A Novel Distance Measure for Ocean Reconstruction from Sparse Observations Demonstrated on the Atlantic

We introduce a distance measure for use in scattered data approximation. Reconstruction from sparse, non-uniformly distributed data should utilize application-specific knowledge to produce highquality results. Our distance measure is considering the specific problem of computing reconstructions from sparse observational paleoceanography data, where it is possible to consider certain problem-specific knowledge to produce reconstructions of scientific value. Our approach to the problem combines the new distance measure with the well-known moving least squares (MLS) method. We demonstrate that our approach produces high-quality results, by contrasting our distance measure against Euclidean and geodesic distances. We have used our method to generate reconstructions from data in the Atlantic Ocean.