A proof of concept for scale-adaptive parameterizations: the case of the Lorenz '96 model

Abstract

Constructing efficient and accurate parameterizations of sub-grid scale processes is a central area of interest in the numerical modelling of geophysical fluids. Using a modified version of the two-level Lorenz '96 model, we present here a proof of concept of a scale-adaptive parameterization constructed using statistical mechanical arguments. By a suitable use of the Ruelle response theory and of the Mori-Zwanzig projection method, it is possible to derive explicitly a parameterization for the fast variables that translates into deterministic, stochastic and non-markovian contributions to the equations of motion of the variables of interest. We show that our approach is computationally parsimonious, has great flexibility, as it is explicitly scale-adaptive, and we prove that it is competitive compared to empirical ad-hoc approaches. While the parameterization proposed here is universal and can be easily analytically adapted to changes in the parameters' values by a simple rescaling procedure, the parameterization constructed with the ad-hoc approach needs to be recomputed each time the parameters of the systems are changed. The price of the higher flexibility of the method proposed here is having a lower accuracy in each individual case.

39 pages, 17 figures; improved discussion of the results and of the theory

References in corpus (5)

• A review of linear response theory for general differentiable dynamical systems
• Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model
• Logarithmic bred vectors in spatiotemporal chaos: structure and growth
• Parametrization of stochastic multiscale triads
• Response Formulae for $n$-point Correlations in Statistical Mechanical Systems and Application to a Problem of Coarse Graining

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