Power Law Scaling and Recurrence Intervals of Tsunamis

Many natural systems have cumulative frequency-size distributions that follow a power law. Using tsunami runup data archived by the U.S. National Geophysical Data Center, we study eight locations in Japan where the tsunami record spans at least one order of magnitude in runup height and the temporal record extends back several decades. A power law describes the cumulative frequency-size distribution of tsunami runup heights at these eight locations. The scaling relationship determined for each location may be used to predict the recurrence intervals of tsunami runup heights. In addition to the tsunami record used to determine the scaling relationship, at some of the examined locations the record extends back several centuries for large events with runup heights greater than five meters. We find that the recurrence intervals of these large events are consistent with the frequency predicted from the more recent record.