On some computational aspects of the variational data assimilation techniques

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. 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 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 will be reported. Parallel techniques described in [1] are used in the runs related to this paper. 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 [1], [24] The ideas are rather general and can easily be applied in connection with other mathematical models. © Springer-Verlag Berlin Heidelberg 2007.