Many geophysical processes, and in particular those related to natural hazards, are characterized by heavy-tailed distributions for the most extreme events. Examples include earthquakes, rockfalls, volcanic eruptions, forest fires, auroras, and tsunamis. One possible explanation is self-organized criticality, which models phenomena as avalanches or branching processes close to the critical point of a transition between attenuation and intensification.
We explore how these ideas can be applied to meteorological phenomena such as hurricanes or rainfall. Statistical procedures to deal with heavy-tailed distributions are also explained.