Geophysical flows under location uncertainty, Part I Random transport and general models

Resseguier, Valentin; Mémin, Étienne; Chapron, Bertrand

doi:10.1080/03091929.2017.1310210

Cited by 68 publications

(144 citation statements)

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“…However, we start from a stochastic Boussinesq system, derived itself from physical conservation principles and a stochastic representation of the flow. Such a representation, termed as modelling under location uncertainty, has recently been proposed in Mémin () and Resseguier et al () and is outlined hereafter. Note that similar models could be derived from Hamiltonian principles, as described in Holm ().…”

Section: Stochastic Representation Of the Lorenz‐63 Modelmentioning

confidence: 99%

“…This material derivative has the remarkable property of conserving the energy of any randomly transported tracer realization (Resseguier et al , ):

\frac{d}{normald t} \int_{Ω} Θ^{2} = \int_{Ω} D_{t} Θ^{2} = 0 .

Given the RTT, the classical conservation laws of mechanics (linear momentum, energy, mass) can be expressed within a stochastic flow of form . It should be noted that an incompressible homogeneous noise, i.e.…”

Section: Stochastic Representation Of the Lorenz‐63 Modelmentioning

confidence: 99%

“…Following the location uncertainty principle, stochastic Navier–Stokes and Boussinesq models have been derived by Mémin () and Resseguier et al (), respectively. In a 2D inertial frame of reference indexed by the horizontal and vertical coordinates x and z , an incompressible anisotropic homogeneous random field (i.e.…”

Section: Stochastic Representation Of the Lorenz‐63 Modelmentioning

confidence: 99%

“…It corresponds to the random interaction between the small‐scale velocity and the stratification δ T appearing in . This term and its influence on the buoyancy variations have been detailed in Resseguier et al ().…”

Section: Stochastic Representation Of the Lorenz‐63 Modelmentioning

confidence: 99%

“…To represent the large‐scale evolution of turbulent fluid flows, a different strategy can be envisaged, considering the decomposition of the flow into a large‐scale smooth component and a fast oscillating velocity component modelled as a random field (seen as decorrelated at large scales). However, such a decomposition requires us to modify the material derivative through the introduction of a stochastic transport operator (Mémin, ; Resseguier et al , ).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Stochastic Representation Of the Lorenz‐63 Modelmentioning

confidence: 99%

“…This material derivative has the remarkable property of conserving the energy of any randomly transported tracer realization (Resseguier et al , ):

\frac{d}{normald t} \int_{Ω} Θ^{2} = \int_{Ω} D_{t} Θ^{2} = 0 .

Section: Stochastic Representation Of the Lorenz‐63 Modelmentioning

confidence: 99%

Section: Stochastic Representation Of the Lorenz‐63 Modelmentioning

confidence: 99%

Section: Stochastic Representation Of the Lorenz‐63 Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Chapron

Dérian

Mémin

et al. 2017

Quart J Royal Meteoro Soc

Self Cite

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Spatial Covariance Modeling for Stochastic Subgrid-Scale Parameterizations Using Dynamic Mode Decomposition

