A bridge between invariant dynamical structures and uncertainty quantification

•A notion of uncertainty quantification is proposed and illustrated with an application to an actual oil spill.•Uncertainty quantification allows quantifying the transport performance of different ocean data sets.•Uncertainty quantifiers for deterministic models are functions that contain a very rich structure related to invariant dynamical structures. We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show 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. We apply our approach to an ocean data set, as well as standard benchmark models from deterministic dynamical systems theory. A significant application of our 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 our methodology provides avenues for assessing the effective use of these data sets in a variety of situations.