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FTLE (Finite Time Lyapunov Exponent) computation is one of the standardapproaches to Lagrangian flow analysis. The main features of interest in FTLEfields are ridges that represent hyperbolic Lagrangian Coherent Structures.FTLE ridges tend to become sharp and crisp with increasing integration time,where the sharpness of the ridges is an indicator of the strength ofseparation. The additional consideration of uncertainty in flows leads to moreblurred ridges in the FTLE fields. There are multiple causes for such blurredridges: either the locations of the ridges are uncertain, or the strength ofthe ridges is uncertain, or there is low uncertainty but weak separation.Existing approaches for uncertain FTLE computation are unable to distinguishthese different sources of uncertainty in the ridges. We introduce a newapproach to define and visualize FTLE fields for flow ensembles. Beforecomputing and comparing FTLE fields for the ensemble members, we computeoptimal displacements of the domains to mutually align the ridges of theensemble members as much as possible. We do so in a way that an explicitgeometry extraction and alignment of the ridges is not necessary. Theadditional consideration of these displacements allows for a visual distinctionbetween uncertainty in ridge location, ridge sharpness, and separationstrength. We apply the approach to several synthetic and real ensemble datasets.

FTLE for Flow Ensembles by Optimal Domain Displacement