Standard Article

Circular Data

Ecological Statistics

  1. Bennett Sango Otieno1,
  2. Christine M. Anderson-Cook2

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vac021.pub2

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Otieno, B. S. and Anderson-Cook, C. M. 2013. Circular Data . Encyclopedia of Environmetrics. 1.

Author Information

  1. 1

    Grand Valley State University, Allendale, MI, USA

  2. 2

    Los Alamos National Laboratory, Los Alamos, NM, USA

Publication History

  1. Published Online: 15 JAN 2013


Circular data are the simplest case of directional data, which commonly occur in environmental studies when measurements are taken from an orientation or cyclical timing application. Circular data have a single response which is not scalar, but angular or directional. Typical orientation observations are measured by a compass and indicate direction, whereas cyclical timing applications are measured by a clock or calendar. The key characteristic that differentiates circular data from data measured on a linear scale is its wrap-around nature, with no maximum or minimum. Specific environmental applications that use directional measures include wind direction, plant or animal migration (orientation), as well as timing of meteorological or life cycle events during the day or in the calendar year (cyclical timing). These include long-axis orientations of fieldspar laths, cross-bed azimuths of paleocurrents, and orientations of pebbles or rock cores. Also, the repeating nature of time increments, such as days, months, or years, is captured by the wrapping around of the circle. Examples can include time of the daily maximum temperature, or occurrence of hurricanes during the year.


  • directional data;
  • Von Mises distribution;
  • orientation;
  • angular;
  • polar coordinates