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| Titel |
Fine-grained data assimilation algorithm with uncertainty assessment in variational modeling technology |
| VerfasserIn |
Alexey Penenko, Vladimir Penenko, Elena Tsvetova |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250079314
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| Zusammenfassung |
| We consider an approach to data-assimilation schemes design based on introduction of the
special control functions into the structure of the model equations to take into account various
uncertainties. In the presence of measurement data this augmented model is treated with
variation technique for the functional describing the misfit between measured and calculated
values with the introduced control functions as the quantities to be minimized in the phase
space of the augmented model state functions. Due to uncertainty, the weak-constraint
variational principle is formulated. Then a discrete analogue of the variational principle
functional is constructed by means of decomposition, splitting and finite–volume methods.
From the stationary conditions for the variational principle functionals the systems of direct
and adjoint equations as well as the uncertainty equations are obtained [1, 2]. In general
case the systems can be solved iteratively with some conditions imposed to the
parameters.
As the splitting schemes is used, we propose to assimilate all available data at one model
time step but on the corresponding splitting stages by means of direct algorithms without
iterations. The approach can be called fine-grained data-assimilation. Such versions of
algorithms are cost-effective, easy to be parallelized and may be useful for integrated models
of atmospheric dynamics and chemistry.
In the case of convection-diffusion stage and one time step analysis window the
multidimensional model can be further decomposed with the splitting technique to a set of
one-dimensional models. Each resulting one-dimensional fragment has the form of three
diagonal block-matrix linear problem that can be solved with the matrix sweep method [3]. In
the case of assimilation windows longer than one time step the result of fine-grained
algorithm analysis can be used as initial guess.
The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of
Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of
SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action
ES1004.
References:
V. V. Penenko. Variational methods of data assimilation and inverse problems
for studying the atmosphere, ocean, and environment // Numerical Analysis and
Applications, 2009, V. 2, No 4, 341-351.
V. Penenko, A.Baklanov, E. Tsvetova and A. Mahura. Direct and Inverse
Problems in a Variational Concept of Environmental Modeling // Pure Appl.
Geophys . DOI: 10.1007/s00024-011-0380-5, (2012) 169: 447-465.
A. Penenko. Some theoretical and applied aspects of sequential variational data
assimilation // Comp. tech. v.11, Part 2, (2006) 35-40 (In Russian). |
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