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Does it help to point out that the water path looks suspiciously like the day/night line on a map?

Like this: https://svs.gsfc.nasa.gov/5477/

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yes!! why is that ? :)
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The day/light line is a great circle. The "straight line paths" are great-circle segments.
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It's going South and then trying to close the loop from behind. It gets interrupted by land before the loop closes.

Hope it makes sense.

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Open the linked paper and scroll down, they have images of the path on a globe as well as the flat map view.
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