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: 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 13 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. 14