Toward a stochastic parameterization of ocean mesoscale eddies

Ocean Modelling

Volumn 79, Issue , 2014, Pages 1-20

  Porta Mana, PierGianLuca ^a   Zanna, Laure ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Eddy backscatter; Mesoscale eddies; Stochastic parametrization; Sub grid scale fluctuations

Indexed keywords

COMPUTER SIMULATION; HIGHER ORDER STATISTICS; NON NEWTONIAN FLOW; OCEANOGRAPHY; PARAMETERIZATION; PROBABILITY DENSITY FUNCTION; REYNOLDS NUMBER; STOCHASTIC SYSTEMS; STRAIN RATE;

EDDY-RESOLVING SIMULATIONS; HIGH-RESOLUTION MODELS; MESOSCALE EDDY; PROBABILITY DENSITY FUNCTIONS (PDFS); STOCHASTIC CLOSURES; STOCHASTIC PARAMETRIZATION; SUBGRID SCALE; VISCO-ELASTIC MEDIUMS;

STOCHASTIC MODELS;

BACKSCATTER; GYRE; MESOSCALE EDDY; NON-NEWTONIAN FLUID; PARAMETERIZATION; PROBABILITY DENSITY FUNCTION; QUASI-GEOSTROPHIC FLOW; REYNOLDS NUMBER; SKEWNESS; STOCHASTICITY; STRATIFICATION;

EID: 84900804533     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2014.04.002     Document Type: Article

References (108)

