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

• Published in: Geophysical and astrophysical fluid dynamics Vol. 111; no. 3; pp. 177 - 208
• Main Authors: Resseguier, V., Mémin, E., Chapron, B.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.05.2017; Taylor & Francis Ltd
• Subjects: Advection; Atmospheric and Oceanic Physics; Boussinesq approximation; Boussinesq equations; Computer simulation; Dye dispersion; Dynamics; Engineering Sciences; ensemble forecasts; Fluid dynamics; Fluid mechanics; Geophysics; Geostrophy; Mathematical models; Mechanics; Numerical simulations; Physics; Scaling; Signal and Image processing; Stochastic sub-grid parameterization; Uncertainty; Uncertainty quantification; Velocity; stochastic sub-grid parameterization; ensemble forecasts; uncertainty quantification
• ISSN: 0309-1929; 1029-0419
• DOI: 10.1080/03091929.2017.1312101

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 and the Surface Quasi-Geostrophy 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.