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Obtaining natural oscillatory modes of bays and harbors via Empirical Orthogonal Function analysis of tsunami wave fields

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Abstract

To a tsunami wave, bays and harbors represent oscillatory systems, whose resonance (normal) modes determine the response to tsunami and consequently the potential hazard. The direct way to obtain the resonance modes of a water reservoir is by solving the boundary problem for the eigenfunctions of the linearized shallow-water wave equation. The principal difficulty of posing such a problem for a basin coupled to an ocean is specifying the boundary between the two. The technique developed in this work allows the normal modes of a semi-enclosed water body to be obtained without a-priori restricting the resonator area. The technique utilizes complex Empirical Orthogonal Function analysis of modeled tsunami wave fields. On the examples of Poverty Bay in New Zealand and Monterey Bay in California (United States), we demonstrate that the normal modes can be identified and isolated using the EOFs of a data set comprised of the concatenated time-series collected from different tsunami scenarios in a basin. The analysis of the modeled tsunami wave fields for the normal modes can also answer the question of how likely and under which conditions the different modes are exited, due to feasible natural events.

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Acknowledgements

We acknowledge the New Zealand GeoNet project and its sponsors EQC, GNS Science and LINZ, for providing Poverty Bay gauge records, and NOAA/NOS for providing Monterey gauge records used in this study. Sincere thanks to Prof. Margaret Anne McManus and Ms. Anna Pfeiffer-Herbert for Santa Cruz pressure records. Elena Tolkova would like to acknowledge the support for her work from the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) under NOAA Cooperative Agreement No. NA17RJ1232, Contribution #1830 (JISAO), #3620 (NOAA/PMEL). William Power would like to acknowledge the support for his work from the Natural Hazards Reseach Platform of the New Zealand Foundation for Research Science and Technology (FRST).

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Authors and Affiliations

  1. JISAO/NOAA Center for Tsunami Research, Box 354925, Seattle, WA, 98195, USA

    Elena Tolkova

  2. GNS Science, 1 Fairway Drive, Avalon, Lower Hutt, New Zealand

    William Power

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  1. Elena Tolkova
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  2. William Power
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Correspondence to Elena Tolkova.

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Responsible Editor: Joachim W. Dippner

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Tolkova, E., Power, W. Obtaining natural oscillatory modes of bays and harbors via Empirical Orthogonal Function analysis of tsunami wave fields. Ocean Dynamics 61, 731–751 (2011). https://doi.org/10.1007/s10236-011-0388-5

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  • DOI: https://doi.org/10.1007/s10236-011-0388-5

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