Advanced Data Assimilation Schemes: Physical
and Interdisciplinary Research
Pierre F. Lermusiaux
Harvard University
Data assimilation is a modern methodology combining natural data
and dynamical models. All dynamical models are to some extent
approximate, and all data sets are finite and to some extent
limited by error bounds. The purpose of data assimilation is to
provide estimates of nature which are better estimates than can be
obtained by using only observations or a dynamical model. Most
assimilation schemes are rooted in control theory, estimation theory
and inverse techniques. State variables, parameters and their
respective uncertainties can be estimated, processes inferred,
dynamical hypothesis tested, necessary data identified, and
fundamental models developed. However, the complexity and scope
of advanced studies require substantial computational resources
and adequate data sets, and will likely continue to necessitate
new developments.
The presentation overviews, compares and illustrates different
schemes and their applications to physical and interdisciplinary
research. Research issues are discussed and some future challenges
identified. A scheme for efficient data assimilation with
nonlinear models, error subspace statistical estimation (ESSE),
is overviewed. ESSE is based on evolving an error subspace, of
variable size, that spans and tracks the scales and processes
where dominant errors occur. The methodology and its results
are discussed and evaluated for several physical, acoustical
and biological applications of scientific and operational
relevance.