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We explore applicability of entropy-regularized Wasserstein (pseudo-)distances as new tools for analyzing environmental and ecological data. In this paper, the two specific examples are considered and are numerically analyzed using the Sinkhorn algorithm. The first example is the inflow and outflow discharges of a dam-reservoir system. The inflow and outflow discharges are described as discrete-time Markov chains, and their transition rates among the discharge regimes and the corresponding stationary probability distributions are identified. The optimal transport plan leading to the regularized Wasserstein distance between the two Markov chains is considered as the system optimization policy decided by the operator. The second example is the body weight distributions of a fish serving as a major inland fishery resource in Japan. We quantify differences of the collected body weight distributions among the different years focusing on the summer growing season. The obtained analysis results imply usefulness of the regularized Wasserstein distances for assessing probability distributions arising in environmental and ecological problems.

aquatic environment and ecology; entropy-regularized Wasserstein distance; Sinkhorn algorithm