1. Arakawa A. Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I. J. Comput. Phys. 1966, 1(1):119-143.
2. Berloff P.S. On dynamically consistent eddy fluxes. Dyn. Atmos. Oceans 2005, 38(3-4):123-146.
3. Berloff P.S. Random-forcing model of the mesoscale oceanic eddies. J. Fluid Mech. 2005, 529:71-95.
4. Berloff P.S., Dewar W., Kravtsov S., McWilliams J. Ocean eddy dynamics in a coupled ocean-atmosphere model. J. Phys. Oceanogr. 2007, 37(5):1103-1121.
5. Berloff P.S., Hogg A.M.C., Dewar W. The turbulent oscillator: a mechanism of low-frequency variability of the wind-driven ocean gyres. J. Phys. Oceanogr. 2007, 37(9):2363-2386.
6. Bernardo J.-M. Expected information as expected utility. Ann. Stat. 1979, 7(3):686-690.
7. Bourlioux A., Majda A.J. Elementary models with probability distribution function intermittency for passive scalars with a mean gradient. Phys. Fluids 2002, 14(2):881-897.
8. Bowler N.E., Arribas A., Beare S.E., Mylne K.R., Shutts G.J. The local ETKF and SKEB: upgrades to the MOGREPS short-range ensemble prediction system. Q.J.R. Meteorol. Soc. 2009, 135(640):767-776.
9. Brankart J.-M. Impact of uncertainties in the horizontal density gradient upon low resolution global ocean modelling. Ocean Modell. 2013, 66:64-76.
10. Buizza R., Miller M., Palmer T.N. Stochastic representation of model uncertainties in the ECMWF ensemble prediction system. Q.J.R. Meteorol. Soc. 1999, 125(560):2887-2908.
11. Burbidge J.B., Magee L., Robb A.L. Alternative transformations to handle extreme values of the dependent variable. J. Am. Stat. Assoc. 1988, 83(401):123-127.
12. Cessi P., Fantini M. The eddy-driven thermocline. J. Phys. Oceanogr. 2004, 34(12):2642-2658.
13. Chen S., Foias C., Holm D.D., Olson E., Titi E.S., Wynne S. Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Phys. Rev. Lett. 1998, 81(24):5338-5341.
14. Ching E.S.C., Kraichnan R.H. Exact results for conditional means of a passive scalar in certain statistically homogeneous flows. J. Stat. Phys. 1998, 93(3-4):787-795.
15. Cooper F.C., Haynes P.H. Climate sensitivity via a nonparametric fluctuation-dissipation theorem. J. Atmos. Sci. 2011, 68(5):937-953.
16. Crommelin D.T., Vanden-Eijnden E. Subgrid-scale parameterization with conditional Markov chains. J. Atmos. Sci. 2008, 65(8):2661-2675.
17. Crow S.C. Viscoelastic character of finegrained isotropic turbulence. Phys. Fluids 1967, 10(7):1587-1589.
18. Danabasoglu G., McWilliams J., Gent P. The role of mesoscale tracer transports in the global ocean circulation. Science 1994, 264(5162):1123-1126.
19. Dorrestijn J., Crommelin D.T., Siebesma A.P., Jonker H.J.J. Stochastic parameterization of shallow cumulus convection estimated from high-resolution model data. Theor. Comput. Fluid Dyn. 2013, 27(1-2):133-148.
20. Duan J., Nadiga B.T. Stochastic parameterization for large eddy simulation of geophysical flows. Proc. Am. Math. Soc. 2007, 135(4):1187-1196.
21. Dunn J.E., Fosdick R.L. Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade. Arch. Ration. Mech. Anal. 1974, 56(3):191-252.
22. Eden C. Parameterising meso-scale eddy momentum fluxes based on potential vorticity mixing and a gauge term. Ocean Modell. 2010, 32(1-2):58-71.
23. Eden C., Greatbatch R.J. Diapycnal mixing by meso-scale eddies. Ocean Modell. 2008, 23(3-4):113-120.
24. Eden C., Greatbatch R.J. Towards a mesoscale eddy closure. Ocean Modell. 2008, 20(3):223-239.
25. Farrell B.F., Ioannou P.J. Structural stability of turbulent jets. J. Atmos. Sci. 2003, 60(17):2101-2118.
26. Farrell B.F., Ioannou P.J. Structure and spacing of jets in barotropic turbulence. J. Atmos. Sci. 2007, 64(10):3652-3665.
27. Foiaş C., Holm D.D., Titi E.S. The Navier-Stokes-alpha model of fluid turbulence. Physica D 2001, 152-153:505-519.
28. Franzke C., Majda A.J., Branstator G. The origin of nonlinear signatures of planetary wave dynamics: mean phase space tendencies and contributions from non-gaussianity. J. Atmos. Sci. 2007, 64(11):3987-4003.
