Variational Stochastic Parameterisations and Their Applications to Primitive Equation Models

Ruiao, Hu,; Patching, Stuart

doi:10.1007/978-3-031-18988-3_9

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…Alternatives exist, such as, for example, Jansen et al (2019), where barotropic subgrid energy is advected by the resolved 2D barotropic flow. While stochastic advection is another potentially interesting approach, constraining it presents its own set of challenges, as discussed in the literature on stochastic advection (e.g., Hu and Patching (2023)).…”

Section: Journal Of Advances In Modeling Earth Systemsmentioning

confidence: 99%

Advancing Eddy Parameterizations: Dynamic Energy Backscatter and the Role of Subgrid Energy Advection and Stochastic Forcing

Bagaeva,

Danilov,

Oliver

et al. 2024

J Adv Model Earth Syst

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Viscosity in the momentum equation is needed for numerical stability, as well as to arrest the direct cascade of enstrophy at grid scales. However, a viscous momentum closure tends to over‐dissipate eddy kinetic energy. To return excessively dissipated energy to the system, the viscous closure is equipped with what is called dynamic kinetic energy backscatter. The amplitude of backscatter is based on the amount of unresolved kinetic energy (UKE). This energy is tracked through space and time via a prognostic equation. Our study proposes to add advection of UKE by the resolved flow to that equation to explicitly consider the effects of nonlocality on the subgrid energy budget. UKE can consequently be advected by the resolved flow before it is reinjected via backscatter. Furthermore, we suggest incorporating a stochastic element into the UKE equation to account for missing small‐scale variability, which is not present in the purely deterministic approach. The implementations are tested on two intermediate complexity setups of the global ocean model FESOM2: an idealized channel setup and a double‐gyre setup. The impacts of these additional terms are analyzed, highlighting increased eddy activity and improved flow characteristics when advection and carefully tuned, stochastic sources are incorporated into the UKE budget. Additionally, we provide diagnostics to gain further insights into the effects of scale separation between the viscous dissipation operator and the backscatter operator responsible for the energy injection.

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Section: Journal Of Advances In Modeling Earth Systemsmentioning

confidence: 99%

Advancing Eddy Parameterizations: Dynamic Energy Backscatter and the Role of Subgrid Energy Advection and Stochastic Forcing

Bagaeva,

Danilov,

Oliver

et al. 2024

J Adv Model Earth Syst

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Deterministic and stochastic geometric mechanics for Hall magnetohydrodynamics

Holm,

Hu,

Street

2024

Proc. R. Soc. A.

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We derive new models of stochastic Hall magnetohydrodynamics (MHD) by applying Lie group symmetry reduction in a stochastic Euler–Poincaré variational principle. The resulting new theory of stochastic Hall MHD has potential applications for uncertainty quantification and data assimilation in space plasma (space weather), planetary science and solar physics. The stochastic geometric mechanics approach we take here produces coordinate-free results that may then be applied in a variety of spatial configurations.

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Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model

et al. 2023

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This paper investigates the mathematical properties of a stochastic version of the balanced 2D thermal quasigeostrophic (TQG) model of potential vorticity dynamics. This stochastic TQG model is intended as a basis for parametrization of the dynamical creation of unresolved degrees of freedom in computational simulations of upper ocean dynamics when horizontal buoyancy gradients and bathymetry affect the dynamics, particularly at the submesoscale (250[Formula: see text]m–10[Formula: see text]km). Specifically, we have chosen the Stochastic Advection by Lie Transport (SALT) algorithm introduced in [D. D. Holm, Variational principles for stochastic fluid dynamics, Proc. Roy. Soc. A: Math. Phys. Eng. Sci. 471 (2015) 20140963, http://dx.doi.org/10.1098/rspa.2014.0963 ] and applied in [C. Cotter, D. Crisan, D. Holm, W. Pan and I. Shevchenko, Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model, Found. Data Sci. 2 (2020) 173, https://doi.org/10.3934/fods.2020010 ; Numerically modeling stochastic lie transport in fluid dynamics, SIAM Multiscale Model. Simul. 17 (2019) 192–232, https://doi.org/10.1137/18M1167929 ] as our modeling approach. The SALT approach preserves the Kelvin circulation theorem and an infinite family of integral conservation laws for TQG. The goal of the SALT algorithm is to quantify the uncertainty in the process of up-scaling, or coarse-graining of either observed or synthetic data at fine scales, for use in computational simulations at coarser scales. The present work provides a rigorous mathematical analysis of the solution properties of the thermal quasigeostrophic (TQG) equations with SALT [D. D. Holm and E. Luesink, Stochastic wave-current interaction in thermal shallow water dynamics, J. Nonlinear Sci. 31 (2021), https://doi.org/10.1007/s00332-021-09682-9 ; D. D. Holm, E. Luesink and W. Pan, Stochastic mesoscale circulation dynamics in the thermal ocean, Phys. Fluids 33 (2021) 046603, https://doi.org/10.1063/5.0040026 ].

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Variational Stochastic Parameterisations and Their Applications to Primitive Equation Models

Cited by 3 publications

References 27 publications

Advancing Eddy Parameterizations: Dynamic Energy Backscatter and the Role of Subgrid Energy Advection and Stochastic Forcing

Advancing Eddy Parameterizations: Dynamic Energy Backscatter and the Role of Subgrid Energy Advection and Stochastic Forcing

Deterministic and stochastic geometric mechanics for Hall magnetohydrodynamics

Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model

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