Hilbert-Huang Transform Analysis of Hydrological and Environmental Time Series

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Springer Science & Business Media, Jan 8, 2008 - Science - 248 pages
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To accommodate the inherent non-linearity and non-stationarity of many natural time series, empirical mode decomposition (EMD) and Hilbert-Huang transform (HHT) provide an adaptive and efficient method. The HHT is based on the local characteristic time scale of the data. The HHT method provides not only a precise definition in time-frequency representation than the other conventional signal processing methods, but also more physically meaningful interpretation of the underlying dynamic processes. The EMD also works as a filter to extract the variability of signals with different scales and is applicable to non-linear and n- stationary processes. This promising algorithm has been applied in many fields since it was developed, but it has not been applied to hydrological and climatic time series. The discussion in this book starts with several simulated data sets in order to investigate the capability of this method and to compare it to other conventional frequency-domain analysis methods that assume stationarity. Rainfall, streamflow, temperature, wind speed time series and lake temperature data are investigated in this study. The aim of the work is to investigate periodicity, long term oscillations and trends embedded in these data by using HHT. The analysis is performed in both the time and frequency domains. The results from HHT are compared to those from the multi-taper method (MTM) which is based on Fourier Transform of the data.
 

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Contents

INTRODUCTION
1
HILBERTHUANG TRANSFORM HHT SPECTRAL ANALYSIS
5
222 MultiTaper Method MTM of Spectral Analysis
6
223 Spectrogram
7
23 EMPIRICAL MODE DECOMPOSITION
8
24 HILBERTHUANG SPECTRA
12
25 RELATIONSHIP BETWEEN HHT AND FOURIER SPECTRA
14
26 VOLATILITY OF TIME SERIES
17
44 CONCLUDING COMMENTS
118
STREAMFLOW DATA ANALYSIS
121
52 USGS STREAMFLOW DATA
125
522 TimeFrequency Distribution
126
523 Comparison with MTM Spectra
130
53 ANALYSIS OF WARTA GODAVARI AND KRISHNA RIVER FLOW DATA
135
532 Warta River Monthly Streamflow Data
140
533 Godavari River Monthly Streamflow Data
143

27 DEGREE OF STATIONARITY OF TIME SERIES
19
28 STATIONARITY TESTS
20
282 Trend Test of Segments Derived from IMFs
22
29 CONCLUDING COMMENTS
25
HILBERTHUANG SPECTRA OF SIMULATED DATA
27
322 Simple Harmonic Data
28
323 Decaying Signal
31
324 A Signal with Three Close Frequencies
32
325 Autoregressive Model
34
33 SIMULATION OF NONSTATIONARY RANDOM PROCESSES
38
333 Simulation with Random Phases and Amplitudes
44
334 Simulation by WenYeh Method
57
34 CONFIDENCE INTERVALS FOR MARGINAL HILBERT SPECTRUM
76
35 CONCLUDING COMMENTS
81
RAINFALL DATA ANALYSIS
83
412 NCDC Average Divisional Rainfall Data
84
42 HCN RAINFALL DATA
86
422 TimeFrequency Distribution
90
423 Frequency Domain Analysis
98
43 NCDC RAINFALL DATA
103
433 Frequency Domain Analysis
112
534 Krishna River Monthly Streamflow Data
144
54 CONCLUDING COMMENTS
147
TEMPERATURE DATA ANALYSIS
149
621 Original Data
152
622 LinearTrend Removed Data
161
623 AnnualCycle Removed Data
165
63 HCN AND NCDC MONTHLY TEMPERATURE TIME SERIES
169
632 NCDC Monthly Temperature Time Series
178
64 CONCLUDING COMMENTS
193
WIND DATA ANALYSIS
195
DAILY AVERAGE WIND SPEED DATA
205
DAILY PEAK WIND SPEED DATA
212
CONCLUDING COMMENTS
216
LAKE TEMPERATURE DATA ANALYSIS
219
82 LAKE TEMPERATURE SPATIAL SERIES ANALYSIS
224
823 Frequency Domain Analysis
229
CONCLUSIONS
235
REFERENCES
239
INDEX
243
Copyright

