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An Application of Robust Parameter Estimation in Environmental Physics

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Model Based Parameter Estimation

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 4))

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Abstract

This article presents a current research application of robust parameter estimation for inverse problems in air–sea gas exchange. The first part illustrates the interaction of measurements, analysis, and parameter estimation in the concept of the modeling cycle: Typical measurement techniques are classified and discussed with respect to application areas and reproducibility. Statistical analysis of the assumed error distributions is presented as the link to parameter estimation via choosing a suitable parameter estimator. In the case that the error distribution cannot be determined definitely and appears to be highly non-Gaussian the use of robust estimators is advised instead of the standard least-squares approach. Huber’s M-estimator is used here as robust method. Reliable parameter reconstruction by the chosen estimator closes the modeling cycle by validating model against experiment. In the second part all previously presented theoretical aspects are applied to the spectral reconstruction approach (SPERA), a special measurement technique for determining water-sided gas concentration fields via Laser-induced fluorescence. In this application the use of a robust estimator allows the reconstruction of local gas concentration as the model parameters of an inverse problem, for which least-squares methods failed. The article finishes with a brief outlook of applying optimal experimental design techniques to measurements in environmental physics.

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Acknowledgements

We gratefully acknowledge financial support by the DFG Research Training Group 1114 ’Optical Techniques for Measurement of Interfacial Transport Phenomena’ and the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, as well as Synmikro, Marburg. Moreover, we want to thank our colleagues for their support, especially Tanja Binder (Marburg), Pascal Bohleber, Evelyn Böhm, Samuel Hammer, Barbara May, Gabriele Schenk, and Martin Wieser (all Institute of Environmental Physics, Heidelberg). Furthermore, special thanks go to Felix Friedl for performing the measurements shown in Fig. 3 and the group of PD D.P. Herten, BioQuant, Heidelberg, for giving us the opportunity to use their fluorescence spectrometer.

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Authors and Affiliations

  1. Institute for Environmental Physics, Im Neuenheimer Feld 229, 69120, Heidelberg, Germany

    Alexandra G. Herzog & Felix R. Vogel

Authors
  1. Alexandra G. Herzog
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  2. Felix R. Vogel
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Correspondence to Alexandra G. Herzog .

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Editors and Affiliations

  1. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Hans Georg Bock

  2. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 294, Heidelberg, 69120, Germany

    Thomas Carraro

  3. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Willi Jäger

  4. Interdisciplinary Center for, Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Stefan Körkel

  5. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Johannes P. Schlöder

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Herzog, A.G., Vogel, F.R. (2013). An Application of Robust Parameter Estimation in Environmental Physics. In: Bock, H., Carraro, T., Jäger, W., Körkel, S., Rannacher, R., Schlöder, J. (eds) Model Based Parameter Estimation. Contributions in Mathematical and Computational Sciences, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30367-8_14

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