• Amodei, L., 1995: Solution approcheé pour un problème d’assimilation de donneés meteorologiques avec prise en compte de l’erreur de modèlè. C. R. Acad. Sci. II, 321 , 10871094.

    • Search Google Scholar
    • Export Citation
  • Barron, C. N., Kara A. B. , Martin P. J. , Rhodes R. C. , and Smedstad L. F. , 2006: Formulation, implementation and examination of vertical coordinate choices in the global Navy Coastal Ocean Model (NCOM). Ocean Modell., 11 , 347375.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., 1985: Array design by inverse methods. Prog. Oceanogr., 15 , 129156.

  • Bennett, A. F., 1992: Inverse Methods in Physical Oceanography. Cambridge University Press, 347 pp.

  • Bennett, A. F., 2002: Inverse Modeling of the Ocean and Atmosphere. Cambridge University Press, 234 pp.

  • Bennett, A. F., and McIntosh P. C. , 1982: Open ocean modeling as an inverse problem: Tidal theory. J. Phys. Oceanogr., 12 , 10041018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., and Budgell W. P. , 1987: Ocean data assimilation and the Kalman filter: Spatial regularity. J. Phys. Oceanogr., 17 , 15831601.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., and Budgell W. P. , 1989: The Kalman smoother for a linear quasi–geostrophic model of ocean circulation. Dyn. Atmos. Oceans, 13 , 219267.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., and Miller R. N. , 1991: Weighting initial conditions in variational assimilation schemes. Mon. Wea. Rev., 119 , 10981102.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., and Baugh J. R. , 1992: A parallel algorithm for variational assimilation in oceanography and meteorology. J. Atmos. Oceanic Technol., 9 , 426433.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., and Thorburn M. A. , 1992: The generalized inverse of a nonlinear quasigeostrophic ocean circulation model. J. Phys. Oceanogr., 22 , 213230.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., Chua B. S. , and Leslie L. M. , 1996: Generalized inversion of a global numerical weather prediction model. Meteor. Atmos. Phys., 60 , 165178.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., Chua B. S. , and Leslie L. M. , 1997: Generalized inversion of a global numerical weather prediction model. II: Analysis and implementation. Meteor. Atmos. Phys., 62 , 129140.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., Chua B. S. , Harrison D. E. , and McPhaden M. J. , 1998: Generalized inversion of Tropical Atmosphere–Ocean data and a coupled model of the tropical Pacific. J. Climate, 11 , 17681792.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., Chua B. S. , Harrison D. E. , and McPhaden M. J. , 2000: Generalized inversion of Tropical Atmosphere–Ocean (TAO) data and a coupled model of the tropical Pacific. Part II: The 1995/96 La Niña and 1997/98 El Niño. J. Climate, 13 , 27702785.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., Chua B. S. , Ngodock H-E. , Harrison D. E. , and McPhaden M. J. , 2006: Generalized inversion of the Gent–Cane model of the tropical Pacific with Tropical Atmosphere–Ocean (TAO) data. J. Mar. Res., 64 , 142.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., Chua B. S. , Pflaum B. L. , Erwig M. , Fu Z. , Loft R. D. , and Muccino J. C. , 2007: Inverse Ocean Modeling System user manual. IOM Tech. Doc. 6, 221 pp. [Available online at ftp://ftp.coas.oregonstate.edu/dist/chua/iom/tech_doc/IOM_TD6.pdf.].

  • Brunk, H. D., 1965: An Introduction to Mathematical Statistics. 2nd ed. Blaisdell, 429 pp.

  • Chua, B. S., and Bennett A. F. , 2001: An inverse ocean modeling system. Ocean Modell., 3 , 137165.

  • Courtier, P., 1997: Dual formulation of four-dimensional assimilation. Quart. J. Roy. Meteor. Soc., 123 , 24492461.

