Marine Ecosystem Model Calibration through Enhanced Surrogate-Based Optimization

  • Malte PrießEmail author
  • Slawomir Koziel
  • Thomas Slawig
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 197)


Mathematical optimization of models based on simulations usually requires a substantial number of computationally expensive model evaluations and it is therefore often impractical. An improved surrogate-based optimization methodology, which addresses these issues, is developed for the optimization of a representative of the class of one-dimensional marine ecosystem models. Our technique is based upon a multiplicative response correction technique to create a computationally cheap but yet reasonably accurate surrogate from a temporarily coarser discretized physics-based coarse model. The original version of this methodology was capable of yielding about 84% computational cost savings when compared to the fine ecosystem model optimization. Here, we demonstrate that by employing relatively simple modifications, the surrogate model accuracy and the efficiency of the optimization process can be further improved. More specifically, for the considered test case, the optimization cost is reduced three times, i.e., from about 15% to only 5% of the cost of the direct fine model optimization.


Marine Ecosystem Models Surrogate-based Optimization Parameter Optimization Response Correction Data Assimilation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bandler, J.W., Cheng, Q.S., Dakroury, S.A., Mohamed, A.S., Bakr, M.H., Madsen, K., Søndergaard, J.: Space mapping: The state of the art. IEEE T. Microw. Theory 52(1) (2004)Google Scholar
  2. 2.
    Banks, H.T., Kunisch, K.: Estimation Techniques for Distributed Parameter Systems. Birkhäuser (1989)Google Scholar
  3. 3.
    Bucker, H.M., Fortmeier, O., Petera, M.: Solving a parameter estimation problem in a three-dimensional conical tube on a parallel and distributed software infrastructure. Journal of Computational Science 2(2), 95–104 (2011); Simulation Software for SupercomputersCrossRefGoogle Scholar
  4. 4.
    Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-region methods. Society for Industrial and Applied Mathematics, Philadelphia (2000)Google Scholar
  5. 5.
    Fennel, W., Neumann, T.: Introduction to the Modelling of Marine Ecosystems. Elsevier (2004)Google Scholar
  6. 6.
    Forrester, A.I.J., Keane, A.J.: Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 45(1-3), 50–79 (2009)CrossRefGoogle Scholar
  7. 7.
    Gill, A.E.: Atmosphere - Ocean Dynamics. International Geophysics Series, vol. 30. Academic Press (1982)Google Scholar
  8. 8.
    Koziel, S., Bandler, J.W., Cheng, Q.S.: Robust trust-region space-mapping algorithms for microwave design optimization. IEEE T. Microw. Theory 58(8), 2166–2174 (2010)CrossRefGoogle Scholar
  9. 9.
    Leifsson, L., Koziel, S.: Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction. Journal of Computational Science 1(2), 98–106 (2010)CrossRefGoogle Scholar
  10. 10.
    Majda, A.: Introduction to PDE’s and Waves for the Atmosphere and Ocean. AMS (2003)Google Scholar
  11. 11.
    Marchuk, G.I.: Methods of Numerical Mathematics, 2nd edn. Springer (1982)Google Scholar
  12. 12.
    McGuffie, K., Henderson-Sellers, A.: A Climate Modelling Primer, 3rd edn. Wiley (2005)Google Scholar
  13. 13.
    Oschlies, A., Garcon, V.: An eddy-permitting coupled physical-biological model of the north atlantic. 1. sensitivity to advection numerics and mixed layer physics. Global Biogeochem. Cy. 13, 135–160 (1999)CrossRefGoogle Scholar
  14. 14.
    Prieß, M., Koziel, S., Slawig, T.: Surrogate-based optimization of climate model parameters using response correction. Journal of Computational Science (2011) (in press)Google Scholar
  15. 15.
    Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R., Tucker, P.K.: Surrogate-based analysis and optimization. Prog. Aerosp. Sci. 41(1), 1–28 (2005)CrossRefGoogle Scholar
  16. 16.
    Rückelt, J., Sauerland, V., Slawig, T., Srivastav, A., Ward, B., Patvardhan, C.: Parameter optimization and uncertainty analysis in a model of oceanic CO 2-uptake using a hybrid algorithm and algorithmic differentiation. Nonlinear Analysis B Real World Applications 10(1016), 3993–4009 (2010)CrossRefGoogle Scholar
  17. 17.
    Sarmiento, J.L., Gruber, N.: Ocean Biogeochemical Dynamics. Princeton University Press (2006)Google Scholar
  18. 18.
    Simpson, T.W., Poplinski, J.D., Koch, P.N., Allen, J.K.: Metamodels for computer-based engineering design: Survey and recommendations. Eng. Comput. 17, 129–150 (2001), 10.1007/PL00007198zbMATHCrossRefGoogle Scholar
  19. 19.
    Smola, A.J., Schölkopf, B.: A tutorial on support vector regression. Stat. Comput. 14, 199–222 (2004), 10.1023/B:STCO.0000035301.49549.88MathSciNetCrossRefGoogle Scholar
  20. 20.
    Søndergaard, J.: Optimization using surrogate models - by the space mapping technique. PhD thesis, Informatics and Mathematical Modelling, Technical University of Denmark, DTU, Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby, Supervisor: Kaj Madsen (2003)Google Scholar
  21. 21.
    Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute for Computer ScienceCluster The Future Ocean, Christian-Albrechts Universität zu KielKielGermany
  2. 2.Engineering Optimization & Modeling Center, School of Science and EngineeringReykjavik UniversityReykjavikIceland

Personalised recommendations