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Abstract:
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Many ocean datasets are large, multi-dimensional, and inherently spatio-temporal. Oceanographers are often interested in comparing ocean datasets along one or several dimensions of latitude, longitude, depth or time. In this paper, we introduce and extend optimal transport and Wasserstein's distance as rich and useful tools for analyzing ocean data. Wasserstein's distance improves upon existing common distance measures that conduct a pixel-by-pixel comparison. Such pixel-wise comparisons are inherently limited in detecting meaningful differences in the spatio-temporal regularity and multi-scale patterns that are common in ocean data. Furthermore, the optimal mass transports can provide a valuable visual aid for oceanographers while making ocean data comparisons. We demonstrate the usefulness of optimal transport and Wasserstein's distance using the key application of comparing synthetic and remote-sensing ocean data.
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