Data Assimilation in a Baroclinic Coastal Ocean Model: Ensemble Statistics and Comparison of Methods

A. L. Kurapov College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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G. D. Egbert College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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R. N. Miller College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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J. S. Allen College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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Abstract

The performance of data assimilation methods in an idealized three-dimensional time-dependent coastal baroclinic model is assessed by computing ensemble error statistics. The analytical representer solution allows for computation of posterior error statistics for the variational generalized inverse method (GIM) as well as sequential methods such as the Kalman filter (KF) and optimal interpolation (OI). Computations can be made in a straightforward way, given the statistics of errors in the model equations and data. The GIM yields solutions with significantly smaller variance than that given by KF or OI if the data contain valuable information about the past flow. This is the case, for instance, when a large fraction of the model error is due to uncertainty in the wind stress. In the scope of the model presented here, the plausibility of simplifications made in a practical OI scheme is analyzed. The unified study of the GIM, KF, and OI allows for the demonstratation of how the forecast error covariance used in a practical OI sequential scheme may be optimized with the use of lagged covariances for the model solution. The effect of the misspecified input error statistics on the solution quality is also assessed. In some practically relevant cases the use of future data by the GIM, in contrast to KF and OI, compensates for incorrectly specified input error covariances.

Corresponding author address: Dr. A. L. Kurapov, College of Oceanic and Atmospheric Sciences, Oregon State University, 104, Ocean Admin. Bldg., Corvallis, OR 97331-5503. Email: kurapov@oce.orst.edu

Abstract

The performance of data assimilation methods in an idealized three-dimensional time-dependent coastal baroclinic model is assessed by computing ensemble error statistics. The analytical representer solution allows for computation of posterior error statistics for the variational generalized inverse method (GIM) as well as sequential methods such as the Kalman filter (KF) and optimal interpolation (OI). Computations can be made in a straightforward way, given the statistics of errors in the model equations and data. The GIM yields solutions with significantly smaller variance than that given by KF or OI if the data contain valuable information about the past flow. This is the case, for instance, when a large fraction of the model error is due to uncertainty in the wind stress. In the scope of the model presented here, the plausibility of simplifications made in a practical OI scheme is analyzed. The unified study of the GIM, KF, and OI allows for the demonstratation of how the forecast error covariance used in a practical OI sequential scheme may be optimized with the use of lagged covariances for the model solution. The effect of the misspecified input error statistics on the solution quality is also assessed. In some practically relevant cases the use of future data by the GIM, in contrast to KF and OI, compensates for incorrectly specified input error covariances.

Corresponding author address: Dr. A. L. Kurapov, College of Oceanic and Atmospheric Sciences, Oregon State University, 104, Ocean Admin. Bldg., Corvallis, OR 97331-5503. Email: kurapov@oce.orst.edu

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  • Bennett, A. F., 1992: Inverse Methods in Physical Oceanography. Cambridge University Press, 346 pp.

  • Cohn, S. E., 1997: An introduction to estimation theory. J. Meteor. Soc. of Japan, 75B , 257288.

  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Gelb, A., Ed.,. 1974: Applied Optimal Estimation. The MIT Press, 374 pp.

  • Gelfand, I. M., and S. V. Fomin, 1963: Calculus of Variations. Prentice Hall, 232 pp.

  • Kosro, P. M., J. A. Barth, and P. T. Strub, 1997: The coastal jet: Observations of surface currents over the Oregon continental shelf from HF radar. Oceanography, 10 , 5356.

    • Search Google Scholar
    • Export Citation
  • Miller, R. N., 1996: Introduction to the Kalman filter. Proc. ECMWF Seminar on Data Assimilation, Reading, United Kingdom, ECMWF, 47–59.

    • Search Google Scholar
    • Export Citation
  • Oke, P. R., J. S. Allen, R. N. Miller, G. D. Egbert, and P. M. Kosro, 2001: Assimilation of surface velocity data into a primitive equation coastal ocean model. J. Geophys. Res., in press.

    • Search Google Scholar
    • Export Citation
  • Scott, R. K., J. S. Allen, G. D. Egbert, and R. N. Miller, 2000: Assimilation of surface current measurements in a coastal ocean model. J. Phys. Oceanogr., 30 , 23592378.

    • Search Google Scholar
    • Export Citation
  • Talagrand, O., 1997: Assimilation of Observations, an Introduction. J. Meteor. Soc. Japan, 75B , 191209.

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