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Evaluating a stochastic parametrization for a fast--slow system using the Wasserstein distance

Vissio, G. and Lucarini, V. (2018) Evaluating a stochastic parametrization for a fast--slow system using the Wasserstein distance. Nonlinear Processes in Geophysics, 25 (2). pp. 413-427. ISSN 1023-5809

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To link to this item DOI: 10.5194/npg-25-413-2018

Abstract/Summary

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modeling of geophysical fluids. We consider here the simple yet paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a parametrization using a recently developed statistical mechanical methodology based on the Ruelle response theory. We derive an expression for the deterministic and the stochastic component of the parametrization and we show that the approach allows for dealing seamlessly with the case of the Lorenz 63 being a fast as well as a slow forcing compared to the characteristic timescales of the Lorenz 84 model. We test our results using both standard metrics based on the moments of the variables of interest as well as Wasserstein distance between the projected measure of the original system on the Lorenz 84 model variables and the measure of the parametrized one. By testing our methods on reduced-phase spaces obtained by projection, we find support for the idea that comparisons based on the Wasserstein distance might be of relevance in many applications despite the curse of dimensionality.

Item Type:Article
Refereed:Yes
Divisions:Interdisciplinary centres and themes > Walker Institute
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:77906
Publisher:European Geosciences Union

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