Application of Data Assimilation to Three-Dimensional Hydrodynamics: the Case of the Odra Lagoon

  • T. Wolf
  • J. Sénégas
  • L. Bertino
  • H. Wackernagel
Part of the Quantitative Geology and Geostatistics book series (QGAG, volume 11)

Abstract

A data assimilation scheme enables to correct a model estimate, or first-guess, of a physical state using measurements of the state variables. The best estimate is given by minimization of the estimation variance, as it is done in kriging. In sequential data assimilation, the spatial covariance of the first-guess error is propagated forward in time using the physical model and requires only the knowledge of the model error (system noise). Since the data are often scarce in space, it is however a real scientific challenge to assess its covariance structure.

We present here an application to three-dimensional hydrodynamics, where a sub-optimal filter is coupled with a numerical model solving the Navier-Stokes equations for shallow water. An original method for the construction of a spatial covariance from time series of water level measurements is introduced, making use of the physical properties of the system. The filtering has been applied to the simulation of water level in the Odra lagoon for the flood period of summer 1997. The method proves very efficient, despite a small number of assimilated measurements, and enables an improved reconstruction of the physical system.

Keywords

Agated Covariance Assimilation Kriging Tempo 

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References

  1. Bertino, L., Sénégas, J., Wackernagel, H., and von Storch, H. (2000). Data assimilation for hydrodynamical modeling of the Odra lagoon. In 6th International Geostatistics Congress, Cape Town, South Africa, 10-14 April 2000.Google Scholar
  2. Buckmann, K., Jonas, P., Lampe, R., and Meyer, H. (1996). Messung und numerische Modellierung von Transport- und Austauschprozessen im Greifswalder Bodden und Oderästuar. In GOAP — Jahresbericht 1996, Greifswald. BMBF.Google Scholar
  3. Casulli, V. and Cattani, E. (1994). Efficiency of a semi-implicit method for three-dimensional shallow water flow. Computers Math. Applic., 27(4):99–112MathSciNetMATHCrossRefGoogle Scholar
  4. Eknes, M. and Evensen, G. (1999). An ensemble Kalman filter with a 1-d marine ecosystem model. Journal of Marine Systems. Submitted.Google Scholar
  5. Evensen, G. (1992). Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model. Journal of Geophysical Research, 97(17): 905–924.Google Scholar
  6. Evensen, G. and van Leuween, P. (1999). An ensemble Kalman smoother for nonlinear dynamics. Mon. Wea. Rev.. Submitted.Google Scholar
  7. Mayer, Z. (1995). Hydraulic problems of the Odra River outlet. Polish Academy of Sciences, Hydroengineering Institut, Gdansk.Google Scholar
  8. Rosenthal, W., Wolf, T., Witte, G., Buchholz, W., and Rybaczok, P. (1998). Measured and modelled water transport in the Odra estuary for the flood period July/August 1997. Germ. J. Hydr., 50(2/3):215–230.Google Scholar
  9. Sénégas, J. (1999). Hydrodynamical modeling and data assimilation within the Odra estuary. External Report GKSS/99/E/42, GKSS, Geesthacht, Germany.Google Scholar
  10. Sénégas, J., Wackernagel, H., Rosenthal, W., and Wolf, T. (2000). Error covariance modeling in sequential data assimilation. To appear in Stochastic Environmental Research and Risk Assessment. Google Scholar
  11. Verlaan, M and Heemink, A. (1995). Reduced rank square root filters for large scale data assimilation problems. In 2nd International Symposium on Assimilation of Observations in Meteorology and Oceanography, p. 247–252. World Meteorological Organization.Google Scholar
  12. Verlaan, M. and Heemink, A. (1999). Non-linearity in data assimilation applications: a practical method for analysis. Mon. Wea. Rev. Submitted.Google Scholar
  13. Von Storch, H. (2000). The PIONEER project as an example of operational coastal analysis. In 4th Symposium on Integrated Observing Systems, p. 215–220. American Meteoroligical Society, Boston.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • T. Wolf
    • 1
  • J. Sénégas
    • 2
  • L. Bertino
    • 2
  • H. Wackernagel
    • 2
  1. 1.Institut für GewässerphysikGKSSGermany
  2. 2.Centre de GéostatistiqueEcole des Mines de ParisFrance

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