29. Frederiksen J.S. Subgrid-scale parameterizations of eddy-topographic force, eddy viscosity, and stochastic backscatter for flow over topography. J. Atmos. Sci. 1999, 56(11):1481-1494.
30. Frederiksen J.S., Davies A.G. Eddy viscosity and stochastic backscatter parameterizations on the sphere for atmospheric circulation models. J. Atmos. Sci. 1997, 54(20):2475-2492.
31. Frederiksen J.S., Kepert S.M. Dynamical subgrid-scale parameterizations from direct numerical simulations. J. Atmos. Sci. 2006, 63(11):3006-3019.
32. Frederiksen J.S., O'Kane T.J., Zidikheri M.J. Stochastic subgrid parameterizations for atmospheric and oceanic flows. Phys. Scr. 2012, 85(6):068202.
33. Gent P.R., McWilliams J.C. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr. 1990, 20(1):150-155.
34. Graham, J.P., Ringler, T. 2013. A framework for the evaluation of turbulence closures used in mesoscale ocean large-eddy simulations.
35. Grooms I., Majda A.J. Efficient stochastic superparameterization for geophysical turbulence. Proc. Natl. Acad. Sci. U.S.A. 2013, 110(12):4464-4469.
36. Henning C., Vallis G. The effects of mesoscale eddies on the main subtropical thermocline. J. Phys. Oceanogr. 2004, 34(11):2428-2443.
37. Herring J.R., Kraichnan R.H. Comparison of some approximations for isotropic turbulence. Lecture Notes in Physics 1972, vol. 12:148-194. Springer-Verlag, Berlin. M. Rosenblatt, C. Van Atta (Eds.).
38. Holloway G. Estimation of oceanic eddy transports from satellite altimetry. Nature 1986, 323(6085):243-244.
39. Holloway G. From classical to statistical ocean dynamics. Surv. Geophys. 2004, 25(3-4):203-219.
40. Holm D.D., Nadiga B.T. Modeling mesoscale turbulence in the barotropic double-gyre circulation. J. Phys. Oceanogr. 2003, 33(11):2355-2365.
41. Holm D.D., Wingate B.A. Baroclinic instabilities of the two-layer quasigeostrophic alpha model. J. Phys. Oceanogr. 2005, 35(7):1287-1296.
42. Hu Y., Pierrehumbert R.T. The advection-diffusion problem for stratospheric flow. Part I: concentration probability distribution function. J. Atmos. Sci. 2001, 58(12):1493-1510.
43. Hughes C.W., Thompson A.F., Wilson C. Identification of jets and mixing barriers from sea level and vorticity measurements using simple statistics. Ocean Modell. 2010, 32(1-2, SI):44-57.
44. Jaynes E.T. On the rationale of maximum-entropy methods. Proc. IEEE 1982, 70(9):939.
45. Johnson N.L. Systems of frequency curves generated by methods of translation. Biometrika 1949, 36(1/2):149-176.
46. Khouider B., Majda A., Katsoulakis M. Coarse-grained stochastic models for tropical convection and climate. Proc. Natl. Acad. Sci. U.S.A. 2003, 100(21):11941-11946.
47. Kirtman, B., Vecchi, G.A. 2011. Why climate modelers should worry about atmospheric and oceanic weather, pp. 511-524.
48. Kitsios V., Frederiksen J.S., Zidikheri M.J. Subgrid model with scaling laws for atmospheric simulations. J. Atmos. Sci. 2012, 69(4):1427-1445.
49. Kitsios V., Frederiksen J.S., Zidikheri M.J. Subgrid parameterisation of the eddy-meanfield interactions in a baroclinic quasi-geostrophic ocean. ANZIAM J. 2012, 54:C459-C475.
50. Kitsios V., Frederiksen J.S., Zidikheri M.J. Scaling laws for parameterisations of subgrid eddy-eddy interactions in simulations of oceanic circulations. Ocean Modell. 2013, 68(8):88-105.
51. Kraichnan R.H. The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 1959, 5(4):497-543.
52. Kraichnan R.H. Eddy viscosity in two and three dimensions. J. Atmos. Sci. 1976, 33(8):1521-1536.
53. Kullback S., Leibler R.A. On information and sufficiency. Ann. Math. Stat. 1951, 22(1):79-86.
54. LaCasce, J.H. 2008. Lagrangian statistics from oceanic and atmospheric observations. In: Weiss, J.B., Provenzale, A. (Eds.), Transport and Mixing in Geophysical Flows, Lecture Notes in Physics, vol. 744, pp. 165-218.
