Geophysical flows under location uncertainty, Part II Quasi-geostrophy and efficient ensemble spreading

Valentin Resseguier 1, 2, * Etienne Mémin 1 Bertrand Chapron 2
* Corresponding author
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 : Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. In this paper, simplified geophysical dynamics are derived from a Boussinesq model under location uncertainty. Invoking usual scaling approximations and a moderate influence of the subgrid terms, stochastic formulations are obtained for the stratified Quasi-Geostrophy (QG) and the Surface Quasi-Geostrophy (SQG) models. Based on numerical simulations, benefits of the proposed stochastic formalism are demonstrated. A single realization of models under location uncertainty can restore small-scale structures. An ensemble of realizations further helps to assess model error prediction and outperforms perturbed deterministic models by one order of magnitude. Such a high uncertainty quantification skill is of primary interests for assimilation ensemble methods. MATLAB R code examples are available online.
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Submitted on : Friday, March 10, 2017 - 6:47:01 AM
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Valentin Resseguier, Etienne Mémin, Bertrand Chapron. Geophysical flows under location uncertainty, Part II Quasi-geostrophy and efficient ensemble spreading. Geophysical and Astrophysical Fluid Dynamics, Taylor & Francis, 2017, 111 (3), pp.177-208. ⟨10.1080/03091929.2017.1312101⟩. ⟨hal-01391476v3⟩

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