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The Transition Path Theory (TPT) of complex systems has proven a robust meansfor statistically characterizing the ensemble of trajectories that connect anytwo preset flow regions, say $\mathcal A$ and $\mathcal B$, directly. Morespecifically, transition paths are such that they start in $\mathcal A$ andthen go to $\mathcal B$ without detouring back to $\mathcal A$ or $\mathcal B$.This way, they make an effective contribution to the transport from $\mathcalA$ to $\mathcal B$. Here, we explore its use for building a scheme that enablespredicting the evolution of an oil spill in the ocean. This involvesappropriately adapting TPT such that it includes a reservoir that pumps oilinto a typically open domain. Additionally, we lift up the restriction of theoil not to return to the spill site en route to a region that there is interestto be protected. TPT is applied on oil trajectories available up to thepresent, e.g., as integrated using velocities produced by a data assimilativesystem or as inferred from high-frequency radars, to make a prediction oftransition oil paths beyond, without relying on forecasted oil trajectories. Asa proof of concept we consider a hypothetical oil spill in the Trion oil field,under development within the Perdido Foldbelt in the northwestern Gulf ofMexico, and the \emph{Deepwater Horizon} oil spill. This is done usingtrajectories integrated from climatological and hindcast surface velocity andwinds as well as produced by satellite-tracked surface drifting buoys, in eachcase discretized into a Markov chain that provides a framework for theTPT-based prediction.

Exploring the use of Transition Path Theory in building an oil spill prediction scheme