Theoretical Analysis and Optimization of Nonlinear ODE Systems for Marine Ecosystem Models

  • Anna Heinle
  • Thomas Slawig
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 391)


We present the investigation of a biogeochemical marine ecosystem model used as part of the climate change research focusing on the enhanced carbon dioxid concentration in the atmosphere. Numerical parameter optimization has been performed to improve represention of observational data using data assimilation techniques. Several local minima were found but no global optimum could be identified. To detect the actual capability of the model in simulating natural systems, a theoretical analysis of the model equations is conducted. Here, basic properties such as continuity and positivity of the model equations are investigated.


Climate models Marine ecosystem models Parameter optimization Ordinary differential equations 


  1. 1.
    Fasham, M.J.R., Ducklow, H.W., McKelvie, S.M.: A nitrogen-based model of plankton dynamics in the oceanic mixed layer. J. Mar. Res. 99, 591–639 (1990)Google Scholar
  2. 2.
    Bissett, W.P., Walsh, J.J., Dieterle, D.A., Carder, K.L.: Carbon cycling in the upper waters of the Sargasso Sea: I. Numerical simulation of differential carbon and nitrogen fluxes. Deep-Sea Res. I 46, 205–269 (1999)CrossRefGoogle Scholar
  3. 3.
    Moore, J.K., Doney, S.C., Kleypas, J.A., Glover, D.M., Fung, I.Y.: An intermediate complexity marine ecosystem model for the global domain. Deep-Sea Res. II 49, 403–462 (2002)CrossRefGoogle Scholar
  4. 4.
    Lancelot, C., Spitz, Y.H., Gypens, N., Ruddick, K., Becquevort, S., Rousseau, V., Billen, G.: Modelling diatom-Phaeocystis blooms and nutrient cycles in the Southern Bight of the North Sea: the MIRO model. Mar. Ecol. Prog. Ser. 289, 63–78 (2005)CrossRefGoogle Scholar
  5. 5.
    Schartau, M., Oschlies, A.: Simultaneous data-based optimization of a 1d-ecosystem model at three locations in the north atlantic: Part I - method and parameter estimates. J. Mar. Res. 61, 765–793 (2003)CrossRefGoogle Scholar
  6. 6.
    Rückelt, J., Sauerland, V., Slawig, T., Srivastav, A., Ward, B., Patvardhan, C.: Parameter optimization and uncertainty analysis in a model of oceanic CO2-uptake using a hybrid algorithm and algorithmic differentiation. Nonlinear Anal. Real, Online (2010)Google Scholar
  7. 7.
    Oschlies, A., Garçon, 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
  8. 8.
    Jassby, A.D., Platt, T.: Mathematical formulation of the relationship between photosynthesis and light for phytoplankton. Limnol. Oceanogr. 21, 540–547 (1976)CrossRefGoogle Scholar
  9. 9.
    Spitz, Y.H., Moisan, J.R., Abbott, M.R.: Configuring an ecosystem model using data from the Bermuda Atlantic time series (BATS). Deep-Sea Res. II 48, 1733–1768 (2001)CrossRefGoogle Scholar
  10. 10.
    Fasham, M.J.R., Evans, G.T.: The use of optimisation techniques to model marine ecosystem dynamics at the JGOFS station at 473N 203W. Philos. T. Roy. Soc. B 348, 206–209 (1995)CrossRefGoogle Scholar
  11. 11.
    Sommer, U., Lengfellner, K.: Climate change and the timing, magnitude, and composition of the phytoplankton spring bloom. Glob. Change Biol. 14, 1199–1208 (2008)CrossRefGoogle Scholar
  12. 12.
    El Jarbi, M., Slawig, T., Oschlies, A.: Introducing Periodic Parameters in a Marine Ecosystem Model Using Discrete Linear Quadratic Control. In: Hömberg, D., Tröltzsch, F. (eds.) CSMO 2011. IFIP AICT, vol. 391, pp. 485–494. Springer, Heidelberg (2013)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2013

Authors and Affiliations

  • Anna Heinle
    • 1
  • Thomas Slawig
    • 1
  1. 1.Institute for Computer ScienceCluster “The Future Ocean”, Christian-Albrechts Universität zu KielGermany

Personalised recommendations