@CONFERENCE\{IMM2007-05180,
    author       = "P. G. Thomsen and Z. Zlatev",
    title        = "Studying the properties of Variational Data Assimilation Methods  by Applying a Set of Test-Examples",
    year         = "2007",
    keywords     = "Variational Data Assimilation, Forward and Backward computation, Numerical solution of Differential Equations, Splitting Procedures.",
    edition      = "1",
    pages        = "492-499",
    booktitle    = "6th International Conference on Numerical Methods and Applications, {NMA} 2006",
    volume       = "",
    series       = "Lecture Notes in Computer Science, volume 4310",
    editor       = "T. Boyanov, S. Dimova, K. Georgiev , G. Nikolov",
    publisher    = "Springer-Verlag",
    organization = "",
    address      = "Berlin",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5180-full.html",
    abstract     = "he variational data assimilation methods can successfully be used
in different fields of science and engineering. An attempt to 
utilize available sets of observations in the efforts to improve
(i) the models used to study different phenomena 
(ii) the model results 
is systematically carried out when data assimilation methods are 
used. 

The main idea, on which the variational data assimilation methods
are based, is pretty general.  A functional is formed by using a 
weighted inner product of differences of model results and 
measurements. The value of this functional is to be minimized. 
Forward and backward computations are carried out by using the 
model under consideration and its adjoint equations (both the 
model and its adjoint are defined by systems of differential 
equations). The major difficulty is caused by the huge increase 
of the computational load (normally by a factor more than 100) 
and the storage needed. This is why it might be appropriate to apply
some splitting procedure in the efforts to reduce the computational 
work.

Five test-examples have been created. Different numerical aspects 
of the data assimilation methods and the interplay between the 
major computational parts of any data assimilation method 
(numerical algorithms for solving differential equations, 
splitting procedures and optimization algorithms) have been 
studied by using these tests. The presentation will include 
results from testing carried out in the study.",
    isbn_issn    = "3-540-70940-1/0302-9743"
}