55. Leith C.E. Stochastic backscatter in a subgridscale model: plane shear mixing layer. Phys. Fluids A 1990, 2(3):297.
56. Li H., von Storch J.-S. On the fluctuating buoyancy fluxes simulated in a 110° OGCM. J. Phys. Oceanogr. 2013, 43(7):1270-1287.
57. Liepmann, H.W. 1962. Free turbulent flows. In: Favre, A. (Ed.), Mécanique de la Turbulence, Colloques Internationaux du CNRS, CNRS, vol. 108, pp. 211-251.
58. Lorenz, E.N. 1995. Predictability: a problem partly solved. In: Seminar on Predictability, 4-8 September 1995, Reading. ECMWF.
59. Lumley J.L. Toward a turbulent constitutive relation. J. Fluid Mech. 1970, 41(2):413-434.
60. Macvean M.K. The effects of horizontal diffusion on baroclinic development in a spectral model. Q.J.R. Meteorol. Soc. 1983, 109(462):771-783.
61. Majda A.J., Gershgorin B. Quantifying uncertainty in climate change science through empirical information theory. Proc. Natl. Acad. Sci. U.S.A. 2010, 107(34):14958-14963.
62. Majda A.J., Gershgorin B. Elementary models for turbulent diffusion with complex physical features: eddy diffusivity, spectrum and intermittency. Philos. Trans. R. Soc. A 2013, 371(1982):20120184.
63. Majda A.J., Kramer P.R. Simplified models for turbulent diffusion: theory, numerical modelling, and physical phenomena. Phys. Rep. 1999, 314(4-5):237-574.
64. Marshall D. Subduction of water masses in an eddying ocean. J. Mar. Res. 1997, 55(2):201-222.
65. Marshall D.P., Maddison J.R., Berloff P.S. A framework for parameterizing eddy potential vorticity fluxes. J. Phys. Oceanogr. 2012, 42(4):539-557.
66. Mason P.J., Thomson D.J. Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 1992, 242(9):51-78.
67. McTigue D.F., Passman S.L., Jones S.J. Normal stress effects in the creep of ice. J. Glaciol. 1985, 31(108):120-126.
68. Mead L.R., Papanicolaou N. Maximum entropy in the problem of moments. J. Math. Phys. 1984, 25(8):2404-2417.
69. Meredith M.P., Hogg A.M. Circumpolar response of southern ocean eddy activity to a change in the southern annular mode. Geophys. Res. Lett. 2006, 33(16):L16608.
70. Munday D.R., Johnson H.L., Marshall D.P. Eddy saturation of equilibrated circumpolar currents. J. Phys. Oceanogr. 2013, 43(3):507-532.
71. Murdoch A.I., Bedeaux D. Continuum equations of balance via weighted averages of microscopic quantities. Proc. R. Soc. London A 1994, 445(1923):157-179.
72. Nadiga B.T., Bouchet F. The equivalence of the Lagrangian-averaged Navier-Stokes-α model and the rational large eddy simulation model in two dimensions. Phys. Fluids 2011, 23(9):95-105.
73. Nadiga B.T., Margolin L.G. Dispersive-dissipative eddy parameterization in a barotropic model. J. Phys. Oceanogr. 2001, 31(8):2525-2531.
74. Neelin J.D., Peters O., Lin J.W.-B., Hales K., Holloway C.E. Rethinking convective quasi-equilibrium: observational constraints for stochastic convective schemes in climate models. Philos. Trans. R. Soc. A 2008, 366(1875):2581-2604.
75. O'Kane T.J., Frederiksen J.S. Statistical dynamical subgrid-scale parameterizations for geophysical flows. Phys. Scr. 2008, 2008:T132.
76. Okubo A. Horizontal dispersion of floatable particles in vicinity of velocity singularities such as convergences. Deep Sea Res. 1970, 17(3):445-454.
77. Palmer T.N. A nonlocal dynamical perspective on model error: a proposal for nonlocal stochastic-dynamic parametrization in weather and climate prediction models. Q.J.R. Meteorol. Soc. 2001, 127:279-304.
78. Palmer T.N. Towards the probabilistic Earth-system simulator: a vision for the future of climate and weather prediction. Q.J.R. Meteorol. Soc. 2012, 138:841-861.
79. Penland C., Sardeshmukh P.D. The optimal growth of tropical sea surface temperature anomalies. J. Climate 1995, 8(8):1999-2024.
80. Qiu B., Scott R.B., Chen S. Length scales of eddy generation and nonlinear evolution of the seasonally modulated South Pacific subtropical countercurrent. J. Phys. Oceanogr. 2008, 38(7):1515-1528.
