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Abstract : Hydrographic surveys for nautical charting contain many discrete data points. Analytical models for ocean bottom topography could save computer storage and reduce the complexity of automating the nautical charting process, but they must meet stringent accuracy requirements. Polynomials, double Fourier series, finite elements, Duchon's analysis, Shepard's formula and Hardy's multiquadric analysis were investigated as possible modeling techniques. Multiquadric analysis in which the surface is represented by an analytical summation of mathematical surfaces such as cones and hyperboloids was the only method found to be suitable. An iterative method of model point selection was found to give the best results. Smooth and unambiguous junctions of adjacent models were made by using a Hermite polynomial weighted sum of overlapping areas. Highly irregular surfaces can be represented by about 20% of the original survey data points; more regular bottom topography can be represented by a smaller percentage. (Author)

Representation of hydrographic surveys and ocean bottom topography by analytical models