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Redacted for Privacy Abstract Approved: / Steve Neshyb( AN ABSTRACT OF THE THESIS OF Rodrigo H. Nunez for the degree of Master of Science in Oceanography presented on August 3, 1990. Title: Prediction of Tidal Propagation and Circulation in Chilean InlandSeas Using a Frequency Domain Model Redacted for privacy Abstract approved: / Steve Neshyb( The calculated flow field and tide wave propagation in the Chilean Inland Seas is modeled with a non-linear tidal embayment method (TEA-NL, Westerink et al, 1988) and assimilation of tide records of the Chilean HydrographicInstitute. Model isvalidated for two testcases with assimilated error-freeboundary conditions. An Inverse Tidal Method (I. T. M.) developed as a time-domain method by Bennett and McIntosh in 1982, is used to calculate the forcing functions, but in the frequency-domain instead. The model is first run using all available tide data. A second run with a subset of five stations shows how the choice and location of stations affect the prediction of tide wave propagation and flow fields.The boundary conditions calculated by the I. T. M. for the cases of seven and five stations reproduced the known data at the stations with like error magnitudes.However, for the seven stations case, the tide wave propagation along the seaward side of Chiloe Island (Pacific Ocean) propagated from South to North (the known direction of propagation is from North to South).After disregarding two stations, the model gave tide waves along the seaward side of ChloeIsland propagating from North to South. The model is clearly sensitive to perturbations introducedby hydraulics factors other than pure tide wave propagation. Charts of model simulation of flow fields are shown at 3, 6, 9and 12 hours of the M2 tidal cycle. Charts of phases and amplitudes are alsoshown. Conclusions from the study are that the I. T. M. is a good dataassimilation technique to calculate the forcing functions of a numericalmodel, even when known data is scarce.Further, the I. T. M. is a valuable aid in chosing locations for new and useful data to improve the simulation. Next steps required to improve the understanding of theChilean Inland Seas are a good field survey (based on theresults of the I. T. M.), the development of a transport model against which measured flow data canbe compared, the inclusion of river discharge in the boundary conditions, the preparationof trajectory charts todemonstrate particlediffusion and advection,the expansiontothree- dimensional models, etc. Prediction of Tidal Propagation andCirculation in Chilean Inland Seas Using a FrequencyDomain Model by Rodrigo H. Nunez A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Completed August 3, 1990 Commencement June 1991 APPROVED: Redacted for privacy in cha4 of major If Redacted for privacy Head of Co1l'ee of Redacted for privacy Dean of Graduate Scf Date thesis is presented August 3, 1990 Typed by Donna Kent forRodrigo H. Nunez Acknowledgements There are several people without whom this work wouldhave been impos- sible.First, I would like to thank Dr. S. Nesbyba for his supportand counsel as my major professor, which wasessential to my training in physical oceanography. I would like to thank Dr. A. Baptista of Oregon GraduateInstitute of Science and Technology for all his suggestions, guidance and patienceduring the last two years. Without the aid of Dr. .J. Davis and Dr. R. Miller the InverseMethod could not have been an integral part of this thesis. Theirwillingness to consult with me was great, and in turn it isgreatly appreciated.Dr. A. Bennett also made valuable suggestions in this section at the beginning of thestudy, and his enthusiasm towards my work was very encouraging. Special thanks to all my friends who helped make mytime in Oregon unforgettable and who gave me their support during this study.Thank you, Ricardo and Anita, Yerko and Cuti, Marcio and Maria, and Jorge. Thanks to Randy and Vassilis who were very special friends to me.They were always ready to help me forget mywork and to force me to have a good time. The typing was done by Donna Kent, who I thank forher patience and efforts made to understand my handwriting and especially myEnglish. Funding was provided by the Chilean Navy through the NavalHydrographic Institute. P TABLE OF CONTENTS CHAPTER I: INTRODUCTION CHAPTER II: DESCRIPTION OF METHODS 6 2.1 Review of the Circulation Model 6 2.2 Inverse Tidal Method 12 2.2.1 Application of the Inverse Tidal Method to the Solution of a Practical Problem 12 2.2.2 Mathematical Formulation of the Inverse Tidal Method 14 CHAPTER III: VALIDATION OF METHODS 22 3.1Rectangular Embayment 24 3.2 North Sea 30 CHAPTER IV: CHILEAN INLAND SEAWATER SYSTEM 62 4.1Analysis of Tidal Data 62 4.2Definition of Boundary Conditions 71 4.3Analysis of Model Results 75 CHAPTERV: CONCLUSIONS 102 5.1Conclusions 102 5.2Outline of the Future Field Survey 103 5.3Outline of Next Steps in Modeling 105 BIBLIOGRAPHY 107 APPENDIX A 109 Governing Equations 109 APPENDIX B 118 Inverse Tidal Method (I. T. M.) 118 LIST OF FIGURES Figure Page 1. Chilean Inland Seawater System of Gulf of Ancud. Geographical Location la 2. Iterative non-linear scheme 10 3. Schematic diagram for the Inverse Tidal Method 15 4. Rectangular embayment, finite element grid. 25 5. Known and calculated flow fields using linear and trigonometricbasis functions for the rectangular embayment at instant=11 hours. 