  FTLE (Finite Time Lyapunov Exponent) computation is one of the standard
approaches to Lagrangian flow analysis. The main features of interest in FTLE
fields 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 of
separation. The additional consideration of uncertainty in flows leads to more
blurred ridges in the FTLE fields. There are multiple causes for such blurred
ridges: either the locations of the ridges are uncertain, or the strength of
the ridges is uncertain, or there is low uncertainty but weak separation.
Existing approaches for uncertain FTLE computation are unable to distinguish
these different sources of uncertainty in the ridges. We introduce a new
approach to define and visualize FTLE fields for flow ensembles. Before
computing and comparing FTLE fields for the ensemble members, we compute
optimal displacements of the domains to mutually align the ridges of the
ensemble members as much as possible. We do so in a way that an explicit
geometry extraction and alignment of the ridges is not necessary. The
additional consideration of these displacements allows for a visual distinction
between uncertainty in ridge location, ridge sharpness, and separation
strength. We apply the approach to several synthetic and real ensemble data
sets.