81. Rhines P.B., Young W.R. A theory of wind-driven circulation. I. Mid-ocean gyres. J. Mar. Res. 1982, 40(S):559-596.
82. Rhines P.B., Young W.R. Homogenization of potential vorticity in planetary gyres. J. Fluid Mech. 1982, 122:347-367.
83. Riesen P., Hutter K., Funk M. A viscoelastic Rivlin-Ericksen material model applicable to glacier ice. Nonlinear Processes Geophys. 2010, 17(6):673-684.
84. Ring M.J., Plumb R.A. The response of a simplified GCM to axisymmetric forcings: applicability of the fluctuation-dissipation theorem. J. Atmos. Sci. 2008, 65(12):3880-3898.
85. Rivlin R.S. The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids. Q. Appl. Math. 1957, 15(2):212-215.
86. Rivlin R.S., Ericksen J. Stress-deformation relations for isotropic materials. J. Ration. Mech. Anal. 1955, 4(2):323-425.
87. Roberts M.J., Marshall D.P. On the validity of downgradient eddy closures in ocean models. J. Geophys. Res. 2000, 105(C12):28613-28627.
88. Scott R.B., Arbic B.K. Spectral energy fluxes in geostrophic turbulence: implications for ocean energetics. J. Phys. Oceanogr. 2007, 37(3):673-688.
89. Shannon C.E. A mathematical theory of communication. Bell Syst. Tech. J. 1948, 27(379-423):623-656.
90. Shutts G.J. A kinetic energy backscatter algorithm for use in ensemble prediction systems. Q.J.R. Meteorol. Soc. 2005, 131(612):3079-3102.
91. Shutts G.J., Palmer T.N. Convective forcing fluctuations in a cloud-resolving model: Relevance to the stochastic parameterization problem. J. Climate 2007, 20(2):187-202.
92. Sivia D.S. Bayesian inductive inference, maximum entropy & neutron scattering. Los Alamos Sci. 1990, 4(19):180-207.
93. Smagorinsky J. General circulation experiments with the primitive equations, i, the basic experiment. Mon. Weather Rev. 1963, 91:99-164.
94. Speziale C.G. On nonlinear k - l and k - models of turbulence. J. Fluid Mech. 1987, 178:459-475.
95. Straub D.N. On the transport and angular momentum balance of channel models of the antarctic circumpolar current. J. Phys. Oceanogr. 1993, 23(4):776-782.
96. Treguier A., Held I., Larichev V. Parameterization of quasigeostrophic eddies in primitive equation ocean models. J. Phys. Oceanogr. 1997, 27(4):567-580.
97. Truesdell C.A., Rajagopal K.R. An introduction to the mechanics of fluids. Modern Birkhäuser Classics 2009, Birkhäuser, Boston, First publ. 1999. reprint ed.
98. Vallis G.K. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation 2006, Cambridge University Press, Cambridge.
99. Waterman S., Hoskins B.J. Eddy shape, orientation, propagation, and mean flow feedback in western boundary current jets. J. Phys. Oceanogr. 2013, 43(8):1666-1690.
100. Waterman S., Jayne S.R. Eddy-mean flow interactions in the along-stream development of a western boundary current jet: an idealized model study. J. Phys. Oceanogr. 2011, 41(4):682-707.
101. Waterman S., Jayne S.R. Eddy-driven recirculations from a localized transient forcing. J. Phys. Oceanogr. 2012, 42(3):430-447.
102. Waugh D.W., Keating S.R., Chen M.-L. Diagnosing ocean stirring: comparison of relative dispersion and finite-time Lyapunov exponents. J. Phys. Oceanogr. 2012, 42(7):1173-1185.
103. Weiss J. The dynamics of enstrophy transfer in 2-dimensional hydrodynamics. Physica D 1991, 48(2-3):273-294.
104. Williams P.D. A proposed modification to the Robert-Asselin time filter. Mon. Weather Rev. 2009, 137(8):2538-2546.
105. Williams P.D., Haine T.W.N., Read P.L. Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization. Nonlinear Processes Geophys. 2004, 11(1):127-135.
106. Wilson C., Williams R.G. When are eddy tracer fluxes directed downgradient?. J. Phys. Oceanogr. 2006, 36(2):189-201.
107. Zanna L. Forecast skill and predictability of observed Atlantic sea surface temperatures. J. Climate 2012, 25(14):5047-5056.
108. Zidikheri M.J., Frederiksen J.S. Stochastic modelling of unresolved eddy fluxes. Geophys. Astrophys. Fluid Dyn. 2010, 104(4):323-348.