Data Assimilation Meetings at Reading

Date Meeting type Speakers
28 October 2014
Met 1L61, 10 AM
Invited speaker Heikki Haario (Lappeenranta University of Technology, Finland)
Model parameters of chaotic dynamics: metrics for comparing trajectories
Several concepts of fractal dimension have been developed to characterize properties of a given chaotic trajectory. But a distance concept between trajectories is needed in order to quantify the natural variability of a chaotic system and to be able to distinguish trajectories that do not fall within the variability of a reference system. This task is encountered, e.g, in estimating parameters of a chaotic dynamic model. We review problems involved in previously used methods and propose a solution related to the correlation dimension concept. The major advantage of the new construct is its insensitivity with respect to varying initial values, to the choice of a solver, numeric tolerances, etc. A way to create the statistical likelihood for model parameters is presented, together with a sound framework for Markov chain Monte Carlo sampling. The methodology is illustrated using computational examples for the Lorenz~63 and Lorenz~95 systems.

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