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The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos this property is usually quantified by computing the Lyapunov exponents. In this review, these quantifiers computed in a hierarchy of atmospheric models (coupled or not to an ocean) are analyzed, together with their local counterparts known as the local or finite-time Lyapunov exponents. It is... Topics: Chaotic Dynamics, Nonlinear Sciences Source: http://arxiv.org/abs/1703.04284

We study a simplified coupled atmosphere-ocean model using the formalism of covariant Lyapunov vectors (CLVs), which link physically-based directions of perturbations to growth/decay rates. The model is obtained via a severe truncation of quasi-geostrophic equations for the two fluids, and includes a simple yet physically meaningful representation of their dynamical/thermodynamical coupling. The model has 36 degrees of freedom, and the parameters are chosen so that a chaotic behaviour is... Topics: Nonlinear Sciences, Fluid Dynamics, Atmospheric and Oceanic Physics, Chaotic Dynamics, Physics Source: http://arxiv.org/abs/1510.00298

A stochastic subgrid-scale parameterization based on the Ruelle's response theory and proposed in Wouters and Lucarini [2012] is tested in the context of a low-order coupled ocean-atmosphere model for which a part of the atmospheric modes are considered as unresolved. A natural separation of the phase-space into an invariant set and its complement allows for an analytical derivation of the different terms involved in the parameterization, namely the average, the fluctuation and the long memory... Topics: Statistical Mechanics, Condensed Matter, Atmospheric and Oceanic Physics, Physics Source: http://arxiv.org/abs/1605.00461

We review some recent methods of subgrid-scale parameterization used in the context of climate modeling. These methods are developed to take into account (subgrid) processes playing an important role in the correct representation of the atmospheric and climate variability. We illustrate these methods on a simple stochastic triad system relevant for the atmospheric and climate dynamics, and we show in particular that the stability properties of the underlying dynamics of the subgrid processes... Topics: Physics, Statistical Mechanics, Condensed Matter, Atmospheric and Oceanic Physics Source: http://arxiv.org/abs/1701.04742

This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process fully correlated in time. This allows for the derivation of the evolution equations for the relevant moments of the model error statistics required in data assimilation procedures, along with an approximation suitable for application to large numerical models typical of environmental science. In this contribution we first... Topics: Atmospheric and Oceanic Physics, Physics Source: http://arxiv.org/abs/1503.00842

byStéphane Vannitsem; Jonathan Demaeyer; Lesley De Cruz; Michael Ghil

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We formulate and study a low-order nonlinear coupled ocean-atmosphere model with an emphasis on the impact of radiative and heat fluxes and of the frictional coupling between the two components. This model version extends a previous 24-variable version by adding a dynamical equation for the passive advection of temperature in the ocean, together with an energy balance model. The bifurcation analysis and the numerical integration of the model reveal the presence of low-frequency variability... Topics: Physics, Nonlinear Sciences, Atmospheric and Oceanic Physics, Chaotic Dynamics Source: http://arxiv.org/abs/1412.0621