Quantifying internal variability in large-ensemble climate data with the Wasserstein distance

[2608.14455] Quantifying internal variability in large-ensemble climate data with the Wasserstein distance Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Physics > Atmospheric and Oceanic Physics arXiv:2608.14455 (physics) [Submitted on 14 Aug 2026] Title: Quantifying internal variability in large-ensemble climate data with the Wasserstein distance Authors: Yuki Yasuda , Shoichiro Kido View a PDF of the paper titled Quantifying internal variability in large-ensemble climate data with the Wasserstein distance, by Yuki Yasuda and Shoichiro Kido View PDF HTML (experimental) Abstract: Quantifying forced and internal variability in climate data is fundamental to detecting the climate change signal and assessing uncertainty in climate projections. We propose a metric that quantifies the relative magnitude of internal variability in single-model initial-condition large ensembles (SMILEs). We measure forced and internal variability by two 1-Wasserstein distances, a form of optimal transport cost. The proposed metric is the distance for internal variability divided by the sum of the two. Computing this ratio requires only sorting the samples and differencing the resulting quantiles, with no additional parameters. The metric reflects the entire distribution shape and applies to non-Gaussian variables, because the 1-Wasserstein distance quantifies the difference between any two probability distributions. We validate the metric with synthetic climate data from Gaussian, uniform, and lognormal distributions. Unlike the two existing metrics, the proposed metric gives stable estimates irrespective of the distribution shape and the presence of outliers, provided that the ensemble has about 40 members or more. We then apply the proposed and existing metrics to the 2 m air temperature and total precipitation of the Community Earth System Model Large Ensemble (CESM-LE) under two different forcing scenarios. All the metrics indicate that the relative contribution of internal variability decreases as the forcing increases, but the proposed metric shows this response most clearly. The 1-Wasserstein distance thus provides a simple and useful tool for analyzing large-ensemble datasets. Subjects: Atmospheric and Oceanic Physics (physics.ao-ph) ; Computational Physics (physics.comp-ph) Cite as: arXiv:2608.14455 [physics.ao-ph] (or arXiv:2608.14455v1 [physics.ao-ph] for this version) https://doi.org/10.48550/arXiv.2608.14455 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yuki Yasuda Ph.D. [ view email ] [v1] Fri, 14 Aug 2026 16:41:05 UTC (1,688 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantifying internal variability in large-ensemble climate data with the Wasserstein distance, by Yuki Yasuda and Shoichiro Kido View PDF HTML (experimental) TeX Source view license Current browse context: physics.ao-ph < prev | next > new | recent | 2026-08 Change to browse by: physics physics.comp-ph References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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