In April 2010, fine, airborne ash from a volcanic eruption in Iceland caused chaos throughout European airspace. The same month, the explosion at the Deepwater Horizon drilling rig in the Gulf of Mexico left a gushing oil well on the sea floor that caused the largest offshore oil spill in US history. A year later the Tohoku tsunami hit the coast of Japan, causing great loss of life, the Fukushima nuclear-reactor disaster, and the release of substantial amounts of debris and radioactive contamination into the Pacific Ocean.

Those three globally significant events, depicted in figure 1, share a common theme. In each case, material was released into the environment from what was essentially a point source, and predicting where that material would be transported by the surrounding oceanic or atmospheric flow was of paramount importance.

To predict the outcomes of such events, the standard approach is to run numerical...

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