Ocean Mover's Distance: Using Optimal Transport for Analyzing Oceanographic Data

Modern ocean datasets are large, multi-dimensional, and inherently spatiotemporal. A common oceanographic analysis task is the comparison of such datasets along one or several dimensions of latitude, longitude, depth, time as well as across different data modalities. Here, we show that the Wasserstein distance, also known as earth mover's distance, provides a promising optimal transport metric for quantifying differences in ocean spatiotemporal data. The Wasserstein distance complements commonly used point-wise difference methods such as, e.g., the root mean squared error, by quantifying deviations in terms of apparent displacements (in distance units of space or time) rather than magnitudes of a measured quantity. Using large-scale gridded remote sensing and ocean simulation data of Chlorophyll concentration, a proxy for phytoplankton biomass, in the North Pacific, we show that the Wasserstein distance enables meaningful low-dimensional embeddings of marine seasonal cycles, provides oceanographically relevant summaries of Chlorophyll depth profiles and captures hitherto overlooked trends in the temporal variability of Chlorophyll in a warming climate. We also illustrate how the optimal transport vectors underlying the Wasserstein distance calculation can serve as a novel interpretable visual aid in other exploratory ocean data analysis tasks, e.g., in tracking ocean province boundaries across space and time.