Corrected kriging update formulae for batch-sequential data assimilation

Chevalier, Clément; Ginsbourger, David; Emery, Xavier (2014). Corrected kriging update formulae for batch-sequential data assimilation. In: Pardo-Igúzquiza, Eulogio; Guardioloa, Albert; Heredia, Javier; Durán, Juan José; Vargas-Guzmán, Jose Antonio (eds.) Mathematics of Planet Earth: Proceedings of the 15th Annual Conference of the International Association for Mathematical Geosciences. Lecture Notes in Earth System Sciences (pp. 119-122). Berlin: Springer 10.1007/978-3-642-32408-6_29

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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 TeX 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 TeX 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.

Item Type:

Conference or Workshop Item (Paper)


08 Faculty of Science > Institute of Geography
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science
10 Strategic Research Centers > Oeschger Centre for Climate Change Research (OCCR)

UniBE Contributor:

Chevalier, Clément, Ginsbourger, David


500 Science > 550 Earth sciences & geology
300 Social sciences, sociology & anthropology > 360 Social problems & social services
900 History > 910 Geography & travel
500 Science > 510 Mathematics
500 Science > 530 Physics






Lecture Notes in Earth System Sciences






Lutz Dümbgen

Date Deposited:

01 Apr 2014 02:58

Last Modified:

05 Dec 2022 14:28

Publisher DOI:



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