PARAMETRIC ESTIMATION AND REAL-TIME FORECAST OF WIND WAVES
MOURANI SINHA
CENTRE FOR ATMOSPHERIC SCIENCES INDIAN INSTITUTE OF TECHNOLOGY DELHI
NEW DELHI –110 016, INDIA.
September 2012
PARAMETRIC ESTIMATION AND REAL-TIME FORECAST OF WIND WAVES
by
MOURANI SINHA
Centre for Atmospheric Sciences
Submitted in fulfillment of the requirements of the degree of
DOCTOR OF PHILOSOPHY
to the
INDIAN INSTITUTE OF TECHNOLOGY DELHI HAUZ KHAS, NEW DELHI –110 016, INDIA.
September 2012
Dedicated to my
parents and sona.
Certificate
This is to certify that the thesis entitled “PARAMETRIC ESTIMATION AND REAL-TIME FORECAST OF WIND WAVES” being submitted by Ms. Mourani Sinha to the Indian Institute of Technology Delhi for the award of the degree of DOCTOR OF PHILOSOPHY is a record of the original bonafide research carried out by her. Ms. Mourani has worked under our guidance and supervision and has fulfilled the requirements for the submission of this thesis. The results contained in this thesis have not been submitted in part or full to any other University or Institute for the award of any degree or diploma.
(Dr S K Dube) (Dr A D Rao) Professor Professor
Centre for Atmospheric Sciences Centre for Atmospheric Sciences Indian Institute of Technology Delhi Indian Institute of Technology Delhi New Delhi-110016, INDIA New Delhi-110016, INDIA
Acknowledgements
It is my great privilege to express my deep sense of gratitude to Prof. A. D. Rao, Professor, Centre for Atmospheric Sciences (CAS), Indian Institute of Technology Delhi (IITD) and my thesis supervisor for his meticulous guidance, helpful suggestions, personal attention, and overall direction of this research study. Without his help it would have been difficult for me to complete this venture successfully.
I express my heartiest gratitude to Prof. S. K. Dube, Professor, CAS, IITD, and my thesis supervisor for his constant encouragement, constructive criticism, kind inspiration and motivation throughout the period of investigation. He has been always there as an invaluable guiding beacon for catering solution to my PhD research problems.
I am highly indebted to Prof. S.K. Dash, Head, CAS, IIT D and Prof. Pramila Goyal, CRC Chairperson, CAS, IITD, including all CRC members for their pragmatic and relentless support throughout my research work. I am grateful to my SRC committee members for their timely evaluation and guidance for the whole research work progression.
I express my earnest gratitude and warmest regards to Prof. Debabrata Sen, Indian Institute of Technology Kharagpur, for his valuable suggestions from the very initial stage of my research work.
With great pleasure, I express my gratitude to Dr. G. Muraleedaran, Centre for Marine Technology and Engineering, Technical University of Lisbon, Portugal, and Dr. Sujit Basu, Space Application Centre, Indian Space Research Organization (ISRO), India for their enthusiastic interest, personal support, apt advice and untiring help throughout the period of investigation so as to reach to some scientific conclusion. I express my deep regards to Dr. Raj Kumar, Suchandra and Vihang of Space Application Centre, ISRO, for their valuable support during the period of my research work.
I would like to express my sincere gratitude to Dr. Prasad K. Bhaskaran of Indian Institute of Technology Kharagpur and Dr. G. Latha, NIOT, Chennai, India for their time to time help and co-operation during the course of my thesis work.
I am deeply obliged to all the faculty members of CAS, IIT Delhi who guided me as teachers and helped me with wise counseling during the research work. I would also like to thank all the supporting staffs members of CAS, IIT Delhi. I warmly thank my seniors, Dr. Babu, Dr. Indu and Dr. Gagan for their support, suggestions and advices during the entire research period, at the Ocean State Lab, CAS, IITD. My special thanks are due to my senior Mr. Debasish Mahapatra, at present scientist in NCMRWF, India, with whom I had my first learning session of ocean modeling. I wish to thank all my
friends and colleagues, past and present at CAS, IITD, in particular, Aditi, Sujata, Palash, Subrat, Madhu, Himanshu, Jismy, Ravi, P L N Murthy, Smitha, Deepak, Srinivas, Swagat, Neeru, Nachiketa and Abhishekh who extended their helping hands during the entire period of study.
