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

Lekien, F., C. Coulliette, R. Bank, and J.E. Marsden

J. of Geophysical Research, 109, (2004), C12004

Abstract:

Developments in dynamical systems theory have brought a wide range of methods that can be used to analyze and predict Lagrangian behavior in geophysical flows. However, at the present time, this approach requires the velocity field of the ocean to be described using a fairly smooth differential equation. Increasingly accurate remote sensing techniques are available today and techniques such as modal analysis are used to transform, interpolate and regularize the measured velocity fields. Until recently, the modes used did not correctly allow flow across an open boundary of the domain. Open boundaries are an important concept when the domain is not completely closed by a shoreline, which is typical of coastal HF radar data as well as other data sources, such as underwater gliders. Previous modal analysis methods project the data onto closed-boundary modes, and then use an ad hoc procedure to add a zero-order mode to allow flow across the boundary. We present an improved procedure: the theory and a practical use of Open-boundary Modal Analysis (OMA), a complete set of eigenfunctions that can be used to interpolate, extrapolate and filter flows on an arbitrary domain with or without flow through segments of the boundary.