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

Resseguier, Valentin; Mémin, Étienne; Chapron, Bertrand

doi:10.1080/03091929.2017.1312101

Cited by 66 publications

(116 citation statements)

References 51 publications

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“…Recently, stochastic partial differential fluid equations have been proposed to model the influence of unresolved scales on the resolved scales of interest [18,8,22,23,24]. These novel approaches introduce stochasticity into the flow map for the Lagrangian particle trajectories, then the noise in the Lagrangian-to-Euler map produces a random Eulerian vector field.…”

Section: Introductionmentioning

confidence: 99%

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

2017

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In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.096310.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

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Section: Introductionmentioning

confidence: 99%

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

2017

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“…Corresponding eddy‐viscosity models are no longer constant, but are adapted to the dynamics. This random framework also enables us to derive stochastic dynamics from the very same physical conservation principles as in the deterministic case and is amenable to the usual geophysical scaling approximations (Resseguier et al , , ).…”

Section: Introductionmentioning

confidence: 99%

Large‐scale flows under location uncertainty: a consistent stochastic framework

Chapron

Dérian

Mémin

et al. 2017

Quart J Royal Meteoro Soc

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Using a classical example, the Lorenz‐63 model, an original stochastic framework is applied to represent large‐scale geophysical flow dynamics. Rigorously derived from a reformulated material derivative, the proposed framework encompasses several meaningful mechanisms to model geophysical flows. The slightly compressible set‐up, as treated in the Boussinesq approximation, yields a stochastic transport equation for the density and other related thermodynamical variables. Coupled to the momentum equation through a forcing term, the resulting stochastic Lorenz‐63 model is derived consistently. Based on such a reformulated model, the pertinence of this large‐scale stochastic approach is demonstrated over classical eddy‐viscosity based large‐scale representations.

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“…The localization process allows to remove the long distance correlations and provide a more accurate approximation of the background error covariance matrix. Secondly, the stochastic representation of the evolution model [23] is to be investigated. By doing so, the proposed framework can be extended to more general cases for fluid motion estimation problem.…”

Section: Discussionmentioning

confidence: 99%

“…The synthetic data set is generated from a Surface QuasiGeostrophic (SQG) model 1 provided in [23], which represents an idealized oceanic domain with periodic boundary conditions. The corresponding 64×64 pixels grid is initialized with random buoyancy fluctuations for which the power spectral density follows a -5/3 power-law.…”

Section: A Data Descriptionmentioning

confidence: 99%

Sea Surface Flow Estimation via Ensemble-based Variational Data Assimilation

Cai

Mémin

Yin

et al. 2018

2018 Annual American Control Conference (ACC)

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Abstract-In this paper, we propose a data assimilation method for consistently estimating the velocity fields from a whole image sequence depicting the evolution of sea surface temperature transported by oceanic surface flow. The estimator is conducted through an ensemble-based variational data assimilation, which is designed by combining the advantages of two approaches: the ensemble Kalman filter and the variational data assimilation. This idea allows us to obtain the optimal initial condition as well as the full system trajectory. In order to extract the velocity fields from fluid images, a surface quasi-geostrophic model representing the generic evolution of the temperature field of the flow, and the optical flow constraint equation derived from the image intensity constancy assumption, are involved in the assimilation context. Numerical experimental evaluation is presented on a synthetic fluid image sequence. The results indicate good performance and efficiency of the proposed estimator.

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

Cited by 66 publications

References 51 publications

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

Large‐scale flows under location uncertainty: a consistent stochastic framework

Sea Surface Flow Estimation via Ensemble-based Variational Data Assimilation

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