On instabilities in data assimilation algorithms
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.
scientific article; zbMATH DE number 6106792
scientific article