• Bretherton, F. P., , Davis R. E. , , and Fandry C. B. , 1976: A technique for objective analysis and design of oceanographic experiments applied to MODE-73. Deep-Sea Res. Oceanogr. Abstr., 23, 559582, doi:10.1016/0011-7471(76)90001-2.

    • Search Google Scholar
    • Export Citation
  • Chu, P. C., 2006: Applications to data assimilation. P-Vector Inverse Method, Springer, 407–414.

  • Chu, P. C., 2011: Global upper ocean heat content and climate variability. Ocean Dyn., 61, 11891204, doi:10.1007/s10236-011-0411-x.

  • Chu, P. C., , and Fan C. W. , 2010: A conserved minimal adjustment scheme for stabilization of hydrographic profiles. J. Atmos. Oceanic Technol., 27, 10721083, doi:10.1175/2010JTECHO742.1.

    • Search Google Scholar
    • Export Citation
  • Chu, P. C., , Ivanov L. M. , , Korzhova T. P. , , Margolina T. M. , , and Melnichenko O. M. , 2003a: Analysis of sparse and noisy ocean current data using flow decomposition. Part I: Theory. J. Atmos. Oceanic Technol.,20, 478–49, doi:10.1175/1520-0426(2003)20<478:AOSANO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chu, P. C., , Ivanov L. M. , , Korzhova T. P. , , Margolina T. M. , , and Melnichenko O. M. , 2003b: Analysis of sparse and noisy ocean current data using flow decomposition. Part II: Applications to Eulerian and Lagrangian data. J. Atmos. Oceanic Technol.,20, 492–512, doi:10.1175/1520-0426(2003)20<492:AOSANO>2.0.CO;2.

  • Chu, P. C., , Ivanov L. M. , , and Margolina T. M. , 2004a: Rotation method for reconstructing process and field from imperfect data. Int. J. Bifurcation Chaos, 14, 29912997, doi:10.1142/S0218127404010941.

    • Search Google Scholar
    • Export Citation
  • Chu, P. C., , Wang G. H. , , and Fan C. W. , 2004b: Evaluation of the U.S. Navy’s Modular Ocean Data Assimilation System (MODAS) using the South China Sea Monsoon Experiment (SCSMEX) data. J. Oceanogr., 60, 10071021, doi:10.1007/s10872-005-0009-3.

    • Search Google Scholar
    • Export Citation
  • Chu, P. C., , Ivanov L. M. , , and Margolina T. M. , 2005a: Seasonal variability of the Black Sea chlorophyll-a concentration. J. Mar. Syst., 56, 243261, doi:10.1016/j.jmarsys.2005.01.001.

    • Search Google Scholar
    • Export Citation
  • Chu, P. C., , Ivanov L. M. , , and Melnichenko O. M. , 2005b: Fall–winter current reversals on the Texas–Louisiana continental shelf. J. Phys. Oceanogr., 35, 902910, doi:10.1175/JPO2703.1.

    • Search Google Scholar
    • Export Citation
  • Chu, P. C., , Ivanov L. M. , , Melnichenko O. V. , , and Wells N. C. , 2007: Long baroclinic Rossby waves in the tropical North Atlantic observed from profiling floats. J. Geophys. Res., 112, C05032, doi:10.1029/2006JC003698.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. E., 1997: Estimation theory for data assimilation problems: Basic conceptual framework and some open questions. J. Meteor. Soc. Japan, 75, 257288.

    • Search Google Scholar
    • Export Citation
  • Galanis, G. N., , Louka P. , , Katsafados P. , , Kallos G. , , and Pytharoulis I. , 2006: Applications of Kalman filters based on non-linear functions to numerical weather predictions. Ann. Geophys., 24, 24512460, doi:10.5194/angeo-24-2451-2006.

    • Search Google Scholar
    • Export Citation
  • Ide, K., , Courtier P. , , and Ghil M. , 1997: Unified notation for data assimilation: Operational, sequential and variational. J. Meteor. Soc. Japan, 75, 181189.

    • Search Google Scholar
    • Export Citation
  • Large, W., , and Yeager S. , 2009: The global climatology of an interannually varying air–sea flux data set. Climate Dyn., 33, 341364, doi:10.1007/s00382-008-0441-3.

    • Search Google Scholar
    • Export Citation
  • Lozano, C. J., , Robinson A. R. , , Arrango H. G. , , Gangopadhyay A. , , Sloan Q. , , Haley P. J. , , Anderson L. , , and Leslie W. , 1996: An interdisciplinary ocean prediction system: Assimilation strategies and structured data models. Modern Approaches to Data Assimilation in Ocean Modeling, P. Malanotte-Rizzoli, Ed., Elsevier Oceanography Series, Vol. 61, Elsevier, 413–452.

