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would be about 7 s observational points in a half-window. For *J *s 3 and s s 1, there

would be 14 unknowns and 35 equations. For *J *s 3 and s s 4, there would be 35

unknowns and 140 equations. With initial estimates provided by a global Airy theory

approximation, smooth and robust solutions are established in each extra-wide half-

window. These in turn provide routinely appropriate initial estimates for the local

solutions in very much narrower windows.

The algorithm had most difficulty in finding credible local solutions around the

zero-crossings of the P trace. At such regions, profile curvature is very small and a

narrow local window has poor resolution. Often, this is not a region of particular

concern. Two strategies are possible in dealing with this problem. The first would be to

ignore such points and rely on interpolating for the kinematics from adjacent local

solutions that bracket the zero-crossings. The second would be to extend the local

window to improve resolution of the local profile curvature. This second approach has

been adopted, and was the essential rationale for the double-width window introduced

above.

An initial evaluation of the LFI-PUV theory and coding is provided by theoretical

PUV traces from uniform, long-crested wave trains. Three monochromatic waves,

Fig. 4. LFI-PUVw3,3,0.1x predictions for wave `Twenty'.

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