Hilbert-Huang Transform Analysis Of Hydrological And Environmental Time Series
The Hilbert-Huang Transform ((HHT) is a recently developed technique which is used to analyze nonstationary data. Hydrologic and environmental series are, in the main, analyzed by using techniques which were developed for stationary data. This has led to
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Water Science and Technology Library VOLUME 60
Editor-in-Chief V.P. Singh, Texas A&M University, College Station, U.S.A. Editorial Advisory Board M. Anderson, Bristol, U.K. L. Bengtsson, Lund, Sweden J. F. Cruise, Huntsville, U.S.A. U. C. Kothyari, Roorkee, India S. E. Serrano, Philadelphia, U.S.A. D. Stephenson, Johannesburg, South Africa W. G. Strupczewski, Warsaw, Poland
The titles published in this series are listed at the end of this volume.
HILBERT-HUANG TRANSFORM ANALYSIS OF HYDROLOGICAL AND ENVIRONMENTAL TIME SERIES by
A. RAMACHANDRA RAO School of Civil Engineering, Purdue University, West Lafayette, IN, U.S.A.
and
EN-CHING HSU School of Civil Engineering, Purdue University, West Lafayette, IN, U.S.A.
Library of Congress Control Number: 2007936514
ISBN 978-1-4020-6453-1 (HB) ISBN 978-1-4020-6454-8 (e-book)
Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com
Cover Image: Time-frequency distribution of monthly streamflows in the Warta river (Fig 5.3.5 (b))
Printed on acid-free paper
All Rights Reserved © 2008 Springer Science+Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
DEDICATION
This book is respectfully dedicated to the unique yogini of the twentieth century Maatha Jayalakshmi and to her son the great Siddha Purusha Sri Sri Sri Ganapathi Sachchidananda Swamiji of Avadhootha Datta Peetham Sri Ganapathi Sachchidananda Ashrama, Mysore 570 025, India with namaskarams
CONTENTS
Preface
xi
1.
Introduction
1
2.
Hilbert-Huang Transform (HHT) Spectral Analysis 2.1. Introduction 2.2. Conventional Spectral Analysis Methods 2.2.1. Fourier Transform Analysis 2.2.2. Multi-Taper Method (MTM) of Spectral Analysis 2.2.3. Spectrogram 2.3. Empirical Mode Decomposition 2.4. Hilbert-Huang Spectra 2.5. Relationship between HHT and Fourier Spectra 2.6. Volatility of Time Series 2.7. Degree of Stationarity of Time Series 2.8. Stationarity Tests 2.8.1. Modified Mann-Kendall Test 2.8.2. Trend Test of Segments Derived from IMFs 2.9. Concluding Comments
5 5 5 5 6 7 8 12 14 17 19 20 20 22 25
3.
Hilbert-Huang Spectra of Simulated Data 3.1. Introduction 3.2. Synthetic Data Analysis 3.2.1. Introduction 3.2.2. Simple Harmonic Data 3.2.3. Decaying Signal 3.2.4. A Signal with Three Close Frequencies 3.2.5. Autoregressive Model 3.3. Simulation of Nonstationary Random Processes 3.3.1. Introduction 3.3.2. Simulation with Random Phases 3.3.3. Simulation with Random Phases and Amplitudes 3.3.4. Simulation by Wen-Yeh Method
27 27 27 27 28 31 32 34 38 38 38 44 57
vii
viii
CONTENTS
3.4. 3.5.
Confidence Intervals for Marginal Hilbert Spectrum Concluding Comments
76 81
4.
Rainfall Data Analysis 4.1