  • Pham, D. T., , Verron J. , , and Roubaud M. C. , 1998: A singular evolutive extended Kalman filter with EOF initialization for data assimilation in oceanography. J. Mar. Syst., 16, 323340, doi:10.1016/S0924-7963(97)00109-7.

    • Search Google Scholar
    • Export Citation
  • Smith, R. D., , and Gent P. R. , Eds., 2002: Reference manual for the Parallel Ocean Program (POP): Ocean component of the Community Climate System Model (CCSM2.0 and 3.0). Los Alamos National Laboratory Tech. Rep. LA-UR-02-2484, 75 pp. [Available online at http://www.cesm.ucar.edu/models/ccsm3.0/pop/doc/manual.pdf.]

  • Song, Y. T., , Haidvodgel D. B. , , and Glenn S. M. , 2001: Effects of topographic variability on the formation of upwelling centers off New Jersey: A theoretical model. J. Geophys. Res., 106, 92239240, doi:10.1029/2000JC000244.

    • Search Google Scholar
    • Export Citation
  • Sun, L. C., 1999: Data inter-operability driven by oceanic data assimilation needs. Mar. Technol. Soc. J., 33, 5566, doi:10.4031/MTSJ.33.3.7.

    • Search Google Scholar
    • Export Citation
  • Sun, L. C., and Coauthors, 2009: The data management system for the Global Temperature and Salinity Profile Programme (GTSPP). Proceedings of the OceanObs’09: Sustained Ocean Observations and Information for Society, J. Hall, D. E. Harrison, and D. Stammer, D., Eds., Vol. 2, ESA Publ. WPP-306, doi:10.5270/OceanObs09.cwp.86.

  • Tang, Y., , and Kleeman R. , 2004: SST assimilation experiments in a tropical Pacific Ocean model. J. Phys. Oceanogr., 34, 623642, doi:10.1175/3518.1.

    • Search Google Scholar
    • Export Citation
  • Vapnik, V., 2000: The Nature of Statistical Learning Theory. Springer, 315 pp.

  • Wang, X., , Chu P. C. , , Han G. , , Li W. , , Zhang X. , , and Li D. , 2012: A fully conserved minimal adjustment scheme with (T, S) coherency for stabilization of hydrographic profiles. J. Atmos. Oceanic Technol., 29, 18541865, doi:10.1175/JTECH-D-12-00025.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 5 5 3
PDF Downloads 1 1 1

Optimal Spectral Decomposition (OSD) for Ocean Data Assimilation

View More View Less
  • 1 Naval Ocean Analysis and Prediction Laboratory, Department of Oceanography, Naval Postgraduate School, Monterey, California
  • 2 National Oceanographic Data Center, Silver Spring, Maryland
© Get Permissions
Restricted access

Abstract

Optimal spectral decomposition (OSD) is applied to ocean data assimilation with variable (temperature, salinity, or velocity) anomalies (relative to background or modeled values) decomposed into generalized Fourier series, such that any anomaly is represented by a linear combination of products of basis functions and corresponding spectral coefficients. It has three steps: 1) determination of the basis functions, 2) optimal mode truncation, and 3) update of the spectral coefficients from innovation (observational increment). The basis functions, depending only on the topography of the ocean basin, are the eigenvectors of the Laplacian operator with the same lateral boundary conditions as the assimilated variable anomalies. The Vapnik–Chervonkis dimension is used to determine the optimal mode truncation. After that, the model field updates due to innovation through solving a set of a linear algebraic equations of the spectral coefficients. The strength and weakness of the OSD method are demonstrated through a twin experiment using the Parallel Ocean Program (POP) model.

Corresponding author address: Peter Chu, Department of Oceanography, Naval Postgraduate School, 833 Dyer Road, RM SP-328, Monterey, CA 93943-5122. E-mail: pcchu@nps.edu

Abstract

Optimal spectral decomposition (OSD) is applied to ocean data assimilation with variable (temperature, salinity, or velocity) anomalies (relative to background or modeled values) decomposed into generalized Fourier series, such that any anomaly is represented by a linear combination of products of basis functions and corresponding spectral coefficients. It has three steps: 1) determination of the basis functions, 2) optimal mode truncation, and 3) update of the spectral coefficients from innovation (observational increment). The basis functions, depending only on the topography of the ocean basin, are the eigenvectors of the Laplacian operator with the same lateral boundary conditions as the assimilated variable anomalies. The Vapnik–Chervonkis dimension is used to determine the optimal mode truncation. After that, the model field updates due to innovation through solving a set of a linear algebraic equations of the spectral coefficients. The strength and weakness of the OSD method are demonstrated through a twin experiment using the Parallel Ocean Program (POP) model.

Corresponding author address: Peter Chu, Department of Oceanography, Naval Postgraduate School, 833 Dyer Road, RM SP-328, Monterey, CA 93943-5122. E-mail: pcchu@nps.edu
Save