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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2018-16
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
09 Mar 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).
A Statistical Mechanical Approach for the Parametrization of the Coupling in a Fast-Slow System
Gabriele Vissio1,2 and Valerio Lucarini2,3,4 1International Max Planck Research School on Earth System Modelling, Hamburg, Germany
2CEN, Meteorological Institute, University of Hamburg, Hamburg, Germany
3Department of Mathematics and Statistics, University of Reading, Reading, UK
4Walker Institute for Climate System Research, University of Reading, Reading, UK
Abstract. Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modelling 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 time scales 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 to the idea that comparisons based on the Wasserstein distance might be of relevance in many applications despite the curse of dimensionality.
Citation: Vissio, G. and Lucarini, V.: A Statistical Mechanical Approach for the Parametrization of the Coupling in a Fast-Slow System, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2018-16, in review, 2018.
Gabriele Vissio and Valerio Lucarini
Gabriele Vissio and Valerio Lucarini
Gabriele Vissio and Valerio Lucarini

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