29 6. North Sea, finite element grid 31 7. North Sea, location of reference stations 32 8. Elevations. Known data vs. calculated data (Expel45) at station St. Malo for a period of 13 hours 35 9. Elevations. Known data vs. calculated data (Expel4S) at station Cherbourg for a period of 13 hours 35 10.Elevations. Known data vs. calculated data (Expel45) at station Christchurch for a period of 13 hours 36 11.Elevations. Known data vs. calculated data (Expel45) at station Dieppe for a period of 13 hours 36 12.Elevations. Known data vs. calculated data (Expel4S) at station Boulogne for a period of 13 hours 37 13.Elevations. Known data vs. calculated data (Expel45) at station Dover for a period of 13 hours 37 14.Elevations. Known data vs. calculated data (Expel45) at station Calais for a period of 13 hours 38 15.Elevations. Known data vs. calculated data (Expel45) atstation Walton for a period of 13 hours 38 16.Elevations. Known data vs. calculated data (Expel45) atstation Zeebrugge for a period of 13 hours 39 17.Elevations. Known data vs. calculated data (Expel45) at station Lowestoft for a period of 13 hours 39 18.Elevations. Known data vs. calculated data (Expel45) at station Hoek Van Holland for a period of 13 hours 40 19.Elevations. Known data vs. calculated data (Expe28O) at station St. Mao for a period of 13 hours 40 20.Elevations. Known data vs. calculated data (Expe28O) atstation Cherbourg for a period of 13 hours 41 21.Elevations. Known data vs. calculated data (Expe28O) at station Christchurch for a period of 13 hours 41 22.Elevations. Known data vs. calculated data (Expe28O) at station Dieppe for a period of 13 hours 42 23.Elevations. Known data vs. calculated data (Expe28O) at station Boulogne for a period of 13 hours 42 24.Elevations. Known data vs. calculated data (Expe28O) at station Dover for a period of 13 hours 43 25.Elevations. Known data vs. calculated data (Expe28O) at station Calais for a period of 13 hours 43 26.Elevations. Known data vs. calculated data (Expe28O) at station Walton for a period of 13 hours 44 27.Elevations. Known data vs. calculated data (Expe28O) atstation Zeebrugge for a period of 13 hours 44 28.Elevations. Known data vs. calculated data (Expe28O) atstation Lowestoft for a period of 13 hours 45 29.Elevations. Known data vs. calculated data (Expe28O) atstation Hoek Van Holland for a period of 13 hours 45 30.Elevations. Known data vs. calculated data (Expe294) atstation St. Malo for a period of 13 hours 46 31. Elevations. Known data vs. calculated data (Expe294) atstation Cherbourg for a period of 13 hours 46 32.Elevations. Known data vs. calculated data (Expe294) atstation Christchurch for a period of 13 hours 47 33.Elevations. Known data vs. calculated data (Expe294) at station Dieppe for a period of 13 hours 47 34.Elevations. Known data vs. calculated data (Expe294) atstation Boulogne for a period of 13 hours 48 35.Elevations. Known data vs. calculated data (Expe294) atstation Dover for a period of 13 hours 48 36.Elevations. Known data vs. calculated data (Expe294) atstation Calais for a period of 13 hours 49 37.Elevations. Known data vs. calculated data (Expe294) atstation Walton for a period of 13 hours 49 38.Elevations. Known data vs. calculated data (Expe294) atstation Zeebrugge for a period of 13 hours 50 39.Elevations. Known data vs. calculated data (Expe294) atstation Lowestoft for a period of 13 hours 50 40.Elevations. Known data vs. calculated data (Expe294) atstation Hoek Van Holland for a period of 13 hours 51 41. Known flow field (Expel66) and calculated flow fields (Expel4S-Expe28O-Expe294) for the North Sea at instant = 3 hours. 53 42. Known flow field (Expel66) and calculated flow fields (Expel45-Expe28O-Expe294) for the North Sea at instant = 6 hours. 54 43. Known flow field (Expel66) and calculated flow fields (Expel45-Expe28O-Expe294) for the North Sea at instant = 9 hours. 55 44. Known flow field (Expel66) and calculated flowfields (Expel4S-Expe28O-Expe294) for the North Sea at instant = 12 hours. 56 45.Isolines of amplitudes for Expel66 (known data) and Expel45-Expe28O-Expe294 (calculated data) for North Sea. 57 46.Isolines of phases for Expel66 (known data) and Expel45-Expe28O-Expe294 (calculated data) for North Sea.
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