REPORTS SECTION COPY - USGS · 5/£:/c,/~ TECHNIQUE FOR ESTIMATING THE MAGNITUDE AND FREQUENCY OF...

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TECHNIQUE FOR ESTIMATING THE MAGNITUDE

AND FREQUENCY OF FLOODS IN TEXAS £Uf0lf(

11-1/V

U.S. GEOLOGICAL SURVEY Water-Resources Investigations 77-110

Open-File Report

REPORTS SECTION COPY

Prepared in rooperation with the State Department of Highways and

Public Transportation and the Department of Transportation, Federal

Highway Administration 1977

CONTENTS

Page

Abstract-----------------------~---------------------------------- 1 Introduction----------------~------------------------------------- 2

Acknowledgments---------------------------------------------- 2 Previous reports--------------------------------------------- 2 Metric conversions------------------------------------------- 3

Flood-frequency analysis------------------------------------------ 3 Regression analysis----------------------------------------------- S Application of regression equations------------------------------- 5 Range of application of equations--------------------------------- 20 Selected references----------------------------------------------- 22

Figure 1.

2. 3.-6.

3.

4.

s.

6.

7.

8.-13. 8.

9.

10.

11.

12.

13.

ILLUSTRATIONS

Map showing location of stream-gaging stations and flood-frequency regions-------------------------

Hap showing mean annual precipitatiQn, 1941-70--------Nomographs for determining peak discharges of floods: With recurrence intervals of 2, S, and 2S

years in region 1-----------------------------------With recurrence intervals of 10, SO, and 100

years in region 1-----------------------------------With recurrence intervals of 2, S, and 2S


years in region 2-----------------------------------Graph for determining peak discharges of floods

with recurrence intervals of 2, S, 10, 2S, SO, 100 years in region 3-------------------------------

Nomographs for determining peak discharges of floods: With recurrence intervals of 2, S, and 2S

years in region 4-----------------------------------With recurrence intervals of 10, 50, and 100

years in region 4-----------------------------------With recurrence intervals of 2, S, and 2S

years in region S-----------------------------------With recurrence intervals of 10, SO, and 100

years in region S-----------------------------------With recurrence intervals of 2, 5, and 2S


years in region 6------------------------------------

4 6

7

8

9

10

11

12

13

14

lS

16

17

TECHNIQUE FOR ESTIMATING THE MAGNITUDE AND FREQUENCY OF FLOODS IN TEXAS

By E. E. Schroeder and B. C. Massey

ABSTRACT

Drainage area, slope, and mean annual precipitation were the only factors that were statistically significant at the 95-percent confidence level when the characteristics of the drainage basins were used as independent variables in a multiple-regression flood-frequency analysis of natural, unregulated streams in Texas. The State was divided into six regions on the basis of the distribution of the residuals from a single statewide regression of the 10-year flood. Equations were developed for predicting the magnitude of floods with recurrence intervals of 2, 5, 10, 25, SO, and 100 years in each of the six regions. These equations are applicable to unregulated rural streams with drainage basins ranging in area from 0.3 square mile to about 5,000 square miles in some regions. Regression equations were not developed for several areas, particularly in south Texas, because of the lack of definition of the flood-frequency characteristics.

INTRODUCTION

A reasonable estimate of the magnitude and frequency of occurrence of peak discharges is required for proper design of structures on the flood plain of a stream. This information is also necessary for floodplain management and for determining flood-insurance rates. This report presents a method for determining the magnitude and frequency of peak discharges on natural streams in Texas.

Flood-frequency relations presented in this report were defined by currently accepted analytical techniques utilizing all applicable floodflow data collected in Texas through September 30, 1974. They provide the basis for reliable estimates of the magnitude of floods with recurrence intervals of 2, 5, 10, 25, 50, and 100 years for unregulated, ungaged rural streams in Texas.

Acknowledgments

This report was prepared by the U.S. Geological Survey in cooperation with the Texas State Department of Highways and Public Transportation. The research study was supported, in part, by highway planning and research funds provided by Texas State Department of Highways and Public Transportation and the Federal Highway Administration. The research results are based on data collected and published by the Geological Survey for many years in cooperation with State, federal, and local agencies. ~1uch of the data on small streams were collected by the Geological Survey through a special project in cooperation with the Texas State Department of Highways and Public Transportation and the Federal Highway Administration. The opinions, findings, and conclusions expressed in this report, however, are not necessarily those of the Federal Highway Administration.

