Computation and approximation of the length scales of harmonic modes with application to the mapping of surface currents in the Gulf of Eilat

Open-boundary modal analysis (OMA) is a generalized Fourier transform that interpolates, extrapolates, and filters scattered current measurements and produces smooth current maps in coastal areas. Boundary conditions are enforced by adjusting the OMA modes to the coastline. Filtering is achieved by discarding OMA modes whose length scales are below a selected threshold. In this paper, we determine the length scale of the OMA modes, and we derive approximated formulas. Operational use of the OMA modes and the length scale formulas are illustrated on surface currents measured by highfrequency radar in the Gulf of Eilat (Gulf of Aqaba).