© 2011 by Taylor and Francis Group, LLC Science Publishers Jersey, British Isles Enfi eld, New Hampshire © 2011 by Taylor and Francis Group, LLC CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20120306 International Standard Book Number-13: 978-1-4398-8341-9 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com © 2011 by Taylor and Francis Group, LLC Foreword Statistical hydrology has long played a critical role in civil and environmental engineering practice and in the design of water resource structures. Hydrology has also played a role in the development of statistics, particularly in extremes. For example, one of the earliest applications of the statistics of extreme values was in the definition and practical computations of the return period of floods. An enormous amount of information can be obtained from the statistical analysis of time series of hydrological and meteorological measurements whose diverging rescaled range with sample size has been pointed out -- notably, by a hydrologist -- as the signature of how Nature works. The fundamental questions addressed in this book concern how to assign a probability to the future occurrence of an event of a given magnitude. Engineering practice involves designing and operating hydraulic structures for water resource exploitation, which have as inputs random events, not deterministic phenomena, as is the rule in other areas of engineering. A wide range of periods of drought and flooding occur across the Earth’s surface. And hydrological extreme events are expected to increase due to the acceleration of the hydrologic cycle as a result of global warming. The role of frequency analysis and the study of trends in hydrology (study of non-stationarity) remain ever more important, with substantial social implications, chiefly associated with current questions of sustainability. The authors of this fine book have clearly laid out the principles of frequency analysis in hydrology at a level suitable for majors in civil and environmental engineering that will beautifully integrate with their other courses in probability and statistics, hydrology, and water resources management. Topics thoroughly treated include probabilistic definitions, risk and data analysis, model selection and parameter estimation, and uncertainty studies, as well as a forward-looking introduction to Bayesian methods, non-stationarity and the use of copulas in hydrology. These topics are discussed in the last chapter and provide an original launching point for further studies in statistical hydrology. © 2011 by Taylor and Francis Group, LLC vi Foreword This book will serve as an important point of reference and should be part of the library of practicing engineers and scientists. The authors have combined their many years of experience in practice, teaching and research in statistical hydrology to produce this superb textbook that will be appreciated by both students and teachers. Professor Marc Parlange School of Architecture, Civil and Environmental Engineering, EPFL © 2011 by Taylor and Francis Group, LLC Preface Data about the natural environment of any region are a vital part of its heritage and provide the most accurate assessment of its condition. Therefore this information is absolutely essential for the engineers, managers and politicians involved in any development or protection efforts. Acquiring this data is an exacting task, and requires significant organization and investment at every step in the process. Because such information concerns systems or processes that are extremely complex, it is both very valuable, and quite rare. In general and no matter the amount, this data – usually local data – is insufficient to provide a reliable representativeness of the system from which it originates and of its space-time evolution. This means that great caution must be used in analyzing the data in order to extract all the information, sometimes hidden, that they contain. Frequency analysis serves this purpose. It is one of the methods and techniques of statistical analysis that are essential before data can be used for specific applications. More precisely, frequency analysis makes possible the projection of data in probabilistic space in order to foresee the behavior and reactions of the systems or processes the data describes or represents, so that decision-makers will have credible and substantiated information before taking any action. For example, before beginning work on any flood management structure, dike, impounding reservoir, or water diversion, it is essential to have relevant and solid information for assessing possible extraordinary rainfall events that could impact the watershed concerned. The appropriate frequency analysis makes it possible to specify the criteria necessary for designing such hydraulic structures, and also provides an estimation of the quality of the information available by determining its degree of certainty or likelihood. These methods and techniques, often resulting from experience, are based on statistical principles and approaches. The intuition, experience and scientific knowledge of the engineer must be confirmed, expanded and justified using a rigorous approach. After this, however, the results must be tested and checked experimentally. This is because in actual © 2011 by Taylor and Francis Group, LLC viii Preface practice, some of the statistical tests that are recommended by the theorists often reveal themselves to be poorly suited for checking certain characteristics of time series, auto-correlation in particular. This book combines experimental approaches and those from scientific developments, which makes it somewhat unique. The methods and approaches contained herein appeared first in teaching materials in the form of course notes. Originally, the material was based on case studies, which was reworked for teaching purposes and designed for students in applied engineering, the