Previous Reports

Johnson and Sayre (1973) defined the relations for estimating flood peaks for the Houston metropolitan area, and Dempster (1974) defined similar relations for the Dallas metropolitan area. In the Houston or Dallas urban areas, those relations should produce more applicable estimates of flood peaks than the relations presented in this report.

An interim report by Schroeder (1974) developed equations for predicting the magnitudes of the 10-, 25-, and 50-year floods for small streams in East Texas. These equations are superseded by those presented in this report.

Previous statewide studies by Benson (1964) and Patterson (1963) defined the relations for estimating flood peaks at sites with rural drainage areas greater than 20 to 50 square miles. The study by Gilbert and Hawkinson (1971) also defined relations for larger drainage areas.

Metric Conversions

The equations and graphs in this report are based on English units of measurement only. To obtain discharge in cubic meters per second, multiply the English units by the factor 0.02832.

FLOOD-FREQUENCY ANALYSIS

Annual peak data at 289 sites were used in this analysis to develop flood-frequency relations for unregulated rural streams (fig. 1). At 249 sites, recorded annual peak data were used in the analysis, and at 40 sites annual peaks derived from a rainfall-runoff simulation model (Massey and Schroeder, 1977) were used.

The peak discharges of floods with recurrence intervals of 2, 5, 10, 25, 50, and 100 years were computed at all stations by using the procedures outlined by the Hydrology Committee of the United States Water Resources Council (U.S. Water Resources Council, 1976). These guidelines recommend using the log-Pearson type III distribution and contain suggestions for dealing with skew weighting, high and low outliers, historical peak information, zero-flow years, and peaks below a base.

The current (1976) version of the Geological Survey's log-Pearson computer program contains options to facilitate skew weighting, conditionalprobability adjustment, and historic-peak adjustment. A flood-frequency relationship was computed for most of the sites by using the Water Resources Council guidelines. The low-outlier test, however, was not beneficial because the level for rejection was set too low.

The data from several stations could not be used because the data array indicated two populations of floods, one population resulting from normal continental storms and the other population resulting from tropical storms or hurricanes originating in the Gulf of Mexico.

Because of the need for better definition of flood-frequency relations for small drainage areas (less than 50 square miles) in Texas, the rainfallrunoff simulation model developed by Dawdy, Lichty, and Bergmann (1972) was used to extend short-term records on small drainage areas so that the magnitude and frequency of floods with recurrence intervals as high as 100 years could be defined (Massey and Schroeder, 1977). The parameters developed from calibration of the simulation model, together with long-term rainfall and evaporation records, were used to simulate an array of annual peaks at each of 40 sites on small drainage areas with short-term records. Flood-frequency curves for each of these sites, using the synthesized peaks, were defined by fitting the log-Pearson type III distribution.

Most of the flood-frequency curves derived from synthesized data exhihited a characteristic regression effect of having a smaller standard deviation than the curves obtained by use of recorded data from several

• 770

~--2.Lo ___ •Lo __ _jsLo _ _ ___leo __ ____jl00 MILES

EXPLANATION

STREAMFLOW OR RESERVOIR-CONTENT STATION

FLOOD-HYDROGRAPH, LOW-FLOW, OR CREST STAGE PARTIAL-RECORD STATION

RIVER BASIN DIVIDE

AREAS-In which flood- frequency relations are undefined

PLAYA-LAKE AREA- In which the equations do not apply

sites with more than 20 years of record (Massey and Schroeder, 1977). Adjustments were made by using a method proposed by W. H. Kirby (oral commun., 1975). This adjustment is included in an experimental version of the Geological Survey's log-Pearson computer program.

REGRESSION ANALYSIS

Multiple linear-regression techniques were used to develop the equations for predicting the selected t-year discharges. The values of the variables were transformed to base 10 logarithms prior to making the regression analysis. The base 10 logarithms of the variable values produce relations that have a higher degree of linearity than the untransformed values.

The basic logarithmic regression model has the following form:

Q B biB b2 .... B bn t = a 1 2 . n

where Qt = discharge in cubic feet per second for recurrence interval t; B1, B2,····Bn are independent variables; b1, b2 ,····bn are regression coefficients; and a is the regression constant.

