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Coupling Tangent-Linear and Adjoint Models

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2668))

Abstract

We consider the solution of a (generalized) eigenvalue problem arising in physical oceanography that involves the evaluation of both the tangent-linear and adjoint versions of the underlying numerical model. Two different approaches are discussed. First, tangent-linear and adjoint models are generated by the software tool TAF and used separately. Second, the two models are combined into a single derivative model based on optimally preaccumulated local gradients of all scalar assignments. The coupled tangent-linear / adjoint model promises to be a good solution for small or medium sized problems. However, the simplicity of the example code at hand prevents us from observing considerable run time differences between the two approaches.

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References

  1. Clark, P., Pisias, N., Stocker, T., Weaver, A.: The role of the thermohaline circulation in abrubt climate change. Nature 415 (2002) 863–869

    Google Scholar 

  2. Wunsch, C.: What is the thermohaline circulation? Science 298 (2002) 1179–1180

    Google Scholar 

  3. Farrell, B., Moore, A.: An adjoint method for obtaining the most rapidly growing perturbation to oceanic flows. J. Phys. Oceanogr. 22 (1992) 338–349

    Google Scholar 

  4. Farrell, B., Ioannou, P.: Perturbation growth and structure in uncertain flows. Part I. J. Atmos. Sci. 59 (2002) 2629–2646

    Article  MathSciNet  Google Scholar 

  5. Tziperman, E., Ioannou, P.: Transient growth and optimal excitation of thermohaline variability. J. Phys. Oceanogr. 32 (2002) 3427–3435

    Article  Google Scholar 

  6. Stommel, H.: Thermohaline convection with two stable regimes of flow. Tellus 13 (1961) 224–230

    Google Scholar 

  7. Tziperman, E.: Inherently unstable climate behaviour due to weak thermohaline ocean circulation. Nature 386 (1997) 592–595

    Google Scholar 

  8. Griewank, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia (2000)

    MATH  Google Scholar 

  9. Giering, R., Kaminski, T.: Recipes for adjoint code construction. ACM Transactions on Mathematical Software 24 (1998) 437–474

    Article  MATH  Google Scholar 

  10. Giering, R.: Transformation of algorithms in Fortran (TAF). User manual version 1.3. Technical report, FastOpt (2001) http://www.fastopt.de/taf.

  11. Marotzke, J., Giering, R., Zhang, K., Stammer, D., Hill, C., Lee, T.: Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport variability. J. Geophys. Res. 104, C12 (1999) 29,529–29,547

    Article  Google Scholar 

  12. Stammer, D., Wunsch, C., Giering, R., Eckert, C., Heimbach, P., Marotzke, J., Adcroft, A., Hill, C., Marshall, J.: The global ocean circulation and transports during 1992–1997, estimated from ocean observations and a general circulation model. J. Geophys. Res. 107(C9) (2002) 3118–3144

    Article  Google Scholar 

  13. Stammer, D., Wunsch, C., Giering, R., Eckert, C., Heimbach, P., Marotzke, J., Adcroft, A., Hill, C., Marshall, J.: Volume, heat and freshwater transports of the global ocean circulation 1993–2000, estimated from a general circulation model constrained by WOCE data. J. Geophys. Res. (2002) in press.

    Google Scholar 

  14. Heimbach, P., Hill, C., Giering, R.: Automatic generation of e.cient adjoint code for a parallel Navier-Stokes solver. In Dongarra, J.J., Sloot, P.M.A., Tan, C.J.K., eds.: Computational Science-ICCS 2002. Volume 2331 of Lecture Notes in Computer Science. Springer-Verlag, Berlin (Germany) (2002) 1019–1028

    Google Scholar 

  15. Heimbach, P., Hill, C., Giering, R.: An efficient exact adjoint of the parallel MIT general circulation model, generated via automatic differentiation. Future Generation Computer Systems (FGCS) (2002) submitted.

    Google Scholar 

  16. Naumann, U.: On optimal Jacobian accumulation for single expression use programs. Preprint ANL-MCS/P944-0402, Argonne National Laboratory (2002)

    Google Scholar 

  17. Naumann, U.: Automatic generation of optimal gradient code for scalar assignments. Preprint ANL-MCS/P1020-0103, Argonne National Laboratory (2003)

    Google Scholar 

  18. Rivin, I., Tziperman, E.: Linear versus self-sustained interdecadal thermohaline variability in a coupled box model. J. Phys. Oceanogr. 27 (1997) 1216–1232

    Article  Google Scholar 

  19. Lehoucq, R.B., Sorensen, D.C., Yang, C.: ARPACK users’ guide: Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. SIAM, Philadelphia (1998)

    Google Scholar 

  20. Restrepo, J., Leaf, G., Griewank, A.: Circumvening storage limitations in variational data assimilation studies. SIAM J. Sci. Comput. 19 (1998) 1586–1605

    Article  MATH  MathSciNet  Google Scholar 

  21. Hovland, P., Naumann, U., Norris, B.: An XML-based platform for semantic transformation of numerical programs. In: M. Hamza, ed., Software Engineering and Applications, Proceedings of the Sixth IASTED International Conference, ACTA Press (2002) 530–538

    Google Scholar 

  22. Griewank, A., Reese, S.: On the calculation of Jacobian matrices by the Markovitz rule. In: [27]. (1991) 126–135

    Google Scholar 

  23. Hascoët, L., Naumann, U., Pascual, V.: TBR analysis in reverse-mode automatic differentiation. Elsevier Science (2002) under review.

    Google Scholar 

  24. Aho, A., Sethi, R., Ullman, J.: Compilers. Principles, Techniques, and Tools. Addison-Wesley, Reading, MA (1986)

    Google Scholar 

  25. Naumann, U.: Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph. Preprint ANL-MCS/P943-0402, Argonne National Laboratory (2002) To appear in Math. Prog.

    Google Scholar 

  26. Naumann, U.: Statement-level optimality of tangent-linear and adjoint models. Preprint ANL-MCS/P1021-0103, Argonne National Laboratory (2002)

    Google Scholar 

  27. Corliss, G., Griewank, A., eds.: Automatic Differentiation: Theory, Implementation, and Application. Proceedings Series, Philadelphia, SIAM (1991)

    Google Scholar 

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Naumann, U., Heimbach, P. (2003). Coupling Tangent-Linear and Adjoint Models. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44843-8_12

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  • DOI: https://doi.org/10.1007/3-540-44843-8_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40161-2

  • Online ISBN: 978-3-540-44843-3

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