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 ‘potential 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.

KEYWORDS:

• Spatio-temporal data models
• moving-object data
• space-time prisms
• uncertainty
• animal tracking

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data and codes availability statement

The data and codes that support the findings of this study are available in figshare.com with the identifier https://doi.org/10.6084/m9.figshare.11694774.v1.

Notes

1. Geodesics, also called great circles, are circles on the sphere whose centres coincide with the centre of the sphere.

2. To be coherent with the space-time terminology, we write the component for the domain of this function (namely, time) as the last, rather than as the first coordinate in the description of the graph of such mappings.

3. Here, $C^1$ is used in the terminology of differential geometry (O’Neill 1997).

4. https://www.movebank.org.

Additional information

Notes on contributors

Bart Kuijpers

Bart Kuijpers has a master degree in Mathematics from the KULeuven (Belgium) and received his Ph.D. in Computer Science from the University of Antwerp (Belgium). He received the FWO-IBM prize in 1999 for his doctoral thesis. He joined the faculty of Hasselt University, Belgium in 1999, where he currently is a full professor. His research interests include constraint databases, spatio-temporal and moving object databases, spatial logics, data mining and the complexity of real algebraic geometry. He published in computer science journals, GIS journals,computational mathematics journals and mathematical logic journals, as well as in various conferences. He received, with his co-authors, the best paper award of the Journal of Complexity in 2013 He participated in several European and national projects on mobility data and privacy and he was member of the European Privacy Observatory. He (co-)organised conferences, workshops, three Dagstuhl seminars and a summer school (on Mobility Data and Privacy).

Georgios Technitis

Georgios Technitis is leading a geomodelling team in the reinsurance domain. He is interested in SMART applications of GIS methods and remote sensing techniques in the fields of movement ecology, natural hazards and climate change monitoring. His passion for microelectronics and virtual reality technology gave him extensive industrial R&D experience in product design and development. Indoors/outdoors localization solutions, wireless sensor networks and behavior monitoring services are few keywords of his work. Technitis’ main involvement lies in feasibility studies, advanced product quality planning, benchmarking, and validation processes. A geographer by training (Harokopio University of Athens, Upper Class Honors), Technitis completed his specialization in Geo-Informatics at the National Technical University of Athens (Valedictorian M.Sc. 2008–2010). He is currently completing his Ph.D.in the field of GIScience at University of Zurich.