  Simulating oil transport in the ocean can be done successfully provided that
accurate ocean currents and surface winds are available -- this is often too
big of a challenge. Deficient ocean currents can sometimes be remediated by
parameterizing missing physics -- this is often not enough. In this chapter, we
focus on some of the main problems oil-spill modelers face, which is
determining accurate trajectories when the velocity may be missing important
physics, or when the velocity has localized errors that result in large
trajectory errors. A foundation of physical mechanisms driving motion in the
ocean may help identify currents lacking certain types of physics, and the
remedy. Recent progress in our understanding of motion in the upper centimeters
of the ocean supports unconventional parameterizations; we present as an
example the 2003 Point Wells oil spill which had remained unexplained until
recently. When the velocity realistically represents trajectory forcing
mechanisms, advanced Lagrangian techniques that build on the theory of
Lagrangian Coherent Structures can bypass localized velocity errors by
identifying regions of attraction likely to dictate fluid deformation. The
usefulness of Objective Eulerian Coherent Structures is demonstrated to the
oil-spill modeling community by revisiting the 2010 Deepwater Horizon accident
in the Gulf of Mexico and predicting a prominent transport pattern from an
imperfect altimetry velocity eight days in advance.
