Skip to main content

Corrected Kriging Update Formulae for Batch-Sequential Data Assimilation

  • Conference paper
  • First Online:
Mathematics of Planet Earth

Abstract

Recently, a lot of effort has been spent in the efficient computation of kriging predictors when observations are assimilated sequentially. In particular, kriging update formulae enabling significant computational savings were derived. Taking advantage of the previous kriging mean and variance computations helps avoiding a costly matrix inversion when adding one observation to the \(n\) already available ones. In addition to traditional update formulae taking into account a single new observation, Emery (2009) proposed formulae for the batch-sequential case, i.e. when \(k\,>\,1\) new observations are simultaneously assimilated. However, the kriging variance and covariance formulae given in Emery (2009) for the batch-sequential case are not correct. In this paper, we fix this issue and establish correct expressions for updated kriging variances and covariances when assimilating observations in parallel. An application in sequential conditional simulation finally shows that coupling update and residual substitution approaches may enable significant speed-ups.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Chevalier, C., & Ginsbourger, D. (2012): Corrected kriging update formulae for batch-sequential data assimilation. http://arxiv.org/abs/1203.6452

  2. Chilès, J. P., & Delfiner, P. (2012). Geostatistics: Modeling spatial uncertainty (2nd edn.). New York: Wiley.

    Google Scholar 

  3. Emery, X. (2009). The kriging update equations and their application to the selection of neighboring data. Computational Geosciences, 13(1), 211–219.

    Article  Google Scholar 

  4. Hoshiya, M. (1995). Kriging and conditional simulation of gaussian field. Journal of Engineering Mechanics, 121(2), 181–186.

    Article  Google Scholar 

Download references

Acknowledgments

Part of this work has been conducted within the frame of the ReDice Consortium, gathering industrial (CEA, EDF, IFPEN, IRSN, Renault) and academic (Ecole des Mines de Saint-Etienne, INRIA, and the University of Bern) partners around advanced methods for Computer Experiments. Clément Chevalier also gratefully acknowledges support from the French Nuclear Safety Institute (IRSN) and warmly thanks Prof. Julien Bect for fruitful discussions on Gaussian process simulations. David acknowledges support from the IMSV.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Clément Chevalier .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chevalier, C., Ginsbourger, D., Emery, X. (2014). Corrected Kriging Update Formulae for Batch-Sequential Data Assimilation. In: Pardo-Igúzquiza, E., Guardiola-Albert, C., Heredia, J., Moreno-Merino, L., Durán, J., Vargas-Guzmán, J. (eds) Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32408-6_29

Download citation

Publish with us

Policies and ethics