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Stochastic parameterization of geophysical flows through modelling under location uncertainty

Valentin Resseguier 1 Etienne Mémin 1 Bertrand Chapron 2 Pierre Dérian 1 
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : In this talk we will describe a framework for the systematic derivation of stochastic representations of geophysical flows. This paradigm, quoted as modelling under location uncertainty, relies on a Lagrangian decomposition of the flow velocity in terms of a large-scale, smooth in time, component and a random field uncorrelated in time, which represents the small-scale velocity component. This possibly anisotropic non-homogeneous random field corresponds to the aliasing of the unresolved velocity component. Such a Lagrangian decomposition leads to a stochastic representation of the Reynolds transport theorem (RTT) and of the material derivative [1,2]. Those expressions involve a diffusive subgrid term balanced by a multiplicative noise and a modified advection drift induced by the small-scale inhomogeneity. The stochastic material derivative together with the RTT enables us to express random versions any geophysical flow dynamics within the usual physical scaling approximation. Through the presentation we will provide several stochastic representations of classical systems. Quasi-Geostrophic models (QG), and Surface Quasi Geostrophic (SQG) models will be in particular explored. We will show how different SQG approximations can be derived from different levels of noise; we will demonstrate that such systems lead to improved large-scale representations and meaningful ensemble of realizations. Compared to traditional ensemble built from a perturbation of the initial condition, the ensemble generated by the proposed stochastic representation exhibits a larger spread; this allows estimating accurately the model errors in terms of location and magnitude [2]; it leads also to efficient tracking of likely scenarios [3]. The nice properties of this derivation should be particularly useful for ensemble-based data assimilation techniques or for ensemble forecasting analysis. [1] E. Mémin, Fluid flow dynamics under location uncertainty, Geophysical & Astrophysical Fluid Dynamics, 108, 2, 119–146, (2014). [2] V. Resseguier, E. Mémin, B. Chapron (2016). Geophysical flows under location uncertainty, paper submitted to Geophysical & Astrophysical Fluid Dynamics. [3] V. Resseguier, E. Mémin, B. Chapron (2016). Chaotic transitions and location uncertainty in geophysical flows, paper submitted to Chaos.
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Submitted on : Wednesday, November 9, 2016 - 6:02:38 PM
Last modification on : Friday, May 20, 2022 - 9:04:52 AM
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  • HAL Id : hal-01377719, version 1


Valentin Resseguier, Etienne Mémin, Bertrand Chapron, Pierre Dérian. Stochastic parameterization of geophysical flows through modelling under location uncertainty. Data Analysis and Modeling in Earth Sciences (DAMES) 2016, Sep 2016, Hambourg, Germany. ⟨hal-01377719⟩



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