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Mathematical Paradigms of Climate Science pp 175–213Cite as

Deterministic Treatment of Model Error in Geophysical Data Assimilation

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Part of the book series: Springer INdAM Series ((SINDAMS,volume 15))

Abstract

This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process correlated in time. This allows for the derivation of the evolution equations for the relevant moments of the model error statistics required in data assimilation procedures, along with an approximation suitable for application to large numerical models typical of environmental science. In this contribution we first derive the equations for the model error dynamics in the general case, and then for the particular situation of parametric error. We show how this deterministic description of the model error can be incorporated in sequential and variational data assimilation procedures. A numerical comparison with standard methods is given using low-order dynamical systems, prototypes of atmospheric circulation, and a realistic soil model. The deterministic approach proves to be very competitive with only minor additional computational cost. Most importantly, it offers a new way to address the problem of accounting for model error in data assimilation that can easily be implemented in systems of increasing complexity and in the context of modern ensemble-based procedures.

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Notes

  1. 1.

    The values of \(\sigma _{w_{g}}\) and \(\sigma _{w_{2}}\) are expressed as soil wetness index SWI = (w − w wilt )∕(w fc − w wilt ) where w fc is the volumetric field capacity and w wilt is the wilting point.

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Author information

Authors and Affiliations

  1. NERSC – Nansen Environmental and Remote Sensing Center, Bergen, Norway

    Alberto Carrassi

  2. RMI – Royal Meteorological Institute of Belgium, Brussels, Belgium

    Stéphane Vannitsem

Authors
  1. Alberto Carrassi
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  2. Stéphane Vannitsem
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Corresponding author

Correspondence to Alberto Carrassi .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, Padova, Italy

    Fabio Ancona

  2. Dipartimento di Matematica, Università di Roma - Tor Vergata, Roma, Italy

    Piermarco Cannarsa

  3. Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina, USA

    Christopher Jones

  4. Scienze Agrarie, Forestali e Alimentari, Università degli Studi di Torino, Torino, Italy

    Alessandro Portaluri

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Carrassi, A., Vannitsem, S. (2016). Deterministic Treatment of Model Error in Geophysical Data Assimilation. In: Ancona, F., Cannarsa, P., Jones, C., Portaluri, A. (eds) Mathematical Paradigms of Climate Science. Springer INdAM Series, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-39092-5_9

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