GEOLOGICAL SURVEY CIRCULAR 365 A FLOOD-FLOW FORMULA FOR CONNECTICUT A FLOOD-FLOW FORMULA FOR CONNECTICUT By B. L. Bigwood and M. P. Thomas GEOLOGICAL SURVEY CIRCULAR 365 Washington, D C., 1965 Free on application to the Geological Survey, Washington 26, D. C. United States Department of the Interior STEWART 1. UDALL, SECRETARY Geological Survey THOMAS B. NOLAN, DIRECTOR REPRINTED 1963 Free on application to the U.S. Geological Survey, Washington 25, 0. C. PREFACE Recognizing that a flood-magnitude-and-frequency parts in the annual surface water series of the water- relation for Connecticut streams, based on actual flood supply papers. The first one to be published will be events recorded at gaging stations on typical streams that for part 1A, comprising virtually all New England, within the State or closely bordering territory, would including Connecticut. This first volume is now in in all likelihood provide reliable estimates of flood preparation but will not be forthcoming immediately; probabilities for ungaged sites on State streams, the because of the nature of statistical studies, it may lead State Board of Supervision of Dams and the State High­ to a different form of analysis than is developed here. way Department, in cooperation with the United States Geological Survey, have sponsored the study described Cooperating State agencies, namely, the State Board in this report. The investigation is especially needed of Supervision of Dams under the chairmanship of Mr. in connection with regulative functions of the Board of Richard Martin, succeeded by Mr. William S. Wise; Supervision of Dams and for purposes of hydraulic de­ and the State Highway Department, Mr. William J. Cox, sign in the State Highway Department. The derived Commissioner, succeeded by Dr. G. Albert Hill, ren­ flood-flow formula also might be expected to answer dered most valuable assistance. Acknowledgments are design needs of private engineers and consultants due also to individual members and staff personnel of throughout the State and, as well, those outside the the Board of Supervision of Dams and to the engineering State who might have interest in Connecticut hydraulic staff of the State Highway Department for helpful cooper­ projects. ation. A formula was envisioned which would incorporate The basic flood discharge records and some other drainage -basin characteristics that could readily be hydro logic data used in this study have been collected scaled from standard topographic maps. A highly de­ and compiled largely under the continuing surface- sired attribute of the formula would be simplicity in water investigational programs maintained--in Connect­ form and application. Involved analysis, resulting in icut, in cooperation with the State Water Commission, a profusion of terms having but little weight in final the Hartford Department of Public Works (succeeding results, was to be avoided. In brief, a formula of few the Hartford Flood Investigation & Improvement Com­ and simple terms, giving results of reasonable prac­ mission), the New Britain Board of Water Commis­ tical accuracy, was the goal. These desired general sioners, and other agencies; in New York, in cooper­ requirements influenced the derivation of the formula ation with the Westchester County Department of Public set forth in this study. Works; and in Massachusetts in cooperation with the State Department of Public Works. The U. S. Geological Survey has planned a nation­ wide flood-frequency study, which is to be issued sep­ arately for sections of the country corresponding to the CONTENTS Page Abstract ........................................................................................... 1 Introduction ........................................................................................ 1 Method of analysis .................................................................................. 2 Flood magnitude and frequency relation ............................................................... 2 Influence of topographic characteristics ............................................................... 11 Summary of procedure............................................................................... 13 Example of application of formula .................................................................... 15 Literature cited..................................................................................... 16 ILLUSTRATIONS Page Figure 1. Map of Connecticut showing location of gaging stations used .................................. 3 2. Chronological record of gaging stations .................................................... 8 3. Flood magnitude and frequency curve, ratios to mean annual flood ............................ 11 4. Relation of mean annual flood to drainage area.............................................. 13 5. Relation of mean annual flood to product of drainage area and basin slope...................... 14 6. Topographic characteristics of a typical stream............................................. 16 TABLES Page Table 1. Index of gaging stations used in Connecticut flood-frequency report ........................... 4 2. Annual peak discharges, before 1929. ...................................................... 5 3. Annual peak discharges, 1929 to 1953 ...................................................... 6 4. Characteristics of streams ............................................................... 9 A FLOOD-FLOW FORMULA FOR CONNECTICUT By B. L. Bigwood and M. P. Thomas ABSTRACT mation of frequency was impossible. A study of the frequency and magnitude of floods Enveloping curves of maximum known discharge per within the Connecticut area is contained in this report. square mile were also commonly used in the design of Annual flood discharges for 44 stream-gaging stations hydraulic structures. These curves likewise ignored whose records range in length from 10 to 40 years are the element of frequency and the effect of the physical presented and a regional flood-frequency relationship characteristics of the drainage basin other than the developed based upon the ratios of all floods to the mean drainage area, which have an important bearing upon annual flood at each of these locations. Definition of the problem. this curve for floods of larger recurrence intervals is based upon historical studies of extraordinary floods In 1913, the late Weston E. Fuller introduced the which have occurred within the area. For ungaged concept of a magnitude-frequency relationship based areas, the mean annual flood value may be determined upon statistical methods applied to floods in the United by use of a flood-flow formula based upon the topogra­ States, following a line of reasoning that was introduced phic characteristics of drainage area and basin slope. into studies of riverflow about the same time by the The development of this formula also is included. late Alien Hazen. From that time on, as streamflow records have become more extensive and reliable, the concept of maximum flood values for hydraulic design INTRODUCTION based on limited experience has been superseded by magnitude-frequency relationships computed on the Problems relating to flood flows in river channels basis of methods involving the use of rainfall-runoff have been the concern of man ever since he chose to relationships or physical characteristics of the drain­ settle in river valleys where rich soil was available age basins. for agriculture, where grades for highways and rail - roads were moderate, and where abundant water was It has long been recognized that equal amounts of available. Through the years he has learned to his rainfall of similar intensities would produce widely dismay that rivers are not always friendly. At times varied peak discharge rates in this region. In 1944 the they overflow their banks in uncontrolled fury and Geological Survey (Kinnison and Colby, 1945) completed ruthlessly destroy everything before them. In order a study to relate the magnitude of flood peaks of various to control flood flows properly and to design and locate frequencies on Massachusetts streams to certain signif­ structures, such as dams, bridges, culverts, highways, icant drainage-basin characteristics. Short discharge railroads, residential and industrial buildings, water- records necessitated the use of rainfall-runoff studies supply and sewage-disposal works, and other facilities, through unit-hydrograph relationships for flood frequen­ it becomes necessary to evaluate the magnitude and cies greater than 15 years. The resulting formulas are probable frequency of recurrence of floods. Where loss free of coefficients or estimated terms and are designed of life or great property damage is involved if the struc­ to give the peak discharge for minor (15 -year), major ture be overtopped or destroyed, the "design flood" (100-year), rare (1, 000-year), or maximum floods on must be of such magnitude that it may never be exceeded. any stream in or near the Massachusetts area. In general, however, it is adequate and economical to design for a flood which may be expected to occur on In Connecticut, also, there has developed a pressing an average of from once in 10 to once in 100 years, need for a flood-flow formula for hydraulic design, par­ depending upon the type of structure involved. ticularly for streams having drainage areas under 100 square miles. Previous reliance on outmoded formulas Before 1900, engineers attempted to evaluate the has resulted in a wide divergence of results. It was, flood-producing