Dr. Roberto De Almeida
In this iPython notebook we use ocean data to look at the trajectory of a migrating whale. When traveling on the surface of the Earth one cannot take a constant heading (an angle with respect to North) to travel the shortest route from point $A$ to $B$. Instead, the heading must be constantly readjusted so that the arc of the trajectory corresponds to the intersection between the globe and a plane that passes through the center of the Earth:
This is called Great-circle Navigation, and is done by airplanes and ships (wherever possible).
There are also other factors that define the shortest route in time when travelling from $A$ to $B$. For airplanes the wind is an important factor (the jet streams are the reason why it's faster to fly from west to east compared to east to west), and for ships the ocean currents, tides and storms may be an important factor.
What about whales? I always wondered if whales could benefit from the ocean currents when migrating, by travelling along favorable currents and avoiding counter-currents. To investigate this, we develop here an algorithm for identifying the optimal path along two points considering a 2D field of ocean velocity that varies in time. We then compare the whale track with the optimal path to see how much they agree.
The data used corresponds to a track of a humpback whale travelling from the coast of Brazil to the Southern Ocean. The whale started its migration on 2003-12-24 leaving from 20.465 S, 40.04 W, and finished on 2004-02-28 at 54.67 S, 26.261 W: