### Abstract

It is important to incorporate all available observations when large-scale mathematical models arising in different fields of science and engineering are used to study various physical and chemical processes. Variational data assimilation techniques can be used in the attempts to utilize efficiently observations in a large-scale model (for example, in order to obtain more reliable initial values). Variational data assimilation techniques are based on a combination of three very important components
• numerical methods for solving differential equations,
• splitting procedures and
• optimization algorithms.
It is crucial to select an optimal (or, at least, a good) combination of these three components, because models which are very expensive computationally will become much more expensive (the computing time being often increased by a factor greater than 100) when a variational data assimilation technique is applied. Therefore, it is important to study the interplay between the three components of the variational data assimilation techniques as well as to apply powerful parallel computers in the computations.
Some results obtained in the search for a good combination of numerical methods, splitting techniques and optimization algorithms will be reported. Parallel techniques described in [V.N. Alexandrov, W. Owczarz, P.G. Thomsen, Z. Zlatev, Parallel runs of a large air pollution model on a grid of Sun computers, Mathematics and Computers in Simulation, 65 (2004) 557–577] are used in the runs.
Modules from a particular large-scale mathematical model, the Unified Danish Eulerian Model (UNI-DEM), are used in the
experiments. The mathematical background of UNI-DEM is discussed in [V.N. Alexandrov,W. Owczarz, P.G. Thomsen, Z. Zlatev,
Parallel runs of a large air pollution model on a grid of Sun computers, Mathematics and Computers in Simulation, 65 (2004)
557–577, Z. Zlatev, Computer Treatment of Large Air Pollution Models, Kluwer Academic Publishers, Dordrecht, Boston, London,
1995]. The ideas are rather general and can easily be applied in connection with other mathematical models.

Original language | English |
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Journal | Computers & Mathematics with Applications |

Volume | 55 |

Issue number | 10 |

Pages (from-to) | 2381-2393 |

ISSN | 0898-1221 |

DOIs | |

Publication status | Published - 2008 |

### Keywords

- Stiff systems
- Scientific models
- Splitting techniques
- Systems of PDE's
- Data assimilation

## Cite this

Thomsen, P. G., & Zlatev, Z. (2008). Development of a data assimilation algorithm.

*Computers & Mathematics with Applications*,*55*(10), 2381-2393. https://doi.org/10.1016/j.camwa.2007.11.018