  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.
