Before revision:  We show how to learn a height-optimal triangulation and a  k-order height-optimal triangulation using an exact algorithm based on integer linear programming and evaluate our approaches both with respect to its running times and the quality of the reconstructions in contrast to a solution by a Delaunay triangulationwhich has earlier been used for sea-surface modeling. For existing data of the North Sea we show that we can better reconstruct the dynamic sea surface for about 156 months back in time using the height-optimal triangulation than the Delaunay triangulation and even for about 180 months using the k-order height-optimal triangulation for k=2.
After revision:  We show how to learn a height-optimal triangulation and a k-order height-optimal triangulation using an exact algorithm based on integer linear programming . We confront our reconstructions against the Delaunay triangulation. With real data for the North Sea we show that we can better reconstruct the dynamic sea surface for about 156 months back in time using the height-optimal triangulation than the Delaunay triangulation and even for about 180 months using the k-order height-optimal triangulation for k=2.