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DY: Fachverband Dynamik und Statistische Physik

DY 28: Data Analysis Methods and Modelling of Geophysical Systems

DY 28.10: Topical Talk

Donnerstag, 29. März 2012, 17:15–17:45, MA 144

Sensitivity and out-of-sample error in data assimilation — •Jochen Bröcker — Max-Planck-Institut für Physik komplexer Systeme

“Data Assimilation” is one of many names for the following problem: Given a history of observations as well as a dynamical model, find trajectories which are, on the one hand, consistent with the model, and on the other hand, consistent with the observations. Attaining both objectives at the same time is essentially never possible (nor in fact desired) in reality, since our models are invariably simplifications. Any data assimilation algorithm should therefore allow for deviations from the proposed model equations as well as from the observations. How we might trade off between these two is the subject of this talk. It is shown how we can still find “good” trajectories, where the measure of goodness obviously cannot be just the deviation from the observations. Rather, a measure similar to the out-of-sample error from statistical learning is considered. The connection between the out-of-sample error and the sensitivity is elucidated, including some numerical examples.
Reference:
J.B., Ivan G. Szendro, Sensitivity and out–of–sample error in continuous time data assimilation, Quarterly Journal of the Royal Meteorological Society, 2011.