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About the author (2008)

I. GENERAL INFORMATION

Name: A. Ramachandra Rao

Date of Birth: 23 October 1939

Academic Record

School Attended Degree Date

University of Illinois 1964-68 Ph.D. 1968

University of Minnesota 1962-64 M.S.C.E. 1964

University of Mysore (India) 1956-60 B.E. 1960

1. Professional Experience:

Employer Position Date

University of Mysore Lecturer in Civil 1960-62

(India) Engineering

University of Minnesota Research Assistant 1962-64

University of Illinois Research Assistant 1964-68

Purdue University Visiting Assistant 1968-70

Professor

Purdue University Assistant Professor 1970-73

Govt. of New Zealand NRAC Senior Research Fellow 1977-78

Purdue University Associate Professor 1973-80

Purdue University Professor 1980-

Construction Engineering Visiting Faculty May-July, 1983

Research Laboratory Member 1983

Purdue University Acting Head, Hydraulics 1983-84

and Systems Engineering Area

Indian Institute of Science, Visiting Professor of Jan-July,

Bangalore, India Civil Engineering 1989

University of Illinois, Visiting Professor of Jan-May

Urbana, IL Civil Engineering 1998

2. Awards, Honors, Citations

Awarded a Senior Research Fellowship by the National Research Advisory Council, Government of New Zealand, for research in hydrology with the Ministry of Works and Development during 1977-78.

Awarded (but not accepted) a "Senior Scientist Fellowship" by the Alexander Von Humboldt Foundation, West Germany (1977).

Awarded (but not accepted) the "C.H. Munro Fellowship" of the Water Research Foundation of Australia, for research in Hydrology, at Monash University, Clayton, Victoria, Australia (1977).

Honorary Societies

Member, Chi Epsilon, Sigma Xi

Citations

American Men and Women of Science

Who's Who in the Midwest

Who's Who in Frontier Science and Technology

Who's Who in Science and Engineering

Who's Who, Environmental Registry

Who’s Who in the World

Who’s Who in American Education

Invited Activities and Lectures

Invited by UNESCO to attend the "International Symposium on Hydrologic Aspects of Droughts", New Delhi, 3-8 December 1979.

Member, American Delegation to the XVIII General Assembly, IUGG, Hamburg, Federal Republic of Germany, August 15-27, 1983.

Invited Specialist, IAWPRC Seminar on "Rainfall as the Basis for Urban Runoff Design and Analysis", Technical University of Denmark, Lyngby, Denmark, August 24-26, 1983.

Invited lecture, "Detection of Climatic Changes in Hydrologic Time Series". Eighth IHD Endowment Lecture, Anna University, Madras, India, April 13, 1989.

Keynote lecture, "Bayesian Unit Hydrographs" International Conference on Hydrology and Water Resources, Delhi, India, December, 1993.

Member, Editorial Board of "Water Science and Technology Library", Kluwer Academic Publishers B.V. Dordrecht, The Netherlands, (1993-99).

Editor, "Journal of Irrigation and Drainage Engineering", ASCE, 1992 - 1998.

Keynote lecture, "Bayesian Unit Hydrographs" International Conference on Hydrology and Water Resources, Delhi, India, December, 1993.

Founder/honorary member, "Center of Resource Management and Eco-development Studies", I.I.T., Delhi, 1994.

Fellow, Indian Association of Hydrologists.

"Edmund M. Burke Outstanding Civil Engineering Professor", School of Civil Engineering, Purdue University, April 1995.

Invited paper, "Principal Component Analysis of Hydrologic Data", A.R. Rao and T.T. Burke, Jr., NATO Advanced Research Workshop on "Integrated Approach to Environmental Data Systems", Izmir, Turkey, Sept. 16-20, 1996.

Invited to deliver a keynote paper in the International Symposium on "Emerging Trends in Hydrology", Department of Hydrology, University of Roorkee, India, Sept. 25-27, 1997.

tp, Dean Marion B. Scott 1997 Exemplary Character Award, Purdue University.

