floods estimated from the regional regression equations. The mean residuals of the 2-, 25-, and 100-year floods estimated from the regional regression equations are 13.5 percent, 19.9 percent, and 22.4 percent higher, respectively, than the mean residuals of the corresponding floods computed from the 20 years of simulated annual peak flows. The t-tests indicate that the differences are significant in all cases; however, the differences are within the range of the standard error of prediction for the statewide regression equations (Inman, 1995). These 20-year-period comparisons eliminate model error as the cause of the regression-equation discharges being higher than observed discharges, because both the 20-year-period annual peak flows and the annual peak flows used for developing the regression equations were simulated with the same model.

Table 6. Results of comparison testing of flood-frequency data based on student's t-test at 0.05 level of significance
and statistical analysis of regression results for the final 26 urban stations used in this study
l>. greater than]

Recurrence interval, in years
2 25 100

Mean residual (x) biased
no yes yes

Percent equation mean greater than observed mean

Normal distribution

2.5

yes

26.2

yes

31.6

yes

Slope biased
no no no

Constant biased
no no no

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SUMMARY
The U.S. Geological Survey, in cooperation with the Georgia Department of Transportation, began a study in 1987 to monitor small urban streams in Georgia to verify the accuracy of the urban flood-frequency estimating equations previously published in 1995. Data collection for the monitoring study consisted of obtaining additional annual peak-flow data at 28 selected gaging stations in 10 cities, all of which were part of the previous study. These additional data provided an adequate data base for computing flood-frequency relations with observed data at the selected stations.
Flood-frequency relations were computed for the 28 urban stations and the 2-, 25-, and 100-year recurrence interval floods were compared to the 2-, 25-, and 100-year recurrence interval floods computed from the regional regression equations from the previous study. Two stations were deleted from further comparisons, or analyses, because neither station had as much as a 2-year recurrence interval flood during the period of observed record.
Comparisons at the 26 remaining stations were based on the student's t-test statistics at the 0.05 level of
significance. The mean (x) residual of the 2-year
recurrence interval floods computed from observed data was about 2.5 percent lower than the mean (x) residual of the 2-year recurrence interval floods computed from the regional regression equations; however, the t-test indicated that the bias was not significant at the 0.05 level of significance. The mean (x) residuals of the 25- and 1OO-year recurrence interval floods computed from observed data were 26.2 and 31.6 percent lower than the mean residuals of the 25- and 100-year recurrence interval floods computed from the regional regression equations; both floods were significantly biased according to the t-test at the 0.05 level of significance, but were within or close to the limits of the standard error of prediction for the statewide equations. A comparison also was made by regressing logarithms of the 2-, 25-, and 100-year recurrence interval floods computed from observed discharges against logarithms of the 2-, 25- and 100-year recurrence interval floods estimated from the regional regression equations. This regression "best-fit" line was compared to a line of equality and results of the student's t-test indicated that the slope of the regression line was not significantly different from 1.0 at the 0.05 significance level. Therefore, the bias did not vary with discharge.

The primary reason that the mean (x) of the observed 25- and 100-year floods were biased (less than) the mean (x) of the 25- and 100-year floods computed from the regional regression equations is because the observed period of record was a relatively dry period. At 25 of the 26 stations, the two highest simulated peaks used in developing the estimating equations occurred before the observed record began. However, no attempt was made to adjust the estimating equations because higher peaks could occur after the period of observed record, and an adjustment could cause an underestimation of design floods.
REFERENCES CITED
Iman, R.L., and Conover, WJ. 1983, A modem approach to statistics: New York, John Wiley, 497 p.
Inman, EJ., 1983, Flood-frequency relations for urban streams in Metropolitan Atlanta, Georgia: U.S. Geological Survey Water-Resources Investigations Report 83-4204, 38 p.
---1988, Flood-frequency relations for urban streams in Georgia: U.S. Geological Survey Water-Resources Investigations Report 88-4085, 36 p.
---1995, Flood-frequency relations for urban streams in Georgia-1994 update: U.S. Geological Survey Water-Resources Investigations Report 95-4017, 27 p.
Interagency Advisory Committee on Water Data, 1982, Guidelines for determining flood-flow frequency, revised 1981: Washington, D.C., Bulletin 17B, 183 p.
SAS Institute, Inc., 1989, SAS user's guide: Statistics, 583 p.
U.S. Department ofCommerce, 1948-94, Climatological data, monthly publications for Georgia: Asheville, N.C., National Oceanic and Atmospheric Administration, National Climatic Data Center, variously paged.

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