Power-law scaling and probabilistic forecasting of tsunami runup heights

A power-law scaling relationship describes tsunami runup heights at ten locations in Japan. Knowledge of the scaling law for tsunamis can be the basis for probabilistic forecasting of the size and number of future events and for estimating probabilities of extremely large events. Using tsunami runup data archived by the U.S. National Geophysical Data Center, we study ten locations 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 or upper-truncated power law describes the cumulative frequency-size distribution of tsunami runup heights at all ten locations. Where the record is sufficient to examine shorter time intervals within the record, the scaling relationship for the shorter time intervals is consistent with the scaling relationship for the entire record. The scaling relationship is used to determine recurrence intervals for tsunami runup heights at each location. In addition to the tsunami record used to determine the scaling relationship, at some of the locations a record of large events ( > 5 m) extends back several centuries. We find that the recurrence intervals of these large events are consistent with the frequency predicted from the more recent record. For tsunami prone locations where a scaling relationship is determined, the predicted recurrence intervals may be useful for planning by coastal engineers and emergency management agencies.