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Flood Frequency of Streams in Rural Basins of Tennessee

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Flood Frequency of Streams in Rural Basins of Tennessee FLOOD FREQUENCY OF STREAMS IN RURAL BASINS OF TENNESSEE By Jess D. Weaver and Charles R. Gamble U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 92-4165 Prepared in cooperation with the TENNESSEE DEPARTMENT OF TRANSPORTATION Nashville, Tennessee 1993 U.S. DEPARTMENT OF THE INTERIOR MANUEL LUJAN, Jr., Secretary U.S. GEOLOGICAL SURVEY Dallas L. Peck, Director For additional information write to: Copies of this report can be purchased from: District Chief U.S. Geological Survey U.S. Geological Survey Books and Open-File Reports Section 810 Broadway, Suite 500 Federal Center Nashville, Tennessee 37203 Box 25425 Denver, Colorado 80225 CONTENTS Abstract .......................................................... 1 Introduction ....................................................... 1 Description of the study area ......................................... 1 Data used in the analysis ............................................ 4 Flood-frequency analysis at gaging stations .................................... 4 Regional flood-frequency analysis .......................................... 4 Ordinary least-squares regression analysis ................................. 18 Generalized least-squares regression analysis ................................ 18 Methods of estimating flood frequency ....................................... 20 Gaged sites .................................................... 20 Ungaged sites ................................................... 20 Method A .................................................. 20 Method B .................................................. 21 Method C .................................................. 21 Computation examples ............................................. 22 Accuracy and limitations of flood-frequency estimates .......................... 22 Miscellaneous flood discharge information ..................................... 23 Summary ......................................................... 37 References cited ..................................................... 37 FIGURE 1. Map showing location of gaging stations used in analysis and hydrologic area boundaries, counties in Tennessee, and physiographic provinces ............................. 2 TABLES 1. Discharges for selected recurrence intervals at gaging stations in Tennessee ..................................................... 5 2. Standard error of estimate for regional (ordinary least-squares) regression equations using basin characteristics having a 5-percent level of significance .......................................... 18 3. Summary of generalized least-squares regression equations ........................ 19 4. Hierarchy of discharge computation methods for ungaged sites ...................... 20 5. Maximum known discharges at gaging stations in Tennessee ....................... 24 6. Peak discharge at miscellaneous sites in Tennessee since 1972 ...................... 37 Contents iii CONVERSION FACTORS AND VERTICAL DATUM Multiply By To obtain inch (in.) 25.4 millimeter foot (ft) 0.3048 meter mile (mi) 1.609 kilometer square mile (mi2) 2.590 square kilometer cubic foot per second (ftVs) 0.02832 cubic meter per second Sea level: In this report "sea level" refers to the National Geodetic Vertical Datum of 1929 a geodetic datum derived from a general adjustment of the first-order level nets of both the United States and Canada, formerly called Sea Level Datum of 1929. iv Flood frequency of streams in rural basins of Tennessee Flood Frequency of Streams in Rural Basins of Tennessee By Jess D. Weaver and Charles R. Gamble ABSTRACT Council, Bulletin 17 (1976) for at-site frequency analysis and ordinary least-squares regression for regional analy­ Multiple regression equations and other infor­ sis. This report uses log-Pearson Type III methods as mation are presented for estimating the flood fre­ recommended by the Interagency Advisory Committee on quency of streams in Tennessee. Flood-frequency Water Data, Bulletin 17B (1982) for at-site frequency characteristics are defined for 223 gaging stations in analysis and generalized least-squares regression for Tennessee having 10 or more years of record regional analysis. This report uses 16 years of additional through 1986. Regression equations were computed data and additional sites representing a larger variety of using the generalized least-squares regression proce­ stream types and sizes as compared to Randolph and dure. The resulting equations can be used to esti­ Gamble (1976). mate the magnitude of floods having recurrence The purpose of this report is to update previous flood- intervals of as much as 500 years on ungaged frequency reports for Tennessee by providing