A bridge between invariant dynamical structures and uncertainty quantification
This paper develops a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. An uncertainty quantifier is defined on the phase space in which the trajectories evolve and it is shown that it has a rich structure that is directly related to phase space structures from dynamical systems theory, such as hyperbolic trajectories and their stable and unstable manifolds. The approach is applied to an ocean data set, as well as standard benchmark models from deterministic dynamical systems theory. A significant application of these results, is that they allow a quantitative comparison of the transport performance described from different ocean data sets. This is particularly interesting nowadays when a wide variety of sources are available, since the methodology provides avenues for assessing the effective use of these data sets in a variety of situations.
This publication describes mathematical findings to assess the performance of ocean data sets. It is obtained from IMPRESSIVE results, but this result was not scheduled or planned in IMPRESSIVE Work Plan.
¹Instituto de Ciencias Matem´aticas, CSIC, C/Nicol´as Cabrera 15, Campus Cantoblanco, 28049 Madrid, Spain
²School of Mathematics, Fry Building, Woodland Road, University of Bristol, Bristol BS8 1UG, United Kingdom
