Large explosive volcanic eruptions can have severe consequences for life, property
and climate. In the most extreme cases this can cause catastrophes on a global scale.
Extreme value statistics can be used to evaluate the magnitude-frequency relationship
of large magnitude explosive events, and also to assess how the quality of the volcanic
record affects these results. Applying extreme value statistics to databases of explosive
volcanic eruptions with a Volcanic Explosivity Index (VEI) of 4 or greater in
the last 2000 and 10,000 years has yielded results that suggest the ability to constrain
magnitude-frequency relationships for very large events is limited due to underrecording
of the data which increases with age. Further analysis shows that this is dependent
on both timing and the size of a given eruption; larger eruptions are more likely to
be found in the historical or geological records. Analysis of the 10,000 year dataset
predicted that a magnitude 8.0 eruption has a 40% chance of being recorded prior to 1
AD, and a magnitude 6.0 eruption only a 20% chance. However, as the repose period
between events will increase with the size of the eruptions, the return periods of the
largest and most devastating explosive eruptions are likely to exceed 10,000 years.
In order to build on previous results, the eruption database has been expanded to include
data extending back to greater than 1,000,000 years, with the aim of again using
extreme value statistics to determine global frequency of large magnitude explosive
eruptions. As predicted by earlier results, the record of volcanism decreases dramatically
back through time, particularly beyond 100,000 years and the statistical model
can be applied to take account of underrecording to quantify its effects. An updated
magnitude-frequency relationship for large explosive eruptions is presented.