Gugole¹,

Franzke²

2019

Preprint

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Stochastic parameterizations are increasingly being used in climate modeling to represent subgrid-scale processes. While different parameterizations are being developed considering different aspects of the physical phenomena, less attention is given to technical and numerical aspects. In particular, empirical orthogonal functions (EOFs) are employed when a spatial structure is required. Here, we provide evidence they might not be the most suitable choice. By applying an energy-consistent parameterization to the two-layer quasi-geostrophic (QG) model, we investigate the model sensitivity to a priori assumptions made on the parameterization. In particular, we consider here two methods to prescribe the spatial covariance of the noise: first, by using climatological variability patterns provided by EOFs, and second, by using time-varying dynamics-adapted Koopman modes, approximated by dynamic mode decomposition (DMD). The performance of the two methods are analyzed through numerical simulations of the stochastic system on a coarse spatial resolution and the outcomes compared to a high-resolution simulation of the original deterministic system. The comparison reveals that the DMD-based noise covariance scheme outperforms the EOF-based one. The use of EOFs leads to a significant increase of the ensemble spread and to a meridional misplacement of the bimodal eddy kinetic energy (EKE) distribution. Conversely, using DMDs, the ensemble spread is confined, the meridional propagation of the zonal jet stream is accurately captured, and the total variance of the system is improved. Our results highlight the importance of the systematic design of stochastic parameterizations with dynamically adapted spatial correlations, rather than relying on statistical spatial patterns.Plain Language Summary Exact and accurate representations of the climate system would require enormous amounts of computational resources and data storage. Hence, to circumvent this problem, climate models resolve explicitly only the large slow scales, while the fast small modes are represented inside climate models via parameterizations. Due to the different evolution times of the resolved and unresolved scales, the latter can be represented by means of a stochastic process. While different parameterizations are being developed considering different aspects of the physical phenomena, less attention is given to the technical and numerical aspects. In particular, the use of a constant in time noise covariance for the noise is very common. In the framework of a simplified model for the large-scale dynamics, we propose an alternative method to define the noise covariance, which allows it to be regularly updated during the simulation. This might be of crucial importance in the context of climate change. The results show that a dynamically adapted spatial correlation leads to a reduced growth of the uncertainties and better captures the system behavior.

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Non-local Eddy-Mean Kinetic Energy Transfers in Submesoscale-Permitting Ensemble Simulations

Jamet

leroux.ste@gmail.com

wdewar@fsu.edu

et al. 2022

Preprint

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Understanding processes associated with eddy-mean flow interactions helps our interpretation of ocean energetics, and guides the development of parameterizations. Here, we focus on the non-local nature of Kinetic Energy (KE) transfers between mean and turbulent reservoirs. Transfers are interpreted as nonlocal when the energy extracted from the mean flow does not locally sustain an growth of energy in the turbulent flow, or vice versa. The novelty of our approach is to use ensemble statistics to define the mean and the turbulent flow. Based on KE budget considerations, we first rationalize the eddy-mean separation in the ensemble framework, and discuss the interpretation of a mean flow driven by the prescribed (surface and boundary) forcing and a turbulent flow u′ driven by non-linear dynamics sensitive to initial conditions. We then analyze 120-day long, 20-member ensemble simulations of the Western Mediterranean basin run at resolution. Our main contribution is to recognize the prominent contribution of the cross energy term to explain non-local energy transfers, which provides a strong constraint on the horizontal organization of eddy-mean flow KE transfers since the cross energy term vanishes identically for perturbations orthogonal to the mean flow . We also highlight the prominent contribution of vertical turbulent fluxes for energy transfers within the surface mixed layer. Analyzing the scale dependence of non-local energy transfers supports the local approximation usually made in the development of mesoscale, energy-aware parameterizations for non-eddying models, but points out to the necessity of accounting for non-local dynamics in the meso-to-submeso scale range. Key Points► Ensemble-based eddy-mean decomposition of kinetic energy budget supports the view of an ocean turbulence driven by internal dynamics ► Turbulent fluxes of the cross energy term provide a potentially strong horizontal constraint on eddy-mean flow interactions ► Non-localities are leading order at small scales and should be accounted for in submesoscale parameterizations Please note that this is an author-produced PDF of an article accepted for publication following peer review. The definitive publisher-authenticated version is available on the publisher Web site.

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Geophysical flows under location uncertainty, Part I Random transport and general models

Cited by 68 publications

References 64 publications

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

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

Spatial Covariance Modeling for Stochastic Subgrid-Scale Parameterizations Using Dynamic Mode Decomposition

Non-local Eddy-Mean Kinetic Energy Transfers in Submesoscale-Permitting Ensemble Simulations

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