  • Courtier, P., and Talagrand O. , 1987: Variational assimilation of meteorological observations with the adjoint vorticity equation. II: Numerical results. Quart. J. Roy. Meteor. Soc., 113 , 13291347.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Daley, R. A., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Duncan, W. J., 1944: Some devices for the solution of large sets of simultaneous equations (with an appendix on the reciprocation of partitioned matrices). London Edinburgh Dublin Philos. Mag. J. Sci., 35 , 660.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., Bennett A. F. , and Foreman M. G. G. , 1994: TOPEX/POSEIDON tides estimated using a global inverse model. J. Geophys. Res., 99 , 2482124852.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Erwig, M., and Fu Z. , 2004: Parametric Fortran—A program generator for generic Fortran programming. Proc. Sixth Int. Symp. on Practical Aspects of Declarative Languages, Charleston, SC, COMPULOG Americas, 209–223.

    • Search Google Scholar
    • Export Citation
  • Erwig, M., Fu Z. , and Pflaum B. , 2006: Generic programming in Fortran. Proc. ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, Charleston, SC, Association for Computing Machinery, 130–139.

    • Search Google Scholar
    • Export Citation
  • Erwig, M., Fu Z. , and Pflaum B. , 2007: Parametric Fortran: Program generation in scientific computing. J. Software Maint. Evol., 19 , 155182.

  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 , 1014310162.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2006: Data Assimilation: The Ensemble Kalman Filter. Springer-Verlag, 280 pp.

  • Fu, Z., 2006: Automatic program generation for scientific applications. Ph.D. dissertation, Oregon State University, 200 pp.

  • Fukumori, I., and Malanotte-Rizzoli P. , 1995: An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model. J. Geophys. Res., 100 , 67776793.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gelb, A., 1974: Applied Optimal Estimation. MIT Press, 374 pp.

  • Giering, R., and Kaminski T. , 1998: Recipes for adjoint code construction. ACM Trans. Math. Software, 24 , 437474.

  • Golub, G. H., and van Loan C. F. , 1989: Matrix Computations. The Johns Hopkins University Press, 642 pp.

  • Jacobs, G. A., and Ngodock H. , 2003: The maintenance of conservative physical laws within data assimilation systems. Mon. Wea. Rev., 131 , 25952607.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Le Dimet, F., Ngodock H. , Luong B. , and Verron J. , 1997: Sensitivity analysis in variational data assimilation. J. Meteor. Soc. Japan, 75 , 245255.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lewis, J. M., Lakshmivarahan S. , and Dhall S. , 2006: Dynamic Data Assimilation: A Least Squares Approach. Cambridge University Press, 676 pp.

    • Search Google Scholar
    • Export Citation
  • McIntosh, P. C., and Bennett A. F. , 1984: Open ocean modeling as an inverse problem: M2 tides in Bass Strait. J. Phys. Oceanogr., 14 , 601614.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Muccino, J. C., and Luo H. , 2005: Picard iterations for a finite element shallow water equation model. Ocean Modell., 10 , 316341.

  • Muccino, J. C., and Coauthors, 2008: The Inverse Ocean Modeling system. Part II: Applications. J. Atmos. Oceanic Technol., 25 , 16231637.

  • Ngodock, H. E., Chua B. S. , and Bennett A. F. , 2000: Generalized inverse of a reduced gravity primitive equation model and Tropical Atmosphere–Ocean data. Mon. Wea. Rev., 128 , 17571777.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ngodock, H. E., Jacobs G. , and Chen M. , 2006: The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: A comparison study using a nonlinear reduced gravity ocean model. Ocean Modell., 12 , 378400.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Riedel, K. S., 1991: A Sherman Morrison Woodbury identity for rank augmenting matrices with application to centering. SIAM J. Matrix Anal. Appl., 13 , 659662.

    • Search Google Scholar
    • Export Citation
  • Rosmond, T., and Xu L. , 2006: Development of NAVDAS-AR: Nonlinear formulation and outer loop tests. Tellus, 58A , 4558.

  • Talagrand, O., 2008: Data Assimilation in Meteorology and Oceanography. Academic Press.

  • Talagrand, O., and Courtier P. , 1987: Variational assimilation of meteorological observations with the adjoint vorticity equation. I. Theory. Quart. J. Roy. Meteor. Soc., 113 , 13111328.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wahba, G., and Wendelberger J. , 1980: Some new mathematical methods for variational objective analysis using splines and cross validation. Mon. Wea. Rev., 108 , 11221143.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 1996: The Ocean Circulation Inverse Problem. Cambridge University Press, 442 pp.

