The detection and characterization of self-organized criticality (SOC), in
both real and simulated data, has undergone many significant revisions over the
past 25 years. The explosive advances in the many numerical methods available
for detecting, discriminating, and ultimately testing, SOC have played a
critical role in developing our understanding of how systems experience and
exhibit SOC. In this article, methods of detecting SOC are reviewed; from
correlations to complexity to critical quantities. A description of the basic
autocorrelation method leads into a detailed analysis of application-oriented
methods developed in the last 25 years. In the second half of this manuscript
space-based, time-based and spatial-temporal methods are reviewed and the
prevalence of power laws in nature is described, with an emphasis on event
detection and characterization. The search for numerical methods to clearly and
unambiguously detect SOC in data often leads us outside the comfort zone of our
own disciplines - the answers to these questions are often obtained by studying
the advances made in other fields of study. In addition, numerical detection
methods often provide the optimum link between simulations and experiments in
scientific research. We seek to explore this boundary where the rubber meets
the road, to review this expanding field of research of numerical detection of
SOC systems over the past 25 years, and to iterate forwards so as to provide
some foresight and guidance into developing breakthroughs in this subject over
the next quarter of a century.Comment: Space Science Review series on SO
