Stochastic superparameterization in quasigeostrophic turbulence

Grooms, Ian

doi:10.1016/J.JCP.2013.09.020

Title: Stochastic superparameterization in quasigeostrophic turbulence

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Abstract

In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddiesmore »« less

Authors:

Grooms, Ian ^[1]

Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States)

Publication Date:: Fri Aug 15 00:00:00 EDT 2014

OSTI Identifier:: 22314892

Resource Type:: Journal Article

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 271; Conference: 1. international conference on frontiers in computational physics, Boulder, CO (United States), 16-20 Dec 2012; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DECOUPLING; ENERGY CONSERVATION; ENERGY SPECTRA; LAYERS; NONLINEAR PROBLEMS; PERIODICITY; RESOLUTION; SENSITIVITY; SHEAR; STOCHASTIC PROCESSES; TURBULENCE; VORTICES

Citation Formats


                    Grooms, Ian, Majda, Andrew J., E-mail: jonjon@cims.nyu.edu, and Center for Prototype Climate Modelling, NYU-Abu Dhabi. Stochastic superparameterization in quasigeostrophic turbulence.  United States: N. p., 2014. 
        Web.  doi:10.1016/J.JCP.2013.09.020.

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                    Grooms, Ian, Majda, Andrew J., E-mail: jonjon@cims.nyu.edu, & Center for Prototype Climate Modelling, NYU-Abu Dhabi. Stochastic superparameterization in quasigeostrophic turbulence.  United States.  https://doi.org/10.1016/J.JCP.2013.09.020

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                    Grooms, Ian, Majda, Andrew J., E-mail: jonjon@cims.nyu.edu, and Center for Prototype Climate Modelling, NYU-Abu Dhabi. 2014.  
        "Stochastic superparameterization in quasigeostrophic turbulence".  United States.  https://doi.org/10.1016/J.JCP.2013.09.020.

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@article{osti_22314892,

  title        = {Stochastic superparameterization in quasigeostrophic turbulence},

  author       = {Grooms, Ian and Majda, Andrew J., E-mail: jonjon@cims.nyu.edu and Center for Prototype Climate Modelling, NYU-Abu Dhabi},

  abstractNote = {In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and efficient stochastic parameterizations for use in ensemble-based state estimation and prediction.},

  doi          = {10.1016/J.JCP.2013.09.020},

  url          = {https://www.osti.gov/biblio/22314892},
  journal      = {Journal of Computational Physics},

  issn         = {0021-9991},

  number       = ,

  volume       = 271,

  place        = {United States},

  year         = {Fri Aug 15 00:00:00 EDT 2014},

  month        = {Fri Aug 15 00:00:00 EDT 2014}

}

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