University of Arkansas, Fayetteville ScholarWorks@UARK Theses and Dissertations 8-2012 Magnitude and Frequency of Floods for Rural, Unregulated Streams of Tennessee by L-Moments Method Hongxiang Yan University of Arkansas, Fayetteville Follow this and additional works at: http://scholarworks.uark.edu/etd Part of the Hydraulic Engineering Commons, and the Water Resource Management Commons Recommended Citation Yan, Hongxiang, "Magnitude and Frequency of Floods for Rural, Unregulated Streams of Tennessee by L-Moments Method" (2012). Theses and Dissertations. 451. http://scholarworks.uark.edu/etd/451 This Thesis is brought to you for free and open access by ScholarWorks@UARK. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of ScholarWorks@UARK. For more information, please contact [email protected], [email protected]. MAGNITUDE AND FREQUENCY OF FLOODS FOR RURAL, UNREGULATED STREAMS OF TENNESSEE BY L-MOMENTS METHOD MAGNITUDE AND FREQUENCY OF FLOODS FOR RURAL, UNREGULATED STREAMS OF TENNESSEE BY L-MOMENTS METHOD A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering By Hongxiang Yan North China Electric Power University Bachelor of Engineering in Hydraulics and Hydropower, 2010 August 2012 University of Arkansas ABSTRACT This study presents a regional frequency analysis of Tennessee using the well-known Bulletin-17B method standardly used in the United States and the relatively new and developing L-Moments methods. Flood frequency characteristics were defined for 416 gaging stations located primarily in rural and lightly developed areas of Tennessee. All the gaging stations have 10 or more years of record through 2006. Using the L-Moments method, the generalized extreme value distribution was identified as the most robust distribution for each of four hydrologic areas. Multiple regression equations were also calculated for estimating the flood frequency of ungaged, unregulated, rural streams in each of the four hydrologic areas of Tennessee. Regression equations were computed using the ordinary least squares regression procedure. The standard error of prediction for the regression equations were calculated and used to compare the Bulletin 17B and L-Moments methods. This is the first study to indicate that the L-Moments method is, on average, the better of the two methods tested for predicting flood frequency for unregulated streams and rivers in Tennessee. This thesis is approved for recommendation to the Graduate Council. Thesis Director: _______________________________________ Dr. Findlay G. Edwards Thesis Committee: _______________________________________ Dr. Brian E. Haggard _______________________________________ Dr. Manuel D. Rossetti THESIS DUPLICATION RELEASE I hereby authorize the University of Arkansas Libraries to duplicate this thesis when needed for research and/or scholarship. Agreed __________________________________________ Hongxiang Yan Refused __________________________________________ Hongxiang Yan ACKNOWLEDGMENTS First I want to thank my advisor, Dr. Findlay Edwards, who tutored me to this topic. Without his kind guidance and valuable suggestions, I could not have finished this study. Also special thanks to Dr. Brian Haggard and Dr. Manuel Rossetti; thanks so much for being on my committee. Thanks to Dr. Yang Peng in China, without her patient teaching and helping, I cannot have a chance to study in America. Second I want to thank all my friends in America: Cheng Li, Drew Cunningham, Fan Wang, Jeff Rudolph, Jin Zhang, Lei Huang, Robert Rembert, Jiao Wang, Xin Xiao, Yaohua Cheng, YoYo, and Yiwei Qian. Thank you so much for being my friends and helping me to get through the difficult parts. Third I want to thank the Hunter Family: Joey, Tammy, and Lydia. Thanks so much for picking me as your student in the Friendship Family Program. I feel so lucky that I could be one of your family in America. Finally, I want to thank my family in China: my parents, my big brother and my sister in law. You guys always encourage me when I feel down; thank God that we are a family in this life. TABLE OF CONTENTS CHAPTER 1 INTRODUCTION ..................................................................................... 1 Statement of Problem ...................................................................................................... 1 Purpose of Study ............................................................................................................. 4 CHAPTER 2 LITERATURE REVIEW .......................................................................... 5 Overview ......................................................................................................................... 5 Previous Studies in Tennessee ........................................................................................ 5 Flood Frequency Studies in Other States ...................................................................... 10 L-Moments Method ...................................................................................................... 11 Need for This Study ...................................................................................................... 15 CHAPTER 3 METHODS.............................................................................................. 16 Overview ....................................................................................................................... 16 Description of the Study Area ....................................................................................... 17 Annual Peak Flow Data ................................................................................................ 20 Physical Basin Characteristics ...................................................................................... 23 Data Sources ................................................................................................................. 25 Watershed Modeling System (WMS) ........................................................................... 26 Bulletin 17B Method..................................................................................................... 26 Screening the Data ........................................................................................................ 28 Identification of Homogeneous Areas .......................................................................... 29 Choice of a Frequency Distribution .............................................................................. 33 FORTRAN Program for L-Moments............................................................................ 34 Regression Analysis for Annual Peak Flow ................................................................. 37 Regression Model Adequacy Checking ........................................................................ 38 CHAPTER 4 RESULTS AND DISCUSSION ............................................................. 42 Overview ....................................................................................................................... 42 Basin Characteristics ..................................................................................................... 42 L-Moments .................................................................................................................... 43 Data Screening .............................................................................................................. 43 Formation of Homogeneous Areas ............................................................................... 47 Choice of Frequency Distribution for the Four Hydrologic Areas ............................... 54 Choice of Frequency Distribution for the Five Hydrologic Sets .................................. 56 Bulletin-17B Method .................................................................................................... 58 Regression Analysis ...................................................................................................... 59 Comparison of Methods ................................................................................................ 63 Computation Examples ................................................................................................. 66 CHAPTER 5 CONCLUSION ....................................................................................... 68 FURTHER RESEARCH .................................................................................................. 70 REFERENCE .................................................................................................................... 72 APPENDIX CONTENT ................................................................................................... 78 APPENDIX A: SUMMARY OF SIX PREVIOUS STUDIES IN TENNESSEE ............ 79 APPENDIX B: THE SELECTED BASIN CHARACTERISTICS AND FLOOD-FREQUENCY ESTIMATES..................................................................................................................... 91 APPENDIX C: THE C++ CODE FOR L-MOMENT RATIO CALCULATION ......... 175 APPENDIX D: THE C++ CODE FOR DISCORDANCE CALCULATION ............... 177 LIST OF TABLES Table 1.1. Problems in practice by using flood frequency analysis (Wang, 1999) ............ 3 Table 1.2. The 3rd generation flood control standard of world dam (Berga, 1992) ............ 3 Table 3.1. Summary of the distribution of data and average length of record ................. 22 Table 3.2. Eight basin characteristics used