Invited speaker, Int. Conference on Water, Environment, Ecology, Socio-Economics and Health Engineering, Seoul National University, Seoul, Korea, Oct. 18-21, 1999.

Invited speaker, Int. Conference on Integrated Water Resources Management for Sustainable Development, Roorkee, India, Dec. 2000.

Invited speaker, Golden Jubilee Celebration of the Civil Engineering Department, Indian Institute of Science, Bangalore, India, July 2001.

Keynote Address, "Studies in Regionalization of Watersheds,” International Conference on Water and Environment, Bhopal, India, 20 pp., Dec. 15-18, 2003.

State and National Offices

Chairman of the Engineering Division of the Indiana Academy of Sciences (1978-79)

3. Society Memberships and Activities

Member, American Society of Civil Engineers

Member, American Association for the Advancement of Science

Member, American Geophysical Union

Member, International Association for Hydraulic Research

National Committee Activity

Member, Task Committee on Rainfall-Runoff Quality

Data Systems, Urban Water Resources Council, ASCE (1970-71)

Member, Task Committee on Effects of Urbanization on Low Flow, Total

Runoff, Infiltration and Groundwater Recharge, ASCE (1974-76)

Member, Surface Water Hydrology Committee, Hydraulics Division,

American Society of Civil Engineers (1979-present)

Member, Committee on Surface Water, Irrigation and Drainage

Division, American Society of Civil Engineers (1979-present).

Member, Control Group (1982-present), Vice Chairman (1983-84).

Chairman (1984-85), Past Chairman (1985-86)

Member, Committee on Hydrology, American Meteorological Society (1985-87)

Member, Task Committee on Risk, Hydraulics Division, ASCE (1984-85).

Member, Task Committee on Infiltration Manual, Surface Water Committee, Irrigation and

Drainage Division, ASCE (1986-present)

Member, Control Group, Publications Committee, Irrigation and Drainage Division, ASCE (1986-present)

Member, AGU Committee on Education and Human Resources (1986-1990)

Associate Editor, Journal of Irrigation and Drainage Engineering, ASCE, (1990-1992)

Chairman, Task Committee on Droughts, Irrigation and Drainage Division, ASCE, (1990-1992)

Editor, Journal of Irrigation and Drainage Engineering, ASCE (1992-1998)

Chairman, Task Committee on Droughts, Irrigation and Drainage Division, ASCE, (1990-1992)

Chairman, Task Committee on Engineering Approaches to Coping with Droughts, Water Resources Engineering Division, (1994-1996)

Associate Editor, Journal of Irrigation Engineering, ASCE, (1990-1992)

Member, Surface Water Hydrology Committee, Water Resources Division, ASCE (1986-present)

Chairman, Committee on Publications, Irrigation and Drainage Engineering, ASCE, (1992 - 98)

Member, Task Committee on "Role of Run On Effect on Surface and Subsurface Hydrologic Process”, ASCE, Surface Water Committee (2005-2008).

4. Consulting Activities

1. Forest Hills Country Club, Richmond, Indiana. Design of Water Main (1969).

2. The Engineers Collaborative, 110 East Ontario Street, Chicago. Hydrologic design and development of control systems for the flood control reservoir on the north branch of the Chicago River, Deerfield, Illinois (1969-71).

3. Tippecanoe County Surveyor's Office, Industrial park drainage study (1971).

4. "Save Newburgh Waterfront Society", Newburgh, Indiana. Effects of lock and dam construction on the Ohio River on the bank erosion at Newburgh, Indiana (1972).

5. Consultant on Storm Water Flow Measurement into Sewage Treatment Plants of Indianapolis; M.D. Wessler & Assoc. Indianapolis, Indiana (1979-80).

6. Consultant to the city of Greencastle, Indiana, on surcharge in sewer systems in Greencastle (1981).

7. Consultant to the State of Indiana, Office of the Attorney General, in the matter of the Boundary dispute between Indiana and Kentucky, 1981.