I express my heartfelt gratitude to the NIIT University, Neemrana, where I am currently positioned as Assistant Professor, for their constant support and encouragement during the final stage of PhD completion.
No words of mine would be adequate to express my indebtedness to my father, mother, and brother Ramit who have sacrificed many things over the years for my pleasure and progress. Their blessings and love always worked in bringing me nearer to my long cherished aspirations. In this special moment I would like to extend my special gratitude and love to my daughter Samya who has been with me always and the tripartite symbiotic association among Samya, my research and I have proved to be an inspiring milieu for all three of us. I want to thank Soumendu, my husband, too for his patience to support me in this long mission of PhD.
Last, but not the least, I would like to extend my heartiest thanks and deepest affection to my friends Dr Somnath, Amit, and Abhilasha, for their constant encouragement during the finalization of my whole research work as well as providing me moral support.
(MOURANI SINHA) NEW DELHI
i
Abstract
Ocean surface waves have been studied under two broad categories, probabilistic estimation and real-time forecast of wave parameters. Ocean wave properties vary simultaneously on different spatial and time scales. The probabilistic distribution of wave heights is of great importance in ocean and coastal engineering applications. It plays a key role in the stability of coastal and offshore structure studies, in the evaluation of beach and coastal shelves, sediments transport, pollutant dispersion, etc. New advancement in technology allows probabilistic approach to predict the responses of marine systems with reasonable accuracy. It has become an integral part of modern design technology in naval, ocean and coastal engineering. On the other hand real-time forecasting of ocean waves over a short duration such as a few hours is useful in carrying out many engineering activities in the sea, like laying of a submarine pipeline and issuing warnings to fishing community. The literature on ocean wave forecasting suggests two methods, physics-based models and statistical techniques. Physics- based models have been in operation since the 1960s, and the large-scale energy balance models which integrate the fluid governing equations have been the methodology of choice since the 1970s. The statistical literature is more recent. The time series methods originate in the 1990s.
Prediction of a system in time from the observed time series have been performed using various techniques like polynomial fitting, nearest neighbors, neural networks and genetic algorithm.
Recently, several works have been reported combining both methods, by statistical post- processing of physics-based model forecasts. Since these two approaches have evolved independently, it is of interest to determine which approach can predict more accurately, and over what time horizons.
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In the second chapter, we establish the modified Weibull distribution that can generate a family of curves depending upon its tuning and calibration coefficients which will enable us to fix the exact curve that fits the wave height distribution. The parametric relations are derived there from to estimate various wave height statistics including extreme wave heights. The statistical tools suggested and developed here for predicting the required wave height statistics are validated against the wave data (both deep and shallow) of eastern Arabian Sea comprising rough monsoon conditions also, giving reasonable accuracy. The above distribution functions are also applied to simulate the recorded daily maximum wave height in a cyclonic condition. The study reveals the modified Weibull distribution is more effective for maximum wave height simulation.
In the next experiment, we discuss extreme wave heights also known as monster or freak waves. Ships are designed to withstand a maximum wave height of 15m. But monster waves of more than 30m have also been reported from many parts of the world oceans. Unfortunately a return period of 10,000 years is required for such an extreme wave height to occur by the existing techniques. The possibility of higher extreme wave heights to be encountered by the ships in the event of global warming and sea level rise scenario cannot be neglected in future.
The problem is approached using statistical extreme value distributions. The calibration and tuning coefficients incorporated in the modified Weibull, truncated Gumbel (for non-negative data) and 3-parameter generalized Pareto distributions are considered for the purpose. The model parameters are estimated by the maximum likelihood method (MLE). These models are then used to generate the recorded (by deep water buoy; 15.5oN, 69.25oE) daily maximum wave height distributions off Goa during the rough southwest monsoon seasons and also for a cyclone
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prevailed condition. The simulation capabilities of these models are verified using chi-square and it is found that the modified Weibull distribution is superior to the other competing models.
