Editorial Type:
Article
Article Type:
Research Article

Parameter Estimation Using a Particle Method: Inferring Mixing Coefficients from Sea Level Observations

Femke C. Vossepoel Institute for Marine and Atmospheric Research Utrecht (IMAU), and SRON Netherlands Institute for Space Research, Utrecht, Netherlands

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Peter Jan van Leeuwen Institute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht, Netherlands

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Print Publication:
01 Mar 2007
DOI:
https://doi.org/10.1175/MWR3328.1
Page(s):
1006–1020
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Abstract

This paper presents a first attempt to estimate mixing parameters from sea level observations using a particle method based on importance sampling. The method is applied to an ensemble of 128 members of model simulations with a global ocean general circulation model of high complexity. Idealized twin experiments demonstrate that the method is able to accurately reconstruct mixing parameters from an observed mean sea level field when mixing is assumed to be spatially homogeneous. An experiment with inhomogeneous eddy coefficients fails because of the limited ensemble size. This is overcome by the introduction of local weighting, which is able to capture spatial variations in mixing qualitatively. As the sensitivity of sea level for variations in mixing is higher for low values of mixing coefficients, the method works relatively well in regions of low eddy activity.

Corresponding author address: Dr. F. C. Vossepoel, IMAU/SRON, Princetonplein 5, NL-3584 CC Utrecht, Netherlands. Email: F.C.Vossepoel@phys.uu.nl

Abstract

This paper presents a first attempt to estimate mixing parameters from sea level observations using a particle method based on importance sampling. The method is applied to an ensemble of 128 members of model simulations with a global ocean general circulation model of high complexity. Idealized twin experiments demonstrate that the method is able to accurately reconstruct mixing parameters from an observed mean sea level field when mixing is assumed to be spatially homogeneous. An experiment with inhomogeneous eddy coefficients fails because of the limited ensemble size. This is overcome by the introduction of local weighting, which is able to capture spatial variations in mixing qualitatively. As the sensitivity of sea level for variations in mixing is higher for low values of mixing coefficients, the method works relatively well in regions of low eddy activity.

Corresponding author address: Dr. F. C. Vossepoel, IMAU/SRON, Princetonplein 5, NL-3584 CC Utrecht, Netherlands. Email: F.C.Vossepoel@phys.uu.nl

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  • Anderson, J. L. , and S. L. Anderson , 1999: A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilation and forecasts. Mon. Wea. Rev., 127 , 2741–2758.

    • Search Google Scholar
    • Export Citation

  • Annan, J. D. , J. C. Hargreaves , N. R. Edwards , and R. Marsh , 2005: Parameter estimation in an intermediate complexity Earth system model using an Ensemble Kalman filter. Ocean Modell., 8 , 135–154.

    • Search Google Scholar
    • Export Citation

  • Armi, L. , and D. B. Haidvogel , 1982: Effects of variable and anisotropic diffusivities in a steady-state diffusion model. J. Phys. Oceanogr., 12 , 785–794.

    • Search Google Scholar
    • Export Citation

  • Blanke, B. , and P. Delecluse , 1993: Variability of the tropical Atlantic Ocean simulated by a general circulation model with two different mixed-layer physics. J. Phys. Oceanogr., 23 , 1363–1387.

    • Search Google Scholar
    • Export Citation

  • Cox, M. , 1997: Isopycnal diffusion in a z-coordinate ocean model. Ocean Modell., 74 , 1–9.

  • Eknes, M. , and G. Evensen , 1997: Parameter estimation solving a weak constraint variational formulation of an Ekman model. J. Geophys. Res., 102 , 12479–12491.

    • Search Google Scholar
    • Export Citation

  • Gent, P. R. , and J. C. McWilliams , 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20 , 150–156.

  • Holloway, G. , 1986: Estimation of oceanic eddy transports from satellite altimetry. Nature, 323 , 243–244.

  • Kalnay, E. , and Coauthors , 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437–471.

  • Keffer, T. , and G. Holloway , 1988: Estimating Southern Ocean eddy flux of heat and salt from satellite altimetry. Nature, 332 , 624–626.

    • Search Google Scholar
    • Export Citation

  • Kim, S. , G. Eyink , A. Restrepo , and G. Johnson , 2003: Ensemble filtering for nonlinear dynamics. Mon. Wea. Rev., 131 , 2586–2594.

    • Search Google Scholar
    • Export Citation

  • Kivman, G. A. , 2003: Sequential parameter estimation for stochastic systems. Nonlinear Proc. Geophys., 10 , 253–259.

  • Large, W. G. , J. C. McWilliams , and S. C. Doney , 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys., 32 , 363–403.

    • Search Google Scholar
    • Export Citation

  • Lazar, A. , G. Madec , and P. Delecluse , 1999: The deep interior downwelling, the Veronis effect, and mesoscale tracer transport parameterizations in an OGCM. J. Phys. Oceanogr., 29 , 2945–2961.

    • Search Google Scholar
    • Export Citation

  • Levitus, S. , and Coauthors , 1998: Introduction. Vol. 1, World Ocean Database 1998, NOAA Atlas NESDIS 18, 346 pp.

  • Lorenz, E. N. , 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20 , 130–141.

  • Losa, S. N. , G. A. Kivman , J. Schröter , and M. Wenzel , 2003: Sequential weak constraint parameter estimation in an ecosystem model. J. Mar. Syst., 43 , 31–49.

    • Search Google Scholar
    • Export Citation

  • Losa, S. N. , G. A. Kivman , and V. A. Ryabchenko , 2004: Weak constraint parameter estimation for a simple ocean ecosystem model: What can we learn about the model and data? J. Mar. Syst., 45 , 1–20.

    • Search Google Scholar
    • Export Citation

  • Madec, G. , P. Delecluse , M. Imbard , and C. Levy , 1998: OPA 8.1 ocean general circulation model reference manual. Note du Pole de Modelisation 11, Institut Pierre Simon Laplace, 91 pp.

  • Miller, R. N. , E. C. Carter Jr. , and S. T. Blue , 1999: Data assimilation into nonlinear stochastic models. Tellus, 51A , 167–194.

    • Search Google Scholar
    • Export Citation

  • Navon, I. M. , 1997: Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dyn. Atmos. Oceans, 27 , 55–79.

    • Search Google Scholar
    • Export Citation

  • Pham, D. T. , 2001: Stochastic methods for sequential data assimilation in strongly nonlinear systems. Mon. Wea. Rev., 129 , 1194–1207.

    • Search Google Scholar
    • Export Citation

  • Reynolds, R. W. , and D. C. Marsico , 1993: An improved real-time global sea surface temperature analysis. J. Climate, 6 , 114–119.

  • Roullet, G. , and G. Madec , 2000: Salt conservation, free surface and varying volume: A new formulation for ocean GCMs. J. Geophys. Res., 105 , 23927–23942.

    • Search Google Scholar
    • Export Citation

  • Stammer, D. , 1998: On eddy characteristics, eddy transports, and mean flow properties. J. Phys. Oceanogr., 28 , 727–739.

  • van Leeuwen, P. J. , 2003: A variance-minimizing filter for large-scale applications. Mon. Wea. Rev., 131 , 2071–2084.

  • van Leeuwen, P. J. , and G. Evensen , 1996: Data assimilation and inverse methods in terms of a probabilistic formulation. Mon. Wea. Rev., 124 , 2898–2913.

    • Search Google Scholar
    • Export Citation

  • Vossepoel, F. C. , A. T. Weaver , J. Vialard , and P. Delecluse , 2004: Adjustment of near-equatorial wind stress with four-dimensional variational data assimilation in a model of the Pacific Ocean. Mon. Wea. Rev., 132 , 2070–2083.

    • Search Google Scholar
    • Export Citation
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