On instabilities in data assimilation algorithms
type: Item
instance of: scholarly article
title: On instabilities in data assimilation algorithms
zbMATH Open document ID: 1269.65051
author: Boris A. Marx
author: Roland Potthast
published in: GEM - International Journal on Geomathematics
publication date: 2012-11-15T00:00:00Z
review text: This is an interesting paper on data assimilation algorithms which are used widely in numerical weather prediction, hydrology, climate science, medical applications and manufacturing processes. In almost all areas of forecasting problems in geosciences, the inversion of data measurements are often ill-posed as the inverse operator is unbounded and leads to instabilities in the data assimilation algorithms. This paper provides a rigorous mathematical analysis of the instability of the well-known data assimilation methods. It is shown that cycling of standard assimilation schemes can lead to severe instabilities of the analysis, i.e., small measurement errors accumulate over time and can lead to large analysis errors. The three-dimensional and four-dimensional variational assimilations with cycled Tikhonov regularizations are discussed in details. Numerical examples are used to demonstrate the occurrence of instabilities and observations in dynamic magnetic tomography.
reviewed by: Zhen Mei
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 45Q05
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 86A22
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 6106792
zbMATH Keywords: data assimilation
zbMATH Keywords: instability analysis
zbMATH Keywords: numerical weather prediction
zbMATH Keywords: dynamic magnetic tomography
zbMATH Keywords: forecasting problems in geosciences
zbMATH Keywords: Tikhonov regularizations
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: s13137-012-0034-5
OpenAlex ID: W2065845751
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DOI: 10.1007/S13137-012-0034-5
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description: scientific article; zbMATH DE number 6106792