In the third chapter, for the multi-peaked energy sea-states a theoretical spectrum is developed from the modified Weibull distribution. It is compared with single peaked JONSWAP and double peaked Torsethaugen spectra and found to be more efficient. In the next part of the chapter the modified Weibull spectrum is utilised to calculate the zeroth spectral moment (mo) using Monte Carlo integration methods. Significant wave height (Hs) is calculated using the formula Hs = 4 mo . This is validated with observed buoy data and numerical wave model (WAM) predicted significant wave heights. The Weibull parameters have been calculated using energy densities from observed spectra recorded by DS5 buoy (13.80° N , 82.52° E , depth 3355.48m) by the method of maximum likelihood (MLE). The RRMS (relative root mean square error) and relative bias error criteria show that modified Weibull spectrum estimated significant wave heights are better than those predicted by WAM model. The monthly averaged observed wave power spectra for the year 2005 recorded by deep water buoy DS5 is considered in this work. The spectra exhibit bimodal sea states for several months of the year.
There are three parts to the fourth chapter. In the first part wave model WAM-4C is run for the Indian Ocean region (IO) and the Bay of Bengal region (BOB) for the year 2005.
Comparison is held among the observed and the above two types of model computed energy density spectra at a particular location. There is a distinct improvement in the shape of the spectrum for the IO run making obvious the impact of southern ocean swells in the Indian Ocean region. In the second part of the chapter we study the characteristics of Southern Ocean swells propagating into the northern Indian Ocean. It is a well known fact that the northern Indian
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Ocean is distinguished from other oceans primarily by the annual reversal of wind twice during the southwest and northeast monsoon seasons. In this context a comparative study has been conducted regarding swell propagation for the months of July and December of 2005. In the Arabian Sea and Bay of Bengal regions the swell waves follow the wind direction in July representing the southwest monsoons whereas they move opposite to the wind direction in December representing the northeast monsoons. The swells generated between 400S-600S take 6- 8 days to reach the northern Indian Ocean and the speed calculated is nearly 1100km per day.
In the last part of the chapter the spatial-temporal variability of significant wave height (SWH) over the Indian Ocean is explored. The SWH have been generated for the period 2000-08 using WAM-4C forced by six hourly QSCAT/NCEP blended winds. After a preliminary validation of the model generated SWH, the two dimensional fields of the same have been subjected to empirical orthogonal function (EOF) analysis. Analysis has been carried out separately in four regions, which are oceanographically distinct because of the prevailing wind regimes. These are namely Bay of Bengal (BOB), Arabian Sea (AS), equatorial and off- equatorial southern Indian Ocean (EOESIO) and Southern Indian Ocean (SIO). The first eigenmode accounts for 75%, 83%, 40% and 23% of the total variability for the BOB, AS, EOESIO and SIO respectively. In the BOB the maximum loading is in the northeast corner of the basin due to the predominant northeastward propagation of the waves due to the prevailing strong southwesterly monsoon winds, while in the AS there is an alignment of the maximum loading along the Findlater jet. As regards the other two regions, it can be inferred that there is a trend of increasing loading as one move gradually southwards due to the increase in the strength of the winds.
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In the fifth chapter prediction of significant wave height (SWH) field is carried out in the Bay of Bengal (BOB) using a combination of empirical orthogonal function (EOF) analysis and genetic algorithm (GA). In the first experiment EOF analysis is performed on 8 years (2000-07) of WAM-4C generated SWH field, and analyzed fields of zonal (U) and meridional (V) winds.