water sciences in particular. Paul Meylan, my unfailing friend on this project, made a significant contribution in developing this instructional material and converting it into the appropriate scientific language. Afterwards, Anne-Catherine Favre, a mathematician and statistician, brought some careful and authoritative improvements to the analysis and its rigor and introduced some very promising fields of research. The end result is a book that combines the very different training and backgrounds of the authors, and especially their distinctive scientific and teaching interests. However, this book would never have been completed without the enormous dedication and perseverance of the two scientists named above, who conducted research under my supervision during several years at the Laboratoire Hydrologie et Aménagements HYDRAM (now ECOL : Ecological Engineering Laboratory) at the École Polytechnique Fédérale de Lausanne. For this I will be forever grateful. This book is slanted towards the hydrological sciences and their applications in terms of water and environmental engineering. It describes the treatment of all sorts of data, but focuses especially on data about meteoric and terrestrial water, with an emphasis on rare and unusual events, or what are commonly referred to as “extreme events”. This book is aimed particularly at students in civil engineering, environmental sciences and technology, hydrology, geography, geology and ecology, all of whom must be concerned with the judicious use of data for the design and construction of water management structures. This book will also be useful for engineering practitioners, who are faced constantly with problems regarding data, or the lack thereof, when attempting to develop an accurate portrayal of hydrological processes and to analyze their behavior. And finally, this book will be useful for teachers in disciplines involving the processing of environmental data or any other data concerning the evolution over time of a system (data linked to traffic, air quality, water quality, etc. …). The topics covered in this book are by no means exhaustive, but they do provide some answers to the main questions that arise during the design or restoration of water management structures or when © 2011 by Taylor and Francis Group, LLC Preface ix assessing their impacts on the natural or built environment. This book also addresses some difficult problems, such as the non-stationarity of natural phenomena or the multidimensional aspects of risk, and provides some alternative solutions or at least suggests some pathways for finding a resolution. My hope is that readers will find the methods and techniques they need for the successful realization of projects related to water management and connected fields, and thus contribute to the sustainable development of our societies and our environment. André Musy Honorary Professor, EPFL TRANSLATION Given the success of the French-language versions of this book, which was first published in 2008, we received a great deal of encouragement to translate it into English for the benefit of a broader readership. This we were able to do with the help of translation and revision by Ms Robyn Bryant and especially the committed involvement of the co-authors. Financial support for this translation was provided by the Institut d’ingénierie de l’environnement (Institute of Environmental Engineering) at EPFL and The Federal office of environment of Switzerland, Hydrological division at Bern. The authors are deeply grateful to these individuals and institutions and to the administrative structures where these various individuals are involved, namely the AIC consulting firm in Lausanne. © 2011 by Taylor and Francis Group, LLC Contents Foreword v-vi Preface vii-ix 1. Introduction 1 1.1 Forecasting and Prediction 1 1.2 Frequency Analysis 2 1.3 The Principle of Frequency Analysis 3 1.4 Outline of this Book 13 2. Return Period, Probability and Risk 15 2.1 Return Period 15 2.2 The Probability of Events 19 2.3 Risk 21 2.4 Utilization of Standards 27 3. Selecting and Checking Data Series 29 3.1 Choices of Events 30 3.2 Types of Series 38 3.3 Types of Errors 43 3.4 Error Identification and Measurement Correction 44 3.5 Introduction to Statistical Tests 46 3.6 Test of One Parameter, Local Scale 52 3.7 One Parameter – Regional Scale 66 4. Selecting a Model 71 4.1 The Gamble of Frequency Analysis 71 4.2 Possible Approaches to Choosing the Type of Model 76 4.3 Conclusions 89 5. Estimation of Model Parameters 91 5.1 The Maximum Likelihood Method 91 5.2 The Method of Moments 93 © 2011 by Taylor and Francis Group, LLC xii Contents 5.3 The Method of Probability Weighted Moments 94 5.4 The Method of L-Moments 96 5.5 The Graphical Method 96 5.6 A Comparison of Parameter Estimation Methods 101 6. Validation of the Model 103 6.1 Visual Examination 103 6.2 The Chi-Square Test 103 6.3 The Kolmogorov-Smirnov Test 108 6.4 The Anderson-Darling Test 111 6.5 Goodness-of-Fit Indices 115 6.6 Comparison of Models 116 6.7 Conclusions 117 7. Uncertainties Analysis 119 7.1 Sources of Uncertainties 119 7.2 The Confidence Interval 121 7.3 Confidence Interval and Return Period 126 7.4 Confidence Interval using the Parametric Bootstrap 133 7.5 Conclusions 133 8. Using the Frequency Model 135 8.1 The Probability of Hydrological Events 136 8.2 Annualization of Infra-annual Series 137 8.3 The Frequency Use of Nonsystematic Data 144 8.4 Frequency Use of IDF Curves 145 8.5 Considering Uncertainties in the Case of a Function with Several Variables 150 8.6 Frequency Analysis by Counting 154 9. Perspectives 161 9.1 Bayesian Frequency Analysis 161 9.2 Multivariate Frequency Analysis using Copulas 164 9.3 Frequency Analysis in a Non-stationarity Context 176 9.4 Regional Frequency Analysis 179 Bibliography 189-202 List of Acronyms 203-204 Index and List of Proper Names 205-206 Subject Index 207-212 © 2011 by Taylor and Francis Group, LLC