Pseudo-Orbit Data Assimilation. Part II: Assimilation with Imperfect Models

Du, Hailiang; Smith, Leonard A.

Abstract

Data assimilation and state estimation for nonlinear models is a challenging task mathematically. Performing this task in real time, as in operational weather forecasting, is even more challenging as the models are imperfect: the mathematical system that generated the observations (if such a thing exists) is not a member of the available model class (i.e., the set of mathematical structures admitted as potential models). To the extent that traditional approaches address structural model error at all, most fail to produce consistent treatments. This results in questionable estimates both of the model state and of its uncertainty. A promising alternative approach is proposed to produce more consistent estimates of the model state and to estimate the (state dependent) model error simultaneously. This alternative consists of pseudo-orbit data assimilation with a stopping criterion. It is argued to be more efficient and more coherent than one alternative variational approach [a version of weak-constraint four-dimensional variational data assimilation (4DVAR)]. Results that demonstrate the pseudo-orbit data assimilation approach can also outperform an ensemble Kalman filter approach are presented. Both comparisons are made in the context of the 18-dimensional Lorenz96 flow and the two-dimensional Ikeda map. Many challenges remain outside the perfect model scenario, both in defining the goals of data assimilation and in achieving high-quality state estimation. The pseudo-orbit data assimilation approach provides a new tool for approaching this open problem.

Citation

Du, H., & Smith, L. A. (2014). Pseudo-Orbit Data Assimilation. Part II: Assimilation with Imperfect Models. Journal of the Atmospheric Sciences, 71(2), 483-495. https://doi.org/10.1175/jas-d-13-033.1

• Journal Article Type: Article
• Online Publication Date: Jan 31, 2014
• Publication Date: Feb 1, 2014
• Deposit Date: Jul 31, 2018
• Publicly Available Date: Aug 21, 2018
• Journal: Journal of the Atmospheric Sciences
• Print ISSN: 0022-4928
• Electronic ISSN: 1520-0469
• Publisher: American Meteorological Society
• Peer Reviewed: Peer Reviewed
• Volume: 71
• Issue: 2
• Pages: 483-495
• DOI: https://doi.org/10.1175/jas-d-13-033.1
• Public URL: https://durham-repository.worktribe.com/output/1324998
• Related Public URLs: http://eprints.lse.ac.uk/55850/