8. Consultant in the Matter of Amazon Dam Failure, Indiana 1984.

9. Wolf Construction Co., Logansport, IN. 1985.

10. The city of Portage, IN. 1985.

11. "Mary E. Vinton Estates", Lafayette, IN 1986.

12. Frankfort KY, drainage problems, 1987 - 1990.

13. U.S. AID, "Indo-Nepal Water Problems", Patna, India, 1992.

II. TEACHING AND RELATED ACTIVITIES

1. Courses Taught (only list from 1998) Year Sem. No. Title Cr. Enrollment 1998-99

1 CE 340 Hydraulics 4 109

1 CE 597I Computational Hydraulics 3 6

2 CE 340 Hydraulics 4 71

1999-00 1 CE 549 Watershed Modeling 3 9

2 CE 340 Hydraulics 3 59

2000-01 1 CE 340 Hydraulics 3 80

1 CE 498 Senior Design 3 70

2 CE 542 Hydrology 3 15

2001-02 1 CE 440 Urban Hydraulics 3 15

1 CE 549 Watershed Modeling 3 12

2 CE 542 Hydrology 3 24

2002-03 1 CE 340 Hydraulics 3 80

2 CE 542 Hydrology 3 27

2003-04 1 CE 641 Statistical Hydrology 3 7

2 CE 542 Hydrology 3 22

2004-05 1 CE 349 Hydraulics 3 80

2 CE 542 Hydrology 3 24

III. RESEARCH AND RELATED ACTIVITIES

PUBLICATIONS

I. BOOKS AND BOOK CHAPTERS

1. R.L. Kashyap and A.R. Rao, RUSSIAN Edition of "Dynamic Stochastic Models from Empirical Data" "HAYKA" publishers, Moscow, U.S.S.R., 1983.

2. R.L. Kashyap and A.R. Rao, "Dynamic Stochastic Models from Empirical Data", Vol. 122 in the series, "Mathematics in Science and Engineering", Academic Press, New York, NY, 1976, 330 pp.

3. A.R. Rao, "Stochastic Analysis of Thresholds in Hydrologic Time Series", Chapter 9 in "Thresholds in Geomorphology", Ed. D.R. Coates and J.D. Vitek, George Allen and Unwin, Boston, 1980, pp. 179-209.

4. J.W. Delleur and A.R. Rao, "Linear Systems Analysis in Hydrology - The Transform Approach, The Kernal Oscillations and the Effect of Noise", Paper No. 9 in "Systems Approach to Hydrology", Water Resources Publications, Fort Collins, CO, 1971, pp. 116-142.

5. A.R. Rao and K.H. Hamed, "Flood Frequency Analysis”, CRC Press, Boca Raton, FL., 350 pp. 1999.

6. R.S. Govindaraju and A.R. Rao (eds.), "Artificial Neural Networks in Hydrology”, Vol. 36, Water Science and Technology Library, Kluwer Academic Publishers, Dordrecht, Holland, 329 pp. 2000.

7. A. R. Rao, "Surface Water Hydrology", Chapter 31, The Civil Engineering Handbook, pp. 31-1 - 31-29, CRC Press, Boca Raton, FL., 2003.

8. A.R. Rao, C.B. Burke and T.T. Burke, Jr., "Urban Drainage", Chapter 32, The Civil Engineering Handbook, pp. 31-1 – 32-12, CRC Press, Boca Raton, FL., 2003.

9. T.T. Burke, Jr., C.B. Burke and A.R. Rao, "Computer Simulation in Hydraulics and Hydrology", Chapter 38, The Civil Engineering Handbook, pp. 38-1 – 38-35, CRC Press, Boca Raton, FL., 2003.

10. A.R. Rao, K.H. Hamed, and H-L Chen, "Nonstationarities in Hydrologic and Environmental Time Series”, Klewer Academic Publishers, Dordrecht, Holland, 361 pp. 2003.

11. A. R. Rao and V. V. Srinivas, A Book, "Regionalization of Watersheds – An Approach Based on Cluster Analysis”, (Expected 2006).

12. A. R. Rao and En-ching Hsu, A Book, "Hilbert-Huang Transform Hydrologic and Climatic Series”, in preparation.

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