Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster II

DY 27.19: Poster

Thursday, March 26, 2009, 16:00–18:00, P1B

Data assimilation as a hamiltonian boundary value problem — •Jochen Bröcker — Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 34, 01187 Dresden, Germany

Time series are often assumed to arise as observations from an underlying dynamical system. To analyze or forecast such systems, it is necessary to compute trajectories which are on the one hand consistent with the model dynamics, but which on the other hand closely follow (or `shadow') the recent history of observations. This process (referred to as data assimilation in the atmospheric sciences or smoothing in the engineering community) is revisited in this contribution.

An approach to data assimilation using concepts from nonlinear control theory will be presented. The dynamics are augmented by a control force, which is chosen so as to make the discrepancy between the trajectory and the actual observations, the tracking error, small. At the same time, large control actions are penalized as well, in order to create trajectories which are as consistent with the dynamics as possible.

Provided there is no model error, the control is expected to vanish once the dynamics is ``on track''. In the presence of model error though, a small but non-vanishing control will remain necessary to keep the trajectory close to the observations. It is demonstrated that this approach provides an effective means to regularize the problem and to control the trade--off between perfectly following the observations and perfectly obeying the dynamics. Furthermore, an ex--post analysis of the control forces should provide information on model imperfections.