  We use importance sampling in a redefined way to highlight and investigate
rare events in the form of trajectories trapped inside a target coherent set.
We take a transfer operator approach to finding these sets on a reconstructed
2-dimensional flow of the atmosphere from wind velocity fields provided by the
Portable University Model of the Atmosphere. Motivated by extreme value theory,
we consider an observable $\phi(x) = -\log(d(x,\gamma))$ maximized at the
center $\gamma$ of a chosen target coherent set, where it is rare for a
particle to transition. We illustrate that importance sampling maximizing this
observable provides an enriched data set of trajectories that experience such a
rare event. Backwards reconstruction of these trajectories provides valuable
information on initial conditions and most likely paths a trajectory will take.
With this information, we are able to obtain more accurate estimates of rare
transition probabilities compared to those of standard integration techniques.