In the second experiment EOF analysis is performed on 4 years (2005-08) SWH data generated by NOAA WW3 global wave model. For both the experiments separately two different variants of GA are tested. In the first one, univariate GA is applied to the time series of the first principal component (PC) of SWH in the training dataset after a filtering with singular spectrum analysis (SSA) for effecting noise reduction. The generated equations are used to carry out forecast of SWH field with various lead times. In the second method, multivariate GA is applied to the SSA filtered time series of the first PC of SWH, and time- lagged first PCs of U and V and again forecast equations are generated. Once again the forecast of SWH is carried out with same lead times. The quality of forecast is evaluated in terms of root mean square error of forecast. The results are also compared with buoy data at a location. It is concluded that the method can serve as a cost-effective alternate prediction technique in the BOB.
In the sixth chapter an improved multivariate genetic algorithm approach is discussed for basin scale wave forecast. Initially the EOF analysis is performed separately on model generated SWH field, analyzed windspeed (WS) field, analyzed COSTHETA (cosines of wind direction) field and analyzed SINTHETA (sines of wind direction) field for 8 years (2000-07).
Multivariate GA has been applied to the time series of the principal components (PC) of the above components. Statistical evaluation of the quality of forecast leads to encouraging results.
The method has one major advantage. Once the forecast equations are derived, it can be used
vi
without any calculation by a numerical wave model, since only past values of analyzed wind fields are required to predict SWH fields.
Finally, applications of GA over energy density spectrum is discussed. The WAM model is integrated from 2000–2004 for the entire Indian Ocean to generate six hourly energy density spectra at the available buoy location (DS5). The EOF analysis is performed on seasonal scale using the spectrum data for the above 5 years. Then GA is applied to the time series of the PCs of the above variable. The GA forecasted energy density spectra are compared with observed buoy spectra available for 2005.
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Table of Contents Certificate
Acknowledgements
Abstract i - vi
List of Figures ix - xiv
List of Tables xv – xvi
Abbreviations xvii
Chapter I Introduction.
1.1 Introduction 1
1.2 Probabilistic Estimation of Wave Heights 3
1.3 Ocean Wave Spectrum 5
1.4 Numerical Wave Modeling 6
1.5 Southern Ocean Swells 9
1.6 Genetic Algorithms 12
1.7 The Broad Objective of the Thesis 14
Chapter II Modified weibull distribution for significant wave height prediction and application of extreme value distributions.
2.1 Introduction 23
2.2 Methodology 25
2.2.1 Modeling the wave 26
2.2.1.1 Modified Weibull model for maximum wave height distribution
27 2.2.1.2 The Truncated Gumbel distribution 32 2.2.1.3 The 3-parameter Generalized Pareto
distribution 33
2.3 Results and discussion 37
2.4 Conclusions 55
Chapter III Modified Weibull derived spectrum for multi-peaked energy sea states.
3.1 Introduction 57
3.2 Materials and Methods 60
3.2.1 Observed spectra 60
3.2.2 Modified Weibull derived spectrum 60
3.2.3 WAM model 65
3.3 Results and discussion 65
3.4 Conclusions 81
viii
Chapter IV Variability of Significant Wave Height over the Indian Ocean using Empirical Orthogonal Function Analysis.
4.1 Introduction 82
4.2 Methodology 86
4.3 Results and discussion 89
4.4 Conclusions 113
Chapter V Bay of Bengal wave forecast based on genetic algorithm: a comparison of univariate and multivariate approaches.
5.1 Introduction 116
5.2 EOF, GA and SSA 119
5.3 Data 124
5.4 Results and discussion 125
5.4.1 EOF analysis (WAM-data) 125
5.4.2 Forecast of the principal component 128
5.4.3 EOF analysis (WW3-data) 140
5.5 Conclusions 156
Chapter VI Alternate forecasting approaches using GA for SWH and energy density spectrum.
6.1 Introduction 157
6.2 Data 159
6.3 Results and discussion 162
6.3.1 Forecast of SWH 162
6.3.2 Forecast of energy density spectrum 173
6.4 Conclusions 180
Chapter VII Conclusions and Future scope of work
7.1 Summary of results 182
7.2 Future scope of work 186
References 187
Appendices 193
Bio-Data 200
