Using maths to improve ocean rescue

When someone gets lost at sea, every minute counts, as the probability of finding people alive plunges after six hours.

Now a new algorithm might quite literally have come to the rescue.

Using mathematical modelling to identify ocean flow structures, US researchers successfully predicted locations where floating objects drift within two to three hours.

Search and rescue operations already use algorithms to produce maps that combine sea dynamics, weather prediction and on-site observations to predict a missing person’s location.

However, these computations are costly and slow, wasting precious time, and the resulting search plans can be hard to decipher, write Mattia Serra, from Harvard University, US, and colleagues in a paper in the journal Nature Communications.

When you also have to take account of tides, turbulent weather and unpredictable currents, it can be extremely difficult to find someone, making search and rescue planning “as much art as science, where rescuers still often rely as much on their hunches as on the output of sophisticated prediction tools”.

Serra’s team reasoned that a better approach might be to narrow down someone’s location by working out where objects dropped in the water from uncertain locations are most likely to gather.

To explore this, they drew on a clunky-sounding concept called “Objective Eulerian coherent structures” from dynamical systems theory.

For their purposes, that basically meant uncovering what they call TRansient Attracting Profiles (TRAPS) – curves that are invisible to us but can be extracted and tracked from real-time ocean surface data using mathematical modelling.

This would enable quick, accurate planning of search paths that are less prone to uncertainties about the time and place of the accident.

The team tested their algorithm in three separate experiments near Martha’s Vineyard near the northeast coast of the US.

Using the same real-time data available to the Coast Guard, they quickly identified TRAPS and found that objects and mannequins thrown into the water did indeed gather along the curves.

“Of several competing approaches tested in this project, this was the only algorithm that consistently worked in situ,” says senior author George Haller from the Institute for Mechanical Systems in Zurich, Switzerland.

The team envisages that sea TRAPS could save lives by improving search and rescue operations and might also help to quickly locate and control the damage from environmental disasters such as oil spills.