  • Xu, L., Rosmond T. , and Daley R. , 2005: Development of NAVDAS-AR: Formulation and initial tests of the linear problem. Tellus, 57A , 546559.

    • Search Google Scholar
    • Export Citation
  • Xu, L., Langland R. , Baker N. , and Rosmond T. , 2006: Development of the NRL 4DVar data assimilation adjoint system. Geophysical Research Abstracts, Vol. 8, Abstract 08773. [Available online at http://www.cosis.net/abstracts/EGU06/08773/EGU06-J-08773.pdf.].

  • Zahel, W., 1991: Modeling ocean tides with and without assimilating data. J. Geophys. Res., 96 , 2037920391.

  • Zaron, E. D., 2006: A comparison of data assimilation methods using a planetary geostrophic model. Mon. Wea. Rev., 134 , 13161328.

  • Zaron, E. D., and Egbert G. D. , 2006: Verification studies for a z coordinate primitive–equation model: Tidal inversions at a mid-ocean ridge. Ocean Modell., 14 , 257278.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 87 17 1
PDF Downloads 78 19 1

The Inverse Ocean Modeling System. Part I: Implementation

View More View Less
  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
  • | 2 School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, Oregon
  • | 3 Microsoft Corporation, Redmond, Washington
  • | 4 Scientific Computing Division, National Center for Atmospheric Research, Boulder, Colorado
  • | 5 College of Civil and Environmental Engineering, Arizona State University, Tempe, Arizona
Restricted access

Abstract

The Inverse Ocean Modeling (IOM) system constructs and runs weak-constraint, four-dimensional variational data assimilation (W4DVAR) for any dynamical model and any observing array. The dynamics and the observing algorithms may be nonlinear but must be functionally smooth. The user need only provide the model and the observing algorithms, together with an interpolation scheme that relates the model numerics to the observer’s coordinates. All other model-dependent elements of the Inverse Ocean Modeling assimilation algorithm (see both Chua and Bennett), including adjoint generators and Monte Carlo estimates of posteriors, have been derived and coded as templates in Parametric FORTRAN (Erwig et al.). This language has been developed for the IOM but has wider application in scientific programming. Guided by the Parametric FORTRAN templates, and by model information entered via a graphical user interface (GUI), the IOM generates conventional FORTRAN code for each of the many algorithm elements, customized to the user’s model. The IOM also runs the various W4DVAR assimilations, which are monitored by the GUI. The system is supported by a Web site that includes interactive tutorials for the assimilation algorithm.

Corresponding author address: Andrew F. Bennett, 104 COAS Admin. Bldg., Oregon State University, Corvallis, OR 97331-5503. Email: bennett@coas.oregonstate.edu

Abstract

The Inverse Ocean Modeling (IOM) system constructs and runs weak-constraint, four-dimensional variational data assimilation (W4DVAR) for any dynamical model and any observing array. The dynamics and the observing algorithms may be nonlinear but must be functionally smooth. The user need only provide the model and the observing algorithms, together with an interpolation scheme that relates the model numerics to the observer’s coordinates. All other model-dependent elements of the Inverse Ocean Modeling assimilation algorithm (see both Chua and Bennett), including adjoint generators and Monte Carlo estimates of posteriors, have been derived and coded as templates in Parametric FORTRAN (Erwig et al.). This language has been developed for the IOM but has wider application in scientific programming. Guided by the Parametric FORTRAN templates, and by model information entered via a graphical user interface (GUI), the IOM generates conventional FORTRAN code for each of the many algorithm elements, customized to the user’s model. The IOM also runs the various W4DVAR assimilations, which are monitored by the GUI. The system is supported by a Web site that includes interactive tutorials for the assimilation algorithm.

Corresponding author address: Andrew F. Bennett, 104 COAS Admin. Bldg., Oregon State University, Corvallis, OR 97331-5503. Email: bennett@coas.oregonstate.edu

Save