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.

我们为轨迹的前向时间不确定性开发了一个新的量词，轨迹是从数据集生成的模型的解决方案。我们的不确定性量词定义在轨迹演化的相空间上，我们表明它具有丰富的结构，与动力学系统理论中的相空间结构直接相关，例如双曲轨迹及其稳定和不稳定的流形。我们将我们的方法应用于海洋数据集，以及来自确定性动力系统理论的标准基准模型。我们的结果的一个重要应用是，它们允许对不同海洋数据集描述的传输性能进行定量比较。