TY - JOUR

T1 - Efficient stochastic superparameterization for geophysical turbulence

AU - Grooms, Ian

AU - Majda, Andrew J.

PY - 2013/3/19

Y1 - 2013/3/19

N2 - Efficient computation of geophysical turbulence, such as occurs in the atmosphere and ocean, is a formidable challenge for the following reasons: the complex combination of waves, jets, and vortices; significant energetic backscatter from unresolved small scales to resolved large scales; a lack of dynamical scale separation between large and small scales; and small-scale instabilities, conditional on the large scales, which do not saturate. Nevertheless, efficient methods are needed to allow large ensemble simulations of sufficient size to provide meaningful quantifications of uncertainty in future predictions and past reanalyses through data assimilation and filtering. Here, a class of efficient stochastic superparameterization algorithms is introduced. In contrast to conventional superparameterization, the method here (i) does not require the simulation of nonlinear eddy dynamics on periodic embedded domains, (ii) includes a better representation of unresolved smallscale instabilities, and (iii) allows efficient representation of a much wider range of unresolved scales. The simplest algorithm implemented here radically improves efficiency by representing smallscale eddies at and below the limit of computational resolution by a suitable one-dimensional stochastic model of random-direction plane waves. In contrast to heterogeneous multiscale methods, the methods developed here do not require strong scale separation or conditional equilibration of local statistics. The simplest algorithm introduced here shows excellent performance on a difficult test suite of prototype problems for geophysical turbulence with waves, jets, and vortices, with a speedup of several orders of magnitude compared with direct simulation.

AB - Efficient computation of geophysical turbulence, such as occurs in the atmosphere and ocean, is a formidable challenge for the following reasons: the complex combination of waves, jets, and vortices; significant energetic backscatter from unresolved small scales to resolved large scales; a lack of dynamical scale separation between large and small scales; and small-scale instabilities, conditional on the large scales, which do not saturate. Nevertheless, efficient methods are needed to allow large ensemble simulations of sufficient size to provide meaningful quantifications of uncertainty in future predictions and past reanalyses through data assimilation and filtering. Here, a class of efficient stochastic superparameterization algorithms is introduced. In contrast to conventional superparameterization, the method here (i) does not require the simulation of nonlinear eddy dynamics on periodic embedded domains, (ii) includes a better representation of unresolved smallscale instabilities, and (iii) allows efficient representation of a much wider range of unresolved scales. The simplest algorithm implemented here radically improves efficiency by representing smallscale eddies at and below the limit of computational resolution by a suitable one-dimensional stochastic model of random-direction plane waves. In contrast to heterogeneous multiscale methods, the methods developed here do not require strong scale separation or conditional equilibration of local statistics. The simplest algorithm introduced here shows excellent performance on a difficult test suite of prototype problems for geophysical turbulence with waves, jets, and vortices, with a speedup of several orders of magnitude compared with direct simulation.

KW - Random plane waves

KW - Stochastic backscatter

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U2 - 10.1073/pnas.1302548110

DO - 10.1073/pnas.1302548110

M3 - Article

C2 - 23487800

AN - SCOPUS:84875276915

SN - 0027-8424

VL - 110

SP - 4464

EP - 4469

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 12

ER -