The independent variables used in this analysis were drainage area, slope, length, elevation, mean annual precipitation (fig. 2), 24 hour-2 year rainfall intensity, and evaporation. Only those variables that were significant at the 95-percent confidence level (drainage area, slope, and mean annual precipitation) were retained.

The six flood-frequency regions of the State (fig. 1) were determined on the basis of a plot of the residuals (the difference between the computed and the observed discharge values) from the equation of the 10-year flood for all 289 sites. A separate regression analysis was then made for each t-year event.in each flood-frequency region, and regression equations were developed for each event in each region. Drainage area and slope remained significant in regions 1, 2, 4, and 5; drainage area alone was used in region 3; and in region 6, drainage area and mean annual precipitation were used. The residuals for these equations were plotted and no overall bias or areal trends were indicated.

APPLICATION OF REGRESSION EQUATIONS

The regression equations shown in the following table or on the graphs (figs. 3-13) for each flood-frequency region provide a method for computing the magnitudes of floods having recurrence intervals of 2, 5, 10, 25, 50, and 100 years at ungaged rural sites on streams in Texas where unregulated flow conditions prevail.

The flood-frequency region in which a site is located is determined from figure 1, and the appropriate set of equations or graphs are selected. Drainage area (A), in square miles, is obtained by planimetering the area

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Note: Caution should be exercised in interpolating for normal precipitation in the Trans-Pecos region where differences of several inches may occur in a short horizontal distance because of changes in elevation.

EXPLANATION

-24- LINE OF EQUAL ANNUAL PRECIPITATION, IN INCHES. Intervals 2 and 4 inches

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Based on U.S. Department of Commerce, National Oceani Atmospheric Administration Environmental Data "Ciimatograpily of the United States No. 81 (Texas)" for the 1941·1970.

Weather Modification and Technology Division Texas Water Development Board

OKLAHOMA

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July 1974

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---

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0 0 0

contributing surface flows above the site as outlined along the drainage divide on the best available topographic maps. Slope (S), in feet per mile, is the average slope of the streambed between points 10 and 85 percent of the distance along the main-stream channel from the site to the basin divide. The main channel above strea~ junctions is the one draining the largest area. Elevation differences between the 10- and 85-percent points are divided by the distance between the points to determine the slope. Mean annual precipitation (P), in inches, if needed, is determined from figure 2. In the equations and nomographs for region 6, mean annual precipitation minus 7 inches (P-7) is used to reduce the range of values to more nearly represent precipitation related to flood runoff without introducing values of zero or less.

Flood-Frequency Region 1

Regression equation

Q2 89.9A·629s.l30 ft3/s

Qs = 117A·6sss.254 ft3/s

Qlo

Q25

Qso

QlOO

= 131A.714s.317 ft3/s

= 144A.7475 .3s6 ft 3/s

= 152A.769s.431 ft 3/s

= 157A.7ss5 .469 ft 3/s


Regression equation

Q2 216A·574s.l25 ft3/s

Qs 322A·620s.l84 ft3/s

Qlo = 389A·646s.214 ft3/s

485A·66Bs.236 ft3/s

555A· 682S· 250 ft 3/s

628A· 694s- 261 ft3/s

Standard error of estimate (percent)

27.4

25.0

29.7

36.8

43.5

46.8

Standard error of estimate (percent)

54.6

43.0

40.3

40.0

41.4

43.7


Standard error of Regression eguation estimate (percent)

Q2 = 175A· 54 0 ft 3/s 41.2

Qs = 363A· 58 0 ft 3/s 40.7

Ql 0 = 521A·5 99 ft 3/s 43.6

Q2s = 759A· 616 ft 3/s 47.5

Qso = 957A· 627 ft 3/s 50.7

Qloo = 1175A·6 3 8 ft3/s 54.2


Standard error of Regression eguation estimate (Eercent)

Q2 = 13.3A· 676s· 694 ft 3/s 50.3

Qs = 42 . 7A.63o 8 .641 ft 3/s 40.9

Qlo = so.?A·6o48 .s96 ft 3/s 39.2

Q2s = 163A.576s.S35 ft 3/s 40.5

Qso = 248A.s62s.497 ft 3/s 42.8

QlOO = 397A.s4os.442 ft 3/s 46.5


Standard error of Regression eguation estimate (percent)

Q2 = 4.82A· 799s· 966 ft3/s 62.1

Qs = 36 . 4A.776s.7o6 ft3/s 46.6

Qlo = 82 . 6A.776s.622 ft 3/s 42.6

Q2s = 180A.7768 .ss4 ft3/s 41.3

Qso = 278A.71s8 .s22 ft 3/s 42.0

QlOO = 399A.1s28 .497 ft3/s 44.1


Standard error of Regression equation estimate (Eercent)

Q2 = 49.8A·602(P-7)·447 ft 3/s 46.7

Qs = 84.5A·643(P-7)·533 ft 3/s 27.9

Qlo = 111A·666(P-7)·573 ft 3/s 27.9

Q2s = 150A·692(P-7)·608 ft 3/s 34.3

Qso = 182A·709(P-7)·630 ft 3/s 40.2

Qioo = 216A·725(P-7)·647 ft 3/s 46.1

RANGE OF APPLICATION OF EQUATIONS

The flood-frequency equations presented in this report may be used to estimate the magnitude and frequency of floods for most natural, rural streams in Texas. The equations do not apply to urban streams or to streams that are regulated by manmade structures. The streams on part of the Southern High Plains are also excluded because internal drainage into the playa lakes results in varying amounts of noncontributing drainage areas. Data were not sufficient to develop relationships in south Texas or for the Nueces River downstream from the Balcones Fault Zone. In flood-frequency region 6, the equations do not apply to areas above an elevation of 4,000 feet above mean sea level, because no data were available.

The following table shows the range of drainage area and slope within which the equations were developed for each flood-frequency region.

Flood-frequency Drainage area Slope region (square miles) (feet/mile)

1 0.39 - 4,839 0.85 - 206.2

2

3

4

5

6

.33 - 4,233

2.38 - 4,097

1.09 - 3,988

1.08 - 1,947

.32 - 2,730

1.16 - 108.1

2.33 - 74.8

9.15 - 76.8

The equations presented in this report should provide the basis for the most reliable estimates available of the frequency and magnitude of floods on ungaged, unregulated rural streams in Texas, within the range of drainage areas and slope given in the preceding table. The equations were defined by using the most recently developed analytical techniques and by using all applicable floodflow data collected in Texas through September 30, 1974, for floods with recurrence intervals of 2, 5, 10, 25, SO, and 100 years. Because of the refinement of analytical techniques and because of the volume of data used, these equations supersede all equations designed for unregulated rural streams in Texas previously published by the Geological Survey.

SELECTED REFERENCES

Benson, M. A., 1964, Factors affecting the occurrence of floods in the southwest: U.S. Geol. Survey Water-Supply Paper 1580-D, p. Dl-D72.

Dawdy, D. R., Lichty, R. W., and Bergmann, J. M., 1972, A rainfall-runoff simulation model for estimation of flood peaks for small drainage basins: U.S. Geol. Survey Prof. Paper 506-B, 28 p.

Dempster, G. R., Jr., 1974, Effects of urbanization on floods in the Dallas, Texas metropolitan area: U.S. Geol. Survey Water-Resources Inv. 60-73, 51 p.

Gilbert, C. R., and Hawkinson, R. 0., 1971, A proposed streamflow data program for Texas: U.S. Geol. Survey open-file rept., 52 p.

Johnson, S. L., and Sayre, D. M., 1973, Effects of urbanization on floods in the Houston, Texas metropolitan area: U.S. Geol. Survey WaterResources Inv. 3-73, SO p.

Massey, B. C., and Schroeder, E. E., 1977, Application of a U.S. Geological Survey rainfall-runoff model in estimating flood peaks for selected small natural drainage basins in Texas: U.S. Geol. Survey Open-File Rept. 77-792, 2 figs.

Patterson, J. L., 1963, Floods in Texas--magnitude and frequency of peak flows: Texas Water Commission Bull. 6311, 233 p., 19 figs., 2 pls.

Schroeder, E. E.,. 1974, Estimating the magnitude of peak discharges for selected flood frequencies on small streams in East Texas: U.S. Geol. Survey open-file rept., 16 p., 4 figs.

U.S. Water Resources Council, 1976, Guidelines for determining flood-flow frequency: U.S. Water-Resources Council, Hydrology Comm. Bull. 17, 26 p., 14 apps.

REPORTS SECTION COPY - USGS · 5/£:/c,/~ TECHNIQUE FOR ESTIMATING THE MAGNITUDE AND FREQUENCY OF...

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