Disentangling multi-level systems: averaging, correlations and memory

Nonlin. Processes Geophys.

2018

Self Cite

Abstract. 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.

Section: Introductionmentioning

confidence: 83%

Section: Constructing the Parametrizationmentioning

confidence: 99%

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

Vissio

Nonlin. Processes Geophys.

2018

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“…The triad of terms -deterministic, stochastic and non-markovian -was also found by Wouters and Lucarini (2012, 2013, who proposed a method for constructing parametrizations based on the Ruelle response theory (Ruelle, 1998(Ruelle, , 2009). …”

Section: Introductionmentioning

confidence: 81%

A Statistical Mechanical Approach for the Parametrization of the Coupling in a Fast-Slow System

Vissio¹,

2018

Preprint

Self Cite

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 5 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.

“…Adding noise in the equations in the form of stochastic forcing-as in the case of using stochastic parametrizations [24] in multiscale system-provides a way to regularize the problem, but it is not entirely clear how to treat the zero noise limit. Additionally, one should provide a robust and meaningful derivation of the model to be used for constructing the noise: a proposal in this direction is given in [2,25,26].…”

Section: Introductionmentioning

confidence: 99%

Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns

Ragone

Lunkeit³

2016

J Stat Phys

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102

132

The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(10 5 ) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is nonautonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting-at any lead time and in an ensemble sense-the change in climate properties resulting from increase in the concentration of CO 2 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change.Paper prepared for the special issue of the Journal of Statistical Physics dedicated to the 80th birthday of Y.