Space-time prisms on a sphere with applications to long-distance movement

Abstract

We study large-scale movement on the surface of the earth that is recorded at discrete moments in time and are interested in the uncertainty between recorded locations. Hereto, we define and study space-time prisms for movement on the surface of the earth (modelled as a sphere). We give description of these prisms and their spatial projection onto the sphere (the so-called "po-tential path area") with respect to spherical coordinates, given by latitude and longitude, and Cartesian coordinates. We also study space-time prisms and their spatial projections on the Mercator map projection. Finally, we show how these concepts can be applied to intercontinental movement. Possible applications include the flight of birds during the migration seasons, the trail of sea or land mammals over longer periods of time and the path of adrift containers on the oceans.