methods of streams, if contributing drainage area is known. At estimating the magnitude of floods for selected recurrence or near gaged sites, a weighted average of the intervals based on the most recent techniques and data regression results and the gaging station data is available. The scope of the report is statewide. Data for recommended. Updated information on peak dis­ some streams near Tennessee in adjacent states were charge at miscellaneous sites is given. incorporated into the analysis. The report is the result of a cooperative agreement INTRODUCTION between the U.S. Geological Survey (USGS) and the Tennessee Department of Transportation (TDOT). It is Man encroaches upon flood plains for many vital and based on gaging-station data collected and published by worthwhile purposes. Intelligent, safe, and economically the USGS for many years as part of cooperative programs feasible encroachment demands an understanding and with various Federal, State, and municipal agencies, quantitative description of the magnitude and frequency of principally the U.S. Army Corps of Engineers (Nashville floods. A knowledge of the flood-frequency characteris­ District), Tennessee Valley Authority (TVA), Tennessee tics is essential to the design of adequate and economical Department of Environment and Conservation, and bridges, culverts, embankments, dams, levees, and other TDOT. Data at several sites collected and published by structures near streams. Flood-plain management plans the TVA and the U.S. Army Corps of Engineers (Mem­ and flood-insurance rates are based on available informa­ phis District) also were used. tion on flood magnitude and frequency. Previous reports by Jenkins (1960), Patterson (1964), Description of the Study Area Speer and Gamble (1964), and Randolph and Gamble (1976) have presented methods to define flood frequency Tennessee has diverse topography ranging from the for streams in Tennessee. The first three of these reports Great Smoky Mountains in the east to the Coastal Plain in used a graphical fit on Gumbel probability paper for at- the west. Parts of eight physiographic provinces (Blue site frequency analysis and the index flood method Ridge, Valley and Ridge, Cumberland Plateau, Sequatchie (Dalrymple, 1960) for regional analysis. The first two Valley, Central Basin, Highland Rim, Western Valley, reports were based on data collected mostly on large and Coastal Plain) are present in Tennessee (Fenneman, streams. Randolph and Gamble (1976) used log-Pearson 1946; Raisz, 1954; and Miller, 1974) (fig. 1). Elevations Type III methods as described in U.S. Water Resources range from about 300 feet in the Coastal Plain of West Introduction 1 KENTUCKY 36° - 35° - MISSISSIPPI ALABAMA Western Sequotchie Volley Valley Figure 1 . Location of (A) gaging stations used in analysis and hydrologic area boundaries and (B) physiographic provinces. 2 Flood frequency of stream* in rural basin* of Tenne**ee 86 C 85° 84° 83° 82° KENTUCKY 3524500 VIRGINIA 3V60610 7*&«T J47&000 rooo 460)600 "^452000 Q 3459500 Q 459000 100 MILES 100 KILOMETERS EXPLANATION AREA 1 HYDROLOGIC AREA DESIGNATION HYDROLOGIC AREA BOUNDARY 78A GAGING STATION AND NUMBER IN TENNESSEE A 3558000 GAGING STATION AND NUMBER OUTSIDE OF TENNESSEE Introduction 3 Tennessee to about 6,600 feet in the Blue Ridge province Peak discharges for recurrence intervals of 2, 5, 10, 25, in East Tennessee. Average annual precipitation ranges 50, 100, and 500 years were determined for each gaging from about 47 inches in the west to 80 inches in the station (table 1). For those streams where regulation now mountains in the east, and averages about 48 inches I exists, the discharge values presented are based on data statewide (U.S. Geological Survey, 1986). Streams in the collected prior to regulation. Coastal Plain generally have sustained flows during dry . A flood-frequency curve is the relation of flood-peak periods while those on the Cumberland Plateau often go | magnitude to probability of exceedance or recurrence dry. Many streams in the Central Basin also go dryl interval. Probability of exceedance is the chance of a during long periods of no rainfall. Streams in the Blue given flood magnitude being exceeded in any 1 year. A Ridge, Valley and Ridge, and Highland Rim have sus­ 5-year flood, for example, has the probability of 0.2 (or tained flows that vary between these extremes. 20-percent chance) of being exceeded in any given year. Average annual runoff varies from approximately 18 Recurrence interval is the reciprocal of probability of to 40 inches (U.S. Geological Survey, 1986). This exceedance and is the average number of years between variation is caused by seasonal precipitation patterns and exceedances for a long period of record. Recurrence the varied geography and geology of Tennessee. Evapo- interval, or average return period, does not
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