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Open-boundary modal analysis: Interpolation, extrapolation, and filtering

Lekien, F. and Coulliette, C. and Bank, R. and Marsden, J. E. (2004) Open-boundary modal analysis: Interpolation, extrapolation, and filtering. Journal of Geophysical Research C, 109 (C12). Art. No. C12004. ISSN 0148-0227. doi:10.1029/2004JC002323.

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Increasingly accurate remote sensing techniques are available today, and methods such as modal analysis are used to transform, interpolate, and regularize the measured velocity fields. Until recently, the modes used did not incorporate flow across an open boundary of the domain. Open boundaries are an important concept when the domain is not completely closed by a shoreline. Previous modal analysis methods, such as those of Lipphardt et al. (2000), project the data onto closed-boundary modes, and then add a zero-order mode to simulate flow across the boundary. Chu et al. (2003) propose an alternative where the modes are constrained by a prescribed boundary condition. These methods require an a priori knowledge of the normal velocity at the open boundary. This flux must be extrapolated from the data or extracted from a numerical model of a larger-scale domain, increasing the complexity of the operation. In addition, such methods make it difficult to add a threshold on the length scale of open-boundary processes. Moreover, the boundary condition changes in time, and the computation of all or some modes must be done at each time step. Hence real-time applications, where robustness and efficiency are key factors, were hardly practical. We present an improved procedure in which we add scalable boundary modes to the set of eigenfunctions. The end result of open-boundary modal analysis (OMA) is a set of time and data independent eigenfunctions that can be used to interpolate, extrapolate and filter flows on an arbitrary domain with or without flow through segments of the boundary. The modes depend only on the geometry and do not change in time.

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Additional Information:© 2004 American Geophysical Union. Received 12 February 2004; revised 27 June 2004; accepted 26 July 2004; published 4 December 2004. The authors are grateful to the Office of Naval Research for their support (grant N00014-01-1-0208 and the AOSN-ii project N00014-02-1-0826), particularly program managers Manuel Fiedero, Reza Malek-Madani, and Wen Masters. The authors also thank Bruce Lipphardt and Michael Toner for enlightening discussions and enriching ideas. The high-frequency radar data were collected in Monterey Bay by the Naval Postgraduate School, and the authors are grateful to Jeffrey Paduan and Michael Cook for processing and sharing available velocity fields.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-01-1-0208
Office of Naval Research (ONR)AOSN-ii project N00014-02-1-0826
Subject Keywords:modal analysis; interpolation; filtering
Issue or Number:C12
Record Number:CaltechAUTHORS:20101006-101734628
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Official Citation:Lekien, F., C. Coulliette, R. Bank, and J. Marsden (2004), Open-boundary modal analysis: Interpolation, extrapolation, and filtering, J. Geophys. Res., 109, C12004, doi:10.1029/2004JC002323.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20321
Deposited By: Tony Diaz
Deposited On:19 Nov 2010 23:29
Last Modified:08 Nov 2021 23:58

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