Editorial Type:
Article
Article Type:
Research Article

Error Estimation Using Wavelet Analysis for Data Assimilation: EEWADAi

Leland Jameson Frontier Research System for Global Change, and International Pacific Research Center , University of Hawaii, Honolulu, Hawaii

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Takuji Waseda Frontier Research System for Global Change, and International Pacific Research Center , University of Hawaii, Honolulu, Hawaii

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Print Publication:
01 Sep 2000
DOI:
https://doi.org/10.1175/1520-0426(2000)017<1235:EEUWAF>2.0.CO;2
Page(s):
1235–1246
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Abstract

A new method is presented for estimating numerical errors in simulations as a function of space and time. This knowledge of numerical errors can provide critical information for the effective assimilation of external data. The new method utilizes wavelet analysis for the detection of deviation from low-order polynomial structure in the computational data indicating regions of the domain where relatively large numerical errors will occur. This wavelet-based technique has a very low computational cost, and in practice the cost can be considered negligible compared to the computational cost of the simulation. It is proposed here that this be used in the field of data assimilation for fast and efficient assimilation of external data, and a numerical example illustrating that the new method performs better than the existing method of optimal interpolation is given.

Corresponding author address: Dr. Takuji Waseda, IPRC–SOEST, University of Hawaii, MSB213, 1000 Pope Road, Honolulu, HI 96822.

Abstract

A new method is presented for estimating numerical errors in simulations as a function of space and time. This knowledge of numerical errors can provide critical information for the effective assimilation of external data. The new method utilizes wavelet analysis for the detection of deviation from low-order polynomial structure in the computational data indicating regions of the domain where relatively large numerical errors will occur. This wavelet-based technique has a very low computational cost, and in practice the cost can be considered negligible compared to the computational cost of the simulation. It is proposed here that this be used in the field of data assimilation for fast and efficient assimilation of external data, and a numerical example illustrating that the new method performs better than the existing method of optimal interpolation is given.

Corresponding author address: Dr. Takuji Waseda, IPRC–SOEST, University of Hawaii, MSB213, 1000 Pope Road, Honolulu, HI 96822.

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Cover Journal of Atmospheric and Oceanic Technology
Journal of Atmospheric and Oceanic Technology

  • Daubechies, I., 1988: Orthonormal basis of compactly supported wavelets. Commun. Pure Appl. Math.,41, 909–996.

    • Crossref
    • Export Citation

  • Erlebacher, G., M. Y. Hussaini, and L. Jameson, Eds., 1996: Wavelets:Theory and Applications. Oxford University Press, 528 pp.

  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res.,99, 10143–10162.

    • Crossref
    • Export Citation

  • Ezer, T., and G. L. Mellor, 1994: Continuous assimilation of Geosat altimeter data into a three-dimensional primitive equation Gulf Stream model. J. Phys. Oceanogr.,24, 832–847.

    • Crossref
    • Export Citation

  • Jameson, L., 1998: A wavelet-optimized, very high order adaptive grid and order numerical method. SIAM J. Sci. Comput.,19, 1980–2013.

    • Crossref
    • Export Citation

  • Kalman, R. E., 1960: A new approach to linear filtering and prediction problems. J. Basic. Eng.,82D, 35–45.

    • Crossref
    • Export Citation

  • Levitus, S., 1982: Climatological Atlas of the World Ocean. National Oceanic and Atmospheric Administration Prof. Paper 13, 173 pp.

  • Malanotte-Rizzoli, P., and W. R. Holland, 1986: Data constraints applied to models of the ocean general circulation. Part I: The steady case. J. Phys. Oceanogr.,16, 1665–1682.

  • Mitsudera, H., Y. Yoshikawa, B. Taguchi, and H. Nakamura, 1997: High-resolution Kuroshio/Oyashio System Model: Preliminary results (in Japanese with English abstract). Japan Marine Science and Technology Center Rep. 36, 147–155.

  • Strang, G., and T. Nguyen, 1996: Wavelets and Filter Banks. Wellesley-Cambridge Press, 490 pp.

  • Wunsch, C., 1996: The Ocean Circulation Inverse Problem. Cambridge University Press, 442 pp.

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    • Export Citation
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