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arXiv · 1611.03041

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

Valentin Resseguier·Etienne Memin·Bertrand Chapron
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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 code examples are available online.

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Valentin Resseguier, Etienne Memin, Bertrand Chapron. 2016-11-09. Geophysical flows under location uncertainty, Part II: Quasi-geostrophy and efficient ensemble spreading. https://doi.org/10.1